BECKER, Gary S., LANDES, William Gary Becker-Essays in the Economics of Crime and Punishment

ESSAYS IN THE

ECONOMICS OF CRIME

AND PUNISHMENT

I

NATIONAL BUREAU OF ECONOMIC RESEARCH ESS1Human Behavior and Social Institutions

1. The Economics of Hea!tlz and Medical Care, Victor R. Fuchs, Editor ECOI2. Schooling, Experience, and Earnings, by Jacob Mincer3. Essays in the Economics of Cri,ne and Punishment, Gary S. Becker AND

and William M. Landes, Editors

Edited byGARYUniversity oNational Bur

I and

WIUniversity 01

National But

NATIONALNew YorkDistributed b,New York ar

tSEARCH ESSAYS IN THER. Fuchs. Editor ECOOMICS OF CRIME

S. Becker AND PUNISHMENT

Edited byGARY S. BECKERUniversity of Chicago andNational Bureau of Economic Research

and

WILLIAM M. LANDESUniversity of Chicago andNational Bureau of Economic Research

NATIONAL BUREAU OF ECONOMIC RESEARCHNew York 1974Distributed by COLUMBIA UNIVERSITY PRESSNew York and London

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Acknowledgments Permis

Many individuals contributed to the entire manuscript and weshould like to thank them for their efforts. Robert Michael, in his capacityas Acting Director in 1972—73 of the National Bureau's Center forEconomic Analysis of Human Behavior and Social Institutions, activelyencouraged the collection of these essays into a single volume and gavevaluable advice on the organization of the manuscript. Bruce Ackermanof the University of Pennsylvania Law School and Guido Calabresi of theYale University Law School generously gave their time in reviewing allthe essays. Eugene P. Foley, J. Wilson Newman, and Alice M. Rivlinmade helpful comments as members of the Board of Directors' readingcommittee. Skillful assistance in the preparation of the manuscript wasprovided by Ruth Ridler in editing the essays, H. Irving Forman incharting the graphs, and Elisabeth Parshley in typing.

The program of research in law and economics at the National Bu-reau has been funded from its inception in 1971 by the National ScienceFoundation, whose support we gratefully acknowledge. The views ex-pressed in these essays are, of course, not attributable to the NationalScience Foundation.

GARY S. BECKER and WILLIAM M. LANDES

Our thanksterial previouslyEconomy, we haPunishment: AnApril 1968; cop;reserved, and priimum Enforceniercopyright 1970 1printed in the UnActivities: A ThNo. 3, May/Junerights reserved,vised and expanchties: An Economhave chosen tworninistrative Agenthe University ofStates. William Min Volume 11(1),Chicago, all rightsJournal of Law aiLandes, "An EcApril 1971; copyrserved, and printe

Permissions

anuscript and weael, in his capacityreau's Center for

activelyvolume and gave

L Bruce AckermanCalabresi of thein reviewing all

Alice M. RivlinDirectors' reading

he manuscript wasIrving Forman in

it the National Bu-National Science

tae. The views cx-1e to the National

M. LANDES

Our thanks to the following journals for permission to reprint ma-terial previously published by them. From The Journal of PoliticalEconomy, we have chosen three articles: Gary S. Becker, "Crime andPunishment: An Economic Approach," in Volume 76, No. 2, March!April 1968; copyright 1968 by the University of Chicago, all rightsreserved, and printed in the United States. George J. Stigler, "The Opti-mum Enforcement of Laws," in Volume 78, No. 2, March/April 1970;copyright 1970 by the University of Chicago, all rights reserved, andprinted in the United States. Isaac Ehrlich, "Participation in IllegitimateActivities: A Theoretical and Empirical Investigation," in Volume 81,No. 3, May/June 1973; copyright 1973 by the University of Chicago, allrights reserved, and printed in the United States. This last, somewhat re-vised and expanded, appears here as "Participation in Illegitimate Activi-ties: An Economic Analysis." From The Journal of Legal Studies, wehave chosen two articles: Richard A. Posner, "The Behavior of Ad-ministrative Agencies," in Volume 1(2), June 1972; copyright 1972 bythe University of Chicago, all rights reserved, and printed in the UnitedStates. William M. Landes, "The Bail System: An Economic Approach,"

11(1), January 1973; copyright 1973 by the University ofChicago, all rights reserved, and printed in the United States. From TheJournal of Law and Econo,nics we have chosen one article: William M.Landes, "An Economic Analysis of the Courts," Volume X1V(1),April 1971; copyright 1971 by the University of Chicago, all rights re-served, and printed in the United States.

Conter

Preface Wi/ha

Crime and Punishi

The Optimum En

Participation in IiiIsaac Ehrhic/i

The Bail System:

An Economic Am

The Behavior of I

Index

L

Contents

Preface William M. Landes xiii

Crime and Punishment: An Economic Approach GaiyS. Becker 1

The Optimum Enforcement of Laws George J. Stigler 55

Participation in Illegitimate Activities: An Economic AnalysisIsaac Elirlich 68

The Bail System: An Economic Approach William M. Landes 135

An Economic Analysis of the Courts Willia,n M. Landes 164

The Behavior of Administrative Agencies Richard A. Posner 215

Index 263

Prefac

The relationslof study by econoof the Navigatioreconomic theoryalternative legal aMoreover, with tleconomists havequantify the actuaquantitative invesiof enforcement. L;ment is acknowlemist. This failure Icause enforcemenand an economic

Theis the systematic sof the economic aciple of scarcity. Ithe adaptation to 1be made concernito be used in deteon violators, and Ion whetherscarcity, combinements and individiused to analyze ethe legal system, a

All the studie:approach, althougempirical analysisment, including thestimates of the dand court system i

Preface

The relationship between law and economics has long been a subjectof study by economists. At least since the time of Adam Smith's analysisof the Navigation Act in England, economists have used the tools ofeconomic theory to understand and to evaluate the effects of laws andalternative legal arrangements on the workings of an economic system.Moreover, with the rapid growth of empirical methods in recent years,economists have produced a large number of studies that attempt toquantify the actual effects of the laws. However, both the theoretical andquantitative investigations have generally taken for granted the questionof enforcement. Laws are assumed to be enforced, or incomplete enforce-ment is acknowledged but viewed as beyond the expertise of the econo-mist. This failure to study enforcement has been a serious deficiency, be-cause enforcement is an essential link in the relationship between a legaland an economic system.

The distinguishing and unifying feature of the essays in this volumeis the systematic study of enforcement as an economic problem. The coreof the economic approach to enforcement is the application of the prin-.ciple of scarcity. Because enforcement of legal rules and regulations andthe adaptation to them by individuals use scarce resources, choices mustbe made concerning the nature of the rules to be enforced, the methodsto be used in detecting violations, the types of sanctions to be imposedon violators, and the procedures to be employed in adjudicating disputeson whether violations have occurred. Taking the fundamental notion ofscarcity, combined with the specification of decision rules for govern-ments and individuals, the economic theory of resource allocation can beused to analyze enforcement, to provide insights into the operation ofthe legal system, and to derive testable hypotheses for empirical analysis.

All the studies in this volume embody the essentials of the economicapproach, although they differ in the emphasis placed on theoretical andempirical analysis. The studies cover a variety of subjects on enforce-ment, including the design of optimal rules for enforcing laws, quantitativeestimates of the deterrent effect of law enforcement, the role of the bailand court system in the enforcement of laws, and the behavior of adminis-

xiv PREFACE

trative agencies in enforcing violations. The following is a brief descrip-tion of the material presented here.

In the first essay, Gary Becker utilizes the economic theory of re-source allocation to develop optimal public and private policies to combatillegal activities. Optimal policies are defined as those that minimize thesocial loss from crime. That loss depends on the net damage to victims;the resource costs of discovering, apprehending, and convicting offenders;and the costs of punishment itself. These components of the loss, in turn,depend upon the number of criminal offenders, the probability of appre-hending and convicting offenders, the size and form of punishments, thepotential legal incomes of offenders, and several other variables. Theoptimal supply of criminal offenses—in essence, the optimal amount ofcrime—is then determined by selecting values for the probability of con-viction, the penalty, and other variables determined by society thatminimize the social loss from crime. Within this framework, theorems arederived that relate the optimal probability of conviction, the optimalpunishments, and the optimal of criminal offenses to such factorsas the size of the damages from various types of crimes, changes in theoverall costs of apprehending and convicting offenders, and differences inthe relative responsiveness of offenders to conviction probabilities and topenalties. The form of the punishment is analyzed as well, with particularreference to the choice between fines and other methods.

Optimal enforcement is also the subject of the second essay. Here,George Stigler considers (a) the effects on enforcement of cost limita-tions; (b) the appropriate definition of enforcement costs; (c) the optimalstructure of penalties and probabilities of conviction for crimes of vary-ing severity; and (d) the determinants of supply of offenses. He shows,among other things, that an optimal enforcement policy must incorporatethe principle of marginal deterrence — the setting of higher penalties andConviction probabilities for more serious offenses—to account for theoffender's ability to substitute more serious for less serious offenses. Inthe final part of his paper, Stigler develops a model for determining theoptimum enforcement policy for agencies charged with economic regula-tion. He provides some evidence indicating that maximum statutorypenalties for violations of economic regulations have little relationshipto optimal penalties.

The third essay, by Isaac Ehrlich, develops in greater detail thesupply function for criminal activities that is central to Becker's andStigler's models of optimal law enforcement. In Ehrlich's model, legaland illegal activities both yield earnings, but the distinguishing feature ofillegal activities is assumed to be their uncertain outcome due to possible

punishment. mdiparticipate in bot:expected utility. Iother thingstivities andcontribution of EThe continuing dabilities deter illepresented byform CrimeEhrlich is able toresponse of specilrents and gains tothe economic moof penalties, prob

In the fourthbail system, usingsocial benefit fungains to defendanto the rest of thelevel of resource eof defendants tobenefit. The mainof alternative

mm

of

the

of inthe

for the state ILandes' paper cotdetention against Itamed defendantsmen.

The developi

PREFACE XV

is a brief descrip-

pmic theory of re-to combat

F that minimize theamage to victims;nvicting offenders;•f the loss, in turn,bability of appre-

•f punishments, thevariables. The

pptimal amount ofprobability of con-

by society thattheorems are

the optimaltses to such factorsdes, changes in the

and differences inprobabilities and to

with particularbds.

essay. Here,rent of cost limita-sts; (c) the optimal

crimes of vary-He shows,

must incorporateigher penalties and

account for theoffenses. In

determining theh economic regula-

statutorylittle relationship

greater detail theto Becker's and

ich's model, legaluishing feature ofne due to possible

punishment. Individuals may specialize in illegal or legal activities orparticipate in both, depending upon the alternative that maximizes theirexpected utility. Increases in punishments and probabilities of conviction,other things remaining constant, will lower the return from illegal ac-tivities and thereby reduce the incentive to participate in them. The maincontribution of Ehrlich's study is his empirical analysis of deterrence.The continuing debate over whether punishments and conviction prob-abilities deter illegal behavior has been conducted with little evidencepresented by either side. Using data from the 1940, 1950, and 1960 Uni-form Crime Reports, and employing several statistical techniques,Ehrlich is able to measure across states, at different points in time, theresponse of specific felony rates to changes in variables reflecting deter-rents and gains to crime. Ehrlich's results support the basic hypotheses ofthe economic model: crime rates appear to vary inversely with estimatesof penalties, probabilities of conviction, and legal opportunities.

In the fourth essay, William Landes develops a model of an optimalbail system, using the same basic framework as Becker. Landes derives asocial benefit function for the bail system that incorporates both thegains to defendants from being released on bail and the costs and gainsto the rest of the community from the release of defendants. The optimallevel of resource expenditures on the bail system and the optimal numberof defendants to be released are determined by maximizing the socialbenefit. The main contribution of this essay, however, is the developmentof alternative methods for selecting defendants for release. Two basicmethods and variations on them are analyzed. Both are consistent withthe criterion of maximizing the social benefit function. The first, w.hichcorresponds to most existing bail systems, requires defendants to pay fortheir release. The second compensates defendants for their detention bymeans of monetary or other payment. There are several advantages to asystem in which defendants are paid. The major advantage is a reductionin the punitive aspect of the bail system (since those detained are com-pensated for their losses from detention) that still allows the detentionof persons in cases in which the potential damage to the community ex-ceeds the gains from their release. Other advantages include reduced dis-crimination against low-income defendants and greater economic incen-tive for the state to improve pretrial detention facilities. The final part ofLandes' paper considers the advantage of crediting a defendant's pretrialdetention against his eventual sentence, the possibility of tort Suits by de-tained defendants who are acquitted, and the role of bail bonds andmen.

The development of a positive theory of legal decision-making as

xvi PREFACE

applied to enforcement decisions is the common theme of the remainingtwo essays. In Landes' study of the court system, a utility-maximizationmodel is developed that explains the determinants of the choice betweena trial and pretrial settlement in both criminal and civil cases, the termsof a settlement, and the outcome of a trial. For criminal cases, these de-cisions are shown to depend on such factors as estimates of the probabil-ity of conviction by trial, the severity of the crime, the availability andproductivity of resources allocated to the resolution of legal disputes, trialversus settlement costs, and attitudes toward risk. The effects of the exist-ing bail system and court delay are analyzed within the framework of themodel, as well as the likely effects of a variety of proposals designed toimprove the bail system and reduce court delay. Multiple regression tech-niques are used on data from both state and federal courts to test severalhypotheses derived from the model. Considerable empirical evidence isadduced to support the hypothesis that the cost differential between atrial and settlement in criminal cases is a significant determinant of thechoice between going to trial and settling. Cost differentials, which in-clude the implicit value of time, were measured by court queues, pretrialdetention, and the subsidization of legal fees. Landes also undertakes anempirical analysis of conviction rates in criminal cases, and of the trialversus settlement choice in civil cases.

Richard Posner's study of administrative agencies employs a modelsimilar to the one used by Landes to analyze the court system. Posnerassumes that an agency maximizes expected utility subject to a budgetconstraint. The agency's expected utility is defined to be a positive func-tion of both the expected number of successful prosecutions and thepublic benefit from winning various types of cases. Posner's model isused to predict an agency's budgetary allocation across classes of cases,the agency's dismissal rate and successful prosecution rate for differenttypes of cases, and the effects of assigning to a single agency both prose-cution and adjudication functions. The major part of the empirical analy-sis is devoted to examining the thesis that an agency that both initiatesand decides cases will bias adjudication in favor of the agency, as com-pared with an agency in which these functions are separated. In the con-text of the model, Posner derives numerous testable implications of the"bias" hypothesis. Using data from the National Labor Relations Board,which after 1947 no longer initiated complaints, and the Federal TradeCommission, Posner finds little evidence in support of the bias hypothesis.

The essays in this volume were written by members of the NationalBureau's program of basic research in law and economics. This researchprogram, begun in 1971, applies analytical and quantitative techniques of

economics to thefunctioning of thetion, and legal desearch output of t:years in one of Se'of the volume prtools in analyzingseveral volumes rtional Bureautions. The law ancwithin the NatiorHuman Behavior

of the remainingtility-maximization

choice betweencases, the termscases, these de-

tes of the probabil-availability and

disputes, trialeffects of the exist-

framework of thedesigned to

regression tech-to test several

evidence isbiential between adeterminant of the

which in-urt queues, pretrial

undertakes an6, and of the trial

employs a modeltirt system. Posnerubject to a budget

a positive func-and the

:Posner's model isclasses of cases,

fl rate for differentagency both prose-ie empirical analy-that both initiatese agency, as corn-

In the con-mplications of ther Relations Board,the Federal Trade

bias hypothesis.of the National

iics. This researchLtive techniques of

PREFACE XVII

economics to the study of the deterrent effects of criminal sanctions, thefunctioning of the court and bail systems, the behavioral effects of legisla-tion, and legal decision-making. These essays represent part of the re-search output of this project; each has been published over the past fewyears in one of several professional journals. We feel that the publicationof the volume provides convincing evidence of the power of economictools in analyzing the enforcement of law. We expect this to be the first ofseveral volumes reporting the results of this program of research to Na-tional Bureau subscribers and to students of legal behavior and institu-tions. The law and economics research program is one of several housedwithin the National Bureau's new Center for Economic Analysis ofHuman Behavior and Social Institutions.

William M. Landes

TH

ESSAYS THE

ECONOMICS OF CRIME

AND PUNISHMENT

CrimeAn Eco

Gary S. IUniversity of C

I. INTRODUCT]

Since the turn ofpanded rapidly to inineteenth centurytions of person anrestricts "discrimiiarrangements,and thousands ofnumerous but alsosuits and of diversMoreover, the lik

I would like to tha1965 at the Universitycomments on an earlierDemsetz, Jack HirshliI have also benefited fiHebrew University, RColumbia; assistance ations from the editor of

Since the turn of the century, legislation in Western countries has ex-panded rapidly to reverse the brief dominance of laissez faire during thenineteenth century. The state no longer merely protects against viola-tions of person and property through murder, rape, or burglary but alsorestricts "discrimination" against certain minorities, collusive businessarrangements, "jaywalking," travel, the materials used in construction,and thousands of other activities. The activities restricted not only arenumerous but also range widely, affecting persons in very different pur-suits and of diverse social backgrounds, education levels, ages, races, etc.Moreover, the likelihood that an offender will be discovered and con-

I would like to thank the Lilly Endowment for financing a very productive summer in1965 at the University of California at Los Angeles. While there I received very helpfulcomments on an earlier draft from, among others, Armen Alchian, Roland McKean, HaroldDemsetz, Jack Hirshliefer, William Meckling, Gordon Tullock, and Oliver Williamson.I have also benefited from comments received at seminars at the University of Chicago,Hebrew University, RAND Corporation, and several times at the Labor Workshop ofColumbia; assistance and suggestions from Isaac Ehrlich and Robert Michael; and sugges-tions from the editor of the Jour,wl of Political Economy, Robert A. Mundell.

Crime and Punishment:An Economic Approach

University of Chicago and National Bureau of Economic Research

Gary S. Becker

1. INTRODUCTION

2 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH

victed and the nature and extent of punishments differ greatly from personto person and activity to activity. Yet, in spite of such diversity, somecommon properties are shared by practically all legislation, and theseproperties form the subject matter of this essay.

in the first place, obedience to law is not taken for granted, andpublic and private resources are generally spent in order both to preventoffenses and to apprehend offenders. In the second place, conviction is notgenerally considered sufficient punishment in itself; additional and some-times severe punishments are meted out to those convicted. What deter-mines the amount and type of resources and punishments used to enforcea piece of legislation? In particular, why does enforcement differ sogreatly among different kinds of legislation?

The main purpose of this essay is to answer normative versions ofthese questions, namely, how many resources and how much punish-ment should be used to enforce different kinds of legislation? Putequivalently, although more strangely, how many offenses should be per-mitted and how many offenders should go unpunished? The method usedformulates a measure of the social loss from offenses and finds those ex-penditures of resources and punishments that minimize this loss. Thegeneral criterion of social loss is shown to incorporate as special cases,valid under special assumptions, the criteria of vengeance, deterrence,compensation, and rehabilitation that historically have figured soprominently in practice and criminological literature.

The optimal amount of enforcement is shown to depend on, amongother things, the cost of catching and convicting offenders, the nature ofpunishments—for example, whether they are fines or prison terms—andthe responses of offenders to changes in enforcement. The discussion,therefore, inevitably enters into issues in penology and theories ofcriminal behavior. A second, although because of lack of space subsidiary,aim of this essay is to see what insights into these questions are providedby our "economic" approach. It is suggested, for example, that a usefultheory of criminal behavior can dispense with special theories of anomie,psychological inadequacies, or inheritance of special traits and simplyextend the economist's usual analysis of choice.

II. BASIC ANALYSIS

A. THE COST OF CRIME

Although the word "crime" is used in the title to minimize terminologi-cal innovations, the analysis is intended to be sufficiently general to cover

Crimes against persontCrimes against propertIllegal goods andSome other crimes

TotalPublic expenditures onCorrectionsSome private costs of

Overall total

SOURCE. — Presidet

all violations, not jusreceive so much new:white-collar crimes,broadly, "crime" isnotwithstanding theevidence recently puEnforcement and Adireproduced in Tableand local levels on poamounted to over $'guards, counsel, andlion. Unquestionablysignificantly understathe course of enforcii

I. This neglect probatmerit any systematic scieianalysis is seen most clearlgambling is an "economictrue that this loss of probathe excitement of gamblinpleasures of gambling areare likely to engender a rfor the higher and moreAppendix).

GARY S. BECKER 3

reatly from personch diversity, someslation, and these

n for granted, andder both to prevent

conviction is notand some-

What deter-used to enforce

'orcement differ so

rmative versions ofhow much punish-

of legislation? Putshould be per-

The method usedand finds those ex-

mize this loss. Thekte as special cases,

deterrence,have figured so

depend on, amongpders, the nature of

terms—andfit. The discussion,

and theories ofspace subsidiary,

are providedthat a useful

of anomie,11 traits and simply

imize terminologi-tly general to cover

TABLE 1ECONOMIC COSTS OF CRIMES

TypeCosts

(Millions of Dollars)

Crimes against persons 815Crimes against property 3,932Illegal goods and services 8,075Some other crimes 2,036

Total 14,858Public expenditures on police, prosecution, and courts 3,178Corrections 1,034Some private costs of combating crime I ,9 10

Overall total 20,980

SouRcE.—President's Commission (1967d, p. 44).

all violations, not just felonies — like murder, robbery, and assault, whichreceive so much newspaper coverage—but also tax evasion, the so-calledwhite-collar crimes, and traffic and other violations. Looked at thisbroadly, "crime" is an economically important activity or "industry,"notwithstanding the almost total neglect by economists.1 Some relevantevidence recently put together by the President's Commission on LawEnforcement and Administration of Justice (the "Crime Commission") isreproduced in Table 1. Public expenditures in 1965 at the federal, state,and local levels on police, criminal courts and counsel, and "corrections"amounted to over $4 billion, while private outlays on burglar alarms,guards, counsel, and some other forms of protection were about $2 bi!-lion. Unquestionably, public and especially private expenditures aresignificantly understated, since expenditures by many public agencies inthe course of enforcing particular pieces of legislation, such as state fair-

I. This neglect probably resulted from an attitude that illegal activity is too immoral tomerit any systematic scientific attention. The influence of moral attitudes on a scientificanalysis is seen most clearly in a discussion by Alfred Marshall. After arguing that even fairgambling is an "economic blunder" because of diminishing marginal utility, he says, "It istrue that this loss of probable happiness need not be greater than the pleasure derived fromthe excitement of gambling, and we are then thrown back upon the induction [sic] thatpleasures of gambling are in Bentham's phrase 'impure'; since experience shows that theyare likely to engender a restless, feverish character, unsuited for steady work as well asfor the higher and more solid pleasures of life" (Marshall, 1961, Note X, MathematicalAppendix).


employment laws,2 are not included, and a myriad of private precautionsagainst crime, ranging from suburban living to taxis, are also excluded.

Table I also lists the Crime Commission's estimates of the directcosts of various crimes. The gross income from expenditures on variouskinds of illegal consumption, including narcotics, prostitution, and mainlygambling, amounted to over $8 billion. The value of crimes against prop-erty, including fraud, vandalism, and theft, amounted to almost $4 bil-lion,3 while about $3 billion worth resulted from the loss of earningsdue to homicide, assault, or other crimes. All the costs listed in the tabletotal about $21 billion, which is almost 4 per cent of reported nationalincome in 1965. If the sizable omissions were included, the percentagemight be considerably higher.

Crime has probably become more important during the last fortyyears. The Crime Commission presents no evidence on trends in costsbut does present evidence suggesting that the number of major feloniesper capita has grown since the early thirties (President's Commission,1967a, pp. 22—3 1). Moreover, with the large growth of tax and otherlegislation, tax evasion and other kinds of white-collar crime have pre-sumably grown much more rapidly than felonies. One piece of indirectevidence on the growth of crime is the large increase in the amount of cur-rency in circulation since 1929. For sixty years prior to that date, theratio of currency either to all money or to consumer expenditures had de-clined very substantially. Since then, in spite of further urbanization andincome growth and the spread of credit cards and other kinds of credit,4both ratios have increased sizably.3 This reversal can be explained by anunusual increase in illegal activity, since currency has obvious advantages

2. Expenditures by the thirteen states with such legislation in 1959 totaled almost $2million (see Landes, 1966).

3. Superficially, frauds, thefts, etc., do not involve true social costs but are simplytransfers, with the loss to victims being compensated by equal gains to criminals. Whilethese are transfers, their market value is, nevertheless, a first approximation to the directsocial cost. If the theft or fraud industry is "competitive," the sum of the value of thecriminals' time input—including the time of "fences" and prospective time in prison—plusthe value of capital input, compensation for risk, etc., would approximately equal themarket value of the loss to victims. Consequently, aside from the input of intermediateproducts, losses can be taken as a measure of the value of the labor and capital input intothese crimes, which are true social costs.

4. For an analysis of the secular decline to 1929 that stresses urbanization and thegrowth in incomes, see Cagan (1965, chap. iv).

5. In 1965, the ratio of currency outstanding to consumer expenditures was 0.08, com-pared to only 0.05 in 1929. In 1965, currency outstanding per family was a whopping $738.

where H, is the harrconcept of harm anare familiar to econing external disecoran important subsewith the level of cri

The social valu

6. Cagan (1965, cha1929 and 1960 to increa

7. The ith subscriptactivity is being discusse

over checks in illeg:tions) because no rc

B. THE MODEL

It is useful in deteridevelop a model tolisted in Table I. TIbetween (1) the nuncost of offenses, (2:out, (3) the numberpenditures on policcosts of imprisonmeof offenses and theThe first four are d.later section.

1. DAMAGES

Usually a belief thation behind outlawiof harm would tend

with

APPROACH

private precautionsre also excluded.

of the directon various

and mainlyagainst prop-

to almost $4 bil-loss of earnings

listed in the tableof reported national

the percentage

curing the last fortye on trends in costsjer of major felonies

Commission,of tax and other

liar crime have pre-piece of indirect

in the amount of cur-to that date, the

had de-her urbanization andther kinds of credit,4

be explained by anadvantages

1959 totaled almost S2

costs but are simplygains to criminals. Whilejroximation to the directsum of the value of the

time in prison—plusequal the

input of intermediatebor and capital input into

es urbanization and the

nditures was 0.08, corn-ly was a whopping $738.

GARY S. BECKER 5

over checks in illegal transactions (the opposite is true for legal transac-tions) because no record of a transaction remains.6

B. THE MODEL

It is useful in determining how to combat crime in an optimal fashion todevelop a model to incorporate the behavioral relations behind the costslisted in Table 1. These can be divided into five categories: the relationsbetween (1) the number of crimes, called "offenses" in this essay, and thecost of offenses, (2) the number of offenses and the punishments metedout, (3) the number of offenses, arrests, and convictions and the public ex-penditures on police and courts, (4) the number of convictions and thecosts of imprisonments or other kinds of punishments, and (5) the numberof offenses and the private expenditures on protection and apprehension.The first four are discussed in turn, while the fifth is postponed until alater section.

1. DAMAGES

Usually a belief that other members of society are harmed is the motiva-tion behind outlawing or otherwise restricting an activity. The amountof harm would tend to increase with the activity level, as in the relation

H, H,(O,),

0,

(1)with

where H, is the harm from the ith activity and 0, is the activity level.7 Theconcept of harm and the function relating its amount to the activity levelare familiar to economists from their many discussions of activities caus-ing external diseconomies. From this perspective, criminal activities arean important subset of the class of activities that cause diseconomies,with the level of criminal activities measured by the number of offenses.

The social value of the gain to offenders presumably also tends to in-

6. Cagan (1965, chap. iv) attributes much of the increase in currency holdings between1929 and 1960 to increased tax evasion from the increase in tax rates.

7. The ith subscript will be suppressed whenever it is to be understood that only oneactivity is being discussed.


crease with the number of offenses, as in

with

G =

G'

(2)

The net cost or damage to society is simply the difference between theharm and gain and can be written as

D(O) = H(0) — G(0). (3)

If, as seems plausible, offenders usually eventually receive diminish-ing marginal gains and cause increasing marginal harm from additionaloffenses, G" < 0, H" > 0, and

— 0, (4)

which is an important condition used later in the analysis of optimalitypositions (see, for example, the Mathematical Appendix). Since both H'and G' > 0, the sign of D' depends on their relative magnitudes. It fol-lows from (4), however, that

D'(O) > 0 for all 0> if D'(Oa) 0. (5)

Until Section V the discussion is restricted to the region where D' > 0,the region providing the strongest justification for outlawing an activity.In that section the general problem of external diseconomies is recon-sidered from our viewpoint, and there D' < 0 is also permitted.

The top part of Table 1 lists costs of various crimes, which have beeninterpreted by us as estimates of the value of resources used up in thesecrimes. These values are important components of, but are not identicalto, the net damages to society. For example, the cost of murder ismeasured by the loss in earnings of victims and excludes, among otherthings, the value placed by society on life itself; the cost of gamblingexcludes both the utility to those gambling and the "external" disutility tosome clergy and others; the cost of "transfers" like burglary and em-bezzlement excludes social attitudes toward forced wealth redistribu-tions and also the effects on capital accumulation of the possibility oftheft. Consequently, the $1 5 billion estimate for the cost of crime inTable 1 may be a significant understatement of the net damages to society,not only because the costs of many white-collar crimes are omitted, butalso because much of the damage is omitted even for the crimes covered.

2. THE COST OF AF

The more that isequipment, thecan postulate a relaland various input5f(n7, c), wherefi:arts." Given f andcostly, as summariz

and

It would be cheapewere policemen,8 jtveloped the state olprinting, wiretappin!

One approximaber of offenses cleai

where p, the ratiothe overall probabilistituting (7) into (6)

and

if p0 0. Anber of offenses wocreased "activity"

8. According to thewages and salaries (Presi

9. A task-force repand more efficient usage

APPROACH GARY S. BECKER 7

2. THE COST OF APPREHENSION AND CONVICTION

(2)

between the

(3)

Ily receive diminish-krm from additional

(4)

of optimalitySince both H'

magnitudes. It fol-

(5)

where D' > 0,an activity.

is recon-permitted.

ês, which have beenused up in theseare not identical

cost of murder isamong other

cost of gamblingdisutility to

burglary and em-wealth redistribu-the possibility of

k cost of crime indamages to society,es are omitted, buthe crimes covered.

The more that is spent on policemen, court personnel, and specializedequipment, the easier it is to discover offenses and convict offenders. Onecan postulate a relation between the output of police and court "activity"and various inputs of manpower, materials, and capital, as in. A =f(m, c), wheref is a production function summarizing the "state of thearts." Given f and input prices, increased "activity" would be morecostly, as summarized by the relation

and

C=C(A)

(6)

It would be cheaper to achieve any given level of activity the cheaperwere policemen,8 judges, counsel, and juries ana the more highly de-veloped the state of the arts, as determined by technologies like finger-printing, wiretapping, computer control, and lie-detecting.9

One approximation to an empirical measure of "activity" is the num-ber of offenses cleared by conviction. It can be written as

A pO, (7)

where p, the ratio of offenses cleared by convictions to all offenses, isthe overall probability that an offense is cleared by conviction. By sub-stituting (7) into (6) and differentiating, one has

and

aC(pO)cJ,= =c'o>o

ap

C0 = C'p> 0

(8)

if p0 0. An increase in either the probability of conviction or the num-ber of offenses would increase total costs. If the marginal cost of in-creased "activity" were rising, further implications would be that

8. According to the Crime Commission, 85—90 per cent of all police costs consist ofwages and salaries (President's Commission, 1967a, p. 35).

9. A task-force report by the Crime Commission deals with suggestions for greaterand more efficient usage of advanced technologies (President's Commission, 1967e).


of these felonies anceither arrests or coiat least $500 if cond

3. THE SUPPLY OF

Theories about the ifrom emphasis onbringing and disenctheories agree, howincrease in a persovicted would generably, the number of czation by personsability has a greaterpunishment,'2 althou.shed any light on thi

The approach t;choice and assumesutility to him exceedresources at other afore, not because thebut because their bemany general implicriminal behavior benot require ad hoc clike,'4 nor does it assany of the other can

This approach iioffenses by any perscif convicted, and to clegal and other illega'willingness to comm.

12. For example, Lcwith methods of punish.significance than they liiseverity of punishment."sightful eighteenth-centurp. 282).

13. See, however, thc14. For a discussion

C,,,, = C"02 > 0,

= C"p2 > 0, (9)and

C,,0 C,,,, = C"pO + C' > 0.A more sophisticated and realistic approach drops the implication

of (7) that convictions alone measure "activity," or even that p and 0have identical elasticities, and introduces the more general relation

A=h(p,0,a). (10)

The variable a stands for arrests and other determinants of "activity,"and there is no presumption that the elasticity of I, with respect to pequals that with respect to 0. Substitution yields the cost function C =C(p, 0, a). If, as is extremely likely, h,,, h,, and h,, are all greater thanzero, then clearly C1,, C,,, and C,, are all greater than zero.

In order to insure that optimality positions do not lie at "corners," itis necessary to place some restrictions on the second derivatives of thecost function. Combined with some other assumptions, it is sufficient that

C,,,, 0,

(11)

andC,,,, 0

(see the Mathematical Appendix). The first two restrictions are ratherplausible, the third much less so.'°

Table I indicates that in 1965 public expenditures in the UnitedStates on police and courts totaled more than $3 billion, by no means aminor item. Separate estimates were prepared for each of seven majorfelonies." Expenditures on them averaged about $500 per offense (re-ported) and about $2,000 per person arrested, with almost $1,000 beingspent per murder (President's Commission, l967a, pp. 264—65); $500 isan estimate of the average cost

A

10. Differentiating the cost function yields C,,,, C"(h,,)' + C'/i,,; C,,,, = C"(/i,,)' +C'h,,,,; C,,,, = Ch,/i,, + C/i,,,,. If marginal costs were rising, C,,, or C,,. could be negativeonly if h,,, or I'm, were sufficiently negative, which is not very likely. However, C,,,, wouldbe approximately zero only if h,,, were sufficiently negative, which is also unlikely. Notethat if "activity" is measured by convictions alone, h,,, = I,,,, = 0, and h,,,, > 0.

II. They are willful homicide, forcible rape, robbery, aggravated assault, burglary,larceny, and auto theft.

GARY S. BECKER 9

(9)

of these felonies and would presumably be a larger figure if the number ofeither arrests or Convictions were greater. Marginal costs (Ce) would beat least $500 if condition (11), C,,0 0, were assumed to hold throughout.

3. THE SUPPLY OF OFFENSES)pS the implicationeven that p and 0eneral relation

(10)

nants of "activity,"with respect to pcost function C =

rare all greater thanzero.

lie at "corners," itderivatives of the

'is, it is sufficient that

(11)

strictions are rather

tures in the Unitedlion, by no means a

of seven majorper offense (re-

almost $1,000 beingp. 264—65); $500 is

C'h,,,,; C,,, = C"(h0)2 +r could be negatively. However, C,,,, wouldii is also unlikely. Noteand 6,,.. > 0.

vated assault, burglary,

Theories about the determinants of the number of offenses differ greatly,from emphasis on skull types and biological inheritance to family up-bringing and disenchantment with society. Practically all the diversetheories agree, however, that when other variables are held constant, anincrease in a person's probability of conviction or punishment if con-victed would generally decrease, perhaps substantially, perhaps negligi-bly, the number of offenses he commits. In addition, a common generali-zation by persons with judicial experience is that a change in the prob-ability has a greater effect on the number of offenses than a change in thepunishment,'2 although, as far as I can tell, none of the prominent theoriesshed any light on this relation.

The approach taken here follows the economists' usual analysis ofchoice and assumes that a person commits an offense if the expectedutility to him exceeds the utility he could get by using his time and otherresources at other activities. Some persons become "criminals," there-fore, not because their basic motivation differs from that of other persons,but because their benefits and costs differ. I cannot pause to discuss themany general implications of this approach,'3 except to remark thatcriminal behavior becomes part of a much more general theory and doesnot require ad hoc concepts of differential association, anomie, and thelike,'4 nor does it assume perfect knowledge, lightning-fast calculation, orany of the other caricatures of economic theory.

This approach implies that there is a function relating the number ofoffenses by any person to his probability of conviction, to his punishmentif convicted, and to other variables, such as the income available to him inlegal and other illegal activities, the frequency of nuisance arrests, and hiswillingness to commit an illegal act. This can be represented as

12. For example, Lord Shawness (1965) said, "Some judges preoccupy themselveswith methods of punishment. This is their job. But in preventing crime it is of lesssignificance than they like to think. Certainty of detection is far more important thanseverity of punishment." Also see the discussion of the ideas of C. B. Beccaria, an in-sightful eighteenth-century Italian economist and criminologist, in Radzinowicz (1948, 1,p. 282).

13. See, however, the discussions in Smigel (1965) and Ehrlich (1967).14. For a discussion of these concepts, see Sutherland (1960).


O3(p3, f,, U3), (12)

where is the number of offenses he would commit during a particu1arperiod, p3 his probability of conviction per offense, f, his punishment peroffense, and u3 a portnianteau variable representing all these other in-fluences.'5

Since only convicted offenders are punished, in effect there is "pricediscrimination" and uncertainty: if convicted, he pays f per convictedoffense, while otherwise he does not. An increase in either p, orf3 wouldreduce the utility expected from an offense and thus would tend to reducethe number of offenses because either the probability of "paying" thehigher "price" or the "price" itself would increase.'6 That is,

and

<0

ao3°fj= < 0,

(13)

which are the generally accepted restrictions mentioned above. The effectof changes in some components of 113 could also be anticipated. For ex-ample, a rise in the income available in legal activities or an increase inlaw-abidingness due, say, to "education" would reduce the incentive to

15. Both and f3 might be considered distributions that depend on the judge, jury,prosecutor, etc., that j happens to receive. Among other things, U3 depends on the p's andf's meted out for other competing offenses. For evidence indicating that offenders do substi-tute among offenses, see Smigel (1965).

16. The utility expected from committing an offense is defined as

EU., = pjUj(Y3 —J) + (1 —

where Y1 is his income, monetary plus psychic, from an offense; U, is his utility function;and fi is to be interpreted as the monetary equivalent of the punishment. Then

and

= —f,) — <0

<0

as long as the marginal utility of income is positive. One could expand the analysis by in-corporating the costs and probabilities of arrests, detentions, and trials that do not resultin conviction.

enter illegal activitieshift in the form ofwould tend to reduccthey cannot be comi

This approachgreater response toAn increase in "Cwould not change thethe expected utility,shown that an incre2the number of offens.has preference for ri:he has aversion to rineutral.'9 The widesçby the probability ofturns out to imply inpreferrers, at least in

The total numbepend on the set of p3,significantly betweeneducation, previoussimplicity I now cons

17.

18. This means thatutility and offenses.

19. From n. 16

as

=äp3 U1

The term on the left is thc

greater than, equal to, or le

(J > 0, neutrality by =20. p can be defined a

and similar definitions hold

APPROACH

(12)

it during a particularhis punishment per

g all these other in-

effect there is "priceays per convictedeither orf1 would

Nould tend to reducelity of "paying" the6 That is,

(13)

above. The effectanticipated. For ex-

ties or an increase inthe incentive to

,epend on the judge. jury,depends on the p's and

g that offenders do substi-

as

U, is his utility function;ishment. Then

GARY S. BECKER 11

enter illegal activities and thus would reduce the number of offenses. Or ashift in the form of the punishment, say, from a fine to imprisonment,would tend to reduce the number of offenses, at least temporarily, becausethey cannot be committed while in prison.

This approach also has an interesting interpretation of the presumedgreater response to a change in the probability than in the punishment.An increase in p) "compensated" by an equal percentage reduction in f,would not change the expected income from an offense could changethe expected utility, because the amount of risk would change. It is easilyshown that an increase in p,, would reduce the expected utility, and thusthe number of offenses, more than an equal percentage increase inf, jfjhas preference for risk; the increase in would have the greater effect ifhe has aversion to risk; and they would have the same effect if he is riskneutral.15 The widespread generalization that offenders are more deterredby the probability of conviction than by the punishment when convictedturns out to imply in the expected-utility approach that offenders are riskpreferrers, at least in the relevant region of punishments.

The total number of offenses is the sum of all the 0, and would de-pend on the set of p,,f, and U,,. Although these variables are likely to differsignificantly between persons because of differences in intelligence, age,education, previous offense history, wealth, family upbringing, etc., forsimplicity I now consider only their average values, p,f, and u,2° and write

17.

18. This means that an increase in

p,

"compensated" by a reduction in f, would reduceutility and offenses.

19. From n. 16

as

fi—aEU, p,{U,(Y,) — U,(Y, = p,UJ(Y, —fj) —

äp, U,, U,,< c'fj U,, U3

U,(Y,,) — U,,(Y,, —fi)U(Y, —f,)

fi

xpand the analysis by in-d trials that do not result

The term on the left is the average change in utility between Y3 —j5 and Y,. It would be

greater than, equal to, or less than U(Y, —f,,) as U' 0. But risk preference is defined by

U7 > 0, neutrality by 0, and aversion by U7 < 0.20. p can be defined as a weighted average of the p,, as

iTh

i-I

and similar definitions hold fcn-f and u.


the market offense function as

0 = O(p,f, u). (14)

This function is assumed to have the same kinds of properties as theindividual functions, in particular, to be negatively related to p and f andto be more responsive to the former than the latter if, and only if, offenderson balance have risk preference. Smigel (1965) and Ehrlich (1967) esti-mate functions like (14) for seven felonies reported by the Federal Bu-reau of Investigation using state data as the basic unit of observation.They find that the relations are quite stable, as evidenced by high corre-lation coefficients; that there are significant negative effects on 0 of pand f; and that usually the effect of p exceeds that of f, indicatingpreference for risk in the region of observation.

A well-known result states that, in equilibrium, the real incomes ofpersons in risky activities are, at the margin, relatively high or low aspersons are generally risk avoiders or preferrers. If offenders were riskpreferrers, this implies that the real income of offenders would he lower,at the margin, than the incomes they could receive in less risky legalactivities, and conversely if they were risk avoiders. Whether "crimepays" is then an implication of the attitudes offenders have toward riskand is not directly related to the efficiency of the police or the amountspent on combating crime. If, however, risk were preferred at some valuesof p and f and disliked at others, public policy could influence whether"crime pays" by its choice of p andf. Indeed, it is shown later that thesocial loss from illegal activities is usually minimized by selecting p andf in regions where risk is preferred, that is, in regions where "crime doesnot pay."

4. PUNISHMENTS

Mankind has invented a variety of ingenious punishments to inflict onconvicted offenders: death, torture, branding, fines, imprisonment, ban-ishment, restrictions on movement and occupation, and loss of citizen-ship are just the more common ones. In the United States, less seriousoffenses are punished primarily by fines, supplemented occasionally byprobation, petty restrictions like temporary suspension of one's driver'slicense, and imprisonment. The more serious offenses are punished by acombination of probation, imprisonment, parole, fines, and various re-strictions on choice of occupation. A recent survey estimated for anaverage day in 1965 the number of persons who were either on probation,parole, or institutionalized in a jail or juvenile home (President's Corn-

mission, 1967b). Thcame to about l,30CAbout one-half werethe remaining one-si:

The cost of diffiparable by convertiwhich, of course, iscost of an imprisonnand the value placeSince the earnings ftvary from person toduration is not a unitoffenders who couldfender would begone earnings and flength of sentences.

Punishments afTsociety. Aside fromas revenue byas well as offenders::guards, supervisorybillion is being spentand institutionalizaticdously from a low olfor juveniles in detepp. 193—94).

The total socialcost or minus the gaequals the cost tosocial cost of fines iscost of probation, in]erally exceeds that tiivation of optimalityvenient if social cost:

wheref' is the socialThe size of b vane:

21. In this respect, iialso exemplified by queue


(14)

of properties as theelated to p and f andand only if, offendersEhrlich (1967) esti-by the Federal Bu-unit of observation.

enced by high cone-ye effects on 0 of p

of f, indicating

the real incomes ofhigh or low as

(1 offenders were riskwould be lower,

in less risky legalWhether "crimehave toward risk

or the amountat some values

Id influence whethershown later that the

ed by selecting p andwhere "crime does

tshments to inflict onimprisonment, ban-and loss of citizen-

d States, less seriousnted occasionally byion of one's driver's

es are punished by anes, and various re-ey estimated for aneither on probation,

e (President's Corn-

mission, 1967b). The total number of persons in one of these categoriescame to about 1,300,000, which is about 2 per cent of the labor force.About one-half were on probation, one-third were institutionalized, andthe remaining one-sixth were on parole.

The cost of different punishments to an offender can be made com-parable by converting them into their monetary equivalent or worth,which, of course, is directly measured only for fines. For example, thecost of an imprisonment is the discounted sum of the earnings foregoneand the value placed on the restrictions in consumption and freedom.Since the earnings foregone and the value placed on prison restrictionsvary from person to person, the cost even of a prison sentence of givenduration is not a unique quantity but is generally greater, for example, tooffenders who could earn more outside of prison.2' The cost to each of-fender would be greater the longer the prison sentence, since both fore-gone earnings and foregone consumption are positively related to thelength of sentences.

Punishments affect not only offenders but also other members ofsociety. Aside from collection costs, fines paid by offenders are receivedas revenue by others. Most punishments, however, hurt other membersas well as offenders: for example, imprisonment requires expenditures onguards, supervisory personnel, buildings, food, etc. Currently about $1billion is being spent each year in the United States on probation, parole,and institutionalization alone, with the daily cost per case varying tremen-dously from a low of $0.38 for adults on probation to a high of $11.00for juveniles in detention institutions (President's Commission, 1967b,pp. 193—94).

The total social cost of punishments is the cost to offenders plus thecost or minus the gain to others. Fines produce a gain to the latter thatequals the cost to offenders, aside from collection costs, and so thesocial cost of fines is about zero, as befits a transfer payment. The socialcost of probation, imprisonment, and other punishments, however, gen-erally exceeds that to offenders, because others are also hurt. The der-ivation of optimality conditions in the next section is made more con-venient if social costs are written in terms of offender costs as

(15)

wheref' is the social cost and b is a coefficient that transforms fintof'.The size of b varies greatly between different kinds of punishments:

21. In this respect, imprisonment is a special case of "waiting time'S pricing that isalso exemplified by queueing (see Becker, 1965, esp. pp. 5 15—16, and Kleinman, 1967).


b 0 for fines, while b > 1 for torture, probation, parole, imprisonment,and most other punishments. It is especially large for juveniles in deten-tion homes or for adults in prisons and is rather close to unity for tortureor for adults on parole.

III. OPTIMALITY CONDITIONS

The relevant parameters and behavioral functions have been introduced,and the stage is set for a discussion of social policy. If the aim simplywere deterrence, the probability of conviction, p, could be raised clOse to1, and punishments,f, could be made to exceed the gain: in this way thenumber of offenses, 0, could be reduced almost at will. However, an in-crease in p increases the social cost of offenses through its effect on thecost of combating offenses, C, as does an increase inf if b > 0 throughthe effect on the cost of punishments, bf. At relatively modest values ofp and f, these effects might outweigh the social gain from increaseddeterrence. Similarly, if the aim simply were to make "the punishmentfit the crime," p could be set close to 1, and f could be equated to theharm imposed on the rest of society. Again, however, such a policy ig-nores the social cost of increases in p andf.

What is needed is a criterion that goes beyond catchy phrases andgives due weight to the damages from offenses, the costs of apprehendingand convicting offenders, and the social cost of punishments. The social-welfare function of modern welfare economics is such a criterion, andone might assume that society has a function that measures the socialloss from offenses. If

(16)

is the function measuring social loss, with presumably

abf>°' (17)

the aim would be to select values off, C, and possibly b that minimize L.It is more convenient and transparent, however, to develop the dis-

cussion at this point in terms of a less general formulation, namely, toassume that the loss function is identical with the total social loss in realincome from offenses, convictions, and punishments, as in

L=D(0)+C(p, 0)+bpfo. (18)

The term bpfo is the total social loss from punishments, since bf is theloss per offense punished and p0 is the number of offenses punished (if

there are a fairly Iadirectly subject tooffenses, C; the puiform of punishmentvia the D, C, and 0 fthe loss L.

Analytical conya decisionvariabje. Aa given constant gnvariables, and theirthe two first-order o

and

L

If and are notrecombine terms, to

and

D

where

and

The term on theincreasing the numbeinfand in (22) throuto be in a region whe:

22. The Mathematica


Lye been introduced,y. If the aim simplyId be raised close togain: in this way the

nih. However, an in-.ugh its effect on theinfif b > 0 throughrely modest values of

from increasedàke "the punishment

be equated to thever, such a policy ig-

catchy phrases andof apprehending

ishments. The social-such a criterion, andmeasures the social

(16)

(17)

ly b that minimize L., to develop the dis-milation, namely, total social loss in real

as in

(18)

ents, since bf is the

role, imprisonment,rjuveniles in deten-to unity for torture

there are a fairly large number of independent offenses). The variablesdirectly subject to social control are the amounts spent in combatingoffenses, C; the punishment per offense for those convicted, f; and the

form of punishments, summarized by b. Once chosen, these variables,

via the D, C, and 0 functions, indirectly determine p, 0, D, and ultimately

the loss L.Analytical convenience suggests that p rather than C be considered

a decision variable. Also, the coefficient b is assumed in this section to bea given constant greater than zero. Then p and fare the only decisionvariables, and their optimal values are found by differentiating L to findthe two first-order optimality conditions,22

(19)

and

(20)

If 0, and 0,, are not equal to zero, one can divide through by them, andrecombine terms, to get the more interesting expressions

D' + C' =_bpf(1 _!) (21)

and

(22)

where

fCj = Of

and (23)

pLv = 0,,.

The term on the left side of each equation gives the marginal cost ofincreasing the number of offenses, 0: in equation (21) through a reductioninfand in (22) through a reduction in p. Since C' > 0 and 0 is assumed

to be in a region where D' > 0, the marginal cost of increasing 0 through

5ly

ffenses punished (if 22. The Mathematical Appendix discusses second-order conditions.


Marginalcost

Marginalrevenue

FIGURE 1

—!)

!)

Number of offenses

f must be positive. A reduction in p partly reduces the cost of combatingoffenses, and, therefore, the marginal cost of increasing 0 must be lesswhen p rather than when f is reduced (see Figure 1); the former couldeven be negative if were sufficiently large. Average "revenue," givenby —bpf, is negative, but marginal revenue, given by the right-hand side ofequations (21) and (22), is not necessarily negative and would be positiveif the elasticities €,, and e,were less than unity. Since the loss is minimizedwhen marginal revenue equals marginal cost (see Figure 1), the optimalvalue of Cf must be less than unity, and that of e,, could only exceed unityif C,, were sufficiently large. This is a reversal of the usual equilibriumcondition for an income-maximizing firm, which is that the elasticity ofdemand must exceed unity, because in the usual case average revenue isassumed to be

Since the marginal cost of changing 0 through a change in p is lessthan that of changing 0 throughf, the equilibrium marginal revenue fromp must also be less than that fromf. But equations (21) and (22) indicate

23. Thus if b < 0, average revenue would be positive and the optimal value of Ej

would be greater than 1, and that of a,, could be less than I only if C,, were sufficientlylarge.

that the marginal re'pointed out earlier,that offenders havepay." Consequently,selected from thoseferrers. Although oidirectly determine wiinsures that "crime d

I indicated earlicUnited States generaby elasticity) of p on Crisk preferrers andMoreover, both elasttherefore, actual puboptimality analysis.

If the supply ofneutral—a reduction iinf would leaveloss, because the costby the reduction in p.ing p arbitrarily clos(product pf would mdoffenders were risk aarbitrarily close to zeonly C but also 0 an

There was a tentunes in Anglo-Saxonunderdeveloped counirather severely, at thc

24. If b < 0, the optiniOptimal social policy woul

25. Sinceconditions given by eqs. (2

From this condition and ftbe determined.

26. If b < 0, the optilare either risk neutral or nt

MC,= D' +


D' + C'

D' + C' +

MR,=.—bPf(t —!)

umber of offenses

the cost of combating0 must be less

1); the former couldpage "revenue," giventhe right-hand side of

would be positivethe loss is minimized

figure 1), the optimalonly exceed unity

the usual equilibriumthat the elasticity of

tse average revenue is

a change in p is lessarginal revenue from

(21) and (22) indicate

Ld the optimal value of €,nly if C,, were sufficiently

that the marginal revenue from p can be less if, and only if, e,, > Aspointed out earlier, however, this is precisely the condition indicatingthat offenders have preference for risk and thus that "crime does notpay." Consequently, the loss from offenses is minimized if p and f areselected from those regions where offenders are, on balance, risk pre-ferrers. Although only the attitudes offenders have toward risk candirectly determine whether "crime pays," rational public policy indirectlyinsures that "crime does not pay" through its choice of p and f.24

I indicated earlier that the actual p's andf's for major felonies in theUnited States generally seem to be in regions where the effect (measuredby elasticity) of p on offenses exceeds that off, that is, where offenders arerisk preferrers and "crime does not pay" (Smigel, 1965; Ehrlich, 1967).Moreover, both elasticities are generally less than unity. In both respects,therefore, actual public policy is consistent with the implications of theoptimality analysis.

If the supply of offenses depended only on pf—offenders were riskneutral — a reduction in p "compensated" by an equal percentage increaseinf would leave unchanged pf, 0, D(0), and bpfo but would reduce theloss, because the costs of apprehension and conviction would be loweredby the reduction in p. The loss would be minimized, therefore, by lower-ing p arbitrarily close to zero and raisingf sufficiently high so that theproduct pf would induce the optimal number of offenses.25 A fortiori, ifoffenders were risk avoiders, the loss would be minimized by setting parbitrarily close to zero, for a "compensated" reduction in p reduces notonly C but also 0 and thus D and bpf0.2°

There was a tendency during the eighteenth and nineteenth cen-turies in Anglo-Saxon countries (and even today in many Communist andunderdeveloped countries) to punish those convicted of criminal offensesrather severely, at the same time that the probability of captute and con-

24. If b < 0, the optimality condition is that e,. < €1' or that offenders are risk avoiders.Optimal social policy would then be to select p and fin regions where "crime does pay."

25. Since €, = e,, = if 0 depends only on pf, and C = 0 if p = 0, the two equilibriumconditions given by eqs. (21) and (22) reduce to the single condition

D' =_bPf(l .J)

From this condition and the relation 0 = O(pj), the equilibrium values of 0 and pf couldbe determined.

26. If b < 0, the optimal solution is p about zero and f arbitrarily high if offendersare either risk neutral or risk preferrers.

18 CRiME AND PUNISHMENT: AN ECONOMIC APPROACH

viction was set at rather low values.27 A promising explanation of thistendency is that an increased probability of conviction obviously absorbspublic and private resources in the form of more policemen,judges,juries,and so forth. Consequently, a "compensated" reduction in this proba-bility obviously reduces expenditures on combating crime, and, since theexpected punishment is unchanged, there is no "obvious" offsettingincrease in either the amount of damages or the cost of punishments.The result can easily be continuous political pressureto keep police andother expenditures relatively low and to compensate by meting out strongpunishments to those convicted.

Of course, if offenders are risk preferrers, the loss in income fromoffenses is generally minimized by selecting positive and finite values ofp and f, even though there is no "obvious" offset to a compensatedreduction in p. One possible offset already hinted at in footnote 27 isthat judges or juries may be unwilling to convict offenders if punishmentsare set very high. Formally, this means that the cost of apprehension andConviction, C, would depend not only on p and 0 but also on If Cwere more responsive tofthan to p, at least in some regions,29 the loss inincome could be minimized at finite values of p and f even if offenderswere risk avoiders. For then a compensated reduction in p could raise,rather than lower, C and thus contribute to an increase in the loss.

Risk avoidance might also be consistent with optimal behavior ifthe loss function were not simply equal to the reduction in income. Forexample, suppose that the loss were increased by an increase in the expost "price discrimination" between offenses that are not and those thatare cleared by punishment. Then a "compensated" reduction in p wouldincrease the "price discrimination," and the increased loss from thiscould more than offset the reductions in C, D, and bpf0.3°

27. For a discussion of English criminal law in the eighteenth and nineteenth cen-turies, see Radzinowicz (1948, Vol. 1). Punishments were severe then, even though thedeath penalty, while legislated, was seldom implemented for less serious criminal offenses.

Recently South Vietnam executed a prominent businessman allegedly for "specula-tive" dealings in rice, while in recent years a number of persons in the Soviet Union haveeither been executed or given severe prison sentences for economic crimes.

