Efficient Allocation of Radio Spectrum

EFFICIENT ALLOCATION OF RADIO SPECTRUM

BENOIT PIERRE FREYENSUniversity of Canberra

CHRIS JONESAustralian National University

AbstractLegislative reforms in Anglo-American countries requiregovernments to account for efficient spectrum usage subjectto interference control. New spectrum governance regimespromote flexible and competitive usage but the broadcast-ing industry remains exempt from reforms, at a significantcost to society. The need to liberalize broadcast spectrumcannot be overstated, but how should we select among alter-native deregulatory regimes? In a simple stylized model weformalize the welfare effects of allocating licenses for usingbandwidth on broadcast spectrum. We provide optimalityconditions for entry, spectrum usage, and congestion levelsunder different market conditions, which allows us to justifythe selection of specific governance arrangements.

1. Introduction

The efficient usage of high-value very high frequency (VHF) and ultrahigh frequency (UHF) broadcast spectrum is one of the most contentious

Benoıt Pierre Freyens, Faculty of Business, Government and Law, University of Canberra,ACT-2601, Australia ([email protected]). Chris Jones, Research School ofEconomics, The Australian National University, Canberra ACT-0200, Australia.The paper benefited from discussions with (or helpful comments from) Geoffrey Bren-nan, Gerald Faulhaber, Martin Peitz, Martin Richardson, and participants at the 4th In-ternational Telecommunications Society (ITS) AAA conference and at the 1st conferenceof the Network for Economics Research on Electronic Communications (NEREC). Theinspiration for this paper proceeds from a longstanding collaboration between one of theauthors and the Australian Communications and Media Authority, and we are grateful toMark Loney and Michael Poole for numerous conversations about the role and meaningof efficiency in spectrum allocation policy. However, the views and interpretations pre-sented here are the authors’ own and should not be assumed to represent those of ACMAor of the persons mentioned above. We also thank the editor, an associate editor, and twoanonymous referees for comments that improved the paper.

Received August 23, 2010; Accepted October 12, 2011.

C© 2013 Wiley Periodicals, Inc.Journal of Public Economic Theory, 16 (1), 2014, pp. 1–23.

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2 Journal of Public Economic Theory

contemporary issues in radiocommunications policy. Everywhere, govern-ments allocate radio spectrum to broadcasting services by regulatory fiat,and regulatory agencies subsequently manage the frequency bands and as-sociated equipment standards with considerable discretion. Typically, thiscommand and control allocation model, at times referred to as “equity al-location,”1 rewards the politically savvy within the regulated industry and en-courages spectrum hoarding well beyond what is economically desirable. Fordecades, hundreds of MHz of prime “beachfront” radio spectrum have beenentrusted in this fashion to an industry which needs (and indeed uses) farless. In practice, this restrictive allocation model guarantees minimal inter-ference to broadcasters by imposing large buffer zones (white spaces) be-tween contiguous bands, effectively trading the number of users (and alter-native services) for small technical gains in incumbents’ quality of service.

In his most recent critique of the broadcasting allocation regimeThomas Hazlett reiterates this point by emphasizing that “trade-offs be-tween the cost of ‘harmful interference’ in one application and thebenefits of additional activities in another should be perceived as eco-nomic values, not engineering parameters” (Hazlett 2008a). A logicalconsequence of intolerance for interference and use of discretionary li-censing is that competitive entry by other broadcasters has been ar-bitrarily blocked for decades. Generations of economists have stressedthe economic cost of using a control and command approach to al-locate VHF and UHF radio spectrum—especially in view of the in-creasing economic value of the bands (Coase 1959, 1966, Levin 1966,Minasian 1975, Levin 1980, McLauchlan and Westerberg 1982, Hazlett 1990,Faulhaber 2006, Hazlett 2008a). In spite of these controversies, equity al-location of broadcast spectrum has proved remarkably resilient over time.Yet the coming of age of digital TV and digital radio technologies offersclear opportunities to break with the past and experiment with more flex-ible and market-responsive spectrum management methods. The matterthat still needs to be resolved is determining the appropriate governanceregimes and the criteria that will guide their selection. There are differ-ent views about the economic benefits of adopting specific governance ar-rangements due to the range of choices being made, including entry levels,equipment standards, and the extent of property rights conferred with band-width allocations. The ITU (2007), Pogorel (2007), The CEPT (2009), andFreyens (2009) provide a comprehensive account of the policy choices underconsideration.

At the heart of this debate lies the matter of interference manage-ment, which is often misunderstood in the wider public. In a high-demandspectrum environment, such as the broadcasting bands, all transmissions inadjacent bands ineluctably cause some degree of interference. Where do

1 See McLauchlan and Westerberg (1982) and Hazlett (2008a).

Efficient Allocation of Radio Spectrum 3

we draw the line between harmless and harmful interference? For radio-communications services other than broadcasting, harmful interference isrelatively easy to define in terms of threshold levels for signal-to-noise ratios.However, it is particularly difficult to establish interference thresholds forbroadcasting technology. Broadcast stations transmit over a wide coveragearea, the boundary of which is a blurred buffer zone characterized by verysensitive signal reception (Peha 2009). Thus, allowing any third-party trans-missions in or near broadcasting channels will always disturb signal receptionin boundary locations. Trading off broadcasters’ coverage area for additionalinterferences is therefore much more an economic question than a techni-cal one and research that optimizes these trade-offs has an important roleto play in debates over the efficient allocation of broadcast spectrum. Theremaining question is to determine which governance regime best managesthese trade-offs in the public interest.

Whereas most economists recommend reforming the control and com-mand regime through some variant of the Coasian property rights ap-proach, which gives licensees varying degrees of discretion over spectrumuse, others ask “what about applying the commons approach to some ofthe TV-spectrum?” (Bohlin, Weber, and Preissl 2006). Governance arrange-ments such as property rights and open access have received consider-able attention in spectrum policy research, but the existing literature onlyoccasionally makes forays into providing analytically tractable solutions tothe complex trade-offs raised by these alternative spectrum managementregimes. The policy debate would benefit from further advances in thisarea, particularly with a view of developing optimality criteria for spectrumgovernance.

