Price Caps and Incentive Regulation in Telecommunications

PRICE CAPS AND INCENTIVE REGULATION IN TELECOMMUNICATIONS

Topics in Regulatory Economics and Policy Series

Michael A. Crew, Editor Graduate School of Management Rutgers University Newark, New Jersey, U.S.A.

Other Books in the Series:

Rowley, C., R. Tollison, and G. Tullock Political Economy of Rent Seeking

Frantz, R.: X-Efficiency: Theory, Evidence and Applications

Crew, M: Deregulation and Diversification of Utilities

Shogren, J.: The Political Economy of Government Regulation

Hillman, J. and R. Braeutigam: Price Level Regulation for Diversified Public Utilities

Crew, M.: Competition and the Regulation of Utilities

PRICE CAPS AND INCENTIVE REGULATION IN TELECOMMUNICATIONS

edited by Michael A. Einhorn Rutgers University Newark, New Jersey

~.

" Springer Science+Business Media, LLC

Library of Congress Cataloging-in-Publication Data

Price eaps and ineentive regulation in teleeommunications / edited by Miehael A. Einhorn.

p. em. - (Topies in regulatory eeonomics and poliey series ; 6)

Inc1udes bibliographical referenees. ISBN 978-1-4613-6776-5 ISBN 978-1-4615-3976-6 (eBook) DOI 10.1007/978-1-4615-3976-6 1. Telephone-United States-Deregulation. 2. Price regulation

-United States. I. Einhorn, Miehael A. II. Series: Topics in regulatory eeonomics and poliey ; 6. HE8819.P75 1990 384.6'3'0973-de20 90-33723

Copyright © 1991 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 1991 Softeover reprint ofthe hardcover lst edition 1991

CIP

Ali rights reserved. No part of this publieation may be reproduced, stored in a retrieval system ar transmitted in any form orby any means, mechanical, photo-copying, recarding, ar otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC.

Prillted 011 acid-free paper.

To Jan

CONTENTS

Contributing Authors ix

Acknowledgments xi

1 Introduction 1 Michael A. Einhorn

2 A Non-Bayesian Incentive Mechanism Using 15 Two-Part Tariffs Ingo Vogelsang

3 Regulating by Capping Prices 33 Timothy J. Brennan

4 Information, Incentives, and Commitment in 47 Regulatory Mechanisms: Regulatory Innovation in Telecommunications David P. Baron

5 Productivity and Price Caps in Telecommunications 77 John E. Kwoka, Jr.

6 Constant and Variable Productivity Adjustments for 95 Price-Cap Regulation Ferenc Kiss

7 A Sequential Mechanism for Direct Price 127 Regulation Peter B. Linhart, Roy Radner, and Frank W. Sinden

vii

viii PRICE CAPS AND INCENTIVE REGULATION IN TELECOMMUNICATIONS

8 Incentives for Cost Reduction Under Price-Cap 155 Regulation Luis M.B. Cabral and Michael H. Riordan

9 The Quality of Regulation in Regulating Quality: 167 A Proposal for an Integrated Incentive Approach to Telephone Service Performance Eli M. Noam

10 Optional Tariffs for Access Under the FCC's 191 Price-Cap Proposal David S. Sibley, Daniel P. Heyman, and William E. Taylor

11 Optional Calling Plans and Bypass Efficiency 207 Michael A. Einhorn

12 Pricing and Investment Incentives Under Price 221 Ceiling Regulation Calvin S. Monson and Alexander C. Larson

Index 239

Contributing Authors

David P. Baron, William R. Kimball Professor of Business, Economics, and the Environment, Graduate School of Business, Stanford University, Stanford, California

Timothy J. Brennan, Associate Professor of Public Policy, Communication, and Economics, George Washington University, Washington, D.C.

Luis M. B. Cabral, Assistant Professor of Economics, New University of Lisbon, Lisbon, Portugal

Michael A. Einhorn, Assistant Professor of Economics, Rutgers University, Newark, New Jersey

Daniel P. Heyman, Distinguished Member of Technical Staff, Bell Communications Research, Morristown, New Jersey

Ferenc Kiss, Member of Technical Staff, Bell Communications Research, Livingston, New Jersey

John E. Kwoka, Jr., Professor of Economics, George Washington University, Washington, D.C.; Special Assistant to the Chief, Common Carrier Bureau, Federal Communications Commission, Washington, D.C.

Alexander C. Larson, Senior Economist, Southwestern Bell, S1. Louis, Missouri

Peter B. Linhart, Distinguished Member of Technical Staff, AT&T Bell Laboratories, Murray Hill, New Jersey

Calvin S. Monson, Economist, Southwestern Bell, S1. Louis, Missouri

Eli M. Noam, Professor of Business, Graduate School of Business, Columbia University, New York, New York; former Commissioner, New York Public Service Commission, Albany, New York

Roy Radner, Distinguished Member of Technical Staff, AT&T Bell Laboratories, Murray Hill, New Jersey; Research Professor of Economics, New York University, New Yark

Michael H. Riordan, Professor of Economics, Boston University, Boston, W,.assachusetts

ix

x PRICE CAPS AND INCENITVE REGULATION IN TELECOMMUNICATIONS

David S. Sibley, District Manager, Economic Research Group, Bell Communications Research, Morristown, New Jersey

Frank W. Sinden, Distinguished Member of Technical S taff, AT&T Bell Laboratories, Murray Hill, New Jersey

William E. Taylor, Vice President, National Economic Research Associates, Boston, Massachusetts

Ingo Vogelsang, Professor of Economics, Boston University, Boston, Massachusetts

Acknowledgments

In the course of preparing this book, I have benefitted from the efforts of many individuals. The Columbia University Center for Telecommunications and Information Studies sponsored a one-day conference in 1987 in which four volume papers were presented; Douglas Conn, Richard Kramer, Martin Elton, and Barry Cole of the Center were prominent organizers in this event David Hosford (Rutgers University-Newark) provided additional funding for the conference; Peter Linhart (AT&T), David Sappington (University of Florida) and David Sibley (Bell Communications Research) gave much appreciated technical advice. Barbara Ryder (Kluwer Academic Publishers) provided clerical assistance in graph preparation; Linda Brennan (Rutgers University-Newark) prepared each ofthe final manuscripts for publication, a time-consuming and sometimes tedious task that she performed exceptionally. Zachary Rolnik of Kluwer was a warm and encouraging adviser who kept up my spirits during a long document preparation process. Final thanks must go to each of the authors who really did make the volume possible. To these individuals, my heartfelt thanks.

xi

1 INTRODUCTION Michael A. Einhorn

In continuing to deregulate telecommunications companies, regulators have begun to consider alternative approaches to traditional cost-based price regulation as a means of encouraging monopoly efficiency, promulgating technological innovation, protecting consumers, and reducing administrative costs. Under cost-based regulatory procedures that had been used, prices were designed to recover the regulated company's costs plus an allowed rate of return on its rate base; this strategy was costly to administer, provided no consistent incentives to cost-efficiency and technological improvement, afforded many opportunities for strategic misrepresentation of reported costs, and may have encouraged both uneconomic expansion of the utility's rate base and cross-subsidization of its competitive services.

A category of alternative regulatory approaches can be classified broadly as social contracts. Under the general strategy of social contract regulation, regulators first delimit a group of regulated core services that they continue to regulate and then stipulate a list of constraints that the utility must agree to meet in the future; in exchange, regulators agree to detariff or deregulate entirely other competitive or nonessential services that the utility may offer. As long as no stipulated constraints are violated, the utility may price freely any service; if it reduces costs, it may keep a share of its profits. According to the National Telecommunications Information Administration (NTIA, 1987), social contract agreements of one form or another have been considered or implemented in a majority of American states.

Following the lead of Britain's Office of Telecommunications, the Federal Communications Commission (FCC) recently enacted a form of social contract regulation - the institution of price-caps on interstate tariffs of AT&T and, perhaps in 1990, local exchange companies. Under price-caps, regulators place aggregate index ceilings on prespecified groups of services (called "baskets"); the company is free to price any service freely, so long as no index ceiling constraint is violated. Index ceilings are adjusted over time to allow for expected cost-inflation and a precommitted rate of productivity improvement. The company is permitted to keep

2 PRICE CAPS AND INCENTIVE REGULATION IN TELECOMMUNICATIONS

any profits that may result from cost-cutting or technological innovation. In the past two decades, academic economists have focused on the economic

implications of imperfect information and moral hazard; incentive regulation has emerged as an important research topic in American universities. On November 13, 1987, the Center for Telecommunications and Information Studies at Columbia University's Graduate School of Business, with partial funding from Rutgers University, Newark, New Jersey, organized a one-day conference, Prices. Costs. and Capital Decisions in Telecommunications: Incentive Mechanisms for Economic Efficiency, that focused on many of these regulatory issues. Six papers were presented, four of which appear in this volume.

Afterward, I invited additional papers that addressed interesting topics that conference papers did not consider. The collected papers now address a range of topics-the efficiency of long-run equilibria, strategic misrepresentation issues, regulator commitment difficulties, measuring productivity adjustments, protecting against uneconomic bypass, ensuring service quality, and capacity sizing. The resulting collection, therefore, can serve both as an introduction to the incentive contract issue as well as a collection of detailed articles that focus on important contemporary issues in the theory and implementation of alternative regulatory procedures.

The intention of this volume is not to advocate social contracts or price-caps as necessarily better options to traditional regulation but rather to identify objectively the beriefits and weaknesses of such regulation as well as means of improvement.

1. Traditional Academic Theory

In traditional rate-of-return regulation, regulators price utility services in order to recover the company's variable costs plus an allowed rate-of-return on its rate base. At times, prices are set at fully distributed costs; cost distribution methods attempt to assign joint and common costs fairly across the utility's different services.

Economists frequently contend that distributed cost allocation is inefficient and that regulated prices instead should be set at marginal cost. If the resulting profit level were inappropriately high or low, Baumol and Bradford (1970) prescribed second-best pricing rules that were designed to maximize consumer surplus while ensuring a more satisfactory level of utility profits. Ng and Weisser (1974) and Schmalensee (1981) shortly followed with second-best two-part tariffs that incorporated access and usage charges. Spence (1977) and Goldman, Leland, and Sibley (1984) derived an optimal nonuniform price schedule that Mirman and Sibley (1980) extended to multiproduct monopolies. Einhorn (1987) considered the implications of nonuniform pricing for multiline customers and customer bypass.

In the past decade, both regulator practice and academic models of traditional utility regulation have been roundly criticized for several reasons.

1. Under rate-of-return regulation that automatically attempts to cover company costs, both decreases and increases in company costs are passed on to consumers. Consequently, regulated monopolies have little incentive to manage inputs effi-

INTRODUCTION 3

ciently or to adopt cost-reducing innovations. 2. When regulators base allowed prices upon reported cost data, utilities may

have economic incentives to misrepresent reported cost data in order to secure higher prices or rates of return; Baron and Myerson (1982) term these informational asymmetries. In a different context, Noll and Owen (1987, 10) confirm this point:

The FCC could not detennine AT&T's costs, nor could it settle on a sensible cost-based method for pricing. One set of AT&T prices, the Telpak tariff, went through nearly two decades of hearings without a [mal determination of its lawfulness. It was apparent that even with a fully informed regulatory policy and the best will possible, the FCC could not cope successfully within available administrative procedures with AT&T's control of the information necessary to regulate prices effectively.

3. Should the allowed return on rate base capital exceed its market value, a regulated monopoly may have an incentive to expand its rate base uneconomically or to "gold plate" its capital stock (for theoretical expansion, see Averch and Johnson, 1962; and Wellisz, 1963; for empirical support, see Courville, 1974; Spann, 1974; and Atkinson and Halvorsen, 1980). However, many have disputed both the theoretical and empirical presence of the Averch-Johnson effect; seeZajac (1972) and Bailey (1973).

4. Accounting rules (such as those that appear in the FCC's separations manual) that allocate joint and common costs across alternative services involve notions of fairness that have no relationship to the true incremental costs of providing service; historically, these rules have produced a toll-to-local subsidy and consequently stopped AT&T from reducing its long-distance prices after lowering costs. As a result, prices that are based upon fully distributed cost allocations are often inefficient (see Baumol, Koehn, and Willig, 1987). Griffin (1982) estimated an annual welfare loss from fully distributed costs of $1.5 billion in toll service; Wenders (1987, 85) contends that Griffm's estimate is conservative.

5. When common costs must be allocated to monopolized services, regulated utilities may attempt as well to shift some of the costs of their competitive services on to their captive monopolized customers. In securing this subsidy, the utilities can then reduce the prices for their competitive service. As a further consequence of uneconomic cost allocation, certain customers might be able to profitably bypass the utility in favor of an alternative supplier with lower prices; this result can be economically inefficient

6. The regulatory process diverts utility attention from competitive rivalrywhich could lead to new innovations and products-to political gainseeking often involving zero-sum rent-transfers.

7. The administration costs of regulation are substantial and growing. The National Telecommunications and Information Administration (1987) estimated that the costs of regulation in the telecommunications sector to exceed $1 billion and to be between $8 to $10 per access line; even larger per line burdens befall smaller companies. During periods of inflationary buildup, the administrative cost


problem becomes particularly pronounced; this is because utilities must repeatedly come back to the commission for interim rate relief (a process known sometimes as "pancaking"). For example, from 1967 to 1981 (a period of inflationary buildup), total expenditures by state regulatory bodies increased by 312%, well beyond the coincident rate of inflation (NTIA, 1987).

2. Alternative Strategies for Regulation

We now overview some of the social contract/price-cap strategies that have emerged in recent years in telecommunications regulation.

2.1 British Experience Great Britain spun off British Telecommunications from the British Post Office

in 1981 and privatized it three years later; the Office of Telecommunications was established to regulate it. Under the influence of Prof. Steven Littlechild (1983), the new regulators implemented price-cap regulation. Under this regulatory strategy, the Office of Telecommunications specified a group of essential network services that included line rental, local service, and domestic long-distance; regulators specified that the core price index (Le., the sum of percent price increases weighted by the share of the respective service in the previous year's revenues) could not increase by more than the annual rate of inflation (as measured by the retail price index) less a 3% adjustment for expected productivity improvements (this is notationally represented as RPI-3). Additionally, line rentals were permitted to increase annually at a rate that could not exceed RPI+2; this was to allow a gradual elimination of the subsidies that line rental customers had enjoyed at the expense of long-distance customers. Connection charges, customer premises equipment, international calls, operator services, pay phones, value added services, and private line services were not capped. Subject to these constraints, the company was permitted to price as it saw fit; as the regulatory strategy did not pass the company's actual cost increases or decreases through to ratepayers, any cost reduction (increase) would have increased (reduced) its profits. (For a critical overview of the British experience, see Vickers and Yarrow, 1987; B hattacharyya and Laughhunn, 1987).

Between 1984 and 1988, the RPIrose 25.6%, the productivity-adjusted maximum price-index (RPI-3) 8.6%, and British Telecom's actual price index for its capped services 5.5% (Meek, 1988); Le., the company did not increase its prices to the maximum extent possible. (In the last two years, the company agreed to a voluntary price freeze.) Overall, the rate of price increase for a basket of telephone services in Great Britain was lower than in France, West Germany, and Italy in the same time period (Oftel, 1988).

However, the price-cap strategy affected different services quite assymetrically. Long-distance rates, which were originally distorted upward but are now under increasing competition (from Mercury Communications Limited), fell 32% in the peak: and standard period in between 1984 and 1988. However, line rentals rates,

INTRODUCTION 5

which had been subsidized prior to 1981, increased over 20%; short-distance rates increased anywhere from 9.5% to 34.5%.

British Telecom did fairly well financially over the five-year period. Its rate of return rose gradually from 19.3% in 1983 to 21.4% in 1987; its labor productivity (output/worker) rose as well (Oftel, 1988). Some analysts feel that the company would have done even better financially but for its self-imposed price restraint in the last two years (Johnson, 1989).

In 1989, the Office of Telecommunications elected to continue the program for four more years, increasing the annual productivity offset from 3% to 4.5%.

2.2 State Experience In 1987, the National Telecommunications Information Administration (1987)

claimed that 35 states considered or adopted some form of social contract or banded price regulation; Megdal and Lain (1988) offers an overview of what had been tried.

Alan Mathios and Robert Rogers (1989) of the Federal Trade Commission performed an econometric analysis of the effect of price-cap regulation of AT&T intrastate long-distance rates using state cross-sectional data. The study concluded that toll service prices are about 7% higher in states that continue to use rate-ofreturn regulation. The authors estimated that a consumer savings of $157 million would result if all states were to switch to price-cap regulation of AT&T's intrastate toll service.

Turning to individual examples, the Michigan Public Service Commission implemented the first form of price-cap regulation in the United States in 1980. Their adopted regulatory mechanism annually adjusted intrastate rates across-theboard by .9 times the annual rate of inflation (as measured by the urban consumer price index) less a 4% allowance for expected productivity growth. A noticeable advantage of the plan was the considerably streamlined regulation that followed; compared to the immediately previous rate case, the number of witnesses fell from 50 to 2, days of hearing from 57 to 1{2, months between hearing and interim rate relief from 6 to 0, and necessary pages of transcript from 8400 to 66 (Face, 1988). Though the company failed to attain its allowed rate of return (which it had failed to do following the last eight full scale rate hearings as well), a statistical study by Michigan Bell economist Howard K. Face (1988) shows that this revenue shortfall resulted mainly as a result of the severe recession that had contemporaneously affected Michigan. Face also estimates that management saved $40 million dollars in 1982 in response to the improved incentives allowed by the price-cap strategy.

The plan terminated relatively unnoticed in 1983, which was prior to divestiture; however, the Michigan legislature granted the Commission the authority to implement flexible regulation and to deregulate all services (except basic exchange) by 1992 (Megdal and Lain, 1988). In a similar vein, the South Carolina Public Service Commission filed testimony with the FCC in 1988, stating that it had successfully applied price caps to AT&T's intrastate services since 1984, resulting in rates that had decreased below the maximum permitted increase.


In 1987, the Vermont Department of Public Service and New England Telephone reached the Vermont Telecommunications Agreement, a social contract that combined aspects of deregulation and rate moratoria; the Public Service Board enacted a modified version of the agreement in January, 1989. Under the modified agreement, New England Telephone agreed to freeze its line or message service rates until 1992, to upgrade all of its switches in Vermont to stored program control by the same year, and to provide blocking for all 976 calls. In return, the Department agreed to deregulate both the company's competiti ve and nonessential service prices and its rate of return; it reconfirmed an earlier agreement that all customers must convert to measured local service where economically efficient.

The outcome in Vermont appears to be felicitous. Despite a substantial increase in the subscriber plant factor, local rates have not increased. The commission now exercises service quality oversight in each of 99 central offices. The transition to stored program control switches is on schedule; 100% changeover will result by 1992. The company's average toll rates have fallen between 5 and 10%, in some places more; as a result, the company's revenue and earnings growth rates have been less than anticipated.

A somewhat different story emerges in New York. In 1986, New York Telephone and the New York Public Service Commission agreed to a rate moratorium at first through 1989; this was eventually extended to 1990. The commission delimited a group of core monopoly services; New York Telephone agreed to pass through to consumers only pre-specified cost increases, which were to include wage contract negotiations and changes in tax laws, separations procedures, and depreciation rates. The company was permitted greater price flexibility in discretionary services, such as custom calling, remote call forwarding, TOUCHTONE, lNTELLIP A TH, optional calling plans, and Centrex lines. In return for its price freeze, the company was permitted to keep one-half of all net earnings that it had attained in excess of its authorizedretum of 14% on the equity portion of its intrastate rate base (New York Telephone, Case 28691, Opinion No. 85-17 (D), N.Y.P.S.C., May 11, 1987).

From 1987 through 1989, the company's net earnings have performed basically as had been expected, although not as well as the company might have hoped. More significantly, the company is now projecting (as of November, 1988) more significant shortfalls in net earnings in 1990, the moratorium extension year. The company and the commission are now renegotiating in a very important test of the rate moratorium.

Other states have experimented with deregulation and/or limited forms of social contract regulation. In 1983, Iowa became the first state to deregulate some local company services, including inside wire, public coin, Centrex, and mobile radio; Montana deregulated inside wire, jacks, and radio in 1985, and Colorado deregulated inside wire, jacks, and billing and collections in 1987. In 1986, the Nebraska legislature eliminated rate of return regulation and, by 1991, the regulation of all jurisdictional services, including local; the Idaho Telecommunications Act of 1988 permits a company to remove all services, except forresidential and small business,

IN1RODUCTION 7

from rate-of-return regulation. Alabama (1986), Connecticut (1987), and Wisconsin (1987) introduced rate moratoria similar to New York's.

2.3 Federal Experience Significantly, rate-of-return regulation did not begin in order to protect con

sumers but rather to ensure that AT&T did not predatorily price competitive services (Levitz, 1987). From its inception in 1934 through 1967, the FCC instead regulated AT&T's interstate services by "continuing surveillance," which was

a process by which many previous interstate rate adjustments have been brought without formal proceedings ... [in which] either the Commission or [AT&T] would initiate discussions looking toward appropriate rate changes whenever the level of ... total interstate earnings has appeared to warrant such action. (Docket No. 16258,2 FCC 2d 173,177 (1965))

In response to concerns that AT&T would attempt to subsidize its competitive private line services against the newly emerging competition, the commission adoptedrate-of-returnregulationin 1967 (DocketNo.16258, 9FCC2d30(1967». It then followed with additional filing requirements of relevant cost data and issued a cost allocation manual in 1981.

As dissatisfaction with rate-of-return regulation of AT&T grew, price-cap strategies attracted proponents at the FCC (Haring and Kwerel, 1987; Patrick, 1987), AT&T (Linhart and Radner, 1986; Faulhaber, 1987), Bell Communications Research (Egan and Taylor, 1987), and the National Telecommunications and Information Administration (1987). After several years of testimony and proposed rulemaking, the FCC enacted on July 1, 1989, a price-cap mechanism for regulating AT&T's interstate rates (Policy and Rules Concerning Rates for Dominant Carriers, CC Docket No. 87-313, FCC 89-91, Released 4/17/89).

Under the FCC's latest price-cap mechanism, AT&T's services are divided into three "baskets"; each basket index is to be individually capped. (The FCC regards this as a more certain means than British Telecommunications' single price index to protect residential customers against "excessive" price hikes.) Each basket index level is permitted to increase by an inflation index (gross national product (GNP) deflator) less 3% for the expected productivity improvement, which exceeds its historically demonstrated rate of 2.5%; a means of passing through changes in access and certain other exogenous costs was also devised. Finally, except for two service components, no individual rate change may exceed 5%; changes in off-peak residential rates are banded at 4%. These bandwidths will presumably offer additional protection against rate shock and predatory pricing. Subject to these constraints, the company may price as it wishes and may keep any resulting profits.

3. Advantages of Social Contracts and Price Caps

We now can summarize the advantages that social contract and price caps may offer as compared to cost-based regulation.


1. Under the above incentive mechanisms, regulators do not pass through to consumers actual increases or decreases in the company's costs. Under these circumstances, the company would have every incentive to minimize costs and to adopt efficient technological improvements. With detariffed competitive and new services, utilities would have the same options and incentives to innovate and market as would a deregulated profit-maximizing firm under similar circumstances.

2. Under price-cap regulation, utilities do not report actual cost data to the regulators; they therefore have no reason or opportunity to distort their reported cost data strategically.

3. Because the commission specifies neither a rate base nor a maximum rate of return on invested capital, the utility has no incentive to expand its rate base uneconomically or to "gold plate" it.

4. Depending upon the exact structure of the price-cap procedure, prices may evolve in the long run toward second-best Ramsey (1927) levels (Vogelsang and Finsinger, 1979); price competition can be ensured at times by deregulating competitive services. By allowing pricing freedom, regulators permit the firm the flexibility to respond quickly to competition, often to the benefit of its ratepayers.

5. Because rate-base regulation is abandoned, there is no opportunity for utilities to shift rate-based costs of competitive services on to their captive monopolized customers.

6. In reducing company-regulator contact over the regulatory period, the opportunities for political gainseeking may be diminished as well.

7. As Face has shown, a price-cap mechanism may reduce the associated administration costs of regulation.

4. Ongoing Problems

Nonetheless, price caps and social contracts pose a series of problems that must be resolved if any strategy is to work successfully. Some of these problems have attracted the attention of authors in this volume.

1. Under price caps, companies are permitted to adjust service prices freely; consequently, relative price ratios may be expected to change over time. A serious concern then entails whether rates will evolve toward an efficient price structure in the long run.

In this volume, Ingo Vogelsang extends the Vogelsang-Finsinger (1979) mechanism in two respects. First, the earlier mechanism assumed that the regulated utility always priced in order to maximize profits in the subsequent year; Sappington (1980) proved that strategic distortion may occur if a less myopic objective function were to prevail. In this volume, Vogelsang now allows the strategizing utility to maximize long-run profits subject to the binding constraint on its revenues and costs in each period. Second, Vogelsang considers two-part tariffs, which are the prevailing price structure in telephone companies today; he permits both customer usage and number of customers to vary.

INTRODUCTION 9

Vogelsang now shows that access and usage prices converge to profit-constrained optimal two-part tariffs (Ng and Weisser, 1974; Schmalensee, 1981), which are equivalent to Ramsey prices. The particular benefits of the Vogelsang mechanism inhere in its second-best optimal equilibrium, its use of readily available data (i.e., accounting costs and quantities from the previous period), its simple price constraint rule, and the fact that regulators are not required to conjecture Bayesian distributions on any cost or parameter.

In a subsequent chapter, Timothy Brennan demonstrates that capping the Laspeyre price index of a regulated firm can be represented as the solution to a monopoly profit-maximizing problem, subject to the constraint that the aggregate level of consumer welfare exceeds a prespecified minimum. He then presents and evaluates optimality conditions under non-marginal price changes. If demand changes over time, results are considerably less sanguine than Vogelsang finds; Brennan shows that the regulated firm may distort information or undertake intertemporal welfare-reducing output strategies. Additionally, he finds that legal and political constraints may prevent the government from credibly precommitting to price caps, thereby introducing the issue of optimal regulatory lag. In short, Brennan demonstrates some continuing practical difficulties of using the index ceiling over the long run.

2. David Baron considers further the issue of regulator commitment, extending in the process a Bayesian incentive mechanism that he and Roger Myerson (Baron and Myerson, 1982) codeveloped to a multiperiod world in which regulators and utilities interact repeatedly with one another. In Baron's model, regulators do not know utility marginal cost but can form a Bayesian prior distribution on it; they then offer the utility a menu of prices based upon their Bayesian expectations of marginal cost. The utility is asked to reveal its marginal cost; each different revealed cost has a different corresponding price in the menu. As previously shown (Dasgupta, Hammond, and Maskin, 1979; Harris and Townsend, 1982) regulators can limit themselves, without detriment to consumers, to menus that encourage honest cost revelation.

Under multiperiod price-cap regulation, regulators would eventually learn the company's prices, profits, and costs; if a supernormal profit level were revealed at any time, regulators may at some later point attempt to reduce prices in order to secure a larger share for consumers, especially when faced with an upcoming reappointment decision. Additionally, even the least opportunistic regulators are unable to precommit their eventual successors to not using revealed company cost data to the detriment of the company. Therefore, regulated utilities may have less incentive to innovate and may otherwise misrepresent reported cost data in an attempt to "game" the outcome in a multiperiod process.

Baron then shows that regulators who cannot precommit to not exploiting utility information over time must offer the utility higher menu prices initially in order to induce it to reveal its marginal costs accurately. This would reduce consumer surplus and economic efficiency. Therefore, even partially credible commitments, such as a guaranteed capital recovery rule, could go some way to reducing


present-day prices and improving long-run allocative efficiency. 3. In any price-cap mechanism, expected rates of technical change must be

prespecified. This is an extremely important part of price-cap regulation, as it implicitly involves how much of a company's expected cost reductions will be shared with its ratepayers. In an important Bell Communications Research paper, Egan and Taylor (1988) suggested four alternative productivity benchmarksaverage productivity of the industry as a whole or of its deregulated services, an amount based on historical performance of the firm, a productivity adjustment obtained by monitoring company profit levels at certain intervals, and a negotiated amount reached as part of the social contract.

Two chapters in this book deal with productivity benchmarks; a third considers a mechanism for specifying a sharing rule. John Kwoka is Special Assistant to the Chief of the Common Carrier Bureau at the FCC. Kwoka discusses how the FCC designed its total factor productivity measure based on several estimates of telephone company productivity that prominent witnesses had fIled.

Ferenc Kiss complements K woka' s article, discussing the difficulties in measuring company productivity and the dangers of the FCC's present methodology. Kiss discusses four productivity measures-total factor productivity of the individual carrier, labor productivity of the individual carrier, total factor productivity of the industry, and dual productivity measures based on cost and price data. He runs an historical simulation that compares one of these measures with AT&T's actual performance; the historical correspondence is less than satisfactory. Kiss concludes that any aggregate productivity measure will inevitably fail in future use; he suggests that measures of future expected productivity growth be based upon disaggregate historical estimates that should incorporate two separate effectsscale economies (in tum related to output growth) and exogenous technical advance.

In the light of Kiss' pessimism, a contract approach that establishes a benchmark productivity index through political negotiation rather than measurement may be the only realistic option; Peter Linhart, Roy Radner, and Frank Sinden offer a suitable strategy. In their model, a firm is required to lower its real prices at a prescribed annual rate that is arrived at through negotiation; as the price ceiling declines, management must reduce costs in order to keep net earnings at an acceptable level. The decline in prices may eventually squeeze utility profits below an acceptable level, at which point present management is dismissed. Once this point is reached, regulators must reset prices at a higher level, allow a suitable period for financial recovery, and begin a new downward trajectory. Significantly, the authors show that if management does not discount future utility excessively, its expected tenure will be long and the achieved price decline will be near the regulator's initial target

4. Perhaps with an eye to airlines and trucking, some have contended that service quality could be seriously degraded if price-capped utilities were given broad incentives to cut costs; e.g., companies could profitably reduce investment and maintenance, layoff personnel, and allow plant to deteriorate.

INIRODUCTION 11

Luis Cabral and Michael Riordan present a formal analysis of the incentives for cost reduction under a price-cap regime. As the price ceiling is reduced below its unconstrained monopoly level, the firm at first has an incentive to expand more effort to reduce costs. This is because lower prices increase both consumer demand and associated production costs; therefore, company efforts to reduce these costs become more cost-effective. However, this relationship is not monotonic; after a certain point, the firm's incentive to reduce its costs falls discontinuously to zero. Excessive price reductions then present an important problem.

New York Commissioner Eli Noam offers a more practical article; he proposes an incentive-based system for rewarding service quality in a price-cap mechanism. In Noam's five-step process, regulators must select relevant quality dimensions, define associated measurable standards, assign appropriate weights to each standard based on revealed preference or surveys, construct an aggregate weighting index and monitor component quality, and tie quality performance to financial incentives. The result is an innovative price-cap mechanism that explicitly incorporates service quality as an incentive variable.

S. Under deregulation, telecommunications companies may profitably introduce new services and options, to the eventual benefit of their consumers, that may include volume-based optional calling plans. David Sibley, Daniel Heyman, and William Taylor contend that volume-based optional calling plans would likely be treated as new services under the FCC price-cap proposal, meaning that each would have only to pass a net revenue test, instead of the Part 69 test based on fully distributed costs. Consequently, local companies will face less difficulty in implementing such tariffs than they now do under the current system of regulation. The article then estimates the profit and welfare gains to volume-based optional calling plans and concludes that they are quite significant.

Einhorn applies optional calling plans to the bypass problem. Under a social contract agreement, regulators will be permitted to specify the terms of one two-part tariff calling plan for switched access; the utility may offer as many alternative calling plans as it likes. Each customer is free to select any offered option for any access channel. Since regulators get to design one calling plan in a manner that is presumably fair, the eventual outcome can be regarded as fair.

The article demonstrates that a profit-maximizing company constrained to offer the fair tariff will design a menu of optional calling plans for switched access that will permit bypass if and only if it is economically efficient; usage prices under some calling plans may be below marginal cost. Significantly, each calling plan would pass the net revenue test and could therefore be regarded as a legitimately deregulated line of business.

6. Calvin Monson and Alex Larson of Southwestern Bell consider the implications of price caps for capacity sizing; this would evidently be an important issue in any regulated industry that must grow to meet increasing demands. As compared with unconstrained profit-maximization, the authors find that price ceiling regulation gives the utility more incentive to increase its capacity and to permit more supply; additionally, price caps may increase the incentive of the firm to heighten

12 PRICE CAPS AND INCENTIVE REGULATION IN TELECOMMUNlCA TIONS

marketing activity if such activity increases the elasticity of customer demand. Finally, Monson and Larson demonstrate that the incentives for cost minimization under price-ceiling regulation are independent of the profit level and that a change to price-ceiling regulation, with the ceiling set at the former rate-of-return-regulated price, will increase cost-reducing investments.

References

Atkinson, S., and R. Halvorsen. 1980. "A Test of Relative and Absolute Price Efficiency in Regulated Industries." Review of Economics and Statistics 62(1 ):81-8.

Avercll, H., and L.L. Johnson. 1962. "Behavior of the Firm under Regulatory Constraint." American Economic Review 52 (6): 1053-69.

Bailey, E.E. 1973. Economic Theory of Regulatory Constraint. Lexington, Mass: D.C. Heath and Company.

Bailey, E.E., and R.D. Coleman. 1971. "The Effect of Lagged Regulation in the AverchJohnson Model." Bell Journal of Economics and Management Science 2(2): 278-92.

Baron, D.P., and R.B. Myerson. 1982. "Regulating a Monopolist with Unknown Costs." Econometrica 50 (4): 911-30.

Baumol, W.J., and D. F. Bradford. 1970. "Optimal Departures from Marginal Cost Pricing." American Economic Review 60(3): 265-83.

Baumol, W.J., M. F. Koehn, and R.D. Willig. 1987. "How Arbitrary is 'Arbitrary'? or, Toward the Deserved Demise of Full Cost Allocation." Public Utilities Fortnightly 120(5): 16-21.

Bhattacharyya, S.K., and D.J. Laughhunn. 1987. "Price Cap Regulation: Can We Learn from the British Telecommunications Experience?" Public Utilities Fortnightly 120(8): 22-9.

Courville, L. 1974. "Regulation and Efficiency in the Electric Utility Industry." B ell Journal of Economics and Management Science 5(1): 53-74.

Dasgupta, P.S., P.I. Hanunond, and E.S. Maskin. 1979. "The Implementation of Social Choice Rules: Some Results on Incentive Compatibility." Review of Economic Studies 46 (2): 185- 216.

Egan, B.L., and W.E. Taylor. 1987. 'The Economics of Ceiling Price Regulation." Unpublished manuscript. Bell Communications Research. Livingston, New Jersey.

Face, H.K. 1988. "The First Case Study in Telecommunications Social Contracts." Public Utilities Fortnightly 122(7): 27-31.

Faulhaber, G.R. 1987. 'The FCC's Path to Deregulation: Turnpike or Quagmire." Public Utilities Fortnightly 120(5): 22-6.

Goldman, M.B., H.E. Leland, and D.S. Sibley. 1984. "Optimal Nonuniform Prices." Review of Economic Studies (51) 2: 305-19.

Griffin, J. 1982. 'The Welfare Implications of Externalities and Price Elasticities for Telecommunications Pricing." Review of Economics and Statistics 64(3): 354-63.

Haring, J., and E. Kwerel. 1987. "Competition Policy in the Post- Equal Access Market." opp Working Paper. DA 87-211. Office of Plans and Policy. Federal Communications Commission. Washington, D.C.

Harris, M., and R.M. Townsend. 1981. "Resource Allocation under Assymetric Information." Econometrica 49 (1): 33-64.

Johnson, L.L. 1989. "Price Caps in Telecommunications Regulatory Reform." Rand Cor-

INTRODUCTION 13

poration. Santa Monica, California. Levitz, K.B. 1987. "Loosening the Ties that Bind: Regulating the Interexchange Services

Market for the 1990's." OPP Working Paper DA 87-224. Office of Plans and Policy. Federal Communications Commission. Washington, D.C.

Liebenstein, H. 1966. "Allocative Efficiency vs. X-Efficiency." American Economic Review 56(3): 392-413.

Linhart, P.B., and R. Radner. 1986. "Relaxed Regulation of AT&T, Reconsidered." delivered at the Fourteenth Annual Telecommunications Policy Research Conference. Airlie, Virginia.

Littlechild, S. 1983. "Regulation of British Telecommunications' Profitability." Report to the Secretary of State. Dept. of Trade. London, England.

Mathios, A., and R. P. Rogers. 1989. 'The Impact of Alternative Forms of State Regulation of AT&T on Direct Dial Long Distance Telephone Rates." Rand Journal of Economics 20(3):437-53.

Megdal, S. B., and D. Lain. 1988. "A Comparison of Alternative Methods for Regulating Local Exchange Companies." Presented to the Sixth National Regulatory Research Institute Biennial Regulatory Information Conference. Columbus, Ohio. September, 1988.

Mirman, L.J., and D.S. Sibley. 1980. "Optimal Nonuniform Pricing for Multiproduct Monopolies." Bell Journal of Economics 11(2): 659-70.

National Telecommunications and Information Administration. 1987. NT/A Regulatory AlternativesReport. U. S. Dept. of Commerce. Washington, D.C.

Noll, R.G., and B.M. Owen. 1987. "United States v. AT&T: An Interim Assessment." Working paper. Stanford University. Palo Alto, California.

N g, Y.K. and M. Weisser. 1974. "Optimal Pricing with a Budget Constraint - The Case of the Two-Part Tariff." Review of Economic Studies 41 (3): 337 -45.

Office of Telecommunications. 1988. "The Regulation of British Telecom's Prices: A Consultative Document." London, England.

Patrick, D.R. 1987. "Long-Distance Carrier Service: Other Modes of Regulation." Public Utilities Fortnightly 119(5): 11-5.

Ramsey, F. 1927. "A Contribution to the Theory of Taxation." Economic Journal (March): 47-61.

Sappington, D. 1980. "Strategic Firm Behavior Under a Dynamic Regulatory Adjustment Process." Bell Journal of Economics 11(1): 360-72.

Schmalensee, R. 1981. "Monopolistic Two-Part Pricing Arrangements." Bell Journal of Economics 11(2): 445-66.

Smith, V.K. 1974. 'The Implications of Regulation for Induced Technical Change." Bell Journal of Economics and Management Science 5(2): 623-33.

Spann, R.M. 1974. "Rate of Return Regulation and Efficiency of Production: An Empirical Test of the Averch-Johnson Thesis." Bell Journal of Economics and Management Science 5(1): 38- 52.

Spence, A.M. 1977. "Nonlinear Prices and Welfare." Journal of Public Economics 8(1): 1-18.

Vickers, J., and G. Yarrow. 1988. Privatization in Britain. Cambridge, Mass.: MIT Press. Vogelsang, I., and J. Finsinger. 1979. "A Regulatory Adjustment Process for Optimal Pricing

by Multiproduct Monopoly Firms." Bell Journal of Economics 10(1): 157-71. Wellisz, S. 1963. "Regulation of Natural Gas Pipeline Companies." Journal of Political

Economy 71(1): 30-53. Wenders, J.T. 1987. The Economics of Telecommunications: Theory and Policy.


Cambridge, Mass.: Ballinger Publishing Company. Zajac, E.E. 1972. "Note on 'Gold Plating' or 'Rate Base Padding'." Bell Journal of

Economics and Management Science 3(1): 311-5.

2 A NON-BAYESIAN INCENTIVE

MECHANISM USING TWO-PART TARIFFS Ingo Vogelsang

1. Introduction

The regulatory incentive mechanism to be discussed in this article may be seen as a contribution to the issue of the optimality of marginal cost pricing. The case for and against marginal cost pricing by public utilities has a somewhat dialectic history. Hotelling (1938) set the stage for the thesis by arguing that in decreasing cost industries, buyers should only pay the marginal costs of serving them. The resulting deficit should simply burden the taxpayers. Coase (1945, 1946) soon vehemently opposed this suggestion. He argued first that marginal cost pricing does not pass the test that consumers' total willingness to pay exceeds production costs of the good in question; second, that subsidies jeopardize efficient operation of the monopoly supplier; and third, that tax financing of subsidies results in an unjustified redistribution from general taxpayers to the consumers of goods produced under increasing returns. However, Coase's antithesis did not initially win the profession. This took much longer and resulted in Ramsey prices as the synthesis. Ramsey prices maximize total surplus under a balanced budget constraint for the public utility. Such a balanced budget constraint fulfills several functions. It neutralizes income distributional issues between shareholders of the firm and its customers. The shareholders exactly receive a competitive return, neither more nor less. Without any more specific information, it further allows us to state that consumers in total value the output of the public utility at least at production cost. Third, it puts a (sometimes generous) cap on any inefficiencies in the production of the output. Last, it avoids subsidies and the accompanying distortions.

In spite of the virtues of Ramsey prices, marginal cost prices have had a recent comeback. The reasons belong into two categories. First, Ramsey prices are difficult to implement. They discriminate between low elasticity and high elasticity customer groups. This makes them politically unpopular. And they require the regulator to have substantial information about cost and demand functions.


This makes them difficult to calculate. Second, implementation problems for marginal cost prices have been reduced by now through various incentive schemes. Still, there seems to remain the problem that marginal cost prices may necessitate subsidies. In particular, subsidies may now be required as an incentive device. In this paper I instead suggest that the subsidy be paid by consumers in the form of the fixed part of a two-part tariff. The properties of these new tariffs are a further indication that the distinct superiority of two-part tariffs over Ramsey prices could form a new pricing synthesis for most regulated industries and public enterprises.

The economic literature on regulatory incentive mechanisms has grown substantially over the past ten years. Before this time, economists were mostly concerned with the theoretical derivation of welfare optimality conditions for prices and costs of regulated monopoly firms. Practical approaches to regulatory pricing, such as rate-of-return regulation, were mostly criticized for failing to obey these conditions. They were not seen as necessarily imperfect attempts to implement these conditions. If anything has been brought out very clearly by the new incentive literature, it is that the originally derived optimality conditions fail to be optimal in an imperfect world with asymmetric information and risk aversion. 1

This message has come across most clearly through the Bayesian approach to regulatory incentive mechanisms (pioneered by Baron and Myerson, 1982).

In Bayesian mechanisms the regulator acts as a principal while the firm (or its management) is an agent whom the principal wants to induce to behave in the principal's interest. The principal wants to maximize a welfare function. She has certain (unbiased) a priori expectations, for instance on the firm's cost function, and can observe certain variables, for instance the firm's total expenses. The agent wants to maximize his own utility which is assumed to be a function of income (profit) or income and effort (or risk-taking). Maximizing welfare is usually not in the interest of the agent because that requires effort or a sacrifice of profits. The principal, therefore, has to compensate the agent for maximizing welfare. In the absence of lumpsum taxes such a compensation will itself influence welfare and hence affect the desired welfare optimum. The Bayesian literature has worked out this point very clearly. It has also provided a number of very basic insights which are discussed in other chapters of this volume. I want to argue, however, that non-Bayesian approaches continue to be useful. In my view, the Bayesian approach has three major drawbacks.

The first drawback is that the a priori information of the regulator is non-verifiable. This would cause no problem if the regulator were the true welfare-maximizing principal known from the simple principal-agent framework. However, the principal-agent framework is hardly a correct description of the regulatory process. The regulator is usually a public official or, more likely, a bureau. In both cases, unless being a dictator, the regulator should be acting on behalf of the polity. This in itself could constitute a principal-agent relationship if it were not for conceptual difficulties in formulating preference formation of the polity as the principal. In practice, the regulator is guided by legal rules and the voting mechanism. The problem of responsibility of the regulator and her control by third parties are

A NON-BAYESIAN INCENTIVE MECHANISM USING lWO-PART TARIFFS 17

addressed in courts or by auditors or in elections. How can judges, auditors or the electorate control regulatory decisions without any direct observation of the a priori beliefs of the regulator? There is a clear moral hazard problem in differentiating between subjective probabilities and political opinions. If the regulator has different welfare weights than the electorate, then she can implement them by misstating her true a priori probabilities. In addition to the moral hazard problem the different public officials in the regulatory bureau among themselves face an aggregation problem for their a priori probabilities. They have to find jointly held subjective probabilities before determining optimal regulation.

The second drawback of Bayesian mechanisms is that the regulator's a priori information may be very poor and incomplete. Chances are high then that the resulting mechanism will provide the wrong incentives.

The third drawback is that optimal Bayesian incentive mechanisms are extremely hard to derive for all but the very simplest functional forms. This means that the problems treated by these mechanisms so far are quite remote from practical implementation? It does not mean that the general insights provided by Bayesian mechanisms are not empirically relevant, though.

In this article we discuss an alternative to the Bayesian approach which is based on the tradition of adjustment processes known in the economic literature at least since Walras. The current process is a blend of two adjustment processes previously suggested by J. Finsinger and myself. The first of these processes (Vogelsang and Finsinger, 1979, in the following: V -F) is a regulatory adjustment process for private firms leading to Ramsey prices. The second one (Finsinger and Vogelsang, 1982, in the following: F-V) is a performance index for public enterprise managers leading to marginal cost prices. These approaches are quite different from the Bayesian approach in several respects.

First, uncertainty is not explicitly introduced. Rather, the firm (or its management) is assumed to know cost and demand functions for its outputs while the regulator is assumed to know only very general properties of these functions such as the sign of derivatives. The regulator, however, can ex post observe bookkeeping data on prices, quantities, and total costs (expenses). While uncertainty could be introduced, it is not an essential part of the framework.

Second, the approach is essentially dynamic, and it is based on a lagged adjustment. With the exception of mechanisms that converge in one period this means that the mechanisms will only develop their full properties in a stationary environment. Also, the mechanisms will deviate from the full information optimum in all periods before convergence to a steady state. Strategic behavior rilaY occur that reduces the speed of convergence. Therefore, the discounted value of welfare levels provided by these mechanisms will differ from the present value of full information optima. On the other hand, the mechanisms usually improve welfare in every period. They might, therefore, better be regarded as piecemeal approaches using a gradient method.


Third, the incentives or regulatory constraints used are simple approximations to the welfare change effected by the fIrm. They are therefore simple formulas that can be easily understood by regulators and managers.

The frrst and the last of these properties clearly suggest that the approach is more readily implementable than the Bayesian approach. The second property is really what seems to count against it However, this property is also a consequence of practicality. Lags are necessary for the observation of the cost and quantity data. If lags could be avoided altogether, then one could make the lag period of the mechanisms arbitrarily small and thereby achieve convergence in an essentially stationary environment.

In terms of philosophy, the main difference between Bayesian mechanisms and the regulatory schemes discussed in this article seems to lie in their view of the regulator. The Bayesian approach views the regulator as benevolent and well informed, the British ideal of a civil servant Our approach views the regulator as a potentially imperfect executor of rules and laws, someone who has to be subject to third-party control.

In the next section, we introduce a regulatory constraint as the fixed part of a two-part tariff. In order to bring home the main points, it is first assumed that the regulatory constraint acts as a lumpsum tax on consumers. This assumption is then relaxed in Section 3, and it is shown that the scheme is likely to work under more general conditions. Section 4 contains some possible extensions. The article ends with short conclusions in Section 5.

2. Two-part Tariffs with a Fixed Number of Customers

We use a discrete dynamic model in a stationary environment Assume a regulated monopoly firm producing a single output in quantity q/ in period t. The frrm faces a cost function C(q/), but it is not necessarily producing on it. The difference between its actual cost, Ct , and C(q/» could be any kind of inefficiency, but for simplicity here is assumed to be pure waste, W,. In the initial period 0 there is no regulatory constraint, although the frrm knows that regulation will be installed in period 1. Thus, the price of the product in period 0 is Po, and the frrm' s profIt is 1to = Poqo - Co. Starting in period 1, the regulatory constraint is introduced as the fixed portion F 1 of a two-part tariff.

The general form of the constraint for period t is

- [1t,_1 - (PH - P,)q,-l] F/= N '

(1)

where N is the number of consumers buying from the frrm.3

Equation (1) says that the firm must disburse its profits of the previous period either through a fixed fee (refund), Fh or a price decrease, PI-l - Ph denominated at last period's quantity, q,-l. Any combination, which makes the sum of the two changes equal to the previous profit, is feasible. Thus the frrm may actually

A NON-BAYESIAN INCENTIVE MECHANISM USING 1WO-PARTTARIFFS 19

increase P as long as F is sufficiently decreased, and vice versa it may increase F as long as P is sufficiently decreased. Should the fIrm make a loss in a period it can similarly ask the customers to reimburse it for this loss in the next period.

Noting the definition of t we may rewrite the constraint as

Ct- 1 qt-l _ _ Ft=N- PiN--= ct-l - qt--1Pt'

(2)

where Ct--l and Ilt-l are, respectively, average cost and average quantity per customer in period t-1. Equation (2) clearly shows the tradeoff between Ft and Pt.

Here F t can be interpreted as the difference between average cost and average variable revenue per customer.

In a sense, the constraint turns customers into shareholders of the firm, but as in a cooperative they receive their dividend on a per capita basis. Here the fixed fee can be seen as a membership contribution which entitles the member to a price discount. Similarly, a negative fIxed fee would appear as a form of profIt distribution to the members. So we could interpret the situation as one which turns the public utility into a cooperative. Note that cooperatives tend to distribute profits, both, as per capita dividends and as price discounts. Henceforth, we therefore call F either the 'consumer dividend' or the 'membership fee,' depending on whether it is negative or positive; P will simply be the 'price.,4

In the current section we take N, the number and identity of members of the cooperative, to be fixed and, in particular, to be independent of the firm's pricing policy. Hence, F t is a lumpsum subsidy for the consumers. Now, post-dividend profIts of the firm in period t are

where Ttt is defined as Tto above. In the following, fIt is referred to as total profit. All demand has to be served at prices Pt.

Assume that the firm maximizes the discounted stream of future profits

max fICO = L.. [p/qt - C(qt) - Wt + Ft N] 13t s.t. (1) and F 0 = 0 or W"P, t=O

max LIT = L..[Pt q/ - C(qt) - Wt + Ft N - ~t(Pt qH - Ct--1 + F t N)] 13t , (4) W"P, 1=0


aL1t

allt =Ptqt-l-Ct-l +FtN=O.

Accounting for (6). the steady state solution to (5) is

aLIT =~( _aC)(I_ A)=O. ap ap (aq I-'

where dropping of the time subscript indicates the steady state.

(7)

(8)

(9)

Thus. provided 13*1. price will equal marginal cost in the steady state. The question then is whether the sequence of prices converges. Here it helps to see that the current two-part pricing scheme iscIosely related toF-V (1982) and V-F (1979). F-V (1982) suggest a performance index for the managers of a public enterprise of the form It = 1tt -1tH + qt-l(Pl-l - PI). Thus. the problem set up in (4) is exactly the same as in F-V (1982). On the other hand. in their Ramsey pricing problem. V-F (1979) suggest that the regulator impose a regulatory constraint of the form PtllH - C(qH)<Oon the regulated firm for each successive period t = 1 •...• 00. The firm then is constrained on average to reduce its price(s) by the previous period's profit margin. To make V -F and F-V comparable. it can easily be translated into an equivalent tax/subsidy TS I for a private enterprise by setting TSt = -1tI-l + ql-l(Pt-l - PI)' For the owner-manager of the privatefrrm this yields the same incentive as it does for the manager of a public enterprise. Thus. two-part tariffs using the formula of the V-F constraint in the fixed part exactly mimic the subsidy-based F-V performance index.

Therefore. the results from F-V (1982) carry through and also extend to the multiproduct case with differentiated fixed fees. In particular. it is shown there that the firm will never use pure waste and that prices will eventually converge to marginal cost prices. Besides N = constant and the usual differentiability assumptions the further assumptions needed on demand and cost functions are surprisingly weak: Demand has to be such that consumers' surplus is convex in prices. p. Furthermore. in each period the regulator has to be able to observe quantities. prices. and total costs for the last period.5

The reason why the mechanism will converge to marginal cost prices is that under the scheme the firm's total profit III is an approximation to the change in social surplus. In figure 1 the shaded area gives the firm's profit. III> while F t N is given by the rectangle EFGH. As can be seen from this and from the last formulation in equation (3). the change in producer surplus is exact while consumers' surplus is quite crudely approximated by ql-l (Pt-l - PI)'

A NON-BAYESIAN INCENTIVE MECHANISM USING lWO-PART TARIFFS 21

p,bClbq

P. - •

p.

D

H

E

G ~

F~

bC/cSq

o

L-____ ~~------~------------------------q q. - I q.

Figure 1: Profits and the Fixed Fee with Constant N

By convexity of consumers' surplus, however, this approximation is always weakly smaller than the true change in consumers' surplus. The difference is the nonappropriated triangle GKL. Thus, the firm will in any period receive a total profit Ilt that is no greater than the change in social surplus. If there is no improvement in surplus, then profit will be zero or negative. In terms of figure 1, ifprices are increased above the previous level, then there is an additional triangle outside the demand curve that is lost by the firm. The firm can in any period t assure itself at least of zero profits by setting PI = PI-I. Due to the differentiability assumption the firm can reap any increase in surplus through infinitely small price changes. Thus, if surplus can be increased through price changes the firm will do just that. The firm, however, will usually refrain from infinitely small steps, because profits incurred later have to be discounted. Hence, convergence in prices will pursue at a reasonable pace. Because the producer surplus change in equation


(3) is exact, the firm will not want to waste, and it will invest optimally. Hence, while optimal pricing takes time, cost minimization occurs instantaneously.6

3. Two-part Tariffs with a Variable Number of Customers

By making a strong assumption on consumer behavior (N = constant) we were able to show the equivalence between a subsidy scheme and a two-part tariff. This kind of equivalence has potential empirical importance?

The case of constantN probably covers the vast majority of cases for two-part tariffs by public utilities, such as electricity, gas, water, and even telephone services, in highly industrialized countries. However, in developing countries and for the poor in developed countries, such as the United States, participation in these services may still depend on pricing. We therefore have to address the following question: What happens if for each consumer i demand depends on both, the price p and the membership fee (consumer dividend) F, in such a way that the number of consumers varies as F and p are changed? In terms of the cooperative interpretation, membership now becomes a variable. Thus, qti = qti (Pr. Ft) and Nt = Nt(Pt,Ft).

Before describing the consequences of this generalization, we make the following additional assumptions:

1. We have to redefine the regulatory constraint (1). This now becomes

Ct- 1 - Pt qt-l F t = -----:--::----

N t- 1

2. C( q) exhibits (weakly) decreasing average costs. 3. ITo > O.

(10)

4. Consumers' surplus V(pr. Ft) is convex in both Pt and Ft. V(pr. Ft) is twice differentiable with iJV liJpt = - qt and iJV liJFt = - Nt.

5. The inverse demand functions p(q. N) and F(q. N) are continuous and

nonnegative for all q e R+, N e R+. lim (po ~l + pON') ~ 0, where qO = rq,

N' = rN,r eR+. pO and pO are the price and fixed fee that fulfill q(p0, pO) = qO and

N(p°. FO) = N'. These assumptions require some explanation. In assumption I, the reason for choosing Nt-l instead of Nt in the denominator

on the right hand side of (10) is that otherwise the constraint would be on the revenues generated from the fixed fee rather than on the fixed fee itself. This would allow the firm to choose a higher fixed fee and a lower number of customers than otherwise.

Assumptions 2, 3, and 5 are needed to assure feasibility of the process in the sense that the firm can always survive without making losses.

A NON-BAYESIAN INCENTIVE MECHANISM USING 1WO-PART TARIFFS 23

The nonnegativity of the fixed fee in assumption 5 is not necessarily compatible with the regulatory constraint (10). We do not want to restrict the constraint, though. Instead, we show below that the firm can always make profits and thus avoid a negative fixed fee.

Assumption 4 is necessary to assure convergence and optimality. It imposes some restrictions. First, the number of customers, Nt. always has to be so large that it can be treated as a continuous variable. Also, the exit or entry of a customer has such a small effect that it does not hurt the differentiability of V(Pt. Ft}. Second, the assumed convexity comes out as a standard result of consumption theory if we postulate the strong axiom of revealed preference to hold and income effects to be absent. In that case V, would be linear (and hence weakly convex) with respect to F, and it would be convex with respect to P (V-F, 1979, Appendix). But note that, even with declining marginal utility of income, convexity of V(Pt, F t} could still hold in the aggregate. Each consumer j would have a reservation price Pj for given F and a reservation membership fee Fj for given P such that the demanded quantity at any higher price or fee is zero. Hence, individual welfare is not affected by price changes occurring in the range above these prices. Now, if the distribution of consumer demands is sufficiently spread out, then any increase in P or F will result in the exit of customers which is essentially a convexifying phenomenon.

The interpretation of (10) is similar to that of (1). In the cooperative interpretation, the difference is that the consumer dividend (membership fee) now is paid to (by) the current members but is based on membership in the previous period. This is not out of line with cooperative practice. Total profit of the firm now becomes

Ct- 1 - Pt qt-l IIt = Pt qt - Ct + Ft Nt = PI qt - Ct + ---=-N=---

t-l (11)

Whenever we have Nt t: Nt-I, the process described by (11) will differ from the F-V performance index. Hence, one wonders in what way the optimization problem is changed.

The firm now wants to maximize

max II"" = L [ptqt - C(qt} - Wt + F/ Nt] pt S.t. (10) and F 0 = O. (12) W"P, t=O

Although, compared to the case whereN is constant, the only change is in pricing and in the shape of the demand function, the possibility for waste now arises. The first order condition for (12) with respect to waste is analogous to (7). However, in general, Ilt t: Ill+ 1 t: 1. The condition then implies that the absence of waste is guaranteed as long as Ill+ 1 < 1 +i. The intuition behind this inequality is that current profit reductions due to waste only pay if they are at least offset by an equivalent discounted relaxation in the constraint next period. We postpone a discussion of incentives for cost minimization to the next section and assume in the current section that waste poses no problem. Then (4) becomes


max LIT = L [ptqt - C(qt) + Ft Nt - Jl/Ptqt-l - C(qt-l) + Ft Nt-I] j3t, (13) P, t=O

where qt = qlpto Ft) and Nt = Nt(Pr. Ft). The first order conditions for this problem are:

dL IT dqt( dCt) dNt [~. dCt ) dNt] dPt = qt + dprI!!t - dqt + Ft dPt - Jltqt-l -j3qt+1 dPt(t+1 - aqt + Ft+l apt = 0

(14)

dLIT aqt( aCt) aNt [aqt( aCt) aNt] aFt =Nt + aFt(t- aql + FtaFt -Jl~I-I-j3qt+1 aFt(t+I- aqt + Fl+laFt =0

(15) and

aLIT -a - = P/qt-I - C(qt-l) + Ft Nt- l = o.

Jlt (16)

In the steady state (14) and (15) become

a~IT = [~r -~~)+ F~;] (1- Jlj3) + q(l - Jl) = 0, (17)

a:; = [~r -~~)+ F~~ ](1- Jl13) + N(1 - Jl) = 0, (18)

dLIT aJl =pq-C+FN=O. (19)

Let us compare these conditions to the first order conditions of the corresponding welfare maximization problem. Since no subsidies are allowed and since by construction of F t profits vanish in the steady state, the relevant welfare maximum is the constrained two-part tariff optimum S* with

S* = max[S(p, F): IT (p, F) + V(p, F) s.t.IT = 0]

where V(p,F) is aggregate consumer surplus. The first order conditions to this problem are

-= P-- +F- (l-y) -yq=O aLS [~( ac) aN] ap ap aq ap

-= p-- +F- (l-y) -yq= 0 aLS [k( ac) ON] of of oq dF

(20)

(21)

(22)

A NON-BAYESIAN INCENTIVE MECHANISM USING lWO-PARTTARIFFS 25

oLS oy =pq-C+FN=O. (23)

Dividing equation (21) through equation (22) and (17) through (18) yields equation (24) for both, for the problem of welfare maximization and for the steady state of our mechanism:

~( :"'OC)+FON op (oq op -=--+-~~_~ _!L k( _ OC) FoN- N· OF( oq+ of

(24)

Since the constraint on profit is the same in both cases, the first order conditions must be the same in both problems. That means we must have ~= [1--y(I-j3)]-1.

Note that marginal cost pricing is not the usual outcome of the welfare maximizing problem (20). This would be true even for an inequality constraint that is not binding (y= 0). We are here in an essentially second-best world where nondistortionary head taxes are not possible. Hence, marginal cost pricing could be suboptimal. Also note that in a situation of decreasing returns to scale the optimum may involve a negative F and/or p. The Ramsey pricing equivalent to the first-order condition (21) is

oLS ~( OC) op = op (- oq (l - 9) - 9q = O. (25)

Proposition. Under assumptions 1 through 4 the process described by problem (13) will converge to the constrained welfare optimum described by equations (20) through (23).

The proof to this proposition contains four steps.8 In step 1 profitability of the firm under the process is assured for all periods

1, ... ,00 given that Ilt > O. The reasoning is by induction: Given that Ilt-l > 0 the constraint in period t becomes more stringent than in period t-l. The firm therefore has to offer the output at a price combination that allows the consumers to continue to buy the quantity they bought in the previous period and pay less. By convexity of consumer surplus they will buy more. This larger output can be sold at a profit because average cost is falling. Therefore Ilt+l > O.

Hence the firm can always find a sequence of prices which leads to nonnegative profit in every single period. Should the firm decide to make losses in a period it will do so for strategic reasons, making up for these losses later. Hence, the regulator in this model should not take losses as a malfunctioning of the process and therefore should let the process continue after loss-making periods.

In step 2, it is shown that social surplus increases monotonically under the process. The reason is that for each period the change in social surplus is always larger than or equal to the profit of the firm.