28. 1 owe the emphasis on this point to Evsey Domar.29. This is probably more likely for higher values off and lower values of p.30. if p is the probability that an offense would be cleared with the punishment f,

then I — p is the probability of no punishment. The expected punishment would be = pf.the variance = p(l — p)ft, and the coefficient of variation

IT::-;;v =— = 'p

IV. SHIFTS iN T

This section analyztions—the damage,mal values of p and,matical Appendix, hproofs Tiwhy more damagingsive offenders less s

An increase in thD', increases the maip or f (see Figuresnecessarily decrease,increase. In this casevalues of p and fmo'

An interesting a,of offenses. Althougtdone by most offensthat offenses like mularceny or auto theft.

v increases monotonicallyp =0.

If the loss function eq

the optimality conditions v

and

0' -f

Since the term çV(dv/dp)(:I

31. 1 stress this prima,that "the more deficient inii of section entitled "Of(orf) were exogenously defor then the optimal value c(see the Mathematical Aprfrequently they move in thi

GARY S. BECKER 19APPROACH

g explanation of thisrn obviously absorbsemen, judges, juries,iction in this proba-crime, and, since the"obvious" offsetting:ost of punishments.re to keep police andby meting out strong

loss in income fromand finite values of

et to a compensatedin footnote 27 is

if punishmentsof apprehension and

also on If Cregions,29 the loss in

id I even if offendersin p could raise,

base in the loss.optimal behavior if

Iction in income. Forincrease in the exnot and those that

in p wouldloss from this

and nineteenth cen-re then, even though theserious criminal offenses.

allegedly for "specula-n the Soviet Union haveic crimes.

wer values of p.with the punishment f,

shment would be = pf,

IV. SHIFTS IN THE BEHAViORAL RELATIONS

This section analyzes the effects of shifts in the basic behavioral rela-tions—the damage, cost, and supply-of-offenses functions—on the opti-mal values of p andf Since rigorous proofs can be found in the Mathe-matical Appendix, here the implications are stressed, and only intuitiveproofs are given. The results are used to explain, among other things,why more damaging offenses are punished more severely and more impul-sive offenders less severely.

An increase in the marginal damages from a given number of offenses,D', increases the marginal cost of changing offenses by a change in eitherp or f (see Figures 2a and b). The optimal number of offenses wouldnecessarily decrease, because the optimal values of both p and f wouldincrease. In this case (and, as shortly seen, in several others), the optimalvalues of p and f move in the same, rather than in opposite, directions.3'

An interesting application of these conclusions is to different kindsof offenses. Although there are few objective measures of the damagesdone by most offenses, it does not take much imagination to concludethat offenses like murder or rape generally do more damage than pettylarceny or auto theft. If the other components of the loss in income were

t' increases monotonically from a low of zero when p = I to an infinitely high value whenp = ci.

If the loss function equaled

the optimality conditions would become

and

D'+C'=_bpf(l (21)

(22)

Since the term is positive, it could more than offset the negative term

31. 1 stress this primarily because of Bentham's famous and seemingly plausible dictumthat "the more deficient in certainty a punishment is, the severer it should be" (1931, chap.ii of section entitled "Of Punishment," second rule). The dictum would be correct if p(orf) were exogenously determined and if L were minimized with respect tof(orp) alone,for then the optimal value off(or p) would be inversely related to the given value of p (orf)(see the Mathematical Appendix). If, however. L is minimized with respect to both, thenfrequently they move in the same direction.

— -


Marginal Marginalcost cost =

Marginal Marginal c + crevenue revenue

a0-J

0

b.

FIGuRE 2

the same, the optimal probability of apprehension and conviction and thepunishment when convicted would be greater for the more serious offenses.

Table 2 presents some evidence on the actual probabilities andpunishments in the United States for seven felonies. The punishments H

are simply the average prison sentences served, while the probabilitiesare ratios of the estimated number of convictions to the estimated numberof offenses and unquestionably contain a large error (see the discussions i—

in Smigel, 1965, and Ehrlich, 1967). If other components of the loss func-tion are ignored, and if actual and optimal probabilities and punishmentsare positively related, one should find that the more serious felonies havehigher probabilities and longer prison terms. And one does: in the table, —

which lists the felonies in decreasing order of presumed seriousness, <

both the actual probabilities and the prison terms are positively relatedto seriousness.

Since an increase in the marginal cost of apprehension and convic-tion for a given number of offenses, C', has identical effects as an increasein marginal damages, it must also reduce the optimal number of offensesand increase the optimal values of p andf. On the other hand, an increasein the other component of the cost of apprehension and conviction,has no direct effect on the marginal cost of changing offenses with f andreduces the cost of changing offenses with p (see Figure 3). It thereforereduces the optimal value of p and only partially compensates with anincrease in f, so that the optimal number of pifenses increases. Accord-ingly, an increase in both C' and C,. must increase the optimaif but caneither increase or decrease the optimal p and optimal number of offenses,depending on the relative importance of the changes in C' and C,..

MR

a.

Number of offenses

If) -.:i

CD

(P

- C

-.

CD

°F

-—

c"C

D If)<

C)

PC

->C

D0

•

CD

CD

CD

CD

r .4-

C)

TA

BL

E 2

PRO

BA

BIL

ITY

OF

CoN

vIcT

IoN

AN

D A

VE

RA

GE

PR

ISO

N T

ER

M F

OR

SE

VE

RA

L M

AJO

R F

ELO

NIE

S, 1

960

Mur

der

and

Non

-ne

glig

ent

Agg

ra-

All

The

seM

an-

Forc

ible

vate

dA

uto

Felo

nies

slau

ghte

rR

ape

Rob

bery

Ass

ault

Bur

glar

yL

arce

nyT

heft

Com

bine

d

1.A

vera

ge ti

me

serv

ed (

mon

ths)

.

befo

re f

irst

rel

ease

:a)

Fed

eral

civ

il in

stitu

tions

111.

063

.656

.127

.126

.216

.220

.618

.8b)

Sta

tein

stitu

tions

121.

444

.842

.425

.024

.619

.821

.328

.42.

Prob

abili

ties

of a

ppre

hens

ion

and

conv

ictio

n (p

er c

ent)

:a)

Tho

se f

ound

gui

lty o

fof

fens

es k

now

n57

.937

.725

.127

.313

.010

.713

.715

.1b)

Tho

sefo

und

guilt

y of

offe

nses

cha

rged

40.7

26.9

17.8

16.1

10.2

9.8

11.5

15.0

c) T

hose

ente

ring

fed

eral

and

stat

e pr

ison

s(e

xclu

des

man

y ju

veni

les)

39.8

22.7

8.4

3.0

2.4

2.2

2.1

2.8

SOU

RC

E.—

I, B

urea

u of

Pri

sons

(19

60, T

able

3);

2 (

a) a

nd (

b),

Fed

eral

Bur

eau

of I

nves

tigat

ion

(196

0, T

able

10)

; 2(c

),Fe

dera

l Bur

eau

of I

nves

tigat

ion

(196

1, T

able

2),

Bur

eau

of P

riso

ns (

n.d.

,Tab

le A

l; 19

61, T

able

8).

(P

—•

O (P(P

(pC

#iO ,

CD

C 0 0 0

0 > C-)


offenses observed in:tion between C,, (or

if b > 0, a redincreases the margilFigure 4a). The resua decrease in the opithe optima! p. Simirespect top also in4b), decreases the 0;f. An equalthe optimal number

- If b = 0, both margand changes in thesp andf

The cost of apprehending and convicting offenders is affected by avariety of forces. An increase in the salaries of policemen increases bothC' and C,,, while improved police technology in the form of fingerprinting,ballistic techniques, computer control, and chemical analysis, or policeand court "reform" with an emphasis on professionalism and merit,would tend to reduce both, not necessarily by the same extent. Our anal y-sis implies, therefore, that although an improvement in technology andreform may or may not increase the optimal p and reduce the optimalnumber of offenses, it does reduce the optimalf and thus the need to relyon severe punishments for those convicted. Possibly this explains why thesecular improvement in police technology and reform has gone hand inhand with a secular decline in punishments.

C,,, and to a lesser extent C', differ significantly between differentkinds of offenses. It is easier, for example, to solve a rape or armed rob-bery than a burglary or auto theft, because the evidence of personal identi-fication is often available in the former and not in the latter offenses.32This might tempt one to argue that the p's decline significantly as onemoves across Table 2 (left to right) primarily because the Co's are sig-nificantly lower for the "personal" felonies listed to the left than for the"impersonal" felonies listed to the right. But this implies that the f'swould increase as one moved across the table, which is patently false.Consequently, the positive correlation between p,f, and the severity of

Marginalcost

Marginalrevenue

C

MR

Number of offenses

FIGURE 3

The income oflittle cost, its total i

ferent elasticities ofmarkets having lowoffenses could bethe elasticities of suçthe total loss wouldlower p's and f's — ii

Sometimes itisoffense into groupsexample, unpremediimpulsively and, the

Marginalcost

Marginalrevenue \

Nua-32. "If a suspect is neither known to the victim nor arrested at the scene of the crime,

the chances of ever arresting him are very slim" (President's Commission, 1967e, p. 8).This conclusion is based on a study of crimes in parts of Los Angeles during January, 1966.


offenses observed in the table cannot be explained by a negative correla-tion between (or C') and severity.

If b > 0, a reduction in the elasticity of offenses with respect to fincreases the marginal revenue of changing offenses by changing f (seeFigure 4a). The result is an increase in the optimal number of offenses anda decrease in the optimalf that is partially compensated by an increase inthe optimal p. Similarly, a reduction in the elasticity of offenses withrespect to p also increases the optimal number of offenses (see Figure4b), decreases the optimal p. and partially compensates by an increase inf An equal percentage reduction in both elasticities a fortiori increasesthe optimal number of offenses and also tends to reduce both p and fIf b = 0, both marginal revenue functions lie along the horizontal axis,and changes in these elasticities have no effect on the optimal values ofp andf

The income of a firm would usually be larger if it could separate, atlittle cost, its total market into submarkets that have substantially dif-ferent elasticities of demand: higher prices would be charged in the sub-markets having lower elasticities. Similarly, if the total "market" foroffenses could be separated into submarkets that differ significantly inthe elasticities of supply of offenses, the results above imply that if b > 0the total loss would be reduced by "charging" lower "prices" —that is,lower p's and f's—in markets with !owei- elasticities.

Sometimes it is possible to separate persons committing the sameoffense into groups that have different responses to punishments. Forexample, unpremeditated murderers or robbers are supposed to actimpulsively and, therefore, to be relatively unresponsive to the size of

Marginalcost

Marginalrevenue

tders is affected by aincreases both

of fingerprinting,àl analysis, or police

and merit,extent. Our analy-

nt in technology andI recuce the optimal

the need to relythis explains why therrn has gone hand in

y between differentrape or armed rob-of personal identi-

latter offenses.32significantly as onese the are sig-the left than for theimplies that the f'scli is patently false.and the severity of

at the scene of the crime,)fflmiSSiOn, l967e, p. 8).les during January, 1966.

Marginalcost

MC Marginalrevenue

a-

Number of offenses

—bpf (i

b.

Number of offenses

FIGURE 4


punishments; likewise, the insane or the young are probably less affectedthan other offenders by future consequences and, therefore,33 probablyless deterred by increases in the probability of conviction or in the pun-ishment when convicted. The trend during the twentieth century towardrelatively smaller prison terms and greater use of probation and therapyfor such groups and, more generally, the trend away from the doctrine of"a given punishment for a given crime" is apparently at least broadlyconsistent with the implications of the optimality analysis.

An increase in b increases the marginal revenue from changing thenumber of offenses by changing p orf and thereby increases the optimalnumber of offenses, reduces the optimal value off, and increases the opti-mal value of p. Some evidence presented in Section II indicates that b isespecially large for juveniles in detention homes or adults in prison andis small for fines or adults on parole. The analysis implies, therefore, thatother things the same, the optimal f's would be smaller and the optimalp's larger if punishment were by one of the former rather than one of thelatter methods.

V. FINES

of the payment "b'society, and a net sioffenses then beconditions, because itchange in punishme

Although trans:today, the other isCommunist countriother punishments awaiting-time formsing (see Becker, 196conditions. It is mtoptimality conditiorassumptions about t

B. OPTIMALITY Co

If b = 0, say, becauhending and convicconditions (21) and

A. WELFARE THEOREMS AND TRANSFERABLE PRICING

The usual optimality conditions in welfare economics depend only on thelevels and not on the slopes of marginal cost and average revenue func-tions, as in the well-known condition that marginal costs equal prices.The social loss from offenses was explicitly introduced as an applicationof the approach used itt welfare economics, and yet slopes as incorporatedinto elasticities of supply do significantly affect the optimality conditions.Why this difference? The primary explanation would appear to be thatit is almost always implicitly assumed that prices paid by consumers arefully transferred to firms and governments, so that there is no social lossfrom payment.

If there were no social loss from punishments, as with fines, b wouldequal zero, and the elasticity of supply would drop out of the optimalitycondition given by equation If b > 0, as with imprisonment, some

33. But see Becker (1962) for an analysis indicating that impulsive and other "irra-tional" persons may be as deterred from purchasing a commodity whose price has risenas more "rational" persons.

34. It remains in eq. (22), through the slope because ordinarily prices do not affectmarginal costs, while they do here through the influence of p on C.

Economists generallsuch as factories thlland, should be taxeexternal harm equal.net damages equaledharm always exceedsumed to be zero, a:suitable inequality ccof apprehending, conoffense caused moreoffenses would beeliminate all offenseswith the criterion 01high.35

Equation (24) dthe fine and probabi

35. "The evil of the(Bentham, 1931, first rule


of the payment "by" offenders would not be received by the rest ofsociety, and a net social loss would result. The elasticity of the supply ofoffenses then becomes an important determinant of the optimality con-ditions, because it determines the change in social costs caused by achange in punishments.

Although transferable monetary pricing is the most common kindtoday, the other is not unimportant, especially in underdeveloped andCommunist countries. Examples in addition to imprisonment and manyother punishments are the draft, payments in kind, and queues and otherwaiting-time forms of rationing that result from legal restrictions on pric-ing (see Becker, 1965) and from random variations in demand and supplyconditions. it is interesting, and deserves further exploration, that theoptimality conditions are so significantly affected by a change in theassumptions about the transferability of pricing.

B. OPTEMALITY CoNDITIoNs

If b = 0, say, because punishment was by fine, and if the cost of appre-hending and convicting offenders were also zero, the two optinialityconditions (21) and (22) would reduce to the same simple condition

D'(O) 0. (24)

Economists generally conclude that activities causing "external" harm,such as factories that pollute the air or lumber operations that strip theland, should be taxed or otherwise restricted in level until the marginalexternal harm equaled the marginal private gain, that is, until marginalnet damages equaled zero, which is what equation (24) says. If marginalharm always exceeded marginal gain, the optimum level would be pre-sumed to be zero, and that would also be the implication of (24) whensuitable inequality conditions were brought in. In other words, if the costsof apprehending, convicting, and punishing offenders were nil and if eachoffense caused more external harm than private gain, the social loss fromoffenses would be minimized by setting punishments high enough toeliminate all offenses. Minimizing the social loss would become identicalwith the criterion of minimizing crime by setting penalties sufficientlyhigh.35

Equation (24) determines the optimal number of offenses, O, andthe fine and probability of conviction must be set at levels that induce

35. "The evil of the punishment must be made to exceed the advantage of the offense"(Bentham, 1931, first rule).

obably less affectedherefore,33 probablyiction or in the pun-tieth century towardobation and therapyfrom the doctrine oftly at least broadly

alysis.e from changing the

increases the optimalincreases the opti-

II indicates that b isin prison and

nplies, therefore, thatand the optimal

rather than one of the

CING

depend only on thetverage revenue func-

I costs equal prices.ced as an applicationopes as incorporatedptimality conditions.

appear to be thatby consumers are

there is no social loss

s with fines, b would)ut of the optimalityimprisonment, some

npulsive and other "irra-ity whose price has risen

narily prices do not affectC.


offenders to commit just O offenses. If the economists' usual theory ofchoice is applied to illegal activities (see Sec. II), the marginal value ofthese penalties has to equal the marginal private gain:

V= G'(O), (25)

where G '(O) is the marginal private gain at O and V is the monetary valueof the marginal penalties. Since by equations (3) and (24), D'(O) = H'(O)— G'(O) = 0, one has by substitution in (25)

V= H'(O). (26)

The monetary value of the penalties would equal the marginal harmcaused by offenses.

Since the cost of apprehension and conviction is assumed equal tozero, the probability of apprehension and conviction could be set equalto unity without cost. The monetary value of penalties would then simplyequal the fines imposed, and equation (26) would become

f = H'(Ô). (27)

Since fines are paid by offenders to the rest of society, a fine determinedby (27) would exactly compensate thelatter for the marginal harm suf-fered, and the criterion of minimizing the social loss would be identical,at the margin, with the criterion of compensating "victims." if the harmto victims always exceeded the gain to offenders, both criteria wouldreduce in turn to eliminating all offenses.

If the cost of apprehension and conviction were not zero, the optimal-ity condition would have to incorporate marginal costs as well as marginaldamages and would become, if the probability of conviction were stillassumed to equal unity,

D'(O)+C'(O, 1)=0. (28)

Since C' > 0, (28) requires that D' < 0 or that the marginal private gainexceed the marginal external harm, which generally means a smallernumber of offenses than when D' = It is easy to show that equation(28) would be satisfied if the fine equaled the sum of marginal harm andmarginal costs:

36. By "victims" is meant the rest of society and not just the persons actually harmed.37. This result can also be derived as a special case of the results in the Mathematical

Appendix on the effects of increases in C'.

In other words, offthem as well as for Iization of the usual

The optimality

- D'

would replace equalconviction were fixe> 0,39 and thus thatnumber when costsVictjon increase or dpends, therefore, onfine or in the probabjcontrol, the optimal j:

to zero, unless the scthe discussion in Sec.

C. THE CASE FOR F

Just as the probabiljt3subject to control by susually specifies wheiinstitutionalization or

38. Since equilibrium ri

then (29) follows directly by

39. That is, if, as seems

then

and


sts' usual theory ofe marginal value of

(25)

the monetary value(24), D'(O) = H(O)

(26)

the marginal harm

assumed equal tocould be set equalwould then simply

kome

(27)

a fine determinedmarginal harm suf-would be identical,

'ctims." 36 If the harmtboth criteria would

z.ero, the optimal-Ls as well as marginal:onviction were still

(28)

private gainly means a smallershow that equation

f marginal harm and

persons actually harmed.suits in the Mathematical

f= H'(O) + C'(O, l).38 (29)

In other words, offenders have to compensate for the cost of catchingthem as well as for the harm they directly do, which is a natural general-ization of the usual externality analysis.

The optimality condition

D'(O) + C'(O, j5) + CP(O, j5) =0 (30)

would replace equation (28) if the fine rather than the probability ofConviction were fixed. Equation (30) would usually imply that D'(O)> and thus that the number of offenses would exceed the optimalnumber when costs were zero. Whether costs of apprehension and con-viction increase or decrease the optimal number of offenses largely de-pends, therefore, on whether penalties are changed by a change in thefine or in the probability of conviction. Of course, if both are subject tocontrol, the optimal probability of conviction would be arbitrarily closeto zero, unless the social loss function differed from equation (18) (seethe discussion in Sec. III).

C. THE CASE FOR FINES

Just as the probability of conviction and the severity of punishment aresubject to control by society, so too is the form of punishment: legislationusually specifies whether an offense is punishable by fines, probation,institutionalization, or some combination. Is it merely an accident, or

38. Since equilibrium requires thatf= G'(O), and since from (28)

0(O) = H'(O) — G'(O) = — C'(O, 1),

then (29) follows directly by substitution.

39. That is, if, as seems plausible,

then

and

= ± > 0,dp ap

C, + <0,

D'(O) = _(c' + c,. > 0.


have optimality considerations determined that today, in most countries,fines are the predominant form of punishment, with institutionalization re-served for the more serious offenses? This section presents several argu-ments which imply that social welfare is increased if fines are used it'hen-ever feasible.

In the first place, probation and institutionalization use up social re-sources, and fines do not, since the latter are basically just transfer pay-ments, while the former use resources in the form of guards, supervisorypersonnel, probation officers, and the offenders' own time.4° Table 1 indi-cates that the cost is not minor either: in the United States in 1965, about$1 billion was spent on "correction," and this estimate excludes, ofcourse, the value of the loss in offenders' time.41

Moreover, the determination of the optimal number of offenses andseverity of punishments is somewhat simplified by the use of fines. Awise use of fines requires knowledge of marginal gains and harm and ofmarginal apprehension and conviction costs; admittedly, such knowledgeis not easily acquired. A wise user of imprisonment and other punish-ments must know this too, however; and, in addition, must know aboutthe elasticities of response of offenses to changes in punishments. As thebitter controversies over the abolition of capital punishment suggest, ithas been difficult to learn about these elasticities.

I suggested earlier that premeditation, sanity, and age can enter intothe determination of punishments as proxies for the elasticities of re-sponse. These characteristics may not have to be considered in levyingfines, because the optimal fines, as determined, say, by equations (27)or (29), do not depend on elasticities. Perhaps this partly explains whyeconomists discussing externalities almost never mention motivation orintent, while sociologists and lawyers discussing criminal behavior in-variably do. The former assume that punishment is by a monetary tax orfine, while the latter assume that nonmonetary punishments are used.

Fines provide compensation to victims, and optimal fines at the mar-gin fully compensate victims and restore the status quo ante, so that

40. Several early writers on criminology recognized this advantage of fines. For ex-ample. "Pecuniary punishments are highly economical, since all the evil felt by him whopays turns into an advantage for him who receives" (Bentham, 1931, chap. vi), and "Im-prisonment would have been regarded in these old times Ica. tenth as a uselesspunishment; it does not satisfy revenge, it keeps the criminal idle, and do what we may,ii is cost/v' (Pollock and Maitland, 1952, p. 516; my italics).

41. On the other hand, some transfer payments in the form of food, clothing, andshelter are included.

they are no worse 01other punishmentsspend additional resprising, therefore, thfact have not "paidpunishments,43 incluopportunities and

absenotherwise "rehabilitherapy, and other pimuch additional costsons do not easily dusually levied againhabilitate" them.

One argument nin effect, they permitbread or other gooththe price of an offemexample, the "price'only difference is inin monetary units, inIf anything, monetarpreferred iii pricing a

Optimal fines dmarginal harm and ccers. This has been ci

42. Bentham recogniianother useful quality in apunishing an offense andto alarm. This is a charact

43. In the same way.society, has led to addit,bonuses, hospitalization ri

44. See Sutherland (I45. The very early Et

it has been said that "eveprice, and much of the juthese preappointed prices'

The same idea was ppolice car carrying a signspeed limit—pick Out spee


y, in most countries,stitutionalization re-

resents several argu-fines are used when-

tion use up social re-ily just transfer pay-

I guards, supervisoryTable 1 mdi-

in 1965, aboutestimate excludes, of

of offenses andthe use of fines. A

and harm and ofsuch knowledge

and other punish-on, must know about

As thesuggest, it

d age can enter intothe elasticities of re-

in levyingby equations (27)

partly explains whyention motivation orcriminal behavior in-by a monetary tax ortishments are used.ma! fines at the mar-s quo ante, so that

vantage of fines. For cx-the evil felt by him who1931, chap. vi), and "Im-nth century] as a uselessle, and do what we may,

rn of food, clothing, and

they are no worse off than if offenses were not committed.42 Not only doother punishments fail to compensate, but they also require "victims" tospend additional resources in carrying out the punishment. It is not sur-prising, therefore, that the anger and fear felt toward ex-convicts who infact have not "paid their debt to society" have resulted in additionafpunishments,43 including legal restrictions on their political and economicopportunities and informal restrictions on their social acceptance.Moreover, the absence of compensation encourages efforts to change andotherwise "rehabilitate" offenders through psychiatric counseling,therapy, and other programs. Since fines do compensate and do not createmuch additional cost, anger toward and fear of appropriately fined per-sons do not easily develop. As a result, additional punishments are notusually levied against "ex-finees," nor are strong efforts made to "re-habilitate" them.

One argument made against fines is that they are immoral because,in effect, they permit offenses to be bought for a price in the same way thatbread or other goods are bought for a price.45 A fine can be consideredthe price of an offense, but so too can any other form of punishment; forexample, the "price" of stealing a car might be six months in jail. Theonly difference is in the units of measurement: fines are prices measuredin monetary units, imprisonments are prices measured in time units, etc.If anything, monetary units are to be preferred here as they are generallypreferred in pricing and accounting.

Optimal fines determined from equation (29) depend only on themarginal harm and cost and not at all on the economic positions of offend-ers. This has been criticized as unfair, and fines proportional to the in-

42. Bentham recognized this and said, "To furnish an indemnity to the injured party isanother useful quality in a punishment. It is a means of accomplishing two objects at once—punishing an offense and repairing it: removing the evil of the first order, and putting a stopto alarm. This is a characteristic advantage of pecuniary punishments" (1931, chap. vi).

43. In the same way, the guilt felt by society in using the draft, a forced transfer tosociety, has led to additional payments to veterans in the form of education benefits,bonuses, hospitalization rights, etc.

44. See Sutherland (1960, pp. 267—68) for a list of some ut these.45. The very early English law relied heavily on monetary fines, even for murder, and

it has been said that "every kind of blow or wound given to every kind of person had itsprice, and much of the jurisprudence of the time must have consisted of a knowledge ofthese preappointed prices" (Pollock and Maitland, 1952, p. 451).

The same idea was put amusingly in a recent Mutt and Jeff cartoon which showed apolice car carrying a sign that read: "Speed limit 30 M per H—$5 fine every mile overspeed limit—pick out speed you can afford."


comes of offenders have been suggested.46 If the goal is to minimize thesocial loss in income from offenses, and not to take vengeance or to inflictharm on offenders, then fines should depend on the total harm done byoffenders, and not directly on their income, race, sex, etc. In the sameway, the monetary value of optimal prison sentences and other punish-ments depends on the harm, costs, and elasticities of response, but notdirectly on an offender's income. Indeed, if the monetary value of thepunishment by, say, imprisonment were independent of income, thelength of the sentence would be inversely related to income, because thevalue placed on a given sentence is positively related to income.

We might detour briefly to point out some interesting implicationsfor the probability of conviction of the fact that the monetary value of agiven fine is obviously the same for all offenders, while the monetaryequivalent or "value" of a given prison sentence or probation period isgenerally positively related to an offender's income. The discussion inSection 11 suggested that actual probabilities of conviction are not fixedto all offenders but usually vary with their age, sex, race, and, in particu-lar, income. Offenders with higher earnings have an incentive to spendmore on planning their offenses, on good lawyers, on legal appeals, andeven on bribery to reduce the probability of apprehension and convictionfor offenses punishable by, say, a given prison term, because the cost tothem of conviction is relatively large compared to the cost of these ex-penditures. Similarly, however, poorer offenders have an incentive touse more of their time in planning their offenses, in court appearances, andthe like, to reduce the probability of conviction for offenses punishableby a given fine, because the cost to them of conviction is relatively largecompared to the value of their time.47 The implication is that the prob-ability of conviction would be systematically related to the earnings ofoffenders: negatively for offenses punishable by imprisonment and pos-itively for those punishable by fines. Although a negative relation for

46. For example, Bentham said, "A pecuniary punishment, if the sum is fixed, is in thehighest degree unequal. . . Fines have been determined without regard to the profit of theoffense, to its evil, or to the wealth of the offender. . . . Pecuniary punishments should al-ways be regulated by the fortune of the offender. The relative amount of the fine should befixed, not its absolute amount; for such an offense, such a part of the offender's fortune"(1931, chap. ix). Note that optimal fines, as determined by eq. (29), do depend on "the profitof the offense" and on "its evil."

47. Note that the incentive to use time to rcduce the probability of a given prison sen-tence is unrelated to earnings, because the punishment is fixed in time, not monetary, units;likewise, the incentive to use money to reduce the probability of a given fine is also unrelatedto earnings, because the punishment is fixed in monetary, not time, units.

felonies and other cquently observed an139—53), 1 do not knrecognition that thequence of the nature

Another argumcmurder or rape, arepensate the harmspecial case of the nexclusively wheneve:then victims could nohave to be supplemerto discourageprobation, and paroleies; considerable hanresources to compenneed for a flexiblefines more readily an

This analysis imgiven offense and oth'by fine and the lattethese methodsfore the cry is raised ticonsider the follOwin1

Those punishedagreed to by their "

for which sucreditors. Moreover,voluntary market trat"debtors" and others.one, the former is cowhen apprehended. Ysubsequentlythe poor man, in effec

Whether a punisoffenders lacking suffi

48. In one study, abou(see President's Commissk

49. The "debtor prisorepay loans.


al is to minimize theengeance or to inflicttotal harm done by

ex, etc. In the sameand other punish-

of response, but notonetary value of thelent of income, theincome, because thed to income.eresting implicationsmonetary value of awhile the monetary

fr probation period isThe discussion in

riviction are not fixedand, in particu-

in incentive to spendlegal appeals, and

and convictionbecause the cost to

cost of these ex-aye an incentive tourt appearances, andoffenses punishable

Ion is relatively largeis that the prob-

to the earnings ofprisonment and pos-kegative relation for

the sum is fixed, is in theregard to the profit of they punishments should al-ount of the fine should bef the offender's fortune",do depend on 'the profit

ity of a given prison sen-me, not monetary, units;iven fine is also unrelatede, units.

felonies and other offenses punishable by imprisonment has been fre-quently observed and deplored (see President's Commission, 1967c, pp.1 39—53), I do not know of any studies of the relation for fines or of anyrecognition that the observed negative relation may be more a conse-quence of the nature of the punishment than of the influence of wealth.

Another argument made against fines is that certain crimes, likemurder or rape, are so heinous that no amount of money could com-pensate for the harm inflicted. This argument has obvious merit and is aspecial case of the more general principle that fines cannot be relied onexclusively whenever the harm exceeds the resources of offenders. Forthen victims could not be fully compensated by offenders, and fines wouldhave to be supplemented with prison terms or other punishments in orderto discourage offenses optimally. This explains why imprisonments,probation, and parole are major punishments for the more serious felon-ies; considerable harm is inflicted, and felonious offenders lack sufficientresources to compensate. Since fines are preferable, it also suggests theneed for a flexible system of instalment fines to enable offenders to payfines more readily and thus avoid other punishments.

This analysis implies that if some offenders could pay the fine for agiven offense and others could not,48 the former should be punished solelyby fine and the latter partly by other methods. In essence, therefore,these methods become a vehicle for punishing "debtors" to society. Be-fore the cry is raised that the system is unfair, especially to poor offenders,consider the following.

Those punished would be debtors in "transactions" that were neveragreed to by their "creditors," not in voluntary transactions, such asloans,48 for which suitable precautions could be taken in advance bycreditors. Moreover, punishment in any economic system based onvoluntary market transactions inevitably must distinguish between such"debtors" and others. If a rich man purchases a car and a poor man stealsone, the former is congratulated, while the latter is often sent to prisonwhen apprehended. Yet the rich man's purchase is equivalent to a "theft"subsequently compensated by a "fine" equal to the price of the car, whilethe poor man, in effect, goes to prison because he cannot pay this "fine."

Whether a punishment like imprisonment in lieu of a full fine foroffenders lacking sufficient resources is "fair" depends, of course, on the

48. In one study, about half of those convicted of misdemeanors could not pay the fines(see President's Commission, 1967c. p. 148).

49. The "debtor prisons" of earlier centuries generally housed persons who could notrepay loans.


larger than $1,000 amonths or a fine nc1030, Arts. 70 andexcessive prison seiimprisonment in lietoften must "choose',

D. COMPENSATION'

Actual criminal procof deterrence, comfthat these goals aresimultaneously achiminimizing the sodasating "victims" fu.partially pursued. Tbishment by optimalcriminal law would

First and forembecome the same: nment of the "harm"would become a bralthe public would coIlwould be defined funthe inability of a perThus an action woulcpensated "harm" towhile tort law would

As a practical ewrought, consider thclassic demonstratiorand reduce econom;

52. "Violations,"days or fines no largerimposed by the courts canpunish by imprisonment, b

53. "The cardinalcompensation for the injulJames, 1956, p. 1299).

54. Of course, many Ibe criminal under this app

length of the prison term compared to the fine.50 For example, a prisonterm of one week in lieu of a $10,000 fine would, if anything, be "unfair"to wealthy offenders paying the fine. Since imprisonment is a more costlypunishment to society than fines, the loss from offenses would be reducedby a policy of leniency toward persons who are imprisoned because theycannot pay fines. Consequently, optimal prison terms for "debtors" wouldnot be "unfair" to them in the sense that the monetary equivalent to themof the prison terms would be less than the value of optimal fines, which inturn would equal the harm caused or the "debt." 51

It appears, however, that "debtors" are often imprisoned at rates ofexchange with fines that place a low value on time in prison. Although Ihave not seen systematic evidence on the different punishments actuallyoffered convicted offenders, and the choices they made, many statutes inthe United States do permit fines and imprisonment that place a low valueon time in prison. For example, in New York State, Class A Misde-meanors can be punished by a prison term as long as one year or a fine no

50. \'et without any discussion of the actual alternatives offered, the statement is madethat "the money judgment assessed the punitive damages defendant hardly seems compara-ble in effect to the criminal sanctions of death, imprisonment, and stigmatization" ("CriminalSafeguards 1967).

SI. A formal proof is straightforward if for simplicity the probability of conviction istaken as equal to unity. For then the sole optimality condition is

(1')\

Since D' = H' — C', by substitution one has

(2')

and since equilibrium requires that C' =f,

1= H' + C' + bf(l (3')

or

H'+C', (4')

I — b(I — 11€,)

If b > 0, €, < I (see Sec. 111), and hence by eq. (4'),

(5')

where the term on the right is the full marginal harm. If p as well asfis free to vary, theanalysis becomes more complicated, but the conclusion about the relative monetary valuesof optimal imprisonments and fines remains the same (see the Mathematical Appendix).


or example, a prisonnything, be "unfair"nent is a more costlyes would be reduced•isoned because theyfor "debtors" wouldy equivalent to them

ptimal fines, which in

nprisoned at rates ofin prison. Although I1punishments actuallyçade., many statutes in'that place a low valuetate, Class A Misde-

one year or a fine no

cred, the statement is madehardly seems corn

('Criminal

probability of conviction is

(1')

(2')

(3')

(4')

(5')

II asfis free to vary, therelative monetary values

Mathematical Appendix).

larger than $1,000 and Class B Misdemeanors, by a term as long as threemonths or a fine no larger than $500 (Laws of New York, 1965, chap.1030, Arts. 70 and 80).52 According to my analysis, these statutes permitexcessive prison sentences relative to the fines, which may explain whyimprisonment in lieu of fines is considered unfair to poor offenders, whooften must "choose" the prison alternative.

D. COMPENSATION AND THE CRIMINAL LAW

Actual criminal proceedings in the United States appear to seek a mixtureof deterrence, compensation, and vengeance. I have already indicatedthat these goals are somewhat contradictory and cannot generally besimultaneously achieved; for example, if punishment were by fine,minimizing the social loss from offenses would be equivalent to compen-sating "victims" fully, and deterrence or vengeance could only bepartially pursued. Therefore, if the case for fines were accepted, and pun-ishment by optimal fines became the norm, the traditional approach tocriminal law would have to be significantly modified.

First and foremost, the primary aim of all legal proceedings wouldbecome the same: not punishment or deterrence, but simply the assess-ment of the "harm" done by defendants. Much of traditional criminal lawwould become a branch of the law of torts,53 say "social torts," in whichthe public would collectively sue for "public" harm. A "criminal" actionwould be defined fundamentally not by the nature of the action but bythe inability of a person to compensate for the "harm" that he caused.Thus an action would be "criminal" precisely because it results in uncom-pensated "harm" to others. Criminal law would cover all such actions,while tort law would cover all other (civil) actions.

As a practical example of the fundamental changes that would bewrought, consider the antitrust field. Inspired in part by the economist'sclassic demonstration that monopolies distort the allocation of resourcesand reduce economic welfare, the United States has outlawed con-

52. "Violations," however, can only be punished by prison terms as long as fifteendays or fines no larger than $250. Since these are maximum punishments, the actual onesimposed by the courts can, and often are, considerably less. Note, too, that the courts canpunish by imprisonment, by fine, or by both(La,i's of York, 1965, chap. 1030, Art. 60).

53. "The cardinal principle of damages in Anglo-American law [of torts] is that ofconzpensatiolz for the injury caused to plaintiff by defendant's breach of duty" (Harper andJames, 1956, p. 1299).

54. Of course, many traditional criminal actions like murder or rape would still usuallybe criminal under this approach too.


spiracies and other constraints of trade. In practice, defendants are oftensimply required to cease the objectionable activity, although sometimesthey are also fined, become subject to damage suits, or are jailed.

if compensation were stressed, the main purpose of legal proceedingswould be to levy fines equal to the harm inflicted on society by con-straints of trade. There would be no point to cease and desist orders,imprisonment, ridicule, or dissolution of companies. If the economist'stheory about monopoly is correct, and if optimal fines were levied, firmswould automatically cease any constraints of trade, because the gain tothem would be less than the harm they cause and thus less than the finesexpected. On the other hand, if Schumpeter and other critics are correct,and certain constraints of trade raise the level of economic welfare,fines could fully compensate society for the harm done, and yet someconstraints would not cease, because the gain to participants would ex-ceed the harm to others.56

One unexpected advantage, therefore, from stressing compensationand fines rather than punishment and deterrence is that the validity of theclassical position need not be judged a priori. If valid, compensatingfines would discourage all constraints of trade and would achieve theclassical aims. If not, such fines would permit the socially desirableconstraints to continue and, at the same time, would compensate societyfor the harm done.

Of course, as participants in triple-damage suits are well aware, theharm done is not easily measured, and serious mistakes would be inevit-able. However, it is also extremely difficult to measure the harm in manycivil suits,57 yet these continue to function, probably reasonably well onthe whole. Moreover, as experience accumulated, the margin of errorwould decline, and rules of thumb would develop. Finally, one must

55. Actually, fines should exceed the harm done if the probability of conviction wereless than unity. The possibility of avoiding conviction is the intellectual justification forpunitive, such as triple, damages against those convicted.

56. The classical view is that D'(M) always is greater than zero, where M measuresthe different constraints of trade and D' measures the marginal damage; the critic's view isthat for some Al, D'(M) < 0. It has been shown above that if D' always is greater thanzero, compensating fines would discourage all offenses, in this case constraints of trade,while if D' sometimes is less than zero, some offenses would remain (unless themarginal cost of detecting and convicting offenders, were sufficiently large relative to D').

57. Harper and James said, "Sometimes [compensation] can be accomplished witha fair degree of accuracy. But obviously it cannot be done in anything but a figurativeand essentially speculative way for many of the consequences of personal injury. Yet it isthe aim of the law to attain at least a rough correspondence between the amount awarded asdamages and the extent of the suffering" (1956, p. 1301).

realize that difficult jupolicy, such as decidirtive or that certain rnand compensation wotattention on the infor

Vi. PRIVATE EXPI

A variety of privatenumber and incidenceemployed, locks and aland neighborhoods avand so on. Table I listand this undoubtedly iprivate action is esreconomies, where freqhis person, to the "car

If each person tncrimes, optimal privatdiscussion of optimalsimilar to that given b

= H

The term represeragainst j, while C,, reprtion of p,, for offensespositively related to 0tures on crime, andpersons.58

The termof offenders committirin a net loss to societyvictims. For example,just a transfer paymen

58. An increase in C1againstj, because more of i

59. The expectedsiderable variance becauseany single person. 1ff weredude a term that dependec

GARY S. BECKER 35

realize that difficult judgments are also required by the present antitrustpolicy, such as deciding that certain industries are "workably" competi-tive or that certain mergers reduce competition. An emphasis on finesand compensation would at least help avoid irrelevant issues by focusingattention on the information iftost needed for intelligent social policy.

VI. PRIVATE EXPENDITURES AGAINST CRIME

A variety of private as well as public actions also attempt to reduce thenumber and incidence of crimes: guards, doormen, and accountants areemployed, locks and alarms installed, insurance coverage extended, parksand neighborhoods avoided, taxis used in place of walking or subways,and so on. Table 1 lists close to $2 billion of such expenditures in 1 965,and this undoubtedly is a gross underestimate of the total. The need forprivate action is especially great in highly interdependent moderneconomies, where frequently a person must trust his resources, includinghis person, to the "care" of employees, employers, customers, or sellers.

If each person tries to minimize his expected loss in income fromcrimes, optimal private decisions can be easily derived from the previousdiscussion of optimal public ones. For each person there is a loss functionsimilar to that given by equation (18):

+ C)(p), C, + (3 1)

The term represents the harm to j from the 0) offenses committedagainstj, while C, represents his cost of achieving a probability of convic-tion of for offenses committed against him. Note that C2 not only ispositively related to 0,, but also is negatively related to C, public expendi-tures on crime, and to Ck, the set of private expenditures by otherpersons.58

The term measures the expected loss toj from punishmentof offenders committing any of the 0,,. Whereas most punishments resultin a net loss to society as a whole, they often produce a gain for the actualvictims. For example, punishment by fines given to the actual victims isjust a transfer payment for society but is a clear gain to victims; similarly,

58. An increase in C1, — 0,, and C held constant—presumably helps solve offensesagainstj, because more of those against k would be solved.

59. The expected private loss, unlike the expected social loss, is apt to have con-siderable variance because of the small number of independent offenses committed againstany single person. 1ff were not risk neutral, therefore, L would have to be modified to in-clude a term that depended on the distribution of

C APPROACH

, defendants are often',although sometimess, or are jailed.se of legal proceedings

on society by con-ise and desist orders,es. If the economist'snes were levied, firmse, because the gain tohus less than the finesler critics are correct,

economic welfare,rn done, and yet someparticipants would ex-

tressing compensationthe validity of the

valid, compensatingwould achieve thesocially desirable

tid compensate society

Us are well aware, thewould be inevit-

sure the harm in manyly reasonably well on

the margin of errorp. Finally, one must

bability of conviction werejustification for

zero, where M measuresdamage; the critic's view is

D' always is greater thancase constraints of trade,remain (unless C'[M], theently large relative to D').can be accomplished with

anything but a figurativef personal injury. Yet it iseen the amount awarded as

probability of apprelable, and in treatingwell as by monetaryanalytically from anwhen crimes are punvanish.

Discussions offectly symmetrical toanalogues to the lawcannot be collectedcaused, and no publitorneys apprehend atcourse, there is publiother, privilegesofficials, scientists,private bodies. Amorthe Congressionalthese are piecemealand lack the guidancferent kinds of advan

Possibly the expdeveloped at the timvantages, or possiblyconsidered too pronemetry in the law doformal analysis of ad'that is quite symmetrers. A function A(Bfrom B benefits in thoffenses. Likewise,rewarding benefactoiand > 0; B(p1, aaward per benefit anaB/aa> 0; and b1 castead of a loss funcoffenses, there can 1from benefits:

If 11 is maximizoptimality condition:


punishment by imprisonment is a net loss to society but is a negligibleloss to victims, since they usually pay a negligible part of imprisonmentcosts. This is why is often less than or equal to zero, at the same timethat b, the coefficient of social loss, is greater than or equal to zero.

Since are determined primarily by public policy on punish-ments, the main decision variable directly controlled by j is p,. If hechooses a p,, that minimizes the optimality condition analogous toequation (22) is

a / 1\60u' i_ c" c' — 1lAj T — —€)Pj

The elasticity measures the effect of a change in on the number ofoffenses committed against j. If b, < 0, and if the left-hand side of equa-tion (32), the marginal cost of changing were greater than zero, then(32) implies that > 1. Since offenders can substitute among victims,

is probably much larger than E,,, the response of the total number ofoffenses to a change in the average probability, p. There is no incon-sistency, therefore, between a requirement from the optimality condi-tion given by (22) that ç < I and a requirement from (32) that > 1.

VII. SOME APPLICATIONS

A. OPTIMAL BENEFITS

Our analysis of crime is a generalization of the economist's analysis ofexternal harm or diseconomies. Analytically, the generalization consistsin introducing costs of apprehension and conviction, which make the

60. 1 have assumed that

äCk— = — = 0,3p,

in other words, that j is too "unimportant" to influence other expenditures. Althoughusually reasonable, this does suggest a modification to the optimality conditions givenby eqs. (21) and (22). Since the effects of public expenditures depend on the level of privateones, and since the public is sufficiently "important" to influence private actions, eq. (!2)has to be modified to

(22')

and similarly for eq. (21). "The" probability p is, of course, a weighted average of thep,. Eq. (22') incorporates the presumption that an increase in public expenditures would bepartially thwarted by an induced decrease in private ones.


Discussions of external economies or advantages are usually per-fectly symmetrical to those of diseconomies, yet one searches in vain foranalogues to the law of torts and criminality. Generally, compensationcannot be collected for the external advantages as opposed to harmcaused, and no public officials comparable to policemen and district at-torneys apprehend and "convict" benefactors rather than offenders. Ofcourse, there is public interest in benefactors: medals, prizes, titles, andother privileges have been awarded to military heroes, governmentofficials, scientists, scholars, artists, and businessmen by public andprivate bodies. Among the most famous are Nobel Prizes, Lenin Prizes,the Congressional Medal of Honor, knighthood, and patent rights. Butthese are piecemeal efforts that touch a tiny fraction of the populationand lack the guidance of any body of law that codifies and analyzes dif-ferent kinds of advantages.

Possibly the explanation for this lacuna is that criminal and tort lawdeveloped at the time when external harm was more common than ad-vantages, or possibly the latter have been difficult to measure and thusconsidered too prone to favoritism. In any case, it is clear that the asym-metry in the law does not result from any analytical asymmetry, for aformal analysis of advantages, benefits, and benefactors can be developedthat is quite symmetrical to the analysis of damages, offenses, and offend-ers. A function A(B), for example, can give the net social advantagesfrom B benefits in the same way that D(O) gives the net damages from 0offenses. Likewise, K(B, can give the cost of apprehending andrewarding benefactors, where Pi is the probability of so doing, with K'and > 0; B(p1, a, v) can give the supply of benefits, where a is theaward per benefit and v represents other determinants, with aB/ap1 andäB/3a > 0; and b1 can be the fraction of a that is a net loss to society. In-stead of a loss function showing the decrease in social income fromoffenses, there can be a profit function showing the increase in incomefrom benefits:

II = A(B) — K(B, Pi) — b1p1aB.

If [I is maximized by choosing appropriate values of p1 and a, theoptimality conditions analogous to equations (21) and (22) are

probability of apprehension and conviction an important decision vari-able, and in treating punishment by imprisonment and other methods aswell as by monetary payments. A crime is apparently not so differentanalytically from any other activity that produces external harm andwhen crimes are punishable by fines, the analytical differences virtuallyvanish.

y but is a negligibleart of imprisonmentro, at the same timetr equal to zero.lic policy on punish-led by j is p3. If heridition analogous to

60

(32)

on the number offt-hand side of equa-eater than zero, thentitute among victims,f the total number of

p. There is no incon-the optimality condi-rom (32) that > 1.

)nomist's analysis ofneralization consistson, which make the

r expenditures. Althoughtimality conditions givenend on the level of privatee private actions, eq. (!2)

(22')€p /

weighted average of theblic expenditures would be

(33)

38 CRIME AND PUNISHMENT: AN EcoNoMIc APPROACH

marginal income of cless risky legal activi"benefits do pay"—i:factors wouldthis sense it "pays" I

As an illustratioinventors for their iivalue of B inventionone. The function K(tors; if a patent systepreparing applicatiorin patent litigation.62inventors to changesb, measures thea patent system, thethan would otherwis

Equations (34) athe smaller the elastithe probability and nchanged, for exampitthe controversyfrom a basic desirefrom the prospects ofon systematic invesquite consistently ustequally consistently

Even if A', the roptimal decision wouis, to set p, = 0, ife,, and Ca sufficientlyor greatly alter the pcostliness, large K oiexample, Plant, 1934

If a patent systerticities of response

62. These costs are ialone spent $34 million (sspent in preparing applicat

63. Presumably one r'(that is, cost) of discoverir

A' — K' = b,p,a (i +1) (34)

and

(35)

where

a

and

Pi=

are both greater than zero. The implications of these equations are relatedto and yet differ in some important respects from those discussed earlierfor (21) and (22).

For example, if b, > 0, which means that a is not a pure transfer butcosts society resources, clearly (34) and (35) imply that e5 > sinceboth > 0 and ap1/3B > 0. This is analogous to the implication of(21)and (22) that > e,, but, while the latter implies that, at the margin,offenders are risk preferrers, the former implies that, at the margin, bene-factors are risk avoiders.6' Thus, while the optimal values of p and fwould be in a region where "crime does not pay"—in the sense that the

61. The relation e9 > e0 holds if, and only if,

3EUp, aEUa(1')

where

(2')

(see the discussion on pp. 177—78). By differentiating eq. (2'), one can write (I') as

p,[U(Y+a)— U(Y)] > a), (3')

or

U(Y+a)—U(Y) U'(Y+a). (4')

But (4') holds if everywhere U" < 0 and does not hold if everywhere U" 0, which was tobe proved.

GARY S. BECKER 39

marginal income of criminals would be less than that available to them inless risky legal activities—the optimal values of p1 and a would be where"benefits do pay"—in the same sense that the marginal income of bene-factors would exceed that available to them in less risky activities. Inthis sense it "pays" to do "good" and does not "pay" to do "bad."

As an illustration of the analysis,.consider the problem of rewardinginventors for their inventions. The function A(B) gives the total socialvalue of B inventions, and A' gives the marginal value of an additionalone. The function K(B, Pi) gives the cost of finding and rewarding inven-tors; if a patent system is used, it measures the cost of a patent office, ofpreparing applications, and of the lawyers, judges, and others involvedin patent litigation.62 The elasticities e,, and e0 measure the response ofinventors to changes in the probability and magnitude of awards, whileb1 measures the social cost of the method used to award inventors. Witha patent system, the cost consists in a less extensive use of an inventionthan would otherwise occur, and in any monopoly power so created.

Equations (34) and (35) imply that with any system having b1 > 0,the smaller the elasticities of response of inventors, the smaller should bethe probability and magnitude of awards. (The value of a patent can bechanged, for example, by changing its life.) This shows the relevance ofthe controversy between those who maintain that most inventions stemfrom a basic desire "to know" and those who maintain that most stemfrom the prospects of financial awards, especially today with the emphasison systematic investment in research and development. The formerquite consistently usually advocate a weak patent system, while the latterequally consistently advocate its strengthening.

Even if A', the marginal value of an invention, were "sizable," theoptimal decision would be to abolish property rights in an invention, thatis, to set Pt = 0, if b1 and K 63 were sufficiently large and/or the elasticities

and ea sufficiently small. Indeed, practically all arguments to eliminateor greatly alter the patent system have been based either on its allegedcostliness, large K or b1, or lack of effectiveness, low e,) or e(, (see, forexample, Plant, 1934, or Arrow, 1962).

If a patent system were replaced by a system of cash prizes, the elas-ticities of response would become irrelevant for the determination of

62. These costs are not entirely trivial: for example, in 1966 the U.S. Patent Officealone spent $34 million (see Bureau of the Budget, 1967), and much more was probablyspent in preparing applications and in litigation.

63. Presumably one reason patents are not permitted on basic research is the difficulty(that is, cost) of discovering the ownership of new concepts and theorems.

APPROACH

(34)

(35)

equations are relatedrose discussed earlier

a pure transfer butily that e,, > e11, since

implication of(21)that, at the margin,at the margin, bene-

nal values of p and fthe sense that the

(I')

(2')

e can write (I') as

(3')

(4')

ere U' 0, which was to


optimal policies, because b1 would then be approximately zero.64 A sys-tem of prizes would, moreover, have many of the same other advantagesthat fines have in punishing offenders (see the discussion in Sec. V). Onesignificant advantage of a patent system, however, is that it automatically"meters" A', that is, provides an award that is automatically positivelyrelated to A', while a system of prizes (or of fines and imprisonment) hasto estimate A' (or D') independently and often somewhat arbitrarily.

B. THE EFFECTIVENESS OF PUBLIC POLICY

The anticipation of conviction and punishment reduces the loss fromoffenses and thus increases social welfare by discouraging some offenders.What determines the increase in welfare, that is "effectiveness," of publicefforts to discourage offenses? The model developed in Section III canbe used to answer this question if social welfare is measured by incomeand if "effectiveness" is defined as a ratio of the maximum feasible in-crease in income to the increase if all offenses causing net damages wereabolished by fiat. The maximum feasible increase is achieved by choosingoptimal values of the probability of apprehension and conviction, p,and the size of punishments, f (assuming that the coefficient of socialloss from punishment, b, is given). 65

Effectiveness so defined can vary between zero and unity and de-pends essentially on two behavioral relations: the costs of apprehensionand conviction and the elasticities of response of offenses to changes inp andf. The smaller these costs or the greater these elasticities, the smallerthe cost of achieving any given reduction in offenses and thus the greater

64. The right side of both (34) and (35) would vanish, and the optimality conditionswould be

and

A' — K' = 0

A' — K' — K,, 0.

(34')

(35')

Since these equations are not satisfied by any finite values of Pi and a, there is a difficultyin allocating the incentives between and a (see the similar discussion for fines in Sec. V).

65. In symbols, effectiveness is defined as

E= D(0,)—[D(O)+ C(13, Ô)+ b13JO]

D(0,) — D(02)

where j3,f, and O are optimal values, 0, offenses would occur ifp=f= 0, and 0, is thevalue of 0 that minimizes D.

the effectiveness. Thferent kinds of offenrape, or crimes of ysive to changes in plike embezzlement,estimated by Smigeldo differ considerabitheft, and assault tha

Probably effecti'ferences in theticities of response.that varies greatly,offense.67 For the eaibe brought in and tFidentify the offender.bery than for a relatfair-employment legiantitrust and public-u

C. A THEORY OF C

The theory develope.dude certain kinds ("unlawful." As an elude in order to obtaitheory of the determindustry, a theorycompetitive, monopowould emerge. One b:is a theory of collusic

The gain to firmsof their marginal cosi

66. A theoretical arguoffenders are less responsi

67. A study of crimesthan half the arrests weremade within the first week

68. Evidence relatingpenalties for these white-cand Johnson (1967).

69. Jacob Mincer

GARY S. BECKER 41APPROACH

zero.64 A sys-me other advantagessian in Sec. V). Onethat it automatically

ornatically positivelyd imprisonment) has

ewhat arbitrarily.

duces the loss fromsome offenders.

bctiveness," of publiced in Section III can

by incomeTiaximum feasible in-

net damages wereachieved by choosing

and conviction, p.coefficient of social

ro and unity and de-osts of apprehensionifenses to changes inlasticities, the smaller

and thus the greater

the optimality conditions

(34')

(35')

nd a, there is a difficultyssion for fines in Sec. V).

p=f= 0, and 02 is the

the effectiveness. The elasticities may well differ considerably among dif-ferent kinds of offenses. For example, crimes of passion, like murder orrape, or crimes of youth, like auto theft, are often said to be less respon-sive to changes in p and f than are more calculating crimes by adults,like embezzlement, antitrust violation, or bank robbery. The elasticitiesestimated by Smigel (1965) and Ehrlich (1967) for seven major feloniesdo differ considerably but are not clearly smaller for murder, rape, autotheft, and assault than for robbery, burglary, and larceny.66

Probably effectiveness differs among offenses more because of dif-ferences in the costs of apprehension and conviction than in the elas-ticities of response. An important determinant of these costs, and onethat varies greatly, is the time between commission and detection of anoffense.67 For the earlier an offense is detected, the earlier the police canbe brought in and themore likely that the victim is able personally toidentify the offender. This suggests that effectiveness is greater for rob-bery than for a related felony like burglary, or for minimum-wage andfair-employment legislation than for other white-collar legislation likeantitrust and public-utility regulation.68

C. A THEORY OF COLLUSION

The theory developed in this essay can be applied to any effort to pre-clude certain kinds of behavior, regardless of whether the behavior is"unlawful." As an example, consider efforts by competing firms to col-lude in order to obtain monopoly profits. Economists lack a satisfactorytheory of the determinants of price and output policies by firms in anindustry, a theory that could predict under what conditions perfectlycompetitive, monopolistic, or various intermediate kinds of behaviorwould emerge. One by-product of our approach to crime and punishmentis a theory of collusion that appears to fill a good part of this lacuna.6"

The gain to firms from colluding is positively related to the elasticityof their marginal cost curves and is inversely related to the elasticity of

66. A theoretical argument that also casts doubt on the assertion that less "calculating"offenders are less responsive to changes in p andf can be found in Becker (1962).

67. A study of crimes in parts of Los Angeles during January, 1966, found that "morethan half the arrests were made within 8 hours of the crime, and almost two-thirds weremade within the first week" (President's Commission l967e, p. 8).

68. Evidence relating to the effectiveness of actual, which are not necessarily optimal,penalties for these white-collar crimes can be found in Stigler (1962, 1966), Landes (1966),and Johnson (1967).