This paper is an attempt to provide responses to these questions. Op-timal governance rules for transmitting free-to-air programs are examinedin a broadcasting economy under different market structures. We first dis-cuss recent reforms to spectrum management in Section 2 and review thehitherto limited use of applied welfare economics in this area of researchin Section 3, stressing implications for current spectrum governance. A styl-ized model of a broadcasting economy is presented in Section 4 and it isused in Section 5 to analyze efficient provision of free-to-air broadcast ser-vices first when these services are provided competitively, and then whenbroadcasters have some degree of market power. The analysis focuses on de-termining optimal levels of entry and interference in broadcasting bands.In Section 6 we stress the implications of our analysis for the selectionof spectrum governance regimes, ranging from open access with no ac-cess restrictions, to property rights allocations that restrict access and grantbroadcasters discretion over the number of licenses and levels of tolerableinterference. To capture welfare effects of distortions in related marketswe consider entry in the presence of a distorting wage tax in Section 7Finally, the paper concludes with a summary of our main findings inSection 8.


2. Deregulation and New Governance Regimes

Although broadcast spectrum remains highly regulated, other segments ofthe radio spectrum have, since the early to mid 1990s, seen much liberaliza-tion in a few Anglo-American and Central American countries. Bold piecesof telecommunications legislation paved the way for liberal reforms, target-ing either a regime of property rights resting on auction pricing and serviceneutrality (owners decide the appropriate use for the spectrum), or openaccess through unlicensed and collaborative approaches (unrestricted en-try conditional on operating standardized equipment and adhering to “therules of the road”).

These different pathways to reform have generated a heated “either or”deregulatory debate. The ideologically confronting nature of the two mainalternatives to command and control, together with pressures to release spec-trum from legacy users (such as broadcasters or military users) have po-larized the radiocommunications community. Economists foresee a classic“tragedy of the commons” lurking under open access management (i.e., aworld with significant and sustained interference), while also stressing thedisruptive nature of replacing total control with total freedom. In this view,property rights appropriately preserve the exclusive nature of legacy regimeswhile also addressing matters of excess demand through service neutrality,and market pricing.

Supporters of the open access approach, many of them engineers andlegal scholars, decry the immaturity of spectrum markets. In their view, aproperty rights approach merely perpetuates the exclusive nature of oldcommand and control arrangements, this time with reduced governmentoversight and likely market dysfunctions. From that perspective the problemto be solved is spectrum access, not spectrum pricing. Government windfallsfrom spectrum auctions have blurred this distinction and the latter has tooeasily been adopted as a surrogate for the former.

Finally, unwavering supporters of the control and command approach,among whom we mostly find public and commercial free-to-air broadcast-ing services, generally recognize a moderate need to experiment with moreliberal regimes in other spectrum-intensive industries, for instance to helpmeet the growing bandwidth needs of mobile telecommunications carriersto deploy new technologies. However, they strongly dispute the reasons forintroducing either competition or open spectrum access into services withpublic good characteristics. This argument has often been invoked to ex-empt free-to-air broadcasting from spectrum governance reforms. In this pa-per we explain why this position is potentially misleading, and how it hasconsistently undermined social welfare in the industry.

How well did these governance reforms in other spectrum-using indus-tries perform? The evidence is mixed. Property rights operate successfully insome areas (e.g., mobile telephony) but less so in others (e.g., rural broad-band services). Similarly, open access is a worldwide success on 2.4 Ghz bands


(Wi-Fi) and a complete failure on 5.2 GHz bands (U-NII). Different ap-proaches to deregulation have merits and weaknesses of their own, which aredifficult to disentangle from contextual and sector-specific analysis. More-over, radiocommunications law can be difficult to interpret or may set con-flictive goals for regulators to follow in practice. The main purpose of ourpaper is therefore to establish an elementary set of socioeconomic criteriato guide the decisions of a social planner. Because the analysis is positive,rather than normative, we assume along with numerous legislative acts thatthe ultimate goal of spectrum policy is to maximize the overall net benefitsto society from spectrum use. Welfare economics has seldom been used toinform spectrum governance, and we review below the few studies that havepreceded us in this endeavor.

3. Welfare Economics and Spectrum Governance

Research into the welfare effects of regulating or deregulating broadcastingis not new, but it is confined to analyzing different questions than those con-sidered in this paper. For instance, there is an aging economic literature onthe potentially undesirable welfare effects of introducing competition whenprogram diversity is a public good and broadcasters’ income is derived fromadvertising (e.g., Steiner 1952, Spence and Owen 1977). The central argu-ment here is that the intensity of consumers’ benefits from programs diver-sity will not be captured in an advertising-based funding scheme that caresfirst and foremost about audience size. These trade-offs between quality andprofitability have been illustrated by comparing the industrial structures offree-to-air TV, largely oligopolistic and supported by advertising only, and ca-ble television, being competitive and funded by subscription fees (e.g., Web-bink 1973, Spence and Owen 1977). Furthermore, the welfare effects of freeentry may also be affected by the fixed costs of setting up a broadcastingnetwork (Mankiw and Whinston 1986). When there is market demand fordiversity, an additional entrant adds to social welfare (by increasing diver-sity) but fixed costs may prevent these gains from being captured throughprofits, resulting in too few entrants.

The view that emerges is that free entry will only create social efficien-cies if the value of programs to consumers is high enough with respect tothe value of marginal listeners to advertisers, or put another way, if marketprices provide incentives to produce programs when the benefits (but notthe revenues) exceed the costs of providing these programs. More recently,Berry and Waldfogel (1999) provide an empirical estimate of the welfare(consumption) benefits necessary to justify free entry in radio broadcasting(i.e., the benefits required to offset welfare (revenue) losses to incumbentstations and advertisers). Anderson and Coate (2005) discuss the welfare ef-fects of regulation and free entry when advertising is both a good (informingconsumers) and a bad (a nuisance to consumers). Cunningham and Alexan-der (2004) model advertising as a good and analyze optimal responses of


broadcasters to changes in the number of firms in the industry, which de-pend partly on switching-off responses of consumers to induced changes inthe share of broadcast time allocated to advertising. They find direct and in-direct utility losses from higher industry concentration due to reduced pro-gramming choice and reduced utility from higher advertising prices. How-ever, none of these studies give due consideration to the role of spectrumas the critical resource supporting the broadcasting industry, except to stresscapacity constraints (e.g., Spence and Owen 1977).