26 PRICE CAPS AND INCENTIVE REGULATION INTELECOMMUNICA TIONS

This holds by convexity of Yep. F) or, more intuitively. by an aggregate revealed-preference argument. To see this, consider only the Nt customers purchasing in period t, since others, by definition, cannot reduce their purchases. Now, if the old customers in period t+ 1 want to purchase their previous quantities they will have to pay a total Ofpt+lqt + Ft+lNt = Pt+lqt+ ([C(qt) - Pt+lqt]INt)Nt= C(qt}. But this is less than they paid in period t, since then the f'mn was making a profit. This revealed preference argument follows directly from assumption 4:

IfPt+lqt + Ft+lNt <p,qt + F,Nt and qt = q(p" Ft}, then V(pt+lo Ft+l) > V(Pt, Ft}. As a consequence every profitable period for the firm results in a welfare

increase (weakly) greater than the f'mn's current profits. Should the f'mn make a loss during a period, then the reduction in welfare is less than the loss to the firm.

II = 0

p

v* F* - C*/N* - p*q*/N*

L-------------------------------------------------------F

Fi&ure 2; The Constraint. Profits and Consumer Welfare

A NON-BAYESIAN INCENTIVE MECHANISM USING lWO-P ART TARIFFS 27

Hence, any sequence of profits and losses to the finn between two periods m and n will lead to a net welfare gain as long as the sum of profits minus losses from m to n is positive. From step 1, the firm can always make a profit in the period following a profitable period. Therefore, it will suffer loss periods only in order to have more profitable periods later. The firm will not want to move in cycles because summed up that means a net loss which will be further enhanced by any discounting of future profits. Hence, if a loss period follows a profitable period, then the loss period marks the beginning of a finite sequence with a positive sum. Such a sequence can always be ended at a profitable period. Combining such finite sequences into megaperiods of unequal length we get a new sequence of welfare levels that is monotonically increasing.

Step 3 establishes that this sequence is bounded by the constrained welfare maximum and therefore converges.

In step 4, we show that welfare converges to this welfare maximum. We have already seen in equation (25) that the necessary condition for welfare maximization holds in the steady state. Here, we want to make this fact more plausible with an economic argument. Assume the process converged to S < S*. Then welfare could still be increased at the point of convergence. This potential for a welfare increase can be translated into profits by the firm, meaning that the steady state has not yet been reached. An illustrative way to see this is through figure 2. Since the zero-profit constraint would be binding at the optimum we can simply take consumer surplus as the maximand. Thus, the welfare problem becomes max V(p, F) s.t. IT = O. Then in the (p, F)-space pictured in figure 2, the welfare maximum is characterized by the tangency between the zero-profit contour IT = 0 and the maximal iso-welfare line V*. Note that welfare increases toward the origin. Also note that the gradient to any iso-welfare line is given by VV = -(P.F). Further, the constraint can be rewritten as 0 = C(qt-l) - P,qH - FtNt-t. Hence, the constraint is parallel to the tangent through (PH, Ft-l). The constraint simply moves the pricing decision of the fmu in the direction of the steepest welfare increase. Now, assume that the process has converged. At the point of convergence, we have IT=O by the definition of the constraint. So, the constraint has to be stationary at point (p*, F*) and has to be tangent to an iso-welfare line. Hence the first-order condition has to hold.

Theoretically, it is possible that the second order conditions for a maximum do not hold at this point. that is, the iso-welfare line could have a stronger curvature than the zero-profit contour. This would be a case where the finn could lower both p and F and still make a profit. The regulator should be aware of this possibility and agree to such a price reduction if requested by the firm. That is why the inequality constraint, as noted above, might do better than the equality constraint.

4. Extensions

It is by no means clear that public utilities operate under decreasing average costs. Thus, assumption 1 above may be violated. What happens if C( q) can no longer


be restricted to decreasing average costs? The process would still converge to optimal prices if the sum of the firm's profits from any period t to infinity can be held positive. Then the rest of the above proof would go through, because only its first step requires decreasing average cost. For the case of constantN, losses can be avoided altogether. However, with variable N and increasing costs positive, profits cannot be guaranteed for every period t, in particular not ifI1t-l>O. But any loss by the firm via the constraint (10) leads to the permission of a price increase in the following period. This mayor may not be enough to compensate for the loss. Discounting poses an additional problem if losses occur earlier. In this case, the feasibility of the process hinges on the size of the discount rate. The firm could avoid all these ups and subs by charging welfare optimal prices in period 0 and stay there. It is not clear, though, that this strategy maximizes the discounted stream of all profits.

A further problem with increasing average costs is thatF will eventually become negative, turning from a fee into a dividend. This could lead to a discontinuity in demandN(F,p). For instance, it would become beneficial for households to split up their accounts; or new customers could subscribe to the services of the regulated firm without consuming anything. This problem would, however, vanish in an expanding system in which consumers finance investment through their membership fee. Moral hazard caused by the availability of dividends could also be avoided through discriminatory two-part tariffs which, at the same time, could mitigate income distributional concerns over high fixed fees. Ideally, such tariffs would be linked to household incomes. However, due to income being harder to observe, the utility might want to link them to last period's consumption. Then the aggregate constraint on the firm's total revenues from the membership fee would formally remain as before. The membership fee (dividend) for each customer (or customer group) j, however, would become Ft,j = -[7tH - (Pt-l - Pt)qt-l,j]1 qt-t. There could also be a differentiation in the variable price p. This could make the approach one of optional tariffs where the customers self-select into groups.9

The firm could be allowed to attract new customers with any combination (p,F) it wants to, but subsequently the above formula holds. This formulation makes it necessary to adapt our assumptions on consumers' surplus and demand. In particular, consumers could now act strategically since the current fixed fee would depend on last period's individual quantity of consumption. However, if individual consumer demands do not cross, then the firm can always find an optional two-part tariff that is incentive compatible. A simpler type of discriminatory tariffs feasible under our approach would be for the regulator to define lifeline rates or low-price blocks for certain large customer groups. Such prices would then be fixed in advance and be outside the optimization of the regulated firm.

Related in spirit to discriminatory two-part tariffs is the generalization of our framework to a multiproduct monopolist. This has already been achieved for the case of a constant number of customers N. Also, as long as the multiproduct analogue to assumptions 1 through 4 holds, the process with variable Nt should converge in a similar way as in the single product case. In particular, the condition

A NON-BAYESIAN lNCENTIVE MECHANISM USlNO 1WO-PART TARIFFS 29

on decreasing average cost becomes one on decreasing ray average cost. The framework also allows the firm to introduce new products. Since a product introduced in period t would have no sales and no purchasers in period t-l, its price and fixed fee would be unregulated in period t. This is analogous to period 0 for the already existing products. The quantity sold and number of buyers in period t would then form the basis for the constraint in period t+ 1.

A disturbing feature of our process is the possibility of noncost-minimizing behavior by the firm at the beginning of the process. This has been noticed as a major drawback of other regulatory schemes as well and has recently led to suggestions for predetermined price caps. The main incentive property of such price caps is that they do not depend on cost factors that the firm can influence. There are two interpretations of price caps. One is that they represent a divorce of regulated prices from the cost of providing the services only for a limited amount of time. Thereafter, the price caps are recalculated based on the firm's cost during this time interval. Such price caps simply could be an attempt to increase the regulatory lag. The second interpretation is that price caps shall be independent of the firm's cost changes forever.

We can adapt our two-part pricing mechanism to the first interpretation of price caps by differentiating between short periods, during which price level changes by the firm are predetermined and independent of the firm's cost changes, and long periods, at the end of which price caps are recalculated based on the fIrm's actual costs. Then the long periods are relevant for the firm's cost-minimizing behavior, while the short periods are relevant for the allocative efficiency of prices. The longer the long period, the larger the incentives to minimize cost. Prices would still converge to second-best two-part tariffs (Vogelsang, forthcoming).

Under the second interpretation of price caps, cost changes by the firm would be irrelevant. In this case, we could completely redefine our two-part tariff. Instead of giving the fIrm as profit an approximation of the social surplus increase of the last period, the new two-part tariff would give the firm an approximation of the cumulative increase of consumers' surplus achieved from the beginning of the process to the current period. This can again be built into a constraint on the fixed part of a two-part tariff as follows:

I

t:. _ A q/-l(Pt-I-P,) _ ",q8-1(Pe-l-P8) f'/=Ft-1+ N -L.J N .

I-I e-I (26) 8=1

Again, the variable price PI would be determined implicitly in formula (26). This mechanism, starting from predetermined PO, leads to an increase of both consumers' surplus and profit over time. It converges to constrained optimal two-part tariffs in the sense that consumers' surplus cannot be increased further without reducing the firm's profit. The costs are minimized in every period, and there is no restriction on the shape of the firm's cost function. So, at least in theory, this could be an attractive regulatory mechanism.


A last extension is to ask what happens if the fmn management does not know its own cost and demand functions. This case is of obvious importance. Can the fmn still fmd profitable prices satisfying the regulatory constraint? Starting with IIt>O we know that setting Pt+ 1 = Pt will lead to IIt+ 1 = 0 provided that there are no income effects and the number of customers, N, stays constant In case of decreasing marginal cost, the firm could also set Ft+ 1 = Ft and reduce Pt+ 1 to a level that obeys the constraint. Then IIt+l>O. In both cases the process would generally stop short of welfare maximizing prices.

5. Conclusions

In this article we have discussed a regulatory two-part pricing mechanism with a number of desirable properties. It is anonymous in the sense that it does not require regulators to have detailed prior information on the regulated fmn and its environment Also, subsequent observations of the regulator can be restricted to verifiable bookkeeping data. At the same time, the pricing formula is simple and easily interpreted. The fmn is free to choose the variable price of the two-part tariff as long as the fixed part obeys formula (1) and (10). The firm will then in every period receive a profit that approximates, but is smaller than, the welfare change caused by its price changes over the last period. The approach taken in this article is more realistic than most other suggestions for incentive pricing because it requires no government subsidies for the regulated fmn.

Notes

This study was partially funded through a grant from the John and Mal)' R. Marlde Foundation to the RAND Corporation.

1. This is not the same as the second-best issue but related to it in spirit. 2. This point is elaborated in Joskow and Schmalensee (1986). 3. For simplicity in the fonnal arguments we assume this constraint always to be binding. We will

argue below, however, that an inequality constraint 0 might do better. 4. Also note that in connection with cost overruns for nuclear power stations there are strong

tendencies in the United States to engage customers in public utility fmancing and thus de facto to tum public utilities into cooperatives.

5. Following an argument made by Sappington and Sibley (1988), it can also be shown that (at given prices) the finn will invest in a socially optimal manner as long as it is also the social discount rate. In this case {C,} would be the expenses of the finn in period t rather than the cost.

6. For a complete proof, see the appendix to F-V (1982). The average cost curve in figure 1 is drawn as upward sloping in order to suggest the generality of the approach. Under natural monopoly conditions, we would usually expect decreasing average cost.

7. It has been noted before, for instance, by David Sibley in an oral statement to the author. 8. For the fonnal proof, see Vogelsang (forthcoming). 9. Optional two-part tariffs are treated in Sibley (1988) and Vogelsang (1989).

References

Baron, D., and R. Myerson. 1982. "Regulating a Monopolist with Unknown Cost." Econometrica 50:911-930.

A NON-BAYESIAN INCENTIVE MECHANISM USING lWO-P ART TARIFFS 31

Baumol, W.J., and D.P. Bradford. 1970. "Optimal Departures from Marginal Cost Pricing." American Economic Review 60:265-283.

Coase, R.H. 1945. "Price and Output Policy of State Enterprise: A Comment." Economic Journal 55:112-113.

Coase, R.H. 1946. "The Marginal Cost Controversy." Economica 13:169-182. Finsinger, J. 1979. "W ohlfahrtsoptimale Preisstrukturen von Unternehmen unter Staatlicher

Regulierung." Doctoral Dissertation, University of Bonn. Finsinger, J., and I. Vogelsang. 1982. "Performance Indices for Public Enterprises." Public

Enterprise in Less-developed Countries, edited by L.P. Jones. Cambridge, England: Cambridge University Press: 281-296 ..

Hotelling, H .. 1938. "The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates." Econometrica 6:242-269.

Joskow, P.L., and R. Schmalensee. 1986. "Incentive Regulation for Electric Utilities." Yale Journal on Regulation 4:1-49.

Loeb,M., and W.A.Magat. 1979. "A Decentralized Method for Utility Regulation." Journal of Law and Economics 22:399-404.

Ng, Y., and M. Weisser. 1974. "Optimal Pricing with a Budget Constraint - The Case of the Two-part Tariff." Review of Economic Studies 41 :337 -345.

Sappington, D. 1980. "Strategic Firm Behavior Under a Dynamic Regulatory Adjustment Process." Bell Journal of Economics 11:360-372.

Sappington, D., and D. Sibley. 1985. "Regulatory Incentive Schemes Using Historic Cost Data." Working paper, Bell Communications Research, Morristown, NJ (August).

Schmalensee, R. 1981. "Monopolistic Two-part Pricing Arrangements." Bell Journal of Economics 12:445-466.

Sibley, D. 1988. "Asymmetric Information, Incentives and Price Cap Regulation." Mimeo, Bell Communications Research, Morristown, NJ.

Vogelsang, I. "Two-part Tariffs as Regulatory Constraints." Journal of Public Economics, forthcoming.

Vogelsang, I. 1989. "Constrained Optional Two-part Tariffs." Boston University, Mimeo (February);

Vo gelsang, 1., and J. Finsinger. 1979 . "A Regulatory Adjustment Process for Optimal Pricing by Multiproduct Monopoly Firms." Bell Journal of Economics 10:157-171.

3 REGULATING BY CAPPING PRICES

Timothy J. Brennan

1. Introduction

The purpose of this article is to look at the theoretical underpinnings and properties of price caps, specifically, the rules governing how a multiproduct regulated firm may adjust its prices. To identify a standard for implementing price caps, we begin by identifying the constrained optimization to which "price caps" are the solution. Since price caps are at heart a policy in which a firm can do what it likes as long as prices do not rise, the relevant optimization is maximization of welfare or profit subject to a constraint that aggregate consumer welfare must not fall below a given level. Permitting prices to be flexible, subject to maintaining a constant weighted average where the weights are based only upon the quantities sold for each service, can approximate the behavior of a firm maximizing profit subject to an aggregate consumer surplus constraint. Flexibility to change prices is in this sense "optimal," subject to the acceptability of the consumer welfare achieved under the original prices.

These virtues become less apparent over time. As the regulatory periods lengthen, non-marginal changes in price or demand raise the question of whether to base the flexibility constraint on prior or current quantities. Interpreting the weights becomes more difficult, as the regulator has to estimate how much of the shift in sales is exogenous and how much is due to changes in the regulated firm's prices. This will reintroduce some of the information requirements that make conventional cost-of-service regulation so burdensome. We will model both the incentives to supply false information to the regulator and potentially welfarereducing adaptation by the regulated firm. Finally, legal or political inability of the government to commit over time to permit the regulated firm to either lose money or earn supranormal profits will lead to price caps becoming more like conventional regulation, with an institutionalized regulatory lag. While conditions for an optimal lag can be derived in theory, they are likely to be of little practical use. For all of these reasons, the advantages of a price cap appear greater the more likely it is that regulation will cease in the near future.


2. Welfare-Constrained Profit Maximization and Pricing Flexibility Rules

Consider a regulated multiproduct firm, with monopolies in each of its markets.1

Let i = I, ... , n index the markets, qi indicate the output in market i, and Pi(qj) be the demand price in market i for qi. For computational convenience, we assume demand in one market is independent of demand in others? Let Gi(qj) be the gross consumer welfare generated in market i from selling qi goods; G {( q i) = P j{ q i) . Net consumer welfare or consumer surplus, Si, is Gi - Piqi. Let S be the sum of Si over all n markets. The cost of producing the vector of output q = (q1, . .. ,'In) is c(q), with ocloqi=Cj. Profit, n(q) , equals peq-c(q), where

p = (PI (ql), ... ,Pn(qn». Suppose the regulated firm maximizes profit subject to the constraint that

aggregate consumer surplus not fall below So. The Lagrangian is

max L(q) = P e q - c(q) - 'A(S - SO), q

and the associated first-order conditions for each qi are

oL =p.+p.'q. _ c. - 'A(p.-p. -p.'q.) = 0 oqi I I I I I I I I •

Rearranging terms gives

Pi €i

where €i = -p/p{ qi, the elasticity of demand in market i at qi? As with Ramsey prices, the price-cost margins are inversely proportional to the

elasticity of demand. If we let n° equal the firm's profits when maximizing profit subject to this constraint, we obtain the market quantities and prices that maximize welfare subject to permitting the firm to earn n°. These prices and quantities reflect "second best efficiency," in that the firm cannot get more than n° without consumers getting less than So. Moreover, costs are minimized since inefficient production only reduces profits without generating additional consumer surplus to meet the So constraint. Nothing is gained by fabricating cost data, since prices are limited only by the consumer surplus constraint, not by reported cost. A regulatory scheme that would replicate this effect will therefore eliminate the incentives to engage in the inefficient production, cross-subsidization, or transfer pricing to which cost-of-service regulation is prone.4

If the regulator identifies a vector of prices po, e.g., current prices, which generate an acceptable level of consumer surplus So, economic welfare will be maximized if the regulated firm is permitted deviations from pO that do not reduce welfare. Looking at marginal deviations 0Pi from pO, we find that aggregate consumer welfare S is not reduced if

REGULATING BY CAPPING PRICES

Since

n as. dS= L ~dPi~O.

i=l 'Pi

OSi

oSi oqi -P/qi -=-- =--,- =-qi' oPi api -Pi

oqi

35

we obtain the result that all price deviations from pO should be permitted as long as

n (1) -dS = L qi (dp) S;; O.

i= 1

In other words, we should permit price changes where the net average of the changes, weighted by the quantity of output, is negative. A price increase in one market is acceptable as long as price is reduced in other markets to keep (1) satisfied.5 Note that pO need not initially maximize profits subject to the consumer welfare constraint, especially if pO were the vector of prices inherited from an inefficient regulatory scheme. If pO is not already profit-maximizing, the firm will have an incentive to change prices, even where constrained by (1).

3. Problems of Implementation: Non-Marginal Changes and Time

The flexibility rule in equation (1) involves only marginal price changes, where market demands and fringe supply functions are fixed. Non-marginality of price changes and time can lead to divergences from the welfare maxima and impose greater information requirements on the regulator.

3.1 Non-Marginal Price Changes If the regulated fum elects to adjust p from the prescribed level by more than an

infinitesimal amount, the welfare changes will not be accurately represented by (1). Let to and t1 represent the time before and after the regulated firm's price adjustment, and let superscript j represent time period j. In market i, a change

!1 Pi = pI - p? will induce changes in sales from q? to q}. The change in consumer surplus will be

!1 S = S(q(pl» - S(q(p°».

Using standard consumer surplus measures,6 the net consumer welfare change in

market i from a change in prices from p? to p} will be


pI !!.Si = -L qi(Z) dz ,

Pi

and the aggregate change in consumer surplus !!.S is given by

n fP~ !!.S=-I. O~i(z)dz.

i= 1 Pi

The "no consumer surplus reduction" condition becomes

(2)

Implementing an accurate price flexibility rule requires estimating or approximating these integrals. As a practical matter, pre-change quantities will probably be used since, unlike post-change quantities, infonnation on them is available to the

regulator without ex ante prediction? Since qi(Z) is not constant between p? and

pI, this will introduce variations from Ramsey-like pricing rules. Condition (2) becomes equivalent to a rule in which the regulated finn's post-adjustment price average must be less than the adjusted average of pre-adjustment prices, where both are weighted by pre-cap quantities: 8

pI xl $,po x qQ.

Let R = pO X qQ. R is independent of the fInn's post-adjustment output choices.

The regulated flnn' s problem will be to choose qi to maximize constrained profIt

L(ql) = pI X ql _ c(ql) _ A(pI(ql) X qO - R).

First-order conditions imply that in each market i,

pI - c} = 1.. [1 _ Aq?). pI Ei qI

Since A, the "shadow value" to the regulated fInn of increasing the constraint, is positive, pre-cap quantity weighting will induce it to act as a monopolist with more elastic demands. Only if the percentage change in quantity is equal across all markets will the short-tenn result be a welfare optimum for the profit level pennitted under the cap. However, we can show that (a) has the following properties:

Property 1. Let i be the price vector selected by the firm at time t. If S(pt) =

consumer surplus evaluated ati, S(pt+l) ~ S(pt) for all t.

REGULATING BY CAPPING PRICES 37

Property 2. Assume the price vector p that maximizes aggregate consumer

surplus subject to IT(P) = ITO is unique for any ITo. As t ~ 00, the sequence {il converges to a point where consumer surplus and profit satisfy the Ramsey condition, i.e., consumer surplus is maximized subject to the profit received by the firm.9

If one is willing to wait, "prior period" weighting may be preferable to a regulatory method that moves directly to a "Ramsey point" where profits are maximized subject to only the original level of consumer surplus.

3.2 Changes in Demand: Uncertainty and Intertemporal Manipulation We assume the regulator elects to calculate "average" prices using last period's

quantities, and investigate what may happen when demand may change between periods. That the regulator may choose "wrong" weights using data derived from prior period demands goes without saying; in addition, there are ways the regulated firm can take advantage of uncertainty regarding changes in demand over time.

Changing the weights. One way the regulator may account for changes in demand is to weight price changes by what last period's quantities would have been had the current period's demand curve been in effect. This would give the regulated firm correct credit for the welfare gains attributable to its price decreases and correct penalty for the losses attributable to its price increases. For example, if demand exogenously declines in a market in which the regulated firm raised price, it will be excessively penalized if its increase in price is weighted by last period's actual sales, rather than what last period's sales would have been had this period's demand been in place.lO Predicting current demand at past prices to generate weights, though, will invite debate over what the sales at the old price would have been. To maximize the credit it gets for reducing some prices and minimize the penalty for increasing others, the regulated firm will argue that demand curves are

price

~r-----------~~---;

P1r-------------------~

'--____________________ ---1. ________ ~~ ___ quantity

Figure 1. Price Decreases

38 PRICE CAPS AND INCENITVE REGULATION IN TELECOMMUNICATIONS

inelastic, implying that changes in its sales, whether from increased or decreased prices, are attributable to outside factors.

Consider price reductions, as portrayed in figure 1. Let qO be the quantity sold in period 0 at price PO, and qi be the quantity sold in period 1 at price Pl. For illustrative purposes, assume the demand curve does not change from period 0 to period 1, hence that the demand curve in both periods goes through the points labeled qO and qi in figure 1. If the regulator is open to the possibility that demand may have changed, however, the regulated firm may try to persuade the regulator that demand would have been qO', rather than qO, had it not reduced price. This would imply a greater welfare gain to consumers from its price reduction than was in fact the case.

A similar story may be told for price increases, as illustrated in figure 2.

price

L.... _______ ----''--______ --''' ___ quantity

Figure 2. Price Increases

The points are labeled as before. Here, price goes up from PO to PI; demand goes down from qO to qI; the demand curve is assumed not to shift. Here, the regulated firm wants to minimize its penalty for raising price. If it can persuade the regulator that period 1 demand goes through q' 0, exogenous demand shifts rather than the price increase will be "blamed" for the reduction in sales. Generally, since q' 0 is unobservable, the firm may be able to make this argument to the regulator repeatedly.

Similar strategies may be taken by other parties with interests in the regulated firm's pricing policies. Competitors will generally want to discourage price decreases and encourage price increases in their markets. If the regulated firm attempts to cut price in their markets, competitors will argue that demand facing the regulated firm is more elastic in its markets than past data suggest, e.g., that q' 0 is smaller than qO, to minimize the reward the regulated firm gets for cutting price. On the other hand, competitors are likely to support the regulated firm's claims of inelastic demand when it elects to raise price in the competitive firm's markets. Consumers will have interests divergent from competitors; if they expect


a price cut, they will claim demand is less elastic than it appears; if they expect a price increase, they will claim the opposite. In this way, distributional pressures between various parties will invite debate over the relevant standard for price adjustments, increasing the regulator's administrative burden.

If demand is likely to change during the price-cap period, the regulator can either use prior period quantities, with certain error, or it can attempt to ascertain what current sales would have been at the past period price, in which case it will have to resolve contending views and evidence as to whether shifts in sales are due to exogenous shifts in demand or changes in price. We may note, though, that while the regulated firm has a short-run interest in arguing that demand for its products is inelastic, such claims may run against a competition-based case for eventual deregulation. I I

Reactions to anticipated shifts in demand. That the regulator may make a mistake in using old demand data to evaluate current price changes is obvious. What is less obvious is that doing so can induce a regulated firm, who can forecast demand accurately, to act in advance of price changes in ways that may reduce aggregate economic welfare over time. The possibility can be illustrated by looking at a regulated firm in two markets, X and Y.

Consider figure 3, in the space of combinations of PX and py.

~---L----------~~--------------~~-Px

Figure 3. PX-py Space


Assume at period 0 the X and Y markets are in a long-run equilibrium with prices

(Pt p~) at point A, where the fIrm's profits are maximized over the set of prices (px,py) inpy.-py space such that

PxX + pyY ~ I4x(p~) + p~ Y(p~).

These points are indicated by the straight line going through points A and C, with

slope equal to -x(p~)/Y(ph Suppose that before prices are set in period 1, news comes that firms are going to enter market X, with marginal cost ex. Thus, the regulated firm knows that in and after period 2 it will not be able to set px above cx. Absent any reaction to entrY., it would continue to choose point A in period 1, followed by point C in period 2.12

In period 2, the regulated fIrm would rather be at a point directly above C, with a higher price in market Yand the competitive price Cx in marketX. It can achieve this goal by choosing a point such as B between A and C. Since py is greater and px is smaller at B than at A,

X(P~) X(P~) Y(p~) = yep:) .

The line demarcating the set of points available to the regulated fIrm in period 2 going through B will be steeper than the line of period 1 options going through point A, enabling the firm to set prices atD in subsequent periods. The closer point B is to point C, the steeper is the line going through B and the higher will be the price and, up to a certain point, profits in market Y. On the other hand, since A was a long-run equilibrium, the regulated fIrm will lose profIts in period 1 (before demand has changed) by moving away from point A, and will lose more profIts the farther away point B is from point A.I3 Assume points B and D in fIgure 2 reflect the optimum choices for the regulated firm, given its time rate of discount. 14

If we let <l> and 1 - <l> reflect the relative weights given to welfare in period 1 and in period 2 and subsequent periods, and let W(·) refer to net economic welfare, we fInd that welfare is reduced if

1 - <l> W(A) - WeB) ~>W(D)-W(C) ,

i.e., any gains to consumers net of producer losses in period 1 from moving to B are outweighed by the net losses in subsequent periods from moving to D. Since py at D exceeds py at C, WeD) < W(C). While no general conclusion can be reached, ifW(B) < W(A) or <l> is sufficiently small, the firm will adjust to foreseen price changes in ways that lead to overall welfare reductions. IS


4. The Long Term

Over time, inflation or increased resource scarcity may cause cost to rise; technological change or declining input prices may cause it to fall. These changes in costs call into question the regulator's commitment not to tie prices to costs and profits. The Supreme Court's standard that a regulator must provide "just and reasonable" returns to regulated firms itself keep a government agency from committing to set prices regardless of the fIrm's profits. Political impetus to adjust the price cap may be forthcoming if it is perceived that the regulated fIrm's profits constitute too 8l:eat a fraction of the available social surplus if costs decline without rates declining.16 The most a regulator may be able to achieve is an institutionalized "regulatory lag," in which a firm can reduce its costs without fearing imminent price reductions from the regulator, but the regulator will subject the fIrm to periodic review with action taken on the basis of achieved profItP However, to plan "lags" efficiently, the regulator must know the relationship between investment and productivity, but lags are needed to encourage cost-reducing investment only when the regulator cannot monitor it (Brennan, 1988). While some investments by regulated firms may fit these conditions of non-monitorability but with predictable benefits, it does not seem that the benefits of regulatory lag are widespread.

Divorcing price from cost can preserve a regulated firm's incentives to innovate and minimize costs, and eliminate the incentive to cross-subsidize. Allowing pricing flexibility so long as the average of price changes, weighted by quantity sold, is negative will guarantee that social welfare is maximized given the acceptability of either the welfare achieved by the firm's consumers and competitors, or the acceptability of its eventual profit level. Over time, though, non-infinitesimal price changes and changes in demand will confront the regulator with decisions regarding the use of past quantities, estimated "past quantities" under current demand curves, or predicted demands, all of which invite misinformation on demand elasticities and intertemporal strategic behavior. Since these problems, as well as doubt regarding the government's commitment to separate prices from costs, appear to grow more severe as time goes on, the advantages price caps will be greatest as part of a regulatory regime designed for elimination in the near future.

Appendix

Proof of Property 1. For any point pO in price space, as(p)lapi = -qi. Therefore, the aggregate consumer surplus "indifference surface" ({p £ PI S(P) = ScpO)}) is always tangentto the hyperplane of possibilities available to the regulated firm in the next period ({p £ Pip. q(p0) = pO • q<tf)}). Because of the convexity of the consumer surplus indifference surface, 8 this point of tangency is a minimum. Since this tangency point is always the next period "starting point" for the regulated firm, consumer surplus must be at least as great


after the firm's choice of price in period t + 1, p'+I, than before, i.e., S(pt+l) ~ Sept).

Proof of Property 2. The conclusion would follow immediately from the

analysis in section 3.1 if the sequence {p'} converges to a single limit point. We

show that for all limit points of {p'}, consumer surplus and profit are equal and each is the maximum it can be given the value of the other. The "uniqueness"

assumption thus implies that all limit points of {p'} are identical, hence that {p'} converges to a point satisfying the Ramsey condition. The proof that each limit

point of {/} meets the Ramsey condition proceeds as follows: 19

Assume a finite maximum reservation price for each good, and that profits for the regulated firm in the initial equilibrium, IIo, are positive. These, plus continuity of the profit function, ensure that the set of prices in price space such that

II(P) ~ IIo is compact. Call that set r. Since {p'} is a subset of r, it must have at

least one limit point. Let A be the set oflimit points. Since {Sept)} and {II(Pt)} are bounded nondecreasing sequences,z° they have unique limits S* and II*. It

must be the case that for any A E A, S(A) = S* and II(A) = II*.

Let II = {p E Pip. q(/) = / • q(pt)}. The firm chooses pt+l E II such that II(pt+ 1) ~ II(Pt) for all p E II. Thus, the profit indifference surface for II(pt+l)must

be tangenttoll. From the above, S(pt):;;; S(P) forallp E If, implying the consumer

surplus indifference surface for Sept) is tangent to II. Choose some A E A. Let

{/{J)} be a sequence of choices that converges to A, where t(j + 1) > t(j) for all j.

Assuming continuity of derivatives, the gradients of the hyperplanesIl{J) converge

to the gradients of the consumer surplus indifference curves of S = S(pt(j)) at/v) and the gradients of the profit indifference curves for II = (pt(j)+I) at P'(})+1.

By construction, {P'(j)) converges to A. The sequence {p'(i)+I}, being bounded, must have limit points. Suppose there exists one different from A; call it A'. The ~radient of {p E P I S(P) = S(A)} at A is the same as the gradien t of tp E P I II(P) = II(A')} at A', since both equal the limit of the sequence of gradients

of {I1(})}. Let HI. and HI.' be the hyperplanes respectively tangent to the consumer surplus surface at A and the profit surface at A'. Since consumer surplus and profit are identical for any limit point, S(A) = S(A') = S* and II(A) = II(A') = II*. If A"* A', convexity of the consumer surplus indifference curves implies HI.' must lie strictly "above" HI. in the sense of being on the other side of HI. from the origin. By similar argument, convexity of profit surfaces says HI. must lie strictly "above" H'A'. Since this cannot happen, A must equal A'.

If A = A', the consumer surplus and profit indifference surfaces are tangent at A. Hence, A meets the Ramsey condition. Since A was chosen from A arbitrarily, the Ramsey condition must be met for all limit points. If the set of such points is unique

REGULATING BY CAPP1NG PRICES 43

for II*, as assumed, A must be the limit point for all subsequences of {l}, hence

{l} converges to A. Property 1 clearly holds even if the firm acts nonmyopically. Since the regulated

firm may take future effects of its actions into account, though, we cannot assume

II(l) is increasing in t. However, it must be the case that all limit points of the

sequence (II(l)} must be the same; otherwise at some time t' the firm would be

better off staying with l' in perpetuity than by continuing the sequence {l}, contradicting the assumption that {l} maximizes discounted profits. Let n' be the

limit of {n(l)}. Since Property 1 holds, {S(l)} is increasing; being bounded, it

has a unique limit point S'. If there were two price vectors pO and pI such that

S(p°) = S(pl) = S' and II(p°) = II(pl) = II', the uniqueness assumption and convexity of the isoprofit and indifference surfaces imply that there is a price vector

p* with II(p*) > II' and S(p*) ~ S'. Continuity therefore implies that {l} could not be profit-maximizing for the "nonmyopic" flrm.

Notes

The author is Associate Professor, Public Policy, Communication and Economics, George Washington University. This chapter is adapted from versions of his paper, "Regulating by Capping Prices," Antitrust Division Discussion Paper 88-11 and in the Jour7Ul1 of Regulatory &ofU)mics 1 (1989): 133-47. Discussions with Richard Clarke, Michael Einhorn, Bert Smiley, Thomas Spavins, Ingo Vogelsang, Robert Willig, Michael Williams, Glenn Woroch, and especially Mary Fitzpatrick are most appreciated. The author retains sole responsibility for errors.

1. The model extends easily to the case where there is a competitive fringe, where the "market" demand curves are reinterpreted as those facing the regulated finn. The extension requires that fringe finns' profits are included in the aggregate welfare constraint.

2. This is a reasonable assumption in many cases. To take long-distance telephony as an example, the demand to call city A from city B is not likely to be too sensitive to the price of calling city C. It will be a less realistic assumption in other cases, for example, when one "service" is a volume discount version of another or where one price covers initial hookup and another price covers usage, as in a two-part tariff. However, with the exception of the conclusion regarding demand elasticities, these results can be duplicated without the independence assumption. If demands are interdependent, the elasticities can be replaced with "superelasticities" (Brock, 1983) that embody the non-zero cross-elasticities.

3. The model can be generalized to include dynamic Ramsey-like prices, by allowing the index to refer to markets over time and permitting cost complementarities, in that changes in output in a given period may affect marginal cost in subsequent periods. I thank Glenn Woroch for that suggestion.

4. Riordan and Cabral (1988) show that the incentive to innovate may be greater if the regulator holds price low, since the amount of output over which the benefits of innovation would be spread is greater.

5. Where markets include a price-taking competitive fringe, the constraint on marginal price changes to ensure no loss in consumer and fringe welfare is essentially the same, where qi is the output of just the regulated finn rather than total market quantity.

Including fringe profits in the welfare constraint is not only consistent with methodological indifference regarding the distribution of economic gains and the influence both consumer groups and fringe rums may have on the regulator, but it also leads to more efficient welfare standards. If fringe profits are not to be considered in the welfare constraint, price changes are weighted by total supply in the market.


If the fringe are not price takers, the marginal welfare effect of a change in price will be affected by changes in the output of the fringe on marginal outpuL As in other contexts (Stiglitz, 1981; Schwartz, 1984; Mankiw and Whinston, 1986), a more complex oligopoly theory makes general results harder to come by.

6. Subject, of course, to the usual qualifications (e.g., no income effects) on consumer surplus estimates (Willig, 1976).

7. See Brennan (1989) for discussion of adjustment rules employing post-change quantities. 8 This is equivalent to requiring that the "Laspeyres index" of price changes be less than one. 9. I thank Robert Willig for suggesting these intertemporal properties to me; proofs are in the

Appendix. Vogelsang (l988) provides an additional illustration of the proposition that regulation may perfonn less well as the mechauisms more closely correspond to the regulator's goals.

10. Suppose in marketj fringe supply becomes perfectly elastic at price Pi, forcing the regulated rmD to match that price. From the post -adjustment perspective, there is no welfare gain from the regulated rmD's price reduction. If it were to raise price above Pi there would be no welfare loss; consumers would simply tum to the competitors. Brennan (l987b) shows how entry into a subset of regulated marlcets may reduce overall economic welfare, even when the entrants can serve this marlcet at lower cost than can the regulated firm, if prices in less competitive marlcets are allowed to rise as other marlcets become more competitive.

11. Where the regulator elects to base price on predictions of period 1 quantities, the regulated firm will want to convince the regulator that demand is more elastic than is the case, to exaggerate the welfare contributions of its price reductions and to understate the welfare reductions from its price increases.

12. We assume pr;, the monopoly price in marlcet Y, is above the price in market Y that would be set at point C. If not, the regulated rmD would stay at point A in period 1 and move to a point on the vertical line below point C in period 2.

13. This follows from convexity of the profit function, independence of demand functions for X and y, and that the monopoly price in marlcet X is above the price in marlcet X that would obtain at point C.

14. Since A is a period 1 optimum, the marginal loss of profit of moving away from A is zero, while there is a marginal gain in profit from moving up from C. Thus, the optimum B will not coincide with A. But since B is not a period 1 optimum, the marginal profit of moving B incrementally away from A is negative, implying the marginal profit from moving D up must be positive. Thus, the price in marlcet Y at D will still be less than the monopoly price in Y.

15. It may also be noted that shifts in demand for the finn's products may keep it from recovering its costs under a price-cap mechanism, leading to either exit or modification of the caps.

16. See Fitzpatrick (1987) for a discussion and empirical test of this mechanism. 17. FCC (1988, par. 128). Note that the FCC regards "regulatory lag" disparagingly at par. 105. 18. Convexity of this surface for individuals follows from Varian (1984, 139-140). Since the

aggregate surface is the sum of the individuals' surfaces, it too is convex. This is obvious if demands

are independent, for crS(P)/dpt = -q( > 0 and crS(P)ldPidPj = o. 19. The proof is similar in character to a convergence proof of Proposition 1 in Vogelsang and

Finsinger (1979). 20. A virtue of an "optimal control" proof based on the properties of a function p(t) that maximizes

discounted profits subject to the price-cap adjustment constraint is that it would cover strategic behavior by the finn in which short-tenn profits may be sacrificed to put the firm in a position to earn longer tenn gains. Such behavior is predictable when demand changes, as illustrated in section 3.2. If such a strategy is profitable, we cannot assume that {rr(p,)} is a nondecreasing sequence with only one liruit point.

References

Brennan, T. 1988. "Regulating by Capping Prices." Economic Analysis Group Discussion Paper 88-11, Antitrust Division, U.S. Department of Justice.

Brennan, T. 1989. "Regulating by Capping Prices." Journal of Regulatory Economics 1:133-147.


Brock, W. 1983. "Pricing, Predation, and Entry Barriers in Regulated Industries." In Breaking Up Bell, edited by D. Evans. New York: North-Holland.

Federal Communications Commission. 1988. Further Notice of Proposed Rulemaking in the Matter of Policy and Rules Concerning Rates for Dominant Carriers. CC Docket No. 87-313.

Fitzpatrick. M. 1987. "A Test of Passive Regulation Using an Endogenous Switching Regression." Economic Analysis Group Discussion Paper 87-5, Antitrust Division, U.S. Department of Justice.

Mankiw, N., and M. Whinston. 1986. "Free Entry and Social Inefficiency." Rarul Journal of Economics 17:48-58.

Riordan, M., and L. Cabral. 1988. "Incentives for Cost Reduction under Price Cap Regulation." International Telecommunications Society Conference.

Schwartz, M. 1984. "Welfare Effects of Exit-Inducing Innovations." Economic Policy Office Discussion Paper 84-12, Antitrust Division, U.S. Department of Justice.

Stiglitz, J. 1981. "Potential Competition May Reduce Welfare." American Economic Review 71:184-89.

Varian, H. 1984. MicroeconomicAnalysis. New York: Norton. Vogelsang, I. 1988. "A Little Paradox in the Design of Regulatory Mechanisms." Interna

tional Economic Review 29:467-76. Willig, R. 1976. "Consumer Surplus Without Apology." American Economic Review

66:589-97.

4 INFORMATION, INCENTIVES, AND

COMMITMENT IN REGULATORY MECHANISMS: REGULATORY

INNOVATION IN TELECOMMUNICATIONS David P. Baron

1. Introduction

The incentive theory of regulation has generally been developed in the context of monopoly regulation or of supply by a publicly owned firm and thus is most applicable to state regulation of local telephone companies.} Although this theory may not be directly applicable to those segments of the telecommunications industry that are, or soon will be, sufficiently competitive that regulation will not be needed, the principles identified may be applicable to the transition period from regulation to competition. The theory presented here thus is viewed as pertaining to the transition to competition and to the regulation of local telephone service which, in spite of the alternative of cellular and cable systems, is likely to remain regulated for the foreseeable future. The article thus focuses on cost-based pricing policies and the associated incentive problems with particular emphasis on longterm policies that respond to information that is generated through performance in earlier periods. The regulatory mechanisms considered are in the spirit of recent policy proposals to delegate to the firm the authority to make certain decisions subject only to caps on profits or prices. The mechanisms prescribe a set of implementable policies and delegate to the firm the choice of a particular policy based on the information it has about its costs. The policies cover extended periods of time, so they may include provisions that allow prices to adapt to information revealed by either exogenous events or performance in earlier periods.

An important factor affecting the efficiency of such a mechanism is the regulator'S ability to commit credibly to long-term regulatory policies. Commitment refers to the ability of the regulator to specify credibly at the beginning of the regulatory horizon the policies for each future period. When the regulator is unable


to commit credibly to long-term policies, it may act opportunistically either to exploit information that becomes available or to take advantage of sunk investments.

Commitment is a practical problem because one government cannot bind a future government to a specific policy. More fundamentally, citizens cannot bind themselves to act politically in a particular manner; for example, as to how they will vote in the future. Consequently, regulatory commissions cannot be bound to long-term policies even if they want to bind themselves (and to bind future commissions). In addition, regulatory commissions have difficulty making credible commitments because all parties recognize that their membership can change as a consequence of a direct election or an appointment by an executive officer. Furthermore, regulatory commissions may choose to alter policies in response to political pressure or political opportunities.

Consequently, the incentive problems inherent in regulation take on added complexity in a multiperiod setting. As Joskow and Schmalensee (1986) argue,

. . . the nature of the game played by the regulator and the finn changes dramatically when both make decisions over time. In principle, the commission can use repeated observations of firm performance to improve its information, and use that information to fine tune rewards and penalties. Knowing this, the firm has an incentive to try to fool the regulator. perhaps even raising costs and sacrificing profits today in order to make tomorrow's reward/penalty structure more favorable. Since public utility commissioners cannot sign contracts that prevent themselves or their successors - not to mention current and future legislatures - from changing policies. they cannot solve this problem by promising not to use what they learn. Such a head-in-the-sand policy would be plainly irresponsible even if it were credible. When incentives to deceive are taken into account. the problem of designing an optimal dynamic regulatory regime moves to a new level of complexity. (p. 24)

The relation between this commitment problem and politics has been addressed by Noll (1989) in a review of the politics of regulation.

One key issue is whether political agents can credibly commit to durable. long-term arrangements with utilities which. even if optimal ex ante. could produce supracompetitive profits ex post. Such an outcome would leave the architects of a bidding or cost-revelation mechanism vulnerable to attack by political entrepreneurs seeldng elective office. But even if this problem could be solved, interest group theory suggests that such mechanisms are extremely unlikely to be politically acceptable because they reduce to formula the politically relevant act of creating and distributing rents. Only upon the collapse of an economic regulatory process when too many interests are being cut in. combined with natural monopoly. would the political process be likely to consider such a mechanism. These circumstances have taken place in railroads, and may be under way in electricity and local telephone networks. (page 39)

The regulatory policies that are optimal when information is incomplete and commitment is limited are analogous to private long-term contracts but differ in

REGULATORY INNOVATION IN TELECOMMUNICATIONS 49

their incompleteness. In private contracting, parties can conclude an agreement that takes into account all available information and any future events that are anticipated. As long as the variables on which the contracts are based are jointly observable and are verifiable to a court, the parties can be confident that the contract will be implemented as anticipated. Government agencies, however, may have more difficulty in milking credible long-term commitments than do private parties because political forces can cause changes in policies and procedures?

When credible commitments cannot be made, efficiency is reduced by the opportunism of the regulator and the regulated firm. As Baron and Besanko (1987c, 413) argue?

This opportunism may be more characteristic of the policies of public agencies than of private parties because although courts will prohibit inefficient breach by private parties they generally will not proscribe revisions of policies by regulatory or administrative agencies. Instead courts tend to restrict their review to procedure, process, and consistency. Perhaps the greatest impediment to establishing commitment in governmental and regulatory settings arises from electoral competition. Presidential candidates and parties can pledge to preserve or to rescind laws or to force regulatory agencies to alter policies either through the appointment process, executive orders, or the authorization and appropriations process. S irnilarly. Congress can alter policies as well as initiate new ones. The political incentive to respond to an ex post opportunity, even though that opportunity results from an event anticipated under an ex ante efficient policy, seems unavoidable in many settings.

The politics of regulation ultimately spelled the end of the cost-of-service indexing policy for the Public Service Company of New Mexico. As hearing examiner Helman (1984,152-3) stated, "The political atmosphere is such that the consumer and public view with suspicion any automatic rate relief to a utility even when there is no question of 'the appearance of the eye'; therefore, how much more so when suspicions are strengthened.,,4

Even in the absence of political competition, a legislature is likely to prefer to leave open an option to review the policies of a regulator. As State Senator Robert C. Jubelirer of Pennsylvania stated regarding deregulation of intrastate telecommunications services, "It is not altogether clear whether or not deregulation could be achieved solely through state regulatory process. However, even if public utility commissioners have the authority, I do not think they want to take such a step without legislative sanction. And quite frankly, I do not believe most legislators would wantthem to do so." (1987,4) Even when a legislature does establish policy, it may specifically choose to limit commitments to long-term policies. For example, Section 115 of the Public Utility Regulatory Policies Act limits the extent to which state regulatory commissions can commit to automatic adjustment clauses for electric utilities. The Act limits such clauses to four years and requires that they be reviewed at least every two years.5

There are a variety of obvious reasons why a regulatory policy may be altered when one political party succeeds another or when different constituencies prevail


at different points in time. The concern here is with a more fundamental reason for an inability to make credible long-term commitments: the incentive to act opportunistically by taking advantage of ex post inefficiencies associated with ex ante efficient policies. That is, in a setting in which incomplete contracts are a fact of life, events may occur that provide an opportunity to revise policies in order to capture efficiency and/or distributive benefits. This opportunity may result from a desire to reduce "excess" profits, to capture quasi-rents associated with sunk investments, or to revise policies in light of information revealed about the capabilities and costs of the firm. In the setting considered here, the firm has private information about its costs and hence is able to earn rents on that information. Performance provides information about those costs, and the regulator has an ex post incentive to take advantage of that information by revising its policy. Since the firm recognizes that the regulator will have this incentive and cannot commit credibly not to take advantage of it, the firm will anticipate the regulator's behavior and will act strategically at the time the initial policy is formulated This prevents the regulator from implementing ex ante efficient policies.

One reason a regulator might behave opportunistically stems from the objectives that political office holders and commission members have to seek short-run benefits when they recognize that they may not be around to bear the long-run costs. To the extent that regulators, or their reputations, do not bear the long-run consequences of their actions, they may have an incentive to act opportunistically to their own advantage. Particularly when the opportunistic behavior appears on the surface to be promoting ex post efficiency, resisting the temptation may be difficult. The inability to give credible assurances not to act opportunistically then generates the inefficiency.b

The incentive of a regulator to act opportunistically to confiscate rents or quasi-rents in order to serve political or constituent interests is constrained both by the law and by characteristics of the political system. For example, a fum with non-fungible assets is potentially subject to the risk of regulatory "confiscation" of the quasi-rents generated by those assets through prices or mandated service that are not compensatory. In Smith v. Ames, however, the Supreme Court concluded that the Constitution requires a fair return on assets employed in regulated service. What constitutes a fair return, however, is subject to a range of interpretation that allows considerable variation over time and across jurisdictions. That there remains considerable leeway for state regulators is evidenced by the change many states made during the 1970s from a "fair value" system of rate base measurement to an "original cost" method with the objective of holding down rates during a period of high inflation. The theory presented here respects the fair return requirement.

The structure of political institutions can also impede changes in regulatory policies. Legislative changes in regulatory mandates and procedures must command a majority in committee and on the floor of both chambers of the legislature and must be signed by the executive. Failure at any point in the process preserves the status quo and makes legislative modification of regulatory policies difficult.

REGULATORYINNOV A TIONIN TELECOMMUNICATIONS 51

The procedural due process requirements of administrative law also limit regulatory opportunism by requiring that changes in policies be supported by the record. This, however, is a procedural test and as such does not constrain substantive changes in policy for which a basis can be established in the record. That is, the courts will generall y review regulatory decisions for procedural correctness and not for substantive content such as whether the policy change promotes efficiency.

Regulatory opportunism is also restrained by administrative rules that are difficult to change. For example, capital recovery rules limit opportunism by requiring that an asset's cost be recovered from consumer revenue. Unless the regulator determines that the asset is not "used or useful," its cost and return must be included in the revenue requirement. Consequently, regulatory opportunism associated with the confiscation of quasi-rents on long-term investments is restricted if the assets continue to be used. The analysis presented here is intended to be consistent with the requirements of administrative law and the protection of sunk assets. In particular, in the Appendix a capital recovery rule will be shown to be important in limiting the opportunism of the firm, which allows the regulator to implement an expanded class of policies when it is unable to commit credibly not to act opportunistically.

The implications of the incentive theory considered here for this class of regulatory issues are summarized by the following points.

1. In a setting with incomplete information, the regulator prefers to commit to a mechanism, or collection, of regulatory policies with a policy for each possible cost level that the firm might have. The regulator then delegates to the firm the choice of the policy to be implemented. That policy will be chosen as a function of the firm's knowledge ofits costs, and the firm will earn rents on it information. It is generally impossible to hold the firm to a specific ex post rate of return, so a range of returns must be tolerated. The resulting pricing policies are prospectively cost-based and depend on the (prior) information of the regulator and on the observed performance. Prices will be fully responsive to costs when a regularity condition is satisfied.

2. In a setting with incomplete information, commitment to long-term policies by the regulator improves ex ante efficiency, but those policies will generally be ex post inefficient given the information learned by the regulator through performance.

3. In a multiperiod regulatory setting in which the costs of the firm are known to be perfectly correlated over time and in which credible commitments are possible, the regulator prefers not to exploit the information learned through performance; i.e., prices will be constant over time even though costs are learned perfectly at the end of the first period.

4. If costs are anticipated to change over time according to a known stochastic process and if credible commitments are possible, the optimal regulatory mechanism adjusts prices prospectively in every period in response to the changes in costs.


5. When the regulator cannot commit credibly to multiperiod policies, the set of policies the regulator is able to implement is restricted by its opportunism and by the consequent opportunism of the finn. That opportunism may be reduced by regulatory institutions, such as fairness (defined below), or by capital recovery rules that provide a means of deferred compensation.

6. With an inability to commit to multiperiod policies but with either fairness regulation or capital recovery rules that limit the opportunism of the firm, the regulator fully exploits the information obtained from the firm. This allows implementation of policies that are ex post efficient yet ex ante inefficient.

7. With fairness or capital recovery rules the regulator will choose a regulatory mechanism in which prices are only coarsely-responsive to costs. The purpose of such a policy is to limit the opportunism of the regulator.

8. With an inability to commit credibly to multiperiod policies but with either fairness or capital recovery rules that limit opportunism, the incentive to invest is diminished because the regulator will be expected to confiscate the rents the finn earns on its information.

The next section presents optimal multiperiod regulatory mechanisms for the cases in which commitment is and is not possible. The impact on investment decisions is addressed in Section 3, and an example of regulation with the monitoring of performance is presented in Section 4. Conclusions are offered in the fmal section.

2. Optimal Regulatory Policies

2.1 The Model The model is intended to provide a basis for the development of the intuition

underlying the design of regulatory mechanisms and for the presentation of results, most of which are developed in the source papers referenced herein.7 The model incorporates private information about costs with that information evolving over time based on past costs and investments. The firm is assumed to produce a single service, and the cost Ct incurred in period t when the fmn produces a quantity qt isS

Ct = at qt + kt + B(xt), (1)

where at is marginal cost, kt is a fixed cost (e.g., overhead), Xt is the investment made in period t, and B(xt) is the cost of that investment with B(O) = 0, B'(O) = 0, B'(xt) > ° if Xt > 0, and B"(xt) ?! 0.

The cost at is observed by the firm at the beginning of period t but is unobservable to the regulator. The cost thus is the private information of the finn and represents its "type." The private information could correspond to information about the firm's technology or about costs common to regulated and unregulated segments of the firm's business, to opportunity costs of its assets, or to characteristics of technological change.

REGULATORY INNOVA nON IN TELECOMMUNICA nONS 53

The marginal cost et evolves according to a stochastic process with transition function

(2)

where et E e t and ~t is a random variable representing uncertain components of costs that are observable only to the fIrm. Investment Xt-I in period t- I thus directly affects marginal costs in period t and indirectly affects future costs through the relation between e t and ej.i = t + l •...• 't. The marginal cost e t is specifIed as increasing in et-I. so higher costs in one period imply (stochastically) higher costs in the next and every subsequent period Investment reduces cost in the subsequent period. The assumptions on the transition functions thus are

aet aet --<0; ~e >0. Oxt_1 a t-I

The optimal regulatory mechanism in this setting depends importantly on whether the fIrm has private information prior to the regulator's choice of a mechanism or obtains private information after the mechanism has been chosen. The former seems more descriptive of the current state of the telecommunications industry. so attention will be restricted to it. The fIrm thus knows el at the beginning of the regulatory horizon. and the regulator's prior information is represented by the distribution function F I (el). A regularity assumption to be employed is that [el + F(eIV/tel)] is a nondecreasing function of e .. where f(91) is the density function. The random variable ~ in the transition function (2) induces a distribution function Ft(9t I 9t-I. Xt-I) on the marginal cost et.

The regulator is assumed to have the authority to regulate prices and would like to base its pricing policy on the marginal cost of the firm. but it does not know which cost the ftrm actually has. The next best alternative is to design a mechanism that includes a collection of pricing policies and delegate to the ftrm the choice of one of those policies. That choice will be based on its true cost, so the pricing policy can be made responsive to the costs of the firm through its selection of a policy. The task of the regulator is thus to choose a mechanism such that the ftrm 's choice of a pricing policy serves the mandate of the regulator. A two-part price structure will be employed where Pt denotes the price and Tt is a fIxed (or monthly) charge.9 For each period t. a policy specifIes the price Pt(~lt ~t-I •...• ~l) and a transfer or fIxed charge Tt(~lt ~t-I •.•.• ~I). where the arguments denote selection variables by which the fIrm chooses a policy. A strategy of the fIrm in period t is thus a function ~t(et): et ~ et.

In this setting. the fIrm has a natural incentive to choose a pricing policy intended for a higher marginal cost For example. if the regulator were to attempt to implement a marginal cost pricing policy Pt(~t) = ~t with Tt(~t) = kt when Xt = 0, the fum has an incentive to choose a policy intended for a fum with a higher


marginal cost. To illustrate this, consider a one-period model. The profit 1t(~I; 91) for a firm with marginal cost 91 is

II(~I; 91) = (~1 - 91) Q(~I)'

which has a maximum at ~1 > 91. The regulator thus prefers to design the mechanism to counter this incentive to overstate costs. The revelation principle implies that an optimal regulatory mechanism can be found in the class of policies such that the firm prefers to choose the policy designed for its marginal cost, i.e., ~1(91) = 91 for all 9t•

The sequence of moves by the regulator and the firm depends on whether the regulator can credibly commit to a policy for the entire length of the horizon. 10 If the regulator can make such commitments, it chooses a multiperiod mechanism M that specifies pricing policies for every period. The mechanism M thus is a collection

M={(pI(~I' ~I-l' ... , ~1)' TI(~I' ~I-l' ... , ~1»' t= 1, ... ,'t}, (3)

where 't is the number of periods in the horizon. 11 Then, at the beginning of each period, the firm chooses from the policies for that period by selecting ~I. Thus, the regulator moves first and chooses a mechanism M. At the beginning of period one, the firm chooses a particular pricing policy (Pl(~I)' Tl(~I» by selecting ~1 = ~1(91) E 91. At the beginning of period two, the firm observes 92 and chooses a pricing policy (P2(~2' ~1)' T2(~2' ~1» by selecting ~2 = ~2(92) E 92. The subsequent Eeriods are analogous. The equilibrium sought is a Bayesian Nash equilibrium. 2 Since 91 is observed at the beginning of period t, prices are prospectively based on costs for the coming period.

Commitment means than the regulator can credibly pledge not to act opportunistically when it receives information relevant to the cost of the firm. If the regulator is capable of making such credible commitments, the firm need not take into account the future behavior of the regulator but can instead rely on the announced mechanism. The agreements reached between the NYPSC and the New York Telephone Company may be interpreted as attempts to establish credible commitments for the periods of the agreements. This is weaker than full commitment, however, because at the conclusion of the period covered by the agreement the regulator would presumably establish a new policy based on the information available at that time. The regulator's choice of the new policy thus will affect the firm's behavior which in turn affects the choice of the initial agreement. This is the source of the inefficiency addressed by Vickers and Yarrow in their analysis of the price-cap system used to regulate British Telecom.

If, as discussed in Section 1, the regulator is unable to make credible commitments to future policies, the regulator will act optimally in every period, conditional on the information available. The regulator thus will choose its policies for period t at the beginning of that period. The regulator still prefers to rely on self-selection by the firm and therefore will choose a menu

REGULA TORY JNNOVA TION IN TELECOMMUNICATIONS 55

(3a)

at the beginning of each period t. This choice will be made optimally given the information the regulator has about 9t , so the equilibrium sought is a sequential (subgame perfect, Bayesian Nash) equilibrium. In the absence of commitment, the regulator is unable to avoid exploiting whatever opportunities are available in period t. In particular, the regulator is unable to commit not to exploit any information that becomes available regarding marginal cost. The regulator thus cannot avoid acting opportunistically, and recognizing this the firm will act strategically by anticipating the behavior of the regulator. As shown in Section 3.3, this opportunism results in ex ante inefficiency.

The profit 1[/ of the firm in period t is

(4)

where Q(P/) is the demand function. The objective of the firm is to maximize the (expected) discounted sum of its profit over the 't-period horizon. The firm is assumed to be privately owned and is assured a fair return in each period. The regulatory policy is thus chosen subject to the constraints

1[/~O, t= 1, ... ,'t. (5)

The regulator is assumed to maximize the ex ante (expected) discounted sum of consumer surplus where the expectation is taken with respect to the regulator's information about 9/ conditional on the history to that point.13 Consumer surplus S(Q(P/» in period t is given by

(6)

where Y is the aggregate willingness to pay of consumers.

3.2 Optimal Regulatory Mechanisms with Commitment The basic tradeoff facing the regulator is between consumer surplus and the

profit (or information rent) of the firm, since substituting (4) into (6) yields

(7)

If the regulator knew 9/, it could choose a pricing policy that held profit 1[/ to zero. With incomplete information, however, the firm earns profit, or more correctly rents, on its private information. In a one-period model those rents 1[1(81) are14

(8)

as shown in Baron and Myerson (1982). Consequently, the lower are the costs of the firm the higher are the rents it earns. The natural incentive of the firm is to select (~1 > 81) a pricing policy intended for a higher cost firm in order to obtain


higher profits. The rents represent the incentive payment that must be made to the fmn with cost 91 to offset the incentive to select a pricing policy intended for a firm with a higher cost. 15

The objective of the regulator is to maximize ex ante consumer surplus W which from (7) is given by16

W= J[Y(Q(Pl(91)))-91Q(Pl(91))-kl-1tl(91)]tl(91)d91. (7a)

In this setting. the regulator is able to implement a marginal-cost-pricing policy. From (8). however. the higher is the price the lower are the information rents. so the regulator has an incentive to distort price above marginal cost to reduce the rents even though that reduces the surplus [Y(Q(Pl)) - 91Q(Pl) - kd in (7). The price Pl(91) that optimally trades off rents and surplus is17

F 1(91) [ F 1(91) } Pl(91) = 91 + 11(91) = 91 1 + 9til(91)

(9)

whereFl(91)1ft(91) has the interpretation as the marginal information costs to the regulator. Note that as long as (81 + F(91)11(81)) is strictly increasing in 91. the price is "fully responsive" to costs. IS The fixed charges Tl(81) are then chosen to implementpl (91) by inducing the fmn to select the policy (@1(91) = 91) corresponding to its marginal costs. These fixed charges are given by equating (4) and (8) which yields

Tl (91) = 91Q(PI (91)) + kl - PI (81)Q(PI (81)) + r+ Q(PI (8?»d8~. 91

(10)

The incentive for political opportunism is evident from the price in (9). The ex ante efficient price is greater than marginal cost. and hence there is an ex post incentive to reduce the price in the next period to generate efficiency gains. For example. if/l(91) is uniform. then price Pl(91) is twice the marginal cost. The difference between price and marginal cost increases with 910 so the incentive is greater for high costs than for low costs. It is this incentive that is at the heart of the commitment problem studied in Sections 2.3 and 3.2. The optimal multiperiod regulatory mechanism with commitment is characterized next to identify the properties of the ex ante efficient mechanism and to provide a benchmark for the evaluation of mechanisms when credible commitment is not possible.