69. Jacob Mincer first suggested this application to me.


their collective demand curve. A firm that violates a collusive arrange-ment by pricing below or producing more than is specified can be said tocommit an "offense" against the collusion. The resulting harm to the col-lusion would depend on the number of violations and on the elasticitiesof demand and marginal cost curves, since the gain from colluding de-pends on these elasticities.

If violations could be eliminated without cost, the optimal solutionwould obviously be to eliminate all of them and to engage in pure monop-oly pricing, in general, however, as with other kinds of offenses, thereare two costs of eliminating violations. There is first of all the cost ofdiscovering violations and of "apprehending" violators. This cost isgreater, the greater the desired probability of detection and the greaterthe number of violations. Other things the same, the latter is usuallypositively related to the number of firms in an industry, which partlyexplains why economists typically relate monopoly power to concentra-tion. The cost of achieving a given probability of detection also dependson the number of firms, on the number of customers, on the stability ofcustomer buying patterns, and on government policies toward collusivearrangements (see Stigler, 1964).

Second, there is the cost to the collusion of punishing violators. Themost favorable situation is one in which fines could be levied againstviolators and collected by the collusion. If fines and other legal recourseare ruled out, methods like predatory price-cutting or violence have tobe used, and they hurt the collusion as well as violators.

Firms in a collusion are assumed to choose probabilities of detection,punishments to violators, and prices and outputs that minimize their lossfrom violations, which would at the same time maximize their gain fromcolluding. Optimal prices and outputs would be closer to the competitiveposition the more elastic demand curves were, the greater the number ofsellers and buyers, the less transferable punishments were, and the morehostile to collusion governments were. Note that misallocation of re-sources could not be measured simply by the deviation of actual fromcompetitive outputs but would depend also on the cost of enforcing collu-sions. Note further, and more importantly, that this theory, unlike mosttheories of pricing, provides for continuous variation from purely com-petitive through intermediate situations to purely monopolistic pricing.These situations differ primarily because of differences in the "optimal"number of violations, which in turn are related to differences in theelasticities, concentrations, legislation, etc., already mentioned.

These ideas appear to be helpful in understanding the relative successof collusions in illegal industries themselves! Just as firms in legal indus-

tries have an incentivfirms producing illegation, and abortion. Thsuccessful collusion tIlike the United Stateswould seem to have ancould be used againstcourse. On the other F.ized collusions, thosecause violators

clusions in illegal induprewar Germany.

VIII. SUMMARY A

This essay uses econopolicies to combat illeits expenditures on pobility (p) that an offensconvicted, the size ofform of the punishmevalues of these variablthe constraints impostdamages caused by a ganother the cost of ackin p andf on 0.

"Optimal" decisioithe social loss in inconcosts of apprehensionishments imposed, andp, f, and the form ofstrained by "outside"from the minimization Iillustrated by a few

If carrying out thcimprisonment, or parospect to a change in p'

70. An interpretation of

APPROACH

a collusive arrange-ecifled can be said toLlting harm to the cot-nd on the elasticitiesin from colluding de-

the optimal solutionngage in pure monop-tds of offenses, thereirst of all the cost ofolators. This cost isction and the greater

the latter is usuallywhich partly

power to concentra-etection also depends

ers, on the stability oftoward collusive

violators. Thebe levied against

other legal recourseg or violence have totators.babilities of detection,

minimize their losstimize their gain from

to the competitivegreater the number of

were, and the moremisallocation of re-

of actual fromst of enforcing collu-theory, unlike most

)n from purely corn-nonopolistic pricing.ces in the "optimal".0 differences in thementioned.

g the relative successfirms in legal indus-

GARY S. BECKER 43

tries have an incentive to collude to raise prices and profits, so too dofirms producing illegal products, such as narcotics, gambling, prostitu-tion, and abortion. The "syndicate" is an example of a presumably highlysuccessful collusion that covers several illegal products.7° In a countrylike the United States that prohibits collusions, those in illegal industrieswould seem to have an advantage, because force and other illegal methodscould be used against violators without the latter having much legal re-course. On the other hand, in countries like prewar Germany that legal-ized collusions, those in legal industries would have an advantage, be-cause violators could often be legally prosecuted. One would predict,therefore, from this consideration alone, relatively more successful col-lusions in illegal industries in the United States, and in legal ones inprewar Germany.

VIII. SUMMARY AND CONCLUDING REMARKS

his essay uses economic analysis to develop optimal public and privatepolicies to combat illegal behavior. The public's decision variables areits expenditures on police, Courts, etc., which help determine the proba-bility (p) that an offense is discovered and the offender apprehended andconvicted, the size of the punishment for those convicted (f), and theform of the punishment: imprisonment, probation, fine, etc. Optimalvalues of these variables can be chosen subject to, among other things,the constraints imposed by three behavioral relations. One shows thedamages caused by a given number of illegal actions, called offenses (0),another the cost of achieving a given p, and the third the effect of changesin p andf on 0.

"Optimal" decisions are interpreted to mean decisions that minimizethe social loss in income from offenses. This loss is the sum of damages,costs of apprehension and conviction, and costs of carrying out the pun-ishments imposed, and can be minimized simultaneously with respect top, f, and the form of f unless one or more of these variables is Con-strained by "outside" considerations. The optimality conditions derivedfrom the minimization have numerous interesting implications that can beillustrated by a few examples.

If carrying out the punishment were costly, as it is with probation,imprisonment, or parole, the elasticity of response of offenses with re-spect to a change in p would generally, in equilibrium, have to exceed its

70. An interpretation of the syndicate along these lines is also found in Schilling (1967).

SI


response to a change inf. This implies, if entry into illegal activities canbe explained by the same model of choice that economists use to explainentry into legal activities, that offenders are (at the margin) "risk pre-ferrers." Consequently, illegal activities "would not pay" (at the margin)in the sense that the real income received would be less than what couldbe received in less risky legal activities. The conclusion that "crime wouldnot pay" is an optimality condition and not an implication about the effi-ciency of the police or courts; indeed, it holds for any level of efficiency,as long as optimal values of p and! appropriate to each level are chosen.

If costs were the same, the optimal values of both p and f would begreater, the greater the damage caused by an offense. Therefore, offenseslike murder and rape should be solved more frequently and punished moreseverely than milder offenses like auto theft and petty larceny. Evidenceon actual probabilities and punishments in the United States is stronglyconsistent with this implication of the optimality analysis.

Fines have several advantages over other punishments: for example,they conserve resources, compensate society as well as punish offenders,and simplify the determination of optimal p's and f's. Not surprisingly,fines are the most common punishment and have grown in importanceover time. Offenders who cannot pay fines have to be punished in otherways, but the optimality analysis implies that the monetary value to themof these punishments should generally be less than the fines.

Vengeance, deterrence, safety, rehabilitation, and compensation areperhaps the most important of the many desiderata proposed throughouthistory. Next to these, minimizing the social loss in income may seemnarrow, bland, and even quaint. Unquestionably, the income criterion canbe usefully generalized in several directions, and a few have already beensuggested in the essay. Yet one should not lose sight of the fact that it ismore general and powerful than it may seem and actually includes moredramatic desiderata as special cases. For example, if punishment were byan optimal fine, minimizing the loss in income would be equivalent tocompensating "victims" fully and would eliminate the "alarm" that soworried Bentham; or it would be equivalent to deterring all offensescausing great damage if the cost of apprehending, convicting, and punish-ing these offenders were relatively small. Since the same could also bedemonstrated for vengeance or rehabilitation, the moral should be clear:minimizing the loss in income is actually very general and thus is moreuseful than these catchy and dramatic but inflexible desiderata.

This essay concentrates almost entirely on determining optimalpolicies to combat illegal behavior and pays little attention to actual poli-

cies. The small amoLamined certainlycies. For example, itStates that more danelasticity of responsef, and that both are umality analysis. Therethe actual tradeoff beis frequently less, rati,prisoned. Although m:are seriously hamperequantity and qualitythe analytical side bysion-making.

Reasonable menfits caused by differenttive labor markets areminimum are violatioiand even abortion shcmarket price, while tcThese differences arepublic policy but havesus on damages andoptimal implementatic

The main contribioptimal policies to cottion of resources. Sincallocation, an "econolenrich, the analysis ofaspects of the latter eas imprisonments, areas well as to offenderthat enters both the re

Lest the reader beframework for illegaltributors to criminolotBeccaria and Benthantunately, such an appiand my efforts can I

thereby I hope impro\

C APPROACH GARY S. BECKER 45

O illegal activities caniomists use to explain

margin) "risk pre-t pay" (at the margin)

less than what couldion that "crime wouldication about the effi-ny level of efficiency,ach level are chosen.oth p and f would be

e. Therefore, offensestly and punished more

EvidenceStates is strongly

haiysis.hments: for example,as punish offenders,

Not surprisingly,grown in importancebe punished in other

bnetary value to themthe fines.nd compensation areproposed throughout

income may seemincome criterion canw have already beent of the fact that it istually includes more

were byruld be equivalent tothe "alarm" that soeterring all offensesivicting, and punish-same could also be

oral should be clear:ral and thus is moredesiderata.letermining optimal

to actual pofi-

cies. The small amount of evidence on actual policies that I have ex-amined certainly suggests a positive correspondence with optimal poli-cies. For example, it is found for seven major felonies in the UnitedStates that more damaging ones are penalized more severely, that theelasticity of response of offenses to changes in p exceeds the response tof, and that both are usually less than unity, all as predicted by the opti-mality analysis. There are, however, some discrepancies too: for example,the actual tradeoff between imprisonment and fines in different statutesis frequently less, rather than the predicted more, favorable to those im-prisoned. Although many more studies of actual policies are needed, theyare seriously hampered on the empirical side by grave limitations in thequantity and quality of data on offenses, convictions, costs, etc., and onthe analytical side by the absence of a reliable theory of political deci-sion-making.

Reasonable men will often differ on the amount of damages or bene-fits caused by different activities. To same, any wage rates set by competi-tive labor markets are permissible, while to others, rates below a certainminimum are violations of basic rights; to some, gambling, prostitution,and even abortion should be freely available to anyone willing to pay themarket price, while to others, gambling is sinful and abortion is murder.These differences are basic to the development and implementation ofpublic policy but have been excluded from my inquiry. I assume consen-sus on damages and benefits and simply try to work out rules for anoptimal implementation of this consensus.

The main contribution of this essay, as I see it, is to demonstrate thatoptimal policies to combat illegal behavior are part of an optimal alloca-tion of resources. Since economics has been developed to handle resourceallocation, an "economic" framework becomes applicable to, and helpsenrich, the analysis of illegal behavior. At the Same time, certain uniqueaspects of the latter enrich economic analysis: some punishments, suchas imprisonments, are necessarily nonmonetary and are a cost to societyas well as to offenders; the degree of uncertainty is a decision variablethat enters both the revenue and cost functions; etc.

Lest the reader be repelled by the apparent novelty of an "economic"framework for illegal behavior, let him recall that two important con-tributors to criminology during the eighteenth and nineteenth centuries,Beccaria and Bentham, explicitly applied an economic calculus. Unfor-tunately, such an approach has lost favor during the last hundred years,and my efforts can be viewed as a resurrection, modernization, andthereby I hope improvement, of these much earlier pioneering studies.


MATHEMATICAL APPENDIXSince D'+C'>O a

This Appendix derives the effects of changes in vanous parameters on the E1> I Thereforeoptimal values of p andf It is assumed throughout that b> 0 and that equilib- D" + C'1> 0; and /num occurs where the loss L.

aD ac ac ap , , Suppose that D'ofachangeinaon/c

the analysis could easily be extended to cover negative values of b and of thismarginal cost term. The conclusion in the text (Sec. II) that D" + C" > 0 isrelied on here. I take it to be a reasonable first approximation that the elastici-ties of 0 with respect to p or fare constant. At several places a sufficient condi- or

tion for the conclusions reached is that

a2c a2cCpo — Cop

Since a

is "small" relative to some other terms. This condition is utilized in the formof a strong assumption that = 0, although I cannot claim any supportingintuitive or other evidence.

The social loss in income from offenses has been defined as In a similar way itenous variable

LD(O)+C(0,p)+bpf0. (Al)

If b and p were fixed, the value off that minimized L would be found from thenecessary condition .If b is positively re

or

(A2)

or

(D"+C")

0D'+C'+bpf(l—E1), (A3)

if

= 0, Since 1 — < 0, and b

where—af 0

E1— y Note that since lIE1 < IThe sufficient condition would be that a2L/af2 > 0; using aLl af = 0 and E1 isconstant, this condition becomes

= (D" + C")0,2 + bp(1 — E1)01> 0, (A4)If E, is positively re

or


(AS)

Since D' + C' > 0, and b is not less than zero, equation (A3) implies thatus parameters on the E,> 1. Therefore would be greater than zero, since we are assuming that> 0 and that equilib- D" + C"> 0; and f, the value of f satisfying (A3), would minimize (locally)

the loss L.Suppose that D' is positively related to an exogenous variable a. The effect

>0; of a change in a on/can be found by differentiating equation (A3):

'alues of b and of this d/ d/D,+(D"+C")01—+bp(lthat D" + C"> 0 is daation that the elastici-aces a sufficient condi- or

df —(A6)

Since > 0, < 0, and by assumption 0, then

is utilized in the form df — +> 0. (A7)claim any supporting — T

In a similar way it can be shown that, if C' is positively related to an exog-med asenous variable /3,

(Al) df — — ±wid be found from the ;> 0. (A8)

If b is positively related to then

E1O(A2) —Ei) —E1)by=0,

or

(A3)df — —b7pf( I — E,)( I

(A9)

Since 1 — < 0, and by assumption > 0,

df — — <0. (AlO)

Note that since lIE, < 1,

g 0 and E, is d(pfO) <0. (All)dy

If Ef is positively related to &, then0, (A4)

df — —=;<0. (A12)


Since the elasticity of 0 with respect to f equals If were constant,

—f i

(32p/aOap) would be

O=E' and a value of p satisfy:The effects of cha

by (A12), a reduction in E1woulcl reducef. already derived for/anSuppose that p is related to the exogenous variable r. Then the effect of a

shift in r on/can be found from

a! a!(D" + C")01 — + (D" + C")OpPr + Cp0Pr + bp(1 — — + bf(1 — Ei)Pr = 0,

dr ar

orand

dJ_—(D"+ C")Op(l/Ot)pr bf(1 — Ei)pr(l/0i)(A 13)

dr —

since by assumption C,,0 = 0. Since 0,, < 0, and (D" + C") > 0,If E0 is positively•

— C—) + (—) —

dr + (Al4)

1ff rather than p were fixed, the value of p that minimizes L, J3, could be if C,, were positive!found from p would equal

(A 15)

as long as 1ff were related to

82L 1j5 would be given by

+C +C,,0+C,,P PPQ dji—(D"+C")O,,f,(l+ bf(l — > 0. (A16) di

Since = C,,0 = 0, (A 16) would hold if(with C,,0 = 0), since all

+ bf(1 — 0. (A 17) If both p andD" + C" + C ,,,, + C,,

It is suggested in Section II that C,,,, is generally greater than zero. If, as as- 71. If E,, and Er are cosu med, Then

D' + C' + >0,OP

equation (A 15) implies that 1 and thus that .and

bf(1 — E,,) > o.op


If were constant, a2p/aOap would be negative," and, therefore,(a2p/aOap) would be positive. Hence, none of the terms of (A 17) are negative,and a value of p satisfying equation (A 15) would be a local minimum.

The effects of changes in different parameters on are similar to thosealready derived forf and can be written without comment:

r. Then the effect of adp—= , >0, (A18)da

dj3—= , >0, (A19)

andr(lIOi) (A13) d/3—b-),pf(l —E1)(l/O,,)

<0. (A20)

If is positively related to 8',

(A 14) c45< 0. (A21)

d6'[nimizes L, j5, could be If C,. were positively related to the parameter s, the effect of a change in s on

j5 would equal

(Al5) (A22).ds1ff were related to the exogenous parameter i, the effect of a change in t on

j5 would be given by

d13 = —(D" + C")O,.f,(l/O,.) — bf(l — E,,)j(l/O,,) —0

—E,.)]O,.>0. (A16) di

(A23)

(with = 0), since all the terms in the numerator are negative.- E,,)5-> 0. (A 17) If both p and f were subject to control, L would be minimized by choosing

er than zero. If, as as- 71. If E,. and E,are constants, 0 = where a = l/E,, and b = 1/E,.

Then

=ao ka

a21) —((1+1)= afb<()aOap ka


optimal values of both variables simultaneously. These would be given by thesolutions to the two first-order conditions, equations (A2) and (A 15), assumingthat certain more general second-order conditions were satisfied. The effects of or

changes in various parameters on these optimal values can be found by differen-tiating both first-order conditions and incorporating the restrictions of thesecond-order conditions.

The values of p andf satisfying (A2) and (A 15), j5 andf, minimize L if It can be shown that

0, Lif> 0, (A24)

andand, therefore, (A35) i

= (A25) It has now been p

But and L,,= and since both and have been shown conditions (A2) and (i

to be greater than zero, (A24) is proved already, and only (A25) remains. By parameters change the

differentiating Lf with respect to p and utilizing the first-order condition that be found from the two

= 0, one has

+ C" + bf( 1 — E1)p0] = (A 26)

where I equals the term in brackets. Clearly I > 0. andBy substitution, (A25) becomes

> (A27)

and (A27) holds if and are both greater than I. > I means that By Cramer's rule,

D" + C" + bp(I — Ef)f0 > D" + C" + bf(l — E1)p0, (A28) a!t3z

orbfp bpf

— E,)E,<

(1 — E1)E,,. (A29)

Since 1 — < 0, (A29) implies that and the signs of both deConsider the effect

E1> E,,, (A 30) eter It is apparent thwhich necessarily holds given the assumption that b > 0; prove this by combin-ing the two first-order conditions (A2) and (A 15). > I means that

D" + C" + + + bf(1 — > D" + C" + bf(1 — E1)p0. (A3 1) and

Since > 0, and < 0, this necessarily holds if

+ bpf(1 — < bpf(l — Ef). (A32)since 0, and 0,, < 0, D

By eliminating D' + C' from the first-order conditions (A2) and (A15) and by Similarly, if C' is cicombining terms, one has

C,p0 — — = 0. (A33)

By combining (A32) and (A33), one gets the condition and


'ould be given by the C,,ppQ,) < Cpp0, (A34)

and (A 15), assuming ortisfied. The effects of

ibefoundbydifferen- P3Po>(A35)e restrictions of the = Po ap

It can be shown thatminimize L if

(A24)E0

and, therefore, (A35) is proven.(A25) It has now been proved that the values of p and! that satisfy the first-order

conditions (A2) and (A 15) do indeed minimize (locally) L. Changes in differenthave been shownly (A25) remains. By parameters change these optimal values, and the direction and magnitude can

be found from the two linear eqUationst-order condition that

(A26)

and (A37)

af a13— + — = C2

(A27)

I means that By Cramer's rule,

L E1)p0, (A28) C1014' C20p1 — C21),(A38)

az — +

— — CIO1I — C11)(A39)(A 29) — — +

and the signs of both derivatives are the same as the signs of the numerators.Consider the effect of a change in D' resulting from a change in the param-

(A30) eter a. It is apparent that C1 = C2 = and by substitution

prove this by combin- af I) — +0 (A40)aa +

bf(1 — E1)p0. (A31) and

— — I) — ++

(A41)

(A32)since and < 0, > 0, and and > I.

2) and (A15) and by Similarly, if C' is changed by a change in f3, C1 = C2

— I) — +>0 (A42)(A33) +

and

52 CRIME AND PUNISHMENT: AN EcoNoMic APPROACH

— + If is changed>0. (A43)

8/3 + +

If changed by a change in C1 =E,,3bpf, C2 =0,and

=—<0, (A44)+ +and

— —O1E1bpf = ±> 0. (A45)REFERENCES+ +

Similarly, if is changed by a change in C1 = 0, C2 =Arrow, Kenneth J. "E.

aj — — + tion," in National I> (A46)— + — Direciion of Inve,.

and NJ.: PrincetonBecker, Gary S. "Irrat

—

88' — + = <0. (A47) cal Economy 70 (F"A Theory of

If b is changed by a change in y, C1 = —b7pf( 1 — Ef), C2 —b7pf( I — E,j, - ber 1965).

and Bentham. Jeremy.Bureau of the Budget.

— —(1 — — — dix. Washington: U< 0, (A48)+ Bureau of Prisons. Pri

("National Prisonesince E, > > 1 and > also, Characieristics.

8/3 — — — (1 — Ef)I]o, (A49)

U.S. Dept. of Justii

— + + —. Federal PrisonsCagan, Phillip. Deter,ni

for it can be shown that (1 — > (I — Note that when f is held con- 1875)960 New Ystant the optimal value of p is decreased, not increased, by an increase in y. Res.), 1965.

"Criminal Safeguards72. The term (1 — would be greater than (1 — if Chicago Law Revk

(D' + C")(i — + bp(I — E,)(l — E,)f0> (D" + C')(l — Ef) + bf(1 — Ehrlich, Isaac. "The Sscript, Columbia Ut

or Federal Bureau offO p0' Washington: U.S. tbpf

(D"+ > ——b— (1— E1) [(1——p—

(I— E,) Ibid., 1961.

bpfHarper, F. V., and Jam

(D"+ C")(E1— > — E1)[(1 — E,,)(E,) —(1 — & Co., 1956.Johnson, Thomas. "The

bpf Columbia Univ., N—E,)(E,—E9).

KJeinman, E. "The ChcSince the left-hand side is greater than zero, and the right-hand side is less than zero, the Criminal Sentencin€

inequality must hold. 1967.


If is changed by a change in s, C2 = C1 = 0,(A43)

0, (A50)as + + +

and

(A44)<0. (A51)

(A45)REFERENCES

=Arrow, Kenneth J. "Economic Welfare and Allocation of Resources for Inven-

6tion," in National Bureau Committee for Economic Research. The Rate and

(A4 Direction of Inventive Activity: Economic and Social Factors. Princeton,N.J.: Princeton Univ. Press (for the Nat. Bureau of Econ. Res.), 1962.

Becker, Gary S. "irrational Behavior and Economic Theory." Journal of Politi-(A47) cal Economy 70 (February 1962).

"A Theory of the Allocation of Time." Economic Journal 75 (Septem-

Es). —Er), ber 1965).- Bentham, Jeremy. Theory of Legislation. New York: Harcourt Brace Co., 1931.

Bureau of the Budget. The Budget of United States Government, /968, Appen-

: < 0 (A48)dix. Washington: U.S. Government Printing Office, 1967.

+ ' Bureau of Prisons. Prisoners Released from State and Federal Insthurions.("National Prisoner Statistics.") Washington: U.S. Dept. of Justice, 1960.

Characteristics of State Prisoners, 1960. ("National Prisoner Statistics.")U.S. Dept. of Justice, n.d.

0, (A49). Federal Prisons, 1960. Washington: U.S. Dept. of Justice, 1961.

Cagan, Phillip. Deterininamus and Effects of Changes in the Stock of Money,that whenf is held con- 1875—1 960. New York: Columbia Univ. Press (for the Nat. Bureau of Econ.

y an increase in y. Res.), 1965."Criminal Safeguards and the Punitive Damages Defendant." Universil of

Chicago Law Review 34 (Winter 1967).Ehrlich, Isaac. "The Supply of Illegitimate Activities." Unpublished manu-E1)+bf(1 —E1)-p0,

script, Columbia Univ., New York, 1967.Federal Bureau of Investigation. Uniform Crime Reports for the United States.

Washington: U.S. Dept. of Justice, 1960.. Ibid., 1961.

Harper, F. V., and James, F. The Law of Torts. Vol. II. Boston: Little-Brown& Co., 1956.

Johnson, Thomas. "The Effects of the Minimum Wage Law." Ph.D. dissertation,Columbia Univ., New York, 1967.

Kleinman, E. "The Choice between Two 'Bads'—Some Economic Aspects of

side is less than zero, the Criminal Sentencing." Unpublished manuscript, Hebrew Univ., Jerusalem,1967.


Landes, William. "The Effect of State Fair Employment Legislation on theEconomic Position of Nonwhite Males." Ph.D. dissertation, ColumbiaUniv., New York, 1966.

Laws of New York. Vol. 11(1965).Marshall. Alfred. Principles of Economics. 8th ed. New York: Macmillan Co.,

1961.Plant, A. "The Economic Theory concerning Patents for Inventions."

Economica 1 (February 1934).Pollock, F., and Maitland, F. W. The History of English Law. Vol. 11. 2d ed.

Cambridge: Cambridge Univ. Press, 1952.President's Commission on Law Enforcement and Administration of Justice.

The Challenge of Crime in a Free Society. Washington: U.S. GovernmentPrinting Office, 1967(a).

Corrections. ("Task Force Reports.") Washington: U.S. GovernmentPrinting Office, 1967(b).

The Courts. ("Task Force Reports.") Washington: U.S. GovernmentPrinting Office, 1967(c).

Crime and Its Impact—an Assessment. ("Task Force Reports.")Washington: U.S. Government Printing Office, 1967(d).

Science and ('Task Force Reports.") Washington: U.S.Government Printing Office, 1967(e).

Radzi nowica, L. A History of English Criminal Law and Its A dminislration from1750. \'ol. 1. London: Stevens & Sons, 1948.

Schilling, T. C. "Economic Analysis of Organized Crime," in President's Com-mission on Law Enforcement and Administration of Justice. OrganizedCrime. ("Task Force Reports.") Washington: U.S. Government PrintingOffice, 1967.

Shawness, Lord. "Crime Does Pay because We Do Not Back Up the Police."New York Times Magazine, June 13, 1965.

Smigel, Arleen. "Does Crime Pay? An Economic Analysis." M.A. thesis,Columbia Univ., New York, 1965.

Stigler, George J. "What Can Regulators Regulate? The Case of Electricity."Journal of Law and Economics 5 (October 1962).

"A Theory of Oligopoly." Journal of Political Economny 72 (February1964).

"The Economic Effects of the Antitrust Laws." Journal of Law andEconomnics 9 (October 1 966).

Sutherland, E. H. Principles of Criminology. 6th ed. Philadelphia: J. B. Lippin-cott Co., 1960.

The Optiof Laws

George J.University of Chi

All prescriptionUsually the obligativoluntarily by expliteach certainwhich 1, and possibinegotiation, and in tiployer seek to enfortures from the promiis difficult or imposnoble, or steadfast iare either not made.flagrant violation. 1organization generalihas received virtuall:tial explanatory pow

When the prescividual agreement,these unilateral rule:actual from prescrilcould wish for a les

APPROACH

nt Legislation on the[issertation, Columbia

The Optimum EnforcementYork: Macmillan Co.,

nts for Inventions." of Laws

Lou'. Vol. II. 2d ed.

uinistration of Justice. George J. Stiglerton: U.S. Government

University of Chicago and National Bureau of Economic Researchon: U.S. Government

Ion: U.S. Government

Lk Force

ts.") Washington: U.S.

rs A dnuinisirationfroin

," in President's Corn- All prescriptions of behavior for individuals require enforcement.of Justice. Organized Usually the obligation to behave in a prescribed way is entered intoGovernment Printing voluntarily by explicit or implicit contract. For example, I promise to

teach certain classes with designated frequency and to discuss mattersBack Up the Police." which I, and possibly others, believe are relevant to the course titles. By

negotiation, and in the event of its failure, by legal action, I and my em-alysis." MA. thesis, ployer seek to enforce the contract of employment against large depar-

tures from the promised behavior. Performance of some kinds of behaviorCase of Electncity." is difficult or impossible to enforce—such as promises to be creative,

noble, or steadfast in crisis—and as a result such contractual promisesconomy 72 (February .

are either not made or enforced only when there is an uncontroversially

Journa! of Laui' and flagrant violation. The influence upon contract, and upon economicorganization generally, of the costs of enforcing various kinds of contracts

adelphia: J. B. Lippin- has received virtually no study by economists, despite its immense poten-tial explanatory power.

When the prescribed behavior is fixed unilaterally rather than by indi-vidual agreement, we have the regulation or law, and enforcement ofthese unilateral rules is the subject of the present essay. Departures ofactual from prescribed behavior are crimes or violations, although onecould wish for a less formidable description than "criminal" to describe

56 THE OPTIMUM ENFORCEMENT OF LAWS

many of the trifling offenses or the offenses against unjust laws. Myprimary purpose is to construct a theory of rational enforcement, a theorywhich owes much to Gary Becker's major article on the subject (1968). inthe conclusion the problem of explanation, as distinguished from prescrip-tion, will be commented upon.

I. THE GOAL OF ENFORCEMENT

The goal of enforcement, let us assume, is to achieve that degree of com-pliance with the rule of prescribed (or proscribed) behavior that thesociety believes it can afford. There is one decisive reason why the so-ciety must forego "complete" enforcement of the rule: enforcement iscostly.

The extent of enforcement of laws depends upon the amount of re-sources devoted to the task. With enough policemen, almost every speed-ing automobile could be identified. The success of tenacious pursuit ofthe guilty in celebrated crimes (such as the great English train robberyand the assassination of Martin King) suggests that few crimes of sanemen could escape detection. We could make certain that crime does notpay by paying enough to apprehend most criminals. Such a level of en-forcement would of course he enormously expensive, and only in crimesof enormous importance will such expenditures be approached. Thesociety will normally give to the enforcement agencies a budget whichdictates a much lower level of enforcement.

The cost limitation upon the enforcement of laws would prevent thesociety from forestalling, detecting, and punishing all offenders, but itwould appear that punishments which would be meted out to the guiltycould often be increased without using additional resources. The offenderis deterred by the expected punishment, which is (as a first approxima-tion) the probability of punishment times the punishment—$ 100 if theprobability of conviction is 1/10 and the fine $1,000. Hence, increasingthe punishment would seem always to increase the deterrence. Capitalpunishment is cheaper than long term imprisonment; and seizure of allthe offender's property may not be much more expensive than collectinga more moderate fine.

To escape from this conclusion, Becker introduces as a different limi-tation on punishment the "social value of the gain to offenders" from theoffense. The determination of this social value is not explained, and oneis entitled to doubt its usefulness as an explanatory concept: what evi-dence is there that society sets a positive value upon the utility derivedfrom a murder, rape, or arson? In fact the society has branded the utility

derived from such actgain to the offender i:seem too infrequent,upon the size of puni

Instead we takement, which arises odoubt true that thepected netutility togiven offense. Butof life, and the margismall or evensault and for a murdcthief has his hand cu$5,000. Marginal cmarginal deterrenceotherwise appropriat

One special aspneed to avoid overeapprehend most guiland frequent convicsystem, there will in Iparties, and these mland loss of confideidefense of innocent pare part of the costsviction of innocent pmarginal deterrence I

The significancethat will be used tothe gravity of the ofimanifest itself only imore tenaciously th

I. For example, the Iwarms the neighboring ho

2. Becker writes the Iwhere Y is the money valf the fine. (The income,single offense Y must bespect to Y, =tive for all }'. Of coursecrime.

LAWS GEORGE J. STIGLER 57

inst unjust laws. Myenforcement, a theorythe subject (1968). In

from prescrip-

'e that degree of corn-behavior that the

ie reason why the so-rule: enforcement is

the amount of re-!n, almost every speed-

tenacious pursuit ofEnglish train robbery

few crimes of sanethat crime does notSuch a level of en-

ye, and only in crimesbe approached. Thencies a budget which

ws would prevent theall offenders, but it

eted out to the guiltysources. The offender(as a first approxima-ishment—$ 100 if the)O. Hence, increasinge deterrence. Capitalnt; and seizure of allensive than collecting

ces as a different limi-o offenders" from theat explained, and oney concept: what evi-on the utility derivedas branded the utility

derived from such activities as illicit. It may be that in a few offenses somegain to the offender is viewed as a gain to society,' but such social gainsseem too infrequent, small, and capricious to put an effective limitationupon the size of punishments.

Instead we take account of another source of limitation of punish-ment, which arises out of the nature of the supply of offenses. It is nodoubt true that the larger the punishment, the smaller will be the ex-pected net utility to the prospective offender from the commission of agiven offense. But marginal decisions are made here as in the remainderof life, and the marginal deterrence of heavy punishments could be verysmall or even negative. If the offender will be executed for a minor as-sault and for a murder, there is no marginal deterrence to murder. if thethief has his hand cut off for taking five dollars, he had just as well take$5,000. Marginal costs are necessary to marginal deterrence.2 Themarginal deterrence to committing small crimes is also distorted if anotherwise appropriate schedule of penalties is doubled or halved.

One special aspect of this cost limitation upon enforcement is theneed to avoid overenforcement. The enforcement agency could easilyapprehend most guilty people if we placed no limits upon the chargingand frequent conviction of innocent people. in any real enforcementsystem, there will in fact be conviction and punishment of some innocentparties, and these miscarriages of justice impose costs of both resourcesand loss of confidence in the enforcement machinery. The costs ofdefense of innocent parties, whether borne by themselves or by the state,are part of the costs of enforcement from the social viewpoint. The con-viction of innocent persons encourages the crime because it reduces themarginal deterrence to its commission.

The significance of an offense to society — the quantity of resourcesthat will be used to "prevent" the offense—will in general increase withthe gravity of the offense. The increase in resources, however, will notmanifest itself only in an increase in punishments. The state will pursuemore tenaciously the offender who commits a larger crime (or repeti-

1. For example, the thief reduces the welfare expenditures of the state, or the arsonistwarms the neighboring houses.

2. Becker writes the expected utility from an offense as EU=pU(Y—f)+(l —p)U(Y),where Y is the money value of the gain, p the probability of detection and conviction, andf the fine. (The income, Y, and fine,f, must be interpreted as average annual flows; for asingle offense Y must be less than f.) If this expression is differentiated partially with re-spect to Y, —p)U'(Y) U'(Y)—pfU'(Y), which is posi-tive for all Y. Of course p and f will increase with Y to prevent this incitement to largercrime.


tive crimes) and thus increase also the probability of apprehending him.There is a division of labor between the state and the citizen in the

prevention of virtually every offense. The owner of large properties isrequired to do much of his direct policing: there are surely more watch-men and guards than policemen in a typical city. The larger accumula-tions of wealth, moreover, are to be guarded by the owner through devicessuch as nonnegotiability and custody of funds by specialists. Accordingly,the pub/ic punishments for crimes against property do not increase inproportion to the value of the property. In the protection of people, asdistinguished from their property, the individual is required to protecthimself from minor offenses or at least to detect their occurrence andassume a large part of the burden of prosecution (for example, shop-lifting, insults, simple trespass), but he is allowed less discretion in prose-cution for major assaults.

The relationship of duration and nature of penalties to age and sex ofoffender, frequency of previous offenses, and so forth is also explicablein terms of cost of enforcement. The first-time offender may have com-mitted the offense almost accidentally and (given any punishment) withnegligible probability of repetition, so heavy penalties (which havesubstantial costs to the state) are unnecessary. The probability of a rep-etition of an offense by a seasoned offender is also zero during hisimprisonment, so the probability of repetition of an offense is relevantto the penalty also in his case.

Indeed, the problem of determining the efficient penalty may beviewed as one in statistical inference: to estimate the individual's average,durable propensity to offend (the population value) on the basis of asample of his observed behavior and how this propensity responds tochanges in penalties. As in other sequential sampling problems, one canestimate this propensity more accurately, the longer the individual'sbehavior is observed.

The society will be more concerned (because each individual is moreconcerned) with major than minor offenses in the foUowing sense: thereis increasing marginal disutility of offenses, so a theft of $1,000 is morethan twice as harmful as a theft of $500. In the area of offenses to prop-erty, this result is implied by diminishing marginal utility of income. Inthe area of offenses to persons, it is more difficult to measure damage inany direct way, but a similar rule probably holds.

So much for prevention and punishment; let us turn to the offenses.

II. THE SUPPLY

The commission of olact of consumption.speeding in an autorrrival (when the girl i

by theft, smuggling,realm of offenses to pand we may recall Acrime:

The affluence of the ncdriven by want, and prcthe shelter of the civil ris acquired by thetions, can sleep a singiknown enemies, whomfrom whose injustice hmagistrate continuallyextensive property, thgovernment. Where theof two or three days ap. 670).

The professionaof occupational choiexpected returns an'difference with the i

legitimate activities.correspond to the cinjuries to a

of apprehencupations have only

The details of o'from those encountethe locality of maxirman, move from

arin periods of(involuican be expected to

LAWS

of apprehending him.and the citizen in theof large properties ise surely more watch-rhe larger accumula-wner through devicescialists. Accordingly,y do not increase intection of people, as

required to protecttheir occurrence and

(for example, shop-discretion in prose-

tlties to age and sex ofis also explicable

may have corn-punishment) with

Inalties (which haveprobability of a rep-

!aiso zero during hisn offense is relevant

penalty may be(individual's average,

on the basis of apensity responds to

problems, one canthe individual's

ch individual is moreIlowing sense: thereft of $1,000 is moreof offenses to prop-

utility of income. Inmeasure damage in

turn to the offenses.

GEORGE J. STIGLER

II. THE SUPPLY OF OFFENSES

59

The commission of offenses will be an act of production for income or anact of consumption. A consumption offense would be illustrated byspeeding in an automobile used for recreation or assaulting a courtshiprival (when the girl is poor). A production offense would be illustratedby theft, smuggling, and the violation of economic regulations. In therealm of offenses to property, income objectives are of course paramount,and we may recall Adam Smith's emphasis upon the economic nature ofcrime:

The affluence of the rich excites the indignation of the poor, who are often bothdriven by want, and prompted by envy, to invade his possessions. It is only underthe shelter of the civil magistrate that the owner of that valuable property, whichis acquired by the labour of many years, or perhaps of many successive genera-tions, can sleep a single night in security. He is at all times surrounded by un-known enemies, whom, though he never provoked, he can never appease, andfrom whose iniustice he can be protected only by the powerful arm of the civilmagistrate continually held up to chastise it. The acquisition of valuable andextensive property, therefore, necessarily requires the establishment of civilgovernment. Where there is no property, or at least none that exceeds the valueof two or three days labour, civil government is not so necessary (Smith, 1937,p. 670).

The professional criminal seeks income, and for him the usual rulesof occupational choice will hold. He will reckon the present value of theexpected returns and costs of the criminal activity and compare theirdifference with the net returns from other criminal activities and fromlegitimate activities. The costs of failure in the execution of the crimecorrespond to the costs of failure in other occupations. The costs ofinjuries to a professional athlete are comparable to the costs to theoffender of apprehension, defense, and conviction, but normally legal oc-cupations have only monetary costs of failure.

The details of occupational choice in illegal activity are not differentfrom those encountered in the legitimate occupations. One must choosethe locality of maximum income expectation (and perhaps, like a sales-man, move from area to area). One must choose between large, relativelyinfrequent crimes and smaller, more frequent crimes. One must reckonin periods of (involuntary) unemployment due to imprisonment. Earningscan be expected to rise for a time with experience.


The probability of apprehension (and therefore of conviction) is anincreasing function of the frequency of commission of offenses. If theprobability of detection is p for one offense, it is 1 — (1 — p)11 for at leastone conviction in 11 offenses, and this expression approaches unity as nbecomes large. In fact, the probability of detection (p) rises after eachapprehension because the enforcement agency is also learning the offend-er's habits. On this score alone, there is a strong incentive to the criminalto make very infrequent attempts to obtain very large sums of money.The probability of success is also affected by the precautions of theprospective victim: Fort Knox is more difficult to enter than a liquorstore. The efforts of detection will also increase with the size of theoffense.

We may postulate, in summary, a supply of offenses which inequilibrium has the following properties:

1. Net returns are equalized, allowance being made for risk andcosts of special equipment required for various activities.

2. The determinants of supply which are subject to the control ofsociety are: (a) the structure of penalties by offense; (b) theprobability of detection for each offense; (c) certain costs of theconduct of the offending activity; for example, the cost of makingsuccessful counterfeit money can be increased by complicatingthe genuine money.

3. The penalties and chances of detection and punishment must beincreasing functions of the enormity of the offense.

Although it smacks of paradox, it may be useful to reinterpret theoffending activity as providing a variety of products (offenses). Theseoffenses are in a sense demanded by the society: my wallet is an invita-tion to the footpad, my office funds to the embezzler. The costs of pro-duction of the offenses are the ordinary outlays of offenders plus thepenalties imposed by the society. The industry will operate at a scaleand composition of output set by the competition of offenders and thecost of producing offenses.

The structure of rational enforcement activities will have theseproperties:

I. Expected penalties increase with expected gains so there is nomarginal net gain from larger offenses. Let the criminal commitin a year S crimes of size Q, where Q is the monetary value to thecriminal of the successful completion of the crime. The fraction

(p) of crimes:cessful compbamount of exrpunish the criia special fornp = p(E, Q, S)apprehendedtion for margp)SF/dQ.

2. The expenditidiminution inthese resourcyields a returr

d(pSQ')/Q,

where Q' is ti

I do not include foregactivity to society (=the return (taxes asid

III. THE ENFORCA NORMATIVE A

A law is enforced, nctask. That agency mmonition) to enforceincentives to enforcein the methods by wproperly.

The first deficienaccount, at least expl:or persons regulated.will, if anything, wisdefense for guilty penot unnecessary costof criminal justice

3. Currency has thecommodity which does no


e of conviction) is anof offenses. If the

— (1 — p)" for at leastLpproaches unity as n

(p) rises after each;O learning the offend-entive to the criminalarge sums of money.e precautions of the) enter than a liquorwith the size of the

)f offenses which in

g made for risk andous activities.ject to the control of

by offense; (b) the) certain costs of thele, the cost of making

by complicating

punishment must be)ffen Se.

ful to reinterpret the:ts (offenses). Thesey wallet is an invita-

The costs of pro-f offenders plus theII operate at a scaleof offenders and the

ies will have these

gains so there is nothe criminal commitionetary value to thecrime. The fraction

(p) of crimes completed successfully (or the probability of suc-cessful completion of one crime) is a decreasing function of theamount of expenditure (E) undertaken by society to prevent andpunish the crime. (Punishment is used for deterrence, and is onlya special form of prevention.) Hence p = p(E, Q), or possiblyp = p(E, Q, S). The expected punishment is the fraction of crimesapprehended (and punished) times the punishment, F. The condi-tion for marginal deterrence is, for all Q, d(pSQ)/dQ d(l —p)SFIdQ.

2. The expenditures on prevention and enforcement should yield adiminution in offenses, at the margin, equal to the return uponthese resources in other areas. An increment of expendituresyields a return in reduced offenses,

d(pSQ')/dE = marginal return on expenditures elsewhere,

where Q' is the monetary value of the offense to society.3

I do not include foregone lawful services of the criminal in the cost of hisactivity to society (= noncriminals) since he, not others, would receivethe return (taxes aside!) if he shifted from crime to a lawful occupation.

111. THE ENFORCEMENT AGENCY:A NORMATIVE APPROACH

A law is enforced, not by "society," but by an agency instructed to thattask. That agency must be given more than a mandate (an elegant ad-monition) to enforce the statute with vigor and wisdom: it must haveincentives to enforce the law efficiently. There are at least two deficienciesin the methods by which most agencies are induced to enforce the lawsproperly.

The first deficiency is that the enforcement agency does not take intoaccount, at least explicitly and fully, the costs it imposes upon the activityor persons regulated. In the area of ordinary criminal offenses, the societywill, if anything, wish to increase (at no expense to itself) the costs ofdefense for guilty persons, but it should not impose costs (and certainlynot unnecessary costs) upon innocent parties. In fact, the administrationof criminal justice should in principle include as a cost the reimbursement

3. Currency has the same value to the criminal as to society, so Q' = Q. But for anycommodity which does not have a market price independent of ownership, Q < Q'.


of the expenses of defense of people charged and acquitted. The com-pensation actually paid will not exactly compensate injured persons,because of the administrative costs of ascertaining exact compensation,but the taking of an innocent person's personal wealth, including foregoneincome, differs in no respect from the taking of some of his real estate (forwhich under eminent domain it is necessary to compensate him fully).4

In the area of economic regulation, guilt is often an inappropriatenotion, and when it is inappropriate all costs of compliance must bereckoned into the social costs of enforcement. The utility's costs inpreparing a rate case or Texas Gulf Sulfur's Costs in defending itselfagainst the Securities and Exchange Commission are social costs of theregulatory process. Reimbursement is now achieved by charging the con-sumers of the products and the owners of specialized resources of theseindustries: they bear the private costs of the regulatory process. This is atleast an accidental allocation of costs, and when the regulation seeks toaid the poorer consumers or resource owners, a perverse allocation.

The second deficiency in the design of enforcement is the use of in-appropriate methods of determining the extent of enforcement. Theannual report of an enforcement agency is in effect the justification of itsprevious expenditures and the plea for enlarged appropriations. TheFederal Trade Commission will tell us, for example, that in fiscal 1966 aspart of its duty to get truthful labeling of furs and textiles, it inspected1 2,625 plants and settled 213 "cases" for $ 1,272,000 plus overhead. Theagency may recite scandals corrected or others still unrepressed, but itneither offers nor possesses a criterion by which to determine the correctscale of its activities.

A rational measure of enforcement procedure could in principle beestablished in almost any area. Consider the fraudulent labeling of textiles.We could proceed as follows:

1. The damage to the consumer from the purchase of a mislabeledtextile could be estimated, and will obviously vary with the mis-labeling (assuming that the legal standards are sensible!). Thedifference between market value of the true and alleged grades isone component of the damage. A second and more elusive compo-nent is the additional cost of deception (earlier replacement, skinirritation, and so forth): the consumer who would not have pur-chased the inferior quality at a competitive price had he known its

4. It is an interesting aspect of our attitudes in this area that many people believe thatacquitted persons are probably guilty.

inferioritydamage is thetion, that is,value of the a

2. As a matterlabeler shoulcitems: (a) Thiper year. Letsay E, per yecosts of thosedetected) fornotion, as prewish to ignorethis end desecosts should 1multiplied byoffense within

3. The enforcerrplus enforcem

This goal will servement, namely where ienforcement is correone dollar of damage,than that amount of dof cases: the agencydress up its record, bwho does much dama

This sort of critareas. The secret servto the public frominstance of counterfe:by this agency was dthis one must add theThe secret servicemoney passed wouldforcement costs minu

5. The fines will besee Becker (1958), pp. 180


acquitted. The corn-sate injured persons,exact compensation,

th, including foregonee of his real estate (formpensate him fully).4

an inappropriatecompliance must berhe utility's costs ints in defending itselfre social costs of the

d by charging the con-ed resources of theseory process. This is atte regulation seeks torverse allocation.ment is the use of in-of enforcement. Thethe justification of itsappropriations. Thethat in fiscal 1966 astextiles, it inspectedo plus overhead. TheII unrepressed, but itdetermine the correct

could in principle bent labeling of textiles.

hase of a mislabeledly vary with the mis-

are sensible!). Theand alleged grades ismore elusive compo-ier replacement, skinwould not have pur-rice had he known its

many people believe that

inferiority has suffered additional damage. Thus the measure ofdamage is the amount a consumer would pay to avoid the decep-tion, that is, the value of the insured correct quality minus thevalue of the actual quality.

2. As a matter of deterrence, the penalties on the individual mis-labeler should be equal to a properly taken sum of the followingitems: (a) The damage per yard times the number of yards, sayper year. Let this be H. (b) The costs of the enforcement agency,say E, per year. This sum should include reimbursement of thecosts of those charged and acquitted. (c) The costs of defense (ifdetected) for the mislabeler, D. Where guilt is an appropriatenotion, as presumably in the case of mislabeling, the society maywish to ignore these costs, which is to say, resources devoted tothis end deserve no return. Where guilt is inappropriate, thesecosts should be reckoned in. The sum of these penalties must bemultiplied by lip, where p is the probability of detection of theoffense within the year. This probability is a function of E and H.

3. The enforcement agency should minimize the sum of damagesplus enforcement costs, + E) or + + E).5

This goal will serve two functions. The first is to set the scale of enforce-ment, namely where marginal return equals marginal cost. If the scale ofenforcement is correct, society is not spending two dollars to save itselfone dollar of damage, or failing to spend one dollar where it will save morethan that amount of damage. The second function is to guide the selectionof cases: the agency will not (as often now) seek numerous, easy cases todress up its record, but will pursue the frequent violator and the violatorwho does much damage.

This sort of criterion of enforcement is readily available in certainareas. The secret service, for example, reports that in fiscal 1967 the lossto the public from counterfeit money was $1,658,100.75 (an excellentinstance of counterfeit accuracy). Perhaps half of the $17 million spentby this agency was devoted to the suppression of counterfeiting, and tothis one must add the costs of legal actions, imprisonment, and so forth.The secret service should be asking whether the amount of counterfeitmoney passed would fall by a dollar if a dollar more were spent on en-forcement costs minus the corresponding fines collected.

5. The fines will be but the fines per se are transfers rather than social costs;see Becker (1958), pp. 180—8 1.


The penalty structure should incorporate the social appraisal of theimportance of the suppression of the offenses. The law does not in generalprovide this scale of values, as can be shown by the list of maximumpenalties for the violations of economic regulations listed in Table I.

The use of criminal sanctions is erratic, and the implicit equivalenceof fines and imprisonment varies from $1,000 per year to $10,000 per

TABLE 1PUBLIC PENALTIES FOR VIOLATION OF ECONOMIC STATUTES

PUBLIC PENAL

Offense

Enforcement MaximumOffense Agency Penalty Statute

Restraint of trade Antitrust Division $50,000 + 1 year Sherman (1890,(+ triple dam- 1955)ages and costs)

Unfair methods of FTC Cease and desist FTC (1914)competition order

Refusal to testify, FTC $l,000—$5,000 + Sameor testify falsely, 1 yearunder same

Price discrimina- FTC Cease and desist Clayton (1914)tion (+ triple dam-

ages and costs)False advertise- FTC $5,000 + 6 Wheeler-Lea

ments of foods, months (1938)drugs, orcosmetics

Adulteration or Secretary of $1,000 + 1 year, Copeland Actmisbranding of Health, first offense; (1938)food Education,

and Welfare$I0,000±3years, lateroffense

Exporting apples Dept. of Denial of certifi- Apples and Pearsand pears with- Agriculture cate for 10 days; for Exportout certificate of $100—$1,000 for (1933)quality knowing viola-

tionExporting apples Dept. of $1 barrel Standard Barrels

in improper Agriculture and Standardbarrels Grades of

Apples Act(1912)

Exporting otherfruit or vege-tables in im-proper barrels

Exporting grapesin improperbaskets

Giving rebates infreight charges(trucks)

Same, watercarriers

Failure to discloseinterest charges

Falsely certify acheck

Failure to delivergold or certifi-cates to FRBank whenordered

Evasion of excisetaxes

Securities Actviolation

Misbrandhazardoussubstances

DcI

Dc1

IC.

IC

FP

FE

Tr

SE

Se


Statute

Sherman (1890,1955)

FTC (1914)

Same

Wheeler-Lea(1938)

Copeland Act(1938)

Apples and Pearsfor Export(1933)

Standard Barrelsand StandardGrades ofApples Act(1912)

ocial appraisal of the.w does not in generalthe list of maximumlisted in Table 1.implicit equivalence

year to $10,000 per

MIC STATUTES

TABLE 1 (Concluded)PUBLIC PENALTIES FOR VIOLATION OF ECONOMIC STATUTES

Clayton (1914)

OffenseEnforcement

AgencyMaximum

Penalty Statute

Exporting other Dept. of $500 or 6 months Standard Barrelsfruit or vege- Agriculture if willful . . . for Fruits,tables in im- Vegetables andproper barrels . Other Dry

Commodities(1915)

Exporting grapes Dept. of $25 Standard Basketsin improper Agriculture Act (1916)baskets .

Giving rebates in ICC $200—$500 first Motor Carrierfreight charges offense; $250— Act (1935)(trucks) $5,000 repeated

offenseSame, water ICC $5,000 if willful Transportation

carriers Act (1940)Failure to disclose FRB Twice finance Consumer Credit

interest charges charge, within$100—$l,000;$5,000 and/or 1year if willful

Protection Act(1968)

Falsely certify a FBI $5,000 and/or 62 Stat. 749check 5 years (June 25, 1948)

Failure to deliver FRB Twice the number Federal Reservegold or certifi- of dollars Act (1913)cates to FRBank whenordered

Evasion of excise Treasury $10,000 and/or Revenue Acttaxes 5 years if will-

ful; forfeiture ofgoods andconveyance

(1954)

Securities Act SEC $5,000 and/or 5 Securities Actviolation years (1934)

Misbrand Secretary of $500 and 90 days; Hazardoushazardous Health, $3,000 or 1 year Substances Actsubstances Education,

and Welfareif willful orrepeated

(1960)

or


year. Many of the penalties are not even stated in the statutes: the penaltyfor drinking (industrial) alcohol which has not paid its beverage tax issometimes blindness or death. The penalties for the essentially similaroffense (if such it must be called) of reducing freight rates can be tentimes as much for a barge operator as for a trucker. Of course these maxi-mum penalties are not actual penalties, but one is not entitled to hope formuch more rationality or uniformity in the fixing of penalties for specificoffenses. (The lawyers have apparently not studied in adequate detail theactual sanctions for economic offenses.)

One may conjecture that two features of punishment of traditional•criminal law have been carried over to economic regulation: the attribu-tion of a substantial cost to the act of conviction itself, and the relatedbelief that moral guilt does not vary closely with the size of the offense.Whatever the source, the penalty structure is not well designed for eitherdeterrence or guidance of enforcement.

IV. CONCLUSION

The widespread failure to adopt rational criteria of enforcement of lawshas been due often and perhaps ustially.to a simple lack of understandingof the need for and nature of rational enforcement. The clarification ofthe logic of rational enforcement, and the demonstration that large gainswould be obtained by shifting to a rational enforcement scheme, arepresumably the necessary (and hopefully sufficient) conditions for im-proving public understanding of enforcement problems.6

There is, however, a second and wholly different reason for the use ofwhat appear to be inappropriate sanctions and inappropriate appropria-tions to enforcement bodies: the desire of the public not to enforce thelaws. The appropriations to the enforcement agency and the verdicts ofjuries are the instruments by which the community may constantly reviewpublic policy. If the society decides that drinking alcoholic beverages orspeeding in automobiles is not a serious offense in its ordinary form,they may curtail resources for enforcement and so compel the enforce-ment agency to deal only with a smaller number of offenses (perhapsoffenses of larger magnitude, such as chronic drunkenness or driving atextremely high speeds). There is considerable inertia in the legislative

6. The peculiarities of the structure of sanctions in economic regulation are partiallydue also to the response of the regulated businesses. They may effectively lobby to limitappropriations to the regulatory body, but they can also impose costly activities upon theregulatory body which force it to curtail other controls.

process—inertia that scto make continuouspriations committee byto modify the statutcflexibility in public pol

REFERENCES

Becker, Gary. "Crime a

Polilical Economy 7iSmith, Adam. The Weali


statutes: the penaltyd its beverage tax iste essentially similar•ght rates can be tenOf course these maxi-)t entitled to hope for

for specifrcin adequate detail the

shment of traditionalthe attribu-

tself, and the relatedte size of the offense.ell.designed for either

enforcement of lawslack of understanding

The clarification ofation that large gainscernent scheme, aret) conditions for im-

t reason for the use of)proprlate appropria-ic Fiol to enforce they and the verdicts oftay constantly reviewcoholic beverages orin its ordinary form,compel the enforce-

of offenses (perhapsenness or driving at

in the legislative

iic regulation are partiallyeffectively lobby to limit

costly activities upon the

process — inertia that serves highly useful functions — and it is much easierto make continuous marginal adjustments in a policy through the appro-priations committee by varying the resources for its enforcement than it isto modify the statute. Variation in enforcement provides desirableflexibility in public policy.

REFERENCES

Becker, Gary. "Crime and Punishment: An Economic Approach." Journal ofPolitical Economy 76 (March—April 1968). Included in this volume.

Smith, Adam. The Wealth of Nations. New York: Modern Library, 1937.

it Decisions." Atnerican

ago: Quadrangle, 1966.Income." Pub/ic Interest

Administration of JusticeWashington: U.S. Gov-

k Force Reports.") Wash-

conomic Analysis." M.A.

aws." Journal of Political

d. New York: Macmillan,

the U.S.A." Journal of the

us. Prisoners in State andU.S. Government Print-

U.S. Government Printing

U.S. Government Printing

iiers in State and Federal(ashington: U.S. Govern-

istitutions, 1951. NationalPrinting Office.

tional Prisoner Statistics.

Printing Office.istitutions, 1960. National

Printing Office.stitutions, 1964. National

Printing Office.stigation. Unifor,n Crime933 to date. Washington:

gly Unrelated Regressionstnerican StatisticalAssoC-

ining Unobservable Inde-11 (October 1970).