Few studies actually attempt to evaluate the relative merits of differentspectrum governance regimes using standard cost-benefit techniques withan explicit welfare role for signal interferences, which would be expected toincrease with free entry. One that does so is a study undertaken by a researchteam at the Quello Center for Telecommunications Management and Lawto compare the welfare effects of adopting two radically opposed spectrumgovernance regimes for wireless communication: the “open commons”2 andproperty rights regimes (Ting, Wildman, and Bauer 2005). They develop ananalytical model for comparing the welfare effects of different access rightsand levels of interference. Their model specifies linear demand functionsfor the market and (each representative) firm which accommodates in-bandand off-band signal interference. Firms can adopt more robust technologiesto reduce the effects of this interference on their consumers, but at a cost.

This set-up provides four spectrum management regimes, with the levelof entry and robustness of equipment as key dimensions. Welfare effects ofentry under open commons and property rights are compared when, foreach of these two regimes, equipment standards are determined by indi-vidual providers themselves and through government regulation. Based ontheir demand specifications they find that under property rights with re-stricted entry the government cannot improve on robustness choices madeby profit-maximizing firms. When chosen optimally the marginal cost of im-proved equipment standards is matched by an equal rise in price (due to theincrease in demand with lower interference) without any spillover costs andbenefits on other firms. That makes privately determined robustness prefer-able under restricted entry when regulators are less than fully informed pub-lic officials. Privately determined equipment standards were also found to besocially desirable under open commons in this setting because the highercosts and inefficient increases in firm outputs due to marginal reductionsin interference levels dominate the welfare gains from lower entry levels.

2 Note that their notion of “open commons” would generally be interpreted as open ac-cess. The “commons” approach differs from an open access regime in that the communityof users is well-defined (closer to a club than to a free-entry society) and usage is basedon collaboration rather than mere coexistence (Ostrom 1990). Wi-Fi is an example ofopen access (free entry and device coexistence), while ambulatory devices used for specialevents such as concerts are an example of commons (limited entry and required coordi-nation) because equipment standards are not sufficient to prevent interference.


With government determination, base case simulations yield potential socialwelfare gains of 10% under a property right regime as compared to the com-mons regime, but the former requires much more information on demand,interference, and cost parameters than the latter. Getting the parameterswrong consistently yields lower simulated social welfare outcomes for theproperty right regime. Wildman, Bauer, and Ting (2006) confirm the resultsin an expanded version of the original model.

More recently, Hazlett compares command and control with propertyright assignments for 24 countries (Hazlett 2008b). Regressing average auc-tioned license price against governance regime (defined as the extent bywhich property rights have been defined) and other explanatory variables,Hazlett finds that licenses endowed with more generous property rights gen-erate lower auction proceeds than more prescriptive licenses. As the resultappears counterintuitive (more rights should be expected to command ahigher willingness to pay), he offers the conjecture that the extra rights con-ferred to licensees are more than offset by reductions in monopoly rentsand externalities among competitors (who also benefit from additional us-age rights). Hence, property rights eliminate some of the deadweight lossarising from more regulated approaches. In a subsequent paper, Hazlett andMunoz (2009) contrast the positive welfare effects of auctioning licenses (theefficiencies gained from transparent allocation and from not having to raisedistorting taxes) against negative welfare effects arising from (1) uncompet-itive resulting market structure, and (2) compromises between bandwidthallocation and auction revenue targets (e.g., by setting high reserve prices).They report evidence of welfare losses from withholding bandwidth due torevenue targets when expanded bandwidth allocation is correlated with com-petitive market structure. Hence, maximizing revenue objectives may over-ride legitimate concerns about noncompetitive behavior and entry restric-tions in cellular markets. As will be apparent, our analysis differs mainly byfocusing on finding the optimal number of licences to sell in the first place,and by taking into account the marginal congestion costs and indirect wel-fare effects (IWEs) of entry. While our model examines free-to-air broadcast-ing (rather than mobile telephony) and spectrum governance (rather thanspectrum assignment methods), it also provides a framework for dividingspectrum between different types of users and how to manage the alloca-tions within those user groups.

4. A Broadcasting Economy Model

Welfare effects from new entry into free-to-air broadcasting will be measuredby extending a simple model used extensively in the public economics lit-erature to solve the optimal supply of pure public goods—for examples,see Ballard and Fullerton (1992) and Snow and Warren (1996). It is a tax-distorted economy where a large number of identical price-taking consumersare aggregated into a single consumer who purchases a private good X from


after-tax wage income and profits from private production, and gets benefitsfrom leisure H and free-to-air radio services, which are a pure public goodG .3 Each consumer can access this public good without reducing the ben-efits to others, but unlike the standard public good model, which assumessole provision by the government, free-to-air broadcasters in the broadcast-ing model are private operators.4 To cover their operating costs they selladvertising time A to producers of private good X who purchase it to lowertheir trading costs. Advertising does this by informing consumers about thelocation, quality, and availability of good X .5 But the size of the reduction intrading costs is smaller at entry levels where congestion leads to interferenceand loss of quality of broadcasting service.

By providing a complete description of the economy, including the con-straints on private and public sector spending, we can isolate all the netchanges in private surplus from issuing new licences. The wage tax distor-tion to the labor–leisure choice is included to accommodate indirect welfareeffects identified by Diamond and Mirrlees (1971) and Stiglitz and Dasgupta(1971). When a policy change causes resources to flow through distortedmarkets there are additional welfare effects that can affect the optimal pro-vision of the public good. Goulder and Williams (2003) argue these indi-rect welfare effects can frequently be more important than the direct welfarechanges.6 We initially evaluate new entry into free-to-air broadcasting withthe wage tax set at zero to focus on the direct welfare changes. Later theanalysis is extended by including a positive wage tax to account for changesin the excess burden of taxation when new entry affects the labor–leisurechoices of consumers. Atkinson and Stern (1974) refer to this as the spend-ing effect, which alters the optimal supply of public goods.