To indicate the nature of efficient regulation in a multiperiod model. consider the case in which the costs of the firm are characterized by technological change that reduces marginal cost over time. This is intended to be representative of the long-term decline in the real costs of telecommunications services. Marginal cost 9t will initially be assumed to be given by the deterministic transition function

(11)


where the productivity parameter y is less than or equal to one and is common knowledge. Marginal costs are thus perfectly correlated and decrease over time according to a known function. In this case. the regulator need only choose a mechanism M of the form M = {(PI(~I). TI(~I». (P2(~1). T2(~I» • ...• (P't(~I). T't(~I»}' • since the information about costs does not change over time. In the

context of the price cap systems discussed in Section 1. the cap in each period is represented by the pair (P1(~I). TI(~I»' which may be interpreted as caps on both the usage charge and the monthly charge. With these caps the firm. when delegated the choice of prices, will choose the usage charge and the monthly charge at their caps.19

The optimal prices, expressed here as a function of 8 I. can be derived from the characterization in Baron and Besanko (1984) as20

I-I [ 1 F(9 1») pt(81) = "( 81 1 + e; /(91)

/-1 9 ="( PI( 1) . (12)

The price cap thus decreases over time at the same rate at which marginal costs decrease, but in all periods the price is above marginal cost and by the same percent.

As an example, suppose 91 has a triangular distribution with/I(8I) = 291 for 81 E [0,1]. so that high costs are more likely than low costs. Then the prices are givenbl l

Price is thus 50 percent greater than marginal cost in every period but declines at the same rate as does marginal cost.

Viewed from time zero when the regulator designs the regulatory mechanism. the time path of prices is deterministic once the firm has selected the particular policy based on its true 81. Prices decline over time at the same rate as marginal costs. but in every period price incorporates a mark-up above marginal cost equal to the marginal information costs resulting from the fIrm' s private information. An optimal regulatory mechanism thus specifies price caps that decrease over time if y< 1 and are constant over time if y= 1. Since the transition function in (11) is known to the regulator, the regulator is able to specify the caps in advance. In this respect, this mechanism corresponds to the price-cap system used for British Telecom. That system is not directly cost-based. however, but instead was based on the existing prices at the time the system was instituted.

To indicate the significance of commitment for the design of a price-cap mechanism, consider the case in which y = 1. The optimal caps are then to commit to the repetition in each period of the optimal price in (9) for a one-period model with the fixed charges given in (10). Even though the regulator observes the selection of a policy in the fIrst period which completely reveals the marginal cost


91, the regulator prefers to commit not to use that information in subsequent periods. The regulator prefers to implement a policy in which there is no adaptation to the information because that provides the optimal tradeoff between consumer surplus and the rents the firm earns on its private information. Since the frrm has at the beginning of the horizon the same private information about its costs in each future period. it earns rents on that information in each period. The tradeoff between rent reduction and consumer surplus is thus the same for each period.

Of course, after the selection of a regulatory policy in the fIrst period, the regulator knows 91 and hence knows what costs will be in every subsequent period. The regulator thus could implement marginal cost pricing in every period other than the first. The regulator prefers not to exploit that information, however, because the frrm would anticipate that its rents would be exploited and would act strategically in its initial selection of a policy. This would then reduce the efficiency of the regulatory mechanism.

In a multiperiod model, the rents II(91) earned by the firm with transition function in (11) as a consequence of its private information about 91 are analogous to (8)

(8a)

where ~ is the discount factor. The firm thus earns more than its cost of capital, but it does so because of its private information about costs. Because of that private information it is impossible for the regulator to eliminate these "excess" profits because eliminating profits for a frrm with marginal cost 9 would cause a firm with a higher cost not to recover its capital costs. This firm would then be unable to raise capital.

Next consider a stochastic transition function where 'Y is the realization of a random variable ythat is uniformly distributed on the interval [0,1]. Costs are thus imperfectly correlated over time. Initially, consider a two-period horizon so that 'Y is realized once at the beginning of period two. The price cap for the first period is unaffected and is given in (9). Viewed from time zero when the regulator designs the mechanism of regulatory policies, the distribution F2(92 1 91) is given by

92 . F 2(92 1 91) = e If 92 E [0, 91].

1

(13)

At the beginning of period two the regulator does not know 92 and thus designs a

price cap P2*(92, 91). That cap is22

dF2(92 1 91)

d9 1 F 1(91)

P2*(92, 91) = 92 - 12(92 191) 11(91)


(14)

The second term on the right side of (14) is the marginal information cost resulting from the firm's private information about 91. It is important to note that this regulatory mechanism is "nested" in that in each period the firm makes a selection of a pricing policy by reporting ~/ but that policy is conditioned on the selections in earlier periods.

It is important to note that the price caps are set prospectively but are also based on costs in prior periods. That is. in (14). for example. the price cap for period two is proportional to the costs that the firm will have in period two. The margin above that marginal cost. however. depends on the costs in period one. That dependence is due to the information that period-one costs provide for period-two costs. That is. in the first line of (14) the term dF2(92 I 81)/d91 represents the impact of 91 on the information about 82. For the case of perfect correlation. 82 = 81 and this derivative equals -1. The expression in (14) then reduces to (9). If 81 provides no information about period-two marginal costs so that 81 and 82 are statistically

independent. then dF2(92 I 8l)/d81 = 0 and P2*(82. 81) = 82. Thus. itis the information that costs in earlier periods provides for costs in the future periods that determines how the price caps depend on past costs. In all cases. however. the cap for the next period is prospectively based on the costs anticipated for that period.

If 81 has a triangular density !I(81) = 281. then (14) becomes

P2*(82• 91) = ~ 92. (15)

Again. price is marked up above marginal cost by 50 percent of the marginal information costs. Although the markup is present in every period. the path of the price caps is stochastic when viewed from the time at which the regulator chooses the mechanism. In general. the price p/*(9t. 9/-1 •... ,81) in period t is given by

( Fl(81) 1 8/

p/(8/. 8/_1, ...• 81) = 8/ 1 + 8dl(81) =~ Pl(9 1). (16)

The cap on the fixed charges T/*(9/, 9t-l • ... ,91) is then determined in the manner used to obtain (10).

The price patterns when costs evolve deterministically and stochastically can be compared by examining the case in which Y= 112 and!I(91) is triangular. The expected prices, where the expectation is taken at the beginning of period one, are then equal:


EPt=Ep/=I if/=I

= 3/4 yt-l if I > 1. (17)

Although the expected time paths are the same, the path for the case of perfect correlation is deterministic once the firm selects the regulatory policy in the first period, whereas the path is stochastic in the case of imperfect correlation.

The mechanism in the case of y stochastic involves a price cap that is revised at the beginning of each period based on the costs that the firm realizes. Since the realized cost is exogenously determined, this is consistent with the FCC's policy that adjustments in the cap should be based on exogenous factors. Even though the price cap is established in each period and viewed from time zero the cap is a random variable, the formula governing the adjustment is specified in advance. Commitment means that the formula cannot be adjusted. The FCC proposal for price-cap regulation would, however, allow adjustments in the cap. The theory presented here indicates how the price cap should be adjusted if commitment to the mechanism can be made credible. The formula for the adjustment should not be subject to change. If the rate at which costs are anticipated to decline is known with certainty, the rate at which the cap will decrease can be specified in advance. In the more realistic case in which the rate of change is not known in advance, the mechanism should specify the formula by which information will be used to adjust the cap.

2.3. Optimal Regulation with No Commitment If credible commitments to long-term policies cannot be made, as indicated in

(3a) the regulator will at the end of the first period base the mechanism M 2 for the second period on whatever information was revealed by the fIrm's selection from the mechanism M 1 in the fIrst period. The policies that the regulator is able to implement in this case depend importantly on the extent of the opportunism that is possible in the regulatory relationship. In the perfect correlation case specified in (II), Laffont and Tirole (1986a) demonstrate that if the regulator can fully exploit the cost information it obtains in the first period, and thus would implement a marginal-cost price cap in period two if it learned 91 in the first period, the firm has an incentive in the first period to select a pricing policy designed for a lower marginal cost and then not to produce in the second period. Thus in period one, the regulator cannot implement pricing policies that are fully responsive to costs and must resort to "coarse" policies that specify the same price for many different costs. This argument is presented in more detail in the Appendix.

Two forces serve to limit this opportunism. First, if the firm has substantial sunk investment costs that through regulatory rules are recoverable over several years, the incentive of the firm to act strategically is limited as demonstrated in the Appendix. This capital recovery rule, coupled with substantial sunk costs, allows the regulator to implement pricing policies that are continuously responsive to costs. Second, Baron and Besanko (I987c) consider a regulatory relationship,

REGULATORY INNOVA TIONIN TELECOMMUNICATIONS 61

characterized by what they label as "fairness," under which the fIrm agrees not to quit the regulatory relationship as long as the regulator provides the firm with a fair return given the information it reveals through its selection of a pricing policy in the first period?3 This limited form of commitment allows the re~ulator to implement pricing policies that are continuously responsive to costs. 4 In this section the regulatory relationship is assumed to be characterized either by fairness or by substantial sunk costs and a capital recovery rule.

The regulatory policies that would be implemented in the absence of commitment correspond to those that would be implemented at the conclusion of a regulatory mechanism such as that for British Telecom or that implemented in New York. Two aspects of this regulatory setting are of particular interest. First, what mechanism will be implemented at the conclusion of the duration of the fIrst mechanism? Second, what is the impact of the choice of the second-period mechanism on the choice of the mechanism for the prior period? That is, since the firm will anticipate the regulator's choice of a second-period mechanism and will take that into account in making its selection from the mechanism in the fIrst period, the regulators will find it optimal to anticipate the firm's strategic choice. This results in a reduction in ex ante effIciency.

To investigate these issues, consider a two-period ('t = 2) horizon, and suppose that in the fIrst period the regulator implements a mechanism M 1 that is continuously responsive to costs. At the end of the fIrst period, the regulator would then be able to infer 91 from the policy selected by the firm in period one. Since the regulator cannot resist exploiting this information, it will base the price for the second period on the posterior distribution F2(92 I 91). For the case in (11) of perfectly correlated costs, the posterior distribution places mass one on 92 = Y 91. The price in the second period, and in each subsequent period, is then equal to the marginal cost the regulator knows that the firm will have. The fixed charges T2 then equal the fixed cost k1 and the firm earns no rent after the fIrst period. As demonstrated in Baron and Besanko (1987c), this results in a welfare loss compared to the mechansims characterized in the previous section because too large an incentive payment is required in the fIrst period to implement those price caps.

For the case of imperfect correlation, the price P~(92' 91) in period two is analogous to (9) but is based on the posterior distribution F2(92 I 91) or

For the example with 92 uniformly distributed on [0,911 the price is

pg(92, 9 1) = 292 if 92 E [0,91].

(18)

(18a)

In this case, the period-two price is higher when the regulator exploits the information obtained during the first period. A higher price is not necessarily an indication of inefficiency, but it is true that ex ante welfare is strictly lower in the

62 PRICE CAPS AND INCENTIVE REGULA nON IN TELECOMMUNICA nONS

absence of commitment because the regulator prefers to implement the price P2* in (15).25 The ex ante welfare loss when long-term commitments cannot be made and the regulatory relationship is governed by fairness is characterized in Baron and Besanko (1987c).

The answer to the first question posed above is thus that the regulator will act opportunistically by ratcheting price down as low as possible given the information revealed in earlier periods. In addition, profit is ratcheted down to the level of the rents on the remaining private information of the firm. In the case in which marginal costs evolve at a known rate, price ratchets down to the marginal cost and profit ratchets down to zero. To the extent that the renegotiation of a price cap system is similar to the case in which long-term commitment is not credible, renegotiation exploits the information that becomes available through performance. Price cap regulation thus evolves into revenue requirements regulation. Anticipation of this, however, results in inefficiency because a greater incentive payment has to be made in the first period in order to offset the greater incentive of the firm to act strategically when it knows that its profits will be ratcheted down through renegotiation.

Because an ex ante welfare loss results when the regulator cannot credibly commit to long-term policies and thus cannot avoid acting opportunistically when it observes the policy selection in the first period, the regulator would be expected to seek means of restricting its own opportunism. One means of doing so is not to learn 91 in the first period. The regulator can accomplish this by choosing a menu M 1 that contains a single pricing policy; i.e., a single price cap rather than a cap as a function of ~l. In the case of perfectly correlated marginal costs this allows the optimal price cap with commitment to be implemented in the second period, but such a mechanism may not be optimal. For an example, Baron and Besanko (1987b) characterize the optimal mechanism and show that the first-period mechanism contains a countable number of policies that are coarsely responsive to costs. Those policies are more responsive for low costs than for high costs. There is thus a trade-off between coarse pricing in the first period as a means of limiting opportunism in the second period and the welfare loss in the first period that results when prices are not continuously responsive to costs. This suggests that regulatory mechanisms that are coarse and prescribe the same prices for sets of different possible costs may not be inefficient when long-term commitments cannot be made. Coarse price cap mechanisms thus may contribute to informational efficiency when the regulator is able to make only limited commitments to long-term policies.26

3. Investment

3.1 Investment with Commitment The purpose of this section is to examine the importance of commitment for

investment by the regulated fmn. As a benchmark, the optimal investment with


commibnent is characterized, and the invesbnent resulting in the absence of commibnent is then examined.

If the regulator were able to make credible commitments, the incentives for investment would be second-best efficient given the prices set in response to the informational asymmetry. The resulting invesbnent depends on whether the regulator can observe invesbnent and force the investment it prefers. The first case considered is that in which the regulator can dictate investment, and the second case considered is that in which invesbnent is unobservable to the regulator in which case the investment decision is necessarily delegated to the firm.

To illustrate these cases, the perfect correlation case in a two-period model will be used with ez = 91/(1 + Xl). The welfare W maximized by the regulator can be written as

~+ 9 W = J 9- [Y(Q(P1» - 91Q(P1) - k1 + ~(Y(Q(P2» - 1 +lX1 Q(P2) - k2)

[ ~Q(P2)J.F1(91)]

- B(x1) - Q(P1) + 1 + xl 11(91) 11(91)d91• (19)

The optimal (second-best) investmentx1 (9 1) that the regulator can implement when investment is observable satisfies

F 1(91)

(9 1+ 11(81») , ~ 2 Q(P2(91» -B (Xl (91» = O.

(l +x1(9 1» (20)

Substituting 92 = 91/(1 + Xl) yields

~82 ( F 1(91) J ' 1 + xl (81) 1 + 8/1(81) Q(P2(81» -B (x1(8 1» = 0, (20a)

so the second-best invesbnent equates the marginal invesbnent cost and the marginal reduction in the variable production and information cost of producing Q(P2(81».27 The regulator thus takes into account the marginal information cost in specifying the investment.

Compared to the complete information case, the marginal product of investment given the quantity is greater with incomplete information than with complete information because, with this specification investment decreases the information rents earned by the firm?8 The invesbnent decision under incomplete information thus involves a rent-reduction externality, which the regulator takes into account

With the specifications B(X1) = Xl and F1(81) = 81. the optimal investment is given by


(21)

Given the quantity, the investment with incomplete infonnation is greater than the efficient investment for the same quantity by a factor of 2.5. The price cap then satisfies, forl1(81) triangular,

81 F 1(8 1) J 181 181 P2(81) = 1 + x1(81) 1 + 8/1 (81) = 1 + xI(81) (2/38IQ(P2(81»)~'

lfthe investment were unobservable, then the finn would choose its investment to maximize its profit n:(8, ~1; 8) which is given by, using the T1 (81) and T2(81)

that implement PI (81) and PZ(81),

n:(~l' Xl; 81) = (~1 - 81) Q(P1(~1» + /3[ ~~ ~ 1 !lx JQ(P2(~1» 1 + Xl ( 1) 1

o A r9+ ( 0 /3Q(P2(S?» 1 0 + B(x1 (11 1» -B(X1) + J A Q(P1 (81» + 0 0 d81•

III 1 +x1(81) (22)

where x?O is the equilibrium investment. The finn will choose its investment

x1(81), which in the optimal policy equals X?(81), to satisfy, given ~1 = 81,

/3 1 + :1(81) S2Q(P2(81» - B'(X1 (81» = O. (23)

For the same quantity, the finn thus invests less than the regulator prefers as given in (20).29 This results because the finn does not take into account the rent-reduction externality. The regulator will, however, take into account the finn's choice and alter the quantity produced accordingly. The price cap in this case is

P2(81) = 1 + A(81)/3 ----"---81 F 1(81) 81 J 1+x?(81) etll(81) 1+x?(81)

where A(e1) is the multiplier associated with the constraint in (23). Since the regulator prefers a greater investment than does the finn, the multiplier A(e1) is positive. The regulator then will choose a lower price, and hence higher quantity, in the second period so as to increase the marginal product of investment.

3.2 Investment in the Absence of Commitment If the regulator is unable to make credible commitments to future policies but a

fairness relationship is in place, at the end of the first period it would choose a


mechanism M2 that is optimal given its information. That information includes what can be inferred from the policy selected in the first period and from what is known about equilibrium strategies. If, for example, the mechanism M 1 implemented in the first period were continuously responsive to costs (completely separating), the regulator would know 01 from the firm's choice of policy in the first period. From the equilibrium strategies, the regulator then could infer the investment chosen by the firm, so in the case of perfectly correlated marginal costs the regulator would know the marginal cost 02 the firm would have in the second period. The regulator could then fully exploit that information by instituting a marginal cost price cap.

For the case in which investment is observable and the regulator has the authority to control it, the regulatory mechanism M 1 would specify an investment Xl (01) that satisfies (20) with Pl(OI) = 131/(1 + Xl(el». The investment is thus greater than when commitment is possible because the cost reduction pertains to a greater output. If investment were unobservable, the firm would recognize that its profits in the second period will be zero. In the first period, the firm would then only recover its initial investment, so it would have no incentive to invest. 30 To provide some incentive to invest, the regulator would choose a coarse mechanism for period one that would prevent it from learning 01.

If costs were not perfectly correlated, the firm would earn rents in the second period on the information it privately observes at the beginning of period 2, and this could provide an incentive to invest. For the case in which Ml is completely separating, the expected rents Elt2(01, Xl) in period two as viewed from period one are, after integrating by parts,

(24)

Then, when investment is not observable, the firm will choose its investment to maximize Elt2(01, Xl) - B(xt}, and the marginal (value) product of investment is thus

dElt2(01' Xl) _ rB+ 0 aF 2(e~ I 01, Xl) 0 dx - L- Q(P2{02» a d92•

1 0 Xl (25)

If the investment reduces marginal costs as in the specification considered here, the derivative in (25) is negative, so the fum will not invest when it recognizes that the regulator will fully exploit any information it has at the end of the first period? 1

If the investment were to increase the range of marginal costs, then the firm might have an incentive to invest. One would expect, however, that that incentive would be weak and that the investment would be considerably lower than that preferred by the regulator.

As suggested by this example, when the regulator cannot make credible commitments to multi period policies, and thus can be expected to act opportunistically


in response to information obtained, the incentive for investment is nonexistent or weak at best. Since public utilities make considerable capital investments, the question is what generates the incentive to invest. Several explanations seem plausible. First, partial commitments of the type agreed to by the NYPSC and the New York Telephone Company provide the firm an opportunity to capture returns on investments with rapid recovery rates or which are fungible and can be used to provide unregulated services. This explanation is analogous to regulatory lag and allows some profits to be earned before rates are adjusted. Second, the capital recovery rule may be sufficiently protective that regulated firms are confident that the return on non-fungible assets will be forthcoming. This would be characteristic of revenue requirements regulation that provides revenue as a function of original investment. Third, the prospect of deregulation and the returns that potentially can be earned under competition can provide an incentive to invest.

Fourth, an equilibrium may result in which the regulator and the firm give and honor trust. The regulator has an incentive not to act opportunistically because it wants the firm to continue to invest to provide the capacity needed to serve a growing demand and to replace inefficient equipment and facilities. The frrm has an incentive to invest because of the expectation that the regulator will forego the opportunity to take advantage of the information to confiscate profits. When the regulator does act opportunistically, the firm can punish the regulator by not investing and threatening that there will be inadequate capacity to meet demand. The regulator may then find it desirable to return to the strategy of honoring trust by not taking advantage of the frrm and its non-fungible assets. This equilibrium, however, is susceptible to the short-run interests of politically ambitious regulators and legislators, particularly if they do not have to bear the long -run consequences of their opportunism. The possibility of such opportunism reduces the likelihood that such an equilibrium would be supportable. Even if such an equilibrium were attainable, the investment would likely be lower than that preferred by the regulator.

4. Monitoring: An Example

The theory presented in the previous sections is based on the assumption that the regulator is only able to observe the policy chosen or, equivalently, the price, quantity, and the fixed charges. All regulators, of course, closely monitor the accounting profits of the frrms they regulate. Accounting profits are not, however, the same as the economic profits that motivate the frrm, and thus accounting profits are at best a noisy monitor of true profits. When commitment is possible, the availability of a monitor may not affect the prices specified in the regulatory mechanism, but in general the fixed charges will depend on the monitor. In the absence of commitment, the monitor will also be used to update the regulator's information about the costs of the firm.

The example presented here is intended to illustrate the regulatory role of an observable monitor of performance. The example is "non-optimal" in the sense that the pricing policy in the frrst period is assumed to be constant over e, so the


optimal mechanism is not characterized as in Baron and Besanko (1987b). The example focuses solely on the second period and hence does not address how the ability to observe performance might affect the fIrst-period policy.

The example has two periods and perfectly correlated marginal costs 91 = 92 = 9, which are uniformly distributed on the interval [0,1]. The cost C1 incurred in the first period is assumed to be a function of 9 and of a random variable that is not observed until the end of the period. The regulator is able to observe CI, and hence it can use that observation to update its information in period two. Regulation is assumed to be governed by fairness, so the regulator is able to utilize fully this information in form ulating the policy for the second period. The regulator must, however, offer a mechanism of price caps for the second period that allows the type of the firm revealed in the first period to earn nonnegative profits. The price cap PI in the first period is set at the beginning of the period and thus cannot be based on C h which is not observed until the end of the period?2

The first-period cost C1 is assumed to have the form

(26)

where ql is the quantity and EI is the realization of a randon variable e1 that is uniformly distributed on the interval [0,1]?3 The marginal cost thus depends on a random component and on the private information of the firm. Conditional on 9, the density g( C 1 I 9) is

g(Cl I 9) = -.l if C1 E [9q1 + k, (9 + 1)q1 + k]. q1

The unconditional density function g(Cl) is

C1-k . g(C1)=--2- IfCl E [k,ql +k]

ql

2ql +k-C1

qI

. (27)

(28)

If the regulatory policy in the first period pools over the interval [9-, 9+:!, the posterior density 12(9 I C1) at the beginning of the second period is uniform and given by

(29)


The support of a, however, depends on CI, since if CI::; ql + k then

a::; a*(CI) == (CI - k)/ qJ, and if CI > ql + k then a > a**(CI) == (CI - ql - k)/ ql· The marginal cost in the second period is assumed to be a + E2, where E2 is the

realization of a random variable £2 that is uniformly distributed on [0, 1]. Since the posterior density is uniform for any realization C}, the price P2(a I CI) set in the second period is34

1 F2(a I CI ) 1 P2(a I C I )= a+"2+ h(a I CI ) 2a +'2

ife ~ e*(CI) and CI E [k, ql +k], and

1 CI-ql-k P2(e I C I) = 2a + -2 - --=--.:....-

ql

for a ~ 9**(C1) and C1 E [ql + k, 2ql + k].

(30)

(31)

Comparing (30) with (12) evaluated at Y= 1 indicates that the price in period two is higher than in the absence of a monitor if 9 + EI :=;; 1. If 9 + EI > 1, the price from (31) can be lower than that in (12). For high realizations of cost CI,lower prices

thus result because the support of the posterior distribution is [e**(CI), 9"1. This reduces the marginal information costs to the regulator, and the regulator responds by reducing the price.

The rents 1t2(a I CI) earned by the firm in period two then are given by

~·(Cl) ° 1 0. 1t2(a I C1) = Ja Q(2e + '2) de if CI E [k, ql + k], and

><,(01 C,) = J:,290 + ~_ c, -q:' -k }oo for a ~ 9**(C I) and CI E [ql + k, 2ql + k].

The rents 1t2(9) in the absence of the observable performance are given by

I 1t2(9) = J Q(290) deo Vee [0,1].

a

The monitor of performance thus reduces the rents for low realizations of cost but may increase them for high realizations. The expected second-period rents may be greater or less than in the absence of the monitor, depending on the value of 9. Taking the expectation over 9 indicates that the ex ante rents are reduced by the monitor.


Since the rents are affected, the period-one policy will be affected, but the effect is difficult to evaluate. Since the reason for pooling in the first period is that pooling reduces the information rents, intuition suggests that the availability of a monitor may reduce the incentive to pool in the first period. This would result in prices in the first period that are more responsive to first-period costs than is pricing in the absence of a monitor of performance.

The model analyzed here pertains to one regulatory jurisdiction and one regulated firm, but a commission may have authority over several firms in the same industry. In this case, monitors can be based on performance of all the firms. Since the private information of the firms is likely to be correlated, such monitors should sharpen the regulator'S posterior distribution. Similarly, monitors based on firms in other jurisdictions should be employed.

Monitors of performance can improve the efficiency of regulatory mechanisms in several ways. First, a monitor can reduce the rents of the firm by "tightening" the posterior distribution of marginal cost.35 Second, a monitor can affect pricing by altering the marginal information costs. Third, if the firm were risk-averse, a monitor could be used to relieve the firm of some risk.

These benefits suggest that monitoring can be an important function of a regulator when a price cap or delegation mechanism is employed. From a positive perspective, more active monitoring by a regulator would be expected to be correlated with an inability to make credible commitments. That is, monitoring is likely to be more valuable the more likely the regulator is to act opportunistically in response to information obtained through the observation of performance.

5. Conclusions

A variety of factors complicate the application of the principles addressed here. The major complicating factor is incompleteness of the policies due to unanticipated events and the costs of writing complex contingent policies. The theory presented above is based on the assumption that all possible events are known to the regulator and to the firm and their likelihood of occurrence is representable by a probability distribution. In addition, if complexity and its associated costs preclude writing policies that are conditioned on each possible event or possible value of a cost parameter, the regulatory policies will be incomplete. In either the case of incompleteness or when there are unanticipated events, ex ante efficiency may be enhanced by allowing revisions in policies. What is needed are practical means to permit changes in regulatory policies when those changes promote ex ante efficiency and to preclude changes in policies when that would reduce ex ante efficiency.

In terms of the evaluation of regulatory performance, the analysis presented here implies that it is the regulatory mechanism that should be the subject of the evaluation. The optimality of a regulatory mechanism is a function of 1) the information available to the regulator, 2) the transition function that governs how the costs of the firm are anticipated to evolve over time, 3) and the extent to which


commitments can be made credible. If credible commitments can be made. the framework presented in Sections 2.2 and 3.1 provides the basis for the evaluation. An important conclusion from this theory is that a search for ex post efficiency is likely to be misleading. A second conclusion is that even under delegation, administrative rules that provide a degree of commitment can improve efficiency. A capital recovery rule. for example, can reduce strategic behavior in addition to providing a fair return.

If credible commitments cannot be made. the cause of that inability must be assessed. If it is due to the policies of the regulator. then the consequences are attributable to the efficiency of regulation. If. however, the source of the inability to make credible commitments is due to other factors. such as opportunism by a legislature. then its consequences should be evaluated separately.

Appendix

Sunk Costs, the Inability To Commit, and Implementable Policies For the case in which the marginal costs of the frrm are perfectly correlated

(Eh = e2 = e), Laffont and Tirole (1988) have demonstrated that the regulator is unable to implement any regulatory policy that is continuously responsive to costs over any interval of possible costs that has positive probability. This results because of a conjunction of the conditions required for responsive pricing and the expanded strategy set of the regulated frrm when it can make a participation decision in each period. Since the frrm has a natural incentive to overstate its costs in an attempt to obtain a more profitable regulatory policy (i.e .• to choose a policy intended for a higher cost type). the regulator must specify the fixed charges to offset that incentive. To do so in a multiperiod model in which the regulator cannot commit credibly to future policies. the policy in the first period must include a payment that offsets for both periods the incentive to select a policy designed for a higher cost type. The rent II(a) required to implement any prices (PI (a), P2(e» is thus

II(e) = t+ [Q(PI(aO» + (3Q(P2(aO))] daD. s

If the frrm were to select the policy defined for its marginal cost. the regulator in the second period would. knowing the marginal cost e. choose a policy of marginal cost pricing (i.e., (P2(e) = a, T 2(e) = k2». which yields the firm a zero profit If the frrm selected ~ "# e and produced in the second period, the rent 1t2(~; e) in the second period would thus be

1tz(~; e) = (~ - e) Q(~),

which is negative if in the first period the firm selected a pricing policy intended for a ~ less than e.


Because the finn can always limit its period-two profit to zero by refusing to participate in the second period, its two-period profit IT(~; e) is

IT(~;e) = (~- e)Q(Pl (e» + ~+ [Q(Pl(el) + J3Q(P2(el)]deO

+ J3 max {o,(~ - e)Q(Pl(~»}.

Given this profit function, the firm finds it optimal to underreport (~ < e) its costs in the fIrst period and then not to participate in the second period in order to avoid having to produce at a loss?6 This conclusion holds for all intervals of marginal cost, so no policy that is continuously responsive to costs on any interval can be implemented.

In the case of a regulated frrm with long-lived assets that are sunk and non-fungible, the capital recovery rules used by regulatory commissions may eliminate the problem identified by Laffont and Tirole. A capital recovery rule is taken here to be a rule enforceable under administrative law that entitles the finn to recover an asset's cost according to a prescribed schedule as long as the fum continues to produce the quantity specified in the regulatory policy. Suppose that the frrm has a sunk investment B(XO) prior to period one, and suppose that an enforceable recovery rule allows the firm to recover that cost at a constant rate over the n-period life of the asset. In a two-period model, the cash flow in the second period is now lhB(XO) if the frrm continues to participate under a marginal cost pricing policy.

The fum's two-period profit IT* (~; 9) is thus

IT*(~; e) = (~- 9) Q(Pl(~» + ~+ [Q(Pl (eo» + J3Q(P2(eo»] d9°

+ J3 max {O, V2 B(xo) + (~- e) Q(Pl(~»}.

If the sunk assets are sufficiently great, the incentive to underreport costs in the first period and not participate in the second period may be outweighed, allowing the regulator to implement a policy even if it cannot commit to its pricing policy in the second period. This results because a capital recovery rule,g0vides a limited form of commitment that allows compensation to be deferred.3 ,38

The significance of sunk, non-fungible assets and a capital recovery rule is that in the absence of commitment the regulator may be able to implement a regulatory policy that is continuously responsive to costs. In particular, it may allow the regulator to implement a policy that fully exploits the information revealed in the first period. Such a policy is not generally optimal, however, as indicated above.

Notes

This research has been supported by NSF Grant No. IST-8606157.


1. This theory has been surveyed by Baron (1989), Besanko and Sappington (1988), Caillaud, Guesnerie, Rey, and Tirole (1988), and Sappington and Stiglitz (1986). Recent wOlk by Demski, Sappington, and Spiller (1986) has extended the theory to include a market alternative to regulation.

2. The experience with incentive regulatory systems is reviewed by Schmidt (1984) and Joskow and Schmalensee (1986).

3. Even apparently conclusive legislation establishing regulatory policy may not survive subsequent electoral politics. As Kahn (1987, 18) states, "What of the possibility, finally, of total deregulation oflocal service? Nebraska has in fact passed a law-which is, incidently, the subject of strenuous Constitutional challenge-imposing a ceiling of ten percent per year on rate increases for local telephone service, subject to regulatory review if specified percentages of subscribers complainand providing for total deregulation at the end of five years. I find it unsurprising that the bill's sponsor was just defeated in his bid for reelection, obtaining only 38 percent of the vote."

4. Helman refers to three incidents that, although their "overall revenue effects were small," attracted public, staff, and commission attention. One was an incentive compensation system for management, and another was the purchase of a Lear jet that management claimed would reduce transportation expenses. The third was the decision by management not to file a product liability suit to recover a $250,000 insurance deductible.

5. See Schmidt (1984). 6. In practice, regulatory behavior responds to unanticipated events, but the theory addressed here

cannot accommodate such events. 7. The static theory is presented in Baron and Myerson (1982), Guesnerie and Laffont (1984),

Laffont and Tirole (1986), and Sappington (1982). The dynamic theory is presented in Baron and Besanko (1984, 1987) and Laffont and Tirole (1986).

8. Sappington (1983) presents a single-period, multiproduct theory in a related model. 9. The fixed charge is assumed not to affect demand. 10. The model involves no unanticipated events, so the regulator can in principle choose a policy

at time zero and have it govern subsequent decisions for the entire horizon. 11. The policy selected is the only variable observable to the regulator. 12. The optimal regulatory mechanism in the case of commitment is characterized in Baron and

Besanko (1984). 13. The model can be extended directly to the case in which the regulator maximizes a weighted

average of consumer and producer surplus. The optimal mechanism has the same qualitative properties as that considered here.

14. An important issue is whether in a regulatory context a firm has a property right to its information about its costs. If so, the firm may be viewed as having a right to reveal its information only in exchange for adequate compensation. The information rents thus may be viewed as the return extracted by the firm for its information. In a regulatory setting, the regulator has the authority to minimize those rents by making a take-it-or-Ieave-it offer, but the regulator has to trade-off rent reduction against the efficiency of the regulatory policy.

15. If the firm had an unobservable effort decision at to make where marginal cost was c(9t, at), the firm will choose its effort al (91) to satisfy

-Ca(9l. al(9t})Q(Pl(9l» - V(al(9l»=O, where V(al(9l» is the marginal disutility of effort. This is the same effort level the regulator prefers, so with commitment the effort decision can be delegated to the firm. The same is true for the second period. See Baron (1987), Section IV.F, for an analysis of this case. This result would differ if the model were formulated with an ex post monitor z, so that the fixed charges could be based on both ~ and z. Laffont and Tirole (1986) consider such a case and show that the regulator will base prices on the monitor as a means of reducing the information rents. Baron and Besanko (1987a, 1988) consider a similar model with a risk-averse manager.

16. The investment Xl is assumed to be zero here. 17. This is derived by substituting (8) into (7a), integrating by parts, and maximizing pointwise with

respect to PI (91). 18. See Baron and Myerson (1982) or Baron (1989) for a demonstration of the optimality of this

mechanism.


19. This conclusion is based on the condition that prices p,(~) are below the monopoly price for ali 81. This condition seems reasonable, but it is possible from (9) that the regulator would prefer a price above the monopoly price as a means of economizing on the information rents.

20. If the costs were independent across periods, the optimal price cap would be the price in (9) for the first period and in each subsequent period a cap equal to marginal cost. The optimal one-period price is implemented in the first period because the firm has the same informational advantage in the first period as in the single-period model. At the beginning of the regulatory horizon, however, the firm has no informational advantage relative to the regulator about the cost in any future period. The firm thus can earn no information rents associated with its operations in future periods, so the regulator need not trade off efficiency against rent control. The regulator thus implements a marginal cost price cap in every period after the first. Since the firm observes its cost at the beginning of each period and the regulator does not observe it, the regulator still must implement marginal cost pricing by employing in every period a self-selection mechanism. The firm earns rents in that period, but the regulator can costlessly eliminate those rents by charging in the previous period a "franchise fee" equal to the discounted expectation of the future rents. Thus, other than for the first period the rents do not affect the pricing policy.

21. The optimality of the mechanisms characterized here requires verifIcation of global incentive compatibility conditions. See Baron (1987) and Guesnerie and Laffont (1984) for an analysis of these conditions. With commitment and perfectly correlated marginal costs, the condition that 8+F(8)/j(8) be nondecreasing in 8 is sufficient for global incentive compatibility. In other cases, the specification of sufficient conditions is more complicated.

22. This follows from Baron and Besanko (1984). 23. Fairness is directed to the incentive the parties have to revise regulatory policies once

information has been revealed either by self-selection or by performance. An inability to ignore this incentive prevents the implementation of efficient policies in prior periods. For an example, Baron and Besanko demonstrate that both the finn and the regulator may prefer to abide by a regulatory relationship characterized by fairness than to participate in one in which commitment is not possible. Administrative rules and the courts, however, are required to make the fairness agreement credible.

24. Even though continuously responsive prices can be implemented, the regulator may not find them to be optimal but instead may prefer a coarse pricing policy in which different price caps are specified for different sets of possible costs.

25. The price with commitment may be higher than the price with fairness. Consider a triangular distribution /1(81) = 2(1- 81) if 81 E [0,1]. Then, the period-two price cap with commitment is P2*(82, 81) = [821(1- 81)] [2 - 3f28tl. which is greater than the price with fairness for ali 81 and 82 such that 8182> O.

26. With an inability to commit, the effort chosen by the firm will again be second-best efficient. That is, in each period the firm simultaneously chooses the pricing policy and effort a, given the

mechanism M,. The effort choice is efficient given the pricing policy p? 27. Equation (20a) can also be written as

f3 :: Pl(81) Q(PZ(81» - B'(XI (81» = O.

The marginal benefit from investment is thus the proportionate reduction in the variable cost. 28. The information rents are decreasing in the investment because investment reduces the range

of costs to which the regulator must respond. The rents D(81) are

l 0 D(81) = L [Q(Pl(8£» I f3Q(PZC8~»] d8?

01 I+XIC8t} 29. The investment level is given by the expression in (21) with the 2 replaced by 1. 30. The opportunism of the regulator here pertains only to information and because of the fair return

requirement does not involve confiscation of second-period quasi-rents on the (sunk) investment made in the first period.

31. It is important to note that the finn would still be provided a fair return in this case through the amortization of B(Xl). If a capital recovery rule were in effect, then B(Xl) would be recovered over some set of periods.

32. The fixed charges Tl can be based on the monitor.

74 PRICE CAPS AND lNCENTIVE REGULATION IN TELECOMMUNICATIONS

33. The mechanism MI is the pair (ql = Q(PI), TI = TI *). where TI * is a constant, so there is no self-selection in the first period.

34. The term 91+1/2 is the expectation of marginal cost. 35. IT commitment were possible, the regulator would implement prices p,(9) = 29 + 1,12, t = 1,2. 36. Technically, the incentive compatibility constraints bind both upwards and downwards. 37. IT the asset were fungible so that the firm could earn 1,12B(xo) on the asset employed elsewhere,

the capital recovery rule would be ineffective in limiting the incentive to underreport costs. 38. This effect is offset if the firm has financed the asset with debt on which the firm could default.

For example, suppose that an 'I] share of B(xo) is financed with debt with a repayment schedule with half repaid in each period. The cash flow of the owners of the firm is then only 1j2(1 - '1]) B(xo). which provides a diminished incentive to participate in the second period.

References

Baron, David P. 1989. "The Design of Regulatory Mechanisms and Institutions." In The Handbook of Industrial Organization, edited by R. Schmalansee and R. Willig (forthcoming).

Baron, David P., and David Besanko. 1984. "Regulation, and Infonnation in a Continuing Relationship." Information, Economics and Policy 1:267-301.

Baron, David P., and David Besanko. 1987a. "Monitoring, Moral Hazard, Asymmetric Infonnation, and Risk Sharing in Procurement Contracting." Rand Journal of Economics 18 (Winter): 509-532.

Baron, David P., and David Besanko. 1987b. "Commitment, and Fairness in a Dynamic Regulatory Relationship." Review of Economic Studies 54:413-436.

Baron, David P., and David Besanko. 1988. "Monitoring of Perfonnance in Organizational Contracting: The Case of Defense Procurement." Scandinavian Journal of Economics 90 (3): 329-356.

Baron, David P., and Roger B. Myerson. 1982. "Regulating a Monopolist with Unknown Costs." Econometrica 50:911-930.

Besanko, David, and David E. M. Sappington. 1988. "Designing Regulatory Policy with Lintited Infonnation." In FundamenJals of Pure and Applied Economics, vol. 20. New York: Harwood.

Caillaud, B., R. Guesnerie, P. Rey, and J. Tirole. 1988. "Government Intervention in Production, and Incentives Theory: A Review of Recent Contributions." RAND Journal of Economics 19 (Spring): 1-26.

Demski, J.S., Sappington, D.E.M., and Spiller P.T. 1986. "Entry in Regulated Industries: An Infonnation-Based Perspective." Working Paper, Bell Communications Research.

Guesnerie, R., and J.J. Laffont. 1984. "A Complete Solution to a Class of Principal-Agent Problems with an Application to the Control of a Self-Managed Firm. " Journal of Pub! ic Economics 25:239-369.

Helman, Leonard A. 1984. "Rulemaking in Lieu of Ad Hoc Case-by-Case Adjudication: Automatic Adjustment Clauses, the New Mexico Experintent." In Regulatory Reform, edited by J.R. Foster, G.R. Hall, S.R. Holmberg, C.F. Phillips, Jr., and R.L. Wallace. Washington, DC: Institute for Study of Regulation, pp. 148-153

Joskow, Paul R., and Schmalensee, Richard. 1986. "Incentive Regulation for Electric Utilities." Yale Journal of Regulation 4 (Fall): 1-49.

Jubelier, Robert C. 1987. "Comment." In Discussion Paper #22, Fishman-Davidson Center, Wharton, University of Pennsylvania (June).


Kahn, Alfred E. 1987. "The Future ofl.ocal Telephone Service: Technology, and Public Policy." Discussion Paper #22 Fishman-Davidson Center, Wharton, University of Pennsylvania (June).

Laffont, J.J., and Tirole, J. 1986. "Using Cost Observation to Regulate Finns." Journal of Political Economy 94:614-641.

Laffont, J.J., and J. Tirole. 1986a. ''The Dynamics of Incentive Contracts." Econometrica 56 (September): 1153-1175.

Noll, Roger E. 1989. "Economic Perspectives on the Politics of Regulation." In Handbook of Industrial Organization, edited by Richard Schmalensee and Robert Willig. NorthHolland (forthcoming).

Sappington, D.E.M. 1982. "Limited Liability Contracts Between Principal and Agent." Journal of Economic Theory 29: 1-21.

Sappington, D.EM., and J. E. Stiglitz. 1986. "Information and Regulation." Working Paper, Bellcore.

Sappington, David E.M. 1983. ''Optimal Regulation of a Multiproduct Monopoly with Unknown Technological Capabilities." Bell Journal of Economics 14:453-463.

Schmidt, Michael. 1984. "Rulemaking in Lieu of Case-by-Case Adjudiction: An Overview of Automatic Adjustment." In Regulatory Reform, edited by J.R. Foster, G.R. Hall, S.R. Holmberg, C.F. Phillips, Jr., and R. L. Wallace. Washington, DC: Institute for Study of Regulation, pp. 136-147.

5 PRODUCTIVITY AND PRICE CAPS IN

TELECOMMUNICATIONS John E. Kwoka, Jr.

1. Introduction

Although proposals for price caps are numerous and varied, all subscribe to the common purpose of strengthening incentives for cost efficiencies. Indeed, at this level of generality, few question the potential for price caps to improve upon conventional rate of return regulation. Major complexities-and disagreementsarise in the process of moving price caps from the economic drawing board to actual practice. This paper will discuss one of the central implementation issues of most price-cap plans, namely, the need to adjust prices for increases in firm productivity.

The paper proceeds as follows. The next section sets out the relevant considerations for adjusting prices under price-cap plans, followed by a discussion of appropriate productivity measurements. Subsequent sections detail and evaluate the actual productivity adjustment in the Federal Communications Commission's price-cap plan for dominant telecommunications carriers, which is the leading operational example of such plans. A summary section concludes the paper.

2. The Need for Productivity Adjustment

In terms of strengthening incentives, completely fixed prices maximize the regulated firm's efforts to reduce costs. Adjustments to price, on the other hand, are necessitated by the fact that, over time, any fixed price will diverge from underlying cost conditions, create profit windfalls or losses, and result in prices that may not even be superior to those under rate of return regulation. To maintain breakeven operation, therefore, prices must change in accordance with changing unit costs.

In principle, the appropriate corrections to price are straightforward. Consider a firm selling a single product Q at price P, in a production process employing a

78 PRICE CAPS AND INCENTIVE REGULATION IN TELECOMMUNCIA TIONS

Table 1. Annual Rate of Growth in Total Factor Productivity A B C D

BLS- Private APC- Christensen- AT&T-Domestic Communica- Bell Bell

Year Business tions System System 1948 3.3 0.8 1949 -0.8 8.0 -1.1 0.6 1950 7.8 9.4 4.5 4.8 1951 3.6 8.6 4.8 5.1 1952 2.2 3.4 2.3 0.1 1953 3.1 6.0 0.9 -0.6 1954 -0.1 3.3 0.8 1.6 1955 3.3 9.2 5.2 5.3 1956 0.6 2.5 1.4 1.1 1957 1.1 7.1 5.2 6.1 1958 0.7 8.9 1.6 2.4 1959 4.0 7.2 5.8 5.4 1960 0.8 3.4 3.9 4.4 1961 2.3 4.0 2.2 2.2 1962 3.2 4.6 3.0 3.2 1963 3.2 4.6 2.3 3.3 1964 3.7 2.0 3.1 2.9 1965 2.6 2.7 2.9 2.7 1966 1.7 3.3 4.3 5.2 1967 0.9 4.1 3.3 3.5 1968 1.8 3.8 4.4 5.2 1969 -0.6 2.6 3.8 3.6 1970 -1.2 3.2 0.6 3.0 1971 1.8 3.9 1.1 0.3 1972 2.9 3.7 4.0 0.0 1973 1.8 2.6 4.3 4.3 1974 -3.6 1.2 3.7 3.2 1975 -0.5 3.6 2.8 4.9 1976 3.1 3.6 4.4 3.8 1977 2.1 1.9 3.6 4.7 1978 1.2 3.3 4.8 3.8 1979 -1.5 0.8 4.2 4.9 1980 -2.2 3.1 1981 0.3 1.4 1982 -2.5 0.4 1983 2.5 8.3 1984 3.4 -3.0 1985 1.2 -1.8 1986 1.2 -0.3

Sources:A - Bureau of Labor Statistics, Multifactor Producti~ Measure 1986. B - American Productivity Center, Multiple I~ut Pr uctivity Indexes. C - L.A. Christensen Testimony in U.S. v. A &T. D - AT&T, Bell System Productivity Study 1947-78.

single input Z that it purchases at price R. Initially, we assume that the fIrm exactly breaks even, so that

PQ-R Z=O, (1)

PRODUCTIVITY AND PRICE CAPS IN TELECOMMUNICATIONS 79

and that the regulatory objective is to set price so as to maintain breakeven operation over time. Denoting the time rate of change of a variable X by X, this in turn requires

(P + Q) - (R + i) = 0, (2a)

or,

(2b)

Equation (2b) gives the necessary price trajectory for breakeven operation.1

Price P must change in each period by the proportional change in input price R, offset by the difference between the growth rates of output Q and input Z. The latter difference represents the changing number of units of input relative to the changing number of units of output, i.e., productivity growth.

An increase in the number of units of output per unit of input may occur as the result of technological change, increased realization of scale economies, and/or improved usage of existing resources. Regardless of the source, measuring such increases in a one-input, one-output case is trivial. An index Tof such change may be defined simply as

(3)

The time rate of change in T is given by the derivative of the natural logarithm of the above expression, or

dH~)) T=---

dt (4a)

=Q-~ ~~ Equation (4b) demonstrates that the rate of growth of output per unit input

productivity-is simply the difference between the rates of growth of Q and Z. By equation (2b), however, that difference was shown to be the necessary adjustment to input price change for establishing new output prices over time. In the humblest terms, if input prices are rising by five percent per annum, but productivity (output per unit input) increases by two percent, then continued breakeven operation by the firm would require only that output prices rise by the difference, or three percent.

This case of a single input used to produce a single output is not at all typical. All firms of interest employ multiple inputs and produce multiple outputs. The now-standard technique for handling such cases, originally developed by Kendrick (1961),1 is so-called total factor productivity. Total factor productivity measures Q and Z in equation (3) by indexes of the firm's multiple outputs and multiple


inputs. Assuming, for example, that the fIrm produces n distinct outputs {qt, ... , qn}, some common metric for combining these quantities is required. That metric is the corresponding vector of prices {Pt. ... , Pn}. Thus, the initial quantity is expressed in dollar terms as:

(5)

Using the same (base-period) prices as weights, this methodology implies the following output index in year 1:

(6)

The ratio of equation (7) to equation (6) is an index of output, and can be written

where

!L.= "W. qi 1 00 (1] Qo L.. I 0

qi

" 0 0 L..Piqi WI = 0 0 •

Pjqj

(7)

(8)

This technique expresses changes in aggregate output Q as the weighted average of changes in individual product quantities, with weights the revenue shares of each product in the base period. This is a Laspeyres index of output change. Precisely the same approach is employed to account for multiple inputs. That is, a Laspeyres index of input change is constructed, using base period cost-shares as weights. The

difference between the rates of change in the output index Ql/QO and the input

index ZI/z? yields total factor productivity, in accordance with equation (4b). This description is essentially the original formulation of total factor produc

tivity. Diewart (1976, 1978) has shown that the Laspeyres, base-weighting procedure yields exact results only for a linear homogenous production function in which all inputs are perfect substitutes. Otherwise, changing input prices induce changes in factor proportions, which in turn cause growing divergence from the path given by the Laspeyres assumption of constant cost and revenue shares.

The theoretically superior formulation for more general production technologies is provided by the so-called Divisia index. That index is exact for a translog production function, and since the translog form provides a second-order approximation to any arbitrary production function, the Divisia index has quite general applicability. The Divisia index, however, is defined on continuous-time variables, whereas economic data basically come in discrete-time form. As a result,


a discrete-time approximation to the Divisia index is generally employed, the most useful being that due to Tornqvist and given by

(9)

Here Wi = .5(wl + wp), that is, the simple average of the base-period and the current-period weights.

The need for current period data for construction of the weights in the Tornqvist approximation represents a practical obstacle to its use. Moreover, the constantly changing weights imply that the Tornqvist index changes even when the values of the underlying quantity variables do not, a feature often at odds with intuition about such indexes. For these reasons, most-but not all-empirical estimation has employed the base-weighted, Laspeyres methodology.

Actual indexes of total factor productivity may take several forms. The most common variants involve either two or three factors-labor and capital, and possibly purchased materials. Two-factor productivity is most often employed for more aggregated, economy-wide measurement, in which materials purchases largely (except for imports and exports) cancel out. For individual industries or firms, however, materials usage may be subject to productivity differences and changes, and are more appropriately included. Two- and three-factor productivity measures are not directly comparable, since the exclusion of materials tends to make two-factor values larger.3

Each input, as well as the multiple outputs, typically requires subaggregation of various types of the factor. For example, several different occupational groups and skill levels may be separately accounted for in constructing the labor input variable. Capital input measurement, however, is undoubtedly the most complicated component of the task. Different capital of different vintages and technology comprise current stock, which stock, in tum, is subject to different utilization rates. A host of procedures is required to adjust these data and ultimately to derive a measure of the current flow of capital services.4

3. Price Caps in Telecommunciations

Perhaps the major example of the use of price-cap regulation with productivity adjustment is the Federal Communications Commission plan to cap AT&T's long-distance telephone rates and the access prices charged by local exchange carriers. The FCC inquiry opened in August, 1987, and concluded for AT&T in April, 1989 (FCC, 1987, 1988, 1989). The heart of the plan is a cap on a set of price indexes of its various services, subject to limitations on individual service price movements. The cap changes over time in accordance with changes in certain


"exogenous" costs that are regulatory-determined (e.g., AT&T's access charges), input cost inflation, and productivity increases.

The role of these factors is made clear from equation (2) above. For the inflation measure, the FCC adopted the fixed-weight GNP deflator, sometimes called the GNP Price Index or GNP-PI. With respect to productivity, the FCC decided against actually undertaking its own ongoing calculation of productivity. The reasons were twofold. First, the procedures involved in estimating productivity are so complex and judgmental that controversy would inevitably attend any results. Little or nothing would be accomplished if the parties that previously contested key parameters of rate-of-return regulation simply redirected their attention to periodic productivity measurement.

Secondly, an accurate measure of current productivity could not in any event be used to adjust prices directly, since full contemporaneous adjustment would diminish the firm's incentive to conserve on costs. The alternative to direct estimation of the productivity offset is use of some benchmark estimate of telecommunications carrier productivity, i.e., a long-term average or evidence from comparable firms. This has the advantages of once-and-for-all determination, and of exogeneity from the regulated firm's behavior so that (as with fixed prices) incentives are maximized.

Two methodological issues concerning this benchmark approach deserve mention. If the productivity of AT&T and the local exchange carriers is similar to that of the economy as a whole, then no explicit productivity adjustment would be required in a price formula. The reason is that inclusion of an index of price inflation would already correct for economy-wide average productivity gains, i.e., it would be measuring precisely those price changes that remain after such productivity gains are realized.

As a result, it is necessary first to determine the economy-wide average productivity and then whether the productivity of the price-capped flrm or sector diverges from that standard. As we shall see, a considerable body of undisputed literature exists indicating that telecommunications in general and AT&T in particular have long achieved above-average productivity. Therefore, reliance on economy-wide averages would understate this sector's actual productivity, understate the appropriate offset to cost inflation, and lead to excessive prices.

A second methodological issue arises from the fact that all measures of the productivity of telecommunications firms or the industry are necessarily calculated in a rate-of-return environment. Not only does such regulation lower the absolute level of productivity, but it appears that under some circumstances it may also lead to incorrect estimates of the rate of change. Denny, Fuss, and Waverman (1981) derive results showing the nature of the possible bias, but Cowing, Small, and Stevenson (1981) perform some simulations that suggest the magnitude of distortion is quite small. Their results depend on the degree of regulatory stringency and the gap between the cost of capital and the allowed rate of return, but never exceed


0.3 percent of measured productivity. Hence, it appears safe to ignore this possible discrepancy.

For comparison with telecommunications productivity, the appropriate reference may be taken as the Bureau of Labor Statistics Multifactor Productivity Index for the private business sector (BLS, 1987). Annual percentage changes in this measure are given in Column A of table 1. They show that economy-wide productivity rose by an annual average of 1.4 percent from 1949 to 1986, although the rate of increase dropped to 0.4 percent in the post-1973 period. Telecommunications industry productivity measures were sought for comparison with this standard. The BLS itself has indicated plans to develop a multifactor productivity measure for telecommunications, as it has already done for other major business sectors. But this index does not yet exist and persistent data difficulties suggest that it will not be available for some time.

For the telecommunications industry in particular, the only existing index of productivity is one constructed by the American Productivity Center, a private group that uses governmental data for two-factor productivity indexes of numerous sectors of the economy (American Productivity Center, various issues). The productivity increases that it calculates for this sector are in Column B of table 1. They average 3.9 percent over the 1948-85 period, declining steadily from 5.6 percent in 1948-65, to merely 1.3 percent in 1979-85. There are, however, several concerns with the APC index. These include some nontelecommunications activities included within its "Communications" sector, its use of the narrower two-factor productivity, and the peculiar behavior of its index in the past few years (declining rather sharply, when other evidence suggests otherwise). In terms of its utility for the FCC price-cap plan, it is also relevant that its sponsors include major telecommunications firms.

For these reasons, the FCC placed principal reliance on a number of studies of AT&T's own productivity. Two of these studies were submitted by AT&T in the context of the antitrust suit brought by the Department of Justice, and one other represents its own internal productivity study. Each deserves brief description.

One study, performed by Christensen (1981), measured total factor productivity for the Bell System as a whole for the years 1947-79. Christensen defined five output variables-local service, interstate toll, intrastate toll, directory assistance, and miscellaneous services-and examined labor services, capital services, and raw materials as factors. All outputs and inputs were aggregated according to the Tornqvist approximation to the Divisia index. Christensen's results are reproduced in Column C of Table 1. They show Bell System productivity averaging 3.2 percent per year between 1948 and 1979, with annual increases ranging from -1.1 to 5.8 percent. In order to determine the differential relative to the overall economy, Christensen cites his work with Jorgensen that estimated annual productivity growth for the entire private U.S. economy, akin to the BLS measure described above. Based on those figures, he deduces a productivity differential of 2.1 percent for the Bell System.


The data also reveal a notable trend. From 1947 through 1966, the differential favoring the Bell System was 1.6 percent, whereas from 1966 to 1978, it grew to fully 3.0 percent. Most of the differential was due the collapse of productivity in the private economy in the later period.5 Bell System productivity was 3.4 percent-slightly higher than its long-term average--but the private economy as a whole achieved only 0.4 percent growth in productivity.

Christensen performed an essentially parallel study of Bell System productivity using less precise public data on SIC 481, the Telephone Industry. From these, he deduced Bell System total factor productivity of 3.2 percent for the 1947-79 interval, identical to his direct estimate. The disaggregation of SIC 481, while involving difficult procedures, permitted an estimate of the non-Bell portion, largely the independent local exchange carriers. For these, Christensen estimated a considerably smaller productivity of 1.9 percent during the same period.

A second study filed in the antitrust suit was performed by Kendrick himself (Kendrick 1982). This study used the same five output definilions as above, but examined only two factors-labor and capital. Between 1948 and 1979, Bell System productivity increases were found to average 4.9 percent annUally. Relative to the economy-wide average of 2.0 percent that Kendrick reports as comparable, this implies an annual differential of 2.9 percent.6 Although somewhat greater than the results reported above, most of the discrepancy is undoubtedly due to the use of two-factor productivity, as previously discussed.

AT&T has routinely conducted its own internal study of Bell System total factor productivity, using methodology originally developed for it by Kendrick. One such study was put on the record of the FCC's price-cap proceeding (AT&T, 1979). It reports both two-factor productivity as well as the more inclusive three-factor version. The AT&T study concluded that, over the 1947-78 period, three-factor productivity grew at an average annual rate of 3.2 percent, whereas two-factor productivity averaged 3.7 percent annual growth. The latter figure was compared to an economy-wide benchmark of 1.9 percent reported by AT&T, implying a 1.8 percent differential favoring the Bell System.

As with preceding estimates, AT&T's study showed that the differential grew over this interval. From 1948 to 1965, AT&T two-factor productivity averaged 3.5 percent, compared to 2.4 percent for the economy as a whole. From 1965-72, the analogous figures were 3.7 percent and 1.6 percent, and for 1972-78, they were 4.9 percent and 1.0 percent. Therefore, the differential favoring the Bell System initially was 1.1 percent, rising to 2.1 percent and ultimately to 3.9 percent. In contrast to the two previous studies, more of the growing differential reflects rising Bell System productivity and not simply declining productivity in the economy as a whole.

To varying degrees, three other published studies of productivity corroborate these findings. The first, due to Nadiri and Schankerman (1981) distinguishes four inputs, adding research and development to the conventional three, and four outputs-local service, interstate toll, intrastate toll, and miscellaneous. Using

PRODUCTIVITY AND PRICE CAPS IN TELECOMMUNICA nONS 85

proprietary data for the period 1947-76, they estimated thattotal factor productivity grew at an annual average rate of 4.1 percent. rising from 3.5 percent in 1947-57, to 3.6 percent in 1958-67, and to 5.0 percent in 1968-76. These estimates differed slightly for various assumptions concerning demand elasticity.

Two studies have been conducted for productivity in Bell Canada, but because of differences in both scale economy realization and regulatory environment between Canada and the U.S., the results need to be interpreted cautiously. Denny, Fuss, and Wavennan (1981) found annual increase in total factor productivity averaging 3.4 percent from 1952-76. Productivity grew steadily from 1.3 percent in 1952-57 to 4.5 percent in the last five years of the period. Kiss's econometric approach found Bell Canada productivity growing at an annual average rate of 3.44 percent, with more varied gains by subperiod (Kiss 1983). Despite the caveats, the similarity of these results to those reported for the U.S. Bell System is striking.

Further evidence concerning the productivity of the Bell System emerges from an alternative measurement technique. By combining equations (2b) and (4b), one observes that

(10)

That is, the change in total factor productivity (Q - Z) can equivalently be stated as the difference between the rate of growth of input prices (R) and the rate of growth of output prices (P) in the industry. Recalling the earlier example, if input prices rise by 5 percent but output prices increase on11 3 percent. then implied productivity is 2 percent, holding other things constant.

This "implied productivity" approach was also employed by the FCC. The BLS data series on the prices of local and long distance telephone services dating back to 1935 shows an annual average increase of 2.25 percent through 1985.8 Overall CPI-as a benchmark measure of input price increases, since GNP-PI does not exist that far back-i"Ose by 4.20 percent per year, implying a productivity differential of 1.95 for that period. This number is remarkably similar to results such as Christensen's.

Moreover, as do the direct productivity studies, the price data show rising differentials in more recent periods. For example, from 1955 to 1985, telephone prices rose by 2.53 percent annually, compared to overall CPI averaging 4.74 percent. The differential therefore rose to 2.21. In the last ten-year period, the differential increased further, to 2.64 percent. as telephone prices rose by 4.53 percent but overall prices climbed 7.17 percent. All of this evidence is strongly corroborative of the direct productivity estimates.

However consistent these results, little of the evidence bears on the question of the productivity in long-distance service relative to local exchange or access services. Indeed, for most of this period, such a distinction cannot be drawn from existing data, because of the confounding role of separations in the economics of local vs. long-distance service. Starting in 1943, a certain percentage of the costs


associated with the local loop was assigned to interstate Message Toll Service (MTS). By the early 1980s the percentage grew to about 33 percent, and these costs comprised nearly one-half of the per minute charge for MTS. As a result, all indexes of interstate or local rates in this period have embedded within them an essentially arbitrary allocation of very large system costs, and are unreliable guides to underlying cost or productivity changes.