The Bail System:An Economic Approach

William M. LandesUniversity of Chicago and National Bureau of Economic Research

Widespread dissatisfaction with the current state of criminal justicein the United States has revived interest in the long-standing problem ofdetermining what to do with a person charged with a crime between thetime of his arrest and trial.' Should the accused be released or detainedduring this time interval? What factors are relevant to this decision?What requirements, if any, should be imposed on the accused as a con-dition of his release? The fundamental issue these questions raise is thedifficulty of reconciling the defendant's rights to freedom before his guilthas been formally adjudicated with the community's interest in protect-ing itself from possible future harm.2 In practice, most societies try to

This study has been supported by a grant for the study of law and economics from theNational Science Foundation to the National Bureau of Economic Research. I would like tothank Gary Becker, Barry Chiswick, John Hause, Benjamin Klein, and Elisabeth Landes fortheir criticisms and helpful comments, Elisabeth Parshley for her assistance, and H. IrvingForman for charting the graphs. I also benefited from comments at economic seminars atColumbia University, the University of Chicago, and the University of Massachusetts.

1. See, e.g., John N. Mitchell, Bail Reform and the Constitutionality of PretrialDetention, 55 Va. L. Rev. 1223 (1969); Laurence H. Tribe, An Ounce of Detention: Pre.ventive Justice in the World of John Mitchell, 56 Va. L. Rev. 371 (1970).

2. The definition of harm is itself an important source of controversy. See, e.g., JohnN. Mitchell, supra note 1; Laurence H. Tribe, supra note 1. One definition includes only

136 THE BAIL SYSTEM: AN ECONOMIC APPROACH

resolve this conflict by means of a bail system that establishes rules andprocedures to guide decisions on whether or not to release a defendant.These rules may specify which classes of defendants are eligible forrelease, and require an eligible defendant to make a monetary paymentto the court, pledge an asset that will be forfeited if he does not appearfor trial, or have a third party assume responsibility for his presence attrial.

In the U.S., the typical procedure is for the court to set a bond assecurity for the defendant's appearance at trial. If he can post the amountof the bond by pledging acceptable assets or by having a professionalbondsman do it for him, he is released; otherwise he is imprisoned. Datapresented in Table I reveal that a substantial fraction of defendants are infact imprisoned. A survey of more than 4,000 felony defendants across 70counties in 1962 showed that 53 per cent of these defendants were con-fined. A sample of defendants arraigned in New York City in 1971 indi-cates that 68 per cent of those charged with felonies and 5 1 per cent of zthose charged with misdemeanors were imprisoned for average periodsof 38 days and 14 days respectively. Moreover, among felony defendantsboth the likelihood of detention and the average days detained rose the ILl zmore serious the offense. Table 2 views pretrial detention from a differentperspective. It shows that of the more than 127,000 adult inmates in localjails in March 1970 (excluding 25,356 adults yet arraigned or being —

held for other authorities), 41 per cent were pretrial detainees. ThePresident's Commission reports that nearly 40 per cent of adults in prisonare in local jails.3 Thus, about one in 6 adults in prison are persons whoseguilt has not been formally determined.

The fact that large numbers of defendants are denied pretrial liberty—whether this is desirable or not—has important implications for theoverall operation of the criminal justice system. In the first place, the Z

greater the proportion of defendants not released, the lower the numberof trials relative to guilty pleas. The disposition of cases is affected in thisway because the costs of going to trial (specifically, the costs of waitingdue to court delay) are greater for detained defendants than those re-

the expected losses (e.g., a weakening in the deterrent effect of criminal sanctions) thatresult when some defendants flee, tamper with evidence, or intimidate witnesses duringthe period of pretrial release. This leads to (he view that the only justification for deny-ing or placing restraints on pretrial liberty is that the defendant's release would seriouslyimpair the proceedings against him. A broader definition of harm also includes predictionsabout the losses from crimes committed by released defendants. According to this view thepotential dangerousness of the defendant is a legitimate reason for denying pretrial liberty.

3. See U.S. President's Comm'n on Law Enforcement & Admin. of Justice, The Chal-lenge of Crime in a Free Society 172 (1967).

(C)

Cl)0)

>1(00

C-0C-

(0-

C APPROACH

hat establishes rules andto release a defendant.

fendants are eligible forake a monetary paymentted if he does not appearbility for his presence at

te court to set a bond asIf he can post the amountby having a professionale he is imprisoned. Dataction of defendants are inony defendants across 70

defendants were con-v York City in 1971 mdi-lonies and 5 1 per cent ofDned for average periodsamong felony defendants

days detained rose thekietention from a different000 adult inmates in local)t yet arraigned or beingpretrial detainees. The

er cent of adults in prisonare persons whose

are denied pretrial libertytant implications for thei. In the first place, thed, the lower the number

cases is affected in thisally, the costs of waiting

than those re-

ect of criminal sanctions) that)f intimidate witnesses duringhe only justification for deny-dant's release would seriouslyharm also includes predictionsnts. According to this view theon for denying pretrial liberty.

Admin. of.Justice, The Chal-

0

z— Lu

r.ULu

Lu

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0)

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0z

0)(0oz

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0)

0 N

N

00 0)

00

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137


TABLE 2DEFENDANTS NOT RELEASED ON BAIL IN LOCAL JAILS, MARCH 19708

Annual Operating and CapitalCosts Attributed to Inmates

Total

inmates NotReleased on

Bail and % Not

Not Released

Per InmateInmates b Awaiting Trial Released ($000) ($)

127,707 52,565 41.2 161,950 3,081lO6,08Id 2,017d

SouRcE.—U.S. Dep't of Justice, Law Enforcement Assistance Admin.,1970 National Jail Census 9-11 (Nat'l Crim. Justice Inf. & Stat. Serv. 1971).

a Local jails are those operated locally in municipalities which in 1960 had apopulation of 1,000 or more. Facilities which normally detain persons for 2 daysor less were excludecL

b Excludes 25,356 adults who were not yet arraigned or who were being heldfor other authorities, and 7,800 juveniles.

Total was 203,967,000 but this was multiplied by .794 to take account ofinmates who were excluded. Operating costs were for 1969 while capital costswere those planned for 1970.

Operating costs alone.

leased. Secondly, defendants not released are likely to have higher con-viction probabilities in a trial and receive longer sentences if they pleadguilty than defendants released on bail. This occurs because detentionadversely affects the productivity of the defendant's resources (bothmarket and timeinputs). For example, in the case of market inputs de-tention would hamper consultation with lawyers, and in the case of timeinputs detention would make it more difficult to seek out witnesses andengage in other investigatory activities. Finally, if making bail is a positivefunction of wealth, then the effects of pretrial imprisonment would fallmost heavily on low-income defendants.4 Recent empirical research onthe criminal court system provides some support for these hypotheses.5

4. See William M. Landes, An Economic Analysis of the Courts, this volume, for afurther development of these arguments.

5. See William M. Landes, supra note 4, for an empirical analysis across state countycourts using multiple regression techniques. A study by the New York City Legal AidSociety (Brief for Appellee, Bellamy v. Abruczo (N.Y. Sup. CL, March 1972)) of de-fendants in New York City also finds a positive relationship between pretrial detentionand the likelihood of a prison sentence, holding constant the defendant's prior record,

The purpose ofpretrial liberty and bailthe usual one. instead olrices or proposed reforlveloping an economic fll(derive the social benefitgains to defendants fromthe rest of the communitber of defendants tobail system that are cornfit.6 After developing therules derived from an opUnited States: for examserious offenses and forevidence on this), andto bail except for certaicapital offenses). Two cotern—deterring flight andthe model as special casmaximizing the social be

The mainalternative methods to sand variations on them anon of maximizing theresponds to most existirtheir release. The seconca monetary or other fornovel but, as we show, isystems.7 The final part oof crediting a defendant's

family ties, employment statusupports some of these hypothN.Y.U.L. Rev. 641 (1964).

6. This model is based onAn Economic Approach, inclucriminal offenses by selectingminimize the community's lossalthough his approach is applic

7. Gordon Tullock discuson bail in The Logic of Law ILandes, pp. 178—79 this volun

C APPROACH WILLIAM M. LANDES 139

L JAILS, MARCH 1970 a

ual Operating and Capitalts Attributed to Inmates

Not Released

Total C

($000)Per Inmate

($)

61,950 3,08106,081d

ment Assistance Admin.,nf. & Stat. Serv. 1971).alities which in 1960 had ay detain persons for 2 days

ted or who were being held

by .794 to take account ofr 1969 while capital costs

ely to have higher con-sentences if they pleadcurs because detentiondant's resources (bothse of market inputs de-and in the case of timeseek out witnesses andmaking bail is a positivenprisonment would fallempirical research onfor these hypotheses.5

e Courts, this volume, for a

analysis across state countyNew York City Legal Aid. Ct., March 1972)) of de-between pretrial detention

te defendant's prior record,

The purpose of this essay is to reexamine the important questions ofpretrial liberty and bail determination from a different viewpoint thanthe usual one. Instead of focusing on the desirability of actual bail prac-tices or proposed reforms and their constitutionality, we begin by de-veloping an economic model of an optimal bail system. Our approach is toderive the social benefit from pretrial liberty that incorporates both thegains to defendants from being released on bail and the costs and gains tothe rest of the community from their release. We then determine the num-ber of defendants to release and the level of resource expenditures on thebail system that are consistent with the maximization of the social bene-fit.6 After developing the basic model we consider the consistency of therules derived from an optimal system with some existing practices in theUnited States: for example, the practice of setting higher bail for moreserious offenses and for defendants with prior arrests (see Table 1 forevidence on this), and the rationale of legislation that guarantees a rightto bail except for certain classes of defendants (e.g., those accused ofcapital offenses). Two common views on the proper function of a bail sys-tern—deterring flight and preventing future crime—are incorporated intothe model as special cases and compared to the more general criterion ofmaximizing the social benefit.

The main contribution of this essay, however, is the development ofalternative methods to select defendants for release. Two basic methodsand variations on them are analyzed. Both are consistent with the crite-rion of maximizing the social benefit function. The first, which cor-responds to most existing bail systems, requires defendants to pay fortheir release. The second compensates defendants for their detention viaa monetary or other form of payment. The latter proposal is not onlynovel but, as we show, is superior in a number of ways to existing bailsystems.7 The final part of the paper brings into the analysis the advantageof crediting a defendant's pretrial detention against his eventual sentence,

family ties, employment status, and seriousness of the charge. For an early study thatsupports some of these hypotheses see Anne Rankin, The Effect of Pretrial Detention, 39N.Y.U.L. Rev. 641 (1964).

6. This model is based on one presented by Gary S. Becker in Qime and Punishment:An Economic Approach, included in this volume. Becker determines the optimal supply ofcriminal offenses by selecting values for the probability of conviction and the penalty thatminimize the community's loss from crime. He does not explicitly consider the bail system,although his approach is applicable to devising rules for an optimal bail system.

7. Gordon Tutlock discusses the possibility of compensating defendants not releasedon bail in The Logic of Law 194—95 (1971). and I have briefly analyzed it. See William M.Landes, pp. 178—79 this volume.


the possibility of tort suits by detained defendants who are acquitted, andthe role of bail bonds and bondsmen.

THE MODEL

GAINS FROM RELEASE

Let us assume that n defendants have been arrested and accused of com-mitting similar types of crimes. From this group some will be detained injail while others will be released during the period between arrest and trial.Let us also assume that each of the n defendants is expected to do thesame amount of harm prior to trial if released on bail.8 There are twosources of gains to the community from releasing defendants: the gains tothe defendants (whom we assume are members of the community) andthe gains to the rest of the community. The gain to the defendant frombeing released on bail (which is rigorously specified in a later section)depends in part on his earnings outside prison, his wealth, the value heplaces on the nonpecuniary aspects of pretrial liberty net of the con-sumption provided him in prison, and any changes in the expected futurevalue of these variables resulting from pretrial liberty (e.g., higher ex-pected future earnings if pretrial release lowers the probability of convic-tion).9 The aggregate gain to all defendants released is the sum of the in-dividual gains and can be written as

G G(b, t, p, u) (1)

where b is the number released on bail (b n),'° t is the time from arrestto disposition of a case (or, equivalently, the length of pretrial detention),

8. The assumption of equal harm is not unreasonable in view of the earlier assumptionthat defendants are accused of similar crimes, which is one indicator of potential harm. Wemake the assumption of equal harm in order to simplify the presentation of the model.Differences in harm can be handled by dividing n into subgroups of defendants (i.e.,n1, n2 n,,) where each subgroup consists of persons who are each expected to do thesame amount of harm if released on bail. We would then derive the number of defendants torelease in each subgroup instead of simply the total number released. The implications of

differences in harm are discussed later.9. All gains and costs in the paper are measured in terms of monetary equivalents.10. Aggregating the individual gains into the G function depends on which of the n

defendants are released. That is, if b, t, p and u were given and defendants differed in theirgains from release, G would still be unknown unless one specified which defendants werereleased. Therefore, we make the followIng assumption: if only one person is released, it isthe defendant witn the highest gain; if two are released, it is the first defendant plus thedefendant with the second highest gain, etc. The justification for this ordering will become

p is the probability oftrial, and u is the influen(Hereafter, residual tenincrease as more deflengthens, and as the0, and < 0 where aall derivatives in the pa

The seco'hd gain frcto members of the comrdirect costs of providirexpenditures for jails,with b and t as in

where > 0 andinsignificant. The Presidefend ant of pretrial delpresented in Table 2 intlpretrial detention facilitcost per defendant of al

COSTS OF RELEASE

It is not costless to relharm or damage may rcurred had these defendfrom crimes committedand from a possible redsome defendants disapnesses.12 Thus the expcan be written:

clearer when methods for refunctions that are specified I

since defendants can be assuithese functions are independ

11. See U.S. Presidenl'Courts 38 (Task Force Repc

12. As noted earlier (Sdesirability of including predthough we include it, the mocis developed later on.

c APPROACH WILLIAM M. LANDES 141

:s who are acquitted, and

ted and accused of corn-some will be detained inbetween arrest and trial.

its is expected to do theon bail.8 There are two;defendants: the gains toof the community) and

in to the defendant fromcified in a later section)his wealth, the value heliberty net of the con-

es in the expected futureliberty (e.g., higher ex-

he probability of convic-sed is the sum of the in-

(1)

I is the time from arrest;th of pretrial detention),

view of the earlier assumptionndicator of potential harm. Wehe presentation of the model.ubgroups of defendants (i.e.,o are each expected to do theye the number of defendants toreleased. The implications of

rms of monetary equivalents.m depends on which of the nnd defendants differed in theireciuied which defendants were

one person is released, it isis the first defendant plus the'for this ordering will become

p is the probability of reapprehension for a defendant not appearing attrial, and u is the influence of other factors affecting the gains from release.(Hereafter, residual terms such as u are deleted.) One would expect G toincrease as more defendants are released, as the period of releaselengthens, and as the probability of recapture falls. That is, Gb > 0, G1 >0, and G0 < 0 where 9G/ab = (etc.). (The latter notation is used forall derivatives in the paper.)

The second gain from releasing defendants on bail, accruing primarilyto members of the community who are not defendants, is the reduction indirect costs of providing detention services, which includes savings onexpenditures for jails, guards, food, etc. These savings would increasewith b and t as in

J=J(b, 1) (2)

where 0 and f > 0. The savings from releasing defendants are notinsignificant. The President's Commission estimates that the costs perdefendant of pretrial detention are between $3 and $9 per day.1' The datapresented in Table 2 indicate that the annual operating and capital costs ofpretrial detention facilities are more than $161 million, which comes to acost per defendant of about $3,000 annually and $8.50 per day.

COSTS OF RELEASE

It is not costless to release de'fendants on bail. As previously indicated,harm or damage may result to the community that would not have oc-curred had these defendants been in custody. The harm will include lossesfrom crimes committed by defendants during the period of pretrial libertyand from a possible reduction in the effectiveness of the legal system assome defendants disappear, tamper with evidence, or intimidate wit-nesses.12 Thus the expected harm from all defendants released on bailcan be wrItten:

clearer when methods for releasing defendants are considered. The ordering of b in thefunctions that are specified later is identical to the ordering in the G function; however,since defendants can be assumed identical with respect to the other functions, the values ofthese functions are independent of the ordering of b.

11. See U.S. President's Comm'n on Law Enforcement & Admin. of Justice, TheCourts 38 (Task Force Report, 1967).

12. As noted earlier (see supra note 2), considerable controversy exists over thedesirability of including predictions about future crime in decisions on pretrial liberty. Al-though we include it, the model would essentially be unchanged by its exclusion. This pointis developed later on.

142 TI-LE BAIL SYSTEM: AN ECONOMIC APPROACH

H = H(b, t, p). (3)

H will tend to be greater, the greater the number of defendants released onbail, the longer the period of release and the less likely that defendants arereapprehended. That is, 0, H,> 0, and <

A second source of costs (which for convenience are grouped to-gether) consists of expenditures by the state to reapprehend defendantsand to affect the length of pretrial release. These costs may be written as

C = C(b, p, t). (4)

Since an increase in the probability of reapprehension (p) and a decreasein the period of pretrial release (t) require greater resources,C, < 0. Cb is assumed positive for two reasons. First, an increase in b islikely to increase the number of released defendants who flee. With pconstant, this implies a proportionate increase in reapprehensions andhence greater costs. Second, defendants released on bail are more likelyto go to trial (and less likely to plead guilty) than defendants not released,SO that an increase in b will increase trial demand.14 This in turn willincrease court delay and raise t for a given supply of trials. Thus anincrease in b with t constant requires greater expenditures on the courtsystem and hence an increase in C.'5 Note that C is set at 0 when b = 0

13. Since we assume the expected harm from each released defendant is the same,H can be written as b I,(r, p) where ii(z, p) is the expected harm per defendant.

14. See William M. Landes. pp. 176—82 this volume.15. This point is not as obvious as it may first appear. If one believes that the "quality"

of justice resulting from plea bargaining and guilty pleas is about as good as the "quality"from trials, then any additional demand and subsequent expenditures for trial services thatresult from increasing the number of defendants released is a cost to the community. It is acost in the following sense: the "quality" ofjustice is not being enhanced by releasing moredefendants but a more expensive method of disposing of cases (i.e., more trials) is beingused. Alternatively, if one believed that "quality" is raised by more trials and fewer pleas,then part or all of these additional expenditures on trials should be excluded from the abovecost function. These two views come close to those described in "The Crime ControlModel" and "The Due Process Model" in Herbert L. Packer, The Limits of the CriminalSanction 210—21 (1968). For example, "The Crime Control Model" rests on the belief thatmost persons charged with a crime are "factually guilty" and hence a major cost of makingpretrial liberty the norm is that "the increase in time required to litigate cases that don'treally need to be litigated would put an intolerable strain on what is already an overburdenedprocess." In contrast, "The Due Process Model" starts from the assumption that the ac-cused "is not a criminal." Pretrial detention and guilty pleas are often undesirable becausethey lead one "to waive the various safeguards against unjust conviction that the system pro-

When large numbers of defendants are detained and plead guilty, "the adversary sys-tem as a whole suffers, because its vitality depends on effective challenge."

because there are no ex.penditures on the crimin;included in C.

NET BENEFIT FUNCTIO

The net benefit from relecost components specifiand t. In principle, a nurnet benefit function.'6 Buto a simple formulation ccost and gain componentnet gain from releasing

7T G(b, 1,

Optimality requires thatthat maximize the valuerelease in a way that yielmethods for selecting dconsidered. In the first,the defendant is paid fot

THE DEFENDANT PAY!

The n defendants willbe written as

where in is the price dand p are defined as befmum amount they woulopportunity cost of theito prison life, a decline

16. For example, if onevague and difficult to predicbenefits. If part of G includean inappropriate source offunction. Alternatively, if it sbe detained, a greater weightall defendants were released

APPROACH

(3)

defendants released onely that defendants are( 0.13ience are grouped to-apprehend defendantsosts may be written as

(4)

ion (p) and a decreaseesources, > 0 andirst, an increase in b isants who flee. With pi reapprehensions andon bail are more likelyefendants not released,nd.14 This in turnply of trials. Thus anenditures on the courtis set at 0 when b = 0

ased defendant is the same,rm per defendant.

te believes that the "quality"out as good as the "quality"ditures for trial services thatost to the community. It is aenhanced by releasing mores (i.e., more trials) is beingmore trials and fewer pleas,be excluded from the aboveled in "The Crime ControlThe Limits of the Criminal

odel" rests on the belief thatence a major cost of makingI to litigate cases that don't

is already an overburdenedthe assumption that the ac-

re often undesirable becausenviction that the system pro-Id guilty, "the adversary sys-e challenge."

WILLIAM M. LANDES 143

because there are no expenditures on p, and only the increment in ex-penditures on the criminal court system that result from a positive b areincluded in C.

NET BENEFIT FUNCTION

The net benefit from releasing defendants on bail depends on the gain andcost components specified above, which in turn are functions of b, p,and t. In principle, a number of additional considerations could enter thenet benefit function.'6 But in the analysis that follows we restrict ourselvesto a simple formulation of the net benefit function, which is the sum of thecost and gain components. This measures the monetary equivalent of thenet gain from releasing defendants and is denoted by

G(b, t, p) ± J(b, t) — I-I(b, t, p) — C(b, t, p). (5)

Optimality requires that we simultaneously select values for b, t, and pthat maximize the value of ir. By assumption, defendants are selected forrelease in a way that yields the highest G arid therefore the highest 77. Twomethods for selecting defendants that satisfy the above assumption areconsidered. In the first, the defendant pays for his release; in the second,the defendant is paid for remaining in jail prior to trial.

I

THE DEFENDANT PAYS

The n defendants will have a demand function for release on bail that canbe written as

b b(rn, I, p), (6)

where in is the price defendants must pay for pretrial release, and b, t,and p are defined as before. Since defendants generally differ in the maxi-mum amount they would pay for release, depending on differences in theopportunity cost of their time, wealth, and tastes for nonprison comparedto prison life, a decline in ni (holding t and p constant) would lead more

16. For example, if one believed that the harm defendants were expected to do was toovague and difficult to predict, H might be given a small weight in the calculation of netbenefits. If part of G included the gains to persons from further crimes and this was deemedan inappropriate source of utility, C could be discounted in estimating the net benefitfunction. Alternatively, if it was strongly felt that defendants later found innocent should notbe detained, a greater weight could be given to G. (In the extreme, G would be so large thatall defendants were released.)

(Hb) plus marginal(Cb) minus theant would choose rele;exceeded his gain, theif m were set at ui whe:

Thus, defendants are cFmarginal harm and cooptimum is illustrated i

Several implicatior(1) Wealthier defei

their release on bail be

18. Although C is the nmaximize with respect to tvalue of b that satisfies equaconditions would then includ

where (1) and (ii) have been s(i) and (ii) in the subsequent

19. Atthisstagelamigperson to remain in jail altholeased at a price of ut would

20. Second-order condi'62G/ab2, etc.). Figure 1 a;

plausible that Gbb < 0 becaidefendants released value thwould probably be positive bdetention rise with the numbicost saving will fall as more

(7) recapturing defendants andhence Cbs > 0. Note that Iamount of harm if releasedC5—J5 for all values of b, ti

All defendants are char.similar offenses and equal htway bail actually operates.bail rates are often preordadollars for such and such a c'to place is to leave out of cfinancial means but also theto the community." U.S. Pisupra note 3, at 131.

144

Money bail

THE BAIL SYSTEM: AN ECONOMIC APPROACH

(II, + C, —4)

G,

b

m

Number released on bail

FIGURE 1

defendants to choose release on bail in preference to jail.'7 Similarly, anincrease in t and a decrease in p would raise the relative attractiveness ofpretrial release, and increase its demand. Therefore, we would expect thatb,,, < 0, <0, and b1 > 0.

Now consider the optimality conditions for maximizing the netbenefit The variables subject to direct control by the state are C, thecosts of recapturing defendants and reducing the period of pretrial release,and in, the level of money bail or the price of release. These variablesdetermine b, p, and t which then determine ir. Maximizing ir first withrespect to ni yields

Gb= Hb+ Cb—Jb.

In words, money bail should be set at a level where the marginal gain frompretrial release of an additional defendant (Gb) equals the marginal harm

17. Evidence from samples of defendants in the U.S. supports the view that moneybail is both negatively related to and an important determinant of the number of defendantsreleased. See, e.g., Note, A Study of the Administration of Bail in New York City, 106U. Pa. L. Rev. 693 (1958); Charles E. Ares,Anne Rankin & Herbert Sturz, The ManhattanBail Project: An Interim Report on the Use of Pre-Trial Parole, 38 N.Y.U.L. Rev. 67(1967); Note, Compelling Appearance in Court: Administration of Bail in Philadelphia,102 U. Pa. L. Rev. 1031 (1954); U.S. Atty. Gen'l's Comm. on Poverty & Admin. of Crim.Justice, Report, app. 1 (1963).

, + — J,)

th = Gb = + Cb — Jb. (8)

C,

(i)

(ii)

where (i) and (ii) have been simplified by the substitution of equation (7). We largely ignore(i) and (ii) in the subsequent analysis since our main interest is the determination of b and

19. At this stage I am ignoring difficulties of financing ni. These difficulties could lead aperson to remain in jail although his gain exceeded m so that the number of defendants re-leased at a price of th would be less than optimal.

20. Second-order conditions require that C,,,. < H,,,. + Cbb — Jbb at b (where C,,,. =a1G1ab2, etc.). Figure 1 assumes that C,.,, < 0 and (H,,b + C,,, —J,.,,) > 0. It seemsplausible that C,,. < 0 because the ordering of b in the C function is such that additionaldefendants released value their release by smaller and smaller amounts. (H,., + — J,,,)would probably be positive beyond some level of b for two reasons. If the marginal costs ofdetention rise with the number detained, J,., will be negative (and hence—f,,,, > 0) since thecost saving will fall as more defendants are released. If there are diseconomies of scale in

(7) recapturing defendants and reducing court delay, C,, would be a rising function of b andhence C,, > 0. Note that H,,. = 0 because all defendants are assumed to do the sameamount of harm if released. Corner solutions are possible. For example, if C,. > H,, +C,.—f,. for all values of b, then b= a, and ifG, < H,, + Cb—J,. for all b, then b =0.

All defendants are charged the same price for release. In view of our assumptions ofsimilar offenses and equal harm, the use of a single price appears to be consistent with theway bail actually operates. For example, the President's commission reports thatbail rates are often preordained by stationhouse or judicial schedules: so and so manydollars for such and such a crime. The effect of standard rates and their disparity from placeto place is to leave out of consideration not only the important question of a defendant'sfinancial means but also the equally important ones of his background, character, and tiesto the community." U.S. President's Comm'n on Law Enforcement & Admin. of Justice,szipra note 3, at 131.

APPROACH WILLIAM M. LANDES 145

(Ho) plus marginal costs of reapprehension and expanding court services(Cb) minus the marginal savings in detention costs Since a defend-ant would choose release if his gain exceeded m, and prefer jail if rnexceeded his gain, the optimal number of defendants would be releasedif nt were set at th where

Thus, defendants are charged a price for release that compensates for themarginal harm and costs minus the savings in detention costs.19 Theoptimum is illustrated in Figure 1 at b and th.2°

Several implications of the optimality conditions are worth noting.(I) Wealthier defendants would be willing to pay a higher price for

their release on bail because forgone earnings tend to rise with wealth,

18. Although C is the remaining variable subject to control, it is more convenient tomaximize ir with respect to I and p. This would determine the optimal level of C given thevalue of b that satisfies equation (7). In addition to equation (7), the first-order optimalityconditions would then include

to jail.17 Similarly, anlative attractiveness of

we would expect that

r maximizing the netby the state are C, thenod of pretrial release,lease. These variablesaximizing first with

the marginal gain fromials the marginal harm

ports the view that moneyof the number of defendants

au in New York City, 106rbert Sturz, The Manhattan

role, 38 N.Y.U.L. Rev. 67of Bail in Philadelphia,

Poverty & Admin. of Crim.


and "days free" are likely to be, in part, a consumption good with a wealthelasticity greater than zero. Other things being equal, this would lead to agreater frequency of pretrial release for defendants with higher incomes,independent of capital market difficulties in financing bail. Althoughreleased defendants would be buying their freedom, they would never-theless be compensating society for the marginal harm and costs of theirrelease via the payment of money bail.2'

(2) We have assumed that differences among defendants in expectedharm do not exist. Suppose these differences exist and are detectable. Wecould then separate defendants into subgroups where persons in eachsubgroup were expected to inflict the same harm if released on baiL Sub-groups expected to do more marginal harm (i.e., a higher with stillequal to zero for each subgroup) would generally have money bail set at ahigher level and a smaller proportion of defendants released.22 in termsof Figure 1, the supply curve would be further to the left for subgroupsexpected to do more harm, resulting in a higher m and lower b for a givenG function.

(3) Suppose there was an exogenous increase in congestion in thecourt system which increased the delay between arrest and trial. This

21. It has been suggested that bail would be more equitable if it were set with regardto the defendant's ability to pay (i.e., his wealth). In our model this would have the effect ofincreasing the state's revenue without altering the number or composition of released de-fendants. Higher prices to wealthier defendants would enable the state to extract some of thedefendants' surplus (i.e., consumers' surplus) in Figure 1.

22. The net benefit function can be redefined as follows:

= G(b,, b2 ,...,b,, 1, p) + J(b, 1) — H(b, b2 b,,, 1, p) — C(b, t, p),

where b = b, + b, . . . + b,, and where defendants continue to be identical with respect tothe J and C functions. Maximizing 7T with respect to the b's (1 = 1 n) and settingoptimal prices for release yields

th, = Gb, = H,,, — C,, + ib.

If we assume that the demand curve for release is the same for the n groups and ,3(H,,,)Ia,,, = 0. then the greater the group's marginal harm, the lower the proportion released andthe higher the price of release. One might argue that a group's demand curve for releasewould be positively correlated with its marginal harm (i.e., the more harm a defendant islikely to do, the greater is his gain from release on average). Our prediction of a decline inthe proportion released as the marginal harm rises would still hold if the G,, function shiftedup by a smaller amount than the (H,, + C,, — J,,) function. However, it is by no means ob-vious that the marginal harm and gain are positively correlated. Innocent defendants arelikely to do the least harm if released, and their gain from release may be even greater thanfor guilty defendants. The former, if detained, incur losses not only in current but also futureincome resulting from any stigma attached to being in jail. They also may incur sizablesearch costs to obtain employment after being found innocent and released.

would raise theFigure 1. If increasesdoes not change), thereoptimal in and the numchange in H5 more thanthe direction of change

OPTIMAL BAIL AND C

Having set forth the battices with the prescriptisize of the bail bond terand the number of pricharge •and prior arresfendants released declinumber of prior arrestsystem under the assuarrests are indicators c(Cb). The severity of tharm for two reasonsdamages from possibli(holding constant the Icharge, the greater thedefendant's gain (thefrom not appearing forreapprehending defendpositively correlated sihave a lower probabilisoning can be usedmarginal harm and maitenuous in the absenceprior arrests with martprovide some rationalemal system.

23. One difference shotis a cash payment not returrequired to post a bond forference is not important foras the cash fee paid the bonc•net benefit by setting a valuean amount equal to the payieffect on the analysis at thit


ption good with a wealthual, this would lead to aits with higher incomes,nancing bail. AlthoughLom, they would never-harm and costs of their

would raise the defendant's gain from release and shift to the right inFigure 1. If increases in H5 and J5 offset each other as t rises (and C5does not change), there will be no shift in the supply curve and both theoptimal in and the number of defendants released on bail will rise. If thechange in H5 more than offset the change in one could no longer predictthe direction of change in the number released.

defendants in expectedt and are detectable. Wewhere persons in eachif released on bail. Sub-higher Hb with Hbb still

have money bail set at ants released.22 In termso the left for subgroupsand lower b for a given

se in congestion in thearrest and trial. This

ble if it were set with regardthis would have the effect ofcomposition of released de-

ic state to extract some of the

t, p) — C(b, i, p),

be identical with respect tos (1 = 1,..., n) and setting

for the n groups andthe proportion released and's demand curve for releasee more harm a defendant isPur prediction of a decline inold if the G5 function shiftedwever, it is by no means ob-ed. Innocent defendants arese may be even greater thannly in current but also future'hey also may incur sizableand released.

OPTIMAL BAIL AND CURRENT PRACTICES

Having set forth the basic model, we now compare some actual bail prac-tices with the prescriptions of an optimal system.23 Table 1 shows that thesize of the bail bond tends to increase with both the severity of the chargeand the number of prior arrests (though this does not hold for everycharge and prior arrest class). Not surprisingly, the proportion of de-fendants released declines with both the severity of the charge and thenumber of prior arrests. These results are consistent with an optimalsystem under the assumption that the severity of the charge and priorarrests are indicators of greater marginal harm (Rb) and marginal costs(C5). The severity of the charge may provide information on marginalharm for two reasons: (1) present charges are one predictor of thedamages from possible offenses during the period of pretrial release(holding constant the rate of recidivism); and (2) the more serious thecharge, the greater the possible punishment and hence the greater thedefendant's gain (the avoidance of punishment being one component)from not appearing for trial. It follows from (2) that the marginal cost ofreapprehending defendants (Cb) and the seriousness of the charge arepositively correlated since defendants faced with more serious chargeshave a lower probability of voluntarily appearing for trial. Similar rea-soning can be used to relate the number of prior arrests to greatermarginal harm and marginal costs. Admittedly, the above arguments are

• tenuous in the absence of empirical data connecting present charges andprior arrests with marginal harm and marginal costs. Nevertheless, theyprovide some rationale for present practices in the framework of an opti-mal system.

23. One difference should be noted at the outset. Money bail, in, in the optimal systemis a cash payment not returned to the defendant. In actual practice, most defendants are

• required to post a bond for which they pay a cash fee to a bondsman. However, this dif-ference is not important for the analysis because we can redefine in in the optimal system•as the cash fee paid the bondsman. Optimality would then require the state to maximize thenet benefit by setting a value for the bond that resulted in the defendant paying the bondsmanan amount equal to the payment detived in equation (8). Hence, the use of bonds has littleeffect on the analysis at this stage and is left for a later section and the appendix.

148 THE BA[L SYSTEM: AN ECONOMIC APPROACH

For certain offenses, the marginal harm and marginal cost may be sogreat that it is not feasible for the defendant to compensate the communityfor his pretrial release. (in terms of Figure 1, the supply curve would beeverywhere above the demand curve.) Optimality would be consistentwith legislation that prohibited pretrial liberty or permitted the denial ofbail for these offenses. In the United States, state and local laws providedefendants with a right to bail in noncapital offenses but permit the denialof bail in capital offenses. Since capital offenses are the most serious,existing laws would appear to conform to the rules of an optimal system.The classic capital offense, murder, does not entirely fit the argument fordenying bail to defendants accused of more serious offenses. Since"most persons who are charged with this offense murder family membersor paramours and therefore are the least likely of all offenders to berecidivists," the denial of bail could not be based on predictions aboutcommitting more murders during the time of pretrial release. instead, itwould have to rest on the contention that persons faced with the prospectof such severe penalties would be most likely to flee.25

One can interpret the joint effect of the Eighth Amendment, whichstates that "excessive bail shall not be required," and legislation thatgrants a right to bail (except for capital offenses), as requiring that moneybail be set according to the amount the defendant can afford without re-gard to marginal harm and marginal costs. A less extreme position wouldrequire setting art upper limit to money bail at a "reasonable" level. Ifthis level were less than the amount that maximized the net benefit func-tion, some defendants would be released even though marginal damagesand costs exceeded the gains from their release. In response, one mightexpect the development of measures that circumvented constitutionaland legislative restrictions on setting bail: for example, "preventivedetention" in noncapital offenses (in effect, the setting of an infinite bailcharge) or the imposition of travel restrictions, requirements of weeklyappearances, etc., on released defendants to reduce marginal harm andcost.

ALTERNATIVE VIEWS OF OPTIMAL BAIL

There are two views of bail that dominate much of the current discussionon the topic. The first asserts that the primary function of a bail system isto ensure the defendant's appearance at trial. Money bail should be set, ifat all, to prevent flight or more generally to prevent the defendant from

24. See John N. Mitchell, supra note 1, at 1236.25. This point is made forcefully by Laurence H. Tribe, supra note 1.

interfering with the prtives to money bail anasserts that the prevepretrial liberty is a prpotential "dangerousisetting high bail or deposition is termed the"preventive detentiorbasic model developeincorporated into net

Deterring Flight:

Preventive Detention

There areequal values of b, t, ar,of defendants releaselease (He), and from 1greater in the "prevesince the former add:about future crime. Imarginal cost of incrcterring flight" model btrials that results fromIn contrast, a willinggreater demand for trtion" model. Thus, Cducing the period of,cluded from the "dete

We can now con

26. These descriptiontions. Two recent paperssupra note 1, and Laurencetive detention" model, whimodel. An excellent discus"preventive detention" is Iof his "Due Process Mode

27. One should noteexcluded from (5a) and (SIalso assume that C, and ((ention" model tends to ovtext between (5a) and (5tmodels.


interfering with the proceedings against him. Wherever possible, alterna-tives to money bail and detention should be encouraged. The second viewasserts that the prevention of crimes by defendants during the period ofpretrial liberty is a proper concern of the bail process. Accordingly, thepotential "dangerousness" of the defendant is a legitimate reason forsetting high bail or denying bail altogether. For convenience, the formerposition is termed the "deterring flight" model and the latter is called the"preventive detention" model.26 Both models are special cases of thebasic model developed earlier in the paper and, therefore, both can beincorporated into net benefit functions as follows.

Deterring Flight: ir1= G1(b, t, p) — H1(b, t, p) C1(b, p) (5a)

Preventive Detention: IT2 G2(b, t, p) — J1,(b, 1, p) — C0(b, 1, p). (5b)

There are several important differences between (5a) and (5b) atequal values of b, r, and p. The marginal harm from increasing the numberof defendants released (H5), from lengthening the period of pretrial re-lease (H1), and from lowering the probability of reapprehension (HP) aregreater in the "preventive detention" than the "deterring flight" modelsince the former adds another dimension to harm — namely predictionsabout future crime. Hence, H,,, < 1125, H,, < Hi,, and H,,, > Themarginal cost of increasing the number released (C,,) is less in the "de-terring flight" model because it does not regard the additional demand fortrials that results from releasing more persons as a cost of the bail system.In contrast, a willingness to include the costs of added congestion andgreater demand for trials is more characteristic of the "preventive deten-tion" model. Thus, C,,, < C25. It also follows that the direct costs of re-ducing the period of pretrial detention or court delay (C,) would be ex-cluded from the "deterring flight" model.27

We can now compare the optimal values of in, b, t, and p that are

26. These descriptions are simplifications of the two positions and their many varia-tions. Two recent papers that provide more detailed descriptions are John N. Mitchell,siipra note 1, and Laurence H. Tribe, ,cupra note I. Mitchell argues in favor of the "preven-tive detention" model, while Tribe argues against it and in favor of the "deterring flight"model. An excellent discussion is also contained in Herbert L. Packer, supra note 15, where"preventive detention" is part of his "Crime Control Model" and "deterring flight" is partof his "Due Process Model."

27. One should note that the savings irs detention costs (the J function) have beenexcluded from (Sa) and (Sb) since both models give little or no weight to these savings. Wealso assume that G, and C2 are equal, although it may be argued that the "preventive de-tention" model tends to overlook these gains. However, the differences already noted in thetext between (5a) and (Sb) are sufficient for comparing the main implications of the twomodels.

APPROACH

narginal cost may be sopensate the communitysupply curve would be

ty would be consistentpermitted the denial ofand local laws provide

es but permit the denials are the most serious,s of an optimal system.

rely fit the argument forserious offenses. Sincemurder family members

of all offenders to beed on predictions abouttrial release, Instead, itfaced with the prospect

tth Amendment, which," and legislation thatts requiring that moneycan afford without re-

position would"reasonable" level. If

ed the net benefit func-ugh marginal damages.n response, one mightnvented constitutionalexample, "preventivetting of an infinite bail

of weeklyce marginal harm and

the current discussiontion of a bail system is

bail should be set, ifnt the defendant from

upra note 1.


obtained from maximizing the net benefit functions in (5a) and (5b). The"deterring flight" model results in a lower money bail and a greater pro-portion of defendants released than the "preventive detention" modelsince both the marginal harm and marginal costs (and hence the supplycurve in Figure 1) are lower in the former than in the latter. The optimalperiod of pretrial detention is less in the "deterring flight" model as themarginal cost of reducing this time interval is excluded from the model'sspecification. This means that court delay or pretrial detention is kept at aminimum (i.e., where = in the "deterring flight" model. Any-thing greater lowers the net benefit. Supporters of this model would there-fore favor a greater allocation of resources to the judiciary to reducedelay. On the other hand, advocates of the "preventive detention" modelwould put less emphasis on expanding the court's resources because theresulting marginal benefits (a lower H) would eventually be offset by thecosts of reducing delay. In the latter model, the greater harm that resultsfrom longer periods of pretrial liberty is countered by releasing fewer per-sons. Finally, the optimal probability of reapprehending defendantswould be set higher in the "preventive detention" than the "deterringflight" model because one element of harm from a lower probability (i.e.,future crime) is explicitly excluded from the latter model.

THE DEFENDANT Is PAID

Let us return to the original model, summarized by the net benefit func-tion in equation (5), with one important change: the defendant is paid toremain in prison instead of paying for his pretrial liberty. He is offered achoice between jail, where he receives rn* as compensation, or release onbail, where he receives nothing. To distinguish this system from the one inwhich the defendant pays, we first consider the effect on the defendant'schoice between pretrial liberty and detention.

Figure 2 presents a set of indifference curves between the defendant'swealth and "days free" on bail. We assume that both wealth and "daysfree" are sources of utility, "days free" are fixed at and, provisionally,a defendant forgoes no current or future income if he is jailed. A defendantwith an initial wealth of W0 would be willing to pay up to W0 — W1 for hispretrial release. This puts him at E1, which is on the same indifferencecurve as his original position W0, and leaves his utility unchanged.Therefore, W0 — W1 is the monetary equivalent of the defendant's gainfrom pretrial release when "days free" are the property right of the state.Suppose the state is required to pay the defendant for detaining him. Thedefendant would now be at E0 and not W0 since "days free" have become

the property right of iidefendant on a higherThe minimum amountleaves him on the sammeasures the gain frortIf the slopes of the twvalue of t, the indiffenequidistant from the cW2 W0. In this instalthe amount one will acamount one will pay"days free" has a posillute value of the slopeslope of the lower om

28. With a positiveof conviction. To illustrate.are two states of the work

APPROACH

in (Sa) and (5b). Thebail and a greater pro-tive detention" model(and hence the supplythe latter. The optimal

ng flight" model as theluded from the model's

detention is kept at aflight" model. Any-

this model would there-he judiciary to reducentive detention" modelresources because the

ntually be offset by thereater harm that resultsby releasing fewer per-)rehending defendantsi" than the "deterringlower probability (i.e.,model.

FIGURE 2

the property right of the individual. This shift in property rights puts thedefendant on a higher indifference curve and increases his utility level.The minimum amount he will accept to forgo to days is W2 — W0 whichleaves him on the same indifference curve as the point E0. Thus, W2 —measures the gain from release when "days free" belong to the defendant.If the slopes of the two indifference curves in Figure 2 are equal at eachvalue of 1, the indifference curve passing through E0 will be everywhereequidistant from the curve passing through E1 and W0 — W1 will equalW2 — W0. In this instance, "days free" has a zero wealth elasticity so thatthe amount one will accept to give up his pretrial liberty is identical to theamount one will pay to retain it. The former sum will exceed the latter if"days free" has a positive wealth elasticity (which requires that the abso-lute value of the slope of the higher indifference curve be greater than theslope of the lower one at each g).28 The analysis remains essentially the

28. With a positive wealth elasticity a further complication arises due to the uncertaintyof conviction. To illustrate, suppose the defendant is paid for pretrial detention and thereare two states of the world, a Conviction state with a probability P and a nonconviction


Wealth

WI

W, El

1, Days free

y the net benefit func-ie defendant is paid toliberty. He is offered aensation, or release onsystem from the one inèct on the defendant's

the defendant's0th wealth and "days

and, provisionally,is jailed. A defendant

up toW0 — W1 for histhe same indifferenceis utility unchanged.f the defendant's gainerty right of the state.

for detaining him. Thetys free" have become

THE BAIL SYSTEM: AN ECONOMIC APPROACH

same when present or future earnings are lost as a result of pretrial deten-tion. The above monetary gains from release are merely increased by thediscounted value of the forgone earnings (i.e., the latter sum is added toboth W2 — W0 and W0 — W1).

The main point of the preceding discussion is that the monetaryequivalent of the defendant's gain from release, which is summarized bythe G function, and hence the net benefit function depend on the type ofbail system specified unless the wealth elasticity of "days free" is zero.To facilitate a comparison among different bail systems, therefore, wewill make the simplifying assumption of a zero wealth elasticity and thenpoint out the implications of a positive elasticity. If the defendant werepaid to remain in custody, the net benefit function in equation (5) wouldremain unchanged, and would be substituted for m in equation (6).Maximizing with respect to ,n* would yield equation (7). Since a de-fendant chooses freedom or jail depending on whether in" is less than orgreater than his gain from pretrial release, the optimal number of defend-ants released would occur when

= = H5 + Cb — Jb =

Thus, defendants would be paid th* to stay in jail and this equals th, theoptimal payment in the system where defendants pay for their release. Interms of Figure 1, all schedules would remain unchanged and, therefore,the number and composition of defendants released would be identical inboth systems. If the wealth elasticity of days free were positive, the Gbcurve would be further to the right in Figure 1 and both th* and the num-ber released would be greater than their respective optimal values whendefendants must pay for their release.

Although the optimality conditions are the same whether one paysdefendants who are detained or defendants pay for their release, there area number of distinctions to be drawn between the two bail systems.

1. The "presumption of innocence" is part of American legal tradi-tion. Yet, when defendants must pay for their release, persons are jailedwithout compensation who by definition are not guilty. In effect, "in-nocent" persons are punished. The conflict between practice and the

state with a probability (1 — P). The minimum amount the defendant will accept to forgohis pretrial freedom will be greater in the nonconviction state since he has a higher wealth.We can define the expected amount the defendant is willing to accept as the sum of theamounts in the two states weighted by their respective probabilities. However, the expectedamount will differ from the amount he is willing to accept to forgo pretrial release if his tastesfor risk are nonneutral. We do not explicitly introduce the latter result into our model sinceit does not affect the qualitative comparisons between the different bail systems.

"presumption of innothey have advocatedopposed to this view,release of dangerous Idetain them simultancishment aspect of a b2tarily and are fully ccwhere the d

release.2. A major critici

is that it discriminatehas some support eveabove. Capital marketincome defendants tothe money payment reto finance release coulenforcing repayment.

'9'paid, the charge of

" / 3. In a voluntarysums to detain defencosts ofthe payment wouldexample, a psychoticders and certain to beit provides him withcommit additional millustrates an obviouswards to persons the rof the problem is thepresumed innocent urished until found guilicostly. If we are wiments to more danger'ular group of defend:net benefit function icurve is everywhere

29. See, for example,Justice, supra note II, at

30. The institution oflater.

152

esult of pretrial deten-erely increased by thelatter sum is added to

is that the monetaryiich is summarized bydepend on the type of

"days free" is zero.ystems, therefore, weIth elasticity and thenIf the defendant werein equation (5) would

in in equation (6).ation (7). Since a de-

ther in" is less than ornumber of defend-

(9)

md this equals An, they for their release. Inanged and, therefore,would be identical in

were positive, the)Oth th* and the nuns-optimal values when

ne whether one paysheir release, there arewo bail systems.American legal tradi-Se, persons are jailed

In effect, "in-een practice and the

ndant will accept to forgoice he has a higher wealth.accept as the sum of the

es. However, the expectedpretrial release if his tastesresult into our model sinceent bail systems.


"presumption of innocence" principle has so outraged some persons thatthey have advocated the virtual elimination of pretrial detention. Others,opposed to this view, cite the potential harm to the community from therelease of dangerous persons. However, paying persons for the right todetain them simultaneously satisfies both views. It eliminates the pun-ishment aspect of a bail system since those detained are detained volun-tarily and are fully compensated for their losses, and it detains personswhere the potential damages to the community exceed the gains fromrelease.

2. A major criticism of requiring defendants to pay for their releaseis that it discriminates against low-income defendants.29 This argumenthas some support even in the context of the simplified model presentedabove. Capital market difficulties may make it impossible for certain low-income defendants to finance their release, although their gain exceedsthe money payment required for release. A system of loans from the courtto finance release could be instituted, but this brings with it the problem ofenforcing repayment.3° In contrast, when defendants not released arepaid, the charge of discrimination against the poor is eliminated.

3. In a voluntary bail system the community would often pay highersums to detain defendants the greater the marginal harm and marginalcosts of reapprehension that result from their release. In some instances,the payment would be extraordinarily large and possibly infinite. Forexample, a psychotic defendant accused of multiple premeditated mur-ders and certain to be convicted is likely to value his release highly sinceit provides him with the opportunity both to escape conviction and tocommit additional murders. Although this is an extreme example, itillustrates an obvious problem: a volunteer system provides greater re-wards to persons the more dangerous they are or appear to be. The sourceof the problem is the strict adherence to the principle that "persons arepresumed innocent until proven guilty" and, therefore, should not be pun-ished until found guilty. The strict maintenance of a principle can be toocostly. If we are willing to compromise, the problem of larger pay-ments to more dangerous defendants becomes tractable. Suppose a partic-ular group of defendants are deemed sufficiently dangerous so that thenet benefit function is maximized when all are detained (i.e., the supply

ê curve is everywhere above the Gb curve in Figure 1), but the payment to

29. See, for example, U.S. President's Comm'n on Law Enforcement & Admin. ofJustice, .cupra note 11, at 37—39.

30. The institution of bondsmen for financing bail is relevant here. This is discussedlater.


achieve a zero release rate is unacceptably large. We might simply fix amaximum payment and jail (voluntarily or involuntarily) the entire set ofdefendants. It must be emphasized that this modification substantiallyalters the nature of the bail system where defendants are paid. We nolonger allow certain defendants the choice between pretrial release orjail. Instead, this decision is made by the court or prosecutor with thestipulation that a jailed defendant receives some compensation.

4. A problem related to the above is that arrested offenders have anincentive to exaggerate their potential harm and desire to escape if re-leased on bail as a means of extracting a higher payment for remaining injail. Note, however, that this problem exists in reverse when defendantsmust pay for their release. There, the prosecutor has an incentive to exag-gerate the potential danger from releasing the defendant in order to per-suade the magistrate to set a higher bail.3'

S. The physical facilities and living conditions that are provideddetained defendants are often deplorable.32 This is not surprising becausewhen defendants pay for their release there is little incentive for the stateor court to improve these conditions. In contrast, a volunteer or partialvolunteer system (i.e., for some offenses the defendant is given the choicebetween release or jail) would provide such an incentive. Improved de-tention facilities would reduce the nonmoney costs of detention to de-fendants, which in turn would reduce the amount the state would have topay to detain them. The less unpleasant these facilities, the lower the pay-ments. An optimum degree of unpleasantness would be achieved whenthe marginal costs of improved facilities equaled the marginal savings inpayments to jailed defendants.

6. Reducing the time between arrest and disposition has been urgedas the best practical solution to problems of the existing bail system.33

31. The advantage of high bail to the prosecutor is that it raises the likelihood of con-victing the defendant. See William M. Landes, pp. 176—77 this volume.

32. A major complaint of inmates who rioted in the N.Y.C. Tombs (a prison forpersons not released on bail) was the overcrowding, inadequate food and presence ofroaches, lice, etc. Their complaints were verified by public officials and prison guards. (SeeNewsweek, August 24, 1970.) Also see U.S. President's Comm'n on Law Enforcement &Admin. of Justice, supra note 11, at 38. on the poor quality of pretrial detention facilities.

33. Chief Judge Harold Greene of the Court of General Sessions in Washington, D.C.,has argued as follows:

A strict policy favoring the detention of criminal suspects is bound to lead to theincarceration of some who will ultimately be acquitted. On the other hand, a liberal releasepolicy has caused and will continue to cause the pretrial freedom of many who will takeadvantage of their freedom to continue their criminal careers to the detriment of society.Opinions differ as to which is more harmful to our values. . . . Whatever one's view on this

Less pretrial delay weharm that released defOne could argue that ipaid compared to whditional incentive for t:size of payments to at

7. The two bail s:of crime. When defencrimes are lower thanformer, the economicremaining the same, thwhich bail system isvious. For example,optimally set withouting defendants to payresult in overdeterrernare inadequate, we mwhen defendants payexisting penalties andtern produces a moreand probabilities areoptimal deterrence 1ev

SOME MODIFICA1

Two further problemsnow considered: thewhen defendants aresion of incentives fori

issue, no one could reasonalto this dilemma is to escape

Escape is possible, butits suspects so quickly thatof potential repeat offende:(Washington Star, MarchPublic Policy Research, Th

34. Note that the optiriing a zero wealth elasticitythe state are viewed as tratinference in the text regardmality conditions but fromwith a limited budget and h

APPROACH

jWILLIAM M. LANDES 155

I,

We might simply fix aitarily) the entire set ofdification substantiallydants are paid. We noeen pretrial release oror prosecutor with thecompensation.ested offenders have an

desire to escape if re-iyment for remaining inverse when defendantsas an incentive to exag-èndant in order to per-

ions that are providednot surprising because

e incentive for the statet, a volunteer or partialdant is given the choice'icentive. Improved de-

of detention to de-the state would have toities, the lower the pay-)uld be achieved whenthe marginal savings in

)Ositior) has been urgedexisting bail system.33

raises the likelihood of con-is volume.

Tombs (a prison forquate food and presence oficials and prison guards. (Seenm'n on Law Enforcement &)f pretrial detention facilities.ess ions in Washington, D.C.,

ects is bound to lead to thee other hand, a liberal releaseedom of many who will take

to the detriment of society.Whatever one's view on this

Less pretrial delay would diminish the losses to detained defendants, theharm that released defendants might do, and the direct costs of detention.One could argue that delay would be reduced more when defendants arepaid compared to when they pay because the former provides an ad-ditional incentive for the state to reduce delay — namely a reduction in thesize of payments to attract a given number of volunteers.34

7. The two systems will have different effects on the deterrenceof crime. When defendants are paid, the expected cOsts of committingcrimes are lower than when defendants must pay for their release. In theformer, the economic returns to the criminal are higher and, other thingsremaining the same, the amount of crime will tend to be greater. However,which bail system is preferable on deterrence grounds alone is not ob-vious. For example, if penalties and probabilities of conviction areoptimally set without explicitly considering the bail system, then requir-ing defendants to pay for their release will impose added penalties thatresult in overdeterrence. On the other hand, if penalties or probabilitiesare inadequate, we may move closer to an optimal level of deterrencewhen defendants pay for their release. Thus, without knowledge of theexisting penalties and probabilities, we cannot determine which bail sys-tem produces a more desired level of deterrence. Moreover, if penaltiesand probabilities are adjustable, one can adjust them to achieve theoptimal deterrence level for each type of bail system.

SOME MODIFICATIONS

Two further problems in the development of an optimal bail system arenow considered: the "moral hazard" problem, which occurs primarilywhen defendants are compensated for pretrial detention, and the provi-sion of incentives for defendants released on bail to return for trial. The

issue, no one could reasonably quarrel with the proposition that the most desirable solutionto this dilemma is to escape it altogether.

Escape is possible, but only through the construction of a judicial system which triesits suspects so quickly that the incarceration of innocent defendants or the pretrial freedomof potential repeat offenders is so brief as to be acceptable as a practical matter(Washington Star, March 30, 1969, at F2, quoted in American Enterprise Institute forPublic Policy Research, The Bail Reform Act 47—48 (April 1969).)

34. Note that the optimal amount of delay, z, is the same in both bail systems (assum-ing a zero wealth elasticity of days free) because payments made either by defendants orthe state are viewed as transfer payments that do not enter the net benefit function. Theinference in the text regarding "additional incentive" is clearly not derived from the opti-mality conditions but from a view of how the state would actually behave when confrontedwith a limited budget and having to pay defendants.


recognition of each problem leads us to devise alternative paymentschemes to those previously set forth.

THE "MORAL HAZARD" AND CREDIT AGAINST SENTENCE

The "moral hazard" arising when defendants are paid is that a personmay commit and confess to a crime, or confess to a crime he did not com-mit, for the sole purpose of collecting a payment for his detention priorto conviction. This would be most likely to occur for crimes in which thelevels of pretrial payments were high relative to the eventual sentence,and for persons with low opportunity costs. One can avoid this difficultyby paying the defendant for pretrial detention only if he is found innocent,and giving him credit toward his sentence for pretrial detention if he isconvicted.35 With this modification the incentive to confess as a means ofreceiving pretrial payments would be eliminated since a confession wouldlargely preclude receiving payments.36

The payment and credit scheme can be formally incorporated intoour model as follows. Both the gains to defendants (the G function) andthe savings in jail costs (the J function) from pretrial release will be lessthan when payments alone are used. The gains from release are less be-cause one must deduct from each defendant's gain the amount he valuesthe credit for pretrial detention.37 The savings in jail costs are less whencredit is given since we eliminate savings (ignoring discounting) to thecommunity from the pretrial release of defendants who are subsequently

35. In most States pretrial detention is not by law deducted from the sentence re-ceived by the convicted defendant. However, some judges make allowance for this whenfixing sentence by lowering the latter by the amount of time spent injail prior to conviction.See Daniel J. Freed & Patricia M. Wald, Bail in the United States: 1964, at 89—90 (1964).