3 We simplify the analysis by having identical consumers because it removes any distri-butional effects. While there is no doubt they will have an impact on policy choices, weexclude them here to focus on efficiency effects and to simplify the analysis.4 A useful extension would include a public broadcaster in the analysis. It would be fundedfrom government revenue but would presumably face different incentives to private op-erators. In particular, it would likely be a less efficient provider of the service but wouldattempt to broadcast in unprofitable areas for social (or political) reasons. These issues areavoided here to focus on private activity and to identify the externality when congestionoccurs.5 Thus, advertising provides valuable information that reduces trading costs in our broad-casting model. But advertising might also play a persuasive role by affecting consumer pref-erences. For example, firms may use it to create brand loyalty in their customers, wherethat can lead to greater market concentration and higher consumer prices. To avoid theresulting inefficiency, particularly when we model broadcasting as a competitive market,we focus solely on the information role advertising plays.6 These indirect welfare effects arise in economies with distorted markets. The distortionscan result from taxes, subsidies, price controls, quantity controls, and noncompetitive be-havior. Policy changes, like allowing new entrants into free-to-air broadcasting, will havedirect welfare effects on consumers through the benefits and costs from the services pro-vided. But there are additional welfare effects when resources are reallocated in distortedmarkets.


G

nn

G(n)

F < F fn = 0 F = F fn < 0n

dG/dn = 0

dG/dn < 0dG/dn

> 0

Congestion

Figure 1: The effects of broadcasting entry.

Before formalizing the social planner’s problem in the broadcastingeconomy, we examine the way the supply of the public good is affected bynew entrants. Following Hazlett and Munoz (2009) good G is the aggre-gate supply of services provided by n private broadcasters who are each allo-cated bandwidth f on the fixed part of the spectrum F assigned to free-to-airbroadcasting.7 While consumers cannot listen to more than one station theycan switch between them. The total supply of G is determined by the num-ber of broadcasters n and their bandwidth allocations, with n · f = F ≤ F .There are two competing effects of entry—(1) an expansion in the numberof stations/channels which increases productive efficiency of the allocatedspectrum (when there is no congestion), and (2) distortions to the transmis-sions of adjacent stations/channels (a negative externality when the bandis congested). We capture this by writing the supply function for good G asG(n) = G(n, f (n)), where dG/dn = Gn + G f fn ≶ 0; Gn > 0 is the expansioneffect and G f fn ≤ 0 the congestion effect. The relationship between entryand the supply of broadcasting is illustrated in Figure 1.8

7 We follow Ting et al. (2005) by adopting symmetric bandwidth allocations. When con-sumers get different benefits from different broadcast services it may be socially desirableto assign different bandwidth allocations to users.8 The supply of the public good G measures the total equivalent congestion-free broadcasttime made available to consumers. While they cannot listen to simultaneous broadcaststhey do value the opportunity to switch between stations. We capture the additional ben-efits from the extra broadcast time as the summed marginal consumption benefits fromgood G in the following analysis. When new broadcasters enter they utilize their band-width allocation f by operating 24 hours each day. Once entry rises above n congestionreduces the broadcasting service supplied, and that is why the supply function in Figure 1declines beyond n. We could define the supply of good G as the total supply of broadcast


When n is at or below a threshold level n, the bandwidth allocationfor each operator is f , which is the smallest it can be without causing in-terference between neighboring broadcasters on the spectrum (with n · f =F ≤ F ). That is, the service provided by each operator has no adverse im-pact on the quality of services provided by neighboring operators—there isno congestion (with fn = 0).9 In this region additional entry increases thesupply of the public good G by expanding the number of congestion-freeservices consumers can access (with dG/dn = Gn > 0). Once the numberof operators exceeds n the entire spectrum is allocated (with F = F ) andbandwidth for each operator contracts below the critical level f < f wherecongestion occurs at an increasing rate, with fn < 0 and fnn < 0. Initially,the expansion effect dominates (with Gn > 0) until entry reaches n wherethe congestion effect exactly offsets the expansion effect (with dG/dn =Gn + G f fn = 0). Once entry exceeds n the congestion effect dominates(with dG/dn < 0).

The social planner wants to know whether restricting entry is sociallydesirable. A popular view would use licences to eliminate congestion alto-gether. But that is unlikely to be a social optimum at low levels of conges-tion, particularly when transmissions occur at night, or more generally whenthe expansion effect from new entry dominates the congestion effect. Asdiscussed above, the social optimum will crucially depend on the trade-offsinvolved, where some are determined by technical considerations that relateto broadcasting technology, and others on consumer preferences.10

time made available to consumers and include the effects of congestion in their valuationsfor the services provided. Either way we argue the net social benefit schedule rises to apeak and then eventually falls to zero due to congestion. Figure 1 provides a convenientway to identify the effects of congestion from new entry on broadcast services provided.9 An important issue not addressed in the model is how much bandwidth to initially assignto operators, and how to spread these allocations along the radio spectrum, when it iscostly to change bandwidth allocations over time. If the initial bandwidth allocations areset at f to avoid congestion it may result in some or all of the existing operators beingmoved to new frequencies on the spectrum when new licences are issued later in timewhen demand for broadcasting services rises. But it is costly to inform listeners aboutchanges in radio frequencies, and the uncertainty may adversely affect advertising rev-enue. Thus, the socially optimal initial bandwidth allocations will need to anticipate ex-pected changes in demand and the costs of relocating them on the spectrum. That maywell lead to initial allocations being smaller than f , even though the number of operatorsat that time is less than n.10 The model can be used to either describe a hypothetically liberalized broadcast TV in-dustry, or to describe existing compromises between expansion and congestion effects inFM radio broadcasting, such as observed in Italy. Metropolitan areas in Italy use much nar-rower bandwidth (channel rasters of 50 kHz) than elsewhere in Europe (100 or 200 kHz).This allows cities such as Milan or Rome to enjoy much larger content diversity throughlarger numbers of FM broadcasters (100+ stations compared to a European average be-tween 20 and 80). These added marginal consumption benefits come with significant con-gestion effects (clear broadcast reception is limited to confined parts of urban areas) yetthe situation seems to suit all market players.