The FCC price-cap plan, however, contemplates eventually capping the prices ofLEC interstate services as well as AT&T's. Apart from Christensen's result for the independent telephone companies, the only result at all relevant to this disaggregation is again for the Canadian telecommunications system. Denny, deFontenay and Werner's results (1983) are given in table 2, showing that Bell Canada (primarily a provider oflong-distance service) achieved 3.2 percent annual productivity growth, whereas two provincial companies, over slightly different time periods, achieved 3.2 percent and 6.2 percent, respectively. These numbers suggest the possibility of significant differentials between long-distance and local telecommunications service, and indeed, among fmns providing the latter.9 More direct evidence on productivity differentiation was sought by the FCC, focusing on the post-divestiture period in which meaningful disaggregation oflocal and long distance service is more feasible. One piece of such evidence was the FCC's own calculation of AT&T's implied productivity in the price-cap order (FCC, 1989, Appendix C).IO In the four-year period from divestiture to early 1988, the FCC calculated that AT&T's MTS rates declined by 34 percent. Most of that, however, was due to FCC-mandated reductions in access charges, costs not subject to productivity gains. I I Thus, the procedure netted out the effects of various regulatory cost changes, resulting in an annual MTS price change of (positive) 1.28 percent Since GNP-PI rose by 3.60 percent ~er year during this interval, AT&T's implied productivity gain was 2.32 percent. I

Table 2. Annual Rate of Growth of Total Factor Productivity

Year 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979

British Columbia . Alberta Government Telephone Telephone

2.9 5.9 6.0 4.4

-2.2 3.0 2.5

5.3 5.5 4.6 4.2 9.3 7.7

11.9 8.3 3.3 6.6 2.0

Bell Canada 5.9 4.3 2.9 3.7 -0.5 3.7 4.7 4.4 6.9 1.0 0.7 2.3 2.2

Source: Denny, de Fontenay, and Werner. "Comparing the Efficiency of Firms." In Economic Analysis of Telecommunications, edited by Courville, de Fontenay, and Dobell.

PRODUCITVITY AND PRICE CAPS IN TELECOMMUNICATIONS

Table 3. Annual Rate of Growth of Implied Total Factor Productivity (1984-88) Un~ TFP Ameritech Bell Atlantic BeliSouth NYNEX Pacific Southwestern US West 7 RBOC Average Total Industry

1.28 -1.26 -2.61 -0.19 0.35 0.99 6.59 0.62

-0.70

87

Source: Bell Communications Research. 1988. "Impact of FCC Proposed Price Cap Plan on Interstate Consumers-Regional Disaggregation."

The FCC requested the Bell Operating Companies to conduct and provide similar studies of their individual productivity experiences since divestiture to determine whether their productivity adjustment should differ. Initially, the BOCs provided only a study of their combined productivity, calculated as 0.67 percent after correction for regulatory cost changes (Bellcore, August 1988). A subsequent submission disaggregated this result, all the while disputing the reliability and significance of the very large reported differences among the regional Bell holding companies (Bellcore, September 1988). Those productivity estimates are reproduced in table 3.

Both of these studies were subject to intense controversy and criticism in the FCC proceeding. It became clear that the process of correcting revenue flows for various regulatory cost changes can be as difficult and contentious as the direct calculation of productivity. Nonetheless, it is clear that the evidence does not support the view that AT&T and BOC productivity are the same, or even that productivity arrwng the BOCs is similar. We will return to some of the implications of these observations below.

4. Evaluation of the FCC's Evidence

Based on these studies, the FCC concluded that the long-term productivity increases of the telephone industry have averaged approximately 2 percent per year in excess of the overall private economy. However, since this differential has been rising in more recent periods, a better prediction of likely future productivity was taken to be 2.5 percent. Further, in order to ensure net consumer benefit from greater productivity increases, the FCC proposed that prices13 be adjusted by an additional 0.5 percent per year, for a total of 3.0. In terms of the original formulation, therefore, the FCC's price cap plan would change prices each year in the amount of the change in GNP-PI less 3.0 percent.


This general conclusion seems well supported by the evidence. Most of the productivity studies, plus the price evidence, all suggest a differential favoring the Bell System of between 2.0 and 3.0 percent, the larger numbers characterizing more recent years. Although there are some differences in the detailed results of these studies, their similarities predominate. For example, perhaps the most closely matched series-those due to Christensen and AT&T in table I-are highly correlated, with a simple correlation coefficient of .91. They appear to be estimating similar phenomena in a consistent fashion, providing a sound basis for such a conclusion.

The productivity number is a long-term average, of course, subject in any year to a variety of forces that may yield larger or smaller changes. From a policy perspective, annual discrepancies are important since they represent temporary over- or under-payments by consumers to telephone companies, and corresponding windfalls or shortfalls in current revenues to the regulated companies. The revenue consequences of even modest discrepancies are strikingly large. Consider the following stylized example: Let the regulated company's revenue requirement be 100, consisting of operating cost ono, taxes of 10 (based on a tax rate of one-third of operating profit of 30), and accounting profit of 20. With total invested capital of 200, this implies achievement of an assumed authorized rate of return of 10 percent (20 on 200).

Now let revenue requirements be reduced by 3 percent per year, based on long-term average productivity gains and assuming no demand expansion. But in some particular year, assume actual costs fall by 5 percent, that is, two percentage points more than the long-term average. If all costs, including total invested capital, are subject to such gains, the realized rate of return immediately rises to 10.7 percent. If this differential persists, then within five years the company earns 13.7 percent on invested capital, 37 percent in excess of the authorized rate of return. I 4

The extent of variation in the actual data series is illustrated in table 1. For example, the standard deviation of Christensen's annual estimates is 1.6 percent. IS

The average absolute value of deviation is 1.3 percent, ranging from positive 2.6 percent to negative 4.3 percent. This degree of variation is clearly substantial.

The more relevant test of deviations would be a comparison of the FCC formula-the change in GNP-PI minus 3.0 percent-with "actual" values of the productivity differential. The latter can only be estimated, but certain results are nonetheless suggestive. Figure 1 presents the FCC formula as well as an approximation of actual values given by the difference between AT&T's own productivity calculation (column 4 in table 1) and the BLS economy-wide figure (column 1 in table 1).

The series differ in absolute magnitude, with the formula averaging 1.3 percent and actual values averaging 1.8 percent. The average annual absolute value of the difference between the "actual" values and the FCC formula values underlying figure 1 is 2.2 percent, although for the 1970s, this declines to 1.3 percent. Actual values tend to move more smoothly, while the formula is more strongly affected

PRODUCTIVI1Y AND PRICE CAPS IN TELECOMMUNICATIONS 89

by wide swings in the inflation rate. Overall, the series exhibit a simple correlation of.62.

These discrepancies are obviously not trivial, particularly in light of the stylized example above. Yet one might respond that the relevant standard of comparison for policy purposes is not this discrepancy per se, but how this discrepancy compares to that that arises under rate-of-return regulation. The FCC formula would undoubtedly fare better in that comparison.

Further problems attend the effort to apply price caps to the local exchange carriers. To the extent that the LECs have persistently different rates of productivity change, application of the average--or any single number-will result in persistent excess profits to some and losses to others. As the above numerical illustration shows, the realized rate of return of a carrier achieving 5 percent productivity but subject to a 3 percent productivity adjustment will rise by several percentage points in a very few years.

For this reason, capping the prices of differentiated firms requires either firmspecific productivity factors, or alternatively, some feedback mechanism by which errors are identified and rectified. Unfortunately, reliable estimation of firmspecific productivity factors for the 1400 local exchange carriers, or even the seven regional holding companies, is a virtually intractable problem. The controversy surrounding the efforts of the RBOCs thus far makes clear that such estimates will have difficulty standing up to scrutiny.

The alternative is to establish some initial common productivity value for all the carriers, and then to adjust it (or equivalently, directly adjust prices) in accordance with evidence regarding each firm's individual productivity. For example, the so-called "sliding scale" is a long-recognized device by which realized profits (or rate of return) are used as a guide for adjusting prices in a subsequent period of time, high profits indicative of high productivity and the need for price reductions, and low profits the reverse.16 Versions of the sliding scale are present-or at least implicit-in the fixed price plan adopted by the New York State Department of Public Services for New York Telephone and in other price-cap-type plans.

The FCC's proceeding with respect to the local exchange carriers has proposed a similar adjuster, termed an "automatic stabilizer" (FCC, 1989). Whenever a firm's realized rate of return falls outside a 2 percent band around the target rate, the price cap in the following period would be adjusted so as to return the firm's earnings to that band. Thus the firm bears the full profit consequences-positive or negative-up to two percentage points in its rate of return, and the consequences of further deviations for precisely one year, after which its earnings are restored. Whether this represents the optimal structure for firm and consumer sharing of risk and benefit is doubtful, although the principle of the automatic stabilizer is well suited to the problem of LEC productivity differentiation.17


5. Conclusion

Price caps have considerable promise as a regulatory tool. As with most public policies, however, implementation of price caps requires careful analysis and judgment concerning important policy parameters. The productivity adjustment is an example of such a parameter. The choice of productivity factor plays a crucial role in maintaining correspondence between price and cost. It affects large revenue flows and realized rates of return. And it is visible and readily understood. The choice is, therefore, both important and public.

f

o r m u 1

a

10

a c t u

a 1

-2.5 4------------+-----------+----------~----------~

1960 year 1980 comparison of FCC Formula Adjustments and 'Actual' Values

This article has used the Federal Communications Commission's price cap plan as an extended case study of the issues involved in selecting an appropriate productivity offset for telecommunications carriers. Among the alternatives available to the FCC, its chosen approach seems sound, although we have remarked on issues that arise as the result of normal variation in annual productivity, inflation,

PRODUCTIVITY AND PRICE CAPS 1N TELECOMMUNICA nONS 91

and cost changes, as well as discrepancies among carriers whose productivity experience appears to differ significantly. Attention to these various concerns will ensure the realization of the potential of price-cap regulation.

Notes

The author is Professor of Economics, George Washington University, and has served as Special Assistant to the Chief, Common Carrier Bureau, Federal Communications Commission, on the FCC price-cap proposal. The opinions in this article should be construed as reflecting views of the FCC.

1. If the firm initially was not breaking even, equation (2) would still hold so long as the magnitude of profits did not change. A change in profits would require modifying equation (2b) to read

P=R-(Q-Z)-n where n represents the rate of change in profits.

2. See also Denison (1962) for early development and Cowing and Stevenson (1981) for recent discussion and references.

3. This is true even though two-factor measures exclude materials from their output definition. That is, they employ value added instead of total output as the relevant variable.

4. For illustrative discussion of the complexities, see, for example, Christensen (1981). 5. The forces responsible for this collapse are much in dispute, and in any event appear to have been

arrested and slightly reversed in the mid to late 1980s. 6. Kendrick's testimony did not report results by year, although some detail was later published in

his book, Improving Company Productivity (Kendrick, 1984). 7. Also noted previously, among the other things that must be held constant is the level of profit,

i.e., the degree of regulatory sttingency. 8. These and other data employed in this paragraph are conveniently gathered in r. Lande and P.

Wynns (1987). 9. One possible reason for differentials among provincial companies in Canada, and among the

LECs in the U.S., is differing rates of demand growth in various regions. Persistent productivity differentials characterize other regulated industries. See, for example, Caves, Christensen, and Trethway (1981) and Gollop and Roberts (1981).

10. Slightly different numbers appeared in the FCC's Second Notice, (FCC, 1988). 11. As previously noted, access charges and certain otherregulatory-imposed costs are not included

within the FCC price-cap plan, since they represent uncontrollable cost factors not subject to cost-saving efficiencies.

12. Kiss objects to this calculation, asserting that it is inconsistent with the simultaneous use of GNP-PI in the FCC formula (F. Kiss, 1989). This calculation, however, is a separate exercise designed to corroborate other productivity estimates. It does not, and need not, presume the various corollary conditions Kiss asserts.

13. As noted previously, the actual FCC plan involved movements of weighted average prices, with some secondary limits on individual price changes.

14. One might contend that capital stock is not subject to the same productivity improvement possibilities as other factors. This example can be modified to reflect alternative assumptions, for example, that productivity gains are limited to operating costs, OrlO operating costs plus new investment. These alternatives, of course, must imply proportionally larger productivity gains on those otherfactors if total factor productivity rises by 5 percent.

15. Christensen's data are taken as typical for this exercise. Similar results would emerge using most of the other candidates.

16. The sliding scale is originally discussed in Bussing (1936) and more recently in Schmalensee (1979).

17. For discussion of sharing formulas, see Kwoka (1988).


References

American Productivity Center. Various years. Multiple Input Productivity Indexes. Houston, TX.

AT&T 1979. Bell System Productivity Study 1947-78 (November). Bureau of Labor and Statistics. 1987. Multifactor Productivity Measures, 1986 (October

13). Bell Communications Research. 1988. "The Impact of the FCC Proposed Price Cap Plan on

Interstate Consumers." (August 18). Bell Communications Research. 1988. "The Impact of the FCC Proposed Price Cap Plan on

Interstate Consumers-Regional Disaggragation." (September 8). Bussing, I. 1936. Public Utility Regulation and the So-Called Sliding Scale. New York:

Columbia University Press. Caves, D., L. Christensen, and M. Trethway. 1981. "U.S. Trunk Carriers, 1972-77: A

Multilateral Comparison of Total Factor Productivity." In Productivity Measurement in RegulatedIndustries, edited byT. Cowing and R. Stevenson. New York: Academic Press.

Christensen, L. 1981. "Testimony." u.s. v. AT &T(C.A. 74-1698). Cowing, T., J. Small, and R. Stevenson. 1981. "Comparative Measures of Total Factor

Productivity in the Regulated Sector." In Productivity Measurement in Regulated Industries, edited by T. Cowing and R. Stevenson. New York: Academic Press.

Denison, E. 1962. ''The Sources of Economic Growth in the United States." New York: Committee for Economic Development.

Denny,M.,M. Fuss, andL. Waverman.1981. ''The Measurement and Interpretation of Total Factor Productivity in Regulated Industries, with an Application to Canadian Telecommunications."InProductivityMeasurementinRegulatedIndustries,editedbyT. Cowing and R. Stevenson. New York: Academic Press.

Denny, M., A. de Fontenay, and M. Werner. 1983. "Comparing the Efficiency of Firms." In Economic Analysis of Telecommunications, edited by L. Courville, A. de Fontenay, and R. Dobell. Amsterdam: North-Holland.

Diewart, W.E. 1976. "Exact and Superlative Index Numbers." Journal of Econometrics 4(May): 115-145.

Diewart, W.E. 1978. "Superlative Index Numbers and Consistency in Aggregation." Econometrica 46:889-900.

Federal Communications Commission. 1987. "Policy and Rules Concerning Rates for Dorninant Carriers." Notice of Proposed Rulemaking (August).

Federal Comrninications Commission. 1988. Further Notice of Proposed Rulemaking (May).

Federal Communications Commission. 1989. Report and Order and Second Further Notice of Proposed Ru1emaking (March).

Federal Communications Commission. 1989. Final Oder (April). Gollup, F., and M. Roberts. 1981. "The Sources of Economic Growth in the U.S. Electric

Power Industry." In Productivity Measurement in Regulated Industries, edited by T. Cowing and R. Stevenson. New York: Academic Press.

Kendrick, John W. 1961. Productivity Trends in the United States. Princeton, NJ: Princeton University Press.

Kendrick, John W. 1984. Improving Company Productivity. Baltimore, MD: Johns Hopkins University Press.

PRODUCTIVITY AND PRlCE CAPS IN TELECOMMUNICATIONS 93

Kiss, Ferenc. 1983. "Productivity Gains in Bell Canada." In Economic Analysis of Telecommunications, edited by L. Courville, A. de Fontenay, and R. Dobell. Amsterdam: N orth-Holland.

Kiss, Ferenc. 1989. "Constant and Variable Productivity Adjustments in Price Cap Regulation." Bell Communications Reasearch, Mimeo.

Kwoka, John E., Jr. 1988. "Design Criteria for Incentive Regulation." In proceedings from District of Columbia Public Services Commission Symposium on "Competition and Technological Change in State Telephone Markets." Washington, DC (October).

Lande, J., and P. Wynns (1987). "Primer and Sourcebook on Telephone Price Indexes and Rate Levels." FCC (April).

Nadiri, M. Ishaq, and Mark Schankerman. 1981. "The Structure of Production, Technological Change, and the Rate of Growth of Total Productivity in the U.S. Bell System." In Productivity Measurement in Regulated Industries, edited by T. Cowing and R. Stevenson. New York: Academic Press.

Schmalensee, Richard. 1979. The Control of Natural Monopolies. Lexington, MA: Lexington Books.

6 CONSTANT AND VARIABLE

PRODUCTIVITY ADJUSTMENTS FOR PRICE-CAP REGULATION

Ferenc Kiss

It has been suggested by several studies! that price-cap regulation with an adjustment formula for inflation and productivity is capable of offering incentives for regulated firms to improve their efficiency by minimizing costs under existing technologies as well as by improving technologies via increased innovation. It has also been suggested that the allocative efficiency of prices may improve under the price-cap regime, and that considerable social welfare improvement may result from it and from the greater efficiency of the production processes of regulated firms. Whether and to what extent the FCC's now emerging price-cap regulation for U.S. telecommunications will deliver these benefits depends, among other things, on how well its design and execution are adapted to the behavioral characteristics of input prices and productivity in the regulated sector of the U.S. telecommunications industry. Utilizing a broad rnnge of information from empirical evidence on the productivity performances of regulated telecommunications carriers in the past to econometric productivity analysis, this article explores what is, paradoxically, perhaps the most important as well as the least understood aspect of price-cap regulation: productivity adjustments.2

The subject allows for certain simplifying assumptions with regard to the features of the regulatory regime.3 A single aggregate price cap is assumed for all regulated outputs. The price cap is subject to contract negotiations between the regulatory agency and the regulated firm for specified contract periods. The contract periods are severnl years long. Once agreed upon, the price cap does not necessarily remain fixed until the next round of negotiations but becomes subject to intercontractual adjustments. The negotiating parties agree in advance on the precise method of adjustments and also set up both trigger mechanisms and


emergency procedures, in case significant unforeseen cost changes render the agreed upon formula inoperable. The negotiating parties agree that the adjustments are to reflect changes in the cost of production during contract periods. Cost changes are reflected in index numbers of input price, productivity, and specified exogenous cost items. The actual regulatory process consists of (1) negotiations and the resulting input price and productivity adjustment formulae; (2) post factum verification of compliance, say, once a year;4 (3) punitive price adjustment if the regulated firm fails to comply; (4) re-negotiation at the end of the contract period.

The article consists of eight sections. Section 1 describes the general form of the price-cap formula and discusses the various ways in which the price-cap formula may offer incentives to the regulated firm to minimize its production costs. Section 2 deals with the importance of the accuracy of price adjustments in price-cap regulation. Section 3 discusses incentive compatibility for price adjustment formulae. Section 4 investigates the empirical performance of four productivity indexes which may be considered for the price-cap formula. Section 5 shows how price index adjustments would have performed for pre-divestiture AT&T during the 1970's. Since neither the investigated productivity indexes nor the hypothetical AT&T price cap are satisfactory, Section 6 takes an analytic approach and uses causal variables of productivity gains to construct a variable productivity adjustment formula, which can be expected to perform better than existing and proposed formulae. Section 7 details the author's recommendations for variable productivity adjustments, while Section 8 summarizes the recommended formula and evaluates its foreseeable weaknesses and advantages.

1. Output Price Adjustments and Incentive Factors

As several sources-for example, Vogelsang (1988)-suggest, the longer the contractual period the greater the incentive most versions of price-cap regulation offer to the regulated firm to increase its productivity. For this reason, periods are expected to be several years long. This article analyzes cost characteristics for four-year periods. It is likely that unit costs change significantly, in both foreseen and unforeseen ways, during longer periods of time. Hence the need to adjust price caps during contract periods. The price cap allows price adjustments, whenever unit costs change to such a degree that the regulated firm would earn either too much or too little profit under constant prices, relative to the terms of the existing regulatory contract. The objective of the adjustments is to keep the profits of the regulated firm within reasonable limits.

There are three generic sources of cost increases in regulatory contract periods with which price adjustments should concern themselves. These are:

1. Cost inflation; i.e., exogenous inflationary increases in the purchase prices of factor inputs which the firm uses in order to produce its output of telecommunications services.S

CONSTANTN ARIABLE PRODUCTIVITY ADJUSTMENTS FOR PRICE CAPS 97

2. Productivity gains; Le., factor input volume, and thus cost, savings relative to the volume of output produced due to the improved efficiency of the production process of the firm.

3. Exogenous changes in "prescribed" costs. A cost item is prescribed if its magnitude is determined by rules set by outside (government and other) agencies. The examples include taxes, access line charges for interexchange carriers, or changes in separations procedures for local exchange carriers. A cost change is exogenous if, and to the extent, it is due to changes in the rules that govern the cost items; e.g., changes in tax rates or the tax base. Bell Communications Research (1988) itemizes and estimates the magnitude often exogenous changes in prescribed cost items for local exchange carriers.

In addition to cost changes, imperfections in the price-cap formula, non-compliance with the price cap, errors in managerial decision making, and exogenous events may lead to changes in the economic profits of the regulated firm by creating either inadequate or excessive profits, or changes in their magnitudes. Changes in economic profits constitute the fourth component of the price-cap formula. In the telecommunications industry, it is not the price itself but the temporal price index of regulated services that is capped. Price-cap regulation is synonymous with limiting (capping) aggregate output price changes over time. Its most general form is:

p = cww + cy y - -n: ; (1)

where p denotes the proportionate (percentage) change in the price cap over time (e.g., annually); w denotes the proportionate change in the price index of the non-prescribed inputs of the regulated firm; y refers to the proportionate change in prescribed costs; Cw and cy are cost shares for the non-prescribed and prescribed factor inputs, respectively; is the annual total factor productivity (TFP) gain; and it is the proportionate change over time in the economic profit of the regulated firm. Applied post factum, this formula suggests that if inflationary increases in the purchase prices of productive factors alone have increased, say, 80 percent of costs by 4.75 percent (w = 0.04 75), and prescribed costs, amounting to 20 percent of the total production cost of the firm have undergone an exogenous increase of 8 percent <y = 0.08), while the productivity of the firm has improved by 2.1 percent ( = 0.021) and there is no economic profit; then a 2.3 percent price increase (jJ = 0.023) would leave the firm approximately in the same financial position as it enjoyed before the changes took place.

The components of the price adjustment formula of equation (1) may be endogenous or exogenous to the regulated firm. For example, y is exogenous by definition. While some components may be clearly one or the other, most contain both endogenous and exogenous elements. Both wand represent such mixed components, although w is typically mostly exogenous. Regulatory incentives are to be provided in order to influence the firm's decision regarding the endogenous factors of the price adjustment formula in a socially favorable manner. The incentives are built into the price adjustment formula as explicit or implicit


incentive factors which allow the firm to have a share in the profits that result from realizing favorable changes in the endogenous components, and force the fIrm to carry part of the burden that results from unfavorable changes. Contract negotiations formulate expectations for the following contract period regarding each component of the price cap. A system of incentive factors is also agreed upon and explicitly or implicitly included in the adjustment formula. The general form of the price adjustment formula with a full set of explicit incentive factors is:

P = cw(uewe + uat.wl + t.w2) + cy y - (~e<Pe + ~at.<Pl + t.<P2) ; (2)

where subscript e refers to expectations as fonnulated in the regulatory contract, and the deviation between expectation and the subsequent actual value of both input price change and productivity gain is broken down into endogenous (t.Wl and t.<Pl, respectively) and exogenous (t.W2 and t.<P2, respectively) parts. The price cap is fully adjusted for the changes in both exogenous deviations (t.W2 and t.<P2), while the benefits from both endogenous deviations (t.Wl and t.<Pl) are shared between the fIrm and its customers according to the incentive factors Ua and ~a, respectively. The input price expectation We and the productivity expectation cPe are also shared because they contain endogenous as well as exogenous elements.

Unfortunately, it is often impossible to distinguish between the endogenous and exogenous elements of changes in input prices and productivity. The information necessary to disentangle endogenous and exogenous changes is seldom available. Furthermore, in many cases, the endogenous and exogenous aspects co-exist and are intertwined to such a degree that it is not possible to "allocate" them, even in the presence of extensive information. Only the full deviations of the actual input price and productivity from their respective expected values are known and can be incorporated into the adjustment formula in the following manner:

P = cw(uewe + uat.w) + cyY - (~ecPe + ~at.<P)· (3)

Their inability to separate endogenous and exogenous factors certainly hampers the ability of price-cap fonnulae to offer clear and strong cost minimizing incentives. While this weakness is widely regarded as incurable, a careful selection of incentive factors may help reduce its negative impact. For example, the value of ua would normally be close to one because most deviations from expected changes in the input price index may be characterized as exogenous. Other considerations are mentioned below.

Several price-cap formulae exist or have been proposed in Great Britain and in the U.S. None of these formulae contains but they all imply a full set of incentive factors. For instance, W is not formally separated into We and t.w. The input price index expectation is typically formulated by making it equal to some external price index such as the Retail Price Index (RPJ) in Britain or the GNP deflator (pGNP) in the U.S. This solution implies that ue=l and ua=O; i.e., the firm is allowed to pass on to its customers, in the form of higher output prices, the costs of all expected input price increases but must absorb the cost impact of any, exogenous as well as

CONSTANfN ARIABLE PRODUCTIVITY ADJUSTMENTS FOR PRICE CAPS 99

endogenous, deviations from the expectation. Very strong incentive is provided if the deviations are endogenous but the formula merely generates high risk instead of strong incentive if, and to the extent, the deviations are exogenous. This distinction is important because the influence on input prices of exogenous variables is normally much greater than that of endogenous variables. The chief danger in using external price indexes is that they may not be capable of reflecting accurately the input price index of the regulated firm and thereby they may increase the exogenous deviations. It is generally understood that exogenous deviations may be large in any given year, but it is hoped that the annual deviations largely cancel each other and do not materially affect the financial well-being of the regulated firm over regulatory periods of several years. The past performance of AT&T suggests that such hopes are not very well founded. Table 1 indicates that major exogenous price index deviations did occur and, by extension and in the absence of arguments to the contrary, may occur in the future. For AT&T between the late 1940's and the late 1970's, the reduction of price index deviations to comfortable levels would typically have required at least seven- or eight-year regulatory contract periods - too long to consider for regulatory contract periods.

Table 1: Absolute Values of Percentage Point Deviations Between Four-Year Moving Averages of the GNP Deflator (PGNP) and AT&T's Input Price Index

Period Contemporaneous Lagged

1968-71 1970-73 1972-75 1974-77

PGNP PGNP

1.9 1.3 0.1 1.7

1.1 1.1 0.9 1.8

1976-79 0.9 0.7

Average 1.2 1.1

PGNP is lagged by one year; i.e., the input price change of AT&T in 1968-71 is compared to the change in PGNP in 1967-70, etc.

For the productivity component, ~e and ~c. identify the customers' reward and 1 - Pe and I-Pc. represent the regulated firm's reward and, thus, incentive. (1-~e) (1-~c.) will function well if the deviation is largely endogenous, and the opposite relationship is advisable if the deviations are expected to be largely exogenous. Failure to distinguish in an explicit fashion between expectation and deviation (i.e., the setting of a single expected productivity gain such as the constant percentages of British Telecom and AT&T) implies that ~e=l and ~c.=0. The interpretation of these values is that (1) the regulated firm is not given a share of profits from expected productivity gains; (2) the customers do not share with the regulated firm the profits or losses from unexpectedly high or low productivity gains. The expected productivity is implicitly assumed to be fully exogenous and the sub-


sequent deviations from it fully endogenous. Since deviations from expected productivity tend to be very large and also tend to be influenced rather strongly by exogenous developments, this is an extreme case of a high risk and high reward formula for the regulated firm. Risk and reward are further increased if the productivity expectation is not allowed to change from year to year in response to changes in external conditions but must remain constant for the entire contract period. Table 2 contains deviations of annual productivity gains from four-year average gains for a number of firms. The table indicates that the annual deviations may be very high, and that even their average absolute values tend to be uncomfortably high. Naturally, the deviations further increase on average if the average annual productivity gain for the four-year contract period is not accurately foreseen.

Table 2: Average Absolute Values of Percentage Point Deviations of Four-Year Average Productivity Gains from Their Annual Components

Period AT&T AGT BELL BCT

1968-71 1.76 n.a 1.38 n.a 1970-73 1.65 2.04 1.74 n.a

1972-75 0.45 3.29 1.07 n.a 1974-77 0.43 4.26 2.66 3.86 1976-79 0.35 3.99 0.60 2.98 1978-81 n.a 1.26 0.54 1.99

AGT: Alberta Government Telephones. BELL: Bell Canada. BCT: British Columbia Telephone.

2. The Importance of Accuracy

The price-cap formula with incentives excludes the 11: term of equation (1). Regulatory contract negotiations are supposed to arrive at an adjustment formula which contains the perfectly foreseen future annual input price and total factor productivity changes of the regulated firm and, thus, generates neither too low nor too high profits for the regulated firm, so that ic=O. Non-zero 11: values may nevertheless occur either because of non-compliance with the price cap or because of error (inaccuracy) in the adjustment formula. Ad hoc (non-formula-based) punitive action may apply for the former case. While a correction to the profit level would be desirable in the case of inaccuracy, formula-based routine corrective action would probably cause more harm than benefit, as a non-zero 11: would undo the incentive for cost minimization by removing the profits due to unexpectedly favorable endogenous factors and rewarding unexpectedly poor endogenous factors by compensating them for their mistakes. Changes in economic profits that are due to imperfect foresight are best left unaddressed until the re-negotiation of the regulatory contract. However, even during re-negotiation, the regulators must handle the issue of economic profits with care, since the removal of profits, whether due to exogenous factors or unexpectedly good performance by management and

CONSTANTN ARIABLE PRODUCI1VITY ADJUSTMENTS FOR PRICE CAPS 101

employees, would trigger attempts by the regulated firm to hide productivity improvements by generating temporary input price and volume increases during the last year of the regulatory contract period. Forward shifts over time in deliveries of, and payments for, factor inputs would achieve very much the same effect as simple cyclical goldplating. The amount of thus created "cost reserve" would depend on the amount of expected profit adjustment in the re-negotiated regulatory contract.

Inaccuracy may ultimately defeat the regulatory reform itself. A formula with a low degree of accuracy would make it necessary for the regulator and the regulated firm alike to keep a close eye on profits and rates of return. Rates of return would have to be reported, analyzed, and discussed in public, and corrections due to inaccurate adjustments would have to be designed in order to return profits and rates of return to their respective acceptable ranges. Inaccurate price-cap regulation would revert to rate-of-return regulation.

Accuracy is largely a matter of the flexibility of the formula (its ability to react to a variety of unforeseen cost changes during contract periods) and the appropriateness of the component index numbers (their ability to reflect the nature and magnitude of the relevant cost changes). The adjustment formula may be flexible to various degrees.

The most rigid adjustment formula prescribes the annual price adjustment as a constant for each year of the contract period. Such a formula assumes perfect foresight of cost inflation as well as productivity. For example, if perfectly foreseen annual inflation were 3.5 percent (w = 0.035), "prescribed" costs were noUo change cY = 0), and the also perfectly foreseen annual productivity gain were 2 percent per year ( = 0.02), and if there were compelling reasons to believe that the regulated firm should keep the profits of one percentage point's worth of productivity improvement, it would follow that the price cap should be adjusted upward by 2.5 percent every year until the next contract (jJ = 0.025).

A somewhat less inflexible formula would allow a measure of cost inflation to influence the price-cap adjustment, but would pre-set the expected productivity performance. The required annual productivity adjustment may be constant for the entire regulatory period. The current British Telecom and AT&T formulae belong to this category. The pre-set productivity adjustment may also be variable over the years of the regulatory period.

As an alternative to pre-setting productivity, the allowable cost inflation could be pre-set for the contract period and the adjustment could be made sensitive to some measure of the firm's productivity gain. This would be more logical and safer to introduce because inflation is measured, analyzed, and forecast by a large number of forecasters; thus, it is likely to be more accurately foreseen than the largely unknown productivity performance of telecommunications carriers. For this reason, it is somewhat surprising that no proponent of price cap regulation has recommended a, say, "4-TFP" formula, in which expected inflation is 4 percent per year and the adjustment is sensitive to some measure of gain in total factor productivity (TFP). The reluctance of regulators and regulated firms to adopt such


a semi-flexible solution can be explained to a large degree by the complex and expensive nature of total factor productivily measures and analyses.

Finally, the most flexible formula would allow the price cap to change according to index measures of both cost inflation and productivily. Accuracy would be best served by formulae of this class.

3. Incentive Compatibility

Apart from the obvious requirement of being able to accommodate the various desirable incentive factors, the incentive compatibility of the price adjustment formula also requires (1) accuracy in forecasting w, ci> and y; (2) independence of the index measures from the negotiating parties, so that the relevant information cannot be manipUlated; (3) simplicily both in the formula and in the processes of verification of compliance; (4) stability in the rules governing the formula and the verification of compliance.

Inaccuracy is not incentive compatible because it increases exogenous deviations from expectations, and it generates changes in economic profit which are undesirable and cannot be remedied without removing incentives and encouraging harmful strategic behavior by the regulated firm.

Independence is both desirable and controversial. It is desirable because it helps avoid data manipulation by the negotiating parties, and "minus-productivily" type price adjustments. The danger of manipulation is considemble. Productivity data can be manipulated in a number of subtle ways with significantly distorted end results. A minus-productivily adjustment situation6 may develop, when lagged actual productivily gains are used in the price cap formula to adjust regulated prices in the future, or when the regUlated frrms collectively have a very large weight in the industry-wide measure that is used to adjust the price cap. Such arrangements may virtually eliminate the cost minimization incentive either by rewarding the regUlated firm for all of its past cost inefficiencies through building those into future output prices, or by building their collective inefficiencies into their collective adjusted price cap? The independence requirement is also controversial. Since the information that is necessary for the calculation of accurate indexes is in the possession of the regulated frrm, and not available (or partially and insufficiently available) to disinterested third parties, there is a conflict between the requirements of accuracy and independence.

Simplicity is generally regarded as a highly desimble requirement. Indeed, several important practical considerations suggest that adjustable price caps can function successfully as incentives only if the adjustment formula is transparent and its components are readily understood by the negotiating parties as well as by the general public. A further advantage of simple formulae is that they offer an opportunity for easy verification. While the requirements of independence and simplicity seem to go hand-in-hand, there is an obvious conflict between the requirements of accuracy and simplicily. Since both input price and productivily changes are complex phenomena, simpler formulae tend to be less accurate.

CONSTANTN ARIABLE PRODUCTIVITY ADJUS1MENTS FOR PRICE CAPS 103

One-sided solutions to this problem, favoring extremely simple formulae at the detriment of accuracy, represent probably the greatest source of danger to the success of price-cap regulation.

Of course, simple formulae are not necessarily as simple as they appear. Expectations are formed and negotiations are conducted based on lengthy and complicated analyses of input prices and productivity. Once the expectations are agreed upon, the negotiating parties may decide to use a "simple formula" to express them for public consumption. The question is whether the simplicity of the formula matters at all. While it does not seem to matter from the point of view of forming expectations (as long as the formula expresses them faithfully), it matters very much when the expectations fail to materialize. A semi-rigid formula such as British Telecom's is bound to succeed only when the productivity expectation turns out to be correct, but fails otherwise. Only slightly more complicated flexible formulae, on the other hand, that could be generated by the same negotiating process with an approximately equal degree of difficulty, would be able to reflect a range of unexpected developments and, as a result, would perform significantly better in the presence of such developments. Sections 6 and 7 describe such flexible formulae.

The stability ofthe rules of price adjustments is important from the point of view of incentives in the sense that the rules must be independent from the endogenous variables that influence the components of the price adjustment formula. At the same time, the rules should be flexible enough to be influenced by exogenous variables, so that the financial health of the regulated firm is not altered by the impact of changes in circumstances beyond its control. Since it is not possible in practice to distinguish between endogenous and exogenous changes in the price adjustment components, the stability of rules is simply extended by making them insensitive to exogenous as well as endogenous variables. Some sources go as far as suggesting that the formation of a constant productivity expectation is necessary to create incentive compatible stability in the price-cap formula. While a constant expectation is undoubtedly a simpler target than a variable one, its lesser accuracy alone makes it less incentive compatible than a variable expectation which reflects changes in the economic environment of the regulated firm.

4. Productivity Indexes

The task of choosing productivity indexes for price-cap adjustment is made very difficult by the nearly complete lack of productivity measures for U.S. telecommunications. Only a few agencies are engaged in the systematic and regular measurement of productivity gains in the U.S. economy, and only one, the American Productivity Center in Houston, Texas, offers sufficient disaggregation of data to allow for the measurement of the aggregate productivity gains of the telecommunications industry. 8 It is rather unfortunate that, in the absence of detail and background data, their results are practically unanalyzable. Other sources, including the FCC's own effort to construct a "dual" (price-index-based) measure


of the TFP gains of the telecommunications industry, appear to lack adequate information for reliable productivity measurement. Productivity is not measured at all for individual federally regulated telecommunications carriers or for classes of such carriers (e.g., local and interexchange carriers).

Four possible productivity indexes are examined in this section. Due to the lack of empirical evidence, the evaluation of their strengths and weaknesses is supported by less and older empirical material than would be desirable.

4.1 Total Factor Productivity of the Regulated Carrier The idea of using the firm's own measured and forecast TFP index may appear

attractive at first. It is, after all, the firm's own productivity gain that is to be foreseen. The ideal measure is TFP, because only TFP is capable of reflecting the totality of factor input and, thus, cost savings, while partial productivity indexes miss or misrepresent savings in all omitted inputs. Furthermore, the measurement of the regulated firm's TFP would generate an in-depth understanding of productivity performance, and this understanding would likely improve the accuracy of productivity expectations.

The most important argument against the use of the firm's own TFP is that it is not incentive compatible because the disaggregated input and output data are under the control of the regulated firm and, thus, are subject to manipulations. Reliance on each regulated carrier's TFP measure would also increase, rather significantly, the direct cost of price-cap regulation. Finally, and paradoxically, there are several reasons to believe that the accuracy of that could be forecast by relying on the firm's own TFP measure is also suspect.

First, due to the joint use of many factor inputs between regulated and unregulated services, it is not possible to measure the TFP of regulated services alone. The TFP of all services, on the other hand, systematically overestimates (underestimates) the TFP ofregulated services if unregulated services grow faster (slower) and are subject to a higher (lower) rate of technological change. The bias in all-service TFP surrogates would normally work to the disadvantage of the regulated firm.

Second, it is an even greater concern that a sensible application of past TFP gains to a future time period may seldom be possible. Perhaps the most striking characteristic of the annual TFP gains of telecommunications carriers is their great variation both in time and in space (among carriers). Table 3 contains annual TFP gains which show that this was indeed the case during the 1970's and early 1980's. Great variation in time makes it difficult or impossible to choose an appropriate historic TFP gain for the adjustment formula. Lagged historic annual gains are clearly inoperable. Average gains may be attractive at first sight, but closer

. inspection reveals some important problems. Average gains for short and intermediate periods (two to seven years) still tend to vary considerably, due to the presence in the average of extremely high or low values as well as to the existence of some cyclical movement in productivity performance. This can be illustrated by comparing the four-year average productivity gains of the four telecommunications

CONST ANTN ARIABLE PRODUCTIVITY ADJUSTMENTS FOR PRICE CAPS 105

carriers whose annual productivity gains appear in table 3. In the 1947 to 1979 period (not shown), the highest four-year average productivity gain of AT&T was 2.5 times as high as its lowest four-year average productivity gain. Several4-year averages were very high or very low. For variable periods of time (depending on data availability), the similarly calculated multiplier is 2.6 times for British Columbia Telephone and 2.7 times for both Bell Canada and Alberta Government Telephones. The data reveal uncomfortably high degrees of variation and show that telecommunications carriers of radically different sizes, operating under considerably different conditions and having significantly different productivity improvements over time, have been remarkably similar with respect to the degree of variation in their four-year average annual productivity gains. There seems no reason to believe that the observed variation of annual TFP gains will not continue in the future. The available data also reveal that only much longer (eight- to 12-year) averages would reduce the variation in average annual productivity gains to comfortable levels. It is unlikely that such long periods can be considered for regulatory contracts.

Table 3. Annual Total Factor Productivity Gains of Four Carriers

Year AT&T AGT BELL BCT

1973 0.043 0.069 0.053 0.046 1974 0.038 0.135 0.058 0.090 1975 0.027 0.016 0.088 0.077 1976 0.045 -0.014 0.024 0.041 1977 0.037 0.038 0.011 -0.033 1978 0.049 0.090 0.024 0.041 1979 0.043 0.102 0.035 0.056 1980 n.a 0.099 0.040 0.112 1981 n.a 0.061 0.029 0.063

The problem of variation is especially serious under conditions which make TFP accelerate or decelerate for three- or four-year periods. When such conditions prevail, the use of long-term average measures of past TFP gains would have a tendency to rob the needy and reward the undeserving. Suppose that, due to uncontrollable reasons, the productivity gain of the firm decelerates (or simply decreases from its historic average level) in the contract period. If a long moving average of historical TFP gains is used to adjust it, the price cap will be adjusted to decelerating productivity very slowly and partially (the average is, say, 10 years long, while the contract period is only four), thereby prolonging the underestimation of the price adjustment. The use of a fixed average creates an even greater problem because it does not allow any correction at all. The underestimation may reach serious proportions and, because it is both large and prolonged, it may threaten the financial viability of the regulated firm. The process works in a similar


fashion to the disadvantage of the customer if productivity gains increase or accelerate due to exogenous causes. Under accelerating or decelerating productivity, a lO-year average TFP gain in the price-cap formula is capable of causing far more harm or undeserved profit advantage than lagged annual measuresprecisely because it eliminates the quick short-term fluctuation in productivity gains.

Productivity forecasting is a complex and involved process. It can be done with success only if the forecasting effort is extended to include detailed and regular economic and econometric analyses of the entire production process as well as a thorough understanding of, and deep involvement in, the planning and budgeting processes. The mere availability of historical input, output, and productivity data is not sufficient to guarantee its success.

4.2 Labor Productivity of the Regulated Carrier Labor productivity is often substituted for TFP when the former is available and

the latter is not. Labor productivity is easy to measure under price-cap regulation. Detailed revenue data are normally readily available and detailed price information is required for the verification of compliance with the price cap. Thus, direct output price indexes and indirect output volume indexes are fairly easy to obtain. Labor data do not create serious difficulties either, since the number and classification of employees and annual labor costs are readily accessible.

Table 4: Percentage Point Deviations Between the Labor Productivity Gains and Total Factor Productivity Gains of Four Carriers

Year AT&T AGT BELL BCT

1973 3.0 -4.3 0.2 1.1 1974 2.4 -2.5 0.6 0.9 1975 3.2 -6.1 5.1 9.3 1976 4.4 8.0 1.1 10.3 1977 0.2 -3.9 1.6 6.2 1978 0.1 2.4 -1.6 -5.2 1979 0.7 4.2 -0.2 -4.7 1980 n.a -9.0 2.2 0.4 1981 n.a 2.3 -1.8 2.5

The accuracy of the labor productivity proxy is examined for four telecommunications carriers in the 1973 to 1981 period in table 4. The table contains the annual percentage point deviations between each carrier's TFP and labor productivity gains. Even though labor was a large input (30 to 40 percent of the total production cost was typically associated with labor during the late 1970's), the labor productivity gains appear to have been decidedly poor surrogates for TFP gains. There are large deviations between TFP and labor productivity gains for all companies in most years. Some deviations are gigantic. The table also shows that

CONSTANT/V ARIABLE PRODUCTIVITY ADJUSTMENTS FOR PRICE CAPS 107

the labor productivity gain differs from the 1FP gain in the long run. The main reason is capital-labor substitution and a historically rapidly increasing capitallabor ratio. Since labor does not normally increase as fast as total input, labor productivity would systematically overestimate the productivity gain if used in price-cap formulae. By doing so, it would create a downward bias in price adjustments-to the detriment of the regulated firm.

The use of labor productivity measures as surrogates for 1FP is not incentive compatible. It would provide the fIrm with a powerful incentive to increase the prices of its regulated output by substituting labor for capital, so that the labor productivity gains would be lower. Non-optimal factor proportions and at least some retardation in technological progress would be the result of such a practice.

4.3 Total Factor Productivity of the Telecommunications Industry The appropriateness of industry-wide 1FP measures is mainly a matter of the

degree of variation of annua11FP gains in space; i.e., among carriers. The annual 1FP gains offour carriers in table 3 reveal that the use of industry-wide productivity measures would create two serious problems for price-cap formulae. The lesser problem is that the annual productivity gains vary greatly among fIrms in most years; thus, there would be large deviations from any average value as well. The deviations are similarly large between annual firm-specific gains and lagged average values. The result of using any kind of industry-wide measure would be a quick succession of large windfall profIts and losses. The second problem is that, depending mostly if not exclusively on the economic conditions under which they operate, some firms perform consistently below the industry average, while others perform, with comparable consistency, above it. This phenomenon raises the possibility of permanently punishing some and rewarding other regulated firms for the exogenous characteristics of their economic environment. Both the reward and the punishment may be large. To mention an extreme Canadian example, during the last fIve years shown in table 3, the productivity growth of AGT was nearly three times as high as that of Bell Canada and more than 60 percent higher than that of British Columbia Telephone. As fIgure 1 demonstrates, the productivity gains of AGT are exceptionally strongly correlated with their output growth rates, determined largely by increases in demand which, in tum, were related primarily to the oil boom in the area served by AGT. Had a price-cap formula with industry-wide productivity been in existence, it would have given a great opportunity for AGT to increase prices and profits, while punishing other carriers for the very high productivity gains of AGT. Similar cases may easily occur among the potentially more greatly different geographic areas of the United States. It is unfortunate that the deviations of fIrm level productivity gains from the average productivity gain of the federally regulated part of the American telecommunications industry are unknown and the FCC is unable to analyze this potentially very serious problem.


25 percent

20

15

10

5

o+-------------------~~~------------~

year (t) -5+---.--.---r--.---.--.---r--.---.--.---r--,

69 70 71 72 73 74 75 76 77 78 79 80 81

Figure 1: Annual growth rates of output (el) and productivity (<1»

for Alberta Government Telephones

4.4 Indirect (Dual) Productivity Measures If the economic profit of the firm does not change (it = 0), the productivity gain

of the firm can be expressed as the difference between the change in its input price level and the change in its output price level:

CONSTANT/V ARIABLE PRODUCTIVITY ADJUS1MENTS FOR PRICE CAPS 109

. . . q>=W-p. (4)

This alternative expression of the productivity gain, in which the prices (and not the volumes) of output and input appear, is sometimes referred to as the "dual" measure of productivity. Since p is the ultimate unknown variable of the price-cap formula, the firm's own forecast data cannot be used to calculate the productivity gain expectation. Past productivity gains may be calculated if the it = 0 assumption is approximately valid and major "prescribed" cost changes do not disturb the index relations. However, the difficulties of using past TFP gains to form expectations for contract periods, discussed above in Section 4.1, would apply.

Another option is to find external surrogates for w and <p. If sufficiently accurate and incentive compatible price index surrogates for the outputs and the inputs of telecommunications carriers can be found the dual measure offers further possibilities in designing price-cap formulae.

Both the Consumer Price Index (CPI) and the Producer Price Index (PPI) of the Bureau of Labor Statistics (BLS) contain telephone price components. The CPI has sub-indexes for "telephone service," "local service," "intrastate toll," and "interstate toll," while the PPI has sub-indexes for "local service," "toll service" (broken down into intrastate, interstate, international, and W ATS), "interstate private lines," and "directory advertising.,,9 For a detailed description and extensive analysis, see Lande and Wynns (1987). General inflation, as measured by the CPI or PPI, may be considered a surrogate for the input price indexes of regulated telecommunications carriers. If the telephone components of the CPI or PPI can also be used to measure the output price indexes of the same firms, then, at least in concept, they also yield a measure of the productivity gains according to the equation above. Thus, it may be possible to derive productivity measures for use in price-cap formulae from either the CPI or the PPI of the BLS.

Lande and Wynns (1987) note that the CPI has increased eight-fold, while its telephone service component approximately doubled since 1935. This translates to a roughly 5 percent annual input price increase and a 1.7 percent annual output price increase. The implied annual productivity gain corresponds to the primal (volume-based) measure of the long-term performance of AT&T. It seems that for very long periods of time the CPI may offer a sufficiently accurate measure of the productivity gain of the telecommunications industry. Unfortunately, the intermediate-and the short-term performances of the CPI are unacceptable.

The intermediate-term performance can be investigated during the 1978 to 1986 period. When average annual changes of the CPI and its telephone components are calculated in a number of alternative ways,1O the results indicate average annual productivity changes anywhere between a loss of2.1 percent and a 1.6 percent gain for the aggregate telephone service category. For local services, the average annual productivity change is a loss which ranges from 1.0 to 5.1 percent. Average annual gains between 0.5 and 4.0 percent are calculated for intrastate toll, while interstate toll is shown to have had a higher (4.3 to 6.5 percent) average annual gain in productivity. The derived values are obviously unrealistic and inconsistent. The average productivity gain of the local and two toll categories is inconsistent with


the productivity gain that is directly calculated for the total telephone service category. Only unrealistically high local and low interstate toll weights could yield equivalents to the direct result.

The annual calculations offer an extremely distorted picture. For the aggregate telephone service category, very high productivity gains are shown for 1978 to 1980 and productivity losses appear in every year from 1981 to 1986 (with the exception of 1983, when a gain of 0.2 percent is registered). Local service productivity gains are parallel to those of the aggregate category, but the estimated 1FP changes are even more unrealistic. For example, a 4 percent increase in the all-item CPI and a 17.1 percent increase in the local service CPI yield an indication of a local service productivity loss of 13.1 percent during the year 1984. Further losses of 5.1 and 6.0 percent are shown for 1985 and 1986, respectively. Intrastate toll productivity is shown to have remained virtuall y unchanged from 1981 to 1986.

What explains the failure of the dual measure? The all-item CPI is not the source of the problems. The average annual change in the CPI was identical to that in the input price index of AT&T for the period 1970 to 1979 and it is likely that the gradually declining annual changes in the CPI more or less corresponded to the gradually declining inflationary pressures on the costs of telecommunications carriers during the 1980's. The distortions seem to originate from the telephone price components. The fIrst problem is the underestimation of the industry's productivity improvement In this regard, Lande and Wynns (1987) note that telephone prices are lagged by one to three years behind the all-item CPr. In a period of rapidly decelerating inflation, such a lag would result in relatively high telephone price increases and can considerably underestimate the dual measure of productivity improvement. Such an underestimation took place after 1981. During periods of accelerating inflation, the lag in telephone prices achieves the opposite effect and the dual productivity is overestimated. This happened at the end of the 1970s. The second problem is a multitude of distortions in the local and toll price changes. The underestimation of local service productivity can be attributed to upward distortions of changes in the local telephone prices. Lande and Wynns (1987) analyze this problem in great detail and mention weight problems in the CPI as well as some specifIc events which caused overestimation. The outcome of their analysis is that the use of outdated expenditure patterns (based on data from the early 1970s) overstated the local price increase. The weights were updated in 1987; however, it seems that even the new weights, which rely on expenditures in the early 1980s, are outdated in that they do not reflect the continuing rapid change in the structure of expenditures in favor of interstate toll services. Among the special events, Lande and Wynns mention the effect of detariffIng CPE, the appearance of separate charges for inside wire maintenance, federal subscriber line charges, and changes in federal excise taxes. The most important single event, however, is the general movement towards cost-based prices.

Lande and Wynns find that for a long period of time, movements in local and toll service prices were very similar. Their similarity seems justifIed from the point of view of cost inflation, since it is unlikely that the inputs of local and toll services


were subject to significantly different inflationary pressures. On the other hand, the observed similarity of price changes is contrary to the perceived productivity movements. It is generally accepted that toll services achieved considerably higher productivity improvements than local services, on account of both their faster growth rate and their faster introduction of new cost-saving technologies. As the differences in productivity gains were not reflected, the prices of telecommunications carriers grew increasingly less cost based. As Lande and Wynns observe, the 1980s have witnessed a major correction in prices. Local rates increased not only because, and not to the extent, inflationary cost increases exceeded the productivity gain of local carriers, but mainly because they were judged to have been too low relative to the cost characteristics of their production process. Rule changes and new rules concerning the method of cost recovery, 11 mentioned by Lande and Wynns, added further elements of distortion to the picture. The counterpart of the downward distortion of local service productivity is the upward distortion of the productivity of toll, especially interstate, services. This is particularly serious if one considers that the very large capacity additions by the OCCs during the 1980s have not been well utilized and, thus, considerably reduced the productivity of the interstate service industry as a whole, and that this reduction has not manifested itself in higher prices because the competitive pressure of AT&T's price reductions has forced the OCCs to lower, instead of increasing, their prices. As a result, the OCCs failed to earn adequate profits.

In sum, the dual measure of productivity can be useful only if the absence of abnormally high or low profits can be ensured, and if the rules and regulations are stable and do not distort price movements in significant ways. In the present transitory state of the U.S. telecommunications industry, the prevalence of the conditions that would guarantee the satisfactory functioning of dual measures cannot be ensured and is not likely to occur. The adjustments of reported prices and price indexes that would be required to eliminate the effect of price distortions would be numerous, difficult, costly, and controversial.

4.5 The "Double-Dual" Method of the FCC In an effort to overcome measurement difficulties caused by the absence of

productivity data in telecommunications, the FCC has constructed a method which may be called "double-dual" because it is based not on volume information but on the comparison of input and output prices for the economy and for the telecommunications industry. FCC (1988) observes that PGNP "reflects certain productivity gains in the economy," then suggests that equal output price changes imply equal productivity gains and, furthermore, that the absolute values of output price 'change differentials and productivity gain differentials are equal. Observing an approximately 2.5 percentage point differential between changes in PGNP and telecommunications service prices, FCC (1988) comes to the conclusion that on average the TFP gains of the telecommunications industry have been and, by extension, can be reasonably expected to continue to be, about 2.5 percentage points higher than the TFP gains of the economy in general.


Denoting variables of the economy by capital letters and those of the telecommunications industry by small letters, the FCC's suggestion may be expressed as:

P-p=q,-ch=0.025. (5)

In addition to the already discussed difficulties of applying past long -run average annual productivity gains as expectations for future four-year periods (see Section 4.1), there are three major difficulties in this approach. First of all, it is not consistent with the use of PGNP in the price-cap formula. Given that P = W - <b - n and p = "IV - q, - n:, the equality of the price and productivity differential holds only if W = "IV and Ii = n:. However, the use of PGNP (which is, by definition, the output price index of the economy) in the price-cap formula as a proxy for the input price index of the regulated telecommunications industry implies that P = "IV which, in turn, implies that P = Wand therefore <b = 0 (if Ii = 0). In words, it is implied that the economy cannot have a productivity improvement Consistent with this result is the conclusion thatP - P = "IV - p = q,; i.e., the productivity gain measured by the price differential is not the deviation from the economy's productivity gain but the entire productivity gain of the telecommunications industry.

The second difficulty is that the FCC formula cannot offer valid information on productivity unless its two implicit assumptions (W = "IV and Ii = n:) are validated. Unfortunately, the measurement of the input price index of the economy as a whole raises difficulties not only because of unavailability of data but also because the identification of the desired factor inputs is by no means a simple task. Even greater difficulties are presented by the rate of change in economic profits. It seems that in order to overcome some of the complexities of productivity measurement, the double-dual method of the FCC has to deal with and resolve even greater complexities.

The third difficulty stems from the strong possibility of distorted price changes over time in the telecommunications industry as well as in the economy in general. Several distortions of telecommunications service price changes have been discussed in some detail in connection with the dual method in the previous sub-section. The double-dual method is further influenced by disequilibria and price distortions in the economy in general. For this reason, its use is even riskier than the use of the simple dual method.

s. How Price Index Adjustments Would Have Performed for AT&T

The behavior of input prices and productivity for a wide range of telecommunications carriers indicates sufficient similarity both in space and in time to suggest that an examination of how well price index adjustments would have performed for pre-divestiture AT&T during the 1970s may be instructive. In table 5, hypothetical price index adjustments are calculated for general inflation (PGNP) and productivity. The latter is based on the perfectly foreseen long-run (lO-year average) productivity gain of AT&T. Bias in the price index adjustment is calculated by subtracting the proportionate change in PGNP from that in the AT&T input price

CONSTANTN ARIABLE PRODUCITVITY ADJUSTMENTS FOR PRICE CAPS 113

index (inflation bias), and by subtracting the annual TFP gain from the lO-year average TFP gain (productivity bias). The total bias is the sum of the inflation and productivity biases.

Table 5. Short-run Percentage Point Biases in Hypothetical Price Adjustments for AT&T Between 1970 and 1979

Year Inflation Productivity Total

1970 1.7 -2.8 -1.1 1971 1.4 -2.3 -0.9 1972 -3.6 0.8 -2.8 1973 5.9 0.9 6.8 1974 3.1 0.4 3.5 1975 -5.5 -0.7 -6.2 1976 -4.8 1.1 -3.7 1977 0.4 0.3 0.7 1978 -0.6 1.5 0.9 1979 1.5 0.9 2.4

Positive values denote overestimation and negative values denote underestima-tion of actual changes.

The annual biases are generally large. Out of seven possible four-year subperiods between 1970 and 1979, the period-end price level, the consequence of cumulative price adjustments during the four-year period would have been greatly overadjusted in one (1971-74), greatly underadjusted in two (1974-77,1975-78), moderately overadjusted in two (1970-73, 1972-75), and accurately adjusted in two (1973-76, 1976-79). However, overall accuracy at the end of the latter periods would not have resulted from accurate inflation and productivity adjustments, but rather from large offsetting inflation and productivity biases.12

It is unlikely that price cap regulation in U.S. telecommunications in the 1990s will be as accurate as the AT&T example in table 5. First, AT&T's TFP showed less variation during the 1970s than in any other period. Variation of TFP gains may be higher in the 1990s. Second, larger firm size tends to reduce TFP gain variation. This is important because the telecommunications carriers of the 1990s will be considerably smaller than pre-divestiture AT&T. Third, the long-run productivity gain will not be perfectly foreseen. In contrast to these three reasons for poorer performance, price-cap regulation would improve to a considerable degree by the utilization of a variable productivity adjustment formula, recommended in the next two sections.


6. An Analytic Approach

The alternative to simple applications of any of a variety of available or possible measures of past productivity perfonnances to the future is an "analytic approach" which relies on an analysis and understanding of the causes of productivity improvements, and uses estimated causal relationships to fonn expectations. Such an analytic approach has proved to be operable and useful in fonning expectations of factor inputs, costs, and productivity under alternative sets of exogenous variables in at least one carrier's internal strategic planning and budgeting processes. 13

It is not a perfect solution in that, as explained below, part of the inaccuracy remains in the predictions but it demonstrably improves the accuracy of adjustments. It is also incentive compatible; i.e., it accommodates incentive factors, it is independent from the regulated carrier, it is simple, and it gives rise to sufficiently stable rules. Productivity predictions can be obtained and used to satisfy the requirements of price-cap regulation if (1) one can identify the main causal variables; (2) one can quantify, at least approximately, the relationship between causal variables and productivity; (3) the identified causal variables explain a sufficiently large portion of the changes in productivity; (4) one can predict the causal variables. The latter is not necessary if regulatory activity during intercontractual periods is restricted to the post factum verification of compliance.

The most important causal factors of productivity improvements are identified in numerous studies as (1) growth of output in the presence of economies of scale, and (2) technological changes. In addition, it has been suggested that non-optimal input proportions (deviations from the cost minimizing capital-Iaborratio and other input ratios) have an influence on productivity. When the output prices are distorted (i.e., relative to the marginal costs of outputs), the output proportions change and productivity is influenced. Productivity is affected by the finn's inability to adjust its inputs to changing demand and other conditions instantaneously and without incurring significant costs of adjustment. Productivity is also influenced by a host of individual events and circumstances. Despite the existence and the occasionally great importance of these additional causal variables, the following discussion is restricted to growth and technology. Two major reasons explain the restriction. First, in numerous econometric models of telecommunications carriers, growth and technological changes successfully explain large parts of the productivity performance, while efforts to establish the relationship between productivity and other causal factors have not produced usable empirical results (even though considerable progress has been made). Second, the measurement and analysis of the additional causal variables represent a much higher level of complexity in the economic analysis and prediction of productivity gains.

A simple two-factor productivity decomposition is capable of estimating how much productivity gain is due to:

1. output growth in the presence of economies of scale, where a measure of overall economies of scale is allowed to express the relationship between total


input and total output, which relationship is influenced by capacity utilization, economies of scale, economies of scope, and economies of density;

2. the cost-saving effect of newly introduced technologies and technological improvements which, in turn, depend on how fast new technologies and improvements are introduced, and how much cost saving they are capable of generating.

All other positive and negative events and circumstances that may influence productivity are combined in the stochastic error term of the underlying econometric model.

The available extensive empirical evidence indicates that the relationship between the growth rates of total input and total output remains quite stable for longer periods of time and is quite similar among telecommunications carriers. Given output growth expectations or measured actual output growth rates (as in post factum applications of price-cap formulae) this (estimated or observed) relationship can be used with a considerable degree of safety in assessing the rate of productivity improvement which is generated by growth alone. Furthermore, the available empirical evidence suggests that the annual productivity improvements that are generated by technological progress are also fairly stable over time and similar among telecommunications carriers; therefore, their past magnitude can be quite safely predicted to hold for future regulatory contract periods of reasonable length. The existing empirical evidence also suggests that it may well be sufficient to predict productivity gains due to growth and technological change. The sum of these two effects explains a sufficiently large part of productivity improvements. Several sources contain productivity gain decompositions. For detailed empirical results, the reader is referred to the Bell Canada study of Kiss (1983).

The productivity gains of the adjustment formula may be composed as:

cj>=Eq+i; (6)

where E is an elasticity which measures the degree of dependence of productivity gain on the growth rate of output, q is the percentage change in the volume of regulated output, and i is the annual productivity improvement due to cost savings generated by newly introduced technological improvements.

7. Recommendations

7.1 Coefficient Values Currently available evidence on the causal components of the productivity gains

of telecommunications carriers suggests that certain numerical values can be assigned to E and t. Based on an exhaustive review of evidence, the following formula can be recommended for the productivity gain component of the price-cap formula for federally regulated telecommunications carriers in the United States for the period 1989 to 1992:

cj> = I3(O.3q + 0.01) . (7)

116 PRICE CAPS AND INCENTIVE REGULATION INTELECOMMUNICA TIONS

[3 is a single productivity incentive factor which will be discussed at length in the next sub-section. E = 0.3 signifies that each percentage increase in the output of the rmn is expected to generate a corresponding productivity gain of 0.3 percent, which is tantamount to saying that each percentage change in total input generates a 1.43 percent increase in total output The latter relationship is often referred to as scale elasticity or the degree of overall economies of scale (£). The scale elasticity is the inverse of the output elasticity of productivity; i.e., E = 1 - 1/£.14

The value ofE may be estimated with the aid of econometric production or cost models or, in some cases, directly observed and calculated from the input, output, and productivity measures of regulated fmns and industries.