36. The "moral hazard" problem would not be entirely eliminated because a defendantmight initially confess or "plant" evidence making him appear guilty and at the time of trialreveal evidence that resulted in his acquittal. Incentives for such frauds could be reduced bymaking them subject to penalties. However, it appears unlikely that one could design a bailsystem that was entirely free of "moral hazards." For example, we previously noted thateither the defendant or the prosecutor has an incentive to exaggerate the potential harmfrom release depending upon which bail system is operative. Moreover, when the defendantpays for his release, the prosecution may purposely impose large costs (including detention)on a person known to be innocent by having a high bail set. Of course, even a system wheredefendants are paid allows the state to detain innocent persons; however, it raises the costby shifting the burden of the payment from the accused to the state.

37. Let g, and g7 equal the wealth equivalents of the ith defendant's gain from releasewhen no credit is given and when credit is given, respectively. We want to show that

> As previously noted (see supra note 28), is more correctly an expected gainthat equals the gain if convicted times the probability of conviction, plus the gain ifnot convicted times (1 — Pt). The concept of an expected gain is also applicable to Since

convicted; their releaseward the future, inshift in the demand curvan upward shift in the ccosts decline). This in turwhen no credit is given.,.these curves will be greatwill be greater the highevalue defendants attachcount rate on savings into detain a greater propoipayments than when pay

As in the earlier antment to defendants is thedefendants released and

• the defendant is not cor:At what level should thfunction? It can be shogeneral to the release onsample of n defendantwhether or not the defer

• each detained defendant

• the gain from pretrial release iithe amount one values the crewhen > 0. The value of thefuture "days free," the length c

38. Consider two defendtlease are respectively

where P0 and P5 are the probalnot convicted, and andfully compensates for pretrial cSuppose g0 but g00 >leased (because A's expectedpected gain is greater). The rrjail will equal g,0, and the mitwere offered that was sufficietto remain in prison (aswould be consistent with optitexpected gains and gains if notbilities of conviction were equ.lower P's).

APPROACH

e alternative payment

SENTENCE

paid is that a persona crime he did not corn-for his detention prior

for crimes in which thethe eventual sentence,

1:an avoid this difficultyif he is found innocent,

detention if he is6 confess as a means ofInce a confession would

ally incorporated intots (the G function) and

release will be lessrelease are less be-

6 the amount he valuesailcosts are less whenng discounting) to thewho are subsequently

icted from the sentence re-ake allowance for this whennt in jail prior to conviction.ites: 1964, at 89—90 (1964).ninated because a defendant'uilty and at the time of trialfrauds could be reduced bythat one could design a baile, we previously noted thataggerate the potential harm)reover. when the defendante costs (including detention):ourse, even a system where

however, it raises the costState.fendant's gain from releasely. We want to show thatcorrectly an expected gainconviction, plus the gain ifalso applicable to g'. Since


convicted; their release merely transfers jail costs from the present to-ward the future. In terms of Figure 1, these factors lead to a downwardshift in the demand curve for release (as the gains to defendants fall) andan upward shift in the cost curve (as the deduction for savings in jailcosts decline). This in turn results in the release of fewer defendants thanwhen no credit is given. Other things remaining the same, the shifts inthese curves will be greater, and hence the decline in defendants releasedwill be greater, the higher the probabilities of conviction, the greater thevalue defendants attach to credits, and the lower the community's dis-count rate on savings in future jail costs. In sum, optimal policy will beto detain a greater proportion of defendants when credit is combined withpayments than when payments alone are used.

As in the earlier analysis, suppose that varying the size of the pay-• ment to defendants is the means by which the state affects the number of

defendants released and detained. Here the payment is received only ifthe defendant is not convicted, since credit is given if he is convicted.At what level should the payment be set to maximize the net benefitfunction? It can be shown that a uniform payment would not lead ingeneral to the release on bail of the optimal number of persons from oursample of n defendants.38 Instead, the state would first determinewhether or not the defendant should be detained, and then offer to payeach detained defendant an amount that would induce him to remain in

the gain from pretrial release if convicted is less when credit is given than when it is not bythe amount one values the credit (which is equivalent to a reduction in sentence), gç > ge"

when Pf > 0. The value of the credit to the defendant will depend on the rate of discount offuture "days free," the length of his sentence, and the value of days free" in the future.

38. Consider two defendants, A and B, where their expected gains from pretrial re-lease are respectively

= (1 — +

(1 —

P5 and are the gains from release ifnot convicted, and and are the gains if convicted. To simplify, assume that the creditfully compensates for pretrial detention if one is convicted so that and cc5 are both zero.Suppose < but > and optimality requires that A be detained and B be re-leased (because A's expected gain is less than the net costs of his release while B's ex-pected gain is greater). The minimum contingent payment that A will accept to remain injail will equal and the minimum that B will accept will equal If a single paymentwere offered that was sufficient to induce A to remain in jail, then B would also be willingto remain in prison (as g,,, > g5), contrary to the optimality condition. A uniform paymentwould be consistent with optimality in the special case where the rank correlation betweenexpected gains and gains if not convicted were equal to I (e.g., in the case where the proba-bilities of conviction were equal for all defendants or where defendants with higher g0's hadlower P's).

II


prison. The decision to detain or release would depend on the state'sestimate of whether the expected gain to the particular defendant fromhis release was less or greater than the potential harm from his releaseplus the costs of reapprehending him and expanding trial services, minusthe expected savings in jail costs. Such a policy would be consistent withthe maximization of the net benefit function and would lead to the optimalnumker of defendants released. A more attractive payment scheme mightbe to defer the setting of payments until the completion of the defendant'scase. At that time, if he were found innocent, he could bring a tort actionagainst the state to collect payment both for damages suffered duringthe period of pretrial detention and for the costs of bringing the action.The sole question before the court would be the amount of compensationsince the question of liability would have already been decided by the de-fendant's acquittal. One who favored a "voluntary" bail system (even ifonly for certain types of offenses) might initially object to a credit and tortremedy on the ground that it enables the state to detain persons prior totrial without their consent. However, if the tort action permitted the de-fendant to receive full compensation, the latter would equal what hewould have accepted to remain voluntarily in prison prior to the disposi-tion of his case.39

INCENTIVES FOR APPEARING AT TRIAL

In our model, the likelihood of appearing for trial is one of several factorsrelevant in maximizing the net benefit function. The likelihood of appear-ing determines in part the harm from releasing defendants and the costsof reapprehending them (since the frequency of attempts to flee willaffect the cost of achieving a given probability of reapprehension); how-ever, the net benefit function is also affected by considerations of possiblenew crimes, the costs of expanding trial services, and the savings in jailcosts. Nevertheless, appearing for trial is an important factor and it isworthwhile to consider more explicitly what mechanisms can be devisedto provide incentives for the defendant's appearance.

39. When defendants are paid to remain in prison prior to adjudication of their cases 40. See Gary S. Becker, tlbut no credit is given, detained defendants will have funds to replace their forgone earn- 41. The analogy to insuraings, enabling them to finance a defense. However, one could argue that with a tort remedy specializing in bail bonds is to Ithese funds would not be available, which would result in higher probabilities of conviction due, for example, to usury lawfor those detained compared to those not detained, other things remaining the same. How- 42. One survey of 19 courever, this inference is not correct because defendants would be able to make contingent leased, 45% used professionalcontracts with lawyers who would agree to defend them in exchange for receiving a payment posted cash and 8% were rele2only if their client was acquitted. Similar contracts are common in many tort actions (e.g., the State Courts—A Field Stunegligence cases). puted these figures by taking a

The most directitself and set appropriatethis crime.40 One objectiis likely to be small becathe penalty for a defend2that the appropriate degrpenalty for nonappearanpenalty for the crime thMoreover, it follows frondefendants accused of tFappearance may have thbe released on bail.

When defendants mian incentive for the deferment or bond that is retu:a system firms are likely'of nonappearance, and hfee to compensate themarrangement would comfrom defendants to bonchsystem that hasportion were released betanalysis of the bail bond

It has been alleged Ibondsman removes the itneed not be true, for the icollateral from the deferrisks with the accused a(2) The defendant is Iialfeited. (3) The bondsmetvia the expenditure offendant's fleeing. This wcwhereabouts and threats


d depend on the state'sirticular defendant fromLI harm from his releaseling trial services, minusvould be consistent withvould lead to the optimale payment scheme mightletion of the defendant'scould bring a tort actiontarnages suffered durings of bringing the action.amount of compensation

been decided by the de-ry" bail system (even if)bject to a credit and tort) detain persons prior toaction permitted the de-

would equal what heison prior to the disposi-

is one of several factorshe likelihood of appear-efendants and the costs

of attempts to flee willf reapprehension); how-nsiderations of possible

and the savings in jailportant factor and it ishanisms can be devisednce.

The most direct method would be to make nonappearance a crime initself and set appropriate penalties to achieve the optimum deterrence ofthis crime.40 One objection is that the deterrent effect of these penaltiesis likely to be small because they represent only a marginal increment inthe penalty for a defendant likely to be convicted. However, this impliesthat the appropriate degree of deterrence would require a relatively highpenalty for nonappearance and one that is probably in proportion to thepenalty for the crime the defendant is initially accused of committing.Moreover, it follows from the optimality conditions of the bail model thatdefendants accused of the most severe crimes (where penalties for non-appearance may have the smallest deterrent effect) are the least likely tobe released on bail.

When defendants must pay for their release, another way to providean incentive for the defendant's appearance would be to set a money pay-ment or bond that is returned only if the accused appears at trial. In sucha system firms are likely to arise that would be willing to accept the riskof nonappearance, and hence forfeiture of the bail bond, in exchange for afee to compensate them for their expected losses. Thus, an institutionalarrangement would come about for shifting the risks of nonappearancefrom defendants to bondsmen.41 In the United States, this is precisely thesystem that has developed. Of those defendants free on bail, a large pro-portion were released because a bondsman posted a bail bond.42 A formalanalysis of the bail bond system is presented in the appendix.

It has been alleged that the shifting of potential financial loss to thebondsman removes the incentive for the defendant to appear at trial. Thisneed not be true, for the following reasons: (1) Bondsmen usually requirecollateral from the defendant. This is a form of sharing or pooling therisks with the accused and thus both suffer losses from nonappearance.(2) The defendant is liable for the amount of the bond should it be for-feited. (3) The bondsmen have an incentive to protect their investmentvia the expenditure of resources to reduce the likelihood of the de-fendant's fleeing. This would include periodic checkups of the defendant'swhereabouts and threats to revoke the bond (which would make the de-

to adjudication of their caseso replace their forgone earn-

argue that with a tort remedyher probabilities of convictionigs remaining the same. How-d be able to make contingenthange for receiving a paymention in many tort actions (e.g..

40. See Gary S. Becker, this volume, for the derivation of optimal penalties for crimes.41. The analogy to insurance is not perfect, since another important reason for firms

specializing in bail bonds is to provide funds for defendants who cannot borrow from banksdue, for example, to usury laws or poor collateral.

42. One survey of 19 counties in the U.S. in 1962 indicated that among defendants re-leased, 45% used professional bondsmen, 35% had friends or relatives post a bond, 12%posted cash and 8% were released on their own recognizance. See Lee Silverstein, Bail inthe State Courts—A Field Study and Report, 50 Minn. L. Rev. 621, 647 (1966). I com-puted these figures by taking averages for the counties where data were given.

.1


fendant a fugitive). In addition, the bondsman is given the power to arresta defendant who flees, and there are scattered reports of bondsmen re-lentlessly pursuing, apprehending, and returning the defendant.43 (4) Pro-fessional criminals who regularly appear in court have little incentive toflee because bondsmen would be unwilling to post bail for them in thefuture.

CONCLUDING REMARKS

The main contribution of this essay has been to propose and analyze analternative to the existing bail system. This alternative is a system inwhich the defendant is compensated for his pretrial detention in contrastto the present method of having the defendant pay for his release. Com-pensation to detained defendants can take a variety of forms that includemoney payments, credit against sentence for persons subsequently foundguilty, and tort remedies for those acquitted.44 Our approach was first toderive a net benefit function from releasing defendants prior to trial thatincorporated both the gains to defendants and the costs and gains to thecommunity from their release. The optimal number of defendants re-leased was one that maximized the net benefit. Although the optimalityconditions were largely unaffected by whether the defendant had to payor was paid, there are some important advantages to a system in whichdefendants are compensated. The major one is reducing the punitive as-pect of the bail system, since those detained are compensated for lossesresulting from their detention. Other advantages include reducing dis-crimination against low-income defendants and providing incentives forthe states to improve pretrial detention facilities.

Criticisms of the existing bail system and proposals for reform playan important role in current policy debates over effective law enforce-ment. Most proposals call for weakening or even eliminating the require-ment that the defendant pay for his release. In its place, these proposalstypically advocate extensive investigation of the defendant's backgroundto determine suitability for pretrial release. If he is found suitable, the

defendant may be releaseto pay a nominal sum. "5the defendant's ties to thvictions, etc. In Newconducted along these unthese proposals is the fateHe would be jailed witholaw he is still "innocentessay not only lessens thsating jailed defendantsgatory procedures that aris that paying defendantfrom the defendant to thstate to reduce this burddefendants are likely to d

APPENDiX

THE BONDSMAN

In our model both bail(i.e., bondsmen) were omitteassume the following: (1) a nthe defendant's release, butbondsman posts M with thefeited only in the event thefendant shows up, theman charges the defendantand he may also require soamong bondsmen.

Total costs (T) for the gincreases in the number of dthe time from arrest to dispc

43. See Daniel J. Freed & Patricia M. Wald, supra note 35, at 30—31. The incentive toreturn the defendant to custody, after he does not appear, is that the bondsman is usuallygiven a grace period of about 30 days before he forfeits the bond.

44. The question of whether compensation is a realistic alternative to the existing bailsystem is beyond the scope of this paper. However, we should note that one difficulty inimplementing this proposal is that the majority of voters do not expect to be defendants;therefore, it is unlikely that they would favor a proposal that reduced their wealth andincreased the wealth of future defendants.

45. This system would notvalued at M to secure release.on the bondsman.

46. A longer I implies amoment in time. Since wetunity cost) against the contingube associated with a greater vo

C APPROACH

given the power to arrestreports of bondsmen re-the defendant.43 (4) Pro-

rt have little incentive topost bail for them in the

propose and analyze anIternative is a system intrial detention in contrast)ay for his release. Corn-iety of forms that include-sons subsequently foundDur approach was first to

prior to trial thathe costs and gains to theumber of defendants re-Although the optimality

the defendant had to payto a system in which

the punitive as-compensated for losses

es include reducing dis-providing incentives for

roposals for reform playr effective law enforce-

ri eliminating the require-ts place, these proposalsdefendant's background

is found suitable, the

35, at 30—31. The incentive tothat the bondsman is usually

bond.alternative to the existing bailuld note that one difficulty innot expect to be defendants;

hat reduced their wealth and

—I


defendant may be released without having to post a bond or having onlyto pay a nominal sum. "Suitability" would be determined on the basis ofthe defendant's ties to the community, his employment record, past con-victions, etc. In New York City some experiments have already beenconducted along these lines by the Vera Foundation. The major defect ofthese proposals is the fate of the defendant not recommended for release.He would be jailed without compensation and thus punished although bylaw he is still "innocent." In contrast, the proposal advanced in thisessay not only lessens the punitive aspect of the bail system by compen-sating jailed defendants but also provides an incentive to set up investi-gatory procedures that are advocated in the above proposals. The reasonis that paying defendants shifts part of the burden of the bail systemfrom the defendant to the state, and hence there is an incentive for thestate to reduce this burden by allocating resources to discovering whichdefendants are likely to do little harm if released.

APPENDIX

THE BONDSMAN

In our model both bail bonds and firms specializing in the sale of these bonds(i.e., bondsmen) were omitted. Let us now introduce them into the analysis, andassume the following: (I) a money payment, denoted by M, is set by the court forthe defendant's release, but instead of M being paid directly by the defendant, abondsman posts M with the court in behalf of the defendant; (2) M will be for-feited only in the event the defendant does not show up for trial (i.e., if the de-fendant shows up, the bondsman makes no payment to the court); (3) the bonds-man charges the defendant a fee for this service equal to f M where 0 <f < 1and he may also require some collateral; and (4) competition initially prevailsamong bondsmen.

Total costs (T) for the group of firms writing bonds will tend to increase withincreases in the number of defendants not showing up for trial, the size of M, andthe time from arrest to disposition.46 That is

T = T(p, b, M, t), (10)

45. This system would not prevent the defendant from depositing cash or another assetvalued at M to secure release. However, we rule this out in the analysis in order to focuson the bondsman.

46. A longer t implies a greater average volume of bail bonds outstanding at anymoment in time. Since we would expect bondsmen to hold reserves (which have an oppor-tunity cost) against the contingency that a defendant will not appear for trial, a longer t willhe associated with a greater volume of reserves and hence greater costs.

f0M0

where T9 < 0, T5 > 0, > 0 and T, > 0. The demand function of defendantsfor release on bail is similar to the previous demand function (see equation (6))and may be written as

b = b(fM, t, p, ii), (11)

where fM is the fee to the bondsman, and r, p and u are defined as before exceptthat the residual ii would also include the amount of collateral required by thebondsman. Both bf(= ob/afM (M)) and b,11 are assumed to be negative. If Mwere set at M0 (and t and p are given), equilibrium in the market for bail bondswould take place atj0M0 and b0 in Figure 3. At higher levels of M, for example, Tbshifts to the left, fM rises and b falls. Thus, to maximize the net benefit functionir (see equation (5)), M would be set by the court at a value where the number ofdefendants released on bail in Figure 3 was equal to the number that maximizedIT47 That is

JM= T5= Gb=Hb+Cs—Jb. (12)

Although the optimal M in (12) would be greater than the optimal money pay-ment (th) in the model that excluded the bondsman, the number of defendantsreleased on bail and the actual payment for release would be the same.

Let us drop the assumption of a competitive market in the sale of bail bonds,and instead assume a cartel agreement among bondsmen where entry is restrictedand the fee for bonds is set above the competitive price. Both fee-fixing and entry

restrictions are enforced bythe demand curve in FigureM this would result in a higlthan in the competitive cacartel by lowering M belowoptimal number of defendar

48. Some form of statepolitan areas bonds areare regulated as part of the insby the state. Bondsmen are aprohibiting bondsmen fromfor recommending clients, and f;Patricia M. Wald. supra note 3

49. This would require

where e is the elasticity of thcdefendants released in the conare also the same. However,fi

47. We do not explicitly consider the resource costs of bondsmen in the net benefit


Tb

n

FIGURE 3

b

function.

IC APPROACH WILLIAM M. LANDEs 163

restrictions are enforced by the state.48 The cartel would take a curve marginal tothe demand curve in Figure 3 (assuming no price discrimination) and for a givenM this would result in a higherfM (i.e., a higherf) and fewer defendants releasedthan in the competitive case.49 However, the state could compensate for thecartel by lowering M below the competitive level in order to release on bail theoptimal number of defendants.

48. Some form of state regulation appears to be the rule. For example, in large metro-politan areas bonds are generally written by agents (bondsmen) of surety companies thatare regulated as part of the insurance business. Fees and minimum cash reserves are setby the state. Bondsmen are also licensed in some states. In addition, there exist lawsprohibiting bondsmen from giving rebates to attorneys and public officials in exchangefor recommending clients, and from soliciting business in courtrooms. See Daniel J. Freed &Patricia M. Wald, supra note 38, at 36—38.

49. This would require

b JMG?119+Cb—Js (i)

(ii)

function of defendants where e is the elasticity of the demand curve G5 in Figure 3. With the same number ofI function (see equation (6)) defendants released in the competitive and monopoly cases, the fees to defendants (fM)

are also the same. However,f is larger and M smaller with monopoly than competition.

(11)

aredefined as before exceptf collateral required by theumed to be negative. If Mn the market for bail bondslevels of M, for example, T9

the net benefit functionvalue where the number ofthe number that maximized

Jb. (12)

an the optimal money pay-the number of defendants

gould be the same.ket in the sale of bail bonds,ten where entry is restricted

Both fee-fixing and entry

of bondsmen in the net benefit

An Economic Analysisof the Courts

William M. LandesUniversity of Chicago and National Bureau of Economic Research

"The object of our study, then, is prediction, . . . The prophecies of what thecourts will do in fact, and nothing more pretentious, are what I mean by the law."Oliver Wendell Holmes, Jr., The Path of Law (1897).

In the folklore of criminal justice a popular belief is that the accusedwill have his case decided in a trial. Empirical evidence does not supportthis belief. Table 1 indicates that most cases are disposed of before trialby either a guilty plea or a dismissal of the charges. What factors deter-mine the choice between a pretrial settlement and a trial? What accountsfor the large proportion of settlements compared to trials? How are cer-tain aspects of the criminal justice process such as the bail system andcourt delay related to the decision to settle or to go to trial? The main

This study has been supported by a grant for the study of law and economics from theNational Science Foundation to the National Bureau (Grant Number GS-33 14). The viewsexpressed in this essay are not attributable to the National Science Foundation, whosesupport I gratefully acknowledge. I should like to thank Professors Gary Becker, SolomonFabricant, Laurence Miller, Sherwin Rosen, Finis Welch and Neil Wallace, and ElisabethLandes for helpful criticisms. 1 also received useful comments at seminars at the NBER,Columbia, Rochester, U.C.L.A. and the University of Chicago. Charles H. Berry, EugeneP. Foley, and Eli Goldston provided valuable advice as members of the reading committeeof the National Bureau's Board of Directors.

Numi

Area (Year)of D

fenda

132 State County :

Courts (1962) 7,5:U.S. District

Courts (1967)

SOURCES. — Lee Silverican State Courts, A Fieldof the United States Court

a Number of felony de

purpose of this essay is t'cal and empirical analystools of economic theory

A theoretical moderelevant to the choice betion of the model istheir utility, appropriatesources. It is shown thatthe probability of convicability and productivitytrial versus settlement ccthe effects of the bail sysseveral proposals for impThese include "preventifendarits not released onuse of the courts. The mcmade argument that thclow-income defendants.fendant's income orprobability of his convicitions of these factors vexamined.

The second part of tidata on the disposition

Dis


TABLE IDISPOSITION OF CRIMINAL CASES

Area (Year)

Numberof De-

fendants

Tn

Num-ber

als

PerCent

Guilty

Num-ber

Pleas

PerCent

Dismi

Num-ber

ssed

PerCent

132 State CountyCourts (1962) 1,394 19 5,293 70 823 11

U.S. DistrictCourts (1967) 31,535 4,208 13 23,131 73 4,196 13

SOURCES. — Lee Silverstein, Defense of the Poor in Criminal Cases in Amer-ican State Courts, A Field Study and Report (2 v. 1965); Ann. Rep., Admin. Off.of the United States Courts, 1967.

a Number of felony defendants in sample.

The prophecies of what there what I mean by the law."

belief is that the accusedvidence does not support

disposed of before trialges. What factors deter-id a trial? What accountsd to trials? How are cer-h as the bail system andto go to trial? The main

of law and economics from theNumber GS.33 14). The views

al Science Foundation, whosefessors Gary Becker, Solomond Neil Wallace, and Elisabeth

ents at seminars at the NBER,ago. Charles H. Berry, Eugeneibers of the reading committee

purpose of this essay is to answer these questions by means of a theoreti-cal and empirical analysis of the criminal justice system using standardtools of economic theory and statistics.

A theoretical model is first developed that identifies the variablesrelevant to the choice between a settlement and a trial. The basic assump-tion of the model is that both the prosecutor and the defendant maximizetheir utility, appropriately defined, subject to a constraint on their re-sources. It is shown that the decision to settle or to go to trial depends onthe probability of conviction by trial, the severity of the crime, the avail-ability and productivity of the prosecutor's and defendant's resources,trial versus settlement costs, and attitudes toward risk. We then analyzethe effects of the bail system and court delay on settlements, and considerseveral proposals for improving the bail system and reducing court delay.These include "preventive detention," monetary compensation to de-fendants not released on bail, and the imposition of a money price for theuse of the courts. The model is further useful in evaluating the frequentlymade argument that the criminal justice system discriminates againstlow-income defendants. This proposition is analyzed by relating a de-fendant's income or wealth to his decision to settle or go to trial, theprobability of his conviction, and his sentence if convicted. The interac-tions of these factors with the bail system and court delay are alsoexamined.

The second part of this study is an empirical analysis from publisheddata on the disposition of cases in state and federal criminal courts.

Economic Research

•1

I.

166 AN ECONOMIC ANALYSIS OF THE COURTS

Multiple regression techniques are used to test the effects on the demandfor trials (or conversely, settlements) and on the probability of convictionof the following: (1) pretrial detention; (2) court queues; (3) the size of thepotential sentence; (4) judicial expenditures; (5) subsidizing defendants'legal fees; and (6) demographic variables such as population size, region,county income, per cent nonwhite, and urbanization. Finally, in theappendix a theoretical and empirical analysis on the demand for civilcases is presented.

I. THE MODEL

We make the following assumptions.(1) There are n defendants.(2) The probability of conviction in a trial for the ith defendant

(i = 1, . . . , n) depends on the prosecutor's and defendant's inputs of re-sources, and R1 respectively, into the case. That is,

= R1; Z1)

and

F, = P1(Rr, Z,), (1)

where P7 is the prosecutor's, and P, is the defendant's estimates of theprobability of conviction by trial. P7 can be greater, less than, or equal toP,. Z, denotes other factors affecting the level of P7 and for example,the availability of witnesses, the defendant's past record, his alibi, etc.Inputs of R7 would tend to raise P7 and F1, while inputs of R would tendto lower them so that

(3) The sentence, the defendant would receive if convicted in atrial is known to the prosecutor and defendant and independent of R7and R,.'

I. There is some justification for this assumption other than mathematical simplicitysince most crimes carry statutory penalties which are presumably known to both partiesand, independent of R' and However, statutory penalties usually set a minimum andmaximum sentence for the defendant convicted in a trial, and within this range the sen-tence received would partly depend on and R. To allow the sentence to be a functionof R' and would substantially complicate the model at this point (for example, two sen-

(4) Initially, there Inonmoney cost in terms

PROSECUTOR

Let the prosecutor's decConvictions weighted by.sentences—suljject to ahis office (B).2 This decthe following sense. Ifmunity charges for vanequivalent to maximizinprosecution expenditure

The prosecutor

E(C

which yields the equilibr

;c P*

Thus, the prosecutor allowhere the sentence is grein R$.3 If all n defendant:charges would beconviction regardless ofviction he expects a neg

tences would have to be includwithout substantially changingsection on wealth effects, I alIc

2. Other decision rules arcconvictions without weightingorder to increase his cOnvicti(drop a murder charge against;a minor offense (for example,model is to weight by the S,'s.fines could be included in binto sentences keeping his utilil

3. We assume the price olnoted that (4) does not necessprosecutor takes as given thechanges or anticipated changestheir Ri's, and so forth. This pr

aPr

_!_>aR7

—'soaPi

(2)

COURTS WILLIAM M. LANDES 167

effects on the demand)robabihty of convictionueues; (3) the size of thesubsidizing defendants'population size, region,

Lization. Finally, in the)n the demand for civil

al for the ith defendantdefendant's inputs of re-['hat is,

(4) Initially, there is no money charge for the use of the courts nor anonmoney cost in terms of court delay or queues.

PROSECUTOR

Let the prosecutor's decision rule be to maximize the expected number ofconvictions weighted by their respective S,'s — he prefers longer to shortersentences — subject to a constraint on the resources or budget available tohis office (B).2 This decision rule coincides with the social optimum inthe following sense. If expected sentences are regarded as prices the com-munity charges for various offenses, then the prosecutor's behavior isequivalent to maximizing the community's "profit" for a given level ofprosecution expenditures.

The prosecutor maximizes E(C) where

E(C) = ± X(B —f=I

which yields the equilibrium conditions

(3)

Thus, the prosecutor allocates greater resources to cases, ceteris paribus,where the sentence is greater and where is more responsive to changesin R".3 If all ii defendants need not be prosecuted, one would also predictcharges would be dismissed when the prosecutor sees little chance ofconviction regardless of his resource input into the trial, or given a con-viction he expects a negligible sentence. The formulation of (3) is suffi-

0

0.

(2)

receive if convicted in aand independent of

r than mathematical simplicityumably known to both partieses usually set a minimum andand within this range the sen-

the sentence to be a functiOniS point (for example, two sen-

lences would have to be included—the defendant's estimate and the prosecutor's estimate)without substantially changing the analysis of the trial versus settlement decision. In a latersection on wealth effects, I allow the sentence to be a function of resource inputs.

2. Other decision rules are possible; for example, maximizing the expected number ofconvictions without weighting by the S1's. The difficulty here is that the prosecutor, inorder to increase his convictions and conserve his resources, would often be willing todrop a murder charge against a suspected murderer if the latter agreed to plead guilty toa minor offense (for example, a traffic violation). A simple way of eliminating this in themodel is to weight by the S's. (See the analysis of a settlement presented below.) Note thatfines could be included in S by specifying a rate at which the prosecutor transforms finesinto sentences keeping his utility constant.

3. We assume the price of a unit of Rj" is $1.00 and <0. It should also benoted that (4) does not necessarily have a unique solution unless one assumes that theprosecutor takes as given the defendant's inputs, R,'s. If he readjusts his inputs of tochanges or anticipated changes in any of the R's, then the defendants may in turn readjusttheir R1's. and so forth. This process need not converge to a unique solution.

!ndant's estimates of theIter, less than, or equal to

and for example,ast record, his alibi, etc.

inputs of R, would tend

apr aPr aPr(1) Si = . S2 = . . . '

=. Sn. (4)


ciently general to give the prosecutor discretion over the type of chargebrought against each defendant. The charge selected would be one thatmaximized E(C). Further, the maximization of E(C) together with theassumption that 3P,"/I9Rr 0 imply (possibly unrealistically) that theprosecutor would suppress any evidence that reduces the probability ofconviction.

Scarce resources provide an incentive for the prosecutor to avoid atrial and negotiate a pretrial settlement with the defendant. From (3)and (4) it follows that if the prosecutor's transaction costs of a settlementequal his optimal resource expenditure on a trial, he would be willing tooffer the suspect a reduction in the sentence below 5, in exchange for aplea of guilty (which makes = P. = However, since trial costsprobably exceed these transaction costs, he would be willing to offer afurther sentence reduction as the savings in resources can be used toincrease the conviction probabilities in other cases. If denotes thesentence reduction that is a positive function of the difference between theprosecutor's trial costs and transaction costs of a settlement, then

So, = — (5)

where is the minimum sentence th.e prosecutor is willing to offer thedefendant for a guilty plea.5 From (5) we note that the terms offered thedefendant will be more favorable the lower P" and and the greater theprosecutor's resource saving from a settlement. Finally, suppose that cer-tain cases bring the prosecutor considerable notoriety only if a trial Oc-curs. If notoriety were desired, the sentence variable, S,, could be in-creased by a notoriety factor (for example S.(l wherej, is a positivefunction of the amount of notoriety and is Hence in some cases So,could be greater than PrS, and even S,. Unless otherwise stated, we as-sume So1 < Pt'S,.

DEFENDANT

if the defendant goes tosive states: a conviction

or a state

W is his wealth endowmthe average pecuniary anis the average price of aI assume Wc is nonnega

Let U be a continuc.ment. His expected utilil

E(U)

Since inputs of R lower)of R to maximize E(U)

—P'[U(Wn) — L

where p' = dPfdR anddowment in each state.returns of R and the rigithe determinants of the

6. The subscript i is del

4. The prosecutor's transaction costs of a settlement would equal his time spent ex-plaining the terms of the offer to the suspect and judge, paperwork in his office, etc. Thesecosts will generally be less than his total costs of reaching a settlement since the latter mayinvolve substantial negotiating or bargaining costs in order to arrive at a sentence more pre-ferred than the minimum sentence he is willing to offer in a settlement.

5. A settlement that releases resources from any one case will increase the Ri"s inother cases. Thus, the that initially satisfy (4) are not the final equilibrium values be-cause adjustments take place as cases are settled. Moreover, these adjustments raise theSo's in cases not yet settled. I largely ignore these secondary effects in the analysis.

defendant.7. The qualification stater

of also applies the defer8. The second-order con'

marginal returns be less than I

—P"[U(Wn) — U(Wc)] + rP'{L

where P' = d2P/dR2, and U"diminishing marginal productzero and hence marginal retu

THE COURTS WILLIAM M. LANDES 169

ion over the type of chargeselected would be one thatof E(C) together with thely unrealistically) that thet reduces the probability of

•r the prosecutor to avoid ah the defendant. From (3)action costs of a settlementrial, he would be willing tobelow 5, in exchange for a

However, since trial costswould be willing to offer aresources can be used to

r cases. If denotes thef the difference between theof a settlement, then

(5)

cutor is willing to offer thethat the terms offered the

and and the greater thet. Finally, suppose that cer-notoriety only if a trial oc-

variable, could be in-1 wherej1 is a positive). Hence in some cases So,s otherwise stated, we as-

DEFENDANT

If the defendant goes to trial, the outcome is either of two mutually exclu-sive states: a conviction state with an endowment Wc defined as

Wc = W — s S — r R

or a nonconviction state with an endowment Wn defined as

Wn=W—rR.

(6a)

(6b)

W is his wealth endowment prior to arrest, s equals the present value ofthe average pecuniary and nonpecuniary losses per unit of jail sentence,ris the average price of a unit of R, and S and R are defined as before..6I assume Wc is nonnegative.

Let U be a continuous utility function over the defendant's endow-ment. His expected utility from going to trial is then

E(U) PU(Wc) + (1 — P)U(Wn). (7)

Since inputs of R lower F, Wc and Wn, the defendant would select a levelof R to maximize E(U) such that

—P'[U(Wn) — U(Wc)] = r[PU'(Wc) + (1 — P)U'(Wn)], (8)

where p' = dP/dR and U' denotes the marginal utility (>0) of the en-dowment in each state.7 The left-hand side of (8) represents marginalreturns of R and the right-hand side, marginal costs of R.8 An analysis ofthe determinants of the optimal R is presented later.

would equal his time spent ex-aperwork in his office, etc. Thesea settlement since the latter mayto arrive at a sentence more pre.a settlement.

te case will increase the Rr's inthe final equilibrium values be-

ver, these adjustments raise theary effects in the analysis.

6. The subscript i is deleted, since it is explicit that we are now dealing with onedefendant.

7. The qualification stated in footnote 3 regarding the prosecutors equilibrium inputsof R* also applies to the defendant's equilibrium inputs of R.

8. The second-order condition for the optimum R requires that the rate of change ofmarginal returns be less than the rate of change of marginal cost. That is,

—P"[U(Wn) — U(Wc)) + rP'[U'(Wn) — U'(Wc)] <

—rP'[U'(Wn) — U(Wc)] — r2[PU"(Wc) + (I — P)U"(Wn)J,

where P" = d2P/dR2, and U" = the rate of change of U'. P' is assumed >0 to indicatediminishing marginal product of R in reducing P. If U" = 0, the last three terms above arezero and hence marginal returns are falling while marginal costs are constant. If U" 0,


TRIAL VERSUS SETTLEMENT

Let r equal the defendant's transaction costs of a settlement.9 Notethat the defendant's trial costs, r R, are greater than r R because adefendant going to trial will in the process of rejecting a settlement incurmost of the costs in r R, and in addition he has expenditures on the trial.The defendant would choose between a trial or settlement on the basis ofwhether his expected utility from the former, E(U), were greater or lessthan his utility from the latter. Similarly, the prosecutor would choose thealternative that maximizes his conviction function, E(C). Therefore, anecessary condition for a settlement is that both the defendant and prose-cutor simultaneous'y gain from a settlement compared to their expectedtrial outcomes. This requires that

ir U(W—s . So—rjbecause one can then find a negotiated sentence somewhat greater thanSo, the minimum offer of the prosecutor, that leaves the defendant with autility from a settlement greater than E(U) and at the same time increasesE(C) for the prosecutor above its value in a trial. Although (9) explicitlyallows for the prosecutor's and defendant's transaction costs of a settle-inent, the attempt to reach mutually acceptable terms may in certain casesinvolve substantial bargaining costs that are large enough to prevent asettlement even though ir > 0. In spite of this qualification, I will assumethat 7T > 0 is not only a necessary but also a sufficient condition for asettlement. Alternatively, IT < 0 is a necessary and sufficient conditionfor a trial. These conditions are Pareto optimal in that if rr > 0, bothparties expect to gain from a settlement, and if < 0, both parties ex-pect to gain from a trial.

We can derive the following implications from (9) regarding the like-lihood of settling and the resulting sentence.

1. Although the precise sentence in a pretrial settlement is inde-terminate, it must lie between the extremes defined by (9). Within thisrange it would depend on the relative bargaining strengths of the partiesinvolved. In general, one would expect a smaller negotiated sentence the

marginal costs may be rising, falling or constant with increases in R since the two terms onthe right-hand side are of opposite sign. Similarly, when U" < 0, marginal returns mayactually rise since rP'[U'(Wn) — U'(Wc)] is positive but when U"> 0, marginal returnsmust fall.

9. Similar to the definition of the prosecutor's transaction costs (see supra note 4), rRwould be generally less than the defendant's total costs of negotiating a settlement since

excludes bargaining costs.

smaller the probability of.and thus lowers the maxina smaller reduces theidentical reasons, a lower,a lower negotiated senten

2. IT will be positive

since this implies U(WU(Wn) E(U). This restoward risk and his estirrgardless of the trial outcorimplies that a trial is less ii(since So depends on S

(9) cost of going to trial,contrary, I now assume(W — . So — rR).

3. If both partiesa settlement wil

(U" < 0) or risk neutraltrial is equivalent to an utment is less than the se'maximize their expected"gamble," and a fortioriOn the other hand, a tn:even though =

10. This provides an explaiinstead of spending considerabl'

11. U" denotes the rate of12. A trial is an unfair gary

(W — s S

which can be rewritten as

using (5), (6a, 6b) and the assutare both positive, (ii) holds and

13. Given risk preference,the greater the preference for rthis differentiate (9) partially vnegative for and positivecreases in and decreases in

E COURTS WILLIAM M. LANDES 171

ts of a settlement.9 Noteter than r R because ajecting a settlement incurexpenditures on the trial.

settlement on the basis of(U), were greater or lesssecutor would choose thetion, E(C). Therefore, athe defendant and prose-

rnpared to their expected

(U) > 0, (9)

somewhat greater thanayes the defendant with aat the same time increasesal. Although (9) explicitlyisaction costs of a settle-erms may in certain casestrge enough to prevent aualification, I will assumesufficient condition for aj and sufficient conditional in that if ir> 0, bothf <0, both parties ex-

om (9) regarding the like-

etrial settlement is inde-by (9). Within this

g strengths of the partiesr negotiated sentence the

in R since the two terms OnU" < 0, marginal returns may

when U" > 0, marginal returns

tion costs (see supra note 4), rR

f negotiating a settlement since

smaller the probability of conviction in a trial. A smaller P raises E(U)and thus lowers the maximum sentence accepted by the defendant, whilea smaller P" reduces the minimum acceptable to the prosecutor. Foridentical reasons, a lower sentence if convicted by trial, S, should lead toa lower negotiated sentence.

2. ir will be positive and a settlement chosen whenever

s So < r(R — (10)

since this implies U(W — s So — > U(Wn), and by definitionU(Wn) E(U). This result is independent of the defendant's attitudetoward risk and his estimate of the conviction probability, because re-gardless of the trial outcome he is always better off with a settlement. (10)implies that a trial is less likely for offenses with small expected sentences(since So depends on S and p*) lelative to the defendant's differentialcost of going to trial, r(R — R).'° Except when explicitly stated to thecontrary, I now assume s So > r(R — so that Wn is greater than(W s So — rR).

3. If both parties agree on the probability of conviction by trialP), a settlement will take place for defendants who are risk averse

(U" < 0) or risk neutral (U'1 = 0).h1 When P" = P, one can show that atrial is equivalent to an unfair gamble (that is. the expected trial endow-ment is less than the settlement endowment).'2 Risk neutral suspectsmaximize their expected endowment and, therefore, refuse the trial"gamble," and a fortiori risk averse suspects also refuse the "gamble."On the other hand, a trial can still occur for a risk preferrer (U" > 0)even though P.13

10. This provides an explanation of why many persons plead guilty to traffic violationsinstead of spending considerable time in traffic court disputing them.

11. U" denotes the rate of change of U' with respect to one's endowment.12. A trial is an unfair gamble if

which can be rewritten as

(W—s .So—rJ?)—[P. Wc+(l —P)W,i] >0,

s AS + r(R — R)> 0,

(i)

(ii)

using (5), (6a, 6b) and the assumption = P. Since we have assumed s AS and r(R —are both positive, (ii) holds and the gamble is unfair.

13. Given risk preference, a negative ir, which leads to a trial, would be more likelythe greater the preference for risk, the larger rR, and the smaller s AS and rR. To provethis differentiate (9) partially with respect to these variables. The partial derivatives arenegative for and positive for s AS and rR, indicating that falls with respect to in.creases in rR and decreases in s AS and rR.

172 AN ECONOMIC ANALYSiS OF THE COURTS

4. Suppose the prosecutor and defendant differ in their estimates ofthe trial conviction probability. If < P, a trial becomes an even lessfavorable gamble in comparison to = P, and hence risk averse andrisk neutral suspects would continue to settle.'4 Risk preferrers are alsomore likely to settle since in (9) rises. P4 > P is the more interestingcase because this provides an explanation in addition to risk preferenceof why trials occur. When > P a trial becomes a more favorablegamble compared to P" = P, and hence ir falls, increasing the chances ofa trial. Moreover, if P4 > P, one can show that the likelihood of a trial isgenerally greater for defendants accused of crimes that carry strongerpenalties.'5

Several additional points are worth noting in regard to the settlementversus trial decision:

5. The greater the savings in costs from a settlement, other things thesame, the smaller So and rR, and the more likely a settlement. This sug-gests that policy measures designed to eliminate or subsidize the defend-ant's legal fees, which in turn reduce the cost differential between a trialand a settlement, will increase the proportion of trials.

6. Suppose a not-guilty verdict in a trial produces pecuniary and non-pecuniary returns to the defendant. This would raise E(U) and make atrial more likely. Similarly, publicity gains to the prosecutor from a trialwould raise So, as previously noted, and also make a trial more likely.

7. The question of whether the defendant did in fact commit thecrime he is charged with does not explicitly enter the analysis. The pros-ecutor and defendant have been assumed to react to the probability of

14. As P4 falls, So falls, which in turn increases (W — s So — Similarly, the

increase in P lowers [PWc + (1 — P)Wn]. Thus, the value of(i) in footnote 12 rises relativeto the case where = P. Since (i) is already >0 when = F, it is obviously >0 whenP* < P.

15. Differentiating ir with respect to S and noting that So P4 S — (see (5))yields arrIaS 0 according as

P U'(W—s-So--rR)U'(Wc)

<0 when U" 0 since U'(W — s So — rA) a U'(Wc) and P < P4. Thus, riskpreferring and risk neutral defendants are more likely to go to trial as S rises given P4 > P.When U" < 0 risk aversion), both sides of (i) are <1, and the sign of is indeter-minate. However, if the degree of risk aversion is weak (the right-hand side of (i) is close toone), risk averters are also more likely to go to trial as S rises.

In another sense, the likelihood of a trial is greater for large than for smallsentences. \Ve have already shown in (10) that a trial will not occur when s So is less thanthe difference in costs between a trial and a settlement, r(R — R). Thus, for very smallsentences r(R — is likely to dominate and a settlement will take place.

conviction and other vat-li.trial, while their behaviorguilt or innocence of thetwo ways. First, the amoferidant seems likely to diwould reduce the probalprosecutor to dismiss chaiSecond, an perswould have a greater relucperson. This can be intelplea for an innocent susjin (9) and hence increase

8. We observed in thsettled before trial. Our aecutor and suspect agree ctrial to both parties exceeerally risk averse in their

WEALTH AND SENTENCE

In this section two further(R) invested by the defendDo the resources investedendowment or wealth? Tbspread claim that the crimiincome suspects than for ament of resources rises wition in a trial and a negwealthier defendants.

To determine the effctotal differential of the fin

R.'7 This yields dR/dS

(i) 16. See Patricia M. Wald, PEnforcement and Admin. of JutReport: The Courts, at 139, app

17. The differential isdRds

—P'[U(Wn) —

The second-order condition for<0. Hence, dR/dS 0 as P'U'(

{E COURTS WILLIAM M. LANDES 173

differ in their estimates ofrial becomes an even lessnd hence risk averse and11 Risk preferrers are alsoP is the more interesting

ddition to risk preference:comes a more favorableincreasing the chances ofthe likelihood of a trial is

rimes that carry stronger

in regard to the settlement

ettlement, other things thea settlement. This sug-

or subsidize the defend-differential between a trialpf trials.pduces pecuniary and non-

raise E(1J) and make aprosecutor from a trial

make a trial more likely.did in fact commit the

er the analysis. The pros-eact to the probability of

— s So — Similarly, thef(i) in footnote 12 rises relative

P, it is obviously >0 when

that So = S — (see (5))

(i)

"(Wc) and P < F'. Thus, riskto trial as S rises given >

id the sign of is indeter-right-hand side of (i) is close to

ises.greater for large than for smallot occur when s - So is less thanr(R — R). Thus, for very smallwill take place.

conviction and other variables in choosing between settling and going totrial, while their behavior has not been directly influenced by the actualguilt or innocence of the defendant. However, this factor may enter intwo ways. First, the amount and quality of the evidence against the de-fendant seems likely to diminish in the case of an innocent person. Thiswould reduce the probability of conviction in a trial or even lead theprosecutor to dismiss charges more readily since P* may be close to zero.Second, an innocent person may have an aversion to lying so that hewould have a greater reluctance to plead guilty to an offense than a guiltyperson. This can be interpreted as imposing psychic losses on a guiltyplea for an innocent suspect which would reduce U(W — s So —in (9) and hence increase the likelihood of a trial.

8. We observed in the introduction that a large fraction of cases aresettled before trial. Our analysis predicts this if in most cases the pros-ecutor and suspect agree on the expected outcome of a trial, the costs of atrial to both parties exceed their settlement costs, and suspects are gen-erally risk averse in their trial versus settlement choice.

WEALTH AND SENTENCE EFFECTS

In this section two further questions are considered. (1) Do the resources(R) invested by the defendant in a trial rise as the sentence increases? (2)Do the resources invested increase with the level of the defendant's initialendowment or wealth? The latter question is directly related to the wide-spread claim that the criminal justice system works less favorably for lowincome suspects than for affluent ones,'6 because if the defendant's invest-ment of resources rises with wealth, then both the probability of convic-tion in a trial and a negotiated sentence would tend to be lower forwealthier defendants.

To determine the effect of an increase in the sentence, we take thetotal differential of the first-order condition in (8) with respect to S and

R)7 This yields dR/dS 0 according as

16. See Patricia M. Wald, Poverty and Criminal Justice, in U.S. Pres. Comm'n on LawEnforcement and Admin. of Justice, Task Force on the Admin. of Justice, Task ForceReport: The Courts, at 139, app. C (1967).

17. The differential isdRds

s{P'U'(Wc) — rPU"(Wc)]—P"[U(Wn) — U(Wc)) + 2rP'[U'(Wn) — (J'(Wc)j + (I — P)U"(Wn)J

The second-order condition for E(U) to be a maximum requires that the denominator be<0. Hence, dR/dS 0 as P'U'(Wc) — rPU"(Wc) 0.


which increases both i.magnitudes of these tweven if s and r were toof R if tastes for risk deneutrality and in thetastes for risk.

The total different

neutrality, gives

where E5 = t9s/c3W(W/sprice of market inputsinputs for time takes p1because as a first appr.portional to wealth. Th(risk neutrality —P' r/:E8> Er.21 Thus, the arto rise and the probabilin wealth. Note that thfor wealthier defendant

Suppose that the pstead a money fine. E3'value of time do not altnegative. Therefore, th

21. An identical result h.the first-order condition for ti

e U"(Wc)

rR/Wc—Wc

U(Wc)' where 5' = aS/aR 0. The b0 as

which gives dR/dW 0 as

22. An increase in R th,his minimum offer, So, while•from a trial and lower the rnsame, these forces should wo

> U"(Wc)11rP< U'(Wc)'

where —U"(Wc)/U'(Wc) is a measure of absolute risk aversion. From (11)it follows that dR/dS > 0 for defendants who are risk preferrers or riskneutral. If defendants are risk averse, sign of dR/dS is uncertain. It ismore likely to be positive the more responsive P to increases in R, thelower r, and the smaller the level of absolute risk aversion.'8 In sum, for agroup of defendants differing in their attitudes toward risk, we mightexpect to find a greater investment of resources on average for defend-ants charged with crimes carrying longer sentences. Note that this neednot lead to an observed negative relation between the probability of con-viction and the severity of the crime since we have previously shown thatan increase in the potential sentence also induces the prosecutor to al-locate more resources to the case.

The value of one's time is generally related positively to one's incomeand wealth. In consequence, an increase in the defendant's wealth willlead to an increase both in r and s, the prices per unit of R and S respec-tively. To show this for r, let R be produced by both inputs of marketgoods such as the services of lawyers, expert witnesses, etc., and inputsof one's time. The optimal input combination is where the marginal prod-ucts of the inputs over their respective marginal factor costs are equal.Since defendants with greater wealth attach higher prices to their timeinput, they would not only substitute more market intensive methods ofproducing R, but would also have a higher r.'9 Moreover, it follows fromthe equilibrium condition in (8) that a rise in r will lead to fewer inputs ofR. In contrast, the increase in s as wealth rises will usually result in anincrease in R.2° Thus, to predict the net effect of an increase in wealth,

18. (11) may also be rewritten as

where c is the elasticity of P with respect to R, rR/Wc is the share of R in the suspect'sConviction wealth, and —WcU"(Wc)/U'(Wc) is a measure of relative risk aversion. Thevalue of the latter is often argued to hover around 1. (See Kenneth Arrow, Aspects of theTheory of Risk-Bearing, 33—37 (1965).) Thus, if rR/Wc were small, one would expectdRIdS > 0 for risk averse suspects.

19. If higher income or wealth defendants are more productive in their use of time toproduce R. then the marginal product of time would be positively related to income. Thiswould work to offset the substitution of market inputs for time as income and wealth rose.Further, r need not increase with wealth.

20. The condition under which dRids > 0 is identical to that for dR/dS > 0 in (11).


which increases both r and s, one would have to determine the relative(11) magnitudes of these two offsetting forces. In addition, a change in wealth

even if s and r were to remain constant may change the equilibrium inputof R if tastes for risk depend on wealth. We analyze below the case of riskneutrality and in the mathematical appendix we consider nonneutraltastes for risk.

The total differential of (8) with respect to W and R, assuming risk

(12)

where E5 = as/a W(W/s) and Er = ar/aW(W/r). Er will be <1 since theprice of market inputs is unaffected and some substitution of marketinputs for time takes place as wealth rises. E5 can be assumed equal to Ibecause as a first approximation the per unit value of time in jail is pro-portional to wealth. The optimality condition for R (see (8)) becomes withrisk neutrality —P' = rls S, and, therefore, dR/dW will be positive whenE2.> Er.21 Thus, the amount of resources invested in a trial would tendto rise and the probability of conviction would tend to fall with increasesin wealth. Note that this result also implies a lower negotiated sentencefor wealthier defendants.22

Suppose that the penalty for conviction is not a jail sentence but in-stead a money fine. E5 would equal zero with a fine since changes in thevalue of time do not alter the dollar value of a fine, and dR/dW would benegative. Therefore, the effect of wealth on R reverses when penalties

21. An identical result holds when R affects not only P but also S. With risk neutrality,the first-order condition for the optimal R becomes

—P'(s . S) — P(s S') = r, (i)

where S' = aS/aR 0. The total differential of (i) with respect to W and R yields dRIdWOas

E,[—P'(s S) — P(s . S')J E,4r, (ii)

which gives dRIdW 0 as

E, E,.. (iii)

22. An increase in R that is anticipated by the prosecutor would lower and hencehis minimum offer, So, while the reduction in P would raise the defendant's expected utilityfrom a trial and lower the maximum sentence he would accept to settle. Other things thesame, these forces should work to lower the negotiated sentence.

COURTS

isk aversion. From (11)risk preferrers or risk

!R/dSis uncertain. It is' to increases in R, theaversion.18 In sum, for atoward risk, we mighton average for defend-es. Note that this needthe probability of con-

e previously shown thates the prosecutor to al-

>neutrality, gives dR/dW 0 according as

h sitively to one's incomedefendant's wealth willuni,t of R and S respec-both inputs of market

etc., and inputsthe marginal prod-

factor costs are equal.prices to their time

intensive methods oftoreover, it follows fromII lead to fewer inputs ofwill usually result in an

an increase in wealth,

he share of R in the suspectsof relative risk aversion. Theenneth Arrow. Aspects of the

small, one would expect

ductive in their use of time toitivelv related to income. Thisste as income and wealth rose.

o that for dRIdS > Oin(ll).


are in terms of money and not time for risk neutral defendants.23 Oncerisk aversion or preference is introduced, the effect of changes in wealthon R cannot in general be specified unless one has explicit knowledge ofadditional parameters of the defendant's utility function. Nevertheless,one can presume that if the deviation from risk neutrality is small, theeffects of wealth on R will follow the effects for risk neutrality.

II. SOME APPLICATIONS

THE BAIL SYSTEM

In the United States the typical procedure for bail is that shortly after thedefendant's arrest a bond is set as security for his appearance at trial. Ifthe defendant can post the amount of the bond through a deposit of cashor other assets, or have a professional bondsman do it for him, he is re-leased until trial. The bondsman's fee runs about 10 per cent of the valueof the bail bond. If the defendant does not meet the bail requirement, heremains in jail. The bond is generally forfeited should the released de-fendant fail to appear at trial.

Several implications of the bail system can be derived from ourmodel.

1. Bail costs would be deducted from the defendant's endowment,W, so that both U(W — s So — rR) and E(U) in (9) would fall. Fordefendants released on bail there would be no obvious change in (sinceequal dollar amounts are subtracted from (W — s So — Wc andWn) and hence no reason to expect a change in their use of trials com-pared to settlements. Bail costs for defendants not released would equalthe opportunity cost of their time in prison plus losses from restrictions ontheir consumption and freedom. These costs would be greater for a trialthan a settlement because the delay in reaching trial generally exceedsthe time taken to negotiate a settlement.24 This in turn would lower E(U)

23. G. S. Becker, Crime and Punishment: An Economic Approach, this volume,presents a similar argument without presenting a proof. However, he argues that the incen-tive to use time to reduce the probability of a sentence is unrelated to earnings, and the in-centive to use money to reduce the probability of a fine is also unrelated to earnings. Theseresults would follow when in the former case R is produced solely by time and in the lattercase R is produced solely by market inputs. However, once R is produced both time andmarket inputs there is always an incentive to substitute market inputs for time as earningsrise.

24. Empirically, the time difference appears to be positive. For example, in the 89United States district courts the median queues in 1967 were as follows: jury trial5.7 months; court trial = 3.9 months, and settlement (guilty plea) = 1.9 months. See, 1967Ann. Rep. Admin. Off. of the United States Courts, 269—71, table D6.

relative to U(W — s

more likely for defenctime differential betweportionately more settireleased on bail.25

2. The defendant ithe probability of convcosts or lowering the niexample, in the case o:tion with lawyers, anchave greater (even proengaging in other invesginal cost of producirR.26 Thus, other thingshould be greater forbail.27 As noted earlie:leads to worse terms iiSons the prosecutor alhigh bail charges.

3. Finally, if rnaki

25. Two additional poirwere given credit toward hithe only bail deduction in (9convicted. 71 would still riseprobability of conviction. Inwould leave ir unchanged. (bgreater for a trial than a sedefendant goes to trial or armake bail use bondsmen. (SeReport. 50 Minn. L. Rev. 6used as security for bail bon

26. Defendants not ma!that would have been usedthe probability of convictioresources will decline shouexceed the cost of financing•ably have prevented their re

27. Critics of the bail sthe Att'y Gen. Comm. on Fnote that the increase in cosavailability of "legal" advicimportant, one would observpretrial detention instead.