4.1. The Social Planner’s Problem

In the broadcasting economy the problem for the social planner can be sum-marized, as:

max{

u(X, H, G)∣∣∣∣ X ≤ (w − τ)(T − H ) + πX + πA + LL = τN

}, (1)

where u(X, H, G) is the utility function for the single (aggregated) con-sumer; H is the aggregate consumption of leisure; N = T − H is the aggre-gate supply of labor from time endowment T ; w − τ is the after-tax wageon employment; πX = [1 − θ(A, n)]Y (N ) − wN − αA is the aggregate profitfrom production of good X by private firms using strictly concave technol-ogy Y (N ), where 1 − θ(A, n) is the consumer price of the numeraire goodX net of marginal trading costs θ(A, n) that falls at a decreasing rate withadvertising time A, with θ ′

A < 0 and θ ′′A > 0, and rises at an increasing rate

with additional entry n when congestion occurs, with θ ′n > 0 and θ ′′

n > 0 forn > n. They employ labor at market wage w , and pay market price α foreach unit of advertising purchased; πA = αA − βA is the aggregate profitfrom radio broadcasting where αA is total revenue and βA total cost withβ being constant marginal cost;11 and, L = τN the government budget con-straint which returns wage tax revenue to the private sector as a lump-sumtransfer L.12

This is a complete description of the economy where scarcity is definedby the fixed time endowment T , which consumers allocate between leisure Hand private good X through their labor supply N . Any welfare changes fromnew entry are ultimately determined by its impact on consumption of X, H ,and G because they are the variables that enter the utility function. Initiallywe assume all the markets are competitive and later extend the analysis toaccommodate noncompetitive behavior.

4.2. A Conventional Welfare Equation

In a conventional Harberger (1971) analysis the government budget is bal-anced using lump-sum transfers to separate the welfare effects of each policyvariable.13 Following Jones (2005) we obtain a conventional welfare equa-tion by totally differentiating the utility function for the policy variables n

11 The role of fixed costs from supplying advertising is considered in Section 4.2 where aconventional welfare equation is derived.12 We could also include a licence fee which broadcasters would pay to the government forthe right to transmit. It would play no role in the single (aggregated) consumer economywhere the revenue is returned as a lump-sum transfer to the private sector. There arewelfare effects when the government makes these revenue transfers using the distortingwage tax.13 When these transfers are made with distorting taxes, changes in the government budgetare scaled by the marginal cost of funds to account for the excess burden of taxation. Foran example of how this adjustment is made, see Jones (2005).


and τ , and applying the private and public sector budget constraints in (1),together with the first-order conditions for optimally chosen consumption ofgood X and advertising A, where we have14

duλ

= MN Bdn + τdN + (α − β)dA, (2)

with MN B = ∑MRS dG

dn − θ ′nY being the net marginal social benefit from

new entry—it is the summed marginal consumption benefits from marginalincreases in the supply of the public good (with

∑MRS = (∂u/∂G)/λ) less

any increase in marginal trading costs (θ ′nY ) when congestion reduces the

effectiveness of advertising as a mechanism for providing information. λ isthe Lagrangean multiplier on the private budget constraint in (1), it is themarginal utility of income where 1/λ converts the change in utility into unitsof the numeraire good X .15 The second term in (2) isolates indirect welfareeffects when changes in the policy variables affect the excess burden of taxa-tion, and the third term the marginal profit from advertising when α > β.16

5. Optimal Entry in the Absence of Market Distortions

To isolate the direct welfare effects from new entry into free-to-air broadcast-ing we start by initially setting the wage tax to zero to eliminate the secondterm in (2).

14 This welfare equation is derived in the appendix.15 If broadcasters incur fixed costs (F C) the conventional welfare equation becomes

duλ

= MN Bdn − F Cdn + τdN + (α − β)dA,

where the marginal cost of new entry rises by F Cdn. When these fixed costs are fundedusing access fees, they have no impact on social welfare (in the absence of distributionaleffects). They are simply transfers of surplus between producers of private good X andbroadcasters. But if access fees are ruled out, and fixed costs are funded through averagecost pricing, then we must have (α − β)dA > 0 in a competitive equilibrium for firms tobreak even.16 The choice variables X, N , H , and A are all solved as reduced-form functions of theexogenous policy variables n and τ, time endowment T , preferences, and productiontechnologies. Throughout the analysis we hold T , preferences, and technologies constantwhere n and τ are the only variables to change. Thus, we solve all the endogenously deter-mined variables as functions of these policy variables. While consumers choose X, N , H ,and A by taking the relative wage w , market price α and income I as given, they are alsoendogenously determined by n and τ in a competitive equilibrium, where the reducedform demand function for private good X , is

X (n, τ) = X [w(n, τ), α(n, τ), I (n, τ)].

∑MRS is the summed marginal value of the good G measured in units of good X .


NB

nn

NB(n)n

A

A

max

nmax

MNB = 0

n*

NC

NC

MNB > 0

fn = 0 n = 0

MNB < 0

fn < 0 n > 0

Figure 2: Entry with competitive broadcasting.

5.1. Competitive Broadcasting

By using (2) with τ = 0, we find that optimal entry solves

dudn

1λ

= MN B + (a − β)∂A∂n

≥ 0. (3)

It can be satisfied for a number of regulatory regimes ranging from open ac-cess with no barriers to entry, and licence restrictions with varying degrees ofcongestion. The final outcome will depend on the relationship between thenet consumption benefits and profits from new entry. Clearly, these variablesare related because broadcaster profits depend on the benefits consumersget from listening to their service.