A large number of econometric cost models of AT&T and Bell Canada are surveyed by Kiss and Lefebvre (1987). Results for 16 representative econometric models are included in table 6. It is consistent with these econometric models to expect the degree of overall economies of scale in the 1.4 to 1.5 range.1S

The degree of overall economies of scale is one of the most fundamental economic characteristics of the production process. It changes relatively slowly over time as (1) growth in the scale of production gradually exhausts the existing economies of scale, and (2) new economies of scale are generated, also normally gradually in the telecommunications industry, by the introduction of technological improvements. Kiss (1983, 91-96) describes the slowly changing nature of the

Table 6. Summary of Estimated Economies of Scale (e) and Rates of Technical Change (1)

Outputs Author(s) £ T

Nadiri-Shankerman 1.75 0.0120 Christensen et al. 1.50 -1.90 nfa

Smith-Corbo 1.22 nfa One Denny et al. 1.58 0.0068

Kiss et al. 1.75 0.0083 Kiss-Lefebvre 1 . 1.73 0.0075 Kiss-Lefebvre 2. 1.67 0.0084

Smith-Corbo 1.20 nfa Kiss et al. 1.62 0.0130

Two Evans-Heckman 1.39 nfa Charnes et al. 1.39 nfa Kiss-Lefebvre 1.38 0.0063

Denny et al. 1.46 0.0057 - 0.0080 Three Kiss et al. 1.43 0.0094

Breslaw-Smith 1.60 nfa Fuss-Waverman 0.94 nfa

CONSTANTN ARIABLE PRODUCITVITY ADruS1MENTS FOR PRICE CAPS 117

degree of economies of scale and show the influence on it of growth and technological progress. It seems that the value of E can be kept constant for four-year regulatory contract periods with a high degree of safety.

Sometimes it is easy to do non-econometric calculations. For example, figure 1 demonstrates that during the 1970's the productivity gains of AGT depended very strongly on its output growth - and on very little else. It is directly visible to the "naked eye" that the productivity gain was 30 to 50 percent of the output growth rate in most years, and about 40 percent on average. Hence E = 0.4. When, on the other hand, output growth is not very fast and other factors also play important roles, the value of E cannot be observed for individual years. However, the long-term relationships are still approachable. AT&T is a good example. Christensen (1981) reports that AT&T's lo~-run average annual output growth was q = 0.074 for the period 1947 to 1979.1 If E = 0.3 and t = om the formula yields a productivity gain of cp = 0.032, which is equal to the actual long-run average productivity gain of AT&T, reported by Christensen for the same period. Since the output and productivity growth rates (q and cp, respectively) are available for some foreign telecommunications carriers, the numerical values ofE and the corresponding degree of economies of scale can be calculated under the assumption that technological improvements generate a 1 percent improvement in productivity per year. The results are displayed in table 7. The output elasticity of productivity is calculated as E = (CP - 1)/ q, and the degree of economies of scale is E= I/(l-E).

It is interesting to observe that the calculated E is very close to the recommended value of 0.3 not only for AT&T but also for five foreign (one German, one French, and three Canadian) carriers. This is strong evidence that the most fundamental economic characteristics of technologically sophisticated telecommunications carriers tend to be similar under a wide range of circumstances (such as geographic

Table 7. Computed Output Elasticities of Productivity (E) and Degrees of Economies of Scale (e)

Carrier Period q cp E e

AT&T 1970-79 0.0735 0.0335 0.320 1.47 AT&T 1960-69 0.0769 0.0330 0.299 1.43 AT&T 1950-59 0.0712 0.0324 0.315 1.46

AGT 1969-81 0.1419 0.0634 0.376 1.60 BELL 1968-81 0.0818 0.0388 0.352 1.54 BCT 1973-81 0.1138 0.0524 0.372 1.59

DB 1970-79 0.0851 0.0493 0.303 1.44 DGT 1975-80 0.1400 0.0600 0.357 1.55

DB: Deutsche Bundespost, Germany; DGT: Direction Generale des Telecom-munications, France.


location, climate, customer density, size, ownership, regulation, national characteristics, etc.).

The need to calculate q does not represent additional regulatory burden. Regardless of the form of the price cap, a price index must be calculated for the regulated output in order to verify compliance with the adjustment formula. Since the price index exists and revenue indexes can be easily calculated from readily available revenue information, the derivation of an implicit volume index as the ratio of the revenue index and the price index for regulated output is a trivial task.

The constant t term of the decomposed productivity gain expresses the effect on productivity of cost savings generated by improvements in technology in each year of the contract period. In reality, this term is not constant but variable over time. Its value is determined by the rate of introduction of new technologies and the cost elasticity with respect to technological changes. It has been simplified into a constant over time because the survey of Kiss and Lefebvre (1987) concludes that its value was quite stable over time as well as among firms in the past. As table 6 indicates, nearly every one of the reported econometric models estimated it to be close to t = 0.008. Two further considerations are important when forming an estimate of t. First, the econometric models that yielded t = 0.008 were estimated with data for carriers with a high (around 50 percent) revenue share oflong-distance services. Since the rate of technical change was demonstrably faster for long-distance than for local services, a somewhat lower value for local exchange carriers and a correspondingly higher value for interexchange carriers would be appropriate. Second, the rate of technical progress is expected to accelerate in the future as a result of the incentives for innovation to be provided by price-cap regulation. The t of the future will be greater than the t of the past. While it cannot be reasonably expected that additional incentives would double efficiency improvements due to innovation (even a 50 percent increase would be radically overstated, especially in the long run),17 it may not be unrealistic to assume that price-cap regulation has the promise to increase the rate of the already very fast technical change by about 25 percent. Thus, the desirable value can be relatively safely fixed at t = 0.01. This value means that the regulatory agency will expect the regulated carrier to achieve at least a 1 percent productivity improvement from newly introduced technologies and improvements in each year. IS

7.2 Incentive Factor Values The productivity sharing incentive factor [3 must be small enough to generate

sufficiently large profits (according to 1-(3) for the employees of the regulated firm to make their extra efforts to increase efficiency undoubtedly worthwhile. Cost minimization is by no means costless. The firm incurs tangible costs through its management activities to promote and organize efforts aimed at increasing productivity. In addition to the tangible costs thus incurred, there is a probably much larger intangible cost, which can be expressed in terms of increased personal sacrifices and risks of employees. Sacrifices are associated with self-adaptation to higher rates of change in the work environment (philosophy, style, organization, human

CONST ANTN ARIABLE PRODUCTIVITY ADmSTMENTS FOR PRICE CAPS 119

relations, technical requirements), higher labor intensity, increased voluntary and unpaid overtime, increased willingness to take work and related problems home, etc. As the pace of change quickens, career risks also tend to increase in corpomte organizations. Promotional opportunities may be threatened by changing performance evaluation norms. Entire career paths may be jeopardized if certain existing types of human capital become obsolete as a result of faster technological change. The incentive to be provided by the ~ factor must not only be greater than the sum of tangible and intangible costs, as perceived by the management and non-management employees of the regulated firm, but must exceed it by a wide enough margin to demonstrate in a convincing manner to the employees of the regulated frrm that their efforts will be well rewarded.

There is a category of the cost of regulation which particularly strongly influences the desirable level of the ~ factor. This is the cost of short-run "emergency boosts" of productivity in unfavomble years. Whenever the exogenous economic conditions become unfavorable to such a degree that the "normal" productivity gain that can be expected under those conditions is less than the gain that is allowed for price-cap adjustment purposes, the regulated firm will encounter economically unjustifiable and undesirable profit reductions. Since inadequate profits have a number of harmful effects even in the short run, the firm's management has a strong incentive to "boost up" its productivity gain by saving factor inputs which may be dispensable for some time, but not in the long run. Labor and material savings are the best examples of such short-run savings, but capital may be "saved" as well by the postponement of some elements of the construction budget. Such emergency boosts are costly and reduce productivity gains in the long run. (For example, short-run lay-offs lower labor productivity and increase recruiting and training costs in later years.) They are contrary to the long-term cost minimizing behavior of the regulated firm. They are arbitrary-the harmful artifacts of the regulatory regime.

Both the frequency and the size of emergency boosts are reduced if the number of years in which the allowed price adjustment is inadequate for exogenous reasons is reduced. The ~ incentive factor achieves such a reduction by lowering the productivity component of the price-cap formula. Figure 2(a) depicts a regulated firm with an increasing trend of productivity improvements over time and rather strong variation among the annual productivity gains. Assuming constant productivity adjustment and perfect foresight, the expected productivity gain is equal to the period average. Out of a total of 14 years, the annual gains are above the expectation in seven and below it in the other seven years. By reducing the productivity adjustment in the price cap, ~ = 0.7 would eliminate profit reduction, and with it the need for harmful emergency boosts, in four out of seven years. Due to the chosen numerical value of the ~ factor, the regulated frrm encounters financial difficulties only in 21 percent, and not 50 percent, of the time. For four-year regulatory contract periods, the expectation of one year of modemte financial hardship (25 percent) may well be acceptable to the regulated firm but it is difficult to see its reason for embracing price-cap regulation if it means that it


can expect financial problems, sometimes harsh ones, in two years out of four; i.e., 50 percent of the time.

Variable productivity adjustment further improves the situation because it reduces the deviations between the expected and the subsequent actual annual productivity gains. Figure 2(b) depicts the above described regulated firm with variable productivity adjustment While the period-average productivity expectation and adjustment remain unchanged, the number of years of fmancial hardship is reduced from three to one (equivalent to 7 percent of the period's total time), and the extent of hardship is considerably reduced in the remaining one year. Alternatively, the value of ~ may be increased. In the example, the incentive factor could be increased to ~ = 0.82 and the "hardship percentage" would still be lower at 14 percent than in the case of constant productivity adjustment. Variable adjustment allows the setting of the incentive factor at a higher value, thereby benefitting the consumers of the products of the regulated fmn.

What is a desirable value for ~? An investigation of AT&T's productivity characteristics in the 1947 to 1979 period has yielded some interesting results. Using data from Christensen (1981), the 32-year period was segmented into four-year sub-periods. A total of 116 such sub-periods were distinguished. Assuming constant productivity adjustment and perfect foresight, the period-average productivity gain was calculated for each period, and the deviations of each year's actual gains from the average were taken. Hardship was indicated for 48 percent of the total time. The period-average productivity gains were multiplied by various values for the beta factor and the deviations were re-calculated for each year of each of the possible 116 sub-periods. With ~ = 0.7, the hardship percentage was reduced to 25.

There are reasons to believe that ~ should be lower than 0.7, when used in a scheme of constant productivity adjustments. First, it may well be desirable for the regulated firm to lower the hardship percentage somewhat below 25 percent. Second, hardship percentages may be higher in the future on account of smaller firm size and, thus, greater variation in the annual productivity gains. Third, the productivity expectations of the future will not be perfect. Imperfect foresight increases the risk of hardship. Based on a comparison of constant and variable productivity adjustment schemes, it has been concluded above that the value of beta may be higher if variable adjustment is used. However, the advantage of variable adjustment is overstated in figures 2(a) and 2(b). Variable adjustment yields less improvement over constant adjustment if the period of constancy is shorter. A constant adjustment for four years is considerably more "variable" than a constant adjustment for 14 years. Ultimately, the value ~ = 0.7 appears the most reasonable choice.

8. Summary and Evaluation of the Recommended Adjustment Formula

Setting the incentive factor at ~ = 0.7, the recommended price-cap formula becomes:

CONSTANTN ARIABLE PRODUCTIVITY ADJUS1MENTS FOR PRICE CAPS

productivity gain ( <jJ )

----------------- ~~e

year (t)

2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 2ia: Annual productivity gains ('~') and

constant productivity adjustments (,~, and ~ ,~,) for a hypothetical telecommunications carrier

p = w - 0.7(0.3q + 1.0) ;

121

(8)

where, as suggested in FCC (1988), some lagged percentage change in PGNP may represent w. In the case of 4 percent expected general inflation, no change in "prescribed" cost items, and a 4 percent growth in regulated output in a given year of the contract period, the post factum verification of compliance with the price cap would indicate that any aggregate price increase not in excess of 2.46 percent would be acceptable because 0.04 - 0.7 (0.3 x 0.04 + 0.01) = 0.0246.19

The recommended formula is not nearly perfectly accurate. The decomposition of productivity does not explain the entire annual productivity gain. In addition to the growth effect and the technology effect, there is a residual, combining the impact on productivity of all other causal factors. While the residual is zero in the long run, its annual values may be fairly large. Therefore, the recommended adjustment formula does not eliminate-but it reduces-the problem of short-term


productivity gain ( <p )

..... \

'\ .... ..j /' , , , , , , , , ,

, I

"

year{t)

2 3 4 5 6 7 8 9 10 11 12 13 14

Figure 2Jb: Annual productivity gains (<p,) and

variable productivity adjustments (<Pe and Il <pe) for a hypothetical telecommunications carrier

fluctuation in productivity gains. The remaining difficulty notwithstanding, the formula represents a significant improvement over alternative treatments of the productivity adjustment. The only telecommunications carrier for which detailed productivity decomposition is available is Bell Canada. It is evident from Kiss (1983,92) that the actual annual gains are considerably closer to the "calculated,,20 than to the actual average annual gain. For the period 1970 to 1980, their average (absolute) deviation was 1.81 from the average gain, while it was 1.34 from the "decomposed" gain?l

It may also be perceived as a difficulty that the recommended formula necessitates an explicit agreement between the negotiating parties regarding the approximate degree of economies of scale (including scale, scope and density, and capacity utilization) and the rate of technical change. Such an agreement may be difficult to achieve, even if the pay-offs are considerable, because the results of econometric productivity analysis are imperfect, and its terms are not necessarily

CONST ANTN ARIABLE PRODUCTIVITY ADruSTMENTS FOR PRICE CAPS 123

sufficiently familiar to the negotiating parties and to the general public. Nevertheless, the difficulties should not be overstated. Productivity adjustments (even in simple inflexible forms such as British Telecom's 3 and 4.5 percents) require that the negotiators develop some kind of a consensus regarding the causal variables of productivity gains and their expected impact in the future. Without analyzing the nature and role of causal factors, it is not possible to form a valid expectation regarding the magnitude of future productivity gains. The difference is not whether the causes are considered but whether they receive explicit or implicit consideration.

The recommended formula of variable productivity adjustment has several important advantages over its alternatives. First, by utilizing the firm's own output growth rates, the productivity adjustment becomes firm-specific, so that punishment and reward for different exogenous economic conditions are avoided. Second, because the adjustment depends on the growth ofregulated output only , it is specific to the regulated output of the firm. This is important for two reasons. On the one hand, it is expected that with the advances of competition the number of regulated services will decline over time in the future. The recommended formula adjusts to the changing number of regulated services with ease. On the other hand, unregulated services are expected to grow faster than regulated services and, for this reason, to generate higher productivity gains. Higher productivity gains are also expected from the faster rate of introduction of new technologies into the production process of unregulated services. By not distinguishing between the productivity gains of regulated and unregulated services, price-cap formulae would overstate the expected productivity gain from regulated services, understate the necessary increases in the price cap, and thereby harm the regulated firm. Third, the recommended formula exhibits a great degree of flexibility. By being proportional to the growth rate of regulated services, it makes the price adjustment sensitive to the largest and most important determinant of productivity improvement. Furthermore, the flexible formula can be altered in simple ways. The proposed ~(r:q + 1) can be changed into

~Eq + t, which would increase the incentive to innovate because the firm could keep the profits of all technology-related cost savings above the required minimum t;

• Eq + ~t, which would increase the regulated firm's incentive to increase its output (presumably by lowering prices) because the profits of economies of scale would be kept by the firm in their entirety;

• ~qq + ~Tt, which would allow the regulatory contract to balance the two incentives of the regulated firm, depending on specific considerations that may exist at the time of the contract negotiations.22

Fourth, even though the productivity adjustment is firm-specific, the ability of the firm to manipulate the calculations of output growth rate is minimal or non-existent. The regulatory agency has nearly perfect revenue and price information, enabling it to verify the calculation of the output growth rate or to carry out the calculations. This way, compliance with the independence requirement is fully


ensured. Fifth, the formula is simple and represents no additional burden either on the regulator or on the frrm. Sixth, the formula does not require that the results of productivity studies of either the frrm or the industry be directly applied in the process of regulation. However, the ongoing study of productivity performance for a better understanding of the sources of productivity gains and the characteristics of productivity performance (and, thus, of the entire production process) becomes important from the point of view of the successful re-negotiation of the formula.

Notes

1. For example, NTIA (1987), Vogelsang (1988), FCC (1987, 1988). 2. The first manuscript of this article was written as an immediate reaction to the FCC's Note of

Proposed Rulemaking in August 1987. An improved and extended version, identical in contents but somewhat different in appearance from the present article, was presented at the Massachusetts Institute of Technology in July 1988.

3. For the sake of the brevity and clarity of analysis, several otherwise important issues are consistently ignored. No discussion is offered on capped vs. uncapped outputs or possible reasons for treating classes of capped outputs differently. Problems associated with new products are not discussed either. Distinctions between local exchange and interexchange carriers, the relationship between federal and state regulation, and the problems associated with market domination are also ignored.

4. The alternative idea of the regulated finn submitting preestimates of rate revisions to the regulatory agency, presumably accompanied with proof of compliance, has several major shortcomings (cost, delay, rigidity, difficulties due to the simultaneity of price and volume changes, etc.) and, therefore, it is not embraced here.

5. Not all input price changes are exogenous. Allowance is given below for the endogenous nature of some input price changes.

6. "Minus-productivity" is the incentive-incompatible counterpart of "cost-plus" rate-of-retum regulation.

7. In both cases, the dependence of the productivity adjustment on the regulated finn's productivity appears to be the cause of incentive-incompatibility. This appearance, however, is not necessarily true. The danger of providing a counter-incentive is avoided if the lagged or collective productivity measures are not used mechanically but serve instead as tools for an analysis and understanding of the productivity performance of the regulated firm and industry.

8. The Bureau of Labor Statistics (BLS) of the U.S. Department of Commerce also plans further disaggregation of input and output data.

9. These components of the PPJ are not aggregated into a telephone price sub-index. 10. For periods of six to nine years, based on both year-end and average annual values of the indexes. 11. "Prescribed" cost transfers among major service categories. 12. Large and often clustered positive and negative biases would have generated great variation in

consecutive period-end cumulative biases. For example, a one-year postponement of the start of the regulatory period from 1973 to 1974 would have turned accuracy into great underadjustment. A similar delay two years later (1976 instead of 1975) would have created the opposite effect. While AT&T's profits would have changed considerably by the end of most regulatory periods, making incentives inefficient and re-negotiations difficult, there seems to have been a single favorable choice of regulatory periods-namely, 1972-75 and 1976-79-which would have resulted in sufficiently accurate price adjustments and therefore smooth re-negotiations.

13. This statement is made with reference to my presentation entitled "Factor input and productivity forecasting for strategic planning and budgeting" at the Bellcore Economic Cost Modeling Forum in Atlantic City in September 1985.

14. The degree of economies of scale is the ratio between the output growth rate and the input growth rate; i.e.,1l = q/x. Hence, if the degree of overall economies of scale is Il = 1.43, then a I percent increase in total input (x = 0.01) will generate a 1.43 percent increase in total output (q = Il x·= 0.0143). The


productivity gain will be <P = I[ - X= 0.0043. and E, which is the ratio between the productivity change and the output change, will become E = <PI I[ = 0.0043/0.0143 = 0.30.

15. Keeping in mind that the indicator accounts not only for economies of scale but also for some forms of capacity utilization changes, economies of scope and economies of density.

16. The average year-to-year output volume index was 1.077. In traditional percentage terms, this is referred to as a 7.7 percent increase. The reader is reminded that this article uses logarithmic proportionate changes; thus, I[ = log 1.077 = 0.074.

17. More improvement may be expected in the first year or two of price-cap regulation if the regulated carrier has "reserves." However, in view of the very large budget cuts by American carriers throughout the 1980' s, such reserves may be severely reduced or, more likely, non-existent at the beginning of the first regulatory contract period.

18. In addition to this direct impact, technological improvements also tend to improve productivity gains in the long run by increasing the degree of economies of scale. Without this indirect impact, the value of E could not be kept constant over time.

19. This would ensure an at least 40 percent absorption rate of inflation; i.e., at least 40 percent of cost inflation would be "absorbed" by cost savings due to productivity improvement and no more than 60 percent would be passed on to the customers of the firm in the form of output price increases.

20. The sum of the growth effect and the technology effect. 21. The unpublished results of Kiss and Lefebvre (1984) show a greater reduction of the average

absolute deviation for Alberta Government Telephones. 22. These are only the "first order" flexibilities. It is possible to increase the flexihility of the formula

further by introducing "second order" flexibilities, whose most general form is j3qlEqI + j3q1EiJ2 + j3nT 1 + rmt 2,

where I[ = 1[1 + 1[2 and T = T 1 + T 2- In this formula, there is a minimum required output growth (1[1) and technical change (T 1), whose benefits are passed on to the customer partially or in their entirety (depending on the selected values of j3ql and j3n), while the profits of additional output growth and technological progress are shared between the firm and its customers according to j3q2 and I3n.

References

Bell Communications Research. 1988. "The Impact of Federal Price Cap Regulation on Interstate Toll Customers." Manuscript. Livingston, NJ (March 17).

Christensen, L.R. 1981. '1'estimonyin United States v. AT&T." C.A. No. 74-1698. FCC. 1987. "Notice of Proposed Rulemaking." CC Docket No. 87-313, Federal Com

munications Commission, Washington, DC (August 21). FCC. 1988. "Further Notice of Proposed Rulemaking." CC Docket No. 87-313, Federal

Communications Commission, Washington, DC (May 23). Kiss, F. 1983. "Productivity Gains in Bell Canada." In Economic Analysis of Telecom

muniCalions: Theory and Application, edited by L. Courville., A. de Fontenay, and R. Dobell. New York: North-Holland, pp. 85-113.

Kiss, F .• and B. Lefebvre. 1984. "Comparative Analysis and Econometric Forecasting of Factor Inputs and Productivity: Some Empirical Results in Canadian Telecommunications." Fourth International Symposium of Forecasting. London (July).

Kiss, F., and B. Lefebvre. 1987. "Econometric Models of Telecommunications Firms: A Survey." Revue Economique. 38 (no. 2, March): 307-373.

Lande, J.L., and P.L. Wynns. 1987. "Primer and Sourcebook on Telephone Price Indexes and Rate Levels." Industry Analysis Division, Common Carrier Bureau, Federal Communications Commission, Washington. DC.

NTIA. 1987. "Regulatory Alternatives Report." National Telecommunications & Information Administration, U.S. Department of Commerce, Washington, DC (July).

126 PRICE CAPS AND INCENTIVE REGULA TIONIN TELECOMMUNICATIONS

Olley, R.E., and C.D. Le. 1984. "Total Factor Productivity of Canadian Telecommunications Carriers." Project report to the Department of Communications and to members of the Canadian Telecommunications Carriers Association, Ottawa (February).

Vogelsang, 1.1988. "Price Cap Regulation of Telecommunications Services: A Long-Run Approach." The Rand Corporation, Note N-2704-MF, Santa Monica, CA (February).

7 A SEQUENTIAL MECHANISM FOR

DIRECT PRICE REGULATION

1. Introduction

Peter B. Linhart Roy Radner

Frank W. Sinden

In this article, we describe a mathematical model of price-cap regulation, in a simplified institutional setting. We show that, even in the presence of uncertainty as to the success of actions taken to improve productivity. and even in the presence of moral hazard, such a regulatory method can achieve its aim-namely, decreasing output prices and increasing productivity: Thus we consider the problem faced by a regulator who wants to provide incentives for a firm to effect cost reductionsand hence price reductions-through technological change or by other means. We model the manager of the firm as facing constraints imposed by the shareholders and other providers of capital, by the customers, and by the regulator. The regulator's ultimate objective is a secular real decrease in the frrm's prices. However, the manager's private utility may not be maximized by activities that are maximally cost-reducing. Moreover, the regulator cannot directly observe all of the manager's actions, the outcomes of which are also influenced by random exogenous events. Hence a problem of moral hazard arises.

We propose a regulatory policy in which the regulator directly requires the firm to lower its real prices at (or faster than) some prescribed target annual rate. We suppose that the manager is replaced when he can no longer simultaneously repay the cost of capital, lower the prices at the rate prescribed by the regulator, and satisfy the market demand at those prices. Whenever a manager is replaced, the regulator reverts to conventional rate-of-return regulation for a period sufficient to enable the firm to build up a new cash reserve.

The resulting situation leads naturally to a model of a sequential principal-agent relationship, in which the regulator is the principal and the manager is the agent. This is not a repeated game, however, because both the firm's prices and its


productivity are changing through time, endogenously and stochastically. Using new techniques for the analysis of this nonstationary process, we (1) derive a lower bound on the expected length of tenure of a manager, and (2) show that if the manager does not discount future utility too much, then the realized long-run rate of price decrease will be correspondingly close to the target rate (if indeed this target is technically achievable).

1.1 General and Historical Remarks It is commonly believed that regulation should simulate competition in order to

maximize social welfare. This is sometimes taken to imply that regulators should select prices so that the firm's economic profits are always zero. If, however, this rule were actually followed precisely, the firm would be deprived of all economic incentive to minimize cost. In particular, the firm would have no incentive to select an optimal mix of factor inputs, to obtain these inputs from the lowest-cost suppliers, or to invest in cost-reducing innovation.

In fact, the record of productivity improvement in regulated industries compares favorably on the whole with that of the entire economy (Houthakker, 1979, 1981). It would appear, then, that real regulation provides stronger incentives for efficiency than the above simple description suggests.

Both positive and normative theories of regulation have already received considerable attention in the economics literature. In this introductory section, we indicate briefly why there is a need for further study of efficiency incentives under regulation, and sketch several properties that a feasible incentive mechanism should have.

Real competitive markets provide incentives for innovation through temporary monopoly profits, as described by Schumpeter (1942). More or less unintentionally, real regulation provides a similar incentive. Regulation is not exact and continuous, but takes the form of a discrete series of reviews, at which (in a simplified picture of the process) the prices are reset so that economic profit is zero. Between reviews, if the firm can reduce its costs, it can earn a positive economic profit. It has been pointed out (Baumol, 1968) that the imperfection of this process (loosely called "regulatory lag"), far from being a drawback, confers a positive benefit on society. Baumol recommends that it be institutionalized.

It is, of course, difficult to say how efficient or close to the social optimum the incentives provided by regulatory lag are; one of the aims of the present article is to provide a framework within which the efficiency of such regulatory mechanisms can be discussed more precisely. In order to do this, we have found it desirable to go beyond consideration of the firm as an abstraction, and deal with the incentives experienced by the firm's managers. In this respect our analysis is in the spirit of the "managerial theory of the firm;" see, for example, Williamson (1968).

When inflation raises the cost of the firm's inputs, regulatory lag as an incentive mechanism no longer works so well. This comes about as follows: In any industry, given its technological possibilities, there is an economically optimal rate of cost reduction; beyond this rate, the cost of developing and installing new cost-reducing

A SEQUENTIAL MECHANISM FOR DIRECT PRICE REGULATION 129

technology exceeds the cost reduction. Suppose the rate of inflation exceeds this optimal rate of productivity increase, as has arguably been the case for most American industry in some recent years. Then if prices are fixed in nominal terms at regulatory reviews, as they customarily are, the firm will necessarily lose money between reviews no matter what cost-reducing measures it takes.

One would expect, therefore, that unusually rapid inflation would cause firms to apply for rate reviews with unusual frequency in order to reduce their losses. The data bear this out. Figure 1, for example, shows the remarkable correlation between the rate of inflation and the frequency of general rate orders for Bell Operating Companies in the years 1955-81.

RATE ORDERS FOLLOW I NFLAT ION

40 12 CJ) 0:: 0:: >-w 10

....... a :::.\? 0:: 0

0 30 , z w

, 0

l- RATE 8

I-<l: : 0:: ORDERS <l: -l

-l LL <l: 20 6 z 0:: w a z w w <.!) <.!) 4 <.!)

<l: LL -l 0 INFLATION 0:: 10 0::

<l: W , 2 w CD ,

>-~ , ::::l ", 0 z \i ~

0 I-0 ':

1955 1960 1965 1970 1975 1980 1985 YEAR

Frequent rate reviews have two social costs: the direct cost of the extra hearings and the indirect cost of reducing regulatory lag, which weakens incentives to improve productivity. In the limit, as reviews become continuous, productivity incentives approach zero, and the rational firm invests nothing in productivity improvement.


In times of rapid inflation, then, conventional regulation fails in two ways: it leads to losses and it leads to weakened incentives. These problems have led both regulators and utilities to seek fonnulas ("inflation adjustment clauses") that correct for inflation and at the same time preserve productivity incentives.2 This search has in turn led some investigators to examine more closely the game that underlies regulation.

1.2 The Present Approach In this article we present a new approach to regulation that is suggested by the

theory of sequential principal-agent games. A number of principal-agent relations (among shareholders, managers, regulators, and customers, and others) can be found in the situation of the regulated fIrm, as discussed in Section 2, and each such relation has its incentive problems. In the present article, we deal only with the relation between the regulator and manager as principal and agent Our model is sequential and emphasizes productivity improvement (hence costs are endogenously determined).

The model takes account of the following fundamental characteristics, among others, of the regulatory situation:

1. The regulator and the finn's manager have different information. In particular, the manager has more information about the possibilities for productivity improvement than the regulators. In fact, one of the manager's options is to invest in research in order to obtain more of this information. In principle, the regulator could also obtain more information at some cost, but matching the manager's information seldom appears to be part of the regulator's strategy. In the present model, the regulator does not even try to elicit information about the fIrm's costs, hence misrepresentation is not a problem.

2. The regulator and the fIrm's manager to some extent have different goals. The regulator may strive to provide incentives strong enough to overcome the difference, but in general we would not expect an equilibrium outcome to meet the regulator's goals entirely.

3. The service is deemed essential, so that its continued availability must be assured in spite of possible mismanagement andlor bankruptcy.

4. To be acceptable in the real world, a regulatory mechanism must not differ too radically from those that already exist The strategies we discuss resemble conventional regulation in that periods of regulatory inaction alternate with periods of action that are intended to be corrective.

The essence of the regulator'S problem is that he cannot directly observe the manager's actions, nor can he observe the exogenous random events that also affect productivity. He can, however, observe the consequences of those actions and events, namely the realized profIts of the fum, and whether or not demand is met. (He may also, with additional effort, be able to observe productivity changes, but we do not in our model rely on this possibility.) This situation, combined with the divergence of the regulator's and the managers' goals, leads to a problem of moral hazard. (See, for example, Radner, 1981.)


Suppose that the regulator provisionally fixes a sequence of prices that declines in real terms at a fixed "target rate" (which must be suitably chosen). If this sequence of prices is beyond the firm's control, then it has, essentially, the desirable incentive property of a lump sum payment. Suppose further that the regulator requires the firm to meet demand at the given prices, as long as it is feasible to do so, and that the shareholders and directors require the manager to payout the cost of capital at a given rate, again as long as this is feasible. These two requirements can be met as long as the firm's cash reserve is positive. However, through bad luck or bad management, the cash reserve can become negative. This event we call a crisis; when a crisis occurs, the manager is fired and replaced. The regulator must now provide some way for the firm to get back on its feet. Thus time is divided into alternating segments: incentive phases and recovery phases.

In the context of a particular formal model of a single-product firm, we have shown that, under this class of regulatory strategies, the management of the regulated firm will have an incentive to engage in productivity improvement. Furthermore, if the management's behavior is optimal/rom its own point o/view, then the incentive phases will be long relative to the recovery phases, and the resulting long-run average rate of actual price decrease will be close to the regulator's target rate of price decrease, provided the management does not discount its own future benefits too strongly.

Thus, under suitable conditions, this class of regulatory strategies induces approximately efficient behavior on the part of the manager, without placing a large informational burden on the regulators and their staff, and in particular without requiring the regulators to monitor the firm's rate of return.

Several features of our approach should be emphasized. First, as mentioned above, we model the firm's manager as the active decision-maker in the firm, optimizing his own utility subject to constraints imposed by shareholders, customers, and regulators.

Second, we portray the regulators as seeking a mechanism that is easy to administer and that gives "satisfactory" results. In this case, satisfactory means achieving a target rate of price reduction, perhaps only approximately. Thus the regulator does not seek an "optimal" mechanism in any precise sense.

Third, the regulatory mechanism we describe replaces explicit rate-of-return regulation. We are interested in alternatives to rate-of-return regulation because (1) we are concerned about the weakness of its incentive properties, as described above, and (2) its informational requirements are heavy. Rate-of-return regulation is also difficult to administer if some of the firm's activities are regulated and others are not, as in the case of telecommunications today; see Linhart and Radner (1983).

Fourth, from a technical point of view, our model requires an analysis that goes substantially beyond currently available results for repeated principal-agent games. The reason for this is that both the firm's productivity and its prices are changing from period to period, and these changes are bOlh endogenous and stochastic. Thus our model leads to a sequential-but not repealed-principal-agent relationship, with endogenous state variables, which requires new techniques of analysis.


(Further discussion of these features, including how they relate to the previous and current literature on the subject, will be found in Sections 4 and 5.)

Although inflation has played a role in stimulating the present interest in incentives, inflation is not essential to the theoretical structure of the underlying game. We sidestep inflation problems by assuming that prices are always measured in real dollars. We do not address the nontrivial econometric problem of defining a suitable price index.

In Section 2, we discuss in general terms the relations between the so-called "principal-agent" problem and the problem of providing incentives for efficiency in a regulatory situation. In Section 3, we describe a particular formal model that embodies some of the considerations sketched in Section 2 and prove several theorems about efficiency for a class of regulatory strategies. Section 4 provides some remarks on possible generalizations and extensions of the model. Section 5 locates the present model with respect to the previous literature.

2. Regulation and the Principal-Agent Problem

2.1 Principal-Agent Games In a principal-agent situation, a principal hires an agent to act on his behalf,

generally because the agent has better information about some enterprise of interest to the principal. The resulting outcome depends on a random state of the environment as well as on the agent's action. After observing the outcome, the principal makes a payment to the agent according to a pre-announced reward function, which depends directly only on the observed outcome. (This last restriction expresses the fact that the principal cannot directly observe the agent's action, nor can the principal observe the information on which the agent bases his action.)

A short-run principal-agent relationship can be naturally modeled as a two-move game, in which the principal first announces a reward function to the agent, and then the agent chooses an action (or decision function if he has prior information about the environment). An equilibrium of such a game is a reward function (by the principal) and a decision function (by the agent), each of which is optimal given the other. The equilibria of such a game are typically inefficient (unless the agent is neutral towards risk), in the sense that there will typically be another (but nonequilibrium) reward-decision pair that yields higher expected utilities to both players.

If such a game is repeated irifinitely many times, the whole set of repetitions is said to constitute a "supergame." In such a supergame, more efficient equilibria exist, in the sense that both "players" are on the average better off than in the short-run relationship. This is essentially because in the supergame, the principal can design his reward strategy in such a way as to punish noncooperative behavior by the agent.

Of course, since the principal cannot observe the agent's action, but only the outcome of that action, he cannot be sure in case of a bad outcome whether the agent acted in bad faith or was the victim of bad luck (Le., the random state of the

A SEQUENTIAL MECHANISM FOR Dm.ECT PRICE REGULATION 133

environment was unfavorable). However, after many repetitions the principal can distinguish statistically between bad faith and bad luck and impose (or withhold) penalties accordingly.

Finally, if the agent's objective is to maximize the discounted sum (present worth) of future rewards, there is some loss in the efficiency of equilibria, since future penalties lose some of their force compared to present gains. But as the discount rate approaches zero, this loss in efficiency disappears. Repeated principal-agent games, including those with discounting, are discussed in Radner (1981, 1985, 1986).

2.2 Principal-Agent Relationships in Regulation When we begin to look for principal-agent relationships in the regulatory scene,

several immediately spring to mind. First of all, the regulatory body can be seen as an agent of society or the electorate. Regulators may have--doubtless do have-their own personal goals (see, for example, Stigler, 1971). The problem for society, acting through the political process, is then to provide a system of rewards and penalties such that regulators will best further their personal interests by acting in the general interest.

Second, in a simplified picture, the firm can be seen as an agent of the regulators. If incentives for the regulators to act in the interest of society are correct, and if incentives for the firm to act in the interest of the regulators are correct, then the chain will hold and the firm will act in the interest of society. The actions of the firm in which we are most interested (in this article) consist in undertaking productivity-improving projects, typically research and development (R&D). Such projects cost money, involve the expenditure of effort, and mayor may not result in lowering the firm's production costs. The regulators can observe the cost reduction, if any, and the expenditure of dollars on R&D, but not the expenditure of effort Rewards to the firm might take the form of increased allowed profit.

In reality, however, the firm is not a monolith. A principal-agent relation exists between the firm's owners and its managers. It is reasonable to assume that the owners want to maximize the firm's profit, but there is no reason to think that the managers internalize this objective; their direct interests may include salary and bonuses, longevity of employment, span of control, effort (to be avoided), and research interests. The owners' well-known problem is then to provide incentives for managers to act in the direction of profit maximization. In this connection, we may take the owners (shareholders) to be risk-neutral and the managers risk-averse. In the case of a regulated firm, the owners may also be thought of as transmitting 1:0 the managers the constraints (such as the requirement that demand be met at specified prices) imposed by the regulators.

Neither the regulators nor the owners can discriminate between bad luck and bad faith on the part of the managers, except statistically, so both regulatory rewards and penalties to the firm (in terms of profit) and the owners' rewards and penalties


to the management (in tenns of bonuses, promotions, etc.) will have to be based on statistical evidence.

Other principal-agent relationships can be discerned. For example, a board of directors may be interposed between the owners (shareholders) and the managers. Also, we have said nothing about those of the fIrm's employees who are not managers; a whole hierarchy of principal-agent relationships exists here. Moreover, these workers, if they are unionized, may employ union officials as their agents in negotiations with management.

For our present purposes, we concentrate on a single principal-agent relationship, that between the regulator and the manager. The owners are represented by their power to fire the manager, and by the requirement that the fInn earn enough to pay the cost of capital. The electorate is represented in the regulator's desire to reduce prices. Furthennore, we do not explicitly model the relationship as a game, in the sense that (1) we do not fonnally describe the entire set of alternative strategies available to the regulator, and (2) we do not completely specify the goals of the regulator. What we do analyze are the implications of a class of simple strategies for the regulator, under the hypothesis that the manager will respond optimally (in his own interest) to any particular regulator's strategy. A full-blown game-theoretic analysis might be desirable, and in Section 4 we make some suggestions about the directions such an analysis might take.

3. Description of a Formal Model

We have claimed that a certain class of regulatory strategies (sketched in Section 1), which is consistent with the infonnational asymmetry between the manager and the regulator, can induce economically efficient behavior on the part of the manager. We now substantiate this claim by showing that it is so, and in what sense it is so, in the context of a particular model. This model, although much simplifIed for purposes of tractability, is plausibly representative of a wide class of regulatory models.

3.1 Technological Model We assume that all the firm's inputs, including capital, can be adjusted in each

period so that the firm can just meet demand in that period at minimum cost Thus capital investment is reversible, and questions of excess capacity do not arise.

We assume that the real cost, per unit of output, to the fum of each of its factor inputs, including capital, is the same in each period. We take the unit cost of capital to be in a fIxed ratio to the cost of all other inputs plus the depreciation of capital; this would be the case, for example, if the depreciation schedule were unchanging and if capital and all other inputs were optimally used in fIxed proportions (technically, if the production function were homothetic).

We assume Hicks-neutral technical change, i.e., that changes in productivity affect all inputs proportionally, so that we may take as a measure of productivity either (1) the ratio of output to capital (where "output" is an index of the outputs

A SEQUENTIAL MECHANISM FOR DIRECT PRICEREGULA nON 135

of the firm and "capital" is an index of the capital of the firm, measured in constant dollars), or (2) equivalently, total factor productivity.

We think of changes in productivity as brought about by research and development (R&D). We suppose, for simplicity, that the R&D budget is fixed, so that the manager's choices lie in how he manages the R&D budget and how he implements any resulting productivity improvement. Although in reality the results of R&D activities in anyone period may only be realized after some lags, we suppose here that these results are entirely realized after one period.

We recognize that increases in productivity are affected by the manager's actions, as just described, but are also affected by exogenous or random factors beyond the manager's control (e.g., the unpredictability of the outcomes of research projects). We assume the technology of productivity change to be stationary, in that given managerial actions combined with given exogenous conditions will achieve the same productivity change in any period. Thus,let

Ft = total factor productivity during period t = 1,2, ... , measured as output per unit of capital.

r = cost of capital, e = all other costs per unit capital, C=c+r. Qt = output during period t (or, in the case of a multiproduct fIrm, an index

of output). Then,

Further, let

QtC total cost = F .

t

At = actions taken by manager during period t to improve productivity (the manager may use his knowledge of the past history of productivity change in choosing At),

Xt = random factors beyond the manager's control, G, = In (F,IFH), the logarithmic productivity gain during period t, i.e., from

(t-l) to t, H, = GI + ... + G" the total (logarithmic) productivity gain from 0 to t.

Then

We assume that (1)

and that the random variables (Xt ) are independent and identically distributed with distribution known to the manager. We further assume that the function r is bounded below, i.e., arbitrarily large productivity losses cannot occur in a single period.


3.2 Demand Model With respect to demand, we assume exogenous growth in demand at a constant

rate:

Qt = it D(Pt) , (2)

wherePt is the price (or, in the case ofamultiproduct firm, a price index) of output in period t. We further assume constant price-elasticity (less than unitary) of demand, so that

(3)

Thus, Q _ U+Pt p -ll t- e t·

3.3 The Cash Reserve We assume that the firm's net profits (Le., revenues minus costs, including

capital costs) are accumulated in a cash reserve, which is initially positive. This reserve earns zero real return. Since net profits can be negative, the cash reserve can decrease and even become negative. Each time the cash reserve becomes negative, we say a crisis has occurred. The occurrence of a crisis says something, statistically, about the manager's performance during the periods since the preceding crisis. We shall have more to say below on how the regulator dea1s with a crisis.

It turns out that this device, of hinging the regulator's action solely on the sign of the firm's cash reserve, is the key simplification that makes the model tractable.

Thus, let s = initial value of cash reserve, assume positive, St = va1ue of cash reserve at date t (the end of period t), so that So = s, It = net loss in period t (Le., the negative of profit, net of the cost of capital)

= decrease in cash reserve during period t. All dollar magnitudes are in constant dollars, and we assume that the rea1 rate of interest on the cash reserve is zero. Then the decrease in the cash reserve in period t is cost less revenue:

(4)

3.4 Distribution of Information We assume that the regulator cannot directly observe the manager's actions, nor

can he observe the exogenous random events that also affect productivity changes. This limitation on the regulator's information constitutes the essence of his problem. (He may, with effort, be able to observe the resulting productivity changes, but we do not in our model rely on this possibility.) The regulator can, however, observe the consequences of these managerial actions and random events, namely, the realized profits of the fIrm and whether or not demand is met.


The manager is of course aware of his own past actions, and of the past history of prices and realized productivity changes. Importantly, he is also aware of the regulator's policy, which the regulator has announced. Thus, if it is part of the regulator's policy to reduce (real) prices by a fixed percentage each period (until the next crisis), the manager is aware of this projected schedule of prices. He can base his actions in each period on all this information. A managerial strategy is a rule (sequence of functions) according to which the manager determines his action in each period as a function of his information.

It remains only to add that we assume that both the manager and the regulator know the price elasticities of demand for the firm's products.

3.5 Objectives We assume that the regulator wants low prices for the firm's outputs. Because

of increasing productivity, the firm can afford to lower its prices over time and still remain solvent. Thus, more precisely, the regulator's objective is to maximize the long-run average rate of actual price decrease.

With respect to the manager, we assume that his wage is fixed, and we make the perhaps rather Draconian assumption that at each crisis, when the firm flfst becomes insolvent, the manager is fired and replaced by the owners; the regulator, knowing this will occur, can use the manager's tenure as an incentive tool. Thus, one component of the manager's objective is to maximize his tenure, i.e., the period during which he receives his (fixed) wage.

On the other hand, we admit the possibility that the manager's preferences among the alternative actions he can take in one period would not, other things being equal, lead to maximum productivity increase (and hence maximum price decrease) in the long run. It is this possibility, of course, that motivates the regulator to devise a policy that will enhance the manager's incentive to increase productivity. These preferences form the other component of the manager's objective.

Both sorts of consideration-his desire to continue receiving his salary and his preference for certain managerial actions-will contribute to determining the manager's optimal strategy. For example, we would expect that when the cash reserve gets close to zero, the manager would act so as to increase productivity very rapidly, thus reducing costs more than the regulator is reducing prices. On the other hand, when the cash reserve is very large, we would expect him to act in a way closer to his one-period preference.

Formally, if the manager receives a salary w per period and chooses action At in period t, then his utility for period t is

Ut = U(w, At) . (5)

Let a be the manager's discount rate, and T his tenure in his job (a random variable). Then we assume that he will choose his strategy to maximize his expected discounted utility for the duration of his employment, i.e.,


T

v=(1-0)ELOI- 1 U1 ,

1=1

(6)

where E denotes expectation. Thus we make the convention that after he is fired the manager's utility per

period is zero (i.e., this is the origin from which the manager's utility is measured). The normalization factor (1 - 0) has the effect of keeping v uniformly bounded in 0(0 $ 01).

We assume that there exists a managerial action ~ such that

~==U(w,~»O, (7)

~ == E r (~, X) > 0 . (8)

This assumption states that it is possible for the manager to achieve a positive expected rate of productivity growth and still be better off during employment than after being fired.

Define A * to be the management action that maximizes his one-period utility in (5), given w; let y* be the corresponding expected logarithmic rate of change of productivity, namely,

y* =Ef (A*,X), (9)

and let u* be the manager's corresponding one-period utility,

u* == U(w,A*). (10)

Finally, without loss of generality, we assume that a managerial action ~ exists so that not only (7) and (8) are satisfied, but moreover

~> y* , (11)

~<u* (12)

(If (11) could not be satisfied, Le., if y* were the maximum feasible expected rate of growth of productivity, then there would be no divergence between the manager's short-term goals (as represented by his one-period utility) and the goal of maximizing the long-run rate of price decrease.) We shall assume that some ~ satisfying (7), (8), (11) and (12) has been chosen.

3.6 Strategies As we have said, the manager is required to adjust the firm's output to meet

demand exactly, and to pay all costs including the cost of capital. He is able to do these things as long as the firm is solvent, Le., as long as its cash-reserve is positive. Through bad luck or bad management, the cash reserve can become negative. This event we call a crisis; when a crisis occurs, the manager is fired and replaced. The regulator must now provide some way for the firm to get back on its feet; this part

ASEQU~LMECHANffiMFORDrnECTPruCEREGULATION 139

of the regulator's strategy will be described below. Thus time is divided into alternating segments: incentive phases and recovery phases.

During each incentive phase, the regulator requires that prices decrease at a fixed percentage rate-say <p-in each period. For the scheme to work, <p must be set at a level not greater than the greatest achievable level of productivity increase. The regulator will want to meet this condition, since he wants the firm to be solvent most of the time. We do not go into the problem of how the regulator can elicit true cost information from the firm. but simply assume that his information on the firm's past productivity behavior enables him to choose a <p that is not too high. Thus during an incentive phase

whence, from (2) and (3),

where

Pt =Po e-<pl ,

p=p +1)<P

Qo=i1. PoT} •

(13)

We can now describe completely the behavior of the cash reserve during an incentive phase. From (4), the decline in period t is

I - Q ept (S2. e -H, - P e -<pi) t- 0 Fo 0 •

We assume that the regulator chooses Po so that at the beginning of the incentive phase profit is zero, 10 = 0, i.e.,

Then

It = Qo Po ept (e -H, - e -<pi) . We may choose units such that the initial revenue flow is unity:

QoPo= 1.

Denote the growth rate of revenue during the incentive phase by G= P - <P= P - <p(1-1),

and assume G positive, i.e., p> <p(I-1) .

Let Wt=<pt-Ht · (14)

140 PRICE CAPS AND INCENTIVE REGULA TIONIN TELECOMMUNlCA TIONS

Wt might be called the (logarithmic) "productivity gap" at t. Then the law of motion of the cash reserve during the incentive phase may be stated briefly as

{St = St-l -It,

It = eat (ew, _ 1) , (15)

with initial conditions Wo = 0, and So = s > O. Let Tbe the ftrst t such that St S; 0; the periods t= 1, ... , Tconstitute the first incentive phase. The ftrst crisis is said to occur at the end of period T; the fust manager is fued at this time, and a new manager is appointed.

The fIrst crisis is followed by a recovery phase, t = T + 1, ... , T + T*, where T* is exogenously determined and is the same for every recovery phase. Thus, to summarize, the parameters which the regulator can manipulate are cp, s, and T*. (He may also be able to choose, or at least cap, the manager's salary; see equation (7), above.)

During the recovery phase, the regulator sets prices in such a way that dollar profit is the same in each period, and that at the end the cash reserve is back up to its initial value, s. (Note that to achieve this result some ex post adjustment of the price will in general be required after the value of the random variable Xt is

realized.) Thus the dollar profit, n*, in each recovery period is determined by

(16)

Here ST, the value of the cash reserve at the beginning of the recovery phase, is non-positive. With constant demand elasticity, 1'\, which is strictly less than unity, the condition (15) can always be met This becomes clear when we notice that revenues,

P Q a+j)t p 1-1l ·th 1 tt=e t ,WI 1'\<,

can be given any arbitrary positive value by choice of Pt, while (for any given level of productivity) an increase in price lowers total costs.

Following the end of the fIrst recovery phase, a second incentive phase is started, with PT+T*+1 set so that profit is zero, and thereafter prices decline at the same incentive rate cp until the next crisis, etc.

It is clear that prices are not apt to fall as rapidly as the rate cp during the recovery phase; they may even increase. Thus if the system is to work at all well, the recovery phases must be infrequent, and short relative to the average length of an incentive phase. That this can indeed be the case is one of our results, which we shall prove below (I'heorem 3).

We turn now to the study of the optimal strategy of the manager during the incentive phase.

Theorem 1. Let 1'(3) be the length of the incentive phase, given that the manager's discount factor is (3 and he follows an optimal strategy; then if cp < ~,

A SEQUENTIAL MECHANISM FOR DIRECT PRICE REGULATION

lim Ef(0) = +00 • S-+ 1

141

Proof. Recall that we have assumed that s> O. One strategy available to the manager is to use the action ~ throughout the incentive phase. By assumption, this strategy allows the fIrm to meet the regulator's target rate of price decrease, <p, and remain sol vent, in an average sense. But of course it does not rule out the possibility of insolvency in some particular period. Let Zt = In (PtFt); with this strategy (Zt) is a random walk with increments (Gt - <p) which are bounded from below and which are independent and identically distributed with mean ~ - <po Since ~ - 0, if such a random walk were to continue indefinitely,

~~Prob {t/G. -'1')' 0 for all t> I} >0. (17)

Recall that Po is chosen so that profit is initially zero, i.e., so that

PoFo=C.

Hence Prob{P,Ft~C forall t> 1}=~, (18)

and hence, a fortiori, Prob{St~s forall t}~~. (19)

This is more than sufficient to guarantee that

Prob {f= +oo} ~ ~ , (20)

where f is the length of the incentive phase of this strategy. The expected total discounted utility for the manager from this strategy is

l' ¢ = (1 - 0) E L ot-l ~

t=1

=~(l-E Of) (21)

Now consider an optimal strategy for the manager; let T denote the corresponding length of the incentive period, and v the corresponding expected total discounted utility. By the definition of u*,

for all u" and hence

ut:s: u*

l' v:s: (l-o)E L ot-l u*

1=1

(22)

142 PRICE CAPS AND lNCENTIVE REGULATION IN TELECOMMUNlCA TIONS

= u* (I-Ef/')

Since v is optimal, v ~ 0, so by (21) and (23),

u*(I- E'ft) ~ ~ (1- E'f/') ,

or

Ef/' ~ 1 - (:* ) -E'ft) .

Note that, since 'f/ is convex in t,

so that by (24)

OET ~ 1 - (:* ) (1 - E'ft) ,

_ In [ 1 - (~ ) (l - Ell)] ET"? Ino '

(23)

(24)

(25)

Recall that the optimal strategy of the manager, and hence the distribution of T, depends on o. From (12) and (17), the right-hand side of (25) tends to infmity as o tends to 1. This completes the proof of Theorem 1.

Corresponding to Theorem 1 is a result for the case in which there is an exogenous upper bound on the length of the incentive phase, say 'to Thus let 't be a positive number, define

A A T't = min (T, 't) , (26)

and let Tr. be the (random) length of the incentive phase for the policy of the manager that is optimal given 'to (Recall that Tr. depends on 0, although this is suppressed for the time being in the notation.) It is straightforward to verify that equation (25) is also valid for Tr., i.e., that

(27)

The limit of the right-hand side of (27) is, by an application of 1 'H6pital' s Rule,


(:* ) [Pr cf= 1) + ... + 't PrCf= 't)] .

On the other hand,

Hence (27)-(29) imply:

f AA Pr ( 1: = 't) ~ Pr(T = co) ~ 1t •

143

(28)

(29)

Theorem 2. Let T~5) be the length of the incentive phase, given that it is truncated at't, that the manger's discount factor is 5, and that he follows an optimal strategy; then if cp < 9,

lim inf E 1'1:(5) ~~ (~*). ~~1 u

(30)

We turn next to a study of the long-run average rate of price decrease. For this study, we need to characterize the optimal behavior of managers during the recovery phases. We could assume either that (1) an "acting" manager is appointed during the recovery phase, and a new regular manager is appointed during the subsequent incentive phase, or (2) a new regular manager is appointed at the beginning of each recovery phase, and he continues his assignment to the end of the next incentive phase. In the present analysis, we make the first assumption; the qualitative nature of the results would be the same under the second assumption, but the optimal strategies during the recovery phases would be different.

We are interested in the average rate of price decrease over a sequence of cycles. By a cycle, we mean an incentive phase and the following recovery phase. The behavior of price during the first cycle is shown in figure 2.

PRICE

Po

t = 0 T

I Pre-¢*T

R~+r* I

T+T* t


• Price is initially Po, leading to zero profit when productivity is F 0 and demand isQo.

• Price then falls exponentially at rate cp for T periods to Po e --ffJT • Cash reserve is now non-positive.

• Price is raised to PT. This increase can be thought of as taking place in two

parts: from Po e -q>T to P~, the break-even price at T, and from P~ to PT, the

price which leads to a profit n* at T.

• Price decreases at average rate cp* , which may be negative, during recovery phase.

• At the start of the next incentive phase price is adjusted downward to P~+T*, the break-even price under the conditions that then prevail.

Thus we are interested in the long-run average over cycles of the average rate of price decrease which is, for the first cycle,

~I = T ~~ + T: l' [In [Po;;} In ~,. )]. (3\)

Our strategy will be, very roughly speaking, to show that the terms in the square bracket are uniformly bounded in T, and hence when Tis large the long-run average rate of price decrease is approximately cpT / (T + T*), which in tum is approximately <po

Let successive cycles (where a cycle consists of an incentive phase followed by a recovery phase) be indexed by m. Then the average rate of price decreasing during the first M cycles is

M

I, (<pT m + amT*) - m.:...=--:-:l :--___ _ CPM= M (32)

I, (Tm+ T*) m=l

where the am are random variables dermed by

amT* =-WT + In [ :~ ). PT+T*

(33)

In what follows, we shall assume that the length of the incentive phase is also exogenously bounded, say by 't, as in Theorem 2.

Theorem 3. Under the conditions of Theorem 2,


Corollary.

A cp----(\:0 ) I' 'f - h(o, 't) cp u, 't == 1m ill CPM ~ 1'*'

M~oo 1+-h(o, 't)

lim Cj)(o, 't) ~ cP , o~1 't~oo

where

145

Proof, Consider the optimal strategy of an acting manger during a recovery phase. Since 1'*, the length of the phase, is not affected by his actions, his optimal strategy is to choose the action A * in each period t to m~mize his one-period utility (5). This may result in decreasing productivity, i.e., increasing unit costs. But, because of the assumption that r is bounded below, the total increase in unit costs over the recovery phase is bounded; hence, the change in break-even price is bounded; hence the term

In __ T_ [

pO ]

P~+T* in (31) is bounded, and bounde[~ un~~~mllY over the sequence of cycles.

With respect to the term In o;~ , note that

Po C C-H p-H T=-=-e T= oe T FT Fo

so that

(p e-qlT] ln l °P~ =HT-cpT=-WT·

We shall now show that WT, the productivity gap at the first crisis, is also bounded. Suppose, as before, that the cash reserve first becomes non-positive at T, and let

A W (T, s) == Max WT subject to (34)

't 't

L,==L.is=L.eat(ew'-l)<s for t=I, ... ,T-l (35) 1=1 t=1


and L't;;::s (36)

We want to show that ~ (T, s) is bounded above by a bound independent of T. In fact, it will suffice to produce such a bound subject to the condition, weaker than (33),

LT- 1 < s,

and (34). Lemma. Let # T= Max WT subject to (35') and (36), where cr> 0 and

wt =Wt -Wt_1 $;w for t=2, ... ,T.

(This last is a restatement of the condition that r is bounded below.) Then ~ T is uniformly bounded with respect to T.

(35')

(37)

Proof of Lemma. We fIrst show that ~ T-l is uniformly bounded because of (35') alone. (35') reads

T-l

L ecrt (eW'_ 1) < s. 1=1

Move all terms but the last to the right-hand side:

T-2

eO"(T-l) (ewr-1 - 1) < s - L eO"t (ew, - 1) ,

1=1

T-2

eWr-1 < 1 + se -cr(T-l) - e -cr(T-l) L eO"I (ew, - 1) .

1=1

(38)

(39)

(40)

Choose WI. ... , WT-2 to maximize the right-hand side, i.e., to minimize the sum. The sum is minimal when

W 1 =W2 =···=WT_2 =-oo. (41)

Then the inequality becomes

T-2

eWH < 1 + se-cr(T-l) + e-cr(T-l) Leal (42)

1=1

1- e -a(T-2) 1 (43) eWr-1 < 1 + se-cr(T-l) + < 1 + s+ --.

eO" - 1 eO" - 1

Since the right-hand side is independent of T, eWr-1, hence WT-l> is uniformly bounded. (Note that the bound is finite when cr> 0.)


So far we have not used (37), the upper bound on the Wt. We now invoke it to conclude that, even though the cash reserve goes negative in period T, WT is uniformly bounded (by the implied bound on WT-l, above, plus w). This finishes the proof of the Lemma.

Returning now to (31), we can rewrite this equation as

--~ _1_[ [ P~ J] <PI-T+T*+T+T* -WT+ln P~+T ' (31')

and we have now shown that the second and third terms on the right are bounded. Hence the random variables am in (33) are uniformly bounded.

The random variables in successive cycles are typically neither mutually independent nor identically distributed, since successive cycles will typically have different initial conditions. Nevertheless, we can obtain a renewal-theorem-like result on the asymptotic behavior of CPM. First, let

<P~ = min (am' <p) ; (44)

then M (45) L (Tm<P+ <p~T*)

- n=l <PM ~ "---'M--:----- == PM'

L(Tm+T*) m=l

Second, let Em denote the operation of mathematical expectation conditioned on the history of the exogenous random variables Xt through cycle (m-l). By Levy's Strong Law of Large Numbers for dependent variables,4

M

L (T m<P + <P~ T*)

lim ~= 1 = 1. M~oo ,

L Em(T m<P + <Pm T*) m=l

M

L(Tm+T*)

lim ~= 1 1, M~oo

LEm(Tm+ T*) m=l

both limits holding almost surely. Hence

(46)


PM lim -=1,

M -?oo YM

where M

LEm (Tmcp+ cP~ T*) m=1

YM= M

LEm(Tm+T*) m=1

Since the am are bounded, there exists A such that ,

IEm CPml~A.

Recall that h(o, 't) denotes the right-hand side of (27); thus (27) implies that

Em T m ? h(o, 't) .

Hence, from (44) and (48)-(50), M

L [h(o, 't)cp + EmCP~T*] m=1

YM~ M

L [h(o, 't) + 1'*] m=1

A cP---> h(o, 't) - T*

1 + h(o, 't)

The conclusion of Theorem 3 now follows from (45), (47), (48), and (51).

(47)

(48)

(49)

(50)

(51)

The Corollary obtains when the two limits are taken in either order. That is, it can be shown that the numerator of the expression for h(o, 't) approaches a strictly positive number when the limits are taken in either order. We omit the details.

We have now shown that the long -run average rate of price decrease approaches the target rate, cP, provided that the latter is technologically feasible. The equilibrium described might still not be acceptable if prices could increase without limit during recovery phases, even though such increases are offset when profit is set equal to zero at the end of the recovery phase. It is straightforward to show, however, that for a constant-elasticity demand function, and with r bounded, the

maxim urn price increase during a recovery phase, i.e. the increase from P~ to point A in figure 2, is also bounded.


4. Remarks

In the model of Section 3, we have simplified the real regulatory situation in many ways. Some of these simplifications were made for ease of exposition, others for mathematical tractability, and still others to avoid problems of a more fundamental nature. In this concluding section, we comment on several possible generalizations and extensions of the model.