COURTS WILLiAM M. LANDES 177

ral defendants.23 Once:t of changes in wealthexplicit knowledge of

inction. Nevertheless,is small, the

•sk neutrality.

is that shortly after theappearance at trial. If

1rough a deposit of cashdo it for him, he is re-

!O per cent of the valuejbe bail requirement, hethould the released de-

be derived from our

efendant's endowment,in (9) would fall. Forious change in (since

So — rR), Wc and

their use of trials corn-t released would equalses from restrictions onid be greater for a trialtrial generally exceedsturn would lower E(U)

inic Approach, this volume,ver, he argues that the incen-

lated to earnings, and the in-unrelated to earnings. These)lCly by time and in the latteris produced by both time and

et inputs for time as earnings

ive. For example. in the 89were as follows: jury trialtea) = 1.9 months. See, 1967

table D6.

relative to U(W — s So — in (9), raise ir and make a settlementmore likely for defendants not released on bail. Thus, given a positivetime differential between a trial and settlement one would predict pro-portionately more settlements among defendants not released than thosereleased on bail.25

2. The defendant in jail is restricted in his use of resources to reducethe probability of conviction. This can be interpreted as either raising thecosts or lowering the marginal products of his market and time inputs. Forexample, in the case of market inputs, detention would hamper consulta-tion with lawyers, and in the case of time inputs, the defendant wouldhave greater (even prohibitive) difficulty in seeking out witnesses and inengaging in other investigatory activities. These factors increase the mar-ginal cost of producing a given R and lower the defendant's input ofR.20 Thus, other things the same, the probability of conviction by trialshould be greater for defendants not making bail than for those makingbail.21 As noted earlier, a higher probability of conviction by trial alsoleads to worse terms in a settlement. One should add that for these rea-Sons the prosecutor always has an incentive to request the judge to sethigh bail charges.

3. Finally, if making bail is positively correlated with income, then

25. Two additional points should be noted. (a) If the defendant not released on bailwere given credit toward his sentence for time in prison prior to disposition of his case,the only bail deduction in (9) would be from Wn, the defendant's endowment if he is notconvicted. ir would still rise. However, the rite in IT would be negatively related to theprobability of conviction. In the limit, if the probability of conviction equaled 1, court delaywould leave ir unchanged. (b) Bail costs of defendants released on bail will generally not begreater for a trial than a settlement. The bondsman's fee is independent of whether thedefendant goes to trial or accepts a settlement, and a majority of felony defendants whomake bail use bondsmen. (See, Lee Silverstein, Bail in the State Courts — A Field Study andReport, 50 Minn. L. Rev. 621, 647—52 (1966).) And the returns from assets (except cash)used as security for bail bonds will continue to be received by the owner.

26. Defendants not making bail may have available added resources for legal servicesthat would have been used to finance bail. These can offset the higher costs of R so thatthe probability of conviction need not increase. However, it is also possible that theirresources will decline should the loss in income (excluding a consumption allowance)exceed the cost of financing bail. In the latter case, capital market difficulties would presum-ably have prevented their release.

27. Critics of the bail system have recognized this point. For example, see Report ofthe Att'y Gen. Comm. on Poverty & the Adrnin. of Fed. Crim. Just 74—76 (1963). Alsonote that the increase in cost of R for jailed defendants may be partly offset by the greateravailability of "legal" advice from other inmates. However, if this factor were sufficientlyimportant, one would observe defendants who were able to meet bail requirements acceptingpretrial detention instead.


the effects of pretrial jailing, cited above, would fall most heavily on low-income defendants.

Proposals for bail reform generally focus on eliminating income as anindirect criterion of pretrial release. The Federal Bail Reform Act of 1966requires that criminal defendants in federal courts (which cover a smallminority of criminal defendants) be released prior to trial unless there isreason to believe they would flee. The "President's Commission" sug-gests placing greater reliance on release of defendants without bail, ac-companied by certain restrictions on their behavior (for example, restric-tions on travel, associations), while simultaneously confining suspectswhose release would pose a significant threat to the community, regard-less of their financial ability to make bail,28 the latter provision being aform of "preventive detention." if these reforms were to result in thepretrial release of more defendants and more low-income ones we wouldpredict the following: a decline in the negative correlations between in-come and the effects of pretrial jailing outlined above; a reduction in thefraction of defendants convicted since fewer defendants would be re-stricted in their use of R; and an increase in the demand for trials asdifferential bail costs between a trial and settlement go to zero for moredefendants.29 The latter would probably increase court delay.

These reforms leave persons detained in the same position as beforeand, moreover, their position relative to defendants released may worsenif the latter group does not pay for their release. Suppose those detainedwere paid a monetary compensation that increased with the length of theirdetention. We could then eliminate much of the discriminatory aspectsof the bail system while still detaining persons believed to be dangerous.A higher marginal cost of R for detained suspects would still be present,but they would have additional resources to mitigate the adverse effectsof this on the probability of conviction. Compensation would reduce thedefendant's incentive for a settlement as the differential bail costs be-tween a trial and settlement decline and approach zero for full compensa-tion. If compensation were paid out of the prosecutor's budget, the latter'sincentive for a settlement would increase given that the payment weregreater for a trial than a settlement. This in turn would lower his mini-mum offer, So, and raise U(W — So — in (9). Hence, the incentive

28. U.S. Pres. Comm'n on Law Enforcement and Admin. ofJustice, Task Force on theAdmin. of Justice, Task Force Report: The Courts, at 38—40 (1967). [Hereinafter, TheCourts.]

29. Other effects could be added. For instance, a predicted increase in crime from re-ducing the average probability of conviction, and a savings in resources used for pretrialdetention.

for a settlement needtends to reduce the po:defendants not releas

COURT DELAY

It is widely recognizedof cases than they canprior to trial, and hastinot surprising since usdevelops to ration the

To understand thethe demand for courts,by the loser that clearsbudget is not increaseprosecutor's and defen'mum sentence offeredof (1 — M. This,hood of a settlement. Seby trial, Wc, by an am(9). This also increasesgreater the increase in ia downward sloping deone can venture from tiquantity demanded offrom cases where thereecutor and defendant osentence if convicted 1that still go to trial asments over the probabiMoreover, changing thethe above results, sinceM, a money price

a detailed analy:An Economic Approach, this

31. The Courts. supra n

32. This does not meanrequired by both defendantalleged to run considerably ii

33. Optimal values of P'defendant must now allocate

COURTS

most heavily on low-

liminating income as anlail Reform Act of 1966Is (which cover a smallr to trial unless there isnt's Commission" sug-

without bail, ac-or (for example, restric-usly confining suspectsthe community, regard-latter provision being a

were to result in the'-income ones we would

between in-bove; a reduction in theefendants would be re-

demand for trials aserit go to zero for morecourt delay.same position as before

-jts,released may worsenSuppose those detainedd with the length of theirdiscriminatory aspects

to be dangerous.s would still be present,gate the adverse effectssation would reduce theiferential bail costs be-zero for full compensa-tor's budget, the latter'sthat the payment werer wou]d lower his mini-

). Hence, the incentive

ofiustice,Task Force on the.40 (1967). [Hereinafter, The

:ted increase in crime from re-in resources used for pretrial


for a settlement need not fall with compensation. Note as So falls thistends to reduce the positive difference between negotiated sentences for

• defendants not released compared to defendants released on bail.3°

COURT DELAY

It is widely recognized that the courts are burdened with a larger volumeof cases than they can efficiently handle. The results are often long delaysprior to trial, and hasty considerations when cases reach trial.3' This isnot surprising since users pay a nominal money fee, if any, and a queuedevelops to ration the supply.

• To understand the implications of nonmoney and money pricing onthe demand for courts, assume initially there is a money price, M, paidby the loser that clears the market.:32 We also assume that the prosecutor'sbudget is not increased to cover these court costs. M affects both theprosecutor's and defendant's demand for trial. First, it reduces the mini-mum sentence offered by the prosecutor, So in (5), by a positive functionof (1 — P*)

. Al. This, in turn, raises 'ir in (9) and increases the likeli-hood of a settlement. Second, it lowers the defendant's wealth if convictedby trial, Wc, by an amount equal to Al, reducing E(U) and raising ir in(9). This also increases the chance of a settlement. The larger is M. thegreater the increase in IT, and the more settlements that take place. Thus,a downward sloping demand curve for the courts is generated. Further,one can venture from the analysis of (9) that as Iv! rises, the reduction inquantity demanded of trials (hereafter, trial demand) will be primarilyfrom cases where there is not a significant disagreement between the pros-ecutor and defendant over the probability of conviction, and where thesentence if convicted by trial tends to be small.33 Put differently, casesthat still go to trial as M rises are where there are significant disagree-ments over the probability of conviction and where penalties are severe.Moreover, changing the allocation of the payment of M has little effect onthe above results, since whether the loser or winner pays M, or both shareM, a money price always increases IT in (9) and reduces trial demand.

30. For a detailed analysis of alternative bail systems see my paper, The Bail System:An Economic Approach, this volume.

31. The Courts. supra note 28, at 80—90.32. This does not mean that defendants are immediately brought to trial. Some time is

required by both defendant and prosecutor to prepare a case for trial. Current delays arealleged to run considerably in excess of this.

33. Optimal values of F, R* and 1? may change as Al rises since the prosecutor anddefendant must now allocate some resources to losses from expected court fees.


Compare this pricing scheme with one in which the courts are heavilysubsidized, taking the extreme example of a zero money price. As M goesto zero, So and Wc rise, ir falls and without an increase in supply, trialdemand would exceed supply. Let us assume trial dates are allocated onthe basis of waiting time since arraignment and a trial queue develops.The queue will reach an equilibrium size because, as we will show, trialdemand is a decreasing function of waiting or queueing time. An increasein the queue imposes losses on the prosecutor as it (a) reduces the numberof convictions in the current year from cases commenced in that year bydelaying trial conviction and (b) ties up resources in a case for a longerperiod of time. These losses increase as the queue lengthens, inducing theprosecutor to offer a lower sentence in exchange for a guilty plea. Al-though U(W — s So — rR) in (9) then rises (as So falls) the incentivefor the defendant to settle as the queue grows will depend on whether ornot he is released on bail. For defendants not released, the longer thequeue the higher the bail costs of a trial and hence the lower their expectedutility from a trial.35 This factor, together with the response of the prose-cutor, leads to the prediction that the demand for trials will fall as thequeue lengthens for defendants not released on bail. On the other hand,for defendants released on bail the net effect on their expected utility ofan increase in the queue is unclear. The discounted loss from a sentencereceived in a trial would diminish or increase as the penalty is pushed intothe future, depending on whether earnings are rising at a slower or fasterrate than the defendant's discount rate. In addition, the defendant'searnings may be adversely affected during the period he is free on bail dueto his being under indictment. If on balance their expected utility falls orremains constant and the prosecutor's losses rise, one would expect anincrease in IT and a reduction in trial demand as the queue lengthens fordefendants free on bail. However, one would predict that the demand fortrials among defendants released would be less responsive to an increasein the queue than the demand among defendants not released, since the

34. Even if the prosecutor had no time preference with respect to Convictions, anincrease in the queue would still impose losses on him. For example, suppose the prosecutoris in office for 5 years. An increase in the queue during his tenure would lead to fewer con-victions and a lower weighted conviction function than a constant queue because he willhave left to his successor a greater stock of cases than his predecessor had left to him.

35. This would be partially offset by giving credit towards the eventual sentence fortime spent in jail awaiting trial. W would be unchanged as the queue lengthened, providingthe time spent in jail awaiting trial was less than 5, but Wn would still fall. Hence, E(U)would continue to fall as the queue increased.

cost of an increase ingroup.

These points arc= pretrial

D1 and D2 denote thereleased on bail, respcharge for trials, the nnumber released, andtrial detention. Whenreleased and not releaand settlement are zerduction in supply ofgreater amount for thehence the reduction inlatter group. Thus, Dequilibrium queue mitnot released and T0 foltrials is establishedthe number of trials coifor trials of the releasbecause the differentia

\ç\(Qr

U,,

U

COURTS

w


the courts are heavilyoney price. As M goesicrease in supply, trialdates are allocated ontrial queue develops.as we will show, trial

eing time. An increase(a) reduces the number

in that year byes in a case for a longerengthens, inducing thefor a guilty plea. Al-

So falls) the incentivedepend on whether orleased, the longer thete lower their expectedresponse of the prose-r trials will fall as theau. On the other hand,heir expected utility ofd loss from a sentencepenalty is pushed into

ig at a slower or fasterition, the defendant'sd he is free on bail duexpected utility falls orone would expect an

te queue lengthens forCt that the demand forponsive to an increasenot released, since the

respect to convictions, anpIe, suppose the prosecutorre would lead to fewer con-tant queue because he will

decessor had left to him.s the eventual sentence foriueue lenathened, providing'ould still fall. Hence. E(U)

cost of an increase in the queue is greater for the latter than the formergroup.

These points are illustrated in Figure 1, where Qt = trial queue,Q,, = pretrial settlement queue, and T = fraction of trials per unit of time.D1 and D2 denote the trial demand curves for defendants not released andreleased on bail, respectively. Assume initially that there is no moneycharge for trials, the number of defendants not released on bail equals thenumber released, and credit against one's sentence is not given for pre-trial detention. When — = 0, Twould be the same for defendantsreleased and not released, since the differential bail costs between a trialand settlement are zero for both groups. As — rises, due to a re-duction in supply of trial services, the differential bail costs rise by agreater amount for the not released than for the released defendants andhence the reduction in trials will tend to be greater for the former than thelatter group. Thus, D1 diverges from D2 as (Qt — increases. If theequilibrium queue initially equaled T would equal T1 for defendantsnot released and T2 for defendants released. Suppose a money charge fortrials is established that is sufficient to reduce (Q, — to zero, keepingthe number of trials constant. As a first approximation, the demand curvesfor trials of the released and not released defendants would be identicalbecause the differential bail costs between a trial and settlement are now

j

(Q—Q,.)

M,, Q

M

FIGURE 1

T, T


zero for both groups.36 If the defendant's trial fee were set at M1, a pricethat equals the maximum amount that defendants who are not releasedwould pay at the margin for the same number of trials in order to reduce(Q1 — to zero, the aggregate number of trials demanded would be lessthan the available supply as 2T1 < T1 + T2.37 In order for demand to beequated with supply, the defendant's court fee must be less than M. Let A?in Figure 1 equal the market clearing court fee. At M the fraction of trialsfor each group would equal T3 and by assumption, 2T3 = T1 + T2. Thus,a money charge for the courts that kept constant the number of trials canlead to an increase in the use of the courts on the part of defendants notreleased on bail, and a reduction in use among defendants released onbail. Moreover, if the supply curve of trials were positively sloped withrespect to a money price, one would also expect an increase in the totalnumber of trials.

In sum, we should note that although a zero money price is oftenadvocated as a means of not discouraging low-income defendants fromusing the courts, its effect can be the opposite. A zero price operatingwith a bail system that tends to detain in jail low-income defendants willdiscourage the latter group from going to trial. In contrast, an appropriatemoney price may reduce the demand for the courts of defendants releasedon bail, and by reducing the trial queue can increase the use of the courtsby defendants who do not make bail.36 Surprisingly, the literature thatcriticizes court delay makes no mention of the possibility of charging amoney price, which not only reduces delay, but can distribute the use ofthe courts more equally among defendants independent of their abilityto make bail.

Ill. EMPIRICAL A

In the legal area readiquite limited. Howevpossible to test a nurrtmodel. The first sourcwhich over 11,000 felcourt dockets in nearlyfor several counties wion bail and theirnumber dismissed, acqdata is for the 89 U.S.on civil and criminalof civil and criminal ccdisposition of cases,subsidized legal servicants havethejr cases300,000 persons wereabout 30,000 criminalthe U.S. district courts

THE DEMAND FOR Tt

The theoreticalcriminal trials:

36. Note that the demand curves may differ. For example, if the average wealth of re-leased defendants exceeds that of jailed defendants and the wealth elasticity of trial demandis not zero, then the demand curve of the former group will be to the right of D1. However, aslong as it is still to the left of D2, the results that follow will still hold.

37. The prosecutor's court fee as (Q, — Q,,) falls to zero must be large enough to keepSo constant. if other methods of allocating court fees (for example, winner or loser pays)were used, we could no longer assume that D, is the demand curve when trials are priced.Although the geometry would become more complicated when different pricing schemes areused, the results of the analysis would not be substantially altered.

38. An alternative scheme that would produce similar results is to continue a zeromoney price for the courts but allow defendants to buy and sell their places on the queue.This would presumably reduce the differential costs between a trial and settlement fordefendants not released on ball relative to those released, and hence lead to a shift in courtuse from the latter to the former group. For example, if SX = the equilibrium price for a placein the queue that makes (Q, — Q9) = 0, the differential trial cost would be $X for bothdefendants released and not released, and their trial demands would be approximately equal.

39. Lee Silverstein, DefA Field Study and Report (2punishable by imprisonment

40. See Various years olFed. Offenders in the United

41. Lee Silverstein, supStates Courts, supra note 40.Offenses in the U.S. courtsstolen goods and vehicles,

i

and other federal statutes,other crimes. Theone exception is the U.S. disima! offenses in the area InDistrict of Columbia in order

WILLIAM M. LANDES 183COURTS

were set at a pricewho are not released

rials in order to reduceemanded would be less)rder for demand to be;t be less than M. Let iW

M the fraction of trials2T3 = T1 + T,. Thus,

he number of trials canpart of defendants not

defendants released onpositively sloped with

an increase in the total

o money price is oftendefendants from

A zero price operatingdefendants will

contrast, an appropriateof defendants released

se the use of the courtsgly, the literature that

of charging aban distribute the use ofpendent of their ability

III. EMPIRICAL ANALYSIS

In the legal area readily accessible and systematically collected data arequite limited. However, two sources of data were found that make itpossible to test a number of the important hypotheses in the theoreticalmodel. The first source is an American Bar Foundation (ABF) study, inwhich over 11,000 felony defendants in 1962 were sampled from statecourt dockets in nearly 200 counties.39 From this sample we can estimatefor several counties within most states the number of defendants releasedon bail and their average bail charge, the number going to trial, and thenumber dismissed, acquitted and sentenced. The second major source ofdata is for the 89 U.S. district courts where annually published statisticson civil and criminal cases are available.40 These data contain informationof civil and criminal court queues, the number of cases going to trial, thedisposition of cases, and the number of criminal defendants receivingsubsidized legal services. It should be added that most criminal defend-ants have their cases decided in state not in U.S. courts. In 1962 about300,000 persons were charged with felonies in the state courts, whileabout 30,000 criminal defendants annually have their cases disposed inthe U.S. district courts.4'

THE DEMAND FOR TRIALS

The theoretical analysis suggests the following demand function forcriminal trials:

e. if the average wealth of re-'alth elasticity of trial demando the right of D1. However, ashold.must be large enough to keepample, winner or loser pays)curve trials are pnced.

i different pricing schemes aretered.results is to continue a zeroeli their places on the queue.en a trial and settlement for

hence lead to a shift in courte equilibrium price for a place

cost would be SX for both

vould be approximately equal.

T =f(B, Q,, S, D, U), (13)

39. Lee Silverstein, Defense of the Poor in Criminal Cases in American State Courts,A Field Study and Report (2 v. 1965). Note that a felony is generally defined as any crimepunishable by imprisonment of more than one year.

40. See various years of the Ann. Rep. Admin. Off. of the United States Courts andFed. Offenders in the United States District Courts 1967.

41. Lee Silverstein, supra note 39, at 7—8 and Ann. Rep., Admin. Off. of the UnitedStates Courts, supra note 40. The types of offenses also differ in the state and U.S. courts.Offenses in the U.S. courts include forgery, counterfeiting, interstate transportation ofstolen goods and vehicles, postal theft, and violation of immigration laws, liquor lawsand other federal statutes, while it includes few cases of murder, assault, robbery, andother "violent" crimes. The latter types of offenses are concentrated in state courts. Theone exception is the U.S. district court in the District of Columbia which handles all crim-inal offenses in the area. In the empirical analysis of the U.S. Courts I have excluded theDistrict of Columbia in order to have comparable offenses across districts.


where T is the fraction of defendants going to trial, B is the fraction ofdefendants released on bail, Qt and Q. are the average trial and pretrialsettlement queues respectively, S is the average sentence if convicted bytrial, D is the average cost differential between a trial and settlement, andU is the combined effect of all other factors.42 We would predict on thebasis of our model that B, and S will have positive effects on T, whileQt and D will have negative effects on T. Unfortunately, data limitationsprevent us from estimating the partial effects of these variables in a singleequation. The ABF sample of state county courts has no data on queuesor cost differentials between trials and settlements, while the data for theU.S. courts contain no information on bail. Therefore, the analysis willuse the ABF data to test bail effects, and the U.S. data to test queueeffects. At the same time we will point out possible biases and alternativeinterpretations of the results that arise from leaving out either the bail orqueue variables.

Pop: county poptRe: region dumm

for non-South countieNW: per cent noiUr: per cent urbaY: median family.

Weighted regress:the U.S., the non-Soul(2.1—2.2) the regressidicted positive sign arthe coefficient is notthese results in greateto the bail regression

STATE COUNTY COURTS

Least-squares multiple regression equations were estimated across statecounty courts in 1962. These equations were of the following generalform:

T=a+f31B+f32S+f33Pop+/34Re+f35NW+f36Ur+/37Y+u. (14)

The variables in (14) are defined as follows:

T: the fraction of defendants in a county court whose cases were dis-posed of by trial in 1962. Cases where a plea of guilty was made at timeof trial are not counted as trials.

B: the fraction of defendants in each county released on bail in 1962.S: the average time served of first-released prisoners in 1964 who

had sentences of one year or longer. S is an estimate of the average sen-tence, if convicted by trial, of felony defendants in 1962. Releases in1964 are used because the average time served in state prisons of first-released prisoners was about two years, and hence 1964 should be theaverage release year for defendants sentenced in 1962.

42. U would include factors derived from the ir function (equation (9)) such as thedistribution of estimates of the probability of conviction by trial, and attitudes towardrisk. I have not been able to directly measure these variables and hence they are largelyignored in the empirical analysis. U also includes several demographic variables that willbe specified in the statistical estimation of (13).

43. Observations wertsampled in each county. Thrises with the size of the ccof the likelihood of largerregressions were also compthe results.

where N is the numbebail, and N2 is the nunto go to trial of the rtheory predicts thatthe settlement queue.be rewritten as

Therefore, from a seisimple regression of 7efficient on B would bwould be consistentof these regression ccindependent variablestheir influence on K1 a


al, B is the fraction oferage trial and pretrialntence if convicted by

and settlement, andwould predict on the

tive effects on T, whilelately, data limitationsse variables in a singlehas no data on queueswhile the data for the

the analysis will.S. data to test queuebiases and alternativeout either the bail or

estimated across statethe following general

+ /37Y + U. (14)

whose cases were dis-was made at time

leased on bail in 1962.risoners in 1964 whotte of the average sen-in 1962. Releases instate prisons of first-

e 1964 should be the962.

Pop: county population in 1960.Re: region dummy variable that equals 1 for counties in South and 0

for non-South counties.NW: per cent nonwhite population in county in 1960.Ur: per cent urban population in county in 1960.Y: median family income in county in 1959.

Weighted regressions on T are presented in Table 2 for counties inthe U.S., the non-South and South.43 in the U.S. and non-South equations(2.1—2.2) the regression coefficients of the bail variable have the pre-dicted positive sign and are always highly significant, while in the Souththe coefficient is not significantly different from zero. Before discussingthese results in greater detail, an interesting interpretation can be givento the bail regression coefficient. T can be written as

T — X1N1 + X2N�N

(15)

where N is the number of defendants, N1 is the number not released onbail, and N2 is the number released. A1 and A2 are the average propensitiesto go to trial of the not released and released group respectively. Thetheory predicts that A2 > A1, providing that the trial queue is longer thanthe settlement queue. Since N1/N + N2/N = 1 and N2/N = B, (15) canbe rewritten as

T = A1 + (A2 — A1)B. (16)

Therefore, from a set of observations on T and B, the intercept in asimple regression of T on B would be an estimate of A1 and the beta co-efficient on B would be an estimate of(A2 — A1). A positive beta coefficientwould be consistent with the prediction that A2 > A1. The interpretationsof these regression coefficients are modified with the addition of otherindependent variables, which enter the regression indirectly throughtheir influence on A1 and A2. For example, let

A1 = C1 +2

(17)

I (equation (9)) such as thetrial, and attitudes towardand hence they are largelyographic variables that will

I

43. Observations were weighted by the where n is the number of defendantssampled in each county. The range of ,i is from 3 to 349 with a mean of 58, and n generallyrises with the size of the county population. Weighted regressions were computed becauseof the likelihood of larger variances in the residuals as ii declined. However, unweightedregressions were also computed, and as it turned out, the weighting made little difference inthe results.

TA

BL

E 2

WE

IGH

TE

D R

EG

RE

SSIO

NS

AN

D I-

VA

LUE

S F

OR

CR

IMIN

AL

TR

IALS

IN 1

962,

STA

TE

CO

UN

TY

Cou

RT

sa

Dep

en-

Equ

atio

nN

umbe

rA

rea

Cou

n-tie

s

dent

Van

-ab

le

Reg

ress

ion

Coe

llici

ents

and

i-V

alue

s b

aB

SPo

pR

eN

WU

rV

R2C

2.1

U.S

.13

2T

—.0

65(.

624)

.348

(4.0

71)

—.0

002

(.08

7).0

37(3

.312

).0

98(2

.723

).0

14(.

106)

.062

(.70

9)—

.002

(.10

1).2

6

2.2

N.S

.10

0T

.002

(.02

7).4

98(6

.521

).0

03(1

.515

).0

38(4

.263

)

—.2

17(1

.548

).1

29(1

.513

)—

.043

(2.5

52)

.45

2.3

Sout

h32

T.2

29(.

833)

—.0

12

(.05

9)

—.0

09

(1.7

46)

.463

(3.2

15)

.109

(.48

8)—

.570

(2.7

16)

.095

(2.0

42)

.48

SOU

RC

ES.

—T

and

8fr

om L

ee S

ilver

stei

n, D

efen

se o

f th

eP

oor

in C

rim

inal

Cas

es in

Am

eric

an S

tate

Cou

rts,

AF

ield

Stud

yan

d R

epor

t

(2v.

196

5); P

op, N

W, U

r an

d V

from

U.S

. Bur

eau

of th

e C

ensu

s, C

ount

yan

d C

ity D

ata

Boo

k 19

62; S

fro

m U

.S.

Bur

eau

of P

riso

ns, N

a-

tiona

l Pri

sone

r St

atis

tics

Det

aile

d R

epor

ts:

Stat

e A

dmis

sion

s an

d R

elea

ses,

196

4,ta

ble

R-5

.

aA

lthou

ghth

e A

BF

sam

ple

cove

red

near

ly 2

00co

untie

s, m

any

had

to b

e ex

clud

ed b

ecau

seth

ere

was

no

repo

rtin

g on

the

num

ber

ofde

-

fend

ants

who

mad

e ba

il. I

hav

e no

rea

son

tobe

lieve

that

the

grou

p of

exc

lude

d co

untie

sw

ould

hav

e di

ffer

ed s

yste

mat

icai

Jy f

rom

the

coun

ties

incl

uded

in th

e re

gres

sion

equ

atio

n. T

wo

coun

ties

in N

ew J

erse

y w

ere

excl

uded

beca

use

no d

ata

on S

wer

e av

aila

ble

for

New

Jer

sey.

bi-v

alue

sin

par

enth

eses

.A

llR

2's

are

unad

just

ed in

Tab

le 2

and

all o

ther

tabl

es u

nles

s ex

plic

itly

stat

ed to

the

cont

rary

.

VIII

I

c 1 I

,—.

•

CD

(I)

•-.

P0

CD

CD

——

+ r-.

e-+ 0 9• .. o

C

Co

I-

C-U

jC.1C)

>,

UC)

0) 0)

-CO...—C

0)

01

C)

rCl

C)

Cl

IClI_

•- E —C)

C-C1.C._<

Cl

— CUCC—.-


and

A2 = c2 + (18)

By substitution into (16) we have,

j jT = + (c2 — c1)B + + — j33B X,. (19)

Estimates of equation (19) were not successful because of the largeamount of multicollinearity resulting from the inclusion of interactionvariables. This tended to eliminate statistical significance from any ofthe independent variables. However, if we set a1 = f3. for all = 2,

j, the interaction variables drop out and (19) reduces to the form ofequations estimated in Table 2. It also follows from (17) and (18) thatwhen a, 13. the regression coefficient on B is a measure of (A2 A1), thedifference in trial propensities between defendants released and not re-leased on bail.

Estimates of (A2 — A1) from Table 2 for the U.S. and non-Southimply, for example, that the release of an additional 20 defendants onbail, other things the same, would lead to a desired increase of about 7to 10 trials as a result of the reduction in trial costs associated withmaking bail. One can also get a rough idea of the increased demand fortrial if the existing bail system were replaced with a system of preventivedetention that released all defendants except a few "hard-core" criminalsuspects (for example, 10 per cent). The weighted means of T and B areabout .18 and .45 respectively. Therefore, the release of additional de-fendants to bring the number released to 90 per cent would lead to an in-crease in the fraction desiring trials from 18 per cent to between 34 and40 per cent, or roughly a 100 per cent increase in desired trials.44

Although no direct measures of trial queues are available in the ABFdata, longer trial queues are generally thought to exist in large urbanareas. If the county population variable is interpreted as an imperfectproxy for the difference between trial queues and settlement queues, thesign of the regression coefficient on the population variable would de-pend on the relative strength of two opposing forces. On the one hand,longer queues discourage trials, but on the other hand, longer queues may

44. This is the increase in trials desired with no change in the trial queue. With an in-creased demand and unchanged court capacity the queue would presumably grow so thatthe actual increase in T would be less than the desired increase. In fact, if the courts werefully employed, the queue would grow until the costs of waiting were just sufficient to makedesired trials equal to the previous level of trials.

I188 AN ECONOMIC ANALYSIS OF THE COURTS

be the result of an increased demand for trials. In Table 2, the coefficienton the population variable is positive and significant in all regressions,which suggests that the positive association of trials with queues domi-nates. 2

Further evidence on the effects of population size appears in Table 3where separate regressions are given for counties in the non-South withpopulations greater than 450,000, between 100,000 and 450,000, and lessthan 100,000, and in the South with populations greater than 200,000and less than 108,000. In Table 3 not only does the bail variable continueto have a positive effect on trials in all non-South equations, but its

(5coefficient (or (A2 — A1)) has a systematically greater value as county size >.

rises (.09 in eq. 3.3, .31 in eq. 3.2, and .75 in eq. 3.1), which is preciselywhat one would expect if (Q1 — Q,,) was positively correlated withcounty population.45 (A2 — A1) is statistically significant in the non-Southexcept in counties of less than 100,000. This result could be observed ifthe difference between (Q, — Q,,) was negligible in small counties. More-over, the empirical finding that the coefficient on the bail variable in-creases as county population size rises is indirect evidence that (Qe — (5is in fact larger in counties with bigger populations.

Let us briefly consider the empirical results for the South. The threeregression coefficients on the bail variable in the South in Tables 2 and 3, owere negative and not significantly different than zero. One possible ex-planation is that (Q, — is negligible for counties sampled in the Southso that (A2 — A1) would approach zero, and hence the regression coeffi-cients on bail would not be significant.46 A second explanation is thatgreater measurement errors in the bail variable may exist in the Southcompared to the non-South, which would lower the value of regressioncoefficients on bail in the South relative to the non-South. Along theselines it might be argued that justice is more informally administered inthe South, particularly in rural areas, and this would produce poorerrecords on bail. (A similar argument may be used to rationalize the non-significant but positive bail coefficient in non-Southern counties of lessthan 100,000.) However, it is questionable whether this argument shouldbe given much weight since a nonsignificant bail variable was also ob-

45. If we refer to Figure I, supra, we note that at a given value of (Q, — Q,,) the dif-ference getween D2 and D1 equals X, X, — increases

increase in bail costs of defendants not released compared to defendants released.46. Data for the federal courts indicate that queues are somewhat lower in the South.

In 1966, the mean civil Q,'s were 22.0 and 15.7 months for the non-South and South, andthe mean criminal Q,'s were 6.3 and 5.3 months in the two areas. However, (Q, — Q)for criminal cases was 3.8 and 3.5 months in the non-South and South.

U')

z0

0.0

0

z

z

U)

0U)

U)

N — N —00

COURTS

rable 2, the coefficientcant in all regressions,

with queues domi-

size appears in Table 3in the non-South withand 450,000, and lessgreater than 200,000bail variable continue

uth equations, but itser value as county size

1). which is preciselyively correlated with

kant in the non-Southit could be observed ifsmall counties. More-

n the bail variable in-that (Q, —

S.

r the South. The three)uth in Tables 2 and 3,

One possible ex-sampled in the Souththe regression coeffi-

explanation is thatay exist in the Southte value of regressionn-South. Along thesemally administered in'ould produce poorerto rationalize the non-them counties of lessthis argument should

variable was also ob-

value of (Q, — the dif-X.. — A increases due

d to defendants released.mewhat lower in the South.

non-South and South, andareas. However, (Q, —d South.

U)0.)

a>

0aU)

00)U

C.)

000U)C)C..01.)C.)

C)—0. aa

0

—00 N 00 0000 — m N 00 00

0) 00 O\ \O N N NN — U.)

0 00 N CO NN N U'.) 0'. U.') NN '- — U.) N N a'.

U'.) — C'. NC'. 00 N N '.0 0000 C Q U'.) '.0 N

— U". '.0 N CC N C N C '.0 C —QN0000'.OCC'— '—>

o c'. C'. 0'. I") '.0 0 '0 '0 U".U.) 00 0 —00 N -, rfl 00 NN U".Ffl '0 0 — C C N

C U". N 0'. — 00N N N N

F-, F-.. t

C N m N U'.)N — —

C.0 .00.0 0 0C0O,'.

"? .o o0 0 C0")'O 0 0NZAZ—Z

-: N U".

0". 0".

C0.

NC.)

.0

U)C-)

0C')

189


served for the South in counties with populations greater than 200,000.Although a sufficient explanation is not available for the South, the

overall results of Tables 2 and 3 give strong support to the hypothesisthat the frequency of trials is greater among defendants released on bailthan those not released. A positive and statistically significant relationshipbetween bail and trials was observed for the U.S. and the non-South, andthe latter region included more than three-fourths of our observations.This finding is consistent with the prediction of the theoretical model thatthe costs of going to trial compared to settling are increased by not mak-ing bail, which in turn reduces the likelihood of a trial.

Several additional comments on the results in Tables 2 and 3 are inorder. (1) It might be argued that the bail variable is a proxy for wealthso that a finding that T increases with B is due to differences in wealth andnot to greater trial costs for those not released. First, there is nothingin the theoretical analysis that indicates that wealth directly affects thechoice between a trial and a settlement. If wealth were positively corre-lated with the ability to make bail, one would observe wealthier de-fendants going to trial, but the theoretical explanation lies with dif-ferences in costs not differences in wealth. Second, the empirical analysisof the U.S. courts in the next section contains indirect estimates of a de-fendant's wealth which show that increases in wealth have no observablepositive effect on trials. (2) A second criticism, which if valid wouldweaken my conclusion that increases in B lead to increases in T, is thatspurious correlation exists between B and T. The argument can be madethat defendants planning to plead guilty will not be willing to incur thecosts of making bail, while those planning to go to trial will incur thesecosts. If this were true, an increase in T would lead to an observed in-crease in B and not the reverse. Although this argument has some plausi-bility, it has a defect. A defendant planning a guilty plea presumablydesires the most favorable terms in a settlement. We showed in the modelthat one effect of not making bail is to raise the probability of convictionin a trial, which in turn results in worse settlement terms. Therefore, it isnot obvious that the defendant planning to settle will find it any less de-sirable to post bail than the defendant planning a trial, since both sufferlosses from not being released on bail. (3) The regression coefficients onthe sentence variable, 5, do not support the hypothesis that the likelihoodof a trial is greater for defendants accused of crimes carrying longersentences. In 4 of 8 equations in Tables 2 and 3 the sign of S was positive,and in only one equation (3.4), where S had a negative effect, was thevariable significant. The inconclusive behavior of S may partly be at-

tributed to the data.measures the averagecounty in 1962, whiletime served by all feictunately, the regressictest of the sentence Icourts correspond mcNW, Ur and Y variab2 and 3, should be vrather than as indicatthe relation of these wprior expectations onregression coefficientsNW have negative efithe South, while Ur h;effect in the South. Abefficients are not

U.S. COURTS

Least-squares regressicourts in 1967 of the I

— +

All variables are in naefficients arefollows:

T1: ratio of defendanthe total number of defeion T2 which equals the r

weighted averagcourt trial and by jury tiand jury trials respective

Q,): median time inteS: weighted average

47. Regressions were asion results for the bail,

COURTSWILLIAM M. LANDES 191

greater than 200,000.ble for the South, thetort to the hypothesisdants released on bailignificant relationship

nd the non-South, andof our observations.

theoretical model thatincreased by not mak-rial.Tables 2 and 3 are inis a proxy for wealth

ferences in wealth andFirst, there is nothingth directly affects thewere positively corre-)bserve wealthier de-anation lies with dif-the empirical analysis

red estimates of a de-th have no observablewhich if valid wouldincreases in T, is thatrgument can be madee willing to incur thetrial will incur these

ad to an observed in-nent has some plausi-iilty plea presumablye showed in the modelbabiity of conviction

terms. Therefore, it isill find it any less de-rial, since both sufferession coefficients onsis that the likelihoodimes carrying longersign of S was positive,gative effect, was theS may partly be at-

tributed to the data. The theoretical analysis calls for a variable thatmeasures the average severity of offenses for defendants sampled in eachcounty in 1962, while data limitations have forced us to use the averagetime served by all felons in a state who were first released in 1964. For-tunately, the regressions for the U.S. courts provide us with a strongertest of the sentence hypothesis because data on sentences in the U.S.courts correspond more closely to the theoretical requirements. (4) TheNW, Ur and Y variables, which are included in the regressions of Tables2 and 3, should be viewed as demographic characteristics of countiesrather than as indicators of socioeconomic classes of defendants, sincethe relation of these variables to defendants may be remote. There are noprior expectations on the effects of these variables on trials, and theirregression coefficients do not show a consistent pattern. In Table 2 YandNW have negative effects on T in the non-South and positive effects inthe South, while Ur has a positive effect in the non-South and a negativeeffect in the South. About two-thirds of the NW, Ur and Y regression co-efficients are not statistically significant.47

U.S. COURTS

Least-squares regression equations were estimated across U.S. districtcourts in 1967 of the following form:

(20)

All variables are in natural logs except Re and hence the regression co-efficients are elasticity measures. The variables in (20) are defined asfollows:

T1: ratio of defendants whose cases were disposed of by trials during 1967 tothe total number of defendants disposed of in 1967. Regressions were also fittedon T2 which equals the ratio of trials to defendants for 1968.

Q: weighted average of median time intervals from filing to disposition bycourt trial and by jury trial in 1967, where weights are the proportion of courtand jury trials respectively.

Q9: median time interval from filing to disposition by a plea of guilty in 1967.S: weighted average of sentences received by convicted defendants whose

47. Regressions were also estimated without the NW, Ur and Y variables. The regres-sion results for the bail, population, and sentence variables were largely unaffected.

192 AN ECONOMIC ANALYSIS OF THE COURTS00

cases were disposed of in 1967, where weights are the proportion of convicteddefendants receiving each type of sentence.48

D: proportion of criminal defendants disposed of in 1967 who are assignedcounsel by the court under provisions of the Federal Criminal Justice Act of 1964.The Act provides for counsel when defendants are unable to pay all or part oftheir legal fees.49 Thus, D is a direct measure of the fraction of defendants withsubsidized legal counsel. Since the ability to pay for counsel is related to the de-fendant's wealth, D would also serve as a rough measure of the fraction of de-fendants with low incomes or wealth.

Re: region dummy variable where 1 is assigned to district courts in the Southand 0 to district courts in the non-South. 0

I-

Data on Qt are available for only 44 of 89 district courts in 1967 (seenote b to Table 4), while data on Qt and Q,, are not available for otheryears. Regressions were first estimated for the 44 districts in 1967. How-ever, in order to incorporate observations for the remaining districts, andto work with years other than 1967, a proxy variable for was used thatcart be computed for all years and districts. The proxy for in year ,nis the ratio of pending cases (Pc) at the end of year ni-i to the averageannual number of cases that go to trial (T) in years in and in-i. One wouldexpect Pc to estimate the backlog and T to roughly measure the availabil-ity of trial services, and hence should serve as a measure of eventhough not all pending cases eventually go to trial.50 The accuracy of

_________________________

048. Obvious problems arise in evaluating a diversity of sentences that include imprison-

ment, fines, probation with and without supervision, suspended sentence, etc. The Ad- La

ministrative Office of the U.S. Courts has devised a common set of values for these sen-tences (see Fed. Offenders, supra note 40, at 4) that assign 0 to suspended sentences andprobation without supervision, 1—4 for fines and various terms of probation with super-vision, and 3—50 for imprisonment with sentences that range from I to more than 120months. Although higher values are generally given to more severe sentences, the methodis still arbitrary. For example, why all fines and probation with supervision from 1 to 12months are both assigned the value 1 is never explained. Nevertheless, the use of thisvariable as an estimate of the average potential sentences of accused defendants in eachdistrict seems preferable to using just the mean prison sentence, since the latter group 2includes only 38 per cent of all defendants disposed of in 1967, while the former group in-eludes 77 per cent. Both measures suffer because they exclude defendants not convictedwhen the relevant theoretical variable is the average potential sentence faced by all de-fendants before disposition of their case.

49. See The Courts, supra note 28, at 59—6 1.

50. There were 10,771 pending criminal cases in the beginning of fiscal year 1967, and3,924 trials in the 1967 fiscal year. Since the average trial queue is about six months, thiswould suggest as a first approximation that roughly one-half of the trials in 1967 were frompending cases in the beginning of the year. Thus, about 20 per cent of pending cases wouldgo to trial.

Co

C.'

0z

N'.00.'

'.00.'

I—

0

I-I.)

C..

Ct

Cr)

zCt

:5

U

0IC.

CtIC)

0z

Ctz0Ct(I,'U

'U

0CU

0CCC

— CO N N '.0 N 00'.o r

r I,,

00—

OURTS

proportion of convicted

i 1967 who are assignedtinaiiustice Act of 1964.tble to pay all or part ofction of defendants with

unset is related to the de-ire of the fraction of de-

istrict courts in the South

rict courts in 1967 (seenot available for otherlistricts in 1967. How-

remaining districts, andfor Qt was used that

jProxY for in yearear ,n-i to the averagein and rn-i. One wouldmeasure the avail abil-a measure of even

ial.5° The accuracy of

ences that include imprison-led sentence, The Ad-set of values for these sen-

to suspended sentences andns of probation with super-e from I to more than 120vere sentences, the methodth supervision from 1 to 12evertheless, the use of thisaccused defendants in each

since the latter group1, while the former group in-ie defendants not convictedal sentence faced by all de-

fling of fiscal year 1967,andis about six months, this

the trials in 1967 were fromcent of pending cases would

k

C,'C)

>

CC

4)C)

C) CC

C'. 0'. 0'. 0'. I". N N N '.0 N C'.' N'I.' rt I— 0'. N Co 0'.CC". 000 ON Or.'.

N 0'. —0'. — '.0 0'. N 00'. N 0'. '.0 '.0 N C'. N———' —

0 'r'. . '.0 '.0 '.0 00 Co '.0 N C".— V.' — N 0'.— C'. — — 0'ON N V

N — — '— N

N Co -0' C". 0 N 00 Co00'. — '0 C'- — 0'.0 00 V.' N en

0'.— Co N- — Co N Co NN 0 0 N 0' Co en 0' N 00'.0 N '00 C". N- C". C". 00

C,'.

'0'.O en00C'C00

en '0— 0' en C C C C". en '.0— If'. N 0'. en Co N V.' a'. '0 N a'. a'.00 00 '0 C 000'. C— Co r.C en N 0'.

k k

0'. '.000 Co

N N 00 Co N'.0 '.0 '.0 '.0 '.0 '.0 '.00'. 0'. 0' 0'. 0'. 0'. 0'.

"CC)

C1I-

'.2C)00CO

00C

0

'.2C)C)

Cl)

193

194 AN EcoNoMic ANALYSIS OF THE COURTS

NOTES TO TABLE 4

SOURCES—TI, Q,, PcIT for equations 4.1 through 4.5 are from 1967 Ann. Rep.,Admin. Office of the United States Courts, tables D6, Dl, C7; T2 for equations 4.1 through4.5 is from 1968 Ann. Rep., Admin. Office of the United States Courts, table D6; S andW for equations 4.1 through 4.5 are from Fed. Offenders in the United States District Courts1967, tables Dl0, Dli; T, PcI T,E(T) in equations 4.6 and 4.7 are from 1960 Ann. Rep.Admin. Office of the United States Courts tables C7, Dl, D3, D4; S for equations 4.6 and4.7 is from U.S. Bureau of Prisons, Federal Prisons 1960, table 20.

Weighted by where ,i is the number of defendants disposed (equations 4.1 through4.5) and the number of cases commenced (equations 4.6 and 4.7). All variables except Reare in natural logarithms.

is the district average of the median court trial queue and median jury trial queue.Data on either median were available only if there were at least 25 observations for thattype of trial. 44 out of 89 districts had figures on at least one of two trial queues. Since mosttrials are jury trials (about 67 per cent), 29 out of the above 44 districts did not publish anyinformation on court trial queues. The latter were estimated by assuming the ratio of thecourt trial to jury trial queue in the circuit (the 89 district courts are divided into ten circuits)was equal to the ratio in the district. Information was available on the aggregated circuitlevel, and hence the median court trial queue in a district could be directly estimated. Esti-mates were generally required in districts that had a small proportion of court relative tojury trials. Therefore, any errors in estimating the court trial queue would have a small effecton the weighted average Q,. Finally, note that in 5 districts the queue for court trials but notjury trials was available. The procedure described above was then used to estimate the jurytrial queue.

E(T) in the ith district equals T where T is the proportion of defendantsin the jth offense category whose cases were disposed of by trial for all districts taken to-gether in 1960, and is the proportion of defendants accused of the jth offense in district i.There were 16 offense categories. Thus, variations in E(T) across districts are due solely todifferences in the composition of offenses. E(T) was devised to take account of the possi-bility that differences in the fraction of trials across districts were the result of E(T) ratherthan the queue. Data did not permit a similar calculation for 1967—68.

II In 1960 there were 86 district courts. By 1967 there were 89 district courts as severalwere eliminated and new ones were added. There are several small differences between the1960 and 1967 data. They are: (I) T is the ratio of the number of cases that went to trialover the number of cases commenced in 1960. This differs from 1967 where the trial dataare for defendants not cases, and the denominator is disposed defendants not commencedcases. In a given year the number of new defendants is about 25 per cent greater than thenumber of cases commenced, indicating that the number of cases with more than one de-fendant exceed the number of defendants involved in more than one case. Since this isreflected in the numerator of the trial variable as well, the correlation in a given year betweenT for cases and defendants would be very high; (2) S in 1960 is the average prison sentenceof convicted defendants, and excludes defendants who were fined or put on probation withsupervision. The latter groups are included in the 1967 S variable.

Regressions computed from districts in 1960 that match those districts in 1967 thathad data on Q,.

Pc/T as an estimate'gressions of Qp, 1that Pc/1 is positive!counting for nearly his also positively relaplaining variations inmeasure of general decontrary, isa measureThis result allows us1967, and to check titions to an earlier yea:

If equation (20)analysis predicts thatnegative, and the regrsingle-equationdemand for trials vanecase, higher observedthe right in demandSimilar behavior woul.in guilty pleas loweretion problem in two vthat are expected to Iand D constant, the liiA region variable, Re,Re operates more on t:have been estimatedQt and If defendacurrent queues on thestill be inversely relaicaused a positive corr

51. The regression eqt

C

(Qt—Q

Pc/T, Q, andwhere n is the number of d

OURTS WILLIAM M. LANDES 195

are from 1967 Ann. Rep.,

2 equations 4.1 through.s Courts, table D6; S andnited States District Courtaare from 1960 Ann. Rep.)4; S for equations 4.6 and

20.rted (equations 4.1 through7). All variables except Re

od median jury trial queue.st 25 observations for thatwo trial queues. Since most

districts did not publish anyy assuming the ratio of the

e divided into ten circuits)Ic on the aggregated circuitbe directly estimated. Esti-portion of court relative to

would have a small effectcue for court trials but notused to estimate the jury

ji e proportion of defendants

j.ial for all districts taken to-of the jth offense in district i.ss districts are due solely to

take account of the possi-the result of E(T) rather

89 district courts as severalnail differences between ther of cases that went to trialm 1967 where the trial datadefendants not commenced25 per cent greater than theises with more than one de-han one case. Since this isition in a given year betweenthe average prison sentenceied or put on probation withble.those districts in 1967 that

Pc/T as an estimate of trial queues was checked by running simple re-gressions of and (Qt — Q,) on Pc/T.51 These equations indicatethat PcIT is positively and significantly related to and — ac-counting for nearly half the variation in these variables. Although PcI?is also positively related to it is substantially more important in ex-plaining variations in and — Q,,). Therefore, Pc/T is not merely ameasure of general delay in the disposition of criminal cases, but, on thecontrary, is a measure of differential delay between trials and guilty pleas.This result allows us to estimate regressions for all 89 district courts in1967, and to check the stability of the model over time by fitting equa-tions to an earlier year, 1960, in which direct data on queues were absent.

If equation (20) estimates a demand curve for trials, the theoreticalanalysis predicts that the regression coefficient on (and PcIT) will benegative, and the regression coefficient on will be positive. However,single-equation estimates may identify a supply curve instead, if thedemand for trials varied more than the supply across districts. In the lattercase, higher observed values for would have resulted from shifts tothe right in demand curves, giving rise to a positive coefficient on Qt.Similar behavior would produce a negative coefficient on Q9 if a reductionin guilty pleas lowered 1 have attempted to deal with this identifica-tion problem in two ways: (1) Equation (20) includes S and D variablesthat are expected to lead to shifts in the demand for trials. By holding Sand D constant, the likelihood of identifying a demand curve is increased.A region variable, Re, also enters equation (20), but it is not obvious thatRe operates more on the demand than supply side of trials. (2) Regressionshave been estimated with a 1968 trial variable, T2, against 1967 values ofQ, and If defendants and prosecutors form their expectations aboutcurrent queues on the basis of last year's queue, then in 1967 couldstill be inversely related to T2 even though demand shifts in 1967 hadcaused a positive correlation between T1 and Qt.

51. The regression equations for the 44 districts in 1967 were

Qt = 1.272 + .420(PcIT)(14.961) (5.689)

Q9= .489 + .167(Pc/?)(4.087) (1.603)

(Q, — Q,,) = .516 + .629(Pc/T)(4.155) (5.844)

R2 = .44

R2 = .06

R2 = 45

Pc/t. Q,, and (Q, — are in natural logs, and all observations are weighted by \/nwhere ii is the number of defendants disposed of in each district in 1967.

196 AN ECONOMiC ANALYSIS OF THE COURTS

Regression estimates of equation (20) are presented in Table 4 for theyears 1960, 1967, and 1968. In districts where Q1 and are available,the regression results strongly support the hypothesis that increases inQt, holding constant, have significant negative effects on T1 and T2,and increases in with constant, have significant positive effects onT1 and T2. When Pc/T is substituted for Q1, in equations 4.2 and 4.4,Pc/T has the predicted negative sign and is statistically significant, whileQ,, has the same effects on T1 and T2 as before.52 Further, when thesample is expanded to include all 89 districts in equation 4.5, the signs andsignificance of and Pc/T are similar to the results for the 44 districts.This suggests that any biases in estimating the effects of queues on trialdemand due to excluding 45 districts in equations 4. 1—4.4 are probably ofsmall magnitude. Estimation of regressions for 1960 indicates that for alldistricts (equation 4.6) the queue, as measured by Pc/T, had about thesame effects as in 1967 and 1968. However, for districts in 1960 thatmatch the districts in which Q, were available in 1967 (equation 4.7), theregression coefficient of Pc/D was still negative but with a smaller abso-lute value. The latter partially results from the absence in 1960 of a mea-sure of Since and PelT are positively correlated, part of thepositive effect of on trials would be picked up by Pc/T which, in turn,would diminish the negative effect of Pc/T on trials. I have tested this for1967 by reestimating equation 4.2 without which reduces the re-gression coefficient of Pc/i from —.407 to —.331.

Although the regressions in Table 4 are consistent with the hypoth-esis on Qt and these results contain an interesting puzzle. In bothequations 4.1 and 4.3, trials are substantially more responsive tochanges in than Q,. One possible explanation is that errors in measure-ment are more important in than Qt is based on a sample of de-fendants that in each district averages less than 25 per cent of the samplesize of and in addition, Qt often had to be estimated because eitherdata on the jury trial queue or the court trial queue were absent (see noteb in Table 4).53

52. The significance of Q,, improves with this substitution, and the R2's rise. Theformer is due to the substantially higher correlation between Q,, and Q than between Q,.and PcI? (.54 compared to .24), while the latter is related to some spurious negative cor-relation since trials are present in the denominator of Pc/T and the numerator of T, and T2.This spurious correlation probably explains why the absolute value of the regression co-efficient of PcI? is larger than Q,.

53. Errors in measurement of Q, would also bias downward the regression coefficientof Q,, since the regression coefficient of Q, and the partial correlation between Qt andare of opposite signs. See G. C. Chow, Demand for Automobiles in the United States, AStudy in Consumer Durables app. 1(13 Contributions to Economic Analysis 1957).

The effects on tn.may be summarized asas predicted by the ththe 1967 equations. Tprobably due to the fatwhereas S refers to de:S in 1960 reflects thethe average prison senwho were fined, placmeasures the fractionsubsidies reduce the csubsidized legal fees aturn increases the denhypothesis. The coeffinificant in 4 out of 5analysis of state courthad higher trial propedifferentials between aants not making bail.wealthy persons wererelation between bailbetween wealth and tIcourts does not suppoiimportant determinantmore likely to go to tn;tive sign, since D shotdefendants in a districfindings for state couriand settlements, and 1important factor in tnhad no systematic effistrong positive effect cthe region effect in thetrial queues in the Soucourts.

54. If one still believedobserved positive coefficiento go to trial. This contraddefendants were more likelyof the ability to make bail insign. However, the Bail Reeliminated the correlation b

OURTS

ited in Table 4 for theand are available,esis that increases ineffects on T1 and T2,

positive effects onuations 4.2 and 4.4,ally significant, while52 Further, when thetion 4.5, the signs andts for the 44 districts.cts of queues on trial.1—4.4 are probably of0 indicates that for allPcJT, had about the

districts in 1960 that67 4.7), thewith a smaller abso-

in 1960 of a mea-iDrrelated. part of the

PtiT which, in turn,I have tested this for

phich reduces the re-

tent with the hypoth-sting puzzle. In bothmore responsive to

hat errors in measure-ed on a sample of de-er cent of the sample

because eitherwere absent (see note

n, and the R2s rise. The),, and Q, than between Q9me spurious negative cor-he numerator of T1 and T2.value of the regression CO-

d the regression coefficient-elation between Q and Q,,les in the United States, Aomic Analysis 1957).


The effects on trial demand of the remaining variables in Table 4may be summarized as follows: (1) S has a positive sign in all regressionsas predicted by the theoretical analysis, and is statistically significant inthe 1967 equations. The lack of significance in equations 4.3 and 4.4 isprobably due to the fact that T2 denotes defendants going to trial in 1968,whereas S refers to defendants sentenced in 1967. The nonsignificance ofS in 1960 reflects the less comprehensive measure of S in that year. S isthe average prison sentence in 1960, while in 1967, S includes defendantswho were fined, placed on probation, and sentenced to prison. (2) Dmeasures the fraction of defendants with subsidized legal counsel. Thesesubsidies reduce the cost of a trial relative to a settlement, providing un-subsidized legal fees are greater for the former than the latter, and this inturn increases the demand for trials. The results of Table 4 support thishypothesis. The coefficient on D is positive in all regressions and sig-nificant in 4 out of 5 equations. This finding is relevant to the previousanalysis of state courts where it was shown that defendants making bailhad higher trial propensities. The latter was explained in terms of costdifferentials between a trial and settlement that were greater for defend-ants not making bail. However, an alternative explanation was thatwealthy persons were more likely to go to trial, and hence the observedrelation between bail and trials resulted from the positive correlationbetween wealth and the ability to make bail. The analysis of the U.S.courts does not support this view. If differences in wealth per se were animportant determinant of trial demand and wealthier defendants weremore likely to go to trial, then the coefficient on D would have had a nega-tive sign, since D should be inversely related to the fraction of wealthydefendants in a district. Thus, the results in Table 4, together with thefindings for state courts, indicate that the cost differential between trialsand settlements, and not differences in wealth among defendants, is animportant factor in trial demand.54 (3) The South dummy variable, Re,had no systematic effect on trials in Table 3, which contrasts with thestrong positive effect of Re in the state data. This is not surprising, sincethe region effect in the state courts may have picked up the effect of lowertrial queues in the South, whereas queues were held constant in the U.S.courts.