Before we can look at policies to restrict entry we need to identify theopen access solution where entry is unrestricted (without licence fees). Newbroadcasters enter until profits are driven to zero, with α = β and πA = 0,which is less than the maximum possible number of entrants (nmax ) whenthe population under the footprint of the broadcast signal is too small togenerate enough profit from advertising. Two profit functions are illustratedin Figure 2—the first is πN C

A where profit is eliminated at entry level nN C ≤n with no congestion (N C), and the second is πmax

A with profit eliminatedat nmax where congestion drives the supply of the public good to zero. Werefer to functions like πN C

A with entry below n as regional profit functionswhich are more likely in rural communities with dispersed populations, whilefunctions like πmax

A will be referred to as metropolitan profit functions whichare much more likely in cities and other densely populated areas.17

17 Our model implicitly assumes an essentially uniform distribution of licenses. Yet,in our hypothetically liberalized broadcasting industry it is reasonable to assume that


Ultimately the shapes of these functions will be determined by the de-mand for advertising, which depends not only on population size but alsoon the real incomes of consumers and their propensity to spend it on ad-vertised products and the degree of competition in broadcasting, as well asbroadcasting costs. The key feature of these functions under open access isthe entry level where profits are driven to zero. It is likely to occur at lowentry levels in rural areas where demand for advertising is less due to smallerpopulations.18

The welfare effects from unrestricted entry inform the choice of regu-latory regime, and they are determined by the shapes and locations of thenet benefit schedule (N B) and profit functions (πA) in Figure 2. There isno congestion under open access when entry is at or below n where broad-casters have bandwidth f , with fn = 0 and θ ′

n = 0. In this region new entryincreases the supply of the public good by dG/dn = Gn > 0 and generates anet welfare gain of MN B = ∑

MRS · Gn > 0. Once entry rises above n, how-ever, congestion occurs and it has two effects—it reduces the supply of thepublic good (with fn < 0) and increases marginal trading costs (with θ ′

n > 0).When entry reaches n∗ (< n), the social marginal benefit is driven to zero,with MN B = 0, while beyond n∗ entry under open access (with α = β) is

broadcasters could trade and concentrate licenses broadly in the way licenses are currentlybeing traded in cellular and broadband markets in a number of countries. To preventexcessive concentration in urban areas these markets are typically regulated with own-ership caps (“spectrum caps”). There are currently efforts, in the United States and Eu-rope, to loosen these caps to provide more technological flexibility to network operators—particularly for broadband. A referee asked us to sketch the urban/rural implications ofloosening caps in our model. The first point is that a model with caps on spectrum hold-ings means interpreting n as number of licences (that could be pooled up to a cappedpoint). Multiple licences acquired by one firm may then be used (1) as a buffer againstcongestion protection (idle use, no effects on advertising profits), or (2) for providing fur-ther program diversity (generating above-normal-advertising-profits and reducing tradingcosts in the private sector). Therefore, license concentration may or may not ease con-gestion, depending on the use made of the accumulated licences. In a rural setting, theacquired licenses will be productively used to provide program diversity. Removing thecap reduces potential entry but in practice there are few implications given low demandand low congestion in rural areas. In an urban setting, the use of some licences as a bufferagainst congestion may be profitable in the range where the marginal costs of congestionexceeds marginal profits. Licenses used as buffer reduce the quantity of programs sup-plied but also reduce congestion (i.e., improve reception quality of supplied programs). Ifthe net supply effect is positive, the supply curve rotates upwards in that range. Assuminglicense acquisition cost is low, removing the cap in this context expands the above-normalprofitability of the broadcaster, while expanding supply. If the licences are not used asbuffer, then removing caps simply lifts an upper bound on cartel size.18 We assume in the following diagrams and discussion that profits in rural areas are alwayslower at each entry level than they are in urban areas due to lower demand for advertising.But there may be circumstances where profits are higher in rural areas at low entry levelsdue to, for example, noncompetitive behavior and/or lower operating costs.


socially undesirable due to net welfare losses from congestion of MN B < 0.19

Thus, open access is socially desirable for regional profit functions like πN CA

where entry is at or below n, and for metropolitan profit functions whenprofits are eliminated over entry levels n < n ≤ n∗. In this region, entry gen-erates net consumption benefits. Restrictions on entry are socially desirablefor metropolitan profit functions like πmax

A where profits are eliminated atentry levels above n∗.

What is the optimal number of broadcasters when entry needs to berestricted? It is tempting to conclude that it should be n∗ where the netmarginal social benefits from entry are zero, but that is not the case. Oncethere are barriers to entry incumbent broadcasters make marginal profits(with α − β > 0) that can offset some of the marginal costs of congestion.Thus, when entry is at a social optimum (nS) it satisfies MN B + (α − β) ∂A

∂n =0, where some congestion is socially desirable, with MN B < 0 for n∗ < nS <

nmax.It is not straightforward for regulators to determine the optimal number

of broadcasters because they need estimates of the marginal congestion costsand profits which may be difficult to obtain. Getting them wrong can leadto entry restrictions where welfare may be even lower than it would be un-der open access. A preferable option may be to define property rights overinterference-free bandwidth f , and let owners trade some of their unusedbandwidth with new entrants when the price they receive offsets the con-gestion cost imposed on them. There is a tendency for regulators to adoptwhat is referred to as the scientist/engineering solution which would elim-inate congestion altogether and restrict entry to n. Clearly, this would betoo restrictive for entry levels under open access between n and n∗ due topositive net marginal consumption benefits, and for entry above n∗ whenmarginal profits offset the net congestion costs when entry is restrictedabove n∗. Privately negotiated solutions may provide a more efficient wayof restricting entry when broadcasters can use the legal system (rather thanlobby administrators) to enforce rights and obligations from new entrants(and obtain compensation for the cost of any nonnegotiated interferencecaused). The choice between regulated and privately negotiated entry willdepend on the transaction costs involved (from negotiating, contracting,quality of service concerns, due diligence, stamp duty, etc.). They are de-termined, in part, by the size of the information gap between regulatorsand property right owners. The lower the costs of negotiating property righttrades the greater the likelihood that property rights regimes will be sociallypreferred.

19 Entry level n∗ is where N MB = ∑MRS dG

dn− θ ′

nY = 0, and it is less than n where entryhas no impact on the supply of good G due to the impact of congestion on the marginaltrading costs, with

∑MRS dG

dn= 0 and MN B = −θ ′

nY < 0.


NB

nn

NB(n)n* =n

A

A

max

nmax

NC

MNCM

MNB = 0

nNC nmax

Figure 3: Entry under the club solution (M).

5.2. Noncompetitive Broadcasting

Having determined economic criteria for optimal governance under a com-petitive liberalization agenda, we now consider these criteria when broad-casting is noncompetitive under entry restrictions. Two possible outcomesare considered—one where broadcasters form a cartel, and the other wherethey choose outputs in a Cournot equilibrium.