Two extensions which seem not to be fundamental are the following: 1. We have supposed that the productivity consequences of R&D are all realized

with a one-period lag. Actually, it is characteristic of R&D efforts that their benefits are realized after long and distributed lags. Inclusion of this complication, although perhaps difficult, would not entail a basic change in the model.

2. We have assumed that the firm's output just meets demand. The firm may provide several products, in which case we speak: of output and price indices. It is easy to see how, by counting outputs of different quality as different outputs, quality can be included in the output index; thus when we assume demand is met we also assume quality is maintained.

In reality, of course, utilities may fail to meet demand, in a quantitative sense, and may fail to meet standards of quality. It would be reasonable to let such failures trigger a recovery phase, just as cash insolvency triggers it in our example. In fact, in one sense our model may be reinterpreted as already having this feature: namely, if there is in the model no reason other than insolvency for the firm to fail to meet demand or quality standards, then such failures are subsumed in the triggering mechanism we have already described.

Three much more fundamental extensions are the following: 3. We have included in the model the action the regulators take if the firm runs

out of cash, but have not mentioned various possibilities for regulatory action if the firm prospers too greatly, i.e., if the cash reserve becomes very large. The regulator will be tempted to take some action in this case, because enormous profits for the firm will be politically unpopular, even if the firm's prices are dropping rapidly. For instance, it would clearly be possible to distribute part of a large cash reserve to the customers either in the form of still further reduced prices or as a lumpsum refund. To complete the specification of an equilibrium of this regulatory game, it would be necessary to describe the regulator'S announced strategy when the cash reserve becomes very large and to say what deterrent the manager provides to prevent the regulator from reneging on this strategy.

4. We have assumed that amounts of capital and other inputs can be optimally adjusted in each period. This ignores any irreversibility of capital investment by a regulated firm, as well as difficulties associated with laying off employees. Actually, the problem of how to best perform even "conventional" rate-of-return regulation when demand falls off and there is irreversible investment may not have been treated in the literature. To deal with this requires a more general sequential principal-agent model.


5. We have not included in the model the possibility of treating the distribution of information as endogenous. That is, we could include as a parameter of the regulators' strategy the amount of information they obtain, at a cost, about the fIrm's technological possibilities, and perhaps even about the manager's "private" utility.

In addition: 6. We have not attempted numerical estimates of the magnitude of the effects

we are discussing. We have shown, in a simplified exam pIe, that there are equilibria of the sequential game (corresponding to productivity incentive clauses) that are more efficient than short-term equilibria (corresponding to conventional rate-ofreturn regulation), but how much more efficient are they?

Such questions are difficult to answer, for two reasons. First, the technological possibilities open to the firm will (in the real world) usually be known to the managers only very incompletely, and will be even less well known to the regulators. Thus it is hard to estimate the maximum achievable growth in productivity, and hence the maximum achievable rate of price decrease. Second, it is hard to know how to estimate the manager's private utility (or dis utility) for various actions, and hence how great a share of the cost-savings the managers must receive in order to be persuaded to act in a cost-minimizing way. (The managers may, for example, receive this share in the form of increased longevity in office, which requires a larger cash reserve, undistributed to customers.) S till, examination of the productivity growth of utilities as a function of the intervals between regulatory reviews might yield some empirical evidence on these points.

7. Finally, if we were to analyze this problem explicitly as a sequential game, we would have to specify the regulator's objectives and the set of regulatory strategies that are available. In doing so, we would try to take into account the issues raised in point (3) above. In addition, such sequential games typically have a multiplicity of equilibria. If one of these is better than all others for both the firm and society, it may well be adopted. Otherwise, the choice of an equilibrium strategy pair will have to be established by bargaining between the regulators and the firm. Such bargaining mechanisms are not discussed in this article.

5. The Literature

Without attempting to be exhaustive, we comment on the relationship of the present article to some of the more recent literature dealing with incentives in regulation.

The modem literature on this subject may be said to start with Averch and Johnson (1962). The Averch-Johnson model is a static model in which the regulator's function is to impose an upper bound on a single-product monopoly firm's rate ofretum on capital, while the firm acts to maximize profit subject to this constraint. Both the regulator and the firm have complete knowledge of cost and demand, and there is no stochastic element in the situation. A thorough critique of this model is given in Klevorick (1973). In that study, Klevorick introduces a multi-period model that recognizes the regulator's role in setting price as well as


bounding the rate of return, and in which regulatory review is occasional and uncertain (although exogenously determined). Hence, he is able to consider the incentive effects of regulatory lag, discussed in Section 1 above. In particular, he considers, as we do, the incentives for investment in technological progress. Informational asymmetry is recognized in this model: the regulator has complete know ledge ofthe firm's current parameters (cost, output, capital stock, technological level), but cannot forecast the effects of technological and demand changes as accurately as can the firm itself.

This multiperiod or sequential line of modeling is continued in studies by Bawa and Sibley (1980) and by Vogelsang and Finsinger (1979). In Bawa-Sibley, the probability of regulatory review is no longer exogenous; it depends on the firm's financial results in the previous period. These results are known to the regulatori.e., the fIrm's past costs are known to the regulator. In Vogelsang-Finsinger, the discussion is extended to a multiproduct fIrm; here the regulator no longer sets the firm's prices, but constrains them in such a way that the profit-maximizing fIrm is induced to converge to Ramsey pricing. The fIrm's incentives to subvert such a scheme by deliberate waste are discussed in Sappington (1980).

All of these sequential models exist in the context of rate-base, rate-of-return regulation. In all of them except Klevorick's, the firm's cost function is assumed stationary. In general, except for Sappington's comment (1980), the emphasis is not on possible strategic behavior-misrepresentation, waste, etc.--on the part of the firm.

A somewhat different line of thought starts with Demsetz (1968). Here the firm's costs are not assumed known to the regulator, even retrospectively (in fact, these are single-period or stationary models), and the context is not that of rate-base rate-of-return regulation. Demsetz' suggestion is that a monopoly franchise be awarded to the bidding firm that undertakes to supply service at the lowest price; this will lead essentially to the competitive price. It is not said how the price is to be adjusted as costs change. A second study in this line is that of Loeb and Magat (1979), in which it is proposed that the monopoly firm set its own price (in a manner which could be responsive to changing cost and demand conditions). The fIrm would then receive a subsidy, so designed as a function of its price, that the profIt-maximizing firm would set price equal to marginal cost. Unfortunately, this subsidy would leave the firm with all the surplus associated with its operation. Loeb and Magat propose removing part or all of this surplus from the firm by prefIxing a process of competitive bidding for the franchise.

But what if there is only one bidder? As Baron and Myerson (1982) remark, a lumpsum tax might be levied on the firm; however, in the absence of cost information the regulator might set the tax too high, in which case the firm would decline to produce. (This is equivalent to the event, in our model, that the regulator sets the rate of price decrease, <p, beyond the technological capability of the firm. We have not analyzed this problem in the present article.) .

The regulator's objective function, for Baron-Myerson, is maximization of an arbitrarily weighted sum of profit and consumer surplus; when these weights are


equal, so that total surplus is being maximized, their solution reduces to that of Loeb-Magat. Their solution is explicitly incentive-compatible, i.e., it offers the fmn no incentive to misrepresent its costs.

Finally, in a further extension of this line of thought, Sappington (1983) extends the analysis to a multiproduct fIrm; a single parameter of this fmn' s cost function is unknown to the regulator. In Sappington's model, the regulator presents the fmn with a menu of a finite number of regulatory regimes, from which it makes a binding choice.

The present article differs from all of the above most saliently in that we focus on the incentives of the manager, rather than the more abstract "firm." (Thus profit maximization now appears indirectly in the form of the manager's desire to extend his tenure by keeping the cash reserve high. ) We also differ from all of the studies mentioned above, except Klevorick's, in that we emphasize technological charge, i.e., the firm's costs are endogenously determined. Because the manager's "tastes" differ from the regulator's and because the regulator cannot observe the manager's cost-reducing efforts but only their outcome (which also depends on an unobserved random variable), we deal with the problem of moral hazard. The sequential nature of our model enables us to design a regulatory mechanism that leads to improved efficiency in the face of moral hazard. We have not claimed that this regulatory mechanism is optimal; we are satisficing rather than optimizing.

Notes

The views expressed here are those of the authors, and not necessarily those of AT&T Bell Laboratories.

1. A version of the ideas in the present article was published-without the mathematics-in the proceedings of an .. Airlie House" conference that took place in 1982 (see Linhart, Radner, and Sinden, 1983). The term "price-cap" was not yet in use at that time.

2. One such clause had a three-year trial for Michigan Bell. The Michigan plan required that a price index of the firm's output drop in real terms by a fixed percentage every year (subject to a rate-of -return ceiling) to allow for expected productivity improvement. This allowance (initially 4%/year), along with the rest of the formula, was to be reviewed every three years. Incentive clauses of this general sort are discussed in Baumol (1982) and in Linhart and Sinden (1982). In the Michigan trial, the Commission may have set the productivity growth target unachievably high.

3. We do not explore in this article the complex econometric problems associated with the construction of appropriate quantity and price indices, or with the conversion of prices from nominal to real terms.

4. See Sec. 1 of D. Freedman, "Another Note on the Borel-Cantelli Lemma and the Strong Law," Annals a/Probability, 1 (1973).

References

Averch, R., and J. L. Johnson. 1962. "Behavior of the Firm under Regulatory Constraint." American EC01wmic Review 52: 1 052-1069.

Bawa, V. S., and D. S. Sibley. 1980. "Dynamic Behavior of a Firm Subject to Stochastic Regulatory Review." InternaJional Economic Review 21:627-642.

Baron, D. P., and R. B. Meyerson. 1982. "Regulating a Monopolist with Unknown Costs." Econometrica 50:911-930.


Baumol, W. J. 1968. "Reasonable Rules for Rate Regulation: Plausible Policies for an Imperfect World." In Prices: Issues in Theory, Practice, and Public Policy, edited by Almarin Phillips. Philadelphia, PA: University of Pennsylvania Press.

Baumol, W. J. 1982. "Productivity Incentive Clauses and Rate Adjustments for Inflation." Public Utilities Fortnightly 110:11-18.

Demsetz, H. 1968. "Why Regulate Utilities. " Journal of Law and Economics 11 :55-65. Houthakker, H. S. 1979. "Growth and Inflation: Analysis by Industry." Brookings Papers

on Economic Activity 1:241-256. Houthakker, H. S. 1981. "Competition, Regulation and Efficiency." In Regulation and

Deregulation, edited by Jules Backman. Indianapolis: Bobbs-Merrill. Klevorick, A. K. 1973. "The Behavior of a Firm SUbject to Stochastic Regulatory Review."

Bell Journal of Economics and Management Science 4:57 -88. Linhart, P. B., and F. W. Sinden. 1982. "Productivity Incentives Under Rate Regulation."

Bell Labs Economic Discussion Paper 236. Linhart, P. B., R. Radner, and F. W. Sinden. 1983. "A Sequential Principal-Agent Approach

to Regulation." In Proceedings from the Tenth Annual Telecommunications Policy Research Conference, edited by O. H. Gandy, Jr., P. Espinosa, and J. A. Ordover. Norwood, NJ: Ablex Publishing Corp.

Linhart, P. B., and R. Radner. 1984. "Deregulation of Long-Distance Telecommunications." In Policy Research in Telecommunications, edited by V. Mosco. Norwood, NJ: Ablex Publishing Corp.

Loeb, M., and W. Magat. 1979. "A Decentralized Method for Utility Regulation." Journal of Law and Economics 22:399-404.

Radner, R. 1981. "Monitoring Cooperative Agreements in a Repeated Principal-Agent Relationship." Econometrica 49:1127-1148.

Radner, R. 1985. "Repeated Principal-Agent Games with Discounting." Econometrica 53:1173-1197.

Radner, R. 1986. "Repeated Moral Hazard with Low Discount Rates." In Uncertainty, Information, and Communication, edited by W. P. Heller, R. M. Starr, and D. Starrett. Cambridge: Cambridge University Press, pp. 25-64.

Sappington, D. 1980. "Strategic Firm Behavior under a Dynamic Regulatory Adjustment Process." Bell Journal of Economics 11:360-372.

Sappington, D. 1983. "Optimal Regulation of a Multiproduct Monopoly with Unknown Technological Capabilities." B ell Journal of Economics 14:453-463.

Schumpeter, J. A. 1942. Capitalism, Socialism, and Democracy. New York: Harper and Row.

Stigler, G. T. 1971. "The Theory of Economic Regulation." Bell Journal of Economics 2:3-21.

Williamson, O. 1968. "A Dynamic Stochastic Theory of Managerial Behavior." In Prices: Issues in Theory, Policy, and Practice, edited by A. Phillips and O. Williamson. Philadelphia, P A: University of Pennsylvania Press.

8 INCENTIVES FOR COST REDUCTION

UNDER PRICE CAP REGULATION

1. Introduction

Luis M. B. Cabral Michael H. Riordan

In this article, we present a formal analysis of the incentives for cost reduction under a regime of price-cap regulation. We assume price-cap regulation establishes a ceiling below which a monopolist has complete price flexibility, while prices above the ceiling are subject to cost-based regulation. Our main conclusions are that a marginal reduction in the price cap increases the regulated firm's investment in cost reduction. However, very low price caps might destroy investment incentives completely. Therefore, investment is a discontinuous function of the price-cap level.

Our analysis includes a stylized comparison between price-cap regulation and rate-of-return regulation. We show that investment in cost reduction is higher under an optimal price-cap regime. However, while expected cost is lower under price cap regulation, the same is not necessarily true for expected price.

The article is organized as follows. The next section introduces the basic results for the case when there is no cost uncertainty, and the following section generalizes these results. The comparison between price-cap regulation and rate-of-return regulation is the object of the next section. The final section includes concluding remarks.

2. Monopoly Regulation

Throughout the article, we assume that the market for telecommunications is a monopoly. This is the case of local exchange carriers, for practical purposes. While the market for domestic long distance service is not a monopoly, the present

156 PRICE CAPS AND INCENTIVE REGULA nON IN TELECOMMUNlCA nONS

analysis provides a useful benchmark for examining the dominant firm case, and the key tradeoffs are in fact very similar for the two cases.1

We thus consider a monopolized market where the rate of demand is bounded and given by D(P) , with dD/dP < O. Marginal cost is a function of an investment devoted to cost reduction. Specillcally, denote by e the level of investment ("effort") in cost reduction and define d as the lag between the time of investment (normalized to t = 0) and the time when the cost reduction occurs. Then, marginal cost is C(O) for t < d, and C( e) for t > d. We assume that C( e) ~ 0, 0 < -dC/de < 00, and C is invariant with quantity produced.

Price-cap regulation is portrayed as follows. The regulator sets an initial price cap Po and an adjustment term x to take place at time d. The firm then makes an investment e in cost reduction. At time d, it can unilaterally set any price below Po - x, or it can request a rate hearing, the outcome of which is that the regulator sets price equal to C. We assume the regulation horizon is Tyears, T~ d.2

Since ceO) is exogenously given and known to the regulator, it is no loss of generality to assume that Po is chosen such that the firm finds it optimal to set price equal to Po for t < d. For the most part, our analysis focuses on the firm's pricing decision for t > d.

Denote by M(C) the firm's unconstrained monopoly price, which we assume is unique for any cost level C. Under price-cap regulation, the firm's actual price is given by

Price

P -x o

o

.. '

~~--~----~------------- C c· c ..

FIGURE 1: PRICE AS A FUNCTION OF COST UNDER PRICE CAP REGULA nON.

M(C): UNCONSTRAINED MONOPOLY PRICE; P: PRICE CAP; B(P,C): PRICE AC1UALLY SET.

INCENTIVES FOR COST REDUCTION UNDER PRICE CAP REGULATION 157

B(P 0 - x, C) = max {C, min {po - x, M(C)} } (1)

This function is depicted in figure 1. For values of cost lower than c', the firm prices as an unconstrained monopolist. If C lies between c' and c", then the price cap Po - x is binding. Finally, if cost is higher than c", the fum requests a rate hearing and price is set equal to marginal cost.

The firm's optimization problem can be described as

max 1t(po -x, e);; [B(Po-x, C(e»- C(e)] D[B(Po-x, C(e»] -e? (2) e

Denote by e*(x) the solution to this problem. The first thing to notice about the monopolist's problem is that when price-cap regulation is too "tight" then there is no incentive for cost reduction. A very low price cap cannot possibly compensate the fum for an amount of effort sufficient to reduce cost below the price cap. Formally:

Proposition 2.1. Suppose that e(O) > O. Then, there exists an x* such that e*(x) = 0 for x> x* and e*(x) > 0 for x < x*.4

The formal proof of this and the following propositions may be found in the Appendix. Our next result is that an increase in x (a decrease in the price cap) marginally increases the level of investment in cost reduction.

p

p m

o q m

q c

C

C-J

q

FIGURE 2: RETURNS ON COST REDUCTION UNDER COMPETITIVE AND MONOPOLISTIC CONDmONS


Proposition 2.2. If the price cap is binding and the frrm' s problem has an interior solution, then the optimal level of investment in cost reduction is increasing in x, i.e., de*/dx;;:: 0 for x < x*.5

The explanation for the result lies in what is known as the "Arrow effect." In a seminal study, Arrow (1962) compared the incentives for process innovation under a monopolistic and a competitive downstream market. He concluded that the returns to R&D are greater under competition than under monopoly:

The monopolist's incentive is always less than the cost reduction on the postinvention monopoly output, which in this case is, in turn, less than competitive output .... Since the inventor's incentive under competition is the cost reduction on the competitive output, it will again always exceed the monopolist's incentive. (p. 621)

In other words, a monopolist achieves a higher price by restricting quantity. Consequently, the savings from a reduction in unit cost are applied to a smaller number of units. This is illustrated in figure 2. The value of a one-dollar reduction in marginal cost is worth the area A+B under competitive conditions, while for a monopolist it is only worth A. Raising the price cap leads the regulated frrm to a situation closer to the monopolistic one.

Finally, Propositions 2.1 and 2.2 imply the following corollary.

Cost, Benefit o

45

B (x")

B(x*)

B(x' I ')

e o

e I e I I e*

FIGURE 3: EXPECTED BENEFIT AS A FUNCTION OF e AND x.


Corollary 2.3. e* (x) is maximized at x*. These ideas can be understood from figure 3, which illustrates the net

profitability of expenditures in cost reduction. The 45° line measures the direct cost of R&D effort. The remaining family of curves illustrates the expected profits from cost reduction for different levels of the adjustment tenn x. A higher value of x shifts expected benefits downward.

Two important effects are illustrated. First, if x is above some critical level x* then expected net benefit from cost reduction is maximized at e = O. Thus the firm will not make any investment in cost reduction unless x is sufficiently low.

Second, if x is below x*, then the firm will optimally choose a strictly positive level of cost reduction effort that equates marginal benefit to marginal cost. That is, at an optimum, the slope of the expected benefit curve is equal to the slope of the 45° line. Thus, for x equal to x' (x") the finn invests e' (e").

Finally, for values of x below x* , optimal R&D effort is increasing with x, i.e., a lower price cap encourages cost reduction.

3. Cost Uncertainty

In the previous section, we treated second-period cost as a deterministic function of investment in cost reduction. In this section, we generalize the main results to the case when costs are uncertain.

Costs, Benefits

e" e' e*

FIGURE 4:EXPECIED BENEFIT AS A FUNCTION OF e AND x.

e


Suppose that actual cost is a random variable c with a cumulative distribution F(c I e) that depends on the level of investment in cost reduction. We assume that the support of c is contained in [0, c~, where cO is the initial cost, and that of joe> 0, that is more effort makes lower cost realizations more likely.5

Proposition 3.1. For low values of x, the optimal level of investment in cost

ed . .. .. . .oe* I 0 r uctlOn IS mcreasmg m x ,i.e., -0 > . x x=o

Proposition 3.2. There exists x* such that e*(x) = 0 for x> x*.

Example. Suppose that Po = cO = 1, D(P) = ex - p,andmarginal cost is uniformly distributed on [0, exp([3e)], where ex and [3 are constants. Figure 4 depicts expected benefit and the firm's optimal solution for different values of x. Notice that in contrast with figure 3 (certainty case) expected benefit is always positive, because some cost reduction occurs even when e = O. Therefore, at the point of discontinuity, where the firm is indifferent between e* = 0 and a positive value of e*, net expected benefit is positive. Other than this, the discussion on the qualitative properties of figure 3 can be extended to figure 4.

Based on figure 4, we can map the optimal value e* as a function of x. This is done in figure 5, for particular values of ex and [3 (ex = 2.05 and [3 = 2). The main points of Propositions 2.1-2.3 are depicted in this figure: (1) for low values of x the optimal level of investment is increasing with x; (2) there is a level x* such that

e*

.075

.05

.025

o 8.5

FIGURE 5: INVESTMENT IN COST REDUCTION AS A FUNCTION OF x.


e* = 0 for x> x* and e* > 0 for x < x*; (3) e* is maximized atx = x* (approximately 8.5% in this example). Note, however, that the characterization of Propositions 3.1 and 3.2 is not as complete as that of Propositions 2.1-2.3. In order for the latter to extend to the uncertainty case, we need the uncertain cost distribution to be sufficiently "close" to the certainty case. In general, we can only characterize the behavior of e*(x) for very low and very high values of x.

Comparison with Cost-Based Regulation

Cost-based regulation with regulatory lag is portrayed as follows. At time zero, a rate hearing occurs and price is set equal to cost co. This price remains valid until time T, when a new regulatory hearing occurs. We assume that T> A. This implies that there is a positive incentive for investment in cost reduction, for the benefits of a lower cost during the period [A, 1] remain with the firm. However, we will show that these benefits are weakly lower than under price-cap regulation.

In order to make a comparison between the two regimes, we assume that the second-period price cap remains valid for a length of time 5. It seems reasonable to suppose that A + 5 ~ T, i.e., switching to the price-cap regime will not shorten the period of time the regulator can commit to.

Price-cap regulation can be understood as cost-based regulation with a (possibly) longer period of regulatory lag and downward price flexibility. Both of these differences tend to promote investment in cost reduction.

Proposition 4.1. The level of investment in cost reduction is the same or lower under cost-based regulation than under price-cap regulation.

This conclusion is easily understood in terms of the Arrow effect and wellknown results in the regulatory lag literature (e.g., Baumol and Klevorick, 1970).

Consider price-cap regulation when Po = co, x = 0, and 5 = T - A. In this case the only difference between price-cap regulation and cost-based regulation is that the former allows downward price flexibility. By the Arrow effect, this difference promotes incentives for cost reduction. Moreover, the level of investment in cost reduction is non decreasing in 5, which determines the length of time over which the frrm is able to appropriate the benefits of cost reduction.

Another important point of comparison between price-cap and cost-based regulation is the level of prices in each regime. Under cost-based regulation, initial price is set at the level of initial cost cO. This price is maintained for a period T, and then revised to the level of cost at time T, which is a function of the firm's optimal level of investment. Under price-cap regulation, the frrm is free to set any

price lower or equal to pO - x during the period [A, A + 5). Note that given the assumptions previously made, the period [A, A + 5] can be subdivided into [A,11 and [T, A+5]. Since, pO - x is less than cO, we can be sure that during the period [A,11 prices will be lower under price-cap regulation than under cost-based regulation. However, the same is not true for the period [T, A + 5). The intuition

for this result can be seen from figure 1. Suppose, for simplicity, that pO - x = cO.

162 PRICE CAPS AND lNCENTIVE REGULATION IN TELECOMMUNlCA TIONS

Under price cap regulation, in order for price to be lower than cO during the period [T, A + 0], it must be the case that cost at time T is lower than c'; and even if this is the case price declines at a lower rate than cost.6 Under cost-based regulation, however, any value of c below cO translates into a lower price during the period [T, A+ 0].

We thus conclude that while the proposed price-cap rule guarantees declining rates in real terms, it is unclear that rates will be, at all times, lower than what they would be under rate-of-return regulation. However, since price-cap regulation would promote a more efficient investment in cost reduction, it is possible, if not likely, that consumers would prefer the change of regime. In fact, since the regulator is able to set both Po and x, there is no reason why there should be any conflict between efficiency and equity. As we saw earlier in the article, X influences the ftrm' s investment in cost reduction, while Po does not. Therefore, the regulator should choose x so as to maximize efficiency, and use Po as an instrument to divide the efficiency gains between the firm and consumers.

In general, consumer welfare is increased by setting the initial price cap somewhat below current cost. This guarantees to consumers a period of lower prices without compromising the firm's incentives for cost reduction. At its best, price-cap regulation promotes cost reduction by promising the firm an ex post rent from its investment. Setting the initial price cap below cost is a way to redistribute that rent to consumers ex ante.

5. Conclusion

We have argued that price-cap regulation promotes incentives for investments in cost reduction, compared to cost-of-service regulation, provided that future price caps are not too low. On the other hand, a price cap that declines too precipitously might destroy investment incentives altogether. Moreover, even a price cap that successfully promotes cost reduction does not necessarily guarantee consumers lower prices in the future. Regulators should consider initially setting the price cap below current cost as a method forredistributing the benefits of price-cap regulation to consumers.

There are various issues relating to price-cap regulation which our analysis did not address, including regulation of a dominant firm, incentives for quality improvement, and information asymmetries? However, we would expect the main results of our stylized model to hold in more general contexts.

Appendix

Proof of Proposition 2.1. If x = Po, then the benefits from cost reduction are zero, and so e*(x) = O. Since

demand and Ce are bounded, this is also true for values of x close to Po. Q.E.D.


The following mathematical lemma is well known.

Lemma A.1. Consider a twice differentiable functionf(x,y),f 9\2 ~ 9\. Suppose z(y) = arg maxf(x,y). Then,

x

sign - = Sign ~ . (dZ) . ((l') dy axay (AI)

Proof of Proposition 2.2. If the price cap is binding, then 1t = [Po - x- C(e)] D(Po - x) - e, and by (AI),

. (de*) . (a21t) . (de dD) Sign - = sign -- = sign --dx ae ax de dB (A2)

which is positive, given the assumptions previously made. Q.E.D.

Proof of Proposition 3.1. Denote by M(e) the unconstrained monopoly price. The firm's expected profit

is given by

l td1 (Po-x) (M(e) - c) D(M(e» dF(e I e)

o f

Po-x + 1 (Po-x-e)D(Po-x)dF(ele)

td (Po-X)

The derivative with respect to x is given by

an fPo-x aD -a =- (Po-x-e)-a +D(Po-x)dF(ele) x tdl (Po-x) x

JPo-x

( laD =- td(Po-x)-e)a-dF(ele),

td l (Po-x) x

for D(P) + (p - tdl(e» ~~ = O. Finally,

a2n a JPo-x I aD -a a =--a (td (Po-x)-e)-a dF(ele). x e e td1 (Po-x) x

(A3)

(A4)

(AS)

Given thatF e is positive, e" > e' implies that F(e I e') dominates F(e I e") in the sense of first-order stochastic dominance. Therefore, since the integrand is an


increasing function of c, the right-hand-side of (AS) is positive (cf., Milgrom, 1981). Finally, the result follows from Lemma A. I. Q.E.D. Proof of Proposition 3.2

Suppose that x = pO - E. For a small enough E, expected benefits from cost

reduction are given by r (E - c) D(E) dF(c I e). Since dF is bounded, both ex-o

peeted benefits and the derivative of expected benefits with respect to e converge uniformly to zero with E. Therefore, there exists a small enough E such that the derivative of expected benefits with respect to e is less than one, and the optimal solution is e = O.

Q.E.D.

Proof of Proposition 4.1 Since we assume marginal cost to be constant after .1, the rate of profit is constant

during the period [.1, .1 + 5], and total benefit under price-cap regulation is proportional to o. The result follows from the Arrow effect, just as in Proposition 2.2.

Q.E.D.

Notes

Previous versions of this anicle were presented at the C.E.P.R. Conference on Utility Regulation (Stanford University, April, 1988) and at the 7th International Conference on Telecommunications (Ml.T., June, 1988). We are grateful to Evan Kwerel, John Litwak, Roger Noll, David Sibley, and William Taylor for comments and suggestions. This research has been supported by the Center for Economic Policy Research at Stanford University and by the National Science Foundation (grant # IRI-8706150).

1. For an analysis of the dominant finn case, see Cabral (1988). 2. Alternatively, one can make the asswnption that at time T regulation revens to a regime of

cost-based regulation without regulatory lag. 3. The rate of profit is integrated over the period [4, 1]. Since profn is constant, (2) is obtained by

an appropriate change in units. 4. If the price cap is not binding, then the level of investment is invariant with respect to x. 5. FonnaJly, increased effon reduces cost in the sense of fmt-<>rder stochastic dominance. See

Milgrorn (1981). 6. It can be shown that the derivative of monopoly price with respect to marginal cost is less than

one (one half, in the case of linear demand). 7. Some of these issues are covered in Baron (1988) and Cabral (1988).

References

Arrow. KennethJ. 1962. "Economic Welfare and the Allocation of Resources for Invention." In National Bureau of Economic Research. The Rate and Direction of Inventive Activity. Princeton: Princeton University Press.

Baron, David P. 1988. "Incentives and Telecommunications Pricing." Mimeo, Stanford University (March).

Baumol. William J., and Alvin K. Klevorick. 1970. ''Input Choices and Rate-of-Return Regulation: An Overview of the Discussion." Bell Journal of Economics 1: 162-190.

Cabral. Lui's M. B. 1988. "Price Cap RegUlation." Mimeo. Stanford University (May).


Face, Howard K. 1988. "The First Case Study in Telecommunications Social Contracts." Public Utilities Fortnightly (April 28).

Federal Communications Commission. 1987. "Policy and Rules Concerning Rates for DominantCarriers."CC Docket No. 87-263.

Federal Communications Commission. 1988. "Further Notice of Proposed Rulemaking." CC Docket No 87-313.

Mathios, A., and R. Rogers. 1987. "The Impact of Alternative Forms of State Regulation of AT&T on Direct Dial Long Distance Telephone Rates." Working Paper No. 159, Federal Trade Commission (December).

Milgrom, Paul R. 1981. "Good News and Bad News: Representation Theorems and Applications." Bell Journal of Economics 12:380-391.

Office of Telecommunications (Of tel). 1988. "The Regulation of British Telecom's Prices: A Consultive Document." (January).

9 THE QUALITY OF REGULATION IN

REGULATING QUALITY: A Proposal for an Integrated Incentive

Approach to Telephone Service Performance Eli M. Noam

1. Introduction

This article surveys the post-divestiture trend of service quality in the public telephone network and proposes an incentive system for assuring such service quality, while providing greater flexibility to telephone companies in reaching high quality standards. The approach could be part of a price formula involving inflation and productivity; it could also be applied under different regulatory arrangements.

The importance of understanding and measuring the quality of telecommunication services has grown with the tum towards price formulas and incentive forms of regulation and away from pure rate-of-return systems. A price-based regulatory mechanism provides incentives to cut cost, which is good up to a point, but may also lead to undesirable comer-cutting. Any price-based regulation, including a moratorium approach such as New York's, is relevant only in reference to some quality measure. Otherwise, where competition is inadequate, a hidden price increase could be imposed through quality deterioration, or improvements may be forsaken because no financial reward for them is forthcoming.

For a long time, service quality was a subject discussed in the context of the AT&T divestiture. It was greatly feared that a more competitive and decentralized environment would lead to serious service degradation because the local exchange companies would be starved for investment funds. But though many people still firmly believe that these fears have become a reality, there is little evidence to support this view. Section 2 of this discussion provides information on the trend of a quality. The absence of divestiture-induced calamities does not prove that there should be no concern, nor does attention to quality imply that it has deteriorated. In a transmission sequence of multiple carriers, a signal quality will not normally be better than its "weakest link." Hence, a bottleneck carrier with


inferior quality could obviate the efforts of the carriers for higher quality, especially if they compete with each other. Thus, through "quality-matching," overall quality would decline. This would not be the case in a monopoly system with end-to-end responsibility, because a sequential upgrade of quality in the various network element would make more sense. This is a long-term problem that may not be reflected in the data.

The absence of a proper incentive structure in a new regulatory system could lead, over time, to a slide in quality and the aggregation of deficiencies. These can, at some point, accelerate; the experience of telephone service problems in New York City in the early 1970s is a lesson worth remembering. Much better than overcoming crises in the future would be to institute a rational system today that would reward quality, discourage decline, and permit reasoned managerial planning.

The article, in its Part 4, proposes such a mechanism that could be integrated in a more general price-cap formula. Before moving to the proposal itself, the context will be set by discussing the conceptual difficulties of dealing with quality (part 2), and providing empirical evidence for the experience ofthe post-divestiture years (part 3).

2. The Quality Quagmire: Definitional Dilemma and Measuring Morass

Measuring the quality of telephone service seems to be a deceptively straightforward empirical question. But the difficulties start with the basic definition. The term "quality' has many dimensions: reliability, accuracy, security, simplicity, flexibility, speed, availability, responsiveness, courtesy-to name but the most obvious (Richters and Dvorak, 1988,24-35). It also covers many sub-systems, such as transmission, switches, directory service, repair, technical support, coin telephones, etc. Next, there are measuring problems. Some of the quality dimensions can be measured directly and objectively; others only indirectly; still others require subjective assessments that may well change over time.

On the positive side, quality is one issue whose analysis is not stymied by a scarcity of data, at least not on the supply side. To the contrary. For their own operational use, the Bell Operating Companies routinely and continuously collect well over 100 service measurements. The costs of these measurements is part of operations and difficult to identify, but it has been estimated as high as several hundred million dollars per year (Gryb, 1990). On the other hand, information about the demand side--price-quality valuation and tradeoffs by end-users-is limited.

But the main problem is not data but the conceptual ability to handle them, and of linking them to broader regulatory policy.

A literature survey on the subject of telecommunications modernization by the state regulatory commissions' think tank NRRI includes in a 23 page bibliography no citation on service quality (Lawton, 1988,87-114), indicating the absence of

TIlE QUALTIY OF REGULATION IN REGULATING QUALTIY 169

policy analysis articles on the subject. There is, of course, in-house work by teleos, but most is not publicly available, and the work is of a traffic-engineering or operations research type with little regulatory reference. (For an excellent exception, see Buzas, Lynch, and Berg, 1989.)

Part of the problem is that economic analysis does not provide unambiguous answers on what to expect to happen to quality-whatever socially optimal quality is-as regulatory restrictions are being reduced "Economists now have at their disposal a well-developed body of analysis dealing with price and quality behavior in various market structures, but they have no comparable body of analysis relating to the qualitative and alterable attributes of products that consumers value." (Sheshinski, 1976) This has led to disagreement even on basic points. Starting with Wicksell (1934) and Chamberlin (1948), the literature held that a monopolist would provide lower quality then a competitive industry with similar cost conditions. (Dorfman and Steiner, 1954,826-836; Rosse, 1972; Panzar, 1975; Spence, 1975,417-429) But this thinking was challenged by Swan and then Levhari and Peles who found market structure to have no impact on quality. This non-intuitive result was first viewed as depending on seven strict assumptions, but subsequent work (Schmalensee, 1979, 177-196) showed that several of them could be relaxed. Swan's argument still holds under certain conditions, including constant returns to scale. One view is that a regulated monopoly, having to lower rates, may also lower quality. But this, too, has been disputed. Some authors found that price regulation or a maximum price ceiling may actually improve quality (Schmalensee, 1970, 54-64; Besanko, Donnenfeld and White, 1988,411-429). For example, an unregulated monopolist sets quality especially low for those users who hold weak preference for quality in order to be able to charge an extra premium to users with a high quality preference. If a price cap is set on the latter price, the lower quality of the option will rise. But other analyses found that under certain conditions price regulation lowers quality (Kihlstrom and Levhari, 1977,214-234).

The only thing these studies seem to agree on is to treat quality as a one-dimensional variable for analytical convenience. For regulation, however, such simplification does not work. Thus, the economic literature is of only limited help. Taking instead an empirical look at the telecommunications sector, it is plain that liberalization of entry and competition has led in recent years to manifestations of rivalry in quality.l For example, AT&T's 1989 advertising includes claims that MCl's fax network leads to 87% more unreadable pages than if AT&T had been chosen. US Sprint, similarly, stressed the signal quality of its all-fiber network that lets the user "hear a pin drop" -until it was challenged on the accuracy of that claim. But it should be noted that user choice need not necessarily be used to select higher quality. Given the option, many customers could well select lower technical quality if the price is right. Some users prefer a jalopy to a Cadillac.

Furthermore, the advantages of competition may be partly or fully offset by reducing overall economies of scale and scope, and by adding technical incompatibilities and planning problems-between different networks, between networks and customer equipment, and between equipment types. And while these


arguments have lost weight by some self-serving use in the past, they cannot be ignored.

The quality question gets further tangled in the issue of overcapitalization. In the United States, under the rate-of-return regime, it was alleged that regulated utilities had incentives to overcapitalize and to gold-plate, because they arguably could obtain an assured return, in contrast to, for example, expenses on labor: the Averch-Johnson effect. A more competitive regime may well reduce such incentive to overcapitalization and lead to an economically more efficient, but lower quality system? Is this necessarily bad?

Another problem is that customer sovereignty may lead to technical solutions that improve some features, while reducing others, with an indeterminate impact on overall quality. For example, a private packet network provides control and flexibility, but can also cause transmission impairments, such as speech clipping, clicking, and echoes due to packet discarding, misdelivery, and congestion delay (Takehashi, 1988, 17-23). From the perspective of the actual users of this network, overall quality may have declined, while the advantages are reaped by other parts of their organization.

To complicate things still further, quality is not a static concept but a relation between performance and requirements. Since the latter are rising, what constitutes good quality is a moving target What was good enough yesterday may not be enough today, and not just because we tend to take past luxuries soon for granted, but also because past standards move from being merely convenient to being vital. Society depends more and more on the availability of telephone service. An example follows.

In 1988, fire destroyed an lllinois Bell telephone exchange in the Chicago suburb of Hinsdale. As a result, communications between regional air traffic controllers and O'Hare Airport, the nation's largest, were closed down, as were hotel and airlines reservation centers, mail order sales facilities, and the national reservation system for 12,500 florists-on Mother's Day (Block and Levine, 1988,9-10).

Similarly, one-third of regional Illinois automated bank teller machines ceased to function, and hundreds of financial institutions had serious problems in their electronic transfers, with some having to resort to cellular phones operated by the Federal Reserve from a van on a classified and shifting street comer. It took several months to fully restore service at Hinsdale.

A similar demonstration of vulnerability occurred when, in 1985, a computer breakdown at the Bank of New York,lasting less than a day, caused a cash deficit that required the bank to borrow $24 billion overnight from the Federal Reserve Bank (letter from Levine to Hesser, 1988). One can imagine the impact of a more extended breakdown lasting longer and affecting other institutions, as would be the case if telecommunications were to fail.

Vulnerability has also been added by fiber optic transmission. While fiber optic lines are more weather resistant than microwave links, they carry much more traffic and are much harder to repair, so that the failure of such a high-capacity system is

THE QUALITY OF REGULATION IN REGULATING QUALITY 171

potentially more disastrous than that of microwave and coaxial systems (Kraushaar, 1988).

By becoming increasingly dependent on high-tech communications flows, advanced societies also put themselves at risk. In consequence, demands on several dimensions of service quality increase because failure becomes unacceptable.

3. Quality: An Empirical Look at the Post-Divestiture Trend

3.1 A Lost Golden Age? We can now move to the next section of this discussion and deal with the

empirical question: Has service improved or declined in the U.S. in recent years? An important observation at the outset is that, contrary to the nostalgia for the Bell monopoly, there never was a golden age of qUality. In the late 1960s and early 1970s, several major cities experienced serious service problems. For example, the state's major local exchange carrier New York Telephone's service quality declined, largely due to conservative demand forecasting by AT&T's headquarters, maintenance problems, and skills shortages. The New York Times, in an editorial in August, 1969, called telephone service "miserable," "wretched," and "the worst in the memory of older New yorkers ...... Figure 1 shows a major peak in consumer

PSC CONSUMER COMPLAINTS All Telephone Companies In New York

45

40

35

30 No. of

Complaints 25 in 20

Thousands 15

10

5

0 6667686970717273747576777879808182838485868788

Year

Source: New York State Public Service Commission. Consumer Service Division


complaints at that time (preceding much of deregulation, and suggesting that there was a fertile ground for the entry of new service and equipment providers). Notice, too, that the number of complaints has held steady in the past decade of deregulation and divestiture, despite the slightly and steadily increasing number of subscnbers.

The frrst beneficiary of the quality crisis of the early 19708 was the New York State Public Service Commission (PUC) itself, whose telecommunications staff was almost quadrupled by Gov. Rockefeller from an inadequate 25 to 95.

One of the early things the new staff did was to develop telephone service standards, which were at the time, 1972, probably the nation's strictest and were criticized as such by the telephone industry.

Also instituted was an exemplary monitoring system which created incentive for better service to avoid negative pUblicity, and established the Basic Service Index (BSI) with customer rebates of up to 20% (out of telephone companies profits) if service quality in their central office drops to "weakspot" levels for three consecutive months or more, and not due to natural disasters. The BSI, the first plan in the U.S. to provide an automatic link of service deterioration and rates, consists of numerical scores for exchanges (above about 3,000 lines) for five (now seven) factors: customer trouble reports; equipment irregularities; overflows; dial tone speed; and incoming matching loss.

For all the telcos' dire predictions, only about $200,000 were actually rebated to customers during 1972 and none since then, even though the standards were twice tightened and broadened, most recently in 1989.

3.2 Post-Divestiture Quality Trends 3.2.1. Federal This brings us to the present What has happened in recent years? Since

telecommunications are regulated by at least 52 different entities, consistent data on national trends in service performance are difficult to come by. The FCC, commendably, has collected data since 1985, a highly complex task (Kraushaar, 1989). These are its broad findings: since divestiture, the (subjective) satisfaction of large users has greatly increased from 90.3% to 94.5% in 1988, while that of small businesses has risen slightly to 94.2%. Residential customers' level of satisfaction has remained relatively flat, but still high, at 93-94%.

Using more objective technical measurements, the percent of entities meeting FCC dial tone standards has gone up3 from 97.6% in 1985 to 98.8% in 1988.

Similarly, transmission quality (consisting of signal noise, balance, loss, and distortion) has somewhat improved (from 90% to 94.3% of entities meeting objectives), and percent of call completion (network blocking) is slightly up, to a high 99.1.

On the other hand, the manpower-intensive on-time completion of service orders slightly declined for residential users, decreasing from 98% in 1985 to about 97% in 1988 while remaining generally flat around 98% for business users.

THE QUALTIY OF REGULATION IN REGULATING QUAliTY

Source:

Chart 6-Composite Service Quality Index Average No. Indices Above '85 Le~ls

2.6

2.4

2.2

2

18

1.6

1.4

1.2

0.8

0.6

0.4

0.2

0

85 86 87

Reporting period (from 198!!)

(No Penalty for Hissing Data) New York State Public Service Commission

173

BB

Figure 2 provides the FCC's overall assessment of service quality. The index chosen, however, is extremely simple measure-a summary of the five factors described above, each rating a + 1 or -1 if it has moved either up or down since 1985. Overall, the FCC index shows an increase in quality, especially initially. And it concludes: "The composite average index ... reveals that typically service is as good or better than in 1985 ... " (Kraushaar, 1989).

3.2.2. The States Most of service quality monitoring has been at the state leve1. In quality

measurement, several of the states have more experience and involvement than the FCC.

Data will be provided for two states whose data collection is especially strong: a time series for New York, and a cross-section for Florida. (New York PSC, 1989).

In New York, as can be seen in figure 3, consumer trouble reports per 100 lines of New York Tel service have largely been flat (at about 4.2) since 1986 (New York PSC, 1989). They were slightly higher than in 1985, which was, however, a much better year than 1983 and 84 (and much lower than the early 1970s; see figure


NEW YORK TEL --STATEWIDE CONSUMER TROUBLE REPORTS PER 100 LINES

10.----------------------------------------------,10

8

6

4

2

KEY

12 MO MOVING AVERAGE

- MONTHLY DATA WEAKSPOT LEVEL 8

6

4

2

o ~ 0 JAN JAN JAN JAN JAN JAN JAN

1 1983 1 1984 1 1985 1 1986 1 1987 1 1988 11989

Source: New York State Public Service Commission, Consumer Service Division

1). The number of lines out of service for over 24 hours has declined, after an initial increase, to almost its 1984 level, which was lower than 1983.

NY Tel's own surveys indicate that its largest customers today are much more satisfied (98%) with service than immediately after divestiture (65%); that medium -size businesses' level of satisfaction has held steady; and that small users' "comfort level" has slightly improved, after an initial gentle slide (figure 4). Aggregate data, however, may mask localized deterioration. In New York, this was a particular problem in the City outer boroughs of Brooklyn, Queens, and the Bronx. Quality declined there until 1987, prompting regulatory intervention and company commitment, which led to quality improvements to levels superior to those in 1985. Furthermore, the complaint rate to the PSC is higher for NY Tel (about 1.2 complaints/year per 1,000 lines in 1988) than it is for the independent telcos (the six largest of which range between .3-.6 complaints/year per 1,000 lines for the same period). Also, the trend for these companies is to a lower complaint rate, while NY Tel's is flat. Furthermore, since rates have been stable in the past two years, complaints over billing are likely to have dropped off. Thus, a flat overall complaint rate may include an increase in complaints over quality. There have also been problems in NY Tel's on-premises visits, a labor-intensive service.

TIIEQUAUTYOFREGULATIONINREGULATINGQUAUTY

NYT CUSTOMER COMFORT LEVEL COMPOSITE INDEX OF OVERALL

SERVICE QUALITY

100~----------------------------------------------~100

KEY

MONTHLY RESULT 95 ~ 12 MO MOVING AVERAGE

90

85

JUL JAN JUL JAN JUL JAN JUL JAN JUL JAN 11984 1 1985 1 1986 1 1987 1 1988 1 1989 1

NOTE, INDEX IS BASED UPON 18 DIFFERENT SERVICE MEASUREMENTS OF

INSTALLATION AND REPAIR.

Source: New York State Public Service Commission, Consumer Service Division

95

90

85

175

Missed home service calls increased (from 10% to 15%), especially at first after divestiture, with some improvement since.

But with these qualifications, it appears that most quality measures have stayed stable and even improved slightly. A recent staff report on service quality to the New York Commission (second quarter, 1989) shows an overall improving trend for consumer trouble reports; only four of 654 offices experienced three consecutive-months "weakspot" level service in the first quarter of 1989. "This result was the best first quarter result since divestiture ... " (New York PSC, 1989).

The second state for which good information--in this case cross-section data-is available is Florida.

The Florida PSC tested for comparative quality measures for 13 long-distance companies (table 1). The firms uniformly perform at a much higher level than the required 90% call completion rate (1 minus network blocking probability), with the best performer US Sprint at 97.45%, and the lowest Telecommunication Service Corp, at 94.11 %. AT&T, for all of its economies of scale, is ranked only fourth with 97%. But the differences are really quite small.


Table 1. Quality for Long-Distance Comeanies IXC % Com- Noise Noise Insertion

eletions (Metallic} (Imeulse} Loss American Telephone & Telegraph 97.00 17.0 5 2.5

United States Transmission Sys- 96.69 18.0 0 2.0 tems,lnc. MCI Telecommunications, Corp. 96.69 13.0 0 2.0 Microtel, Inc. 96.18 12.5 0 2.0 Metromedia Long Distance, Inc. 96.73 21.0 3 2.1 Southern Net Services, Inc. 96.73 9.5 0 2.1 Telus Communications, Inc. 96.56 15.0 2 0.5 Telecommunications Service Corp. 94.10 13.0 4 2.1 Transcall American Inc. 96.51 11.5 2.3 South Tel, Inc. 97.37 17.5 2 2.0 United Telephone Long Distance, 97.06 12.5 0 2.0 Inc. U.S. Sprint, 97.45 11.8 0 2.0 Western Union Telegraeh Co. 95.85 31.0 1.8 Source: Florida PSC, Various Tables 1989.

Table 1 compares transmission performance of the long ~distance companies for noise and loss. (Lower numbers generally indicate better quality.) According to these figures, AT&T does not perform all that in these measures in comparison with some of its competitors.

When it comes to billing accuracy, only one firm (Southern Net) was found to be overtirning. Four firms were undertiming (including Southern Net). And three companies, including Western Union, apparently did not bill for completed calls!

The Florida PSC also collected comparative data for four local exchange companies. For dial tone delay, answer time (operators, directory assistance, etc.), directory assistance, service availability, etc., the quality of service was found to be substantially above required standards. For public telephone service, however, it was often below standards.

The Florida figures do not provide a time trend, but they show that, whether quality has gotten better or worse, it has almost always been very high in relation to standards.

3.2.3 International It is also useful to briefly compare the U.S. data with other countries. (See more

generally, Noam, forthcoming.) In Great Britain, the establishment of an independent regulatory oversight

agency revealed the serious service problems of a telephone system with a history of antiquated plant and traditional management. Oftel, the regulatory body, received so many complaints that it considered instituting damage liability against

mE QUALITY OF REGULATION IN REGULATING QUAUTY 177

British Telecom. A BT line averaged a technical problem every two years, ten times the rate of the Bell companies in the U.S. Even BT conceded the fault rate to be two to three times higher than in the US. (Hudson, 1987).

Table 2. Performance Comparison: New York Telephone Company vs. British Telecom

Operator Response Long Distance Blocking Service Orders Filled

Complaints to Company per Line Complaints Cleared

New York Tel Average 4 sec.

<1% 92% within 5

business days .04

British Telecom 87% within 15 sec.

3.6% 62.2% withing 8 business days

.22 75-80% within 24 74% within 5 hours

hours 90.2% within 2 days Source: BT and Communication to the author by NYT, 1988.

Table 2 provides a service quality comparison. Of all telephone calls made to operators in March, 1988,86.7% were answered by BT within 15 seconds. In comparison, New York Telephone reported that in July, 1988 calls to operators were answered within four seconds on average. Of long-distance call attempts, less than 1 % of the failures were attributable to New York Telephone. In contrast, 3.6% oflong-distance calls failed because ofBT. In the same year, 62.2% ofBT telephone orders were fIlled within eight working days. There were 0.22 complaint reports received per telephone. Of those, 74% were cleared up within five hours and 90.2% within two working days. For NYT, approximately 92% of telephone orders were fIlled within five business days. There were 0.04 complaints received per telephone line, and of these 75-80% were corrected within 24 hours.

Particular serious problems existed in the UK for coin telephones. A 1985 survey by the Daily Mail showed almost 60% of public telephones out of order at any given time. Oftel commissioned its own study, which found a still extraordinary rate of 50%. Over two years of effort aimed at improving this dismal state produced improvements: at the end of 1987, Of tel found 23% of public phones out of order, and less than 10% by mid 1988 (Of tel, 1988). In 1988, service complaints began to decline somewhat. Problems remained for directory inquiries (20-25% failures), complaints handling, and telephone selling.

As a second country. Denmark is described briefly, because its telecommunications system is similar in structure to that of the U.S.-several regional exchange companies and a national interexchange carrier. But there is no competition and little deregulation outside of customer premises equipment (CPE) and value added networks (VANs).

Blockage for Danish test calls declined up to 1983, but increased again thereafter. A comparison with the U.S. company Southern Bell (figure 5) shows the Danish blockage probability to be about 50% higher, and worsening at a faster rate.


Call Attempts Blocked Trend for Southern Bell-Fla & Denmark

3.5 tPe~r~c~en~t==::::~~========~~::::~~~ __ ~~~==l 3 -------~------- --- - -

2.5

2~~==--~--~---~--==~~==-=--=--=-~-~~ 1.5 f--------C'-

0.5 f-----------

oL--------~-----------L----------~--------~ '85 '86 '87 '88 '89

- Southern Bell(trend) --+-- Denmark (trend) ---r- Southern Bell(actual)

Source: Florida PSC: Danish Ministry of Transportation & Communication

4. Instituting an Integrated System of Quality Incentives

We can now move to the next section and propose an operational way to integrate quality performance with regulatory policy.

Is quality regulation necessary? We have found that service quality, on the whole, has not deteriorated. If it ain't broke, why fix it? The answer is that quality is presently fairly strictly regulated in numerous, usually disconnected, and inflexible ways that make the achievement of overall enduser satisfaction more costly than need be. Quality performance is rarely integrated with economic performance, except for truly substandard situations. The traditional approach reflects a technological rather than economic outlook. Ideally, the two would be merged. Furthermore, if regulation continues to be shifted in many jurisdictions from that of rate of return to prices, quality performance is under pressures not experienced in the past. Spence, for example, fmds attractive second-best benefits of rate-ofreturn regulation to quality performance, which presumably would be lost without such regulation (Spence, 1975,417-429). In the local exchange and the distribution plant where most quality problems occur, alternative user choices do not yet appear available in most instances to protect quality through competition.

TIlE QUALTIY OF REGULATION IN REGULATING QUAUTY 179

Furthermore, the network system is non-transparent to most of its users. In a transmission chain of several carriers, which one is to be blamed for faulty quality? This difficulty to identify the culprit can encourage "free riding" by a carrier to weaken the quality of its own link. This, in turn, can lead to a quality downgrading by other carriers, since it may make no sense to provide quality at a level higher than the weakest link. Indeed, competitive forces and the absence of an end-ta-end responsibility may reduce quality to that lowest performance level.

Finally, there may be selective quality deterioration possibly in poor neighborhoods, which must be identified and dealt with.

One should not assume, a priori, that higher quality is always better. Under many circumstances, it would be best if several quality options would be available to users at different prices. User choice would then settle many quality issues. However. for most services it is not feasible to provide a "Chinese menu" of quality grades. Furthermore, user choice may impose negative externalities: in an interconnected network, one subscriber's low-quality choice negatively affects those who call her. A's fax transmission may take twice as long if B chooses a poor grade of service. Thus, certain basic levels of quality should be protected, while higher grades should be left to choice, where technically feasible.

On the whole, the data presented in the previous section indicate that along several dimensions, service quality in the past six years following divestiture has improved in the U.S. for large users and has remained basicall y stable for residential users. Several other quality variables, however, have declined. And while they appear to be fewer, such judgment is subjective to some extent. How then can one evaluate the trend of overall service quality? To do so requires us to find some global quality measure, and this will be done in the following. Where economists think about quality they invariably assume, for mathematical convenience, a single dimension measure. The marketing literature is more helpful here (Louviere, 1984; Lynch, 1985, 1-19). This discussion has benefitted from the excellent work by Buzas, Lynch, and Berg (1990). But it differs from it in the treatment of weights, adds the connection of quality to incentives which the authors do not reach, provides floors and caps, and an adjustment mechanism for variance.

One could, of course, avoid any summary statistic. But this only means that any judgment on quality improvement that goes beyond a single dimension will be implicit and subjective, with an unavoidable result regulatory informational overload, and that inconsistent, inefficient, or unfair decisions may result.

To measure quality in an overall fashion and to link performance with financial rewards and penalties requires the several steps which follow:

Step 1: Selecting quality dimensions. We must define which dimensions of service are relevant. These dimensions

should be preferably those that can be objectively and easily measured, which are subject to the control of the local exchange company, and (to simplify matters), for which performance standards already have been established.4 A sample of such dimensions is


1. Dial tone delay 2. Call completion

(a) intra-office (b) inter-office (c) extended area service

3. Installation lag 4. Repair service

(a) 24 hour and more restoration (b) missed appointments

5. Emergency (911) service conduit 6. Public telephones

(a) functionality (b) availability

7. Response time (a) operator (b) directory assistance (c) business repair office

8. Directory assistance (a) search time (b) update

For purposes of notation, we designate the various quality criteria by i. Virtually all of these and additional service criteria already are being collected

by telcos as part of their operations. It might be argued that a very short list of criteria may capture the broad trend

of quality at greater simplicity (Newstead, 1989). Butif an automatic link of quality to fmancial reward is adopted, as is proposed below, and if one has a list that is too abbreviated, companies would concentrate solely on the few listed criteria and neglect the others. For example, if consumer complaints are the only criterion of an incentive formula, quality may be dropped for operator assistance response time or directory assistance update, since few users would bother to complain about them. Complaints tend to be caused by a significantly deteriorated performance that causes a major inconvenience. Gradual decline, or inadequate service on small matters, will not lead to many complaints, even if it affects millions, while a few hours of service interruption due to a fallen tree can generate numerous complaints. Complaint rates can also be manipulated by organized campaigns.

On the other hand, one can consciously omit certain factors from the list as a policy decision to leave their quality to company discretion or to competitive forces.

It makes sense to have separate lists of criteria for residential service, business service, and public coin telephone. If an automatic link of quality to financial compensation is set, separated quality accounting would prevent residential users from potentially having to cross-subsidize quality improvements aimed at business

TIlE QU All1Y OF REGULATION IN REGULATING QUAliTY 181

customers, and vice versa. Quality performance in coin telephones could be dealt with in a different manner.

Step 2: Define quality standards. For all or most of the quality criteria, there already exist expected quality

standards.5 We designate them with S(i). The proposal does not aim to modify these standards.

Step 3: Assign weights to quality performance. The factors of quality defined in Step 1 are not likely to have equal importance.

Inadequate functioning of transmission for a 911 emergency service is probably a more serious matter than a slow response time of a business office. Therefore, one should assign weights to the various quality factors. More accurately, the weights should be for deviation from standard, for examFle, for a 10% and 10% under-performance in response time for business offices.

How can these weights be found? There are several possibilities. 1. Revealed preference. In a competitive environment, an analysis of user

choices could measure the preference for various quality dimensions (hedonic pricing analysis). Unfortunately, such user choice is rarely available to residential customers for local service.

2. User and expert surveys. Users' views need be ascertained, because their perceptions about quality, after all, are the ultimate test. But most users are not likely to have spent much time thinking about dial-tone delay, etc., so there is a need for expert involvement, too. Experts, on the other hand, may overemphasize aspects of little utility to users.

Based on the user and expert surveys, and of industry and outside evidence, a set of weights W(z) for various quality performance can be established by, for example, a Delphi-type convergence process, and by negotiation? They can then be standardized so that their sum equals 1.0.

Once one has set the weights, it is easy to define overall average quality Q* as the sum of the relative quality performances Q(z) (actual performance P{i) to standards S(i», multiplied by the weight w(i).

Q* = L Q(i) W(i),

where

Q( .) = P(i) - S(i) z SU).

There is a problem that requires an adjustment of the weights. Averages may mask some very low performances. Suppose, for example, that there are three equal-sized exchanges, and their average quality on dial-tone may be 10 seconds.


However, this may be composed of one exchange enjoying a zero-second wait, while the other is struggling with a very poor 20-second wait.

One way to deal with this variance is multiply the average performance for each quality dimension with an adjustment factor A(i), which is equal to 1 when there are no deviations from the average, and is less than 1 according to the negative deviations (in %) weighted by the subscribers involved (in %). For example, a (10, 10, 10) seconds performance gets an adjustment factor of 1 - 0 = I, while a (5, 10, 15) performance gets an adjustment factor of 1 - (.33 X .5) = .835.

To eliminate purely random deviations around a mean, one should probably drop consideration of the fIrst 10% of deviation.

More formally, the adjustment factor is

A(i) = 1- L.R(j) [x(ij)-s(i)]8, j=-2

where RW denotes the percentage of users for a negative deviation of actual performance X from standards.

Then, adjusted quality is

Q'(.) = [P(i) . A(i)] - S(i) I S(i) .

And overall quality Q* is

Q* = L.Q'(i) W(i) .

Where all standards are met exactly, all P(z) are equal to S(i), all adjustment factors areA(i) are equal to I, all Q'(i) are equal to 0, and the summary Q* is also zero. Where there is over- or underperformance, Q* will be positive or negative, respectively.

Step 4: Monitor qUality. With this system we can now measure quality performance of a company

(differentiated for service to residential and business customers, and public coin telephones). If the company's score is zero or positive, it is performing at the required level or above.

It is important to recognize the flexibility of this system; a company may fail one or several quality standards as long as it made up for this through overperformance in other standards. Instead of insisting on meeting every one of many criteria, one can add efficiency and flexibility by requiring instead an overall score. A company would have to meet Q* = 0 (adjusted for variance). If it fails to meet some standards, it can offset this by a higher performance in others. (See also Buzas, Lynch, and Berg, 1990.9)

If improvements on all dimensions would cost the same, improvements would fIrst be undertaken for factors with a large weight, and where performance varies greatly across exchanges or users. If marginal improvements differ in cost, as seems likely, a company could calculate the optimal quality improvement strategy.

TIlE QUALTIY OF REGULATION IN REGULATING QUAUTY 183

The results are more quality for the money, and greater managerial flexibility as each company is free to reach the overall score in its own way.

There can also be added flexibility for the regulator body: 1. Some quality dimensions can be taken out of the aggregation and made an

absolute requirement with no tradeoff possibility. This may be the case for dimensions considered vital.

2. Some quality dimensions may be deregulated over time and dropped out of the aggregation, without necessarily deregulating others.

It may be objected that the aggregation of performance measures for various dimensions of service is undesirable, because it reduces the transparency of actual performance to commissioners, and because it countenances partial service deterioration as long as it is offset by improvements. And this could divert resources for improvement to the wrong uses.

There are several responses. First, the tradeoff across dimensions is based on a weight scheme that would assure that underperformance in important dimensions of quality would be very costly to the company. Additionally, one can add protections by setting floors on the deterioration of any dimension or by permitting no deterioration at all for some key dimensions. But the tradeoff mechanism as such would permit reaching a given level of overall quality at a lower cost to users, or, similarly, to reach a higher overall quality at a given cost. Second, there is no need to fear that once overall quality is at desired levels, regulators will not be interested in the details. It is the present system that raises an information problem insofar as the flood of the unweighted quality measures cannot be absorbed by regulators.

Aggregating across subscribers10 can be similarly buttressed by adjustment factors, floors, and exemption from tradeoff. There is plenty of flexibility in the proposed system.

One could, of course, take a different route, that of requiring the performance of every standard for every customer and every service. Such a course may appear equitable, but it can easily lead to less overall quality, and not necessarily to more equity.