54. If one still believed that wealth was an important variable in trial demand, then theobserved positive coefficients on D would show that wealthier defendants were less likelyto go to trial. This contradicts the results of the state data which showed that wealthierdefendants were more likely to go to trial. One final note is that if wealth were a determinantof the ability to make bail in the U.S. courts, then the coefficient on D could have a negativesign. However, the Bail Reform Act (to the extent it is effective) would have reduced oreliminated the correlation between wealth and the ability to make bail.


THE PROBABILITY OF CONVICTIONk

STATE COUNTY COURTS

The theoretical analysis predicted that if the defendant were not releasedon bail, the costs of his resource inputs would rise, leading to a reduction Uin these inputs and an increase in the probability of conviction. Therefore,a decline in the fraction of defendants making bail should result in anincrease in the fraction of defendants convicted. A major difficulty intesting this hypothesis relates to the direction of causation between the 0bail and conviction variables. At the time bail is set a prima facie case isoften made against the accused. If the preliminary evidence points to hisguilt, a higher bail bond is likely to be set, which would lower his chance —

of being released. Hence, a selection process would take place beforethe final disposition of cases whereby defendants with a higher probabilityof conviction would be less likely to make bail. I have attempted to dealwith this problem by including as independent variables both the fractionof defendants released on bail (B) and the average money bail charge (C)in regressions on the fraction of defendants convicted. Since setting a highmoney bail is a method of detaining a defendant with a high initial prob- m

ability of conviction, then including C as an independent variable has theeffect of holding constant differences across counties in these prob-abilities.55 This in turn would remove from the regression coefficient on Bany negative correlation due to higher conviction probabilities reducingthe fraction of defendants released on bail.

Weighted regression equations of the form

P = a + /31B + /32Pop + I3aRe + /34NW + f35Ur + f36Y + /37C + + U0

(21)

are presented in Table 5. B, Pop, Re, NW, Ur, Y and T are defined asbefore (see pp. 184—85) and P and C are defined as follows:

P: the fraction of felony defendants sentenced to prison in each county. Someconvicted felony defendants received only fines so that P understates the total

I-

55. The inclusion of C is only an approximation to holding constant variations in theprobabilities because C may reflect other factors as well. For example, the severity of theoffense, variations in the fraction of defendants not appearing for trial, attitudes of judges,etc.

TA

BL

E 5

WEIGHTED

RE

GR

ESS

ION

S A

ND

1-V

AL

UE

S FO

R C

RIM

INA

L C

oNvI

cTio

Ns

IN 1

962,

70

CO

UN

TY

CO

UR

TS

IN U

.S.

\0

Equ

atio

nN

umbe

r

Dep

end-

ent

Van

-ab

le

Reg

ress

ion

Coe

flici

ents

and

t-V

alue

s

aB

Pop

Re

NW

Ur

VC

IR

2

5.1

P.6

83(4

.771

)—

.438

(3.8

21)

.010

(.74

8).0

63(1

.141

)—

.127

(.80

9).0

76(.

581)

—.0

06

(.23

5).2

3

5.2

P.655

(4.545)

—.3

69(2

.917

).0

07(.

544)

.062

(1.1

29)

—.142

(.909)

.105

(.80

0)—

.019

(.66

3).0

15(1

.280

).2

5

5.3

P.676

(4.808)

—.247

(1.822)

.020

(1.4

47)

.051

(.94

7)—

.090

(.58

5).0

56(.

431)

-—.0

17

(.63

2).011

(.989)

--.2

89(2

.130

).3

0

5.4

Ds-f A

.076

(.641)

.227

(1.978)

—.0

19

(1.5

66)

.033

(.7

19)

.010

(.074)

.103

(.94

0)—.031

(1.330)

.015

(1.5

20)

—.2

99(2

.600

).3

0

5.5

5.6

Ds

A

.115

(1.0

44)

—.039

(1.019)

.150

(1.408)

.077

(2.089)

—.012

.063

(1.114)

(1.4

82)

—.0

06—.030

(1.6

53)

(2.0

39)

—.042

(.348)

.052

(1.2

36)

.101

(.994)

.002

(.05

6)

—.031

(1.440)

.0002

(.020)

.013

(1.442)

.002

(.565)

.011

(.101)

.288

(7.789)

.19

.67

57

pa.824

(7.409)

—.430

(4.307)

.016

(1.283)

—.073

(1.729)

.091

(.631)

.014

(.147)

—.028

(1.292)

.17

SO

UR

CE

S. —

See

Tab

le 2

sup

ra, f

or a

ll va

riabl

es e

xcep

t C.

C is

from

Lee

Silv

erst

ein,

Bai

l in

the

Sta

te C

ourt

s—A

Fie

ld S

tudy

and

Rep

ort,

50 M

inn.

L. R

ev. 6

21, t

able

s 2,

3 &

4 (

(966

).a

Equ

atio

n5.

7is

for

all 1

32counties

whe

reda

taon

Bar

eav

aila

ble

whe

reas

equ

atio

ns 5

.1 th

roug

h 5.

6ar

efo

r 70

cou

ntie

s w

here

dat

a on

C a

reav

aila

ble.

Q.(

D a

o' (D .-

. o0C

D

ii' — ..C

D

CD CD

C) + + +

(J.

CD

?.cr

QC

D

CD

—. C

D —

'1 '0

'0

(I,

CD

s'_

'C

DC

D—

CD

() 0 (I,


number of defendants receiving penalties. However, data available in a fewcounties indicate that the fraction of defendants receiving only fines wasnegligible.C: average dollar amount of bail set for defendants in each county.

The negative and statistically significant effect of B in equation 5.1 reflectsin part the negative correlation described above that runs from P to B.C has a positive effect on P in equation 5.2, suggesting that defendantswith greater conviction probabilities had C set at higher amounts.56 Asexpected both the absolute value of the regression coefficient on B andits significance are reduced when C is entered. We have previously shownthat defendants released on bail have greater propensities to go to trial.One would like to determine to what extent the observed effect of B on Pin 5.2 is due to differences in the method of disposition of cases (that is,trials versus settlements) between defendants released and not releasedon bail. In equation 5.3 a trial variable (T) has been added. T further re-duces the regression coefficient of B and its significance because de-fendants going to trial are less likely to be sentenced to prison (that is, theregression coefficient on T is negative and significant) and more likely tomake bail. In sum, the results of equations 5.1—5.3 support the hypothe-sis that the probability of conviction is increased for a defendant when heis not released on bail. At the mean values of P and B (both are about .5)the regression coefficient on B in 5.3 implies that the frequency of prisonconvictions is .38 for defendants released on bail and .62 for defendantsnot released, holding C and T constant. Observe that the coefficient of Bis reduced by about 40 per cent when C and T are held constant— 15per cent due to C and 25 per cent due to T.

Regressions are also presented in Table 5 on the fraction of defend-ants dismissed (Ds) and the fraction acquitted (A). These results confirmthe previous findings that defendants released on bail are less likely to beconvicted. The regression coefficients on B are positive in all three equa-tions where C and T are held constant, and statistically significant in two.Note that 15 per cent of defendants in the sample were acquitted or dis-missed, 50 per cent were sentenced to prison, while the remaining 35per cent were generally given suspended sentences or placed on proba-tion. The latter type of sentences, where the defendant's costs are small

56. Data on Care available in only 70 of the 132 counties used in analysis of trials incounty courts. The exclusion of 62 counties does not create any obvious biases since aregression computed for all 132 counties without C (equation 5.7) yields similar coefficientsto equation 5.1.

in comparison to prisc.convictions. For this rtthan 1 — (Ds + A). Thiin the Ds and A regretenced to prison as C.come from a reductiotthan from fewer dismis

Other findings inpopulation variable getcating that longer trial qof convictions. One shof the uncertain relatiorof strong statistical signgraphic• variables, NW,regression. (3) An addiregression coefficient ations is found, this coula lower cost of resourcship between wealth anthe U.S. court data.

Data on judicial e:counties with populatio]is that these expenditu:prosecutor's budget in acal analysis that thegreater in counties witihypothesis is consistenitures, denoted by J, hasions.57 The primary eliof cases dismissed, wiMoreover, the increaserises can be accounted fvalues of J, Ds and P,and increases P from at,as judicial expenditures—hence an increase in

57. J is not divided by thnot available. However, popinumber of defendants in a co


data available in a feweceiving only fines was

each county.

in equation 5.1 reflectsthat runs from P to B.gesting that defendantst higher amounts.56 As)fl coefficient on B andhave previously shownpensities to go to trial.served effect of B on P

)Sition of cases (that is,eased and not released

added. T further re-because de-

jed to prison (that is, therant) and more likely toj.3 support the hypothe-br a defendant when he

B (both are about .5)frequency of prison

and .62 for defendantshat the coefficient of Bare held constant— 15

the fraction of defend-These results confirmall are less likely to besitive in all three equa-cally significant in two.were acquitted or dis-hue the remaining 35

or placed on proba-costs are small

used in analysis of trials inany obvious biases since a.7) yields similar coefficients

in comparison to prison sentences, should probably be viewed as non-convictions. For this reason P would be a better measure of convictionsthan 1 — (Ds + A). The positive though nonsignificant coefficients on Cin the Ds and A regressions suggest that increases in defendants sen-tenced to prison as C rises, which are found in equations 5.2 and 5.3,come from a reduction in probations and suspended sentences ratherthan from fewer dismissals and acquittals.

Other findings in Table 5 may be summarized as follows. (1) Thepopulation variable generally has a positive effect on convictions, indi-cating that longer trial queues across counties tend to increase the fractionof convictions. One should be cautious with this interpretation becauseof the uncertain relation between queues and population size and the lackof strong statistical significance of the population variable. (2) The demo-graphic variables, NW, Ur and Y are not statistically significant in anyregression. (3) An additional problem relates to the interpretation of theregression coefficient of B. Although a negative effect of B on convic-tions is found, this could be due to a greater average wealth rather than toa lower cost of resources for defendants released on bail. The relation-ship between wealth and convictions will be examined in the analysis ofthe U.S. court data.

Data on judicial expenditures in 1966—67 are available for twentycounties with populations greater than 450,000. A reasonable assumptionis that these expenditures are positively correlated with the size of theprosecutor's budget in a county. We would then predict from the theoreti-cal analysis that the proportion of defendants convicted would begreater in counties with larger judicial expenditures per defendant. Thishypothesis is consistent with findings in Table 6 where judicial expendi-tures, denoted by J, have a positive effect on convictions in all regres-sions.57 The primary effect of an increase in J is to reduce the proportionof cases dismissed, while there is no significant effect on acquittals.Moreover, the increase in the fraction of defendants going to prison as Jrises can be accounted for solely by a reduction in dismissals. At the meanvalues of J, Ds and P, a 15 per cent rise in J reduces Ds from .13 to .11and increases P from about .50 to .52. Thus, the major economizing moveas judicial expenditures fall is to reduce the number of cases prosecuted—hence an increase in dismissals.

57. J is not divided by the number of defertdants in a county because this information isnot available. However, population size, which is probably positively correlated with thenumber of defendants in a county, is held constant in the regression equations.

>C 0

CI-

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U.S

.

CO

UR

TS

Tw

o

conv

ictio

n

vari

al

dist

rict

cour

ts in 1967

F: the

frac

tion

of de

F. the

frac

tion

of de

Pris

on

sent

ence

s

wer

e

of P and F w

ere

.38

Of

cons

ider

able it

the

prop

ortio

n

of defe

r

ti've

and

sign

ific

ant

ef

effe

ct

on F in all

equa

l

fend

ants

redu

ce

(men

carr

ying

pris

on

sent

en

the

frac

tion

of low

er ii

find

ings

are

cons

iste

n

theo

retjc

aJ

sect

ion

wft

whe

n

pena

lties

wer

e ir

lead to an in

crea

se

in

fall in the

prob

abili

ty

0:

of fine

s

an incr

ease

in

abili

ty

of

conv

ictio

n.

rise

s

is that

cour

t-as

sj&

priv

atel

y

hire

d

law

yers

esis

beca

use

mor

e

able

fend

ant's

reso

urce

inpi

plan

atjo

n

wou

ld

also p

the

conv

ictio

n

rate

on I

An

incr

ease

in del2

an incr

ease

in the

frac

t

dent

s

are

posi

tive

for

sion

s

in Tab

le

7. We a

58.

A poss

ible

reco

ncil

fend

ant's

Con

vict

ion

cost

s b

plan

atio

n

wou

ld

be cons

iste

rj

D on F. Ano

ther

poss

ible

ml

dist

rict

s

whe

re

wea

lth is high

likel

y

to be thos

e

carr

ying

flu

202


U.S. COURTS

Two conviction variables are used in regressions computed across U.S.district courts in 1967."S

P: the fraction of defendants sentenced to prison.Cl) F: the fraction of defendants receiving a fine only.

• Prison sentences were more numerous than fines as the weighted meansof P and F were .38 and .07 respectively in the 89 districts.

Of considerable interest in Table 7 is the behavior of the variable D,the proportion of defendants assigned counsel by the court. D has a posi-tive and significant effect on P, and a negative though nonsignificant

Leffect on F in all equations. This suggests that increases in wealth of de-

reduce (increase) the frequency of convictions for offensescarrying prison sentences (fines) since D serves as a proxy variable for

thefraction of lower income defendants in a district (see p. 192). These

findings are consistent with a "wealth" hypothesis developed in the.theoretical section which predicted for risk neutral defendants that (a)

whenpenalties were in the form of jail sentences a rise in wealth would

lead to an increase in the defendant's resource inputs and a subsequentfall in the probability of Conviction and (b) when penalties are in the formof fines an increase in wealth would lower his inputs and raise the prob-ability of conviction. A related interpretation of the increase in P as Drises is that court-assigned lawyers are less effective and less able than

a privately hired lawyers. This is not at variance with the "wealth" hypoth-esis because more able lawyers can be counted as more units of the de-fendant's resource inputs than less able ones. However, the ability ex-

. E planation would also predict that privately hired lawyers would reducethe conviction rate on fines, and the reverse is found in Table

An increase in delay between a trial and settlement is associated withan increase in the fraction of defendants sentenced to prison. The coetfi-

T cients are positive for Qt and PcI? and negative for Qp in the P regres-sions in Table 7. We also observed in the state data that the population

Cl)

58. A possible reconciliation is that more able lawyers are able to lower the de-

'fendant's conviction costs by shifting penalties from prison sentences to fines. This ex-

o planation would be consistent with both a positive effect of D on P and a negative effect ofV.' • .

D on F. Another possible interpretation of the observed effects of D on P and F is that indistricts where wealth is higher (and hence D lower) the types of crimes committed are morelikely to be those carrying fines rather than jail sentences.

--

fl —

N Sr

'—'—

00 C4

—

—o'

—o'

0o

— I —

—

N0\

I..0

UU

C',

C.,,

zz

0I-

U>

zC

—

CU

.U

,-J

>S

..0

zU

)C

'I)U

)(U

(U0

(UQ

(U3:

C

0O\

C

'-, Ir1

'-. '—

C')

>S.

-U

)U

0U

0C

,)(I

)

I-—

p.,

C.

U,

-I'S

C,,

V'S

V-.

C,,

I-..

V0

VV

E0

VI-

0.V I

V

-V

L..

•N

V0)

C,,—

—

I(/ $-

UO

).

09U

,

vari

able

(int

erpr

eted

a

Con

vict

ions

.

One

reas

l

and

pris

on

tive

with

resp

ect

to th

is,

he sele

cts

from an i

grea

test

prob

abili

ty

of

in orde

r

to max

imiz

e t'

pros

ecut

or

view

s

fine

s

we

wou

ld

expe

ct a

of defe

ndan

ts

fine

d. T

poth

esis

alth

ough

the r

are

not

sign

ific

ant.

IV.

SUM

MA

RY

AN

The

mod

el

deve

lope

d

the

pros

ecut

or

max

imj

by thei

r

sent

ence

s,

su

max

imiz

es

the

expe

cte

wor

ld.

Bot

h

part

icip

an

thei

r

inpu

t

of reso

urce

s

a tria

l

or a volu

ntar

y

p

fend

ant.

A settl

emen

t:

maj

or

impl

icat

ions

of tl

1. A settl

emen

t

is

tenc

e if conv

icte

d

by i

com

pare

d

to a settl

eme

and

(d)

the

grea

ter

the

tion

by tria

l

rela

tive

to 1

if the

defe

ndan

t

and

pn

a deci

sion

to go to tria

l

inst

ance

,

a settl

emen

t

fend

ants

.

2. The

both

to the

sent

ence if

—C

r4

Q\

o\

00 00N N N N N

204

59.

The

Adm

inis

trat

ive

impr

ison

men

t

of 1 to 6 moi

sent

ence

s

(see

Fed.

Off

ende

r

dire

ctly

sugg

ests

that

fine

s

mon

ths.

4)

(I,

4)

4)

I-.4)

0I-4)

4)

E0

The model developed in this essay utilizes two behavioral assumptions:the prosecutor maximizes the expected number of convictions weightedby their sentences, subject to a budget constraint, and the defendantmaximizes the expected utility of his endowments in various states of theworld. Both participants can influence the probability of conviction bytheir input of resources into the case, and cases are disposed of either bya trial or a voluntary pretrial settlement between the prosecutor and de-fendant. A settlement results in either a dismissal or a guilty plea. Themajor implications of the model are the following:

1. A settlement is more likely to take place (a) the smaller the sen-tence if convicted by trial, (b) the greater the resource costs of a trialcompared to a settlement, (c) the greater the defendant's aversion to risk,and (d) the greater the defendant's estimate of the probability of convic-tion by trial relative to the prosecutor's estimate. We further showed thatif the defendant and prosecutor agree on the expected outcome of a trial,a decision to go to trial is analogous to accepting an unfair gamble. In thisinstance, a settlement would result for risk neutral and risk averse de-fendants.

2. The defendant's investment of resources into his case is relatedboth to the sentence if convicted by trial and to wealth. Generally, the

59. The Administrative Office of the U.S. Courts assigns the value I to fines and 3 toimprisonment of 1 to 6 months in calculating a weighted average of the severity of allsentences (see Fed. Offenders, supra note 40, at 35, table 10 and note 48, supra). This in-directly suggests that fines are of small magnitude compared to jail sentences of a fewmonths.

ci

0

—

- —


variable (interpreted as a proxy for trial delay) had a positive effect onconvictions. One reason for the positive association between trial delayand prison convictions may be that the prosecutor becomes more selec-tive with respect to the cases he prosecutes as trial delay increases. Thatis, he selects from an inventory of cases the ones he believes to have thegreatest probability of conviction and the highest sentences if convictedin order to maximize his weighted conviction function. Moreover, if theprosecutor views fines as light penalties in comparison to jail sentences,59we would expect a negative relation between trial delay and the frequencyof defendants fined. The equations on• F give some support to this hy-pothesis although the regression coefficients on the Qi and Pc/T variablesare not significant.

IV. SUMMARY AND CONCLUSIONS

.34

—.

4)-,

6)4)0.-:

— ECl i..,-0

Cl

Cl

L—

L'l'

resource investment is greater for crimes carrying larger sentences. Underthe special assumption of risk neutrality (or presumably where the devia-tion from risk neutrality is small), increases in the defendant's wealth leadto greater resource investments when penalties are jail sentences and tosmaller investments when penalties are money fines.

3. Court delays increase the opportunity costs of a trial compared toa settlement for defendants not released on bail. This leads to a smallerlikelihood of going to trial for these defendants than for defendants re-leased on bail. The greater the court delay the greater the difference intrial demand between the two groups. Pretrial detention also raises themarginal costs of the defendant's resources and hence lowers his input.Therefore, defendants not released on bail are likely to have higher con-viction probabilities in a trial and receive longer sentences if they settlethan defendants released on bail. If making bail is a positive function ofwealth, then the effects of pretrial jailing fall primarily on low-income de-fendants. We argued that paying a defendant not released on bail for timespent in jail prior to disposition of his case, or alternatively, crediting himfor this time towards his eventual sentence and paying him only if he isnot convicted would eliminate much of the "discriminatory" aspects ofthe current bail system.

4. In the absence of money pricing for the courts a trial queue arisesto ration the limited supply. An equilibrium queue is reached because trialcosts increase with the length of the queue. Queues could be reduced bycharging a money price for trials, which reduces demand, leading to moresettlements. Various methods of allocating the court fee—loser pays,winner pays, defendant and prosecutor share the cost—are consistentwith a downward sloping demand curve for trials. Pricing trials will notonLy reduce delay but can also distribute trials more equally among de-fendants independent of their ability to make bail.

Available data on criminal defendants in state county courts and inU.S. district courts enabled us to test a number of the hypotheses de-veloped in the theoretical analysis. Multiple regressions were estimatedfor various cross sections in selected years from 1957 to 1968. The prin-cipal findings of the empirical analysis may be summarized as follows.

1. The propensity to go to trial was smaller for defendants not re-leased on bail than defendants released, holding constant the averagesentence and several demographic variables. This was observed for statecounty courts in the United States as a whole, and the non-South. More-over, results from the U.S. district courts indirectly indicate that in-creases in wealth do not increase trial demand. Thus, the observed rela-tion between bail and trials in state courts is probably due to cost dif-


ferences as predicted 1that are positively corr

2. The absolute direleased and not relea:One explanation for thiwith larger populations.available for the state c

3.

related to settlement dand 1968. Thus, as thecreased, the demand fo

4. Subsidizing deficreased the demand foias the cost differential ltrials increases.

5. District courtsproportionately more t,suits for the sentenceThe latter may be duecounties.

6. The probabilitydefendants sentenced ton bail than for defendobserved in regression$the size of money bailsettlement). Money baiduce spurious correlaticdefendants who were nibail set at higher amougressions using the prothe dependent variableon bail were more likei

7. Convictions leawhere estimates of thesuiting in monetary fincOne interpretation of 1fendant's investment cpenalties were jail sent

8. Conviction ratewas greater, and in C

larger. The former ma


larger sentences. Undermably where the devia-defendant's wealth leadre jail sentences and tones.ts of a trial compared toThis leads to a smallerthan for defendants re-

the difference inetention also raises thehence lowers his input.cely to have higher con-sentences if they settle

is a positive function oftardy on low-income de-released on bail for time

1ernatively, crediting himpaying him only if he is

icriminatory" aspects of

a trial queue arisesis reached because trial

could be reduced byIdemand, leading to more

court fee—loser pays,he cost—are consistentls. Pricing trials will notiiore equally among de-

ite county courts and inof the hypotheses de-

ressions were estimated1957 to 1968. The prin-summarized as follows.r for defendants not re-g constant the average

s was observed for stateid the non-South. More-irectly indicate that in-rhus, the observed rela-robably due to cost dif-

ferences as predicted by the model rather than to differences in wealththat are positively correlated with the ability to make bail.

2. The absolute difference in trial propensities between defendantsreleased and not released on bail increased as county population rose.One explanation for this finding is that court delay is greater in countieswith larger populations. Note that direct measures of court delay were notavailable for the state courts.

3. Trial demand was negatively related to trial delay and positivelyrelated to settlement delay across U.S. district courts for 1960, 1967,and 1968. Thus, as the queue differentialbetween a trial and settlement in-creased, the demand for trials fell.

4. Subsidizing defendant's legal fees in the U.S. district courts in-creased the demand for trials. This is consistent with the hypothesis thatas the cost differential between a trial and settlement falls, the demand fortrials increases.

5. District courts in which the average sentence was greater hadproportionately more trials as predicted by the model. However, the re-sults for the sentence variable in the county courts were inconclusive.The latter may be due to the crudity of the sentence variable used incounties.

6. The probability of conviction as measured by the proportion ofdefendants sentenced to prison was greater for defendants not releasedon bail than for defendants released on bail in county courts. This wasobserved in regressions which held constant, among other factors, boththe size of money bail and the method of disposition (that is, trial orsettlement). Money bail was included as an independent variable to re-duce spurious correlation between the conviction and bail variables sincedefendants who were more likely to be convicted were also likely to havebail set at higher amounts, reducing their chance of release on bail. Re-gressions using the proportion of defendants acquitted and dismissed asthe dependent variable supported the finding that defendants not releasedon bail were more likely to be convicted.

7. Convictions leading to prison sentences were lower in districtswhere estimates of the average wealth were higher, while Convictions re-suiting in monetary fines were greater where average wealth was higher.One interpretation of this result is that the effect of wealth on the de-fendant's investment of resources into his case depended on whetherpenalties were jail sentences or fines.

8. Conviction rates were higher in district courts where trial delaywas greater, and in county courts where judicial expenditures werelarger. The former may result from a greater selectivity on the part of


the prosecutor with respect to cases he prosecutes as the backlog in-creases. The latter was consistent with the hypothesis that the size of theprosecutor's budget determined the proportion of defendants convicted.

APPENDIX A

CIVIL CASES

We can extend our model to make it applicable to civil cases. The plaintiffreplaces the prosecutor. Damages replace sentences. Both the plaintiff and de-fendant maximize their expected utility. It is assumed that civil trials decideboth the question of the defendant's liability and the amount of damages. Only thedefendant's guilt was at issue in criminal cases; the sentence if convicted wasfixed and known prior to trial. A similar assumption for damages is not justifiedbecause statutory penalties generally do not exist for various types of civil suits.This modification requires that the plaintiff and defendant form expectations notonly on the probability of the defendant being found liable, but also on the sizeof damages. With these changes, the analysis of civil cases remains quite similarto the model for criminal cases. To avoid excessive duplication I present only abrief outline of the civil model and its more important results.

In civil suits the plaintiff and defendant each select a level of resource inputsthat maximizes his expected utility in the event of a trial. The plaintiff's inputsraise both the estimates of the probability that the defendant will be found liableand the amount of damages awarded in a trial, while the defendant's inputs lowerthese estimates. The plaintiff will determine a settlement payment (= X) thatyields him the same utility as his expected utility from a trial. X would be the mini-mum sum accepted by the plaintiff to settle. If the payment of X by the defendantyields him a higher utility than his expected utility from a trial, a settlement willtake place. This follows because one can find a payment somewhat greater than Xthat gives both parties a higher utility from a settlement than their expected utili-ties from a trial. It can further be shown that a settlement is likely when the follow-ing factors are present: (1) both parties have similar expectations on the proba-bility that the defendant will be found liable in a trial; (2) both parties have similarestimates of the damages, given that the defendant is found liable in a trial; (3)neither party has strong preferences for risk; (4) the costs of a trial includinglawyer's fees, time costs of the plaintiff and defendant, court fees, etc., exceedthe costs of a settlement. Alternatively, the more dissimilar the plaintiff's anddefendant's estimates of liability and damages (providing the plaintiff's estimatesare higher), the greater their preference for risk, and the lower court costs relativeto settlement costs, the more likely a trial.6°

60. This result is similar to one derived by R. H. Coase, The Problem of Social Cost,3 J. Law & Econ. 1 (1960). Coase shows that with well-defined property rights, and in theabsence of transaction costs, a private agreement will be reached between individuals that

The analysis of charicosts, is similar for civilwill raise the maximumlower the minimum settltween what the defendatviding the former was mihood of a settlement. Mtrial. As M falls to zero,.to develop. The queuelengthens, the discounteclower both the amount thoffer in a settlement. Hofrom trial delay. For exaiare directly involved in thket may be adversely affage, the gains and costs cdominate, then the defendas delay increases. The rqueue lengthened, since tcreases while the plaintiff

There are several adThe analysis of queueirigthe defendant is releasedmum sentence offer as delby two offsetting forces. Iinto the future, reducing i:ings may be adversely affeto the bail system could 1ample, defendants in civilor forgo the returns fromcourt during the period bthis procedure would be tqueue as the costs of delresponsiveness of criminative to those released. (3)sum awarded the plaintiff:queues. Interest payment:the minimum sum

internalizes externalities. If'the availability of informatksettlement, and we generalizetical expectations over propeon private agreements woupreference.


tes as the backlog in-esis that the size of thedefendants convicted.

civil cases. The plaintiffloth the plaintiff and de-d that civil trials decide)unt of damages. Only theentence if convicted was

damages is not justifiedarious types of civil suits.ant form expectations notiable, but also on the sizeases remains quite similariplication I present only aresults.a level of resource inputsrial. The plaintiff's inputsndant will be found liabledefendant's inputs ]ower

nerit payment (= X) thattrial. X would be the mini-ent of X by the defendanti a trial, a settlement willsomewhat greater than Xthan their expected utili-

'is likely when the follow-tpectations on the proba-both parties have similar

found liable in a trial; (3)costs of a trial including

court fees, etc., exceedsimilar the plaintiff's andg the plaintiff's estimateslower court costs relative

The Problem of Social Cost,ed property rights, and in thehed between individuals that

The analysis of charging a money price for the courts, as opposed to queuingcosts, is similar for civil and criminal cases. For example, a money price (M)will raise the maximum settlement offered by the defendant in a civil suit andlower the minimum settlement accepted by the plaintiff. M narrows the gap be-tween what the defendant offers and what the plaintiff is willing to accept (pro-viding the former was initially less than the latter sum), and increases the likeli-hood of a settlement. Moreover, the greater M the fewer civil cases that go totrial. As M falls to zero, the demand for trials will increase and a queue is likelyto develop. The queue rations demand in the following way. As the queuelengthens, the discounted value of damages awarded in a trial falls. This wouldlower both the amount the plaintiff will accept and the amount the defendant willoffer in a settlement. However, there are probably some costs to the defendantfrom trial delay.. For example, his ability to dispose of assets (particularly if theyare directly involved in the suit) and his ability to obtain funds in the capital mar-ket may be adversely affected by his being involved in litigation. If, on the aver-age, the gains and costs of delay to the defendant offset each other, or the costsdominate, then the defendant's settlement offer would remain constant or increaseas delay increases. The net effect would be a reduction in desired trials as thequeue lengthened, since the defendant's settlement offer remains constant or in-creases while the plaintiff reduces the amount he is willing to accept.

There are several additional points on court delay that should be noted. (1)The analysis of queueing in civil cases is almost identical to criminal cases wherethe defendant is released on bail. In the latter, the prosecutor reduces his mini-mum sentence offer as delay increases, while the defendant's response is affectedby two offsetting forces. Delay pushes his potential sentence from a trial furtherinto the future, reducing its present value, while simultaneously his current earn-ings may be adversely affected by being under indictment. (2) A system analogousto the bail system could be instituted for civil cases. This would require, for ex-ample, defendants in civil suits to either pay a sum to the court per unit of time,or forgo the returns from all or part of their assets by depositing them with thecourt during the period between filing and disposition of the case. One effect ofthis procedure would be to make trial demand more responsive to a change in thequeue as the costs of delay rise to the defendant. This is similar to the greaterresponsiveness of criminal trial demand for defendants not released on bail rela-tive to those released. (3) A requirement that the defendant pay interest on anysum awarded the plaintiff in a trial would have little effect on trial demand or courtqueues. Interest payments would raise both the defendant's settlement offer andthe minimum sum acceptable to the plaintiff in a settlement. Hence, as a first ap-

internalizes externalities. If we interpret the absence of transaction costs in civil cases asthe availability of information on damages at zero cost and zero bargaining costs of asettlement, and we generalize Coase's notion of well-defined property rights to include iden-tical expectations over property rights or liability decisions in a trial, then Coase's theoremon private agreements would also include pretrial settlements in the absence of riskpreference.


proximation it would not close the gap between the defendant's offer and theplaintiff's acceptance sum and, therefore, would have no effect on the trial versussettlement decision. (4) Differences in the rate at which the plaintiff and de-fendant discount future damages awarded at a trial can give rise to differences inthe response of trial demand to a change in the queue. The higher the plaintiff'sdiscount rate relative to the defendant's, the larger the plaintiff's losses and thesmaller the defendant's gains from an increase in the queue. This, in turn, wouldreduce the sum acceptable to the plaintiff by a greater amount than it reduces thedefendant's offer, making a settlement more likely.

We can test the hypothesis that the demand for civil trials is negatively re-lated to the length of the trial queue. The statistical specification of the demandfunction is

T=cs+131Q7+/39E(T)+f33Re+p. (22)

Data were from the 86 U.S. district courts in 1957—61. The variables are innatural log form except Re and are defined as follows:

T: The ratio of the number of trials from cases that commenced in 1957 overthe number of cases commenced in 1957.61

Estimate of the expected trial queue in 1957 where is an ex-ponentially declining weighted average of 1957, 1956, and 1955 median trialqueues.62 Q,, the median trial queue in 1956, was also used as an estimate of theexpected trial queue.

61. A frequency distribution of civil cases by length of time from filing to disposition bytrial is published for each yearfrom 1957 to 1961. (After 1961 only median trial queues areavailable.) This allows us to trace over time the eventual disposition (that is, trial or settle-ment) of cases commenced in 1957 assuming all of the latter cases are disposed of withinfour years from the date of filing. Since civil trial queues average about one-and-one-halfyears in the U.S. courts, a frequency distribution of trials is an important advantage in esti-mating T, For example, if the number of trials in a given year were used as the numerator ofT, it would be difficult to choose an appropriate denominator for T because the trials werefrom cases commenced over several different time periods with an average queueing time totrial of one-and-one-half years. Moreover, it would be equally difficult to choose a value forthe expected trial queue. Frequency distributions of trials are not available for criminalcases, but the above problems are not as great since criminal queues average about sixmonths.

62. Derived from the assumption that persons form expectations of future queues onthe basis of past expectation and adjustment based on ratio of current value to previousexpected value. That is,

Q,= 17 (i)

where Q7's are expected and Q,'s are actual median queues in a district,)' is the year, andyis the adjustment coefficient. (i) can be rewritten as the following infinite series:

E(T): Expected fractcases commenced in eachplying each group by the Iin Therefore, thein the distribution of type

Re: Region dummyfor non-South district cou

Table 8 presents regrwere also computed for defficients on and Qt hiand are of similar magnitithe demand for trials is n

A difficulty in interprthe trial variable isunder the jurisdiction of Ithese cases are excluded Icases going to trial in a dimeasurement error in Tcorrelated with the indepe

in 1957 was approximateQ,. In logs this becomes

log =y Ic

y was initially set equal to Ationally raised by a factor of

63. Fraction of trials for1. U.S. Plaintiff (exclude2. U.S. Defendant (ex. h3. Federal Question (cx.4. Diversity5. Admiralty

Note that 53,343 civil casesnumber of cases excluded abcand trials for each district dgovernment is involved in athan when the U.S. is the pladelay (that offset the gains 6such as his inability to disposbe present when the defendanexpect more trials when the 1

WILLIAM M. LANDES 211COURTS

efendant's offer and theeffect on the trial versus

ich the plaintiff and de-give rise to differences inThe higher the plaintiff'splaintiff's losses and theeue. This, in turn, wouldnount than it reduces the

vii trials is negatively re-of the demand

- Jh. (22)

61. The variables are in

commenced in 1957 over

)57 where Q7 is an ex-6, and 1955 median trialused as an estimate of the

e from filing to disposition byonly median trial queues areosition (that is, trial or settle-cases are disposed of within

erage about one-and-one-halft important advantage in esti-ere used as the numerator offor T because the trials wereh an average queueing time todifficult to choose a value forre not available for criminalal queues average about six

ectations of future queues onof current value to previous

(i)

a district, y is the year, andving infinite series:

E(T): Expected fraction of trials in a district are estimated by dividing civilcases commenced in each district in 1957 into five broad groups, and then multi-plying each group by the fraction of trials in that group for all U.S. district courtsin 1957.63 Therefore, the inclusion of E(T) allows us to hold constant differencesin the distribution of types of cases across districts.

Re: Region dummy variable that equals 1 for district courts in South and 0for non-South district courts.

Table 8 presents regression estimates of equation (22). Separate regressionswere also computed for districts in the non-South and South. All regression co-efficients on Q7 and have the predicted negative signs, are highly significant,and are of similar magnitude. In sum, these results support the hypothesis thatthe demand for trials is negatively related to the size of the trial queue.

A difficulty in interpreting the findings of Table 8 arises from the way in whichthe trial variable is measured. An unknown number of civil cases that would comeunder the jurisdiction of the U.S. courts are settled before they are filed. Sincethese cases are excluded from the denominator of T, the true proportion of civilcases going to trial in a district each year is less than the observed fraction. Thismeasurement error in T will not bias the regression coefficients if the error is Un-correlated with the independent variables. However, we can show that the error

QI Q),... (ii)

in 1957 was approximated in the empirical analysis by using three previous values forQ,. In logs this becomes

log y log Q,37 + y(l — j)') log -I- y(l — log (iii)

-y was initially set equal to .4, but to have the weights sum to I all weights were propor-tionally raised by a factor of 1.2755.

63. Fraction of trials for various categories are as follows:1. U.S. Plaintiff (excludes land condemnation and forfeiture cases) .0312. U.S. Defendant (ex. habeas corpus) .1883. Federal Question (cx. habeas corpus) .1234. Diversity .1515. Admiralty .081

Note that 53,343 civil cases were commenced in 1957 in 86 U.S. District Courts and thenumber of cases excluded above were 4,613. These were excluded because data on queuesand trials for each district do not include these types of cases. Note that when the U.S.government is involved in a suit as a defendant there is much greater likelihood of a trialthan when the U.S. is the plaintiff. One explanation is that the costs to the defendant fromdelay (that offset the gains from the reduction in the present value of a trial settlement),such as his inability to dispose of assets or to obtain funds in the capital markets, may notbe present when the defendant is the U.S. government. Hence, for a given queue one wouldexpect more trials when the U.S. government is the defendant than when it is the plaintiff.


TABLE 8WEIGHTED REGRESSION EQUATIONS a AND I-VALUES FOR CIVIL TRIALS IN

U.S. DISTRICT COURTS, 1957—61

EquationNumber Area

Dis-tricts a

Regres sion Coefficients and i-Values

Q7 Q1 E(T) Re

8.1 U.S. 86 —.307

(.413)—.410(5.444)

.354(1.051)

—.337(4.014)

.28

8.2 U.S. —.422(.563)

—.369

(5.188).352

(1.032)—.314

(3.757).27

8.3 Non-South

52 .164(.238)

—.429

(6.033).546

(1.770).45

8.4 Non-South

.196(.285)

—.400(6.079)

.596(1.940)

.46

8.5 South 34 —2.005(1.087)

—.376(2.080)

—.255(.288)

.12

8.6 South —2.399(1.283)

—.323

(1.818)—.386(.420)

.10

SouRcEs.— 1956—1962C3 and CS.

Ann. Rep., Admin. Off. of the United States Courts, tables Cl,

a Each observation weighted by where ,i equals the number of cases commenced in1957.

in T is likely to be positively correlated with the trial queue, and this in turn wiflbias downward the absolute value of the queue elasticities.64

In Table 8 E(T) has a positive and significant effect on T in the U.S. and non-South, but a negative and nonsignificant effect in the South. Overall, E(T) wasless important than trial queues in explaining variations in T across districts. Rewhich is significant at the .01 level indicates that the fraction of civil trials wasabout 30 per cent lower in the South holding the queue and E(T) constant. Thisresult is puzzling in view of the finding that Re had no significant effect on the

64. Leti = the number of trials in a district, F the number of cases filed, and C = the

number of cases filed plus those settled before filing. Further, assume that K - F = C, whereK > l. Suppose the relationship between i/C and Q7 is

while the estimating equation is

i/C = Q7sea,

i/F =

where and are error terms. (ii) can be rewritten as

log K ± log (i/C) f3 log Q7 +

(i)

(ii)

(iii)

Let E = log K, Y = log (i/C) and X = log and let e, y, and x denote deviations from

demand for criminal triaaverage size of damagesthe non-South. Thus, theup by the Re variable.

APPENDIX B

MATHEMATICAL NOTI

In this section we analy;has nonneutral tastes forerence can easily be wor:are assumed to reduce bassumption in Section I I

The first- and seconwritten, respectively, as

—P'[U(Wn) — U(Wc)] —.

and

—R"[(J(Wn)-- L/(Wc)J -I-

+ (1 —

Relative risk aversion at

A(Wc) is similarly definedto W and R, noting that (2dR/dW 0 as

U'(Wn) [_P'k — r'(l — P

+ U'(Wc) —

their respective means. The

which will be an unbiased esthat as Q7 rises, K will alsoincrease with the size of Q7.tive, this would result in 1131

:ientS and t-Values

E(T) Re R2

.354(1.051)

.352(1.032)

.546(1.7 70)

.5961 1.940)

—.255(.288)

—.386(.420)

States Courts, tables Cl,

umber of cases corrimenced in

queue, and this in turn willities.64ton Tin the U.S. and non-South. Overall, E(T) wasis in T across districts. Refraction of civil trials wasie and E(T) constant. Thisno significant effect on the

ber of cases filed, and C — the

assume that K . F = C, where

(i)

(ii)

(iii)

and x denote deviations from

their respective means. The least-squares estimator of / is

(iv)

which will be an unbiased estimator of /3 only if Coy (x, e) = 0. However, it is more likelythat as Q7 rises, K will also rise, since the incentives to settle (both before and after filing)increase with the size of This implies that Coy (x, e) > 0. Given that /3 and /3 are nega-tive, this would result in 1131 underestimating 1/31.

COURTS

S FOR CIVIL TRIALS IN61

—.337

(4.0 14)—.3 14

(3.7 57)

.28

.27

.45

.46

.12

.10


demand for criminal trials in the U.S. courts. A possible explanation is that theaverage size of damages in civil suits in the South is considerably lower than inthe non-South. Thus, the negative effect on T of lower damages would be pickedup by the Re variable.

APPENDIX B

MATHEMATICAL NOTES: WEALTH EFFECTS

In this section we analyze the effect of changes in W on R when the defendanthas nonneutral tastes for risk. Risk aversion is assumed. The case of risk pref-erence can easily be worked out from the example of risk aversion. Inputs of Rare assumed to reduce both P and S (that is, S' aS/OR < 0) in contrast to theassumption in Section I that S was a constant and independent of R.

The first- and second-order conditions for E(U) to be a maximum may bewritten, respectively, as

—P'[(J(Wii) — U(Wc)] — sS'P(J'(Wc) — r[PU'( Wc) ± (1 — P)U'(Wn)] = 0 (23)

and

—R"[U(Wn) — U(Wc)J + 2rP'{U'(Wn) — U'(Wc)]+ r2[PU"(Wc)

+ (1 — P)U"(Wn)] — 2sS'P'U'(Wc) — sS"PU'(Wc)

+ 2rsS'PU(Wc) + (sS')2PU"(Wc) < 0. (24)

Relative risk aversion at Wn is defined as follows:

• A(U'n) ——Wn (25)

A(Wc) is similarly defined at Wc. Taking the total differential of (23) with respectto Wand R, noting that (24)is negative, and substituting A(Wn) and A(Wc)givesdR/dW 0 as

U'(Wn) [—P1k — r'(l — .P) +r(1 —

Wn

+ U'(Wc) [P'm — s'S'P +sS'PA(Wc)m

— r'P +rPA(Wc)rn]

0, (26)


The BehaAdministr

Richard A. IUniversity of

Administrative agelegal system. This articcies that can be testedempirical tests.1 The itmaximizing agency di'characteristics. Part Ipirical implications, atalternative models. Parfor an empirical examilaw — whether combinir.contaminates adjudicat

I wish to express my giHelpful comments on previDavis. Owen M. Fiss, Juliusparticipants in the IndustriaNational Bureau of Econom:National Science Foundatioi

1. 1 use the term "adnagency whether or not mdcdeveloped here, however, is IMuch of the analysis is appl

where r' = > 0, s' = as/aW, k = (1 — r'R) and in = (1—s'S — r'R). Notethat 0 < k < 1, 0 < in < I and k > ni. in and k are both positive because an in.crease in W must increase both Wn and Wc. Even with further simplifying as-sumptions the sign of (26) is indeterminate. For example, suppose A(Wn)A(Wc) = 1 and let Er= r'(W/r) and Es = s'(W/s) where 0 Er, Es 1. Thisgives dR/dW 0.

—P'(W — — ErrR)WcsS'P[W —(E8Wc + + ErIR)]

U'(Wn) — rP[W — + E8sS + ErrR)]Wn . (27)

U (Wc) Wc[—P(W — + r(1 — P)(l — Er)WJ

The sign of dR/dW cannot be determined from (27) without additional informa-tion about the defendant's utility function, the elasticities of s and r with respect toW, and the productivity of R in reducing S. If E, = Er = 1. (27) becomes

U'(Wn)(28)

U'(Wc) < Wn

In the special case of a Bernoulli utility function, where the utility of wealth equalsits logarithm, then dR/dW = 0, since U'(Wn)/U'(Wc) = WclWn.

In general, the effects of changes in wealth the defendant's input of re-sources are indeterminate once nonneutral tastes for risk are introduced. Thisconclusion is valid even when the strong assumption is made that relative riskaversion equals one for all levels of the defendant's wealth. Nevertheless, one stillpresumes that if the deviation from risk neutrality is small, the effects of wealthon R will be similar to those for risk neutrality.

The Behavior ofAdministrative Agencies

Richard A. PosnerUniversity of Chicago and Nalional Bureau of Economic Research

Administrative agencies are an increasingly prominent feature of thelegal system. This article presents a model of the behavior of such agen-cies that can be tested empirically and the results of some preliminaryempirical tests.1 The model is designed to predict how a rational utility-maximizing agency divides its attention among cases having differentcharacteristics. Part I develops the model, discusses and tests some em-pirical implications, and compares the implications of the model withalternative models. Part II uses the model developed in Part I as the basisfor an empirical examination of a long-standing issue in administrativelaw — whether combining prosecution and adjudication in the same agencycontaminates adjudication.

I wish to express my gratitude to George J. Stigler for his many helpful suggestions.Helpful comments on previous drafts were also made by Gary S. Becker, Kenneth CuipDavis, Owen M. Fiss, Julius 0. Getman, William M. Landes, Bernard D. Meltzer, and theparticipants in the industrial Organization Workshop of the University of Chicago. TheNational Bureau of Economic Research provided financial support under a grant from theNational Science Foundation for research in law and economics.

I. I use the term "administrative agency" broadly to include any law-enforcementagency whether or not independent of the executive branch of government. The modeldeveloped here, however, is limited to the prosecutorial activities of administrative agencies.Much of the analysis is applicable to conventional criminal law enforcement.

COURTS

= (1 — s'S — r'R). Noteh positive because an in-th further simplifying as-.mple, suppose A(Wn) =re 0 Er, Es 1. This

1E8sS+ErrR)]] (27)- P)(1 — Er)W1

ithout additional informa-s of s and r with respect to

1, (27) becomes

(28)

the utility of wealth equals= Wc/U'n.

defendant's input of re-risk are introduced. Thisis made that relative risk

Nevertheless, one stillthe effects of wealth

216

I. A MODEL OF THE BEHAVIOR OFADMINISTRATIVE AGENCIES

A. THE SIMPLE MODEL

than the defendant,greater impact on thcdefendant (or vice vet

a and b are the numbeand s, and are the

a restrictionand would permit the propJames Meginniss has sugges;probability of winning whenformulation greatly increaserealism would not appear tonote 21, infra).

4. Although administraquantifiable remedy, it isplicitly, in accordance withconferred, of a successful pi

THE BEHAVIOR OF ADMINISTRATIVE AGENCIES

The agency's goal is assumed to be to maximize the utility of its law-enforcement activity. The utility (or more precisely expected utility) of anindividual case is the public benefit, if prosecuted successfully, discounted(multiplied) by the probability of successful prosecution. Discounting isrequired in order to reflect the fact that a case is less worthwhile if, allother things being equal, there is a smaller chance of the agency's winningit.2 For simplicity, the agency is assumed to bring only two types of cases(the cases within each type being homogeneous) and the number of casesof each type is fixed. Both assumptions are unrealistic but only the secondhas analytical significance and it will be relaxed later.

The agency maximizes expected utility by investing resources,mostly lawyers' time, in prosecuting violators. The effectiveness of itsexpenditures in enhancing the probability of successful prosecution andhence utility of a case depends significantly on how much money the de-fendant decides to spend in defending the case. Most simply,

(1)

where p is the probability of the agency's winning, c is the agency'slitigation outlays, and c' the defendant's. If the defendant spends nothingon the litigation, the probability of the agency's winning becomes unity,even if the agency spends very little. If the agency spends nothing, theprobability of its winning falls to zero. If both parties spend the sameamount, the probability of the agency's winning is 50 per cent.

This formulation is too simple, because it assumes that outcome is afunction solely of the ratio of the parties' litigation outlays. If the law iswell settled in favor of the agency, or the agency a more efficient litigator

where e is some factot—that measures theinfluencing thefollow that theparties spent the samagency would have afendant spent twicelarger than 1,

in deciding howagency cannot simplylonger increases expection from Congress. Amodel.

Equations (4) and

2. The bringing of unmeritorious cases imposes costs on innocent parties, comforts theguilty, and weakens the deterrent effect of the law. Merit is not a dichotomous property andis approximated by the probability of a successful outcome. The model could be altered torecognize that on occasion a case may have value for an agency even if it ends in defeat.

An earlier mathematical model of law enforcement from which I have borrowed ispresented in William M. Landes, An Economic Analysis of the Courts, included in thisvolume. Compare Alan E. Friedman, Note, An Analysis of Settlement, 22 Stan. L. Rev.67 (1969).

RICHARD A. POSNER 217

the utility of its law-expected utility) of an:cessfully, discounted:ution. Discounting isless worthwhile if, all

agency's winningnly two types of cases

the number of cases

iinvesting resources,

be effectiveness of itsprosecution and

rmuch money the de-

.ost simply,

(1)

ng, c is the agency'sspends nothing

nning becomes unity,y spends nothing, thearties spend the same50 per cent.mes that outcome is a

i outlays. If the law ismore efficient litigator

nocent parties, comforts thea dichotomous property and

e model could be altered to

cy even if it ends in defeat.which I have borrowed is

the Courts, included in thisettlement, 22 Stan. L. Rev.

than the defendant, a smaller expenditure by the agency may have agreater impact on the outcome than a much larger expenditure by thedefendant (or vice versa). Equation 1 should be restated as

(2)

where e is some factor—it may be a fraction, or it may be larger than one—that measures the effectiveness of the agency's litigation outlays ininfluencing the outcome of a case in its favor.3 If e were 1.5, it wouldfollow that the agency had a 75 per cent chance of winning when bothparties spent the same amount of money on the case. If e were 2, theagency would have a 67 per cent chance of winning even though the de-fendant spent twice as much as the agency. However, since p cannot belarger than 1,

(3)

In deciding how much money to invest in each type of case, theagency cannot simply keep spending until a dollar of expenditure nolonger increases expected utility by a dollar. It is limited to its appropria-tion from Congress. A budget constraint must therefore be added to themodel.

Equations (4) and (5) summarize the model as thus far developed:

E(U) = ac1e1

, + bc9e2

(4)c1+c1 c2+c2 -

ac1 + bc2 = B. (5)

a and b are the number of cases of each type; B is the agency's budget;and S1 and s2 are the agency's gain, expressed in dollars,4 from successful

3. A better formulation would probably be p = (c/c + c' )P, This would avoid thenecessity for a restriction on e (other than e > 0) to prevent p from exceeding unity,and would permit the proportional impact of e on p to vary with changes in c and c'.James Meginniss has suggested an alternative formulation, p = ecic, where e is the agency'sprobability of winning when c = c', that also has desirable properties. Unfortunately, eitherformulation greatly increases the computational difficulties of the model, and the gain inrealism would not appear to have substantial analytical significance (but see text followingnote 21, infra).

4. Although administrative proceedings rarely involve damages or any other readilyquantifiable remedy, it is plausible to suppose that an agency ranks its cases, at least im-plicitly, in accordance with some rough estimate of the dollar equivalent, in public benefitsconferred, of a successful prosecution.

t.

218 THE BEHAVIOR OF ADMINISTRATIVE AGENCIES

prosecution. The budget constraint is expressed as an equation ratherthan an inequality in view of the notorious reluctance of governmentbodies to turn back unused funds to the Treasury.

Clearly, the agency's expenditure on a case is in part a function ofhow much the defendant spends, and the reverse must also be true — thedefendant's expenditure is a function in part of the agency's expenditure.Before we can use equations (4) and (5) to find the agency's optimal ex-penditure on each case, we must know what the defendant is likely tospend. This requires that we construct a model like equation (5) but fromthe defendant's point of view.

Assume that, before the litigation, the defendant in a case of the sec-ond type had a certain wealth position, W. Litigation will produce one oftwo states of the world. If he wins, his wealth will be diminished only byhis litigation expenses; if he loses, his wealth will be diminished by hisstakes in the case as well. By discounting each state by the probabilityof its occurrence, we can express his wealth position after litigation (W')as follows:

= (W — + (1 — (W — — ci). (6)

The first expression on the right-hand side of the equation+ c2) is the probability that the defendant will win rather than the

agency. It should be emphasized that (and therefore like e2 (andtherefore P2) is a subjective term: it is the defendant's estimate of theeffectiveness of his expenditures on the outcome of the suit. The partiesmay have inconsistent estimates. Indeed, as we shall see, without suchdifferences there would be few litigated cases.

The defendant is assumed to operate without a budget constraint.Unlike the agency, he can hire additional legal resources until theirmarginal product falls to zero.

The reader may wonder why the stakes for the defendant, aredistinguished from the stakes for the agency in the same case, s2. Thereason is that they may not be identical. A clear instance of asymmetry ispresented by any monopoly case: the social costs of monopoly exceedthe private benefits to the monopolizer.5 To take another example, an

5. The monopolist who cannot discriminate perfectly in price maximizes profits byselling a smaller quantity at a higher price than under competition. His gain—the differencebetween the monopoly and the competitive price multiplied by the number of Units sold—is also a loss to the purchasers of this output. Another loss, which the monopolist does notcapture, is the loss to those consumers whom the higher, monopoly price deters from con-tinuing to buy the monopolist's product, and who substitute other products that cost more,or are otherwise less desirable, than the monopolist's product when sold at a competitiveprice.

order forbidding the rndeceptive may be mucthe brochure printedagainst the second defiagainst the first. Furthbeyond any effect inedent. Precedent has ato win the next case (ifing in like conduct. Ticance to the defendanwith the agency.6 Fin.ings frequently cannotthe fruits of acosts to the defendant.

The first derivativ

By setting the derivati'how much money a deorder to maximize his

which implies, not unrtively small, an increaon the case, while if thit..7

We may now retumizing expenditure of 1tion (8) into equation

6. Such asymmetry isexample, the usual defendais not shared by themetry is presented in Richa94—96 (1972).

7. The rate of change a

This expression is negativewhen is relatively small,

AGENCIES RICHARD A. POSNER 219

as an equation ratherctance of government

s in part a function ofmust also be true—theagency's expenditure.

e agency's optimal ex-defendant is likely toequation (5) but from

nt in a case of the sec-will produce one of

be diminished only byI be diminished by histate by the probabilityion after litigation (W'),

(6)

of the equationviii win rather than the

p) like e2 (andidant's estimate of theof the suit. The partiesshall see, without such

it a budget constraint.I resources until their

the defendant, s2', arethe same case, s2. Thestance of asymmetry is:s of monopoly exceede another example, an

price maximizes profits byion. His gain—the difference

y the number of units sold—the monopolist does not

Lopoly price deters from con-ther products that cost more,

when sold at a competitive

order forbidding the mailing of a type of advertising brochure found to bedeceptive may be much more costly to a defendant who has already hadthe brochure printed than to a defendant who has not, yet the orderagainst the second defendant is just as valuable to the agency as the orderagainst the first. Furthermore, an order may have importance to an agencybeyond any effect in abating the defendant's illegal conduct: as a prec-edent. Precedent has a dual significance. It makes it easier for the agencyto win the next case (if a similar case), and it may deter others from engag-ing in like conduct. The dismissal of a case will lack comparable signifi-cance to the defendant unless he anticipates frequent future encounterswith the agency.6 Finally, since the benefits of administrative proceed-ings frequently cannot be quantified, the agency's implicit valuation ofthe fruits of a successful prosecution may differ substantially from thecosts to the defendant.