(1) Club Solution:20 When broadcasters are given the right to determinethe number of operators in the industry they will maximize profit byrestricting entry until π ′

A = AM∂α∂A + αM − β = 0, where αM and AM

are, respectively, the monopoly price and supply of advertising. Un-der the club solution entry occurs where the profit function peaks,which means entry must be lower for any given profit function thanit would be in a competitive broadcasting market. Examples usingthe two functions examined earlier in Figure 2 are illustrated inFigure 3 where entry now occurs at nN C

M < nN C under function πN CA ,

and nmaxM < nmax under function πmax

A .

20 This situation could be viewed as a particular case of “the commons.” The anthropol-ogy literature mostly examines a specific type of commons—well-defined communitiesof users collaborating on the joint use of a common resource (e.g., open grazing lands,or irrigation systems). Although a broadcasting cartel would operate on business modelseconomically remote from these examples, it would still entail various characteristics of acommons. As in commons, the boundaries of the community/club are protected by sometier of government (through licenses), and in the club solution examined here, broad-casters maximize their interests by collaborating and jointly managing a shared resource,including the determination of access rights. Freyens (2009) identifies this governanceregime as a “privately run commons.”


The club solution is socially desirable if, by chance, net marginalcongestion costs exactly offset the marginal profits (αM − β) ∂A

∂n > 0,with MN B + (αM − β) ∂A

∂n = 0. For that to happen the profit func-tion needs to peak to the right of n∗ where MN B < 0. Wheneverprofit functions peak at or below n∗ any marginal congestion costsare too small to offset the marginal profits from entry, where entryis too low, while for profit functions that peak to the right of n∗ thecongestion costs eventually exceed the marginal profits from entry,where entry is too high.

(2) Cournot Solution: In reality broadcasters provide differential ser-vices to attract consumers with heterogenous preferences. Ratherthan extend the analysis to accommodate heterogenous consumerswe assume broadcasters provide identical services in a Cournot equi-librium when entry is restricted (say, by auctioned licenses), wherethe advertising output supplied by each operator is large enoughto affect market price α. When choosing advertising output A j eachbroadcaster j takes the output of all other operators as given to max-imize π

jA = α(

∑j A j ) · A j − βA j , where optimal advertising solves

∂πj

A∂A j = αC + AC

∂α∂A j − β = 0, with αC and AC = ∑

j A jC being, respec-

tively, the market price and aggregate output in the Cournot equilib-rium. This leads to more advertising output (AC > AM ) and a lowermarket price (αC < αM ) at each level of entry, where lower profitsmean less congestion when the Cournot solution is socially desir-able, with N MB + (aC − β) ∂A

∂n = 0.

6. Policy Responses

Let us now return to our original aim—that of providing analytically tractableeconomic criteria to guide the selection of optimal spectrum governanceregimes on VHF and UHF broadcasting channels. As described earlier, thepolicy debate is currently centered on three rather extreme governance op-tions; control and command, open access, and property rights. In the pre-ceding sections, we narrowed these alternatives down to a governance regimeconsisting of government-issued licenses (where one possible outcome is thescientific solution—a control and command regime with zero tolerance forinterference), another consisting of no license restrictions (open access),and a third in which the government determines the overall spectrum allo-cation F but lets industry players determine the optimal number of licensesand interference (a property rights regime).

Under the assumption of a competitive market structure for broadcast-ing (perhaps best characterizing FM radio) we showed how the optimal gov-ernance regime depends on the shape of the supply function for the pub-lic good, the effects of congestion on trading costs, and particularly on the


Table 1: Policies under competitive broadcasting

Profit Function Equilibrium Firms (nO A) Optimal Policy (nS) Congestion

Regional: 0 < nOA ≤ n Open access (nS = nOA) NoMetropolitan: n < nOA ≤ n∗ Open access (nS = nOA) Yes

n∗ < nOA ≤ nmax Restricted entry (nS < nOA) Yes

shape and location of the profit function. If broadcaster entry eliminatesprofits before n∗, where extra output of the public good generates no netconsumption benefits, open access is socially optimal. No licensing schemecan improve on this outcome. Intuitively, regional profit functions charac-terize areas where the advertising revenue is limited by sparse audiencesand few consumption outlets. However, once entry under open access elimi-nates profits beyond n∗, some form of access restriction regime is needed. Inthis situation, a property rights regime improves welfare by letting broadcast-ers trade and subdivide licences to the point where additional entry gener-ates marginal profits that offset any net congestion costs. This market-basedrationing mechanism would fit urban areas where profitable opportunitiesfor advertising are highest, as suggested by our correlated profit functionwhere unrestricted entry drives the supply of good G to zero. These policyresponses are summarized in Table 1 with entry nS being a social optimum.

The analysis also demonstrates that, from a purely welfarist perspective,the current command and control regime of zero tolerance for interference(n = n) never dominates other regimes and will almost always be subopti-mal. Only through pure serendipity would this approach be optimal (whennOA happens to be the number of players that drive profits to zero at n), buteven then open access achieves the same outcome with more flexibility. How-ever, for metropolitan profit functions, this solution is never optimal, and aproperty rights approach would be preferable.

The role of the profit function in isolating optimal welfare regimes is noless important under the assumption of imperfect broadcaster competition.We considered regional and metropolitan profit functions under cartel andCournot oligopoly arrangements where restrictions on entry allow broad-casters to make profits. Imperfect competition is never socially optimal forregional profit functions due to the presence of marginal profits. Hence,deregulating the industry (e.g., by using antitrust laws or decreasing levelsof protection) and introducing open access would improve social welfare inthese circumstances. But imperfect competition may be socially desirable formetropolitan profit functions if, by chance, entry generates net congestioncosts that exactly offset the marginal profits. In general, however, the out-come is inefficient (with entry too low or too high). We summarize thesefindings in Table 2 for the two types of profit functions, with entry underimperfect competition (I C) at nI C ; it can be the outcome under the club orCournot solutions. The location of the socially desirable entry level at nS willbe determined by the type of profit function the industry faces.