Most importantly, a disaggregated approach cannot be practicably linked to financial incentives. Or rather, if several quality dimensions are introduced into the overall price equation as a purported "disaggregation," in actuality an aggregation takes place across the common denominator "dollars," which permits a carrier to engage in tradeoffs anyway.

Step 5: Linking quality performance to financial incentives. In an environment of price-cap or incentive regulation it is necessary to link

quality performance to financial rewards. Otherwise, there is pressure for quality short-cuts. Such linkage was not possible in the past because the multiplicity of quality measures precluded an operational way to accomplish such a linkage, and because rate-of-retum regulation put less pressure on cost-cutting. An exception were the customer rebates instituted in 1972 in New York that dealt with serious


and multiperiod deterioration in an exchange. But after 1973, no refunds were ever necessary, and the system must be seen as a safety-net rather than a differentiated instrument.

How can linkage of quality to financial rewards be accomplished? Generally, it means that where aggregate performance improves, there will be added rewards, while there will be negative rewards for underperformance. We should distinguish several situations.

1. Rate-of-return regulation. Here, one could raise (or lower) allowed RoR for the next period, or permit rates

to be raised without the extra revenue being counted against authorized RoR ceilings.

2. Price regulation. Prices would be affected. If the price formula is such that price change is based

on inflation and productivity, it would now also include a quality factor (see below). 3. Hybrid incentive systems. In a hybrid system such as New York's present system, whose moratorium

approach has a price control and a rate-of-return control element, one could establish the incentive in several ways, including:

(a) Raise or lower basic authorized RoR. Incentives would not be effective unless a company performs above the basic

authorized RoR. 11 At present, for example, this incentive would not work for NY Tel.

(b) Provide a different revenue split beyond the RoR. Again, this would be only effective above the sharing threshold.

(c) Accrue a reward or penalty as income, subject to collection (payment) in rates at the next rate change.

(d) Raise or lower maximum prices. The most direct linkage is through prices: where quality is sub-standard, user

prices are cut; where quality is above standard, they may be raised. This is equitable to ratepayers: poor service will cost them less than good service, because it is not the same thing. And it is fair to the company, which gets carrots for quality improvements, and sticks for deterioration. This is the approach recommended. It can be integrated with a more general price formula.

As mentioned above, the financial rewards and penalties should be calculated separately for service to residents, business users, and public coin telephones, so as to avoid cross-subsidization.12 Where feasible, one could desegregate quality and rewards/penalties for specific services, such as for operator assistance or for repair calls. In most instances, however, payments are for a bundle of services and do not lend themselves to a disaggregation of incentives.

Some may object that, while penalties for sub-standard service make sense, there should be no reward to overperformance. Companies should deliver the best performance they can and expect no added incentives. A related objective is that overperformance is unnecessary, because standards are set just right. Thus, incen-

TIlE QUALITY OF REGULA TIONINREGULATING QUALITY 185

tives to do better would be simply an encouragement to gold-plating. There are several responses:

1. In the absence of direct user choice for quality options, regulators should help create a tradeoff schedule. Two quotes help make the point.

Ideally the regulatory authority would manage price-quality tradeoffs by confronting the firm, on behalf of consumers, with a reaction function that reflects rates of substitution between price and quality on the demand side of the market. (Spence, 1975, 428)

Any regulation scheme which is intended to induce optimal quality as well as quantity decisions must involve prices which are sensitive to quality variationsP (Kihlstrom and Levhari, 1977,225)

2. If overperformance beyond standards is not valued at all, this will be reflected in the weights for such overperformance. Recall also that there is no need to have a symmetry of overperformance to underperformance. In other words, one could value the former only slightly, while attaching great significance to the latter. Gold-plating could also be dealt with by setting ceilings for rewards.

3. It is clear that many of the present standards are in no wayan ideal in some absolute sense, but are selected relative to some notion of realistic attainability. A better performance would be of value. For example, a standard that 90% of all service interruptions must be restored within 24 hours is largely arbitrary and related to actual "realistic" ability to restore service. Improvements that would lead to 90% of restorations within two hours would certainly be better if technically and economically feasible. Hence, present standards should not be viewed as a ceiling.

4. The one available empirical survey study (B uzas et al., 1989) concludes that experts value an overperformance as much as an underperformance of similar magnitude.

5. It is short-sighted to be geared only to today's service expectations. As technology is advancing and as complexity is growing, regulators would do well to provide for positive incentives for quality to move forward. To do otherwise could be cutting off one's nose to spite one's face.

Importantly, expected quality need not be static. A commission could determine that technological trends lead to quality improvements, and that a company need therefore not be rewarded for matching the general trend. Similarly, a commission could pick a quality improvement it believes to be necessary, particularly in situations of deterioration. 14 This would be captured by reducing the measure for quality performance Q* by a trend or target factor T. 15

All this then results in the equation

T = I - V + N (Q* - T),

where T = price change I = inflation = V = productivity change N = incentive factor Q* = quality performance

186 PRICE CAPS AND INCENTIVE REGULATION INTELECOMMUNlCA TIONS

T = trend factor of quality improvement. Such adjustment can take place within or outside the sharing price mechanism.

If the former is chosen it would halve the incentive, create a discontinuity, and an asymmetry relative to underperformance (though such asymmetry may actually be considered desirable). An alternative is to permit quality-based price adjustments outside an existing sharing mechanism.

Whichever way is chosen, the main question is at what level to set the quality incentive factor N. Set too low, there will be too little positive incentive, and possibly an incentive to gain by lowering quality. Set too high, there could be quality gold-plating, but also excessive penalties in a low-quality situation that could lead to still further underinvestment. There may be instances where quality deterioration accompany fmancial stress, and where penalties are counter-productive. But such fundamental problems in a company's viability should not be dealt with through the quality variable. They require different responses. Quality must be viewed separately, and setting Nbecomes partly a policy question, based on the extent of incentive to quality one wishes to provide, and partly a matter of experience. The challenge for policy and analysis is to establish a measure for N which induces optimal quality. Because there is little experience in this, one should add predictability by setting floors and ceilings. This would assure regulators, particularly in an initial phase, that the aggregation of quality will not lead to selective deteriorations that are unacceptable, or to excessive price effects. The model can flexibly accommodate this. Examples for such protections are:

1. A ceiling of maximum 1 % price increase per year that are due to quality improvements.

2. A ceiling to RoR changes of a certain number of basis points, perhaps 25 (.25%).

3. A floor of 2% quality decline in a year or some such figure for a multiyear period. Beyond that, the automatic price-reductions would double, for example, and a company-PSC quality improvement schedule be established.

4. An unhitching of some quality dimensions from the aggregate incentive system by setting for them absolute values that must be reached, regardless of offsets. For example, if all reliability is valued to an extent that even a very high weight would not be acceptable as a tradeoff shadow price, it could be set to an absolute value, and any deviations from it would be dealt with outside the aggregate incentive mechanism.

Once the system is established, it should be automatic; this reduces uncertainty and encourages long-term planning. 16

"Excess" quality improvements could also be carried into other years; one could even contemplate transfers and trade in quality bonuses across companies, within some limits. Or one could conceive, once experience is gained, of bidding mechanisms in which the lowest-cost qualified bidder to improve the quality of a service dimension in non-competitive services is selected.

It must be stressed that these quality incentives and standards should apply only to those services and rates which are still being actively regulated. For unregulated

TIlE QU AUfY OF REGULA TION 1N REGULATING QUAU1Y 187

services, one presumes that competition will provide users with adequate choice. But regulators should still maintain quality reporting and monitoring for a period after deregulation to ascertain the working of market forces for that service. Such monitoring may also lead to public reports that would assist in their choice of service providers, and it would provide data to ascertain that regulated services do not cross-subsidize unregulated ones.

5. Outlook

Although much of telecommunications regulation may gradually be on its way out, as long as monopoly bottlenecks persist, regulatory commissions will playa role. The quality variable, as the other side of the coin to price, requires attention, especially if price regulation is substituted for rate-of-return controls. It is better to provide the right incentives for improvements of quality, instead of micromanaging companies' quality investments and performance along each dimension. These incentives should be clear and automatic, so that companies can plan ahead and deploy resources flexibly. And they should permit regulators to assure a favorable trend of quality development. This proposal is meant to contribute to the development of such a system.

Notes

I amgratefulforcomments by Tom Aust, Marge Baker, Allan Bausback, Sandy Berg, Frank Herbert, John Hopley, Sanford Levin, Richard Marshall, Carol Oppedahl, Bob Piller, Dan Rosenblum, Lisa Rosenblum, Roger Sutliff, Y og Varma, and Robert Whitaker.

1. One should also note that there is some quality rivalry even in a monopoly system through internal performance competition among corporate managers and sub·units.

2. Assuming, as most economists do, that quality is capital-intensive. If it is labor-intensive, the opposite would be the case. In the author's view, many quality dimensions are in the process of becoming labor-intensive rather than capital-intensive.

3. The graph scale is such that the improvement looks more dramatic than it actually is. 4. One could also include more subjective variables, such as company representatives' responsive

ness, helpfulness, and courtesy. Measures could be obtained through surveys, and used as the other more technical variables. This would introduce a non-trivial added element of procedure and measurement, however.

5. These have been updated in New York as recently as 1989, and are not likely to require change. Several outstanding issues are under negotiation.

6. Assigning weights to performance relative to standards distinguishes this methodology from weighing factors' importance per se. Under the latter scheme, to fmd the actual quality score would then require the estimation of a second set of coefficients that would measure the relative significance of deviations from a standard, and a multiplication of the two sets of coefficients. If one omitted that step one would have to implicitly assume (1) linearity (2) equality of seriousness for deviations; and (3) symmetry. The present proposal overcomes these problems by collapsing the two measures into one. It asks, in effect, "How serious is a 10% deviation (or a 20% deviation, etc.) from the expected standard for operator response time?" rather than "How Important are operator responses?"

The weight system can be refined. For example, while some may be linear (e.g. a 20% shortfall has a score twice as great as 10%), it can also be more, or less than that. Furthermore, a 10% underperformance need not be symmetrical in weight to a 10% overperformance.

7. The PSC's BSI weights were arrived at by negotiation.


8. To set even higher disincentives against service variance, one could square the deviations (or factor by another number).

9. Temporary deterioration due to natural catastrophes or work stoppages should be factored out. Further flexibility can be provided by establishing separate schedules for different companies, based on their present performance. In that way, a company does not get specially rewarded for continuing to do what it already does.

10. Of course, this is the situation today, where mUltiple aggregations are typical within central offices, across central offices, and then across companies.

11. Strictly speaking, a company could be slightly above the authorized RoR, as long as the added incentive puts it above that rate.

12. For coin telephones, where small price changes are difficult, rewards and penalties may be instituted through some form of a more general true-up.

13. Both Spence and Kihlstrom point to the data problems. 14. Alternatively, a commission may conclude that there is gold-plating in some elements, and

permit qUality reduction by reducing their standards or reducing tradeoff potential. 15. This trend or target variable could be instead introduced into the definitions of standards (t). 16. Of course, if unusual events such as a major strike occur, equity calls for reconsideration.

References

Besanko, David, Shabtai Donnenfeld, and Lawrence J. White. 1988. "The Multiproduct Firm, Quality Choice, and Regulation." Journal of Industrial Economics 36 (June): 411-429.

Block, Ellen G., and Henry D. Levine. 1988. "Protecting the Last Mile: The Quest for a Robust Local Exchange Network." Telematics (October): 9-10.

Buzas, Thomas E., John G. Lynch, Jr., and Sanford V. Berg. 1989. "Regulatory Measurement and Evaluation of Telephone Service QUality." Unpublished manuscript (August 4).

Buzas, Thomas E., John G. Lynch, Jr., and Sanford V. Berg. 1990. "Issues in the MeasurementofTelephone Service Quality." In Divesture Five YearsLaJer, edited by Barry Cole, Columbia University Center for Telecommunications and Information Services. New York: Columbia University Press.

Chamberlin, Edward H. 1948. The Theory of Monopolistic Competition. Cambridge, MA: Harvard University Press.

Dorfman, Robert, and Peter O. Steiner. 1954. "Optimal Advertising and Optimal QUality." American Economic Review 44:826-836.

Gryb, Robert M. 1990. 'The Effects of the Divestiture on Nationwide Telephone Service Quality." In Divesture Five Years LaJer, edited by Barry Cole, Columbia University Center for Telecommunications and Information Services. New York: Columbia University Press.

Hudson, Richard L. 1981. "British Telecom's Modernization Falters." Wall Street Journal (August 21).

Kihlstrom, Richard E., and David Levhari. 1911. "Quality, Regulation and Efficiency." Kyldos 30 (2): 214-234.

Kraushaar, Jonathan M. 1988. Fiber Deployment UpdaJe, End of Year 1988. Industry Analysis Division, Common Carrier Bureau, Federal Communications Commission.

Kraushaar, Jonathan M. 1989. "Report on Quality of Service for the Bell Operating Companies." Common Carrier Bureau, Industry Analysis Division, Federal Communications Commission (March 11).

Lawton, Raymond W. 1988. "Telecommunications Modernization: Issues and Approaches for Regulators." National Regulatory Research Institute Report 87 -114.

TIlE QU ALTIY OF REGULATION IN REGULATING QUAUTY 189

Levhari, David, and Yoram Peles. 1973. "Market Structure, Quality and Durability." Bell Journal of Economics and Management Science 4:235-248.

Levine, Henry D. (letter from), Richard Hesser (letter to) New York PSC, November 23, 1988, re: Central Office Redundancy/Security and PBX Rate Stabilization.

Louviere, J.J. 1984. "Hierarchical Information Integration: A New Method for the Design and the Analysis of Complex Multiattribute Judgement Problems." In Advances in Consumer Research, edited by T. Kinnear (Vol. 2). Provo, UT: Association for Consumer Research.

Lynch, J.G., Jr. 1985. "Uniqueness Issues in the DecompositionalModeling of Multiattribute Overall Evaluations: A Information Integration Perspective." Journal of Marketing Research 22: 1-19.

Newstead, Tony. 1989. Measuring and Monitoring Quality of Service. Unpublished paper. MONICT, Monash University, Melbourne, Australia.

New York State Public Service Commission. 1989. "Quality of Telephone Service - New York Telephone Company, First Quarter, May 9, 1989." Communications Division.

Noam, Eli M. 1990. Telecommunicaitons in Europe. Vol. I and II (forthcoming). Of tel. 1988. "Professor Carlsberg Congratulates BT for Achieving Call Box Target." Press

Release (April 20). OFIEL News "Quality of Service." (no. 12, January, 1989). Panzar, John C. 1975. "Regulation, Service Quality, and Market Performance: a Model of

Air line Riv airy." Research Center in Economic Growth, Memorandum No. 184, Stanford University.

Richters, John S., and Charles A. Dvorak. 1988. "A Framework for Defining the Quality of Communications Services." IEEE Communications Magazine (October): 24-35.

Rosse, James N. 1972. "Product Quality and Regulatory Constraint." Research Center in Economic Growth, Memorandum No. 137, Stanford University.

Schmalensee, Richard. 1979. "Market Structure, Durability, and Quality: A Selective Survey." Economic Inquiry 17 (April): 177-196.

Schmalensee, Richard. 1970. "Regulation and the Durability of Goods." Bell Journal of Economics and Management Science 1 (Spring): 54-64.

Sheshinski, Eytan. 1976. "Price Quality and Quantity Regulation in Monopoly Situations." Economica 43:127-137.

Spence, A. Michael. 1975. "Monopoly, Quality, and Regulation." Bell Journal of Economics 6 (no. 2, Autumn): 417-429.

Swan, Peter L. 1970. "Market Structure and Technological Progress: The Influence of Monopoly on Product Innovation." Quarterly Journal of Economics 84 (November): 627-638.

Takahashi, Kenzo. 1988. ''Transmission Quality of Evolving Telephone Services." IEEE Communications Magazine (October): 17-23.

10 OPTIONAL TARIFFS FOR ACCESS UNDER

THE FCC'S PRICE-CAP PROPOSAL

1. Introduction

David S. Sibley Daniel P. Heyman William E. Taylor

Currently, the FCC is refining a proposal to regulate the access services of the local exchange carriers (LECs) under a price-cap scheme, modifying rate-of-return regulation. See FCC (1988, 1989). One element of the proposal is that new services be treated for tariff review purposes in a manner quite similar to the FCC's Optional Calling Plan Order, which set out a net revenue test for approval. This net revenue test would require that (1) a new service must be projected to increase net revenue for the service subject to price-cap regulation and that (2) this increase be projected to occur within the lesser of two time periods: 24 months from the incorporation of the new service into a price filing, or 36 months from the introduction of the services. This showing must be accompanied by net revenue projections which include marginal costs. price elasticity. and cross-elasticity effects. 1

Under current rate-of-retum regulation an optional tariff would have to pass a Part 69 test, which is based on traditional concepts of fully distributed costs (FDC). The main difference between the price proposal currently under consideration and rate-of-return regulation is that the test for approval would be based on incremental cost, not on FDC. Since there is no real difference in the notice period, the amount of cost support required. etc .• more new services are likely to be approved under the price-cap plan than under current regulation.

Since 1986 there has been periodic discussion of the desirability of allowing the local exchange carrier to offer bulk discounts on access with end-user billing. In 1986 the two NYNEX companies each filed declining block tariffs for carrier access charges to be billed to end users. In its Open Meeting of November 25, 1986.


the FCC rejected these tariffs, partly because their justifications did not include sufficient consideration of economic efficiency.

There is good reason to suspect that tariffs of the kind proposed by the NYNEX companies will enhance economic efficiency. The NYNEX tariffs were decliningblock tapered tariffs, which involved increased usage charges for small users, decreased usage charges at high consumption levels, and a claimed zero net effect on profits. The marginal cost of access was not known exactly, but was almost certainly lower than even the discounted rates. Bearing in mind that small users typically are much less price-elastic than are large users, the deadweight loss from the increased usage charges at low consumption levels would almost certainly have been outweighed by the efficiency gains of moving the marginal usage charge paid by large users closer to marginal cost.

In this article, we argue that bulk discounts with end-user billing, implemented as optional two-part tariffs, will face fewer regulatory constraints than heretofore. By making it easier for such tariffs to be approved by the FCC, the price-cap proposal can potentially increase economic efficiency. Alternatively this article may be taken to argue that optional bulk discounts should be treated with regulatory permissiveness because, as we demonstrate below, the potential exists for both consumers and the firm to gain thereby.

We have in mind a scenario in which the current carrier access charge structure is retained, but the LECs offer, in addition, sets of optional two-part tariffs to be billed to end users. An important feature of the price-cap proposal for LECs is that such options would appear to fit the definition of a new service set out by the FCC, which is that an offering that increases customers' options should be classified as new. Because these optional tariffs are, by definition, options to an existing tariff structure and because they involve end-user billing, it seems likely that they would be treated as new services and justified according to the net revenue test described above, rather than the FDC-based Part 69 test? Because it is based on marginal cost, the net revenue test is easier to pass than the FDC-based Part 69 test

In the balance of the article, we conduct two kinds of pricing simulations. First, as a matter of historical interest, we estimate the efficiency effects of the NYNEX tapered tariffs, and find that they would indeed have increased economic efficiency. Second, we compute optional two-part tariffs for access, billed to the end user, and Imd that both large users and the LECs stand to gain substantially.

2. Tapered Access Charges

The issue of the economic efficiency of proposed access rate structures billed to the end user came to the fore at the November 25, 1986, Open Meeting of the FCC, in which tapered tariffs proposed by NYNEX companies were rejected, partly because their justification did not include sufficient consideration of economic efficiency. In this section, we address this issue in two ways. First, in a highly stylized setting, we compare the consumer and producer surplus obtainable from a simplified version of the proposed New York Telephone tariff which we will call

OPTIONAL TARIFFS FOR ACCESS UNDER FCC PRICE CAP PROPOSAL 193

the "NYNEX" tariff,3 with that obtainable from the carrier access charge then prevailing of7.56 cents per minute.4 Second, we compute an optional tapered tariff which has the characteristic that relative to the carrier access charge then prevailing, no customer is worse off and the firm's profits are higher.

Note that no mention has been made of a cost justification for tapered access charges - either here or in the debate surrounding the NYNEX companies' filings.5

Ignoring costs seems to contradict recent regulatory and legislative actions which discourage declining block tariffs (primarily in electricity) usage.6 However, these actions have generally been based on the belief that charging a large customer less than a small customer will induce the large customer to inefficiently overconsume relative to the small customer. Now the marginal cost for switched access appears to be much lower than any rate that anyone is proposing to charge for any level of usage. Thus proposed tapers do not induce large users to consume an inefficiently large amount of access, since they face a price that is still in excess of marginal cost. The perspective of this section is that some contribution over marginal cost must be raised from access charges and our task is to find the most efficient tariff that will accomplish that goal.

3.1 The Theoretical Setting Suppose initially that there are two consumer types, Big (B) and Little (L) with

demand curves as shown in figure 1: at any price, Big's demand QB(p) exceeds

Little's demand (/(P). Initially, both customer types face a flat rate price of Po per unit. The firm's marginal cost is denoted by mc. Denote fixed cost by F. The firm earns a normal profit

(1)

Now give the two consumers a choice: let them continue to buy at the uniform price Po or buy under a two-part tariff (El, PI) having a flat entry fee

and a usage charge PI' where Po:? PI:? mc

and E 1 is given by the sum of areas a and b in figure 1.

(2)

(3)

Clearly, Little will stick with Po; the increase in consumer surplus he would derive from the lower usage charge Pl is given by the area a, which is more than offset by E1, given in figure 1 by the edged rectangle a+b. Big prefers the two-part tariff because E 1 takes only part of the increase in consumer surplus made possible

by the lower usage charge, leaving him better off by the lined triangle !::J.csB. The firm makes a nonnegative profit from the two-part tariff because of demand

stimulation induced by the lower marginal price: the increment (Qf - Q8) in Big's

consumption takes place at price PI> mc. The rectangle !::J.P sB represents increased


$

~ __ ~ ____ +-~ __ ~ __ r-____ ~ __ -----mc

Q

Figure 1

producer surplus for the frrm? Thus the fIrm as well as both customer types are better off facing the two-part tariff (EI, PI) than facing the uniform price Po; such a tariff is said to "Pareto dominate" the flat rate tariff PO.8

As we see in figure 2, what we have done is equivalent to constructing a

declining block tariff with usage charges Po and PI and a break point at !to. The result is true in general: a declining block tariff can always be viewed as the lower envelope of a set of two-part tariffs from which consumers select their optimal consumption points.9 On that declining block tariff, the two consumer types select

consumption levels drs and dl. Now suppose that there are three consumer types: Big, Medium (M), and Little.

Their demand curves are consistent with the noncrossing assumption and are shown in figure 3. We can construct a set of optional two-part tariffs-(EI, PI), (E2, P2)in the same way we did above:

E1=ft!*(PO-PI )

E2 = d * (po-P2)·

(4)


s

me

Q

FIGURE 2

Using the same arguments as before. it is true that if Medium took (E h PI) and Big took (E2. P2) then each would be better off than under Po and the ftrm would make higher profits. However. there is a potential complication: Big might prefer (El. PI) to (E2. P2). If he did. then the firm might make less profit from him under the optional tariff than under the flat rate po. so that the firm might see higher profits under the flat rate tariff. 10 To ensure that the set of optional two-part tariffs Pareto dominates the flat rate tariff. we have to further constrain PI so that the lower entry fee that Big would pay under (El. Pi) is offset-for his demanded quantity-by the higher usage charge. The decrease in consumer surplus that Big would undergo under (El. PI) due to the fact that PI > P2 is given by the area of the rectangle (C + D + ~2) in figure 3. The reduction in the entry fee is given by the rectangle (B + C + D). Thus. if B < ~2. Big will prefer (E2. P2) to (El. PI) . We refer to this added complication as the incentive-compatibility constraint.

Note that by making PI suitably close to po. we can always ensure that this constraint will be met. As PI approaches po. ~2 rises while B declines. Thus at some level of PI • the increased usage charge in going from P2 to PI more than balances the reduction in the entry fee. inducing Big to select the tariff (E2. P2) which ensures the firm of higher proftts from the optional two-part tariffs.

196 PRICE CAPS Ai"D INCENTIVE REGULATION IN TELECOMMUNlCA TIONS

FIGURE 3

Summarizing the three consumer-type argument, if

mc:5:P2:5:PI :5:PO

EI = Qf/ * (PO-PI)

E2 = Qg * (PO-P2)

and the incentive-compatibility constraint:

B = (Qo- Qf/) * (Po-PI ):5: t:.2

~+dl-2Qg = (Pt- P2) * 2

is met, then the following happens: - Big chooses (E2, P2) ;

- Medium chooses either (Et. PI) or (E2, P2) ;11

- Little stays at Po; and - the firm makes higher profits that at Po.

(5)

(6)

OPTIONAL TARIFFS FOR ACCESS UNDER FCC PRICE CAP PROPOSAL

$

I I

me ~----------_+-I-----------+I---------------:

FIGURE 4

I I I I

Q

197

Relative to the flat rate tariff Po, we refer to the set of optional two-part tariffs {Ei' Pi} (i = 1,2) as Pareto Dominating and Incentive-Compatible (PDIC).

As shown in figure 4, allowing consumers to choose among the set of three optional two part tariffs-(O, Po), (El, PI), and (E2, P2)-is equivalent to presenting them with a declining block tariff with usage charges Po, P h P2 and break points

drf and Qg. Proceeding in much the same fashion, with N consumer types one could construct N - 1 optional two-part tariffs with the result that no economic agent would be worse off than under the flat rate Po and some (including the firm) would be better off. This set of N - 1 two-part tariffs would then be equivalent to a particular N-part declining block tariff which would Pareto dominate the flat rate tariff Po.

3.2 Consumer Welfare Under Tapered Tariffs We assume a simple demand model that relates access demand for a customer

of type i to the full price of interLAT A service. Thus Qi = Qi(r + P) where r is the price charged for IXC service and P is the usage charge for access. If one takes the view that access is an input in the production of long-distance service, then changes in consumer surplus for customer i from changes in P can be calculated by writing


r = r(P) in equilibrium and integrating under the equilibrium input demand curve. Thus if P is reduced from P' to P", the effect on consumer i is given by12

JP' !J..CSi = "Qi[r(P) + P] dp.

P

(7)

Thus to compare the change in consumer surplus from moving from a flat rote to a tapered tariff, all we have to do is calculate the area under each consumer type's demand curve above the marginal price he faces, subtract his entry fee, and subtract his consumer surplus under the flat rate tariff.

Far convenience's sake, we assume that the equilibrium input demand function for consumer type i can be approximated by a simple iso-elastic form

(8)

where Ti is a taste parameter and ei is the price elasticity of demand for customer of type i. We also assume there are six different customer types corresponding to the six steps in a tariff roughly reminiscent of the New York Telephone proposed tapered schedule.

To calibrate these demand curves, we require data on the distribution of usage and price elasticities by customer type. In table 1, we present the current usage distribution for New Yark Telephone MTS customers along with average monthly usage for customers in each band, noting that this usage was generated by a flat rate IXC access price of 7.56 cents per minute and this might differ from the usage distribution under an optional tariff.

Table 1. Distribution of NY Tel MTS Usage Usage Percentage of Monthly MTS Minutes Band Accounts of Use (mou)

0-60 74.03 14.55 61-1000 25.47 160.21

1001-2000 0.26 1364.46 2001-7000 0.17 3547.77

7001-20000 0.05 11026.07 20000 + 0.02 67425.60

Source: NYTel Co., Tariff FCC No. 41, Transmittal No. 775.

From the six usage bands, we construct six user types with taste parameters Ti given by

Ti = [avg mou ]i [.0756]\ (9)

The price elasticities ei for the different customer types are derived from known long-distance service price elasticities in the following way:


alnQi alnQi P e·=---=- *-

I alnP aln(r+P) r+P (lO)

which is the derived price elasticity of demand for !XC access. Usage elasticities by customer size class were approximated by combining econometrically estimated MTS and W ATS elasticities in different proportions for different customer size classes. Given ei, Ti is easily computed from usage data in table 1.

It is important to note that this view of access ignores efficiency gains or losses due to bypass; the access elasticity is merely adjusted to account for the fact that the end-user price includes an IXC component. To allow for the possible effects of increased bypass competition, we analyze an alternative case: one which has sharply higher price elasticities for the larger users. Both sets of elasticities are presented in table 2.13

Table 2. Price Elasticities of Demand Customer Base Alternative

Type Case Case 1 .16 .16 2 .16 .16 3 .22 .50 4 .22 .50 5 .31 .70 6 .31 .98

We initially assume a marginal cost of access for each consumer type of 1 cent per minute, which represents an average of peak and off-peak marginal costs as reported in the New England Telephone filing. Note that this may overstate the true marginal cost for the largest group, since switched access may not be the most efficient form of access for some of these very large customers. The usage charge is for peak-period originating switched access for MTS services: the rate includes both traffic sensitive and non-traffic sensitive components. We effectively ignore W ATS demand in this analysis.14 The NYNEX tariff is given in table 3; the break points in the tariff correspond to the usage bands in table 1.

The efficiency effects of the "NYNEX" tapered tariff are given in table 3, for the high elasticity alternative case. We believe that these elasticities best reflect the future effects of bypass. As many parties have noted, compared to the flat rate of 7.56 cents per minute in the base case, customer types 1 and 2 are mildly worse off; however, together, these types comprise 99.5% of the customer population.


Table 3. Effects of the "NYNEX" Tapered Tariff (relative to flat rate $0.0756) Alternative 2 Elasticities

"NYNEX" Customer Tapered Change in Change in

Type Tariff Consumer Surplus Producer Surplus 1 $.0961 -$0.29

2 $.0713 -$0.80 3 $.0484 $16.85 4 $.0352 $119.61 5 $.0302 $582.87 6 $.0269 $5061.42

Change in aggregate profit = -$0.007 per customer per month. Change in consumer surplus = $1.135 per customer per month. Change in total welfare = $1.127 per customer per month.

$0.25 $0.89 $0.36

-$50.93 -$214.14

-$1134.39

Substantial welfare gains for the largest 0.5% of users generate a significant overall welfare gain. Overall firm profit declines by $.0007 per customer per month as compared with the base case, but total surplus increases by $1.127 because of the increased benefit to the very large users. This last result, although resulting from a highly stylized model and an approximation to the NYNEX tariff actually fIled, suggests that the NYNEX taper increases economic efficiency. Given the concern on this point expressed at the FCC open meeting of November 25,1980, our results strengthen the case for the NYNEX tapered access tariff.

3.3 Calculation of Optional Two-Part Tariffs We now compute the set {Ei, Pi} of optional two-part tariffs which maximize

profit to the local exchange carrier subject to three constraints. The first constraint guarantees that {Ei. Pi} will be selected by type i in preference to a uniform price Po:

(11)

The second set of constraints refers to incentive compatibility. With N types, to guarantee incentive-compatibility of (Ei. Pi) with respect to the other N - 1 two-part tariffs is extremely complicated, in general. However, under the assumption that demand curves do not cross, Qi(P) > Qi-I(P), the problem is reduced to ensuring incentive-compatibility for "downward-adjacent" pairs of two part tariffs. By this, we mean that type i prefers (Ei, Pi) to (Ei-1o Pi-I). To see why, defme

<MP Jco P) = ~j Qi(P) dP - QiP 0) . (Po - P k) + QlP 0) . (Po - P) . k

(12)

The function <Pi(P k, Pj) represents the change in surplus for type i from buying on the two-part tariff (Ek' Pk), instead of (Ej, Pj), k > j. For type i to prefer


(Ei. Pi) to (Ei-I. Pi-I) implies that CPiCPi. Pi-I) => O. Pairwise incentive compatibility is represented by Cf!i(Pi. Pi-I) => 0 and Cf!i-1(Pi-I. Pi-2) => O. From noncrossing. Cf!i(Pi-i. Pi-2) > Cf!i-I(Pi-i. Pi-2) => O. Thus. we have:

Cf!i(Pi' Pi-I) => 0

Cf!i(Pi- I, Pi- 2) > Cf!i-I(Pi- I, Pi- 2) => O.

Because Cf!i(Pi. Pi-I) => 0 and Cf!i(Pi-I, Pi-2) > O. we can add them to obtain

Cf!i(Pi' Pi-I) + Cf!i(Pi- I, P i- 2) = Cf!i(Pi' P i- 2) > O.

(13)

(14)

(15)

Thus. type i strictly prefers (Ei. Pi) to (Ei-2. Pi-2). The same exercise readily establishes that Cf!i(Pi. Pk) > 0 where k < i. Thus, with noncrossing demand curves, incentive compatibility between downward-adjacent two-part tariffs implies incentive compatibility between (E;. Pi) and all two-part tariffs for smaller consumer types.

We must now discuss incentive-compatibility for "upward-adjacent" tariffs. Consider incentive compatibility between (Ei. Pi) and (Ei+I. Pi+I). Iftype i choses (Ei+1o Pi+l). his consumer surplus must be higher than under (Ei. Pi); similarly. because ofC1, the profit contributed to the firm if type i chooses (Ei+1> Pi+I) must be greater than if he selects (Ei, Pi)· But if this occurs, profit cannot have been maximized in the first place. Hence, an optimal solution to the profit maximization problem of the firm must be incentive-compatible between (Ei. Pi) and the two-part tariffs designed for larger consumer types. and we need not explicitly account for incentive-compatibility for upward- adjacent tariffs.

To sum uP. with noncrossing. incentive-compatibility between (Ei. Pi) and all other two part-tariffs is equivalent to the set of N constraints.

fP. C2: Cf!,{Pi• Pi-I) = 'Qj dp - Qi(PO) (Po - Pi) + Qi-I(PO) . (Po - Pi-I) ~ O.

P·l ,- (16)

Finally. we require that Pi lies in the compact interval P = [Po + O. me - 0]. where 0 > O. This is done to ensure the existence of an optimal solution:

C3: PiE P. (17)

Given these constraints, we wish to solve the following program:

N

Maximize I,[Ei+ (Pi-me) Qi(Pi)]gi {Ei' Pi} i = 1

(18)

subject to C1. C2. and C3. wheregi is the share of customers of type i. Note that P is compact and the objective function is continuous. so a solution exists. The following theorem can be shown true: 15


Theorem: Let (Pl*,P2*, .. , ,PN*) and (El*,E2*' .. , ,EN*) be optimal. Then with noncrossing it is true that

Po~P;* >P2*> ... >PN* >mc

0::;E1* <E2* < ... <EN*'

Thus, under profit maximization consumers are faced with the necessity of paying a higher entry fee in order to get a lower usage charge. As noted by Faulhaber and Panzar (1977),16 this implies that the outcome generated by the optimal set of

two-part tariffs {E/ ,*P/}~ can be generated by a single tapered tariff which is 1=1

the lower envelope of {Ei* ,P/}~ . In addition, the Theorem implies Pi lies in the 1=1

interior of P, so that C3 is not binding. Turning to our isoelastic demand example, C1 and C2 can be written

Cl: Ei = Ti · (.0756)-ei*(.0756 - Pi) (19)

(20)

From the results of the theorem, we can ignore C3. Therefore, the maximization problem is

subject to Cl, C2.

6

Maximize L [Ei + (Pi - .01)TiP~iJ gi {Ei,Pi} i= 1

(21)

In table 4, we present results for the base case elasticities. Profit increases by 1.9% over the flat rate tariff, for a dollar gain of $.10 per customer per month. The effects are confined largely to the largest customer types. Consumer surplus weakly increases for each customer type, for an aggregate of $.077, so that total surplus rises by $.177 as compared with the flat rate.

Table 5 presents the results for the higher alternative elasticities. Because types 5 and 6 are assumed to be more price-elastic than in the base case, the effects are more pronounced. The changes in profits, consumer surplus, and total welfare are far higher; profit, for example, rises 9.5%, compared with the level resulting from the uniform price of 7.56 cents per minute.

OPTIONAL TARIFFS FOR ACCESS UNDER FCC PRICE CAP PROPOSAL

Table 4. Optimization Results - Base Case Elasticities (changes relative to flat rate $.0756)

Customer Type

1 2 3 4 5 6

Entry Fee ($/month)

- $0 - $0 - $0

$0.492 $73.27

$2989.17

Usage Charge ($/min) $.0756 $.0756 $.0756 $.0754 $.0690 $.0313

Change in aggregate profit = $.10 customer per month. Change in consumer surplus = $.077 per customer per month. Change in total surplus = $.177 per customer per month.

Change in Welfare

$0 $0 $0

- $0 $1.038

$381.00

203

Table 5. Optimization Results - Alternative 2 Elasticities (changes relative to flat rate $.0756)

Customer Entry Fee Usage Charge Change in Change in Type ($/month) ($/min) Consumer Profits

Surplus

- $0 $.0756 - $0 $0 2 - $0 $.0756 - $0 $0 3 $0.52 $.0752 - $0 $0.23 4 $29.18 $.0674 $0.82 $12.06 5 $342.17 $.0446 $66.0 $170.61 6 $3495.58 $.0238 $2350.0 $1956.60

Change in aggregate profit = $0.50 per customer per month Change in consumer surplus = $0.50 per customer per month Change in total welfare = $1.00 per customer per month

It might be argued that changes in access charge structure since 1986 have greatly narrowed the scope for profit and welfare gains due to the kind of bulk: discounts analyzed here. Most importantly, the 7.56 cents used as the initial price in these simulations was composed of two distinct charges per minute: (1) an artificial rate element (the common line charge) designed to recover a portion of the non-traffic sensitive (NTS) costs of the local loop and; (2) traffic sensitive (TS) rate elements designed to recover traffic sensitive costs of switching and trunking in the LEC's network. Since then, the NTS element has been removed from the carrier access charge (CALC) and added into the CALC paid as a flat amount each month by end users for each access line. Thus, the access charge now paid by carriers is more like 4.5 cents per minute. Table 6 presents the effects of the profit maximizing set of two-part tariffs using the alternative elasticities, but with an initial price of 4.5 cents per minute. The largest consumer, type 6, pays a usage


charge of only 1.9 cents per minute, still a substantial discount, with an entry fee of $1,740.48 per month. Profit rises by 8 percent, lower than in table 5 (which had an initial price of 7.56 cents per minute), but still quite large enough to be interesting. Thus, optional tariffs for access minutes, billed to the end user, are probably still efficient enough so that the ability to file them as new services under the price-cap proposal is of significant benefit to both consumers and LEes.

4. Other Considerations

In this section we discuss qualifications to the above analysis that are of some potential importance.

4.1 End-User Billing Billing the end user for access charges may be very different from current

practice, but it is not at all at odds with economically efficient pricing. Access is not a good desired in and of itself; it is an intermediate good - an input into the production of long-distance services. And for efficient pricing, it is irrelevant whether those who cause access costs pay for that service through direct billing from the LEe or through their long-distance charges.

A bigger concern with end-user billing per se stems from marketing considerations. Since carrier access is purchased by the interexchange carriers (!Xes), the LEes have no direct contact with long-distance customers and, in effect, provide a wholesale service which is being retailed to customers by the !Xes. On the other hand, it has been argued that if access were sold directly to customers by the LEes, interexchange service might be perceived as the wholesale service being marketed or resold to end users by the LEes.I7 Thus, end-user billing for access charges is at the heart of a struggle for retail market presence between local and long-distance carriers, and the standard of economic efficiency has no relevance in deciding the outcome.

4.2 Bypass Most of the arguments favoring tapered tariffs (billed to the end user or not)

have proposed them as ways of extracting a contribution (above marginal cost) from large business customers without encouraging undue bypass. It is easy to understand the LEe's private concern with preventing bypass, but to what extent does this private benefit reflect an increase in social welfare? In our view, bypass and switched access are simply two substitute inputs into the production of a long-distance switched minute. Furthermore, the long-distance technology is fixed proportions-a long -distance minute of use cannot be produced without (roughly) two access minutes of use but all forms of access are essentially perfect substitutes. Extremely large customers will find dedicated access cheaper (whether it be private bypass facilities or LEe special access facilities) and small customers will [md switched access cheaper (whether it be aggregated through private access resale


and sent through a dedicated facility to the IXC or aggregated through the LEC local network).

4.3 Resale A minor problem with tapered tariffs is that since they are based on a form of

price discrimination (the marginal price paid by different size users is different), they set up incentives for customers to aggregate their traffic before presenting it to the exchange carrier network. Just as the WATS tariff has given birth to WATS resellers, bulk discounts in access would give rise to access resellers. However, if access resale (private aggregation of traffic) costs less than aggregation performed by the LEC switch, then society will be better off by allowing such aggregation.

4.4 Response by IXCs Viewing access as an input to IXC service, it is important to take into account

the reactions of the IXCs. With end-user billing, the effects of bulk discounts for access would be that the demand curve for IXC minutes of use for each customer type receiving a discount would shift outward. IXCs might be tempted to simply raise their own prices in response, which would reduce the demand response from the lower access charges and, with it, the profit and welfare effects calculated above. However, fully rational behavior by an IXC would be to extract potential increases in consumer surplus via a system of entry fees, and not cause the total marginal usage charge (access plus IXC charge per minute) faced by users to increase. This would reduce consumer surplus, but would not reduce the profit and total surplus effects calculated above.

5. Conclusions

In this article we have argued that one possible benefit of the FCC's proposed price-cap system for LECs is that it appears to make it easier for LECs to offer optional two-part tariffs billed to end users. Calculations are presented that suggest that the possible social benefits of this feature of the proposal may be large. This suggests that under price-cap regulation the public would be well served by and FCC policy readily allowing receivers from Part 69 tariff structure rules for optional tariffs on access.

Notes

The models, analyses, and conclusions herein are the authors' own and not those of Bellcore or National Economic Research Associates.

1. See FCC (1989), page 393, paragraph 891. 2. h may be that even under price caps, the FCC would have to grant an exemption from Part 69

rules on tariff structure, although the FOC cost test in Part 69 would not have to be passed. 3. Different tapered tariffs were filed by New England Telephone andNew Yark Telephone. Calling

our stylized tariff a "NYNEX" tariff thus emphasizes that it does not precisely correspond to any filed tariff.


4. In this section, the tenn "flat rate" denotes a rate structure with a constant price per minute of use, independent of the amount of usage.

5. There is probably general agreement that the marginal cost of switched access is roughly invariant to the amount of switched access purchased.

6. Recall that the Public Utility Regulatory Policies Act of 1978 (pURPA) recommended the elimination of tapered tariffs unless they reflected the cost of service. See Brown and Sibley (1986, 1987), chapter 4 for a discussion of this issue, in which they conclude that tapers can increase economic efficiency even when the marginal costs of serving large and small users are the same.

7. This is a simplified version of a more general result which appears in R.D. Willig (1979). 8. It is easy to show that if PI> Po , the firm loses money, so to implement (2) with PI > Po does

not Pareto dominate Po. 9. See G.R. Faulhaber and J.C. Panzar (1977). 10. Foran example of this, see S. J. Brown and D.S. Sibley (1986, 87). 11. If Medium takes (E2, Pv instead of(El, PI), he is-by definition-better off and the firm must

necessarily make more money than if he remained on (El, Pl). 12. See J.E. Anderson (1976). 13. Note that price elasticities derived from historical data have two defects if used for our purposes:

(1) they represent the price elasticity of demand for switched long-distance service, not for switched access, and (2) they were estimated from data in which there was no alternative to switched access for long-distance service. In addition, the constant price elasticity of demand assumption is prohably unrealistic when substitution is predominantly driven by bypass.

14. This is technically unrealistic since the traffic sensitive tapered rates apply to W A TS usage as well as MTS and since the price elasticities of demand by band are derived from weighted averages of W A TS and MTS own and cross price elasticities.

15. See Heyman, Lazorchak, Sibley and Taylor (1987). 16. See Faulhaber and Panzar (1977). 17. The Modification of Final Judgment imposes an absolute prohibition on Bell Operating

Companies' carriage of interLATA traffic.

References

Anderson, J. 1976. "The Social Cost of Input Distortions: A Comment and a Generalization." American Economic Review 66(1): 235-238.

Brown, S., and D. Sibley. 1987 . The Theory of Public Utility Pricing. Cambridge: Cambridge University Press.

Heyman, D., J. Lazorchak, D. Sibley, and W. Taylor. 1987. "An Analysis of Tapered Access Charges for End Users." Bellcore Economics Discussion Paper #31.

Faulhaber, G., and J. Panzar. 1977. "Optimal Self-Selecting Two Part Tariffs." Bell Laboratories Economics Discussion Paper #77 (January).

Federal Communications Commission (FCC). 1988. Further Notice of Proposed Rulemaking. CC Docket 87-313 (May 23).

Federal Communications Commission (FCC). 1989. Report and 0 rder and Second Further Notice of Proposed R ulemaking. CC Docket 87 -313 (May 5).

Willig, R. 1979. "Pareto-Superior Nonlinear Outlay Schedules." Bell Journal of Economics (Spring).

1. Introduction

11 OPTIONAL CALLING PLANS AND

BYPASS EFFICIENCY Michael A. Einhorn

In the brave new world of telecommunications regulation, endusers have enjoyed increasing freedom to install and utilize bypass technologies that circumvent regulated utility facilities, such as central office switches. If utility prices were above marginal cost, such bypass could be economically inefficient This issue emerged full force in the mid-1980s, when local companies contended that contemporaneous procedures for recovering nontraffic sensitive costs led to inefficiently high usage charges that posed the danger of uneconomic bypass. While the heat of the issue dissipated somewhat after the FCC increased the subscriber line charge, the concern can reemerge in the future should bypass costs fall considerably.

For three reasons, traditional cost-based regulation may be a seriously flawed means of addressing the issue of uneconomic bypass; alternative suppliers are not legally required to report their costs to regulators, reported costs may be seriously distorted, and forecasting the future of emerging bypass technologies and their associated costs is difficult, if not impossible. We now shall consider a more realistic strategy that involves optional calling plans with an imposed fairness constraint. Under the suggested strategy, the utility and its regulators would agree upon a fair two-part calling plan that any customer may choose for any switched access line; this tariff must be adjusted over time for inflation and anticipated productivity growth. Once the utility offers this fair tariff, it may design as many alternative calling plans as it wishes; a customer may "mix and match" available calling plans across existing switched access lines.

As will be shown, several benefits result First, regulators could design the prices of the fair tariff specificall y with the interests of small captive customers in mind. Second, such a mechanism gives the utility the correct incentive to determine-as best it can-all potentially relevant costs; it can instantaneously modify their prices should these cost estimates change. Third, regulated utilities would


have more of an incentive to reduce costs than under traditional regulation with regulatory lag. Fourth, bypass will result if and only if it is economically efficient.

The article is organized as follows. Section 2 overviews the legal and technical aspects of the price cap and bypass issue. Section 3 introduces a nonuniform price schedule with a regulator-imposed constraint on one tariff. Section 4 complicates the schedule by introducing bypass technologies. Section 5 considers implementation, possible complications, and objections to the approach. Section 6 concludes the article.

2. Legal and Institutional Issues

The FCC has slated July 1, 1990, as the starting date for price-cap regulation of interstate local carrier prices. At that time, the commission must make some decision regarding its future method of switched access cost recovery; it is not clear whether these prices would be appropriately rolled into a composite basket. Indeed, many long-distance carriers, consumer groups, and large users recommended to the FCC that long-distance usage charges be separately capped and adjusted; the motivation is clear-long-distance users could face substantial rote shock if access charges were permitted to increase significantly. Although the commission has not done so yet, there is no reason why direct end-user billing cannot be implemented in the future; indeed, the FCC approved of the idea in principle in 1986 (Petitions for Waiver of Various Sections of Part 69 of the Commission's Rules, FCC 86-145, April 28, 1986).

Local companies have frequently claimed that uneconomic bypass of switched access facilities could result under fully distributed cost recovery methods that would allocate interstate revenue requirements without regard to marginal cost; these claims surfaced in the mid-1980's when the FCC attempted to increase its subscriber line charge to $6 per access line. A Geneml Accounting Office study (1986) estimated that 16 to 29% of large volume telephone customers bypassed their local exchange and that 19 to 53% more were considering additional bypass activity; a loss of 1 % of these customers could produce a 14 to 48% decline in long-distance revenues. Studies by Bell Communications Research (1984) and Jackson and Rohlfs (1985) concurred that uneconomic bypass constituted a present danger to local company revenues. However, not all commenters agreed; state commissions have varied widely in their response (Cross, 1986). In order to determine who is right, we would need to estimate the cost of all relevant technologies, an exercise that is next to impossible. Additionally, these relative costs can change over time; what is true regarding bypass costs at present may be irrelevant in five years.

Any solution to the NTS cost recovery problem cannot ignore the concerns of small users who are captive to the local exchange. Reps. Dingell and Markey issued a joint statement in May, 1988:

"We continue to be concerned that ordinary telephone customers will be worse off under this [price-cap] plan than they would be under an intelligent administra-

OPTIONAL CALLING PLANS AND BYPASS EFFICIENCY 209

tion of the current system. Indeed, some studies show prices would be higher now had a price-cap regime been in place over the past eleven years." (New York Times, May 13, 1988, D-2)

Several state commissions and consumer groups have voiced similar concerns that emphasized the benefits of traditional regulation. This consumerist pressure induced the FCC to revise its earlier suggested price-cap procedure of 1987 from a single-index approach modeled after Great Britain to a multi-index approach that separately capped residential prices.

3. A Mathematical Model

In the following sections, we shall allow a regulated monopoly to design a menu of optional calling plans subject to the constraint that one tariff is regulator-approved. Let Ao and Po represent the respective fixed and usage charges for this calling plan.

Faulhaber and Panzar (1977) establish-for deterministic demand-that a decreasing n-block nonuniform price schedule can be reexpressed as a menu of alternative two-part tariffs with connection and usage charges that are inversely related to one another. (For stochastic demand, these two are similar but not quite identical; under a nonuniform price schedule, the customer would have the additional benefit of being shifted to his best two-part tariff if his actual and expected demands were to differ from one another.) Therefore, designing a constrained menu is nearly equivalent to designing a nonuniform price schedule subject to the constraint that no user is worse off than it would be under Ao, Po. Accordingly, we shall develop in this section a constrained nonuniform price schedule for a profitmaximizing monopoly with captive single-line customers; in later sections, we consider multiline customers and customer bypass.

3.1 Notation and Assumptions Following previous authors, we shall assume that single-line customers vary in

their usage intensities and that customer demand curves do not cross one another (Faulhaber and Panzar, 1977; Spence, 1977; Mirman and Sibley, 1980; and Goldman, Leland, and Sibley, 1984). Consequently, we may index each customer with an ordinal parameter i E [0, 1]; i is continuously distributed with density f(z) and distribution F(i). Let a (e) designate the infimum (supremum) of intensities i of customers who select utility service; in this section, we shall assume that both a and e are fixed at 0 and 1.

Let A represent the connection charge for a utility customer; R(q) represents the necessary revenue payment for a usage level q. At any usage level q, net welfare Wi(q) of consumer i is the difference between his willingness-to-pay U(i, q) and revenue payments A + R(q); i.e.,

Wi(q) = U(i, q) - R(q) - A. (3.1a)

Under a binding fair tariff Ao, Po, net consumer welfare is subscripted with an


0: WiO<q) = U(i, q) -Ao -Po' (3.1b)

Under the assumed fair tariff constraint, no customer can be made worse off underR(q) than he would beunderAo,Po ; i,e., Wi(qi) ~ Wio(qio). If equality holds, we shall term the customer fairness-indifferent. (If customer demand curves are independent of one another, imposing this constraint is equivalent to imposing the requirement that the utility's schedule A, R(q) weakly Pareto-dominates the tariff Ao, Po; see Willig, 1978.)

Einhorn (1987) demonstrates that if users a and e are utility customers and demand curves do not cross, a profit- or constrained welfare-maximizing utility would attract all customers between. We let Z and c represent the respective marginal hookup cost and the running cost of usage, For each customer i, utility profits are the difference between revenues and costs; i.e., A + R(qi) - Z - cqi. Total customer demand cannot exceed in-place capacity Q, which has a per unit cost of k. Total company profits are then:

1t= r [A+R(qi )-Z- cqi] dF(z) -kQ. (3.2)

a

We shall always assume that the resulting price schedule single-crosses (Goldman, Leland, and Sibley, 1984) each customer's demand curve from below at her optimal usage level qi. As a result, second-order conditions for a maximum will always be met and customer usage qi will monotonically increase with user intensity i.

3.2 First-Order Maximizing Conditions The utility then constructs a revenue schedule R( q) to maximize its profits (3.2)

subject to two constraints. First, total customer demand cannot exceed capacity Q;

i.e., J e qi dF(i) :$; Q. Second, no customer is worse off than he would be under the a

tariff Ao, Po; i.e., Wi ~ Wio. The utility's objective function can then be expressed as follows:

L= Je [A +R(qi) - Z- cqi] dF(i) - kQ a

An extension of two earlier derivations (Spence, 1978; Einhorn, 1987) shows:

P _ P( ) _ [1 h] (') liPU(i,q») (3.4a) i - q i - c + v + - i t z oioq

where:

OPTIONAL CALUNG PLANS AND BYPASS EFFICIENCY

(') = F(e) - F(i) > 0 t I f(l)

Wj (qj ) ~ W io(qjo); hj ~ 0; hj[Wj (qj ) - Wjo(qio)] = 0

v-k~O; Q ~O; [v-k]Q=O.

211

(3.4b)

(3.4c)

From (3.4c), if Q > 0, v = k. Therefore, c + v = c + k; the latter is the long-run marginal cost, which we shall represent with a C. We rewrite (3.4a):

[ CPU(i,Q)] Pi = P(qi) = C+[l - hj] 1(1) didq

(3.4a')

Ll in figure 1 illustrates the shape of an optimal nonuniform price schedule when the fairness-indifference constraint is not binding (Le., hi = 0 in (3.4a'). Because

d2U(i,q)/didq > 0, the usage price P( q) must exceed or equal the short-run marginal cost C; since t(e) = 0, P(q) must eventually fall to C. The schedule need not be monotonically decreasing but I shall assume that it is.

price p(q)

customer usage q

FIGURE 1 Profit-maximizing Price Schedule with and wi+-hout Regulator Constraints: e=l

3.3 Fairness Indifference We now consider the implications of adding the fair tariff constraint (3.4b) to

an optimal nonuniform price schedule. Rather than formally deriving the results, we can compare our problem to an earlier paper (Einhorn, 1987) and intuitively justify our conclusions. The more technical reader is referred to the earlier study


for proofs. In Einhorn (1987), the regulated utility attempted to maximize profit-con

strained welfare. The maximand was [1- g]W + g1t, where 1t = utility profits and W = consumer surplus. If g = 1, the maximand is simply 1t. Therefore, by setting g = 1, the general optimizing conditions of Einhorn can be used, mutatis mutandis, for the present problem-at-hand.

Einhorn attempts to maximize [1- g]W + g1t subject to the constraint that no utility customer would be worse off than he would be with a bypass system with respective access and usage prices of Z* and C*. Under these circumstances, the resulting price schedule P(q) reaches a plateau along which the usage price

P(q) = C*; once it reaches the plateau, the price-schedule can never rise above the plateau price for higher levels of customer usage. But for differences in the levels of Ao and Z* or Po and C*, there is evidently a basic similarity between designing a price schedule under bypass and the fairness constraint.

Based on a similar deri vation in Einhorn (1987, 556-7), L2 in figure 1 illustrates the effects of adding the fairness constraint at Ao, Po. Unlike the unconstrained price schedule L}, the constrained schedule L2 reaches a plateau (qb, qdl along which P(q) = Po. Einhorn shows that inframarginal charges prior to point qb under the utility schedule must be identical to those under the fair tariff; i.e., A + R(qb) = Ao + P oqb. All users along the plateau are indifferent between A, R( q) and Ao, Po; all users before and after the plateau strongly prefer A, R ( q) to Ao, Po.

3.4 A Second Fair Tariff By adding a second fair tariff, we set the stage for the analysis of Section 4 that

will introduce customer bypass. If regulators were to impose a second fairness constraint, no customer could be

worse off than he would be under either of the two schedules. We represent these

two tariffs by Ao,Po and AO,po; assume that Ao<Ao and Po > pO. Because consumer demand curves do not cross one another, only one customer could be

indifferent between Ao, Po and A 0, po. Therefore, at most one customer can be simultaneously indifferent between the two fair tariffs and the regulated utility's price schedule P(q). Let [qb, qdl ([qb', qj]) represent the segment over which

customers [b, d] ([b', cf]) would be indifferent between the tariff Ao, Po (Ao, po)

and the utility's nonuniform price schedule A, P( q); since at most one customer can

be indifferent between Ao, Po andAo,Po, d:$ b' is necessary. A double-constrained price schedule P(q) therefore would have two plateaus;

usage price P( q) would be constant over each. figures 2a and 2b illustrate two

possibilities for pO> C. If b' > d (as in figure 2a), an interval of unconstrained customers (d, b') would lie between the two plateaus. If d = b' (Figure 2b), the schedule would jump immediately from one plateau to the second by moving down the demand curve of customer d = b'.

OPTIONALCALUNGPLANSANDBYPASSE~crnNCY

price p(q)

price P ____ 0_

price pO

- - - - - - \----1 ___ \

1\ I \

\ \

T "\ -I \ 1\ I \ _ .J T ;;-I \

\

customer usage q

I \ 1 "\

\

\

FIGURE 2a Profit~maximizing Schedule with Two Regulator Constraints: Case 1

price p (q)

-, I , I

, I

I 1.. 'I - " 1 I I ,

I ,

customer usage q

fIGURE 2b Profit~maximizing Schedule with Two Regulator Constraints: Case 2

213


I _ _ _ _ \L _ ma..:rgi!!aLcQ2t.J; ___ -].1

price p(q)

rice pO yl

customer usage q

FIGURE 3 Profit-maximizing Price Schedule with Regulator Constraint:

As long as A 0 is high enough, there is no reason why pO > C must hold. Figure

3 is analogous with pO < C < Po. Under these circumstances, usage by the largest customers i> h' would be subsidized; i.e., usage would be priced below marginal costC.

4. Fair Tariffs and Bypass

We now shall modify the model of Section 3 to allow for a variable endpoint; i.e., the maximum endpoint e may vary due to large customer bypass. B ypassers pay an up-front connection fee and a per unit usage price. Assuming that bypass vendors constitute a competitive market, their connection and usage prices will be driven to associated costs, represented by Z* and C*.

Assuming that the fair tariff is designed to protect smaller users, Po> C* and

Ao < Z* is probable; i.e., small users will pay higher usage charges but lower connection charges compared to bypassers. We therefore may conceive of the bypass alternative as being a second fairness-indifference constraint with

A 0 = Z* ,po = C*. Accordingly, figures 2a and 2b represent cases where C* > C; figure 3 represents the case where C* < C.

4.1 High Endpoint e We turn to the choice of the high endpoint e. We differentiate (3.3) with respect

OYTIONALCALUNGPLANSANDBYPASSE~crnNCY 215

toe. A +R(qe) - Z - Cqe 2!O; e:S; 1; [e - 1] [A +R(qe> -Z- Cqe] = O. (4.1)

If C* > C, figures 2a and 2b would be relevant. Evidently from both figures, usage price P( q) weakly exceeds marginal cost C for each unit of usage; therefore, each utility customer would genemte positive profits for the company. As Einhorn (1987,556-7) shows, each customer before qb' and after qi strongly prefers utility service to bypass; each customer i E [b', d'] is indifferent between utility and bypass service. In (4.1), e = 1; since P(q) > C, A + R(qe) > Z + Cqe.

If C* < C, figure 3 would be relevant. Since C* < C. the utility evidently would subsidize some usage by the largest customers beyond point W; however, each such customer would generate a cushion of profits RSTVW from its early usage before this point. In selecting its preferred maximum intensity e, a profit-maximizing utility would want to keep customers until the point where the entire profit cushion RSTVW is paid back; i.e., RSTVW = WXYZ. At this point, customer revenues and costs would be equal.

Einhorn shows that all customers along XY are indifferent between utility service and bypass; in order to retain a customer i > e, P(q) = C* < C would be necessary. Because customer revenues and costs are equal to one another at point e, all customers i > e would be nonprofitable and would not be retained. Consequently, a profit-maximizing utility may select an interior endpoint e < 1 where (see (4.1» A +R(qe) = Z+ Cqe.

Because P(q) < C*, all customers i < e are evidently profitable and are retained. Therefore,

For i < (=, » e,A +R(qj) > (=, <) Z+ Cqj. (4.2)

Customer e, who is the transition customer between the two technologies, must be indifferent between utility service and bypass if intensity i is continously distributed; therefore, U(qe) - A - R(qe) = U(qe) - Z* - C* qe must hold. Using (4.2),

(4.3a)

The LHS and RHS expressions respectively represent the net social gains from utility and bypass usage by customer e. From an efficiency perspective, it is then a matter of economic indifference whether user e joins the regulated utility or the bypass technology. Since P(q) = C*, Z+ Cq=Z* + C*qe. Because C* < C,

Z + Cqe > Z* + C*qe for all i > e. For users i < e who join the regulated utility,

U(qj) - A - R(qj) > U(qj*) - Z* - C*qj*; using (4.2),

For i < e, U(qj) - Z - Cqj> U(qj*) - Z* - C* qj* . (4.3b)

Evidently, each customer makes a socially efficient choice regarding his service selection.


5. Implementation and Practical Considerations

We now further consider various aspects of the problem and some advantages of optional calling plans.

5.1 Multiline Customers To this moment, we have assumed that the customer makes one decision

regarding utility service-whether or not to bypass the regulated utility. However, in telecommunications, large users install several access circuits, which may be a mixture of bypass and switched access.

The above results can be extended to a multiline model provided the per unit price on each switched access line is a declining function of line usage (Einhorn, 1987). This constraint ensures that each caller would attempt to concentrate phone calls over as few lines as possible and to route calls over available lines with a nonvarying order of preference. Therefore, intensity of line usage is now unambiguously ranked as had been intensity of customer demand before. The parameter i in Sections 3 and 4 now represents the intensity of line-usage instead of customer demand; previous theoretical results would hold mutatis mutandis if a revenue schedule R ( q) were designed for usage on each access line.