The first derivative of W' with respect to is

dW'— 1 (7)

+ c2)2

By setting the derivative equal to zero and solving for we can discoverhow much money a defendant in our second type of case should spend inorder to maximize his wealth. That expenditure is

= — c2, (8)

which implies, not unrealistically, that if the defendant's stakes are rela-tively small, an increase in c2 will induce him to reduce his expenditureon the case, while if they are relatively large, it will induce him to increase

We may now return to equation (4) and determine the utility-maxi-mizing expenditure of the agency on the same case. By substituting equa-tion (8) into equation (4), solving equation (5) for c3 and substituting the

6. Such asymmetry is not limited to public law enforcement. In accident litigation, forexample, the usual defendants—insurance companies—have an interest in precedent thatis not shared by the accident claimants. Some evidence on the significance of this asym-metry is presented in Richard A. Posner, A Theory of Negligence, 1 J. Leg. Studies 29,94—96 (1972).

7. The rate of change of with respect to c2 is

ad —

ac2

This expression is negative (signifying that an increase in will cause a decrease inwhen is relatively small, and positive when it is relatively large.


result into equation (4), and simplifying, we can restate equation (4) asfollows:

— \/B — bc2 ( c2e2E(U)— ,

Ve1s1 \Vc2e2s2

The first derivative of E(U) with respect to c2 is

P22''— ijs2e2s1ej22' ' •' S.as1e1s2e2 +

Fortwo types of cases auratio between c2 and c

If B, a, and b aresuit in a decrease in c3are also held constant,and c1 rise if the effectof the second type or rdefendants' expenditu:second type; or if defetin the first type.

These factors are i:ecution of type 2 casesassume that s2 is muchfactors that a rationalIt is plausible, moreominor violations and sThe explanation has tceeding against a violawell settled that the ccisely because thecessful prosecution, eprobably high. The ralthat have importancesmall. The usual defencase will have precedthe precedential signilmonetary stakes, s is

A frequent critici

oligopoly problem, and oneproblem of collusive rather IOligopoly, 72 J. Pol. Econ.Industry 39 (1968); RicharcApproach, 21 Stan. L.wealth by agreeing to limitpenditures on litigation. Agexample—but of this more I;

(9)

dE(U) — bs2e2 — be1s1V710

dc2

By setting the derivative equal to zero and solving for c2 we discover thatthe expenditure by the agency on type 2 cases that maximizes theagency's utility is

(11)

An objection to this method of determining the agency's optimum ex-penditure is that while the agency, in deciding how much to spend onprosecuting a case, takes account of the fact that the defendant's expendi-ture is a function in part of how much the agency spends, the defendanttakes the agency's expenditure as given—he does not consider how theagency might react to a change in his expenditure. The asymmetry is notentirely unrealistic. The position of the parties is asymmetrical. Theagency is the moving party in the litigation and controls to a considerableextent its timing and scope. The agency presumably has greater experi-ence with respect to the particular kind of litigation involved than a de-fendant who appears infrequently before it, although this disparity may beoffset to the extent that there are private lawyers who specialize in litiga-tion before the particular agency. Finally, the agency is a bureaucracyin which decisions and procedures presumably tend to be routinized.These factors make it somewhat plausible that the agency, in decidingwhat to spend on a case, will make a rough estimate of the defendant'slikely expenditures (viewed in part as a function of its own expenditures)and the defendant will adjust to the level of the agency's expenditures. Ifthe defendant were assumed to have the same reaction function as theagency's in the model, the optimum expenditure of both parties would beindeterminate.8

8. This indeterminacy resembles that encountered by attempts to determine an oh-gopolist's optimum price when he is assumed to act independently but to take account of hisrivals' reactions to his price changes. See George J. Stigler, The Theory of Price 2 17—19(3d ed. 1966), for a succinct discussion of the problem. An alternative approach to the


(10)bc2)

c2 we discover thatthat maximizes the

(11)

agency's optimum ex-w much to spend ondefendant's expendi-

spends, the defendantnot consider how the

The asymmetry is notis asymmetrical. Thetrols to a considerablely has greater experi-n involved than a de-i this disparity may beho specialize in litiga-ncy is a bureaucracy

end to be routinized.e agency, in decidingate of the defendant'sits own expenditures)ncy's expenditures. Iftction function as theboth parties would be

empts to determine an oh-ly but to take account of hishe Theory of Price 2 17—19

iternative approach to the

equation (4) as

(9)

For understanding how changes in the characteristics of the agency'stwo types of cases alter the allocation of resources between them, theratio between c2 and c1 is helpful:

C2—= - (12)C1

If B, a, and b are assumed to be constant any increase in c2 must re-sult in a decrease in c1, and vice versa. If the agency's stakes (s1 and s9)are also held constant, then it is clear from equation (12) that c2 will falland c1 rise if the effectiveness of the agency's expenditures falls in casesof the second type or rises in cases of the first type; if the effectiveness ofdefendants' expenditures falls in cases of the first type or rises in thesecond type; or if defendants' stakes rise in the second type of case or fallin the first type.

These factors are independent of the social benefits of successful pros-ecution of type 2 cases. Even if those benefits are great—let us henceforthassume that s2 is much larger than s1 — they may be overwhelmed by otherfactors that a rational utility-maximizing agency must take into account.It is plausible, moreover, that e will be higher in a class of relativelyminor violations and smaller in relation to s1 than in relation to s2.The explanation has to do with precedent. The public benefit from pro-ceeding against a violation may be relatively small because the law is sowell settled that the case will have little importance as precedent. Pre-cisely because the law is well settled, however, the probability of suc-cessful prosecution, even without a large expenditure of resources, isprobably high. The rational agency will be especially attracted to casesthat have importance as precedent but in which the monetary stakes aresmall. The usual defendant is uninterested in whether the outcome of hiscase will have precedential significance. Since it would be surprising ifthe precedential significance of a case increased in proportion to themonetary stakes, s is likely to be smaller relative to s1 than to s2.

A frequent criticism of administrative agencies is that they mis-

oligopoly problem, and one with some relevance in the present context, is to treat it as aproblem of collusive rather than of independent action. See George J. Stigler, A Theory ofOligopoly, 72 J. Pol. Econ. 44 (1964), reprinted in George J. Stigler, The Organization ofIndustry 39 (1968); Richard A. Posner, Oligopoly and the Antitrust Laws: A SuggestedApproach, 21 Stan. L. Rev. 1562 (1969). Like ohigopohists, litigants can increase theirwealth by agreeing to limit their rivalry, and specifically by agreeing to reduce their ex-penditures on litigation. Agreements to stipulate rather than litigate facts are a commonexample—but of this more later.


allocate their resources by bringing mostly small cases.9 But our modelsuggests that under plausible assumptions concerning the characteristicsof the agency's cases, a perfectly rational, utility-maximizing administra-tive agency will devote a "disproportionate" amount of its resources torelatively minor cases. Lets1 and be $10, e1 2, .9, and $40, e2 1.5,

1, a 20, b 5, and B $50. Solving equation (11) for c2, and (3) and (8)for c1, and we discover that the agency should spend $3.36 on eachcase of the second type and $1.66 on each case of the first type. (Thedefendant's optimum expenditure is found to be $8.44 in a case of thesecond type and $2.14 in a case of the first type.) Although the aggregatesocial benefits from cases of each type (i.e., as1, bs2) are equal—$200-..the agency devotes two-thirds of its resources to cases of the first type.And although each type 2 case involves four times the social benefits ofeach type 1 case, the agency spends only twice as much money litigatingeach case of the former type. This is optimizing behavior rather than amanifestation of stupidity or timidity. The agency's utility would be lessif it allocated additional monies from its limited budget to the larger cases.

One factor inducing the agency to devote so many resources to casesof the first type is the higher rate of success in such cases that it antici-pates. Another, and related, factor is defendants' relative pessimism aboutsuch cases (ei). A similar effect would also result if s.2' were higher than

as our earlier analysis suggests it might well be.Substituting the results of our numerical example into equation (2),

we discover that the agency expects to win 87 per cent of its type 1 casesbut only 43 per cent of its type 2 cases. The defendants' expectations areinconsistent with the agency's. To determine the objective probability ofthe agency's winning let us assume that the parties are equally good (orbad) estimators so that the true figure is the mean of their predictions.Thus,

Pi 2' (13)

from which we can determine that the agency will win 68 per cent of itstype 1 cases and 36 per cent of its type 2 cases.

Table 1 presents some additional numerical examples. The lastcolumn summarizes the example in the text.

9. See, e.g., ABA Comm'n to Study the Federal Trade Commission, Report, p. 1 (Sept.15, 1969); Commission on Organization of the Executive Branch of the Government(Hoover Commission), Appendix N, Task Force Report on Regulatory Commissions 119(Jan. 1949); Philip Elman, Administrative Reform of the Federal Trade Commission, 59Georgetown Li. 777, 778 (1971).

EXAMPLES

1-lypo-thetical 1

I-I

the

s1($) 10 1

10 1

e, I

e 1

s2($) 40 440 8

e2 1

I

a 20 2b 5

B($) 50 5

C2($) 5.00

c($)

1

2

235 4

B. EMPIRICAL IMPLIC

Our model has several

1. An agency will Igregate, to small

2. However, it willsmall one.

3. The dismissal raand lower in the

4. The average disre50 per cent and


cases.9 But our modelting the characteristicsriaximizing administra-unt of its resources to

1.5,

for cz, and (3) and (8)id spend $3.36 on eachof the first type. (The$8.44 in a case of theAlthough the aggregate"s2) are equal — $200—cases of the first type.s the social benefits ofmuch money litigating

behavior rather than a's utility would be lessdget to the larger cases.tany resources to casesLch cases that it antici-lative pessimism aboutif were higher than

e.mple into equation (2),cent of its type 1 casesdants' expectations are)bjective probability of

are equally good (oran of their predictions.

(13)

1 win 68 per cent of its

'il examples. The last

mmission, Report. p. I (Sept.Branch of the Governmentegulatory Commissions 119leral Trade Commission, 59

TABLE 1EXAMPLES OF DIFFERENT OPTIMUM EXPENDITURES

Hypo-thetical 1

Hypo-thetical 2

Hypo- Hypo-thetical 3 thetical 4

Hypo-thetical 5

Hypo-thetical 6

Independent Variables

s1($) 10 10 10 10 10 10

s($) 10 10 10 10 10 10

e 1 1 .9 .9 .9 .9s2($) 40 40 40 40 40 40

40 80 50 50 40 40e2 1 1 1.7 1.7 1.8 1.5

1 1 1.1 1.1 1.1 1

a 20 20 20 20 20 20b 5 5 5 5 5 5

B(S) 50 50 50 60 60 50

Dependent Variables

c2($) 5.00 3.33 3.11 3.74 4.78 3.369.15 13.01 9.97 10.61 9.37 8.44

c1($) 1.25 1.67 1.72 2.07 1.81 1.66c($) 2.28 2.43 2.21 2.25 2.23 2.14ac1($) 25 33.73 34.45 41.30 36.10 33.20bc2($) 25 16.67 15.55 18.70 23.90 16.80P2(%) 35 20 40 44 61 43p,(%) 35 41 88 96 90 87

p2(%) 35 20 28 31 44 3635 41 68 74 70 68

B. EMPIRICAL IMPLICATIONS AND ALTERNATIVE MODELS

Our model has several testable implications. Among them:

1. An agency will probably devote relatively greater resources, in the ag-gregate, to small cases (as measured by the stakes) than to large.

2. However, it will devote more resources to each large case than to eachsmall one.

3. The dismissal rate will probably be different in different types of casesand lower in the larger cases.

4. The average dismissal rate across all classes of case need not tend toward50 per cent and may well be lower.


Tables 2 and 3 use data relating to the Federal Trade Commission in apreliminary test of these implications. The results in Table 2, whichshows how the FTC allocates its budget among its three classes of case(antitrust cases, deceptive-practice cases, and textile and fur cases), areconsistent with the first and second implications. The FTC devotes aboutone-third as many resources to textile and fur cases as to all other labelingand advertising cases. And it devotes roughly as many resources to alladvertising and labeling cases as it does to antitrust, although virtuallyeveryone believes that the Commission's antitrust work involves p0-tentially much greater social benefits than its efforts to prevent mis-labeling and false advertising. The ratio of resources devoted to textileand fur cases to resources devoted to antitrust is particularly striking.'0 oAt the same time the Commission spends more than five times as manyresources on the average antitrust case than on the average textile or

0 ufur case. U

Textile and fur cases are brought under special statutes" that re-quire little evidence to establish a violation. In addition, the stakes insuch cases are typically small. In our terminology, s and s' (the agency'sand the defendant's stakes, respectively) are low; e (the effectiveness of 2the agency's expenditures in procuring an outcome favorable to it) ishigh; and e' is low. All of these factors work to reduce c, the agency'soptimum expenditure per case, while the high e and low e' make thesecases, as a class, relatively more attractive to the agency (assuming it tobe a rational utility maximizer) than cases in which the difficulties ofestablishing a violation are greater. This explains why the expenditure c

per textile and fur case is low but the aggregate expenditure on the classof these cases high relative to their importance.

Table 3, which compares the dismissal rate in the FTC's antitrustcases with the dismissal rate in all of its cases, supports the third andfourth empirical implications of our model. The dismissal rates in differentclasses of cases are different; they do not average out to 50 per cent; the

10. The ratio of big to little FTC cases is actually overstated in Table 2, since theantitrust category includes the minor provisions of the Robinson-Patman amendments tothe Clayton Act, IS U.S.C. §i 13(c), (d), and (e) (1970). On the propensity of both theFTC and the Antitrust Division of the Department ofJustice to emphasize minor violations,see Richard A. Posner, The Federal Trade Comission, 37 U. Chi. L. Rev. 47 (1969);Richard A. Posner, A Statistical Study of Antitrust Enforcement, 13 J. Law & Econ. 365(1970). For some other evidence consistent with the implications of the model see Id. at

381 (table 11), 382 (table 12); Table 8, infra.11. Wool Products Labeling Act, 15 U.S.C. § 68(1970); Fur Products Labeling Act, 15

U.S.C. § 69 (1970); Textile Fiber Products Identification Act, 15 U.S.C. § 70 (1970).

00

C 0

00

0

+

o 0

o

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0

Cl)

o

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00

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E AGENCIES

Trade Commission in asuits in Table 2, whichits three classes of case

extile and fur cases), areThe FTC devotes about

ses as to all other labelingas many resources to all

although virtuallytrust work involves po-efforts to prevent mis-urces devoted to textileis particularly striking.10than five times as many

rn the average textile or

pecial statutes" that re-h addition, the stakes in

and s' (the agency'se (the effectiveness of

come favorable to it) iso reduce c, the agency's

and low e' make theseagency (assuming it to

which the difficulties ofns why the expenditureexpenditure on the class

in the FTC's antitrustsupports the third and

smissal rates in differente out to 50 per cent; the

rstated in Table 2, since thenson-Patman amendments ton the propensity of both theo emphasize minor violations,U. Chi. L. Rev. 47 (1969);

nent, 13 J. Law & Econ. 365tions of the model see id. at

Products Labeling Act, 15:t, 15 U.s.c. § 70 (1970).

01)

z

0.

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C)

00c..l z

<0

0)00

C-)

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a'.

ri '0 C'. C'.) 00 N '000 /' N C N ri 0 0 C'.) N000\Or')C'l ro

'.0'0 0000($ '.0 0

'0 00 0'..

C'. 0'. N C —C C N — N '.0 riC'.) C". 0'.ri -

00a'.

00\0 N N — 0'. 00o —0 C ri'0Cl'. Ceo '.0 ri

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ri '.ON 00 0'.'.0 '.0 '.0 '.0 '.0'.0 '.C'0

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225


TABLE 3DISMISSAL RATE— FEDERAL TRADE COMMISSION

(Contested Cases Only)

DismissedAntitrust

Period Total CasesAntitrust

Cases a OnlyDismissed ti

(%)Cases Only

(%)

1938 60 4 .12 .251941 61 15 .28 .601943 32 6 .22 .531945 43 6 .21 .331946—47 70 7 .21 .431949—50 53 10 .17 .401951—52 62 3 .19 .331955—56 36 12 .19 .251959—60 58 7 .12 .29

1965

Total"34

50915

85

.29

.20.60.44

S0uRCEs.—Federal Trade Commissioii Decisions, vols. 27, 33, 37, 40, 42—43, 46, 48, 52, 56, 67—68.

a Excluding cases brought exclusively under one of the minor Robinson-Pat-man amendments to the Clayton Act. See note 10, supra.

1) Significant total dismissals, as defined in text, infra, p. 240.c Or average.

average is in fact much lower; and the higher dismissal rate is found in theclass of larger cases.

Results from a single agency can hardly be considered conclusive;and the classification of cases employed in Tables 2 and 3 is crude. Thetests can, however, be refined, and extended to other agencies.

The question arises whether alternative models of the administrativeprocess might not explain the evidence equally well. I believe not. Themodel implicit in the standard criticism mentioned earlier (agencies spendtoo much money on small cases) is that administrative agencies are notcompetent utility maximizers. In that event, however, one would expectthe agency either to dismiss a high proportion of cases or suffer reversalat the hands of reviewing courts in a high proportion of cases. In fact theFTC fares extremely well on judicial review.12

12. See Table 16,infra.

Another model cieffective political grotcussed elsewhere is thof questionable casesfirms that dominate tldismissal, either by thby a reviewing court.'—a high dismissal on

C. THE MODEL MAt

In this subpart, sever2A are progressively rmakes to the predicticj

1. NUMBER OF CASES.

We assumed that the n

was fixed, but in fact tias many or as few of cchoice variable alongtake account of the ftnth case will decline asize class of cases, the:proved with relative eaand litigative effort. TIcides to bring, the mordifficult to win with thtrates this relationship.line is the cumulativen1 cases, given equal es1, the product is thebrings more cases its e:

13. See George 3.agement Sci. 3(1971).

14. See Richard A.15. The negative slope

of a given type an agency bthis will tend to reduce unce(the determinants of settlemtSecond, bringing morerisk of being prosecuted gremore difficult for the agency


Another model characterizes the administrative agencies as tools ofeffective political groups.'3 An implication of this model that I have dis-cussed elsewhere is that the FTC can be expected to bring a large numberof questionable cases to harass the competitors of the firms or groups offirms that dominate the agency.'4 Such cases would rather often end indismissal, either by the agency in anticipation of adverse court action orby a reviewing court. We would therefore expect—but we do not observe—a high dismissal or reversal rate.

C. THE MODEL MADE MORE REALiSTIC

In this subpart, several severely unrealistic assumptions made in subpartA are progressively relaxed, and we ask what difference relaxing themmakes to the predictions derived from the original model.

1. NUMBER OF CASES AS AN ADDITIONAL CHOICE VARIABLE

We assumed that the number of cases of each type brought by the agencywas fixed, but in fact the agency, within the limits of its budget, can bringas many or as few of each type of case as it wants. Once we admit n as achoice variable along with c, we must further modify our original model totake account of the fact that the probability of an agency's winning its/2th case will decline as n increases, other things being equal. Within anysize class of cases, there will be some violations that can be detected andproved with relative ease and others that require much more investigativeand litigative effort. Thus, the more cases in the class that the agency de-cides to bring, the more it will be forced to seek out cases that are moredifficult to win with the same expenditure of resources.'5 Figure 1 illus-trates this relationship. The area under the curve to the left of the brokenline is the cumulative probability (as estimated by the agency) of winningn, cases, given equal expenditures per case. If this area is multiplied bys,, the product is the agency's expected utility from bringing n, cases. If itbrings more cases its expected utility will increase but at a declining rate.

13. See George J. Stigler, The Theory of Economic Regulation, 2 Bell J. Econ. & Man-agement Sci. 3 (1971).

14. See Richard A. Posner, The Federal Trade Commission, supra note 10, at 70—71.15. The negative slope of p(n) is reinforced by two other factors, First, the more cases

of a given type an agency brings, the larger will be the body of applicable precedents andthis will tend to reduce uncertainty and so increase the proportion of cases that are settled(the determinants of settlement are discussed in detail later): contested cases will be scarcer.Second, bringing more cases is likely to increase the deterrent effect of the law. With therisk of being prosecuted greater, fewer violations will be committed and this will make itmore difficult for the agency to find additional violations against which to proceed.

MMLSSION

DismissedAntitrust

missed5 Cases Only(%) (%)

.12

.28

.22

.21.21.17

.25.60.53.33.43.40

.19 .33.19 .25.12 .29

.29 .60

.20 .44

vols. 27, 33, 37, 40, 42—

the minor Robinson-Pat-

ra, p. 240.

issal rate is found in the

considered conclusive;s 2 and 3 is crude. Thether agencies.Is of the administrativeveil. I believe not. Theearlier (agencies spendrative agencies are notever, one would expectcases or suffer reversalion of cases. In fact the

point on the left sideC.,fl

To every point onunique function, of thethat determines the excases and spending a ppected-utility function I

tiona] expenditure of SI perStant s, the $1 increment willin the second (.1 X orthat the agency would be betton the iith. However, an addiwinning are already high mayincrease the agency's chanceall events, Figure 2 could bwould not be affected.

THE BEHAVIOR OF ADMINISTRATIVE AGENCIES

l.0

.9

.8

.7

.6

.5

I

.3

I

I

I

.2

.1

228

N0

FIGURE 1

These new assumptions could be incorporated into a revised alge-braic formulation of the agency's utility function, but such a formulationturns out to be quite awkward to manipulate. For our purposes a graphicapproach (Figure 2) is sufficient. Dollars, on the vertical axis, are plottedagainst number of cases on the horizontal axis. Cases of type I are to theleft of the vertical axis and cases of type 2 to the right. Assume a newagency, groping its way to the optimum combination of c's and n's by aprocess of trial and error. It begins by selecting a point somewhere to theright of the vertical axis (it could just as well, however, have begun onthe left side). That point (c2n2) determines both the number of cases oftype 2 that the agency will bring and the expenditure it will make on eachsuch case.16 The choice of that point also constrains the selection of a

I

E

/////F_•__ I

N

nI

16. The assumption that the agency will spend the same amount of money on caseshaving different probabilities of success is somewhat arbitrary. Assume that the probabilityof the agency's winning the first case is .9 and of winning the nth case .6, and that an addi

d into a revised alge-)ut such a formulation

purposes a graphicrtical axis, are plottedes of type 1 are to theright. Assume a new

ion of c's and n's by aoint somewhere to thewever, have begun on

number of cases ofre it will make on eachtins the selection of a

amount of money on casesAssume that the probabilityith case .6, and that an addi-

point on the left side of the diagram, since B is given and c1n1 = B —

To every point on either side of the vertical axis, there corresponds aunique function, of the kind depicted in Figure 1 but now multiplied by s,that determines the expected utility of bringing a particular number ofcases and spending a particular amount of money on each one. The ex-pected-utility function for c2n2 in the diagram is the curve AB. The area

tional expenditure of $1 per case would increase these probabilities by .1. Assumingstant s, the $1 increment will produce a larger gain in expected utility in the first case thanin the second (.1 x .9s, or .09s, compared to .1 X .6s, or .06s). This would seem to suggestthat the agency would be better off spending more of the increment on the first case and lesson the However, an additional expenditure on a case in which the agency's chances ofwinning are already high may increase those chances less than the same expenditure wouldincrease the agency's chances in a case where those chances would otherwise be poor. Atall events, Figure 2 could be modified to give the c's a negative slope, and the analysiswould not be affected.

RICHARD A. POSNER

A

AGENCIES

—N

B

B

229

N

E

///// id1-

—-I

N

nI 'I; 0 n,

FIGURE 2


between that curve and the baseline is the expected utility of bringing n2cases and spending c2 on each one. Notice that while the curve must lie inthe same vertical plane as c2n2, it need not, and ordinarily will not, touchc2n2. There is no presumption that the expenditure on the iith case isequal to the expected utility of bringing that case. It may be lower; as-suming a tight budget constraint, it may very well be higher (as in thediagram).

The curve PG on the left side of the diagram represents the locus ofpoints c1ti1 equal to B — c2n2, the sum of the rectilinear areas c1n1 and

c2n2 being the constant B. To every point on that curve there again cor-responds some unique expected-utility function. We assume the agencyselects the c1n1 shown in the diagram, with its corresponding utility func-tion DE.

It is no accident that in the diagram c1 is below c2 and DE both belowand flatter than AB. Recall that type 2 comprises the larger cases and type1 the smaller. Since c is an increasing function of s, c.2 will usually (notalways) be larger than C1 when s2 > s1. Since the expected-utility func-tions are the product of s times p, A may well be higher than E even if p1is greater than P2. The only nonobvious assumption is that DE is flatterthan AB, signifying that the probability, of the agency's winning declinesmore slowly, as more cases are brought, in the class of smaller than in theclass of larger cases. This is plausible. It implies that the universe ofmajor violations is smaller than the universe of minor ones. The ratio ofall transactions that can plausibly be characterized as monopolization inviolation of the antitrust laws to those such transactions against whichproceedings are instituted is doubtless much smaller than the comparableratio for consumer frauds. If so, bringing an additional monopolizationcase (and spending no more money on it than was spent on the last suchcase) probably involves a larger drop in the probability of a successfuloutcome for the agency than would bringing an additional fraud case.

Figure 2 illustrates how, on these assumptions, the agency thattakes a critic's advice to "reorder its priorities" by bringing more bigcases and spending more money on each one may actually reduce itsoverall effectiveness. By moving to 17 the agency increases its ex-pected utility from bringing cases of type 2 to the area under the curveA'B', but this reduces the resources it can devote to cases of type 1 tothe locus of points on F'G'. Suppose is the point that generates thelargest expected utility (the area under the curve D'E'). Partly becausethe expected-utility functions for cases of class 1 are flatter than those forcases of class 2 the result of this reallocation of resources is to reduce

17. The prime marks here do not refer to defendants' expenditures.

the total expected ut.smaller than the area i.

Relaxing the assibrought by thethe implications of the2 not only suggests wmore small cases thansources to small cases

2. BUDGET AS AN EN

So far we have ássumis an exogenous variabvariables that the

ageelement,18 but they canno cases or lost everyits budget.

To illustrate the cis exogenous, let us assrises (as discussed mdominates congressionagencies) but to fall if tagency that wanted a Itheir merit). The agencpresumably, in s, but ti

This model has theagency has an incentivby the negative impacThus, that slope, whiciexpecting an agency tcmains a vital element il

3. SETTLEMENTS

Our original model excNot only is this unreali:of the primitive model

18. This is strikingly shagency budgets are much min the size or rate of growthProcess of Economic Regula

AGENCIES

-


utility of bringing n2[le the curve must lie indinarily will not, touch

on the 11th case isIt may be lower; as-

til be higher (as in the

represents the locus oftiinear areas c1n1 andcurve there again cor-

We assume the agencyesponding utility func-

c' c2 and DE both belowie larger cases and typefs, will usually (notexpected-utility func-

iigher than E evenion is that DE is flatter'ncy's winning declinesss of smaller than in thes that the universe ofinor ones. The ratio ofd as monopolization insactions against whicher than the comparableitional monopolization

s spent on the last such)ability of a successfulditional fraud case.ions, the agency thatby bringing more bigay actually reduce its

gency increases its cx-e area under the curvee to cases of type 1 tooint that generates theD'E'). Partly because

ire flatter than those forresources is to reduce

penditures.

the total expected utility of the agency (the area under E'D'A 'B' issmaller than the area under EDAB).

Relaxing the assumption that the number of cases of each typebrought by the agency is fixed thus reinforces rather than underminesthe implications of the primitive model. The analysis that underlies Figure2 not only suggests why (as we have observed) the FTC brings manymore small cases than large but also why it seems to devote excessive re-sources to small cases in the aggregate.

2. BUDGET AS AN ENDOGENOUS TERM

So far we have assumed that the agency's budget, or overall resources,is an exogenous variable, meaning that it is not affected by changes in thevariables that the agency controls, the c's and n's. There is some evidencethat administrative agency budgets do in fact contain a large exogenouselement,18 but they cannot be wholly exogenous. The agency that broughtno cases or lost every case it brought would surely suffer a reduction inits budget.

To illustrate the consequences of abandoning the assumption that Bis exogenous, let us assume that it tends to rise as the agency's work loadrises (as discussed more fully later, discussion of work load in factdominates congressional hearings on appropriations for administrativeagencies) but to fall if the agency's batting average (j3) falls (otherwise anagency that wanted a larger budget would bring cases without regard totheir merit). The agency and the appropriating body are also interested,presumably, in s, but this does not affect the analysis.

This model has the same implications as Figure 2. As in Figure 2, theagency has an incentive to increase ii but this incentive is held in checkby the negative impact on p of a higher n if the slope of p(n) is steep.Thus, that slope, which I have suggested provides additional reason forexpecting an agency to concentrate major resources on small cases, re-mains a vital element in the agency's utility function.

3. SETTLEMENTS

Our original model excluded the possibility of a settlement without trial.Not only is this unrealistic, but it invites the objection that the predictionsof the primitive model may be incorrect. If, for example, large cases are

18. This is strikingly shown in a study by George J. Stigler, who found that changes inagency budgets are much more closely correlated with each other than with differencesin the size or rate of growth of the respective industries regulated. George J. Stigler, TheProcess of Economic Regulation, 17 Antitrust Bull. 207, 218 (1972).

whatever causes the ccause the agency to revpossibility by assuminichances of prevailing isthat arty increase in e' rappendix at the end of(settlement costs are Icalways be a settlementparties' estimates sumcome, so a settlement c

The more interesti:and s' = s, the conditio,

This would seem to indecreases and less likel3in e' and increase in ethe right-hand side ofthat an increase in r, whitions of success, will inthe stakes (s) will alsothat has some empirical

Thus far we havea

is unrebelow which expenditu:ness. If the defendant'sthe case, he will not cotfled as a settlement. Tothreshold, it will not be.induce the defendant nodefendant's) exceed th

20. Assuming (as incideipreferrer. The relevance of atin William M. Landes, p. 171

21. The FTC settles smaand 12 infra with Table A3antitrust eases—the large caceptive-practices cases (the si


more apt to be settled than small, this would imply that the former arerelatively cheap to prosecute, and a rational utility-maximizing agencywill therefore allocate greater resources to large cases than the primitivemodel predicted. We must consider the conditions under which a case willbe tried rather than settled.

The minimum offer that a rational plaintiff will accept in settlement ofhis claim is his expected gain from litigation minus his litigation expenses(which would reduce his net gain from suit) plus the costs of negotiatingthe settlement. The maximum offer that the defendant will tender is whathe expects to owe the plaintiff after the litigation (the stakes to the de-fendant discounted by the probability, in the defendant's eyes, of theplaintiff's winning) plus his litigation expenses (which he would lose any-way) minus his settlement costs. For a settlement to take place, the plain-tiff's minimum settlement price must not exceed the maximum that thedefendant is willing to pay. If it is larger there will be no settlement. Iassume that settlement cost is some fraction of each party's litigationcosts—the same fraction.

The condition for litigation may therefore be expressed as follows:

— > (i + c' (14)

which simplified (with the help of equation (8)) becomes

(15)

The larger the ratio of s' to s the likelier a settlement. (The intuitive ex-planation is that the prospect of a large loss induces the defendant tomake an offer that the agency, with the prospect of a relatively small gainfrom litigation, finds attractive.) And for reasons explained earlier thatratio may be larger in big cases than in small. Notice, however, that whene' > 1, the same percentage increase in s and s' will reduce the likelihoodof settlement by making the first term in brackets a larger negative num-ber.

An increase in settlement costs relative to litigation costs (falling k)reduces the right-hand side of inequality (15): litigation becomes morelikely.'9 An increase in e' (the effectiveness of the defendant's litigationoutlays) produces a more complex effect, but in general the decline in thefirst term in brackets will exceed the rise in the second term. However,it is unrealistic to assume that if e' rises e will remain unchanged, for

19. For some evidence of this effect see Richard A. Posner, supra note 6, at 94—96.

-

ply that the former areity-maximiZing agency;ases than the primitiveunder which a case will

1 accept in settlement ofs his litigation expensesthe costs of negotiatingdant will tender is whati (the stakes to the de-efendant's eyes, of thehich he would lose any-to take place, the plain-

I the maximum that theviii be no settlement. Ieach party's litigation

expressed as follows:

ecomes

1

(14)

(15)

nent. (The intuitive ex-duces the defendant to

a relatively small gains explained earlier thatice, however, that whenill reduce the likelihooda larger negative num-

tigation costs (falling k)•tigation becomes morete defendant's litigationeneral the decline in thesecond term. However,remain unchanged, for

ter, supra note 6, at 94—96.

RiCHARD A. POSNER 233

whatever causes the defendant to revise his chances upward shouldcause the agency to revise its chances downward. We can investigate thispossibility by assuming that the sum of the parties' estimates of theirchances of prevailing is a constant ((ec)/(c + c') + (e'c')/(c + c') = r), sothat any increase in e' must be offset by a decrease in e. As shown in theappendix at the end of this article, in the special case where r = I, k > 1

(settlement costs are lower than litigation costs), and s' = s, there willalways be a settlement, whether e' rises or falls. Intuitively, when theparties' estimates sum to 100 per cent, it means that they agree on the out-come, so a settlement can readily be negotiated.20

The more interesting case is where r > 1. Assuming that k is largeand s' = s, the condition for litigation is (approximately)

Vc (16)

This would seem to indicate that litigation becomes more likely as e'decreases and less likely as it increases. But this is misleading. A decreasein e' and increase in e will produce an increase in c (equation (ii)): thusthe right-hand side of the inequality will also decrease. What is clear isthat an increase in r, which measures the divergence of the parties' predic-tions of success, will increase the likelihood of litigation. An increase inthe stakes (s) will also increase the likelihood of litigation — a predictionthat has some empirical support.2'

Thus far we have assumed that the effectiveness of a dollar expendedin litigation (e) is a constant that is unaffected by the number of dollarsexpended, which is unrealistic. In particular, there is probably a thresholdbelow which expenditures on litigation have no, or negligible, effective-ness. If the defendant's threshold expenditure is larger than his stakes inthe case, he will not contest the agency's case and the case will be classi-fied as a settlement. To be sure, assuming that the agency has the samethreshold, it will not be able to make a credible threat of suing in order toinduce the defendant not to contest unless the agency's stakes (unlike thedefendant's) exceed the threshold. But since s may be larger than s',

20. Assuming (as incidentally I do throughout the paper) that neither party is a riskpreferrer. The relevance of attitude toward risk to the likelihood of settlement is discussedin William M. Landes, p. 171.

21. The FTC settles smafl cases more frequently than large. (Compare Tables 3 supraand 12 infra with Table A3 in the appendix.) But this could be because the outcome ofantitrust cases—the large cases, in our statistics—is less predictable than that of de-

cases (the small cases in our statistics): the r may be greater.


there will be cases where this condition is fulfilled. These will be smallcases, since the threshold litigation expenditure must exceed s'. Here is

then another reason for expecting settlements to include a dispropor-tionately large number of sinai! cases, consistently with the predictionsof the primitive model.

If we solve inequality (15), using the values in our earlier numericalexample and assigning a value of 5 to k (signifying that the costs of settle-ment are one-fifth of the costs of trial) we find that type 1 cases will notbe settled. This is not because the parties have different stakes (s1 and

are the same) but because they disagree sharply about the outcome.The agency estimates the probability of its winning at 87 per cent, whiledefendants estimate the agency's probability of winning at only 51 percent. In cases of the second type, where the spread is smaller (theagency estimates its probability of winning at 43 per cent and the de-fendant estimates the agency's probability of winning at 28 per cent) theparties do settle. Although arbitrary, the numerical example suggestsroughly how great a difference there must be between the parties' esti-mates of probability, given moderate settlement costs and equal stakes,for litigation to occur. Additional examples (again with k = 5) are pre-sented in Table 4.

In the numerical example, the larger difference in the parties' esti-mates of their chances of success was in the smaller case but this is anaccident of the numbers. On the one hand, prediction is more difficult themore complex a case is, and complexity is in part a function of size(though even more of novelty). On the other hand, the greater legal re-sources deployed in the larger case may result in narrowing the area ofuncertainty about the outcome.

Our discussion of settlements assumes that the parties cooperate tomaximize their joint utility. Our discussion of litigation assumed that

TABLE 4SETTLED VS. LITIGATED CASES

Hypo-thetical 1

Hypo-thetical 2

Hypo-thetical 3

Hypo-thetical 4

Hypo-thetical 5

Hypo-thetical 6

Casetype 1 S S L L L L

Case

type 2 S S S S L S

SouRcE.—Table 1.

they make independerlays, even though, bymade better off. Thetion of the operation 0:

parties agree to settletrial. In cases that are•the facts essential to t)to establish the facts bpear to be less commorof the total costs of goin agreements tosince the cases that aretion those in which anthen, a model of coopethe settlement context,appropriate in the

II. DOES COMBINIADJUDICATION U'CONTAMINATE Al

A. THE ELMAN THES

An old debate in admiprosecution and adjudition 22_ has recently I

former member of the]points to several specifmake the combinationunfairness:

1. A high rate ofdof the memberscases in the firs'

2. Itisarebufftoi

22. 1 use "combinationdecides, not that members ofmembers of the prosecutorjajin the decision. The latter forand to my knowledge have n

r

--


they make independent, noncooperating decisions on their litigation out-lays, even though, by agreeing to reduce those outlays, both would bemade better off. The dichotomy corresponds at least to casual observa-tion of the operation of the legal system. In a very large class of cases theparties agree to settle in advance of trial and thereby avoid all costs oftrial. In cases that are tried, the parties frequently do stipulate to many ofthe facts essential to the proceeding in order to avoid the costs of havingto establish the facts by testimony in court, but such side agreements ap-pear to be less common than settlements and to avoid a smaller proportionof the total costs of going to law. Possibly the transaction costs involvedin agreements to curtail the trial process are relatively high, especiallysince the cases that are not settled — a minority of all cases — are by defini-tion those in which an effort at a meeting of the minds failed. In general,then, a model of cooperative decision making seems more appropriate inthe settlement context, and a model of independent decision making moreappropriate in the litigation context.

II. DOES COMBINING PROSECUTION ANDADJUDICATION IN THE SAME AGENCYCONTAMINATE ADJUDICATION?

A. THE ELMAN THEsIs

An old debate in administrative law—over whether the combination ofprosecution and adjudication in a single agency contaminates adjudica-tion22—has recently been revived by Philip Elman, a distinguishedformer member of the Federal Trade Commission. In a recent article, hepoints to several specific characteristics of an administrative agency thatmake the combination of these functions likely, in his judgment, to createunfairness:

1. A high rate of dismissals is a confession of ineptitude on the partof the members of the agency, who authorized the bringing of thecases in the first place.

2. It is a rebuff to the staff that investigated and prosecuted the case

22: I use "combination of functions" to mean that an agency initiates the cases that itdecides, not that members of the Commission participate in the actual prosecution or thatmembers of the prosecutorial staff participate (other than through briefs and oral argument)in the decision. The latter forms of combination have long been considered highly improper,and to my knowledge have never characterized the agencies I shall be discussing.

AGENCIES

d. These will be small'tust exceed s'. Here iso include a dispropor-ly with the predictions

n our earlier numericalthat the costs of settle-tt type 1 cases will notlifferent stakes (s1 andIly about the outcome.ig at 87 per cent, whilebvin ning at only 51 perspread is smaller (the3 per cent and the de-ning at 28 per cent) theneal example suggeststween the parties' esti-costs and equal stakes,in with k = 5) are pre-

nce: in the parties' esti-tailor case but this is anion is more difficult thepart a function of sized, the greater legal re-i narrowing the area of

he parties cooperate toitigation assumed that

S

Hypo- Hypo-4 thetical 5 thetical 6

L L

L S


-

on the agency's behalf—a staff on which the members of theagency depend.

3. It encourages noncompliance with the statute that they are com-mitted to enforcing.23

Although plausible, this reasoning is hardly compelling. It canequally well be argued that an agency will be motivated to review con-tested cases scrupulously in order to keep the staff on its toes and mini-mize the likelihood of reversal by a reviewing court. Furthermore, if it istrue that an agency measures its success by the number of cease and de-sist orders entered, it will refuse to dismiss complaints regardless ofwhether it, its delegate, or a complete outsider brought the case initially.

Nor can we resolve doubt in favor of Professor Elman's position onthe ground that it is implicitly based on his extensive personal observationas a member of the Trade Commission. What he observed is that Com-mission members frequently lack the fair-mindedness expected ofjudges; and this bears hardly at all on the issue under discussion. AreFederal Trade Commissioners more biased than the average judge?Would they be less biased if they sat on a court rather than on the Com-mission or if their authority over the issuance of complaints were re-moved?

B. TESTABLE IMPLICATIONS OF THE ELMAN THESIS

The Elman thesis has several testable implications:

1. An agency in which prosecution and adjudication are separatedwill dismiss a higher fraction of the cases it decides than one inwhich these functions are united, other things being equal.

2. When an agency in which these functions are combined does dis-miss a complaint, it will tend to do so in a manner that avoids anacknowledgment that the agency erred in initially authorizing thecomplaint.

3. Such an agency will be more reluctant to dismiss a case in whichthe issues are primarily factual than one in which the issues areprimarily legal.

4. It will be more reluctant to dismiss a big case—big in terms of theamount of agency resources invested in it—than a small one.

5. It will be more reluctant to dismiss a complaint that the current

23. See Philip Elrnan, supra note 9, at 810. To similar effect see Richard A. Posner,The Federal Trade Commission, supra note 10, at 53.

members of thepredecessors.

6. The decrees ofbe reversed moagency in which

7. In congressionaand in other scrdismissal rate vversal on judici2bined in the age

These hypothesesfederal administrative aof law violators—the FRelations Board. The (the issuance of complaiprogressively diminishebe formally approved bRegional Directors wenotifying the Board orfact or law was presentsystem 70 per cent of;the Board.25 The Taft-further by making thepointee rather than ansive authority over theinteresting opportunitieLabor Board as well as

C. THE EMPIRICAL Es

1. Elman implies tcution and adjudicatioloriginal model supporttoptimum litigation outlagency's winning), and

24. See U.S. Atty. GetProcedure in Government ANLRB Ann. Rep. 5 (1938)NLRB Functions, 11 Indus.

25. See 7 NLRB Ann. I26. See § 2(d) of the Nr


h the members of the

tute that they are corn-

lly compelling. It can)tivated to review con-if on its toes and mini-rt. Furthermore, if it isumber of cease and de-mplaints regardless ofought the case initially.sor Elman's position onye personal observation

observed is that Corn-ndedness expected of• under discussion. Are

the average judge?rather than on the Corn-1of complaints were re-

FIESIS

is:

idication are separatedit decides than one in

•ngs being equal.are combined does dis-i manner that avoids aninitially authorizing the

dismiss a case in whichin which the issues are

ase—big in terms of the—than a small one.nplaint that the current

see Richard A. Posner,

members of the agency authorized than one authorized by theirpredecessors.

6. The decrees of an agency in which the functions arc combined willbe reversed more frequently on judicial review than those of anagency in which the functions are separated.

7. In congressional hearings on an agency's appropriation requests,and in other scrutinies of the agency's performance, the agency'sdismissal rate will receive greater emphasis than its rate of re-versal on judicial review if prosecution and adjudication are com-bined in the agency.

These hypotheses can be explored using data from the majorfederal administrative agencies concerned primarily with the prosecutionof law violators — the Federal Trade Commission and the National LaborRelations Board. The Commission has never relaxed its authority overthe issuance of complaints. The Labor Board's authority, in contrast, hasprogressively diminished.24 Prior to October 1942 all complaints had tobe formally approved by the Board. Beginning with that date the Board'sRegional Directors were authorized to issue complaints without firstnotifying the Board or obtaining its approval, unless a novel question offact or law was presented, and in the first year of operation under the newsystem 70 per cent of all complaints were issued without a reference tothe Board.25 The Taft-Hartley Act in 1947 carried separation one stepfurther by making the General Counsel of the Board a presidential ap-pointee rather than an employee of the Board and by giving him exclu-sive authority over the issuance of complaints.26 This sequence affordsinteresting opportunities for comparison among different periods of theLabor Board as well as between Board and Commission.

C. THE EMPIRICAL EVIDENCE

1. Elman implies that any bias created by the combination of prose-cution and adjudication will show up in a reduced dismissal rate. Ouroriginal model supports this view. Substituting equation (8) (defendant'soptimum litigation outlay) into equation (13) (the true probability of theagency's winning), and rearranging some terms, we have

24. See U.S. Atty. Gen.'s Committee on Administrative. Procedure, AdministrativeProcedure in Government Agencies, S. Doc. No. 8, 77th Cong., 1st Sess. 22—23 (1941); 3NLRB Ann. Rep. 5 (1938); Ida Klaus, The Taft-Hartley Experiment in Separation ofNLRB Functions, 11 Indus. & Lab. Rel. Rev. 371, 372—74 (1958).

25. See 7 NLRB Ann. Rep. 12, n.5 (1942); 8 NLRB Ann. Rep. 13 (1943).26. See § 2(d) of the National Labor Relations Act, 29 U.S.C. § 153(d) (1970).


The effect of introducing bias in the agency's favor is to increase e anddecrease e', making both terms on the right-hand side of the equationlarger.

In the more complex model illustrated in Figure 2, the effect on thedismissal rate of an increase in e and a corresponding decrease in e' isnot so easy to predict. Typically the immediate consequence will be toshift all of the expected-utility functions upward. If each increasesequally and c1n1 and c2n2 were optimum points before the shift, theagency has no reason to move to different points and Pt and P2 (andtherefore and will increase (the dismissal rate will fall). But achange in e ande' could well affect different utility functions differently.In that event the agency might alter its cn points and the new points mightinvolve a larger n and a lower probability of success in the nth case thanbefore the shift. Still, an increase in e accompanied by a decrease in e'will ordinarily reduce the agency's dismissal rate, for the increase in theagency's overall dismissal rate due to bringing some additional cases isunlikely to equal or exceed the decrease in that rate due to a higher e andlower e' in all of its cases.

One effect of a declining e' that we do not predict is a change in thesettlement rate. Any bias introduced by combination of functions wouldpresumably be perceived by both parties roughly equally: the r of in-equality (16) would not change.

Table 5 presents dismissal rates for more than 1,100 NLRB unfairlabor practice cases and FTC cases, drawn from randomly selectedvolumes of the agencies' official decisions for various periods since1938.27 It reveals that the Commission's dismissal rate has in generalbeen a good deal higher than the Board's both before and after 1947, whilethe Board's has actually decreased since the creation of the independentGeneral Counsel. Little significance, however, can be ascribed to these

27. Decisions are published in these volumes in the chronological order in which theywere issued. While a volume of NLRB decisions ordinarily covers no more than twomonths, an FTC volume will usually cover an entire year's decisions. My procedure wasfirst to select volumes of NLRB decisions at random from various periods, concentratingon the years immediately before and immediately after a change in the Board's structurewith respect to separation of functions, and then to select the contemporaneous FTCvolume. I omitted the very early years of the Board's decisions on the ground that its earlyexperience might be unrepresentative; however, some evidence on the earliest period ispresented in Tables 8 and 11 and note 34, infra. I omitted 1969 in the case of the FTCbecause its decisions for that year had not yet appeared in a printed volume and because itdecided very few cases that year.

2

l—e'(17)

Agency Period

NLRB 193819411943194519461947Totala

FTC 19381941

1943

19451946—47

Total

NLRB 19491950195119561960

1965

1969

Total a

FTCb 1949—SO1951—52

1955—56

1959—601965Total a

SOURCES. — Decisions an51, 60, 69, 72, 87, 91, 95, 115

27, 33, 37, 40, 42—43, 46, 48,a Or average.bExclusion of 1969 FTC

.rupra.

AGENCIESRICHARD A. POSNER 239

(17)

or is to increase e andd side of the equation

ure 2, the effect on thending decrease in e' is;onsequence will be tord. If each increasess before the shift, theits and p1 and P2 (and.1 rate will fall). But aty functions differently.nd the new points mighttess in the nth case than

by a decrease in e'for the increase in the

ome additional cases is

te due to a higher e and

is a change in thetion of functions wouldy equally: the r of in-

an 1,100 NLRB unfairom randomly selectedvarious periods since

sal rate has in generalre and after 1947, whiletion of the independentan be ascribed to these

nological order in which theyy covers no more than two

lecisions. My procedure wasarious periods, concentratIng

in the Board's structurethe contemporaneous FTC

on the ground that its earlY

:nce on the earliest period is

1969 in the case of the FTC,rinted volume and because it

TABLE 5DISMISSAL RATE

Corn- %Cease plaint plaint Dis- %

Total and Dis- Dis- missed Dis-Cases Desist missed missed in Part missedCon- Order in Part in Its or in

Agency Period tested Entered or Whole Entirety Whole Whole

NLRB 193819411943194519461947Total3

331826162720

140

2817

2012

2115

113

258

16

7

15

11

82

5

1

646

S

27

.76

.44

.62

.44

.56

.55

.59

.15

.06

.23

.25.22.25

.19

FTC 19381941

194319451946—47

6061

3243

70

266

43

39

19

2621

148

26

31

14

23

56

150

16

2213

17

49

117

.43

.51

.44

.53

.80

.56

.27

.36

.41

.40

.70

.44

NLRB 1949195019511956196019651969Total3

38525757

10510370

482

27434848839054

393

30243335

552835

240

11

9

9

9

2213

16

89

.79.46.58.61.52.27.50.50

.29

.17

.16

.16

.21

.13

.23

.18

FTC'. 1949—501951—521955—561959—60

1965

53

62365834

243

24

41

283919

151

38

37

13

3618

141

2921

8

1915

92

.72

.60

.36

.62

.53

.58

.55

.34

.22

.33

.44

.38

SouRces—Decisions and Orders of the National Labor Relations Board, vols. 8, 35,51, 60, 69, 72, 87, 91, 95, 115, 127, 153, 178; Federal Trade Commission Decisions, vols.27, 33, 37, 40, 42—43, 46, 48, 52, 56, 67—68.

a Or average.Exclusion of 1969 FTC cases, in this and subsequent tables, is explained in note 27,

supra.


findings. Table 1 counts as a dismissal any case in which, and for what-ever reason, any part of the complaint was dismissed.28 Many are unim-portant partial dismissals. And complaints are frequently dismissed incircumstances where the outcome seems better characterized as a victoryfor the agency than as a victory for the defendant, such as where the de-fendant has discontinued the unlawful practice in circumstances whereresumption seems highly unlikely.

Table 6 organizes the dismissal data in a more discriminating manner.Dismissals that, for the reasons just stated, are not really significant areexcluded. According to Table 6 the NLRB's dismissal rate is approxi-mately the same in the period before and in the period after 1947. Ifpartial dismissals are included the FTC's dismissal rate is lower than theBoard's in both periods. If partial dismissals are excluded the Com-mission's dismissal rate is very slightly higher than the Board's in bothperiods.

Although the relative dismissal rates of the Labor Board and theTrade Commission do not support the Elman position, neither do theyrefute it, sinceji (and hence 1 -- ji, the dismissal rate) is, as we know fromour model, influenced by variables whose values cannot be assumed to bethe same in two so dissimilar agencies as the Labor Board and the TradeCommission.29 But even if they cannot be used for direct comparison ofthe agencies, Tables 5 and 6 illuminate our question in two respects.

First, a good deal of the sense that administrative adjudication isbiased against defendants stem from a reaction to the low dismissalrates that characterize administrative adjudication. Instinctively we maythink that in a "fair" system of adjudication the dismissal rate would tendtoward 50 per cent. Our model of the behavior of administrative agenciesshows, however, that a perfectly fair agency might nonetheless dismissfar fewer than 50 per cent of its cases. Tables 5 and 6 reinforce the im-pression that this is a general feature of administrative adjudication,rather than a distinctive attribute of agencies that have specific sources ofcontamination such as combination of functions.

28. A case in which there was a partial dismissal is counted twice—once in the ordercolumn and once in the dismissal column.

29. For this reason I have relegated to the appendix at the end of this article a table thatcompares the dismissal rate in contested cases brought by the Antitrust Division of theDepartment of Justice and in contested antitrust cases brought by the FTC—the area ofoverlap between the jurisdictions of the two agencies. Table Al shows, for what it is worth,that an antitrust defendant is as likely to convince the Commission to dismiss the complaintagainst him as he is to convince a court to dismiss a similar complaint.brought by the De-partment, although the functions of prosecution and adjudication are completely separatein antitrust litigation initiated by the Department.

DISMISSAL

Agency Period

NLRB 193819411943194519461947Total b

FTC 19381941194319451946—47Total b

NLRB 1949195019511956196019651969Total b

FTC 1949—50195 1—52

1955—5 61959—601965Total b

SouRcEs.—See Tabia As defined in text.90r average.

n which, and for what..3sed.28 Many are Unim-requently dismissed inaracterized as a victory, such as where the de-

n circumstances where

discriminating manner.ot really significant aresmissal rate is approxi-e period after 1947. Ifal rate is lower than there excluded the Corn-ian the Board's in both

Labor Board and theosition, neither do theyate) is, as we know from:annot be assumed to beor Board and the Tradeor direct comparison ofestion in two respects.istrative adjudication isiort to the low dismissaln. Instinctively we maysmissal rate would tendadministrative agencies;ht nonetheless dismissand 6 reinforce the im-nistrative adjudication,have specific sources of

ited twice — once In the order

end of this article a table thatthe Antitrust Division of theght by the FTC—the area of

shows, for what it is worth,ssion to dismiss the complaintcomplaint.brought by the Dc-ation are completely separate

AGENCIESRICHARD A. POSNER

TABLE 6DISMISSAL RATE.._SIGNIFICANTa DISMISSALS ONLY

241

Signifi-cant %

Total Signifi- Total Dis-Con- cant Dis- % missed

tested Dis- missals Dis- in En-Agency Period Cases missals Only missed tirety

NLRB 193819411943194519461947Totaib

3318

26162720

140

15

414

5

11

10

59

5

1

646

5

27

.45

.22

.54

.31

.41

.50

.15.06.23.25.22.25A9

FTC 19381941194319451946—47Totalb

6061324370

12

17

8

11

18

7

177

9

15

55

.20

.28

.25

.26

.2625

.12

.28

.22

.21

.21

11

NLRB 1949

1950

1951

1956

1960

1965

1969

Totaib

38

52

57

57

105

103

70

482

26

15

26

30

48

21

29

195

11

9

9

9

22

12

16

88

.68

.29

.46

.53

.46

.20

.41

.40

.29

.17

.16

.16

.21

.12

.23

.18

FTC 1949—50

1951—52

1955—56

1959—60

1965

Totalb

53

62

36

58

34

243

11

15

10

21

12

69

9

12

7

7

10

45

.21

.24

.28

.36

.35

.17

.19

.19

.12

.29

.19

SOURCES. —See Table 5, supra.a As defined in text.b Or average.

F


Second, it may be relevant that the disparity between dismissals andsignificant dismissals should be so much greater for the Commission thanfor the Board (indeed, virtually all total dismissals by the Board are sig-nificant in my sense of that term). The reason for the disparity is simplythat it is not the Board's practice formally to dismiss a complaint when thedefendant has discontinued the unlawful practice and resumption is un-likely — the usual ground of "nonsignificant" dismissal of a complaint inits entirety by the Commission. This procedural difference between theagencies is trivial but it is the opposite of what one would expect if Elmanwere correct, given that it is the Commission, not the Board, that issuesas well as adjudicates complaints. Were the Commission highly sensitiveto criticisms that dismissal of a complaint was an acknowledgment thatthe taxpayer's money had been wasted in bringing the case, it wouldseek wherever possible to avoid characterizing its action in closing a caseas a dismissal. The Commission need not issue and print in its officialdecisions a formal order dismissing the complaint in every case where itfinds entry of a formal order to cease and desist to be unnecessary.

Tables 5 and 6 allow a comparison among the several stages of theseparation of functions at the Board. Table 7 summarizes the dismissalrates for each of the stages—before 1942, between 1943 and 1947, andsince 1947.

The dismissal rate is higher in the two later periods, when prosecu-tion and adjudication were separated, than in the first period, when theywere not. This is consistent with Elman's thesis. The dismissal rate in themost recent period, that of formal separation, is lower than in the previ-ous period, that of limited delegation to the Board's staff of authority toissue complaints; this is inconsistent with the thesis. The significance of

TABLE 7DISMISSAL RATE — SIGNIFICANT a DISMISSALS (NLRB)

Significant

Period

TotalContested

CasesSignificantDismissals

TotalDismissals

Only%

Dismissed

%Dismissedin Entirety

1938—41 51 19 6 .37 .121943—47 89 40 21 .45 .241949—69 482 195 88 .40 .18

Sounca.—Table 5, supra.a As defined in text.

these findings, howevevolumes of the officialunderrepresent the fluby hearing examinersfor this omission and arather than statistics

b

the

Table 8by

thea course of actic

examiner's decision.tested cases in the eaiparities between the re:8. In particular, Tablerate, however computesuit of separation of

30. The FTC volumes,much longer period in theAll of the periods shown in 1following exceptions: 1938 (seach) and 1946—1947 (18 mc

31. Two related tableswithdrawals (often a charge Irecommend a complaint) of cof total charges pending on tition that a higher dismissal nfunctions might manifest itserising precomplaint dismissalimmediately following the fopossible