Table 2: Policies under imperfect competition

Profit Function Equilibrium Firms (nI C) Optimal Policy (nS) Congestion

Regional: 0 < nI C ≤ n Open access (nS > nI C ) NoMetropolitan: n < nI C ≤ n∗ Open access (nS > nI C ) Yes

n∗ < nI C ≤ nmax

⎧⎪⎨⎪⎩

Open access(nS = nIC )Open access(nS > nIC )Restricted entry(nS < nI C )

YesYesYes

The optimal governance regime is clear for regional profit functions un-der imperfect competition; the industry needs to be deregulated to allowopen access. In contrast, the policy response is less clear for metropolitanprofit functions. Deregulation is required for nS > nI C because the marginalprofits under imperfect competition exceed the marginal congestion costs,while the reverse applies when nS < nI C . The best governance regime wouldin this latter case be approximated by its capacity to bring the number of li-cences closest to the social optimum at nS . As under competitive conditions,the engineer/scientist solution (control and command, with n = n) is neverdesirable when further entry restrictions are required. However, unlike ouranalysis under perfectly competitive broadcasting, we do not find here that aproperty rights regime is necessarily a superior approach when traders havemarket power.

7. Indirect Welfare Effects

The role played by welfare changes in distorted markets will be illustratedhere using the welfare equation in (2) with τ > 0. Whenever new entry af-fects the labor–leisure choice there are additional welfare effects. If new en-try increases consumer demand for leisure, the corresponding fall in employ-ment exacerbates the welfare loss from the distorting wage tax. Conversely,if it reduces demand for leisure the rise in employment generates a welfaregain by reducing the excess burden of taxation. Typically, there are poten-tially large numbers of other market distortions, including subsidies, priceand quantity controls, noncompetitive behavior, and underprovision of pub-lic goods. The indirect welfare effects will depend on the nature of thesedistortions and how new entry impacts on the activities where they arise. Amore complete specification of the economy would be required to incorpo-rate them in the analysis. For the purpose of this paper the wage tax willprovide sufficient insight into the role played by indirect welfare effects andtheir impact on spectrum policy.

A positive indirect welfare effect (IWE), with τ ∂N∂n > 0, is illustrated in

Figure 4 where entry causes demand for leisure to fall. The resulting increasein labor supply at each real wage reduces the excess burden of taxation bythe cross-lined rectangle. As consumers reallocate time from labor to leisure


w

N

> 0nNS

N

ND

NS = T-H

w

w- > 0nN

Figure 4: A positive indirect welfare effect.

the reduction in employment has a marginal product greater than its oppor-tunity cost by the wage tax. A negative IWE of τ ∂N

∂n < 0 represents a welfareloss from an increase in the excess burden of taxation.

There are circumstances where endogenous changes in the excess bur-den of taxation affect the outcomes identified in the previous section. Apositive IWE can make entry above n∗ optimal under open access whenever∑

MRS · dGdn − θ ′

nY + τ ∂N∂n ≥ 0. Previously, that was never optimal due to wel-

fare losses from congestion, with∑

MRS · dGdn − θ ′

nY < 0 . But open accessmay not be optimal for entry below n∗ when the IWE is negative. Once it off-sets the summed marginal consumption benefits from good G , entry shouldbe restricted until

∑MRS · Gn + τ ∂N

∂n + (α − β) ∂A∂n = 0.

8. Conclusion

Using a simple stylized model of an economy with free to-air-broadcastingas a public good we have identified welfare criteria for optimal entry. Theanalysis provides a number of useful insights. First, consistent with ob-servations made in the literature about other common property resourceproblems, the open access solution is more suitable at lower levels of de-mand where congestion costs from new entry are small relative to thebenefits consumers derive from additional services. Second, over- or un-derutilization of the spectrum (in terms of interference thresholds) canbe socially optimal. It depends on the profitability of broadcasting andthe impact of new entry on distorted markets. Engineer/scientist solu-tions that impose zero interference on new entry are in general ineffi-cient, confirming Hazlett’s conjecture that trade-offs between congestionand productive use are essentially economic matters. Third, we find thatopen access may not be optimal when advertising profits and consumption


benefits from broadcasting are positively correlated because it can lead tothe “tragedy of the commons,” an outcome well known to spectrum policycommentators. As demand for broadcast services increase the higher adver-tising profits will eventually expand entry to the point where interferencecauses net welfare losses. The “tragedy of the commons” can be averted byoptimal licensing, but in keeping with Hazlett and Munoz (2009) we findthat licensing can also result in noncompetitive market structures, such ascartels, that impose significant costs on society (the “tragedy of theanticommons”). Fourth, indirect welfare effects can play an importantrole in determining optimal entry. It depends on the nature and sizeof distortions in markets affected by new entry. Finally, and consis-tent with an emerging literature that cautions against wholesale gov-ernance reforms, there are circumstances where entry restrictions canraise social welfare. Whether that should be through government reg-ulation or privately negotiated transfers of usage rights depends ontheir associated costs and the veracity of the information regulators canaccess.

Appendix

The conventional welfare equation is obtained by totally differentiating theutility function, where we have:

du = ∂u∂X

dX + ∂u∂H

dH + ∂u∂G

dG.

Using the first-order conditions for optimally chosen consumption of goodX and leisure H , respectively, with ∂u/∂X = λ and ∂u/∂H = λ(w − τ), anddefining the summed marginal consumption benefits from the public goodas

∑MRS = (∂u/∂G)/λ, the dollar change in utility solves:

duλ

= dX + (w − τ)dH +∑

MRS · dG.

By assuming nonsatiation the private budget constraint holds with equality,where after combining the private and public constraints we obtain the vir-tual budget constraint for the economy, of:

X = [1 − θ(A, n)]Y (N ) − βA.

After totally differentiating this constraint, we have:

dX = (1 − θ)YN dN − θ ′nY dn − (θ ′

AY + β)dA.

Optimally chosen private output of good X and private demand for ad-vertising A in competitive markets satisfies, respectively, (1 − θ)YN = wand −θ ′

AY = α, while there is marginal profit from advertising when entry


restrictions bind, with α − β > 0. By using these optimality conditions wecan write the change in consumption demand for good X , as:

dX = wdN − θ ′nY dn + (α − β)dA,

where after substitution the dollar change in utility solves as (2).

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