5.2 The Tariff Menu There is a practical manner in which regulated utilities may implement this price

schedule. As noted, a nonuniform price schedule and a menu of optional calling plans are the same when demand is deterministic and nearly the same when demand is stochastic. Therefore, we might implement the incentive mechanism as follows. Regulators may prescribe access and usage prices Ao, Po for one two-part tariff that the utility must offer; the utility may then design a menu of alternative two-part tariffs that any subscriber may select for any line.

Regulators must determine starting prices for Ao, Po; such starting prices would involve establishing some notions of fairness, an area of theoretical economic research (Kolm, 1973; Varian, 1976; Pazner and Schmeidler, 1978) now lacking application to public utility regulation. Schmeidler (1969), Loehman and Whinston (1971), and Billera and Heath (1982), among many, have suggested an axiomatic cost-allocation procedure that produces prices conforming to a set of properties that are purportedly fair; however, economic efficiency is not a consideration in axiomatic cost allocation. Baumol (1986) advocated a fairness constraint that no utility service be permitted to recover more revenue than its associated stand-alone cost or less than its incremental cost; the FCC disqualified this as the basis for fair prices, arguing that rates based on stand-alone cost could be excessively high and would necessarily involve detailed "paper engineering" of hypothetical utility systems. In the face of theoretical and practical difficulties that have clouded the fair pricing issue, the FCC adopted present fully distributed cost procedures as its fair ratemaking strategy, arguing that such procedures have presumably been designed with the intent of being fair.

OPTIONAL CALLING PLANS AND BYPASS EFFICIENCY 217

To this juncture, we have assumed that regulators specify a fair calling plan individually for each service that the regulated utility offers. Alternatively, regulators may stipulate that a price index of designated core services not exceed a predetermined index limit, to be adjusted over time for general inflation and expected technical change. For each offered utility service, one tariff must be incorporated in the aggregate price index.

Two problems may result. First, as the case of Britain's short-haul rates illustrates (see introduction), certain prices may climb considerably with an index ceiling; this outcome may be politically difficult. Second, indexing invites room for strategizing when demand is changing (see Brennan's chapter in this book). Since long-distance access represents a politically important component of telecommunications service, a single ceiling approach may then be preferable.

5.3 Cost Efficiency To circumvent the inefficient pass-through of the utility's actual costs, Lit

tIechild (1983) and Egan and Taylor (1987) suggest that a general inflation index (such as the consumer price index or the GNP deflator) be used to adjust the price ceiling; this ensures that real prices to consumers do not increase. However, general price indexes might not accurately track company costs reasonably; since 1935, the consumer price index has risen eightfold while its telecommunications component has risen twofold (Lande and Wynns, 1987). For this reason, the National Telecommunications Information Administration (1987) advocates the use of a telephone input price index, which presumably mimics the effect of a competitive market and can more accurately represent a reasonable rate of cost inflation. However, constructing a specific cost inflation index may involve considerably more data-gathering by utilities and oversight by regulators; the FCC used a GNP deflator in its 1989 price-cap decision.

The utility cannot then expect to pass along to its ratepayers its actual cost increases; it therefore has an incentive to reduce its costs at every moment. Furthermore, if it is able to improve productivity beyond expectations, it can keep the resulting profits. This contrasts with traditional cost-based regulation, where prices that are based upon actual cost afford no incentive (but for regulatory lag) for utilities to minimize costs.

5.4 The Resale Problem A reseller of telecommunications services might take advantage of the utility's

menu of optional calling plans by installing a group of switched access lines and charging arbitrage prices to attract small usage customers. By providing this opportunity for arbitrage, the local company could lose its own customers (White, 1982). Assuming that resale is legal, why would a local company choose to implement a declining block schedule?

In response, note that resellers always have the option of concentrating subscriber calls over bypass circuits instead. If the local company does not implement an optional calling plan menu, resale could result nonetheless over bypass circuits.


By designing the menu, the local company would capture all of the reseller's outgoing circuits that it efficiently could. The main issue is not whether optional calling plan menu&.lose customers to resellers; rather, the issue is whether the resellers will use bypass or local company switched access circuits to route customer calls.

5.5 Predation Since some usage prices may be below marginal cost, some may consider this

predatory. Indeed, many commentators to the FCC suggested that the commission establish price floors and/or minimum duration requirements in order to reduce the danger of predatory pricing. Regarding this problem, Section 4 demonstrated that A + R(qj) > Z + Cqj for i < e; a profit-maximizing utility therefore enjoys a positive net contribution from each customer. Therefore, each customer passes the net revenue test and no cross-subsidization occurs (see Sibley, Heyman, and Taylor's chapter in this book). Consequently, if the profit-maximizing utility prices P( q) and selects endpoint e as we have assumed, predation is not a well-founded charge.

However, a strategizing utility could attempt nonetheless to retain some customers i above its profit-maximizing value of e as part of a short-run predatory strategy; as shown in Section 4,A + R(qj) < Z + Cqj must hold for these intensities i. Although predatory pricing cannot be profitable if employed indefinitely, a short-run application might destroy competition and make way for a long-run monopoly.

However, if predatory pricing is a danger, it is, realistically speaking, just as profound a danger under any market-regulated or not-with marginal costs that are difficult to measure. The danger of predation emerges in unregulated markets where large competitors with difficult-to-measure costs can temporarily "take a hit" to eliminate unwanted competitors. Under the traditional regulation schemes that price caps would replace, companies must report to regulators their marginal costs, which can be distorted in order to lower usage prices and stifle competition; whether regulators can confirm that these reports are fallacious is arguable. In a different context, Noll and Owen (1987) write:

The FCC could not determine AT&T's costs, nor could it settle on a sensible cost-based method for pricing. One set of AT&T prices, the Telpak tariff, went through nearly two decades of hearings without a final determination of its lawfulness. It was apparent that even with a fully informed regulatory policy and the best will possible, the FCC could not cope successfully within available administrative procedures with AT&T's control of the information necessary to regulate prices effectively.

Finally, the issue may be more appropriately settled in antitrust litigation than in regulatory hearings.

The problem of predatory pricing does not then hinge upon whether optional calling plans are implemented or not. The danger evidently arises whenever any firm, regulated or not, has marginal costs that are exceptionally difficult to determine.

OPTIONALCALUNGPLANSANDBYPASSE~cmNCY 219

6. Conclusion

We can conclude the article by summarizing the benefits of optional calling plans. But for the fact that regulators design one calling plan for each utility service, utilities may price freely in order to maximize profits. Unless it engages in predatory pricing, the utility will profitably attract only those large customers whom it can efficiently serve; the rest will bypass. Furthermore, it has incentives to reduce costs and to estimate demand and cost parameters as accurately as possible. Finally, regulators benefit from the reduced work load.

References

BalUllol, W.J. 1986. "Modified Regulation of Telecommunications and Public Interest Standard." Unpublished doclUllent filed with National Telecommunications and Information Administration, Washington, DC.

Billera, L.J., and D.C. Heath. 1982. "The Allocation of Shared Costs: A Set of Axioms Yielding a Unique Procedure." Mathematics of Operations Research 7(1): 32-39.

Egan, B.L., and W.E. Taylor. 1987. "The Economics of Ceiling Price Regulation." Unpublished manuscript. Bell Communications Research. Livingston, NJ.

Einhorn, M.A. 1987. "Optimality and Sustainability: Regulation and Intermodal Competition in Telecommunications." Rand Journal of Economics 18(4): 50-63.

Faulhaber, G.R., and J.C. Panzar. 1977. Optimal Two-Part Tariffs with Self-Selection. Discussion Paper 74. Bell Telephone Laboratories. Murray Hill, NJ.

Goldman, M.B., H.E. Leland, and D.S. Sibley. 1984. "Optimal Nonuniform Prices." Review of Economic Studies 51(2): 305-19.

KoIrn, S.C. 1973. "Super-Equite." KykIos(26)4: 841-3. Lande, J.L., and P.L. Wynns. 1987. Primer and Sourcebook on Telephone Price Indexes

and Rate Levels. Industry Analysis Division, Common Carrier Bureau, Federal Communications Commission, Washington, DC.

Littlechild, S. 1983. "Regulation of British Telecommunications' Profitability." Report to the Secretary of State. Department of Trade, London, England.

Loehman, E., and A. Whinston. 1971. "A New Theory of Pricing and Decision Making for Public Investment." Bell Journal of Economics and Management Science 2(2): 606-25.

Mirman, L.J., and D.S. Sibley. 1980. "Optimal Nonuniform Pricing for Multiproduct Monopolies." Bell Journal of Economics 11(2): 659-70.

National Telecommunications and Information Administration. 1987. NTIA Regulatory Alternatives Report. Washington, DC: U.S. Department of Commerce.

Noll, R.G., and B.M. Owen. 1987. "United States v. AT&T: An Interim Assessment." Working Paper, Stanford University, Palo Alto, California.

Pazner, E.A., and D. Schmeidler. 1978. "Egalitarian-Equivalent Allocations: A New Concept of Economic Equity." Quarterly Journal of Economics 92(4): 1-45.

Schmeidler, D. 1969. "The Nucleolus of a Characteristic Function Form Game." SIAM Journal of Applied Mathematics 17(5): 1163-70.

Spence, A.M. 1977. "Nonlinear Prices and Welfare." Journal of Public Economics 8(1): 1-18.

Varian, H.R. 1976. "Two Problems in the Theory of Fairness." Journal of Public Economics 5(3,4): 249-60.

White, L.J. 1982. "On the Welfare Effects of Resale in the Context of a Nonlinear Pricing


Schedule." Bell Journal ofEcorwmics 13(1): 280-5. Willig, R. 1978. "Pareto-Superior Nonlinear Outlay Schedules." Bell Journal ofEcorwmics

9(1): 56-69.

12 PRICING AND INVESTMENT INCENTIVES

UNDER PRICE CEILING REGULATION

1. Introduction

Calvin S. Monson Alexander C. Larson

For decades, public utilities have been regulated by a maximum allowed rate of return. This type of regulation has long been criticized as being outmoded for technologically dynamic industries like telecommunications. For example, it has been argued that rate of return regulation retards new product and service innovation and research and development. It has also been argued that this form of regulation does not encourage rates based on marginal costs.

The Federal Communications Commission (FCC) has proposed that a different form of regulation be examined as an alternative to rate-of-return regulation for the telecommunications industry and has adopted this form of regulation for AT&T. 1

This alternative is price ceiling regulation. Instead of constraining the overall rate of return a telephone company is allowed to earn on federally regulated services, price ceilings would put an upper bound on the aggregate average prices charged for a predetermined "basket" of services. The rate at which such average prices would be allowed to grow would also be constrained.

The allowed growth rate of aggregate prices under a price ceiling regulatory regime would probably be dependent on (1) the growth rate of the general price level in the overall economy, and (2) a "productivity offset." The "productivity offset" is a rate of expected growth for productivity in telecommunications. It is subtracted from the rate at which price ceilings would otherwise be allowed to grow. If the regulated telephone company can be more productive than the rate suggested by the "offset," it is allowed to keep the revenues from such efficiency.

Thus, the FCC proposed an indexed, aggregate price ceiling for a bundle of services that have historically been subject to rate-of-return regulation. The indexing means that the maximum prices allowed by the ceiling are allowed to


grow only at a prespecified rate, which incorporates changes in the purchasing power of money and expected changes in the productivity of the regulated frrm.

One aspect of the economics of price ceiling regulation that has received little analytical attention is the way this new form of regulation affects the incentive of a regulated firm to engage in cost-reducing investment? If a regulated frrm is subject to price ceilings, how does this affect its decision to invest in new capital? Continued investment in cost reduction and the ability to recover that investment determines the long-term viability of the regulated frrm. It is important, then, to examine the investment incentives of a firm subject to price ceiling regulation.

Our principal results are: 1. Given some level of profit earned by the frrm, pricing under price ceiling

regulation in general will not be second-best optimal. 2. A change to price ceiling regulation, with the ceiling set at the former rate

of-return regulated price, will lead to cost-reducing improvements in investment behavior.

3. The frrm's incentive for cost minimization under price ceiling regulation is the same, regardless of the profit level. This is in contrast to rate-of-return regulation, where incentives for cost minimization are strongest when the firm is earning less than the allowed rate of return.

4. As the price ceiling constraint becomes more binding, the price ceiling regulated frrm has a greater incentive than the unconstrained monopolist to develop, promote, and market its services to those customers whose demand is relatively inelastic.

2. Description of the Formal Model

The model employed in this article is similar to one used by Baumol (1971) in examining the optimal depreciation policy for the purchase of durable investment. This analytic framework allows the model to address a wide range of questions on investment decisions under price ceilings. It assumes the multiproduct regulated frrm attempts to maximize the discounted value of profits (over a planning horizon it has chosen for the capital it has purchased), subject to compliance with price ceilings. In addition to the price ceilings, the model implicitly employs a set of capacity constraints that allow the model to address the incentives for cost-reducing investment over time. It is in this latter aspect that our model differs from those employed by other authors.

In this model, several assumptions are employed to avoid a needlessly complex formulation and to make it relevant to the telecommunications industry.

1. The underlying goal of regulators is to ensure that consumers pay "just and reasonable" prices for services for which the regulated frrm has market power (and hence has the ability to raise prices above competitive levels).

2. The regulated firm maximizes profits subject to a regulatory price ceiling constraint.

PRICING & INVESTMENT INCENTIVES UNDER PRICE CEillNGS 223

3. The regulated finn is multiproduct in nature. We make no assumptions on scale economies, since our model will generalize to various formulations of returns to scale. Throughout the analysis. we assume the regulated fmn is purchasing a piece of equipment in the first period of a planning horizon. with no further purchases of equipment. We do not address the case of sporadic investment.

4. Demands for the services produced by the regulated fmn are assumed independent.

5. The level of quality is exogenous to the finn and determined by regulation. 6. The regulated fmn has a common carrier obligation. It must supply all

customers who want a service at the given price. 7. We abstract from all questions of uncertainty in the investment decision.

that is. the model assumes there is perfect certainty when investment in capital is made.

8. Investment need not take place in lumpy increments.

2.1 Defmition of Variables Used in the Model Define the following variables. where i refers to product (i = 1 •...• N) and t refers

to discrete time unit (t = 1 •...• 1): Xit = output quantity Xt = N-vector of products. i.e .• (Xli X2t ••• XNt)

Pit = price of Xit

Yt = capital purchased during t r = per unit cost of acquiring capital K t = total capital accumulated through t Ct = operating costs during t 0= 1/(1 + d). where d is a discount rate Wi = weighting scheme of aggregate price ceiling 1C() = initial value of aggregate price ceiling v = price and productivity indices. Also define

which is the own price elasticity for product i.

2.2 Maximization Problem The regulated firm seeks to maximize the discounted stream of profits. subject

to capacity limits and the price ceilings. Thus. the fmn's programming problem is to maximize the following profit function with respect to the fmn's choice variables: price (Pit). and investment (Yt). for i = 1 •...• Nand t = 1 •...• T:


N T T T

IT = L L Pit Xit (Pit) 'f/ - L Ct (Xt' K t) 'f/- L ryt i/. i=lt=l t= 1 t= 1

It is assumed that additional investment in K reduces both total and marginal costs, so that CK < 0 and Cx!( < O. The firm is subject to a capital accumulation condition that holds in each period t = 1, ... , T:

K t = K t- 1 + Yt .

It is assumed here that capital is completely fungible so that a unit of capital can be used to produce a unit of any product. The fundamental results are not changed by assuming less than perfect substitutability. Also, to simplify it will be assumed that Yt > 0 (interior solution).

In addition, the regulated firm is subject to the indexed aggregate price ceiling that also must hold in each period t = 1, ... , T:

N

L Wi Pit $; Ko(1 + vi. i= 1

It is possible for the price weighting scheme, Wi, to vary over time, as under a revenue-weighting scheme, but for simplicity, we assume a fixed-weight formulation.

Note that, by assumption, the assets acquired do not lose their output capacity over time. That is, we are postulating a form of "one-hoss shay" depreciation. As a tITSt approach to the problem, this is a permissible simplifying assumption.

For convenience, the capital accumulation condition is substituted into the operating cost function. The Lagrangian function is then:

N T T

L(Pit' Yt' (Jt) = L L Pit Xit(Pi/fl - L Ct (Xt , K t- 1 + Yt) 'fi i=lt=l t=1 (1)

T T N

-t~l ryt 'fl +t~l (Jt (Ko(1 +vi -i~ Wi Pit )

2.3 Conditions for Constrained Profit Maximization We get the following first-order necessary Kuhn-Tucker conditions for a max

imum:

(2)

T aL "ac-r; t t a-= -""'aO -ro =0, forYt>O, Yt -r;= t Yt

(3)

PRICING & INVESTMENT INCENTIVES UNDER PRICE CEILINGS 225

(4)

(5)

3. Pricing Incentives

The first-order necessary conditions can be used to examine the pricing incentives of the firm subject to price ceiling regulation. (2) yields:3

1 aCt (aXil t)-1 Pit(I---:)=-a . +crtO)i -a . S .

1:\ xtt 'PIt

(6)

The left-hand side of (6) is marginal revenue. The first term of the right-hand side is marginal cost. Because aXitlapit < 0, the right-hand side shows that the more binding the price ceiling constraint is in t, the lower prices will be in t. (6) also shows that it is possible for price ceiling regulation to lead to an outcome where the finn is forced to operate in a region of inelastic demand. Recall that the unconstrained monopolist maximizes profits by operating where demand is elastic. However, if crt > 0, it is possible for Ei < 1. When the price ceiling constraint is not binding in period t, that is, crt = 0, (6) reduces to the condition for profit maximization of an unconstrained monopolist.

(2) can also be used to derive another interesting result concerning the price ceiling regulated firm's pricing incentives. With some manipulation, (2) implies:

This can also be written as: 1 arr 1 arr

If we define the weights as initial quantity shares in the following way: xiO

we get the following condition:

O)i=-N--'

LXIO 1= 1


1 an 1 an XiO apit = XjO apjt'

(7)

It has been shown previously that the condition for efficient pricing is the following, given some profit level that the ftrm may not exceed:4

1 an 1 an (8)

Only by coincidence will xit = XiO. In general, Xit :# XiO, so the following is implied by the first-order conditions:

1 an 1 an --:#--. Xit apit Xjt apjt

(9)

That is, the following statement can be made about price ceiling regulation: given some level of profit that the ftrm is earning, pricing will not be second-best optimal. Vogelsang and Finsinger (1979) showed that an incentive regulatory mechanism

Figure 1

' .. b ..... ~ ....

c ............ :.:..... Profit> 0

Profit = 0

PRICING & INVESTMENT INCENTIVES UNDER PRICE CElllNGS 227

could result in second-best optimal prices. Our result is that the most commonly discussed implementation of price ceiling regulation, weights fixed at initial quantity shares, will not lead to second-best optimal pricing.

This is illustrated in figure 1. The point of tangency between the isoprofit curve labeled Profit = 0 and the isowelfare curve, point a, is the second-best optimal set of prices. Price ceiling regulation will, in general, lead to some level of profits different from zero, such as the level of profits implied by the isoprofit curve labeled Profit> O. In general, given that different level of profits, the firm under price ceiling regulation will not choose a point tangent to an isowelfare curve but will instead choose some other point, such as point b or point c.

4. Investment Incentives

Let us now turn to the first-order conditions to examine investment behavior. (3) rewritten is:

T ac r= -L a 'to

't=t Yt

(10)

This condition says that the firm will invest in cost reduction until the marginal cost of doing so, r, is equal to the marginal benefit of additional reduced costs. This is another way of saying that price ceiling regulation leads to the minimization of total costs, even in the long run.

Since it is rate-of-return regulation that price ceiling regulation has been proposed to replace, a comparison of investment behavior under price ceiling regulation with rate-of-return regulation would be useful to assist in choosing between these alternatives. But both rate-of-return regulation as traditionally practiced, and price ceiling regulation as proposed defy easy (and extensive) comparisons because of their complexity.

Our analysis does allow the following comparison, however. Assume that rateof-return regulation ensures zero profits and that the regulated price is exogenous to the fmn being regulated. This last assumption conforms with the way that traditional regulation has been viewed by some.s Assume further that the price ceiling is set at the price from rate-of-return regulation. This becomes a point of comparison between the two regimes.

A statement that is widely held and that is frequently articulated about rate-ofreturn regulation is that there is room for cost-reducing investment under this form of regulation. 6 Another way of saying this is that the rate-of-return regulated fmn is minimizing short-run costs but not long-run costs and that the firm has too little capital. If this is the case, then a change to price ceiling regulation with the ceiling set at the price that was effective under rate-of-return regulation will lead to cost-reducing improvements in investment behavior. This is directly implied by (10). The price ceiling regulated fmn will thus see fit to invest more than it did under rate-of-return regulation as we have characterized that form of regulation.


Another interesting result comes from noting that (10) is independent of the firm's ability to pay for additional investment. Since the firm has a common carrier obligation, it must supply all demand that comes forward in response to the prices it sets. (10) says that because it must supply to all comers regardless of its level of profits, the firm's incentive for cost minimization is the same regardless of the profit level. This is in direct contrast to rate-of-retum regulation where incentives for cost minimization, as they exist, are strongest when the firm is earning less than its allowed rate.

S. One-Product, One-Period Case

The one-product, one-period case sheds further light as to how price ceiling regulation affects pricing and investment incentives. The first-order conditions for the case where cr > 0 simplify to:

oL ox oC ox op =rap+x- ox op -cr=O, forp>O, (11)

oL oC oy = - oy - r = 0, for y > 0, (12)

oL ocr = Ko - p = O.

(13)

The pricing condition becomes:

P (1 -~ )= ~~ + cr (~; r. (14)

This condition is illustrated graphically in figure 2. Under a binding price ceiling constraint, marginal revenue (R,) becomes:

lp ifp=p

R'= ( 1) P I-£" ifp<p

where p is the price ceiling. R' is graphed with a heavy line in figure 2. Marginal cost, the first right-hand term in (14), is graphed as C'. The price ceiling has the effect of shifting marginal revenue counter-clockwise as compared to an unconstrained monopolist. Without the price ceiling, the firm would choose Pm and produce xm. While the price ceiling forces the firm to lower price, it faces a higher marginal revenue for the additional output it must produce to meet the greater demand at the lower price.


Figure 2

Me

Demand

Comparative static analysis can also be done with this simple formulation. This analysis yields the following results:

oy* oKa <0 (15)

oy* or <0 (16)

op* = 1 oKa (17)

~=o or (18)

ocr* > --0 (19) OK <

ocr* ->0 (20) or


The signs of (16) and (20) are as expected. (17) and (18) are trivially true when cr> O. (IS) fits with the interpretation of (3) offered above, that the cost minimization incentive exists regardless of the profit level. As Ko is set lower by the regulator, demand increases and the firm will have an incentive to invest to lower the costs of the greater production. (19)'s indeterminate sign means that the marginal value to the firm of relaxing the constraint could either increase or decrease, depending on specific demand and cost conditions.

6. Incentives for Marketing Activity

Understanding that price ceiling regulation rotates the marginal revenue curve of the finn also sheds light on the incentive of the price ceiling regulated firm to undertake activities that will increase the demand for its services, such as advertising and other marketing.7

Suppose that the firm originally faces demand Do. After some marketing activity it faces demand Dl. The incentive faced by a firm to carry out this particular marketing activity would be its additional profits. In this section we will compare the incentive of the price ceiling regulated firm with that of the unconstrained monopolist.S By comparing the incentives in this way, we will be able to see how the imposition of price ceiling regulation could change marketing activity.

The conditions under which the price ceiling regulated firm would have a greater incentive than the unconstrained firm to undertake marketing activity are developed in the following analysis. First, a well-known property of unconstrained monopoly pricing is used. That property is:

pm_ C' 1

pm E (21)

(21) can be used to show a relationship between the prices the unconstrained firm would choose on the two demand curves Do and DI and the price elasticities at those prices.9

Po = p'f iff El = EO'

(22)

(23)

Let us examine first (22), the case where marketing efforts shift the demand curve in a way that causes the unconstrained monopolist to raise price. It is straightforward to see that the unconstrained monopolist has a greater incentive to undertake this particular sort of marketing than the price ceiling regulated finn.

Assume thatp is setatp'{f. At the new demand, the monopolist is free to keep price

atp'{f = pbut finds that his profits are greater atp'{' > p. Therefore, his incentive to

PRICING & INVESTMENT INCENTIVES UNDER PRICE CEll..INGS

Figure 3

pm.Ii .. ~ ____ ~~ _ 0 p=pm 1

MR 1

231

Me

D 1

undertake this marketing is greater than the price ceiling regulated fInn that cannot raise price.

Next we will examine (23), the case where marketing efforts shift the demand curve in a way that the unconstrained monopolist chooses to lower price. The price ceiling regulated fInn is also free to lower price, which complicates the comparison.

If it is assumed that p is set at pW as we did in the frrst case above, they both face

the same incentive. However, if it is assumed that p < pW, then we have an interesting comparison. For the sake of the comparison, assume that p happens to

be the price the monopolist would choose facing D1, that is, PT == p. This is illustrated in fIgure 3. By lowering price, the monopolist gives up

pW - P revenues for each of his XC customers. This is the shaded area in fIgure 3.

However, the monopolist gainsxT - XC customers at his new price pT( = p). Since

the price ceiling regulated frrm also gains.xT - x new customers, the unconstrained

monopolist only gains Xo - XC new customers beyond what the price ceiling regUlated frrm will gain. Thus, the new revenues shown by the cross-hatched area in fIgure 3 should be compared with the lost revenues shown by the shaded area.


Only if the cross-hatched area is greater than the shaded area will the unconstrained monopolist have a greater incentive to undertake this type of marketing activity. Otherwise, the price ceiling regulated firm would have a greater incentive.

This can be represented by the following statement. Only if the following statement is true will the unconstrained monopolist have a greater incentive:

(Po - P> Xo > (p - C') <Xo - x'Q).

By using (21) and the assumption thatp = pi, (24) can be restated as:

I I pXo ->---. eo e'{' Pox'Q

(24)

(25)

But (23) says that lo > pi implies llei < l/elf. (25) can only be consistent with (23) if total revenue of the price ceiling regulated firm from Do is less than the total revenue of the unconstrained monopolist. Since the unconstrained monopolist will only operate in the region of elastic demand, (25) can be contradicted if the price ceiling forces the firm to operate in the region of inelastic demand, which was shown to be possible earlier. Thus, as the price ceiling becomes more binding, the price ceiling regulated firm can have a greater incentive than the unconstrained monopolist to undertake marketing activities.

This result has interesting implications for public policy. Policymakers have expressed interest in protecting the interests of certain classes of customers. That interest can be furthered through price ceiling regulation. Policymakers'interests presumably are not furthered by marketing efforts that increase the regulated firm's desire to raise price. However, marketing efforts that would decrease the firm's desire to raise price should be encouraged, which is what this form of regulation does. This form of regulation would encourage telephone companies to develop and promote their services to those customers whose demand is relatively inelastic, such as those customers who make limited use of the telephone services because of price considerations.

7. Price Ceiling Regulation with Allowed Competition

The preceding sections implicitly assumed that price ceiling regulation was accompanied by entry restrictions. This may not be a realistic assumption, however, and it is instructive to examine the effects of a competitive fringe on the marginal investment conditions derived thus far. This section attempts to do this by assuming that the dominant, price ceiling regulated firm will attract entry if it sets prices too high. lO Competition has the effect of making the demand curve faced by the regulated firm more elastic, further lowering the price seen by customers.


7.1 Stand-Alone Costs, Entry, and Price Ceilings The concept of stand-alone cost (SAC) bears importantly on the idea of price

ceiling regulation. If price ceilings are based on SAC, then they are no higher than the prices a competitive market would have produced. If prices yield revenues that somehow violate SAC levels, entry is profitable for a firm supplying at least a subset of the incumbent firm's products. This has definite implications for pricing and investment under price ceilings. I I

If regulatory price ceilings allow revenues significantly above SAC levels, entry will occur and the ceiling constraint will not be binding because prices will instead be constrained by competition. If regulatory price ceilings are well below the levels dictated by SAC, then the ceiling constraint may be binding (if profit maximization can occur at the binding constraint), and entry will not occur. Thus, within the confines of an admittedly static analysis, we can conclude that allowed competition may make price ceilings unnecessary as a regulatory tool, leading to the same level of investment that would have resulted under price ceilings with entry barriers. This, of course, depends on the nature of competition and the level of the ceiling. Because the classic "dominant firm, competitive fringe" model can lead to prices bounded by the competitive and monopoly outcomes, we could expect free entry to police the upper levels on prices under some conditions, but not in the general case.

7.2 Anticompetitive Pricing Behavior In the recent literature on price ceiling regulation, it has been suggested that the

regulated ftrm has the incentive to practice predatory pricing. For example, Vogelsang's analysis of price ceilings states:

[AJlthough predation is unlikely to occur under a price cap approach, it cannot be fully ruled out. Using average rates for capped services overall, the regulated carrier might lower its rates in competitive areas below the efficient level and charge fully profit-maximizing rates in monopoly areas with the average complying with the caps. After successfully driving out its competitors, it would reduce the previous monopoly rates and increase the previous predatory rates, again leaving the average within the capped range. (Vogelsang, 1988,24-25)

Similarly, the Federal Communications Commission (FCC) is concerned with the prospect of predation under price ceiling regulation. When adopting price ceiling regulation for AT&T, the FCC imposed a 5 percent band for services subject to the ceiling, meaning that such services could not be lowered any more than 5 percent annually. 12

Because a price ceiling in and of itself makes it difficult and risky to recoup short run losses later, the largely anecdotal concern about predation under price ceilings seems groundless. This model of pricing and investment under price ceilings provides a strong qualitative argument against the feasibility of predatory pricing.

Assume that the firm subject to price ceilings chooses to engage in a classical "long purse" predation campaign. If it faces a competitive fringe, then it will


choose to set some of its prices below marginal operating costs to drive out this fringe. Once this fringe has exited the market, the firm will raise prices to levels that allow it to recoup its short run losses due to the predation campaign, plus extract monopoly profits from the market.

This strategy involves a risky economic scenario. First, the firm must price at levels below marginal operating costs, which stimulates demand and requires an expansion of capacity (due to an implied common carrier obligation), but provides no contribution to overhead. Second, the firm must somehow raise prices above competitive levels after all other fIrms have exited the industry. This is difficult for several reasons. The firm still faces the price ceiling constraint, which could be binding in the firm's attempt to enjoy monopoly profits. In addition, the firm has excess capacity in the post-predation period, since it overinvested to meet the demand generated by prices that were less than marginal operating cost. Thus, in the post-predation period, not only does the fum face the price ceiling, it must recover all of its capital investment (including the excess capacity that the predation strategy required). Yet, at the higher post-predation prices, the firm wi11lose customers that would purchase goods only at the low predatory prices.

In this way, it is clear just how counterproductive a predatory pricing strategy would be under price ceilings. In the predation period, excess capacity must be incurred due to demand stimulation, yet operating costs are not covered and no contribution to overhead is made. Sales are made to customers who will only purchase at the predatory price, but not a higher one. Such customers necessitate an expansion of capacity.

Once the competitive fringe has exited the market, the fum raises prices as high as possible, but finds itself constrained by the price ceilings. This constraint by itself may preclude the successful completion of the predation strategy. In addition, recall that the firm must recover all of its capital expenditures during a period of excess capacity. This combined with the price ceilings themselves makes the collection of monopoly profits quite unlikely. Under price ceiling regulation, predation leads most likely to an underrecovery of invested capital, not monopoly profits.

Similarly, this model indicates that cross-subsidization between products subject to the aggregate indexed price ceiling at a given time period is unreasonable. An examination of (6) shows that, for profit maximization, the regulated firm is not likely to set prices below marginal operating cost, which is necessary for cross-subsidization and is the cost benchmark for predatory pricing used in many of the antitrust courts.13 A necessary condition for the firm to choose Pit < aCt/aXit is that crt > 0, that is, that the price ceiling constraint be binding.14

Thus, the only conditions under which this firm would fail the Areeda-Turner test are those thrust on it by regulation. In this situation, cross-subsidization would be made necessary by exit barriers. Predatory intent would be absent under these circumstances.


8. Policy Implications

The results of this analysis have some immediate implications for issues now being addressed by the FCC and some state public utility commissions.

Marketing Activity. Policymakers' interest in protecting the interests of certain classes of customers can be furthered through price ceiling regulation. Price ceiling regulation does encourage marketing efforts that would decrease the firm's desire to raise price. This form of regulation would encourage telephone companies to develop and promote their "Information Age" services to those customers whose demand is relatively inelastic, such as those customers who make limited use of the telephone services because of price considerations.

Price Ceiling Regulation and Investment. Price ceiling regulation offers a solution to the frequently articulated concern that current rate-of-return regulation induces firms to use too little capital. The imposition of price ceiling regulation gives the firm a clear incentive to cost minimize and to invest up to the point where the marginal benefit from doing so is equal to the marginal cost of doing that.

Cross-Subsidization and Predatory Pricing. This analysis suggests that the firm subject to price ceilings does not have an incentive to set prices below marginal operating costs. In other words, in choosing the mix of prices for the basket of services subject to price ceilings, no service will be priced at less than its marginal cost. There is no rational incentive to cross-subsidize under price ceiling regulation. To set prices of any service, even one with a high price elasticity, at levels below marginal cost would only serve to reduce overall profits allowed under the price ceiling. Thus, prices set below costs are not likely under price ceilings.15

However unlikely, prices below marginal cost will only be chosen by the firm if the price ceiling is set at unreasonably low levels (due, for instance, to a low allowed growth index coupled with market exit restrictions). This is of major policy interest because the combination of low price ceilings and barriers to exit are the reasons such pricing would be necessary. A regulated frrm laboring under a poorly chosen price ceiling would first choose to delete services from its product line. If it is prohibited from doing this, its only recourse is to price some services below cost. In this case, prices are not predatory, since there is no predatory intent and the prices set below cost are not part of an orchestrated strategy to injure competitors in illegal ways. While prices produced by a poorly administered price ceiling may not pass the simple Areeda-Turner test used by many antitrust courts in detecting predatory behavior, the full set of legal criteria for predation would be passed because the reason for such low prices would be inefficient regulation, not an orchestrated predatory strategy designed to injure other frrms.

Notes

The views expressed in this article are the opinions of the authors and do not necessarily represent the opinions of Southwestern Bell Telephone Company. The authors gratefully acknowledge the assistance of Michael Einhorn, Roger Klein, Dale Lehman, David Sappington, and David Sibley in the preparation of this article. An earlier version was presented at the Rutgers University Advanced


Workshop in Regulation and Public Utility Economics, Western Conference, Monterey, California, July 7,1988.

1. In the Matter of Policy and Rules Concerning Rates for Dominant Carriers, CC Docket No. 87-313,Notice of Proposed Rulemaking, 2 FCC Red. 5208 (1987), and Report and Order and Second Further Notice of Proposed Rulemaking, 4 FCC Red 2873 (1989).

2. One notable exception is the recent paper by Cabral and Riordan (1989). 3. (6) is obtained easily. First, (2) is rewritten as:

act ~axit tJ-l@XitJ-l Pit = :;::- + CJtOli ~ - Xit -:;- . UAoit <1Pit <1Pit Applying the de mition of Ei to east term and rewriting yields (6). 4. For example, see Baumol and Bradford (1970). 5. For example, Joskow (1974) found long periods where prices were unchanged by regulators.

This was also the assumption employed by Bawa and Sibley (1980) who modeled rate-of-return regulation with the firm taking price as exogenous for considerable periods of time.

6. Sappington (1980) showed that a firm subject to the Vogelsang and Finsinger (1979) regulatory mechanism may have incentives to engage in pure waste. In many ways this is similar to the rate-ofreturn regulation that we are modeling here, although we do not require the existence of pure waste for our result.

7. We are endebted to Michael Einhorn for helpful discussions regarding the line of analysis in this section.

8. We will accomplish this by comparing additional revenues for the two types of firms, with the assumption that marginal costs are constant over the relevant range of output. Also, in both the unconstrained and price ceiling regulated cases, these additional profits are gained only by incurring additional marketing cost. It is assumed that the marketing cost is the same for both cases.

9. This is seen by subtracting (21) applied to Dl from (21) applied to Do and simplifying. 10. See Brock (1983,194-195). 11. The theoretical conditions for these ceilings entail the computation of SAC for all possible

combinations of services, since only this will ensure that profits do not exceed efficient levels. Thus, if a regulated firm produces, say, three services, Xl, X2, and X3, the relevant SAC test requires the following conditions to be met (where R refers to revenues from the services shown in parentheses):

1. R(Xl) ~ SAC(Xl), R(xz) ~ SAC(X2), R(x3) ~ SAC(X3) 2. R(Xl, X2) ~ SAC(Xl, xz), R(Xl, Xl) ~ SAC(Xl, Xl), R(x2, X3) ~ SAC(X2. X3) 3. R(Xl, X2,X3) S; SAC(Xl, X2,X3). Since "cost" includes the cost of capital, this last inequality in the list ensures that the firm earns no

profits above competitive levels, which means that a SAC-derived ceiling on prices, in theory, will prevent monopoly pricing.

12. In the Matter of Policy and Rules Concerning Rates for Dominant Carriers, CC Docket No. 87-313, Report and Order and Second Further Notice of Proposed Rulemaking, 4 FCC Rcd. 2873 (1989), at para. 52.

13. This is the Areeda-Tumer test, which holds that prices below short-run marginal cost are predatory. Areeda and Turner (1975) suggested using average variable cost in practice to surmount difficulties in measuring marginal cost.

14. This is because for price to be less than marginal cost to be optimal requires also that marginal revenue be less than marginal cost, which can only be the case if CJt > o.

15. Our model has not addressed the case in which price ceilings are applied both to "core" services (for which the regulated firm has market power) and "competitive" services (for which the regulated firm is a price taker) and in the form of an aggregate price cap. This scenario is discussed in Braeutigam and Panzar (1988).

References

Areeda, Phillip, and Donald Turner. 1975. "Predatory Pricing and Related Practices Under Section 2 of the Sherman Act." Harvard Law Review 88: 697-733.


Baumol, William J. 1971. "Optimal Depreciation Policy: Pricing the Products of Durable Assets." Bell Journal of Economics and ManagemenJ Science 2 (Autumn): 638-656.

Baumol, William J. 1986. Modified Regulation of Telecommunications and the Public InJerest Standard. Manuscript filed as comments to the National Telecommunications and Information Administration, Docket 61091-6191.

Baumol, William J., and David F. Bradford. 1970. "Optimal Departures From Marginal Cost Pricing." American Economic Review 60 (June): 265-283.

Baumol, William J., John C. Panzar, and Robert D. Willig. 1982. ConJestable Markets and the Theory of Industry Structure. New York: Harcourt Brace Jovanovich.

Baumol, William J., and Robert D. Willig. 1986. "Contestability: Developments Since the Book." Oxford Economic Papers 38: 30-32.

Bawa, Vijay S., and David S. Sibley. 1980. "Dynamic Behavior of a Firm Subject to Stochastic Regulatory Review." InJernational Economic Review 21 (October): 627-642.

Bradley, Ian, and Catherine Price. 1988. "The Economic Regulation of Private Industries by Price Constraints." Journal of Industrial Economics 37 (September): 99-106.

Braeutigam, Ronald R., and John C. Panzar. 1988. "Diversification Incentives Under 'Price-Based' and 'Cost-Based' Regulation." Paper presented at the Sixteenth Annual Telecommunications Policy Conference, Airlie House, Airlie, Virginia.

Brennan, Timothy J. 1989. "Regulating by Capping Prices." Journal of Regulatory Economics 1: 133-147.

Brock, William A. 1983. "Pricing, Predation, and Entry Barriers in Regulated Industries." In Breaking Up Bell: Essays on Industrial Organization and Regulation, edited by David S. Evans. New York: North-Holland, pp. 191- 229.

Cabral, Luis M.B., and Michael H. Riordan. 1989. "Incentives for Cost Reduction Under Price Cap Regulation." Journal of Regulatory Economics 1 (June): 93-102.

Johnson, Leland L. 1989. Price Caps in Telecommunications Regulatory Reform. Santa Monica, CA: The RAND Corporation, N-2894-MF/RC.

Joskow, Paul L. 1974. "Inflation and Environmental Concern: Structural Change in the Process of Public Utility Price Regulation. " Journal of Law and Economics 17 (October): 291-327.

Lipman, Barton L. 1985. "Dynamic Behavior of a Firm Subject to Stochastic Regulatory Review: A Comment." InJernational Economic Review 26 (June): 511-516.

Littlechild, Stephen C. 1986. Economic Regulation of Privatised Water Authorities. Report submitted to the U.K. Department of the Environment. HMSO.

Sappington, David. 1980. "Strategic Firm Behavior Under a Dynamic Regulatory Adjustment Process." Bell Journal of Economics 11 (Spring): 360-372.

Sibley, David S. 1985. "Response to Lipman and Further Results." InJernational Economic Review 26 (June): 517-520.

Varian, Hal R. 1978. Microeconomic Analysis. New York: W.W. Norton. Vogelsang, Ingo. 1988. Price Cap Regulation ofTelecommunications S ervices:ALong-Run

Approach. Santa Monica, CA: The RAND Corporation, N-2704-MF. Vogelsang, Ingo, and J6rg Finsinger. 1979. "A Regulatory Adjustment Process for Optimal

Pricing by Multiproduct Monopoly Firms." Bell Journal of Economics 10 (Spring): 157-171.

access channelll access charge 7, 81-2, 85-6, 110, 193,203-4,

207-8 administrative costs of regulation (see also pan-

caking) 1,3-5,8,39,129-31,219 advertising (see also marketing) 109,230-2,235 airlines 10 Alabama 7 Alberta Govemment Telephone 98, 103-5, 117,

125(n) allocative pricing efficiency 1-3,6,9-11, 15-6,

23-55,27,29,33,41,61,70,93,192,204, 216

American Telephone and Telegraph (see also Bell System) 1,3,5,7, 10,78,81-4,86,88, 94,97-9,103-4,109-13,116-7,120,124(n), 152(n), 167, 169,171, 175-6,233

divestiture 166,171-2, 174 Ameritech 87 Areeda-Turner test (see also net revenue test)

234-5,236(n) Arrow effect 158, 161, 164 asymmetricinforrnation (see also cost uncertain

ty, imperfect information) 3, 16,48-52,55-8, 67,69,71, 73(n), 130-1, 134, 136, 150-1, 162,218

Averch-Johnson effect (see also "gold-plating") 3,150,170

automatic stabilizer 89 axiomatic cost allocation 216

bandwidths 5,7 bankruptcy 130, 149 bargaining (see also negotiation) 150 Basic Service Index 172 baskets 1,7,221 Bayesian-Nash equilibrium (see also sequential

equilibrium, subgame perfect equilibrium) 54-5

Bell Atlantic 87 Bell Canada 85-6, 88, 98, 103-5, 115-6, 122 Bell Communications Research 7, 10, 87,95,

124(n),208 Bell operating company (see also Bell System)

87,89,168 Bell South 87 Bell System (see also American Telephone and

Telegraph, Bell operating company) 84, 171, 177

Subject Index

bidding 48, 57, 61 billing accuracy 176 billing and collections 6 blocking (see call completion) British Columbia Telephone 98-9,103-5 British Telecommunications (see also Great

Britain, Office of Telecommunications) 4, 7, 54,57,61,97,101,1239,177

Bureau of Labor Statistics 78, 83, 85, 88,106-7, 124(n)

business customers 10, 172,174,179,182, 184, 204

bypass (see also dedicated access, private line) 2-3, 11, 189, 194, 207-220

cable 46 call completion 172, 175-78 capacity sizing 2,11,62-6, 115,125(n), 221-38 capital recovery (see also revenue requirements)

51-2,61,66,70-1, 73(n), 130, 138-40 cellular systems 46 Centrex 6 coaxial cable 172 coin telephone service (see public telephone ser-

vice) Colorado 6 common carrier obligation 228, 234 common costs 2-3, 52 common line charge 203 competitive services I, 3-4, 6-7, 11, 38, 41,

43-4(n), 47, 97,172,233-4, 236(n) congestion delay (see also dial tone delay) 170

Connecticut 7 connection charges 4 consumer price index (see also gross national

product price index, inflation, producer price index) 85,109-11,217

continuing surveillance 7 cost-based regulation (see also fully distributed

costs, Part 69, rate-of-retum, rate base, separations process) I, 8, 33, 46, 161-2, 164(n),207

cost minimization 1-3,8,10,21,23,29,34,41, 77,82,93,98,100,114,118,127-154,150-60,167,200,217,221-38

cost uncertainty (see also assymetric information, imperfect information) 159-61

cross-subsidization (see also subsidies) 34, 41, 184,218,234-5


customer access line charge (see access charge) customer complaints 172-4, 177, 180 customer premises equipment 4, 11 0, 170, 177

dedicated access (see also bypass, private line) 204

DenmaIk 177 depreciation 6,134,222-3 deregulation (see alsodetariffing) 1,6,10-1,18,

39,49,66,123,131,168,172,183 detariffing (see also deregulation) I, 8, 110 Deutsche Bundespost 117 dial tone delay (see also congestion delay) 172,

176-77,179,182 Direction Generale des Telecommunications

117 directory assistance (see also operator assis

tance) 62,176-7,180 divestiture (see American Telephone and

Telegraph) Divisia index 80, 83 double dual productivity (see also dual produc

tivity) 111-113 dominant firm 162, 164(n), 233 dual productivity (see also double dual produc

tivity,laborproductivity, totalfactorproductivity) 10, 102, 109-12

dynamic adjustment 17-8, 43(n), 48

economies of density 115,119, 125(n) economies of scale 114-6, 122-3, 124(n), 170,

175 economies of scope 115,122,125(n),170 efficiency (see allocative price efficiency, cost

minimization, productivity, technical change)

electricity 48 embedded cost ratemaking (see fully distributed

costs, rate base, rate of return) emergency boost 119 end-user billing 191-2,204-5,208 equipment irregularities 174-5

fairness 3, 11,50,52,61-2,64,67,70, 73(n), 207,210-4,216-7

Federal Communications Commission 1,3,5,7, 10-1, 60,77·92,93, 102, 105, 111-12, 124(n), 172-3, 191-2, 200,205,207-8,216-8,221,233

Federal Trade Commission 5 fiber optic 169-70 financial hardship 119-20 Florida 173-5 franchise hidding 151 fully distributed costs (see also cost-based

regulation, Part 69, revenue requirements,

separations process) 1-3,11,191-2,208,216 gaming 9 General Accounting Office 208 "gold-plating" (see also Averch-Iohnson) 3, 8,

99, 170, 184-6, 188(n) Great Britain (see also British Telecommunica

tions, Office of Telecommunications) 176, 209,217

gross national product price index (see also consumer price index, inflation, producer price index) 85-7, 90(n), 96-7,lll-12,121, 217

hedonic pricing 181

Idaho 6 Illinois Bell 170 imperfect information (see also assymetric in

formation, cost uncertainty) 2, 4, 9, 196, 200-1

incentive compatible 73-4(n), 94, 96, 100-2, lOS, 114, 123, 124(n), 152, 195-7,200-1

incoming matching loss 172, 176 incremental cost (see also marginal cost; stand

alone cost)3,191, 216 indirect productivity (see dual productivity) inflation 1,4-5,7,41,50,82,89,93-5,99-100,

109-13,121, 125(n), 128-30, 132,167, 184, 207,217

inflation adjustment clauses 129 Information Age 235 information rent (see also assymetric informa

tion, moral hazard, strategic misrepresentation) 55-9, 63-4, 69, 72-3(n)

innovation (see productivity, incentive to in-novate)

inside wire 6, II 0 installation lag 180 INTELLIPATH 6 interexchange carrier (see also long-distance

service) 102, 118, 124(n),199, 204-5 international calls 4, 108 interstate service (see long-distance service) intrastate service (see long-distance service) Iowa 6

jacks 6 just and reasonable 40

labor productivity (see also dual productivity, total factor productivity) 10, 106

Laspeyre price index 19, 44(n), 80-1 line rental 4-6 local companies I, 6, 11,47-8,81-2,84,86,89,

90(n), 95, 104, 118, 124(n), 155, 167, 172, 178,179,183-4,191-3,204-5,207-8

local exchange carrier (see local companies)

INDEX

local loop 203 local service 3-4. 6. 83-6.109-10.181

measured local service 6 long-distance service (see also interexchange

carrier) 3-5. 43(n). 81. 85-6. 109. 118. 155. 177.197.204

interLATA 197.2lO interstate 1.7.83-6.109-11. 206(n) intrastate 5-6. 49. 83-4.109-11 measured toll service (MTS) 198-9. 206(n) wide area toll service (W A TS) 109. 199. 205. 206(n)

loss and distortion (see also signal noise) 172. 176

managerial incentives (see cost minimization. productivity)

managerial theory of the firm 124 marginal cost (see also incremental cost) 2. 9.

15. 17.20-1.25.29.39. 43(n). 52-3. 55-8. 6O.62.65.67-8.73-4(n).151.157.159193. 199.204.207-8.211-3.216.218.221.224

marketing (see also advertising) 12. 2lO. 225-7. 233

MCITelecommunications Corp. 169. 176 measured local service (see local service) measured toll service (see long distance) Metromedia Long Distance. Inc. 176 Michigan Bell, Public Service Commission 5.

152(n) Microtel. Inc. 176 microwave 172 Modified Final Judgment 206(n) monitoring 52. 66-9. 72-3(n) monopoly services 6. 8 Montana 6 moral hazard (see also information rent.

strategic misrepresentation) 2. 17.28. 119. 123.127.130.152

moratorium (see rate moratorium) multiline customers 216 multiproduct monopoly 2. 20. 28. 136. 149.151

Nash equilibrium 54-5 National Regulatory Research Institute 168 Nebraska 6 negotiation (see also bargaining) lO. 62 net revenue test (see also Areeda-Tumertest) 11.

83.216-8 network 169-70. 178.203 New England Telephone 199. 205(n) New York Telephone. Public Service Commis

sion 6. 54. 61. 66. 167- 8. 172. 173-5. 177. 183-4. 187(n). 191. 198. 205(n)

911 calls 181 976 caI1s 6

241

nontraffic sensitive (NTS) costs 147.203.207-8 non-Bayesian incentive mechanism 16-32 nonuniform pricing (see also two-part tariff) 2.

191-206.207-220 NYNEX 87.191-3.199-200. 205(n)

Office of Telecommunications (see also British Te1ecommunications.GreatBritain) 4.176-7

off-peak rates 7 operator response 174.177. 180 operator services (see also directory assistance)

4.176.184 opportunism (see regulator commitment.

politics of regulation) optional tariff menu 191-206. 207-20 "original cost" 50 other common carrier (OCC) 111 overcapitalization (see "gold-plating") overflows 172

Pacific Telesis 87 pancaking (see also administrative costs of

regulation) 4. 129-30 "paper engineering" 216 Pareto-dominance 194-5.197. 206(n). 2lO Part 69 (see also fully distributed costs. separa

tions process) 11. 191-2. 205 Pennsylvania 49 politics of regulation (see also rent-seeking) 48-

50. 66.70. 72(n). 130. 133 predatory pricing 7. 218-9. 233-5 price discrimination 15. 28. 205 price index (see also consumer price index. gross

national product price index. producer price index) 1.4-5.7.9.33-45

principal-agent 16.127. 129. 130-4. 149 private line (see also bypass. dedicated access)

4.7 producer price index (see also consumer price

index. gross national product price index. price index) lO8-9. 124(n)

productivity. incentive to innovate (see also technical change) 1-5. 8-9. 41. 44(n). 79. 82. 93. 95. 105. lO9-13. 115-8. 123. 127-54. 155-66. 233-4 measuring the rate of increase 4-5. 7. 57.

77-92.95-126 public telephone service 4. 168. 176-7.180.182.

184.188(n) Public Utility Regulatory Policies Act (pURPA) 206(n)

quality (see service quality)

radio 6 railroads 48


Ramsey pricing (see also second-best pricing) 8, 9,15-17,20,34,36-7,41, 43(n), 151

rate base (see also rate of retum) 1-3, 6-8, 95, 149-51

rate moratorium 8, 167, 184 rate of return (see also rate base) 1-8, 16,50-1,

55,77,82,88-90,99, 124(n), 127,131,149-51,151,161,167,170,178,186-7,191,221, 227,235

rate shock 7 regional Bell operating company (see Bell

operating company) regulator commitment 2, 9, 41, 47-75 regulatory lag 9,29,33,41, 44(n), 47, 66, 128,

161, 164(n), 208, 217 optimal 33

remote call forwarding 6 rent-seeking (see also politics of regulation) 3, 8 ~&rsennces 168,180,184 repeated game (see also sequential game) 127,

132-3 resale 205, 217-8 residential customers 7, 172, 175, 179, 181-2,

184 ret&! price index 96 revealed preference 23, 26, 181 revelation principle 54 revenue requirements (see also fully distributed

costs, capital recovery) 66, 88, 208 risk aversion 16,69, 133

scale economies 10 second-best pricing (see also Ramsey pricing) 2,

9,25,29, 30(n),34,63,73(n),222, 226 separations process (see also fully distributed

costs, Part 69) 3, 6-7, 85, 95 sequential equilibrium (see also Bayesian-Nash

equilibrium, subgame perfect equilibrium) 55

sequential games (see also ~eated game) 128, 130,149-50

sennce availability 176 sennce order completion 172, 176 sennce quality 2,6, 10-1, 149, 162, 167-90 signal noise (see also loss and distortion) 172,

176 sliding scale 89, 91(n) Smith v. Ames 50 social contract 1-8, 11 Southern Bell 177 Southern Net Services, Inc. 176 South Tel, Inc. 176 Southwestern Bell 11, 87 stand-alone cost (see also incremental cost) 216,

233-4,236(n)

strategic misrepresentation (see also assymetric infonnation, infonnation rent, moral hazard) 1-3,8-9,33-4,37-8,41, 44(n), 48,53-5,58, 70-1,123,130,151,207,217-8

stored program control 6 subgameperfectequilibrium (see also Bayesian

Nash equilibrium, sequential equilibrium) 55

subscriberline charge (see access charge) subscriber plant factor 6 subsidies (see also cross-subsidization) 3-4, 16 sunk costs 60, 70-1 superelasticity 43(n) supergarne (see repeated game) Supreme Court 40, 50 switched access 199,204, 206(n), 208, 218-9 switches 168,203,207

techuical change (see also productivity) 41,52, 105, 115-7, 118-9, 122-3, 124(n), 128, 134, 217

Telecommunications Sennce Corp. 175-6 Telus Communications, Inc. 176 toll sennce (see long-distance sennce) Tornquist index 81, 83 total factor productivity (see also dual produc

tivity,laborproductivity) 79,81,83-5,95, 98-100,102-7,111-14,135

TOUCHTONE6 traffic-sensitive (TS) costs 203 Transcall American, Inc. 176 transfer pricing 34 transition functions 53, 58, 69 translog production function 80 transmission 168, 176 trunk 203 two-part tariffs (see also nonunifonn pricing)

8-9,11,15,16- 32, 43(n), 53, 57, 191-206, 207-220 optional calling plans 6, 11 tariff menu 9, 11,54,62,216

United States Transmission Systems, Inc. 176 United Telephone Long Distance 176 "used and useful" 51 U. S. Sprint 169, 175-6 U. S. West 87

value added services 4, 177 Vogelsang-Finsinger mechanism 17, 20, 151,

222,226,236(n)

Western Union Telegraph Compo 176 Wisconsin 7

American Productivity Center 78, 83,101 American Telephone and Telegraph 78, 84, 88 Anderson, J. 206(n) Arrow, K. 158 Atkinson, S. 3 Averch, H. 150

Bailey, E. 3 Baron, D. 3, 9,16,49,55,57,60-2,66, 71-3(n),

151 Baumol, W. 2-3, 128, 152(n), 161, 216, 220,

236(n) Bawa, V. 151, 236(n) Bell Communications Research 88, 95, 208 Berg, S. 169, 179, 182, 185 Besanko, D. 49, 57, 60-2, 66, 71-3(n), 169 Bhattacharyya,S.4 Billera, L. 216 Block, E. 170 Brennan, T. 9,41, 44(n), 217 Breslaw 116 Brock, W. A. 43(n), 236(n) Brown, S. J. 206(n) Bureau of Labor Statistics 78, 83, 85, 88, 108-9,

124(n) Bussing, 1. 91(n) Buzas, T. 169,179,182,185

Cabral, L 10, 43(n), 164(n) Caillaud, B. 71 (n) Caves, D. 9O(n) Chamberlin, E. 169 Christensen, L 78, 83, 85-6, 88, 90(n), 91(n),

117,120 Coase,R. 15 Corbo 116 Courville, L 3, 86 Cowing, T. 82, 9O(n) Cross, P. 208

Dasgupta, P. 9 de Fontenay, A. 86 Demsetz, H. 151 Demski, J. 71 (n) Denison, E. 9O(n) Denny, M. SO, 85-6, 116 Diewert, W. 80 Dingall, J. 208 Dobell, R. 86

Authors Index

Donnenfeld, S. 169 Dorfman, R. 169 Dvorak, C. 169

Egan, B. 7,10,217 Einhom,M.2,ll,210-2,215-6 Evans, D. 116,211

Face,H.5 Faulhaber, G. R. 7, 206(n), 209 Federal Communications Commission 44(n),

81,89, 90(n),l11,124(n),191, 205(n), 208 Finsinger,J. 8,17,20,23, 30(n), 151,222,226,

237(n) Fitzpatrick, M. 44(n) Freedman, D. 152(n) Fuss, M. 82, 85, 116

Goldman, M. 2, 209-10 Gollop, F. 9O(n) Griffin, J. 3 Gryb,R.l68 Guesnerie, R. 71-2(n)

Halvorsen, R. 3 Hammond, P. 9 Haring,J.7 Harris,M.9 Heath, D. 216 Heckman, J. 116 Hehnan,L49 Heyman, D. 206(n), 218 Hotelling, H. 15 Houthakker, H. 128 Hudson, R. L 177

Jackson, C. 208 Johnson, L 3, 150 Joskow, P. 30(n), 48, 71(n), 236(n) Jubelirer, R. 49

Kahn, A. 71(n) Kendrick, J. 79, 84, 9O(n) Kihlstrom, R. 169, 185, 188(n) Kiss, F. 10,85, 90(n), 115-8, 122, 125(n) Klevorick, A. 150-2, 161 Koehn,M. 3 Kohn,S.216 Kraushaar, J. 173


Kwerel, E. 7 Kwoka, J. 10, 91 (n), 170

Laffont, J. 60, 70, 72(n) Lain,D.5 Lande, I. 9O(n), 109-11,217 Larson, A. 11-2 Laughhwm, D. 4 Lawton,R.I68 Lazorchak, J. 206(n) Lefebvre, B. 116-8, 125(n) Leland, H. 2, 209-210 Levhari, D. 169, 185 Levine, H. 170 Levitz,K.7 Linhart,P.7,10,131,152(n) littiechild,S.4,217 Loeb,M.151-2 Loehman, E. 216 Louviere, J. 179 Lynch,J. 169, 179,182, 185

Magat, W. 151-2 Mankiw, N. 44(n) Markey, E. 208 Maskin,E.9 Mathios, A. 5 Meek,R.4 Megdal,S.5 Milgrom, P. 164(n) Mirman, L. 2, 209 Monson, C. 11-2 Myerson, R. 3,9, 16,55, 72(n), 151

Nadiri, M. 84, 116 National Regulatory Research Institute 168 National Telecommunications Information Ad-

ministration 1,3-5,7, 124(n), 217 Newstead, T. 180 New York Public Service Commission 174-6 Ng,Y.2,9 Noam,E.11 Noll, R. 3, 48,218

Office of Telecommunications 4-5, 176-7 Owen,B.218

Panzar,J.169,206(n),209 Patrick, D. 7 Pazner, E. 216 Peles, Y. 169

Radner, R. 7, 10, 130--3, 152(n) Rey,P.71(n) Richters, I. 168 Riordan, M. 1O,43(n)

Roberts, M. 9O(n) Rogers,R.5 Rohlfs, J. 208 Rosse, I. 169

Sappington, D. 30(0), 71-2(0),81,151-2, 236(n) Schankerman,M.84,116 Schmalensee, R. 2,9,30(0),48, 71(n), 91(0),

169 Schmeidler, D. 216 Schmidt,M. 71(n) Schurnpeter, J. 128 Schwartz, M. 44(0) Sheshinski, E. 169 Sibley, D. 2, 11, 30(n), 151, 206(n), 209-210,

218,236(n) Sinden, F. 10, 152(n) Small,J.82 Smith 116 Spann,R.3 Spence, A.M. 2,169,178,185, 188(n), 209-210

Spiller, P. 71 (0) Steiner, P. 193 Stevenson, R. 82, 9O(n) Stigler, G. 133 Stiglitz, J. 44(n),71(n) Swan,P.169

Takehashi, K. 170 Taylor, W. 7,10--1,217-8 Tirole, I. 60, 70,71-2(0),206(0) Townsend, R. 9 Trethway, M. 9O(n)

Varian, H. 44(0),216 Vickers, J. 4, 54 Vogelsang, I. 8, 17, 20, 22, 29, 30(n), 43(0), 94,

124(n), 151,222,226,233, 236(n)

Waverman,L.82,85,116 Weisser, M. 2, 9 Wellisz, S. 3 Weoders, J. 3 Wemer,M.86 Whinston, A. 44(0), 216 White, L. 103,217 Wicksell, K. 169 Williamson, 0.128 Willig, R. 3, 44(n), 210 Wynns,P.90(n),109,217

Yarrow, G. 4, 54

Zajac, E. 3

Price Caps and Incentive Regulation in Telecommunications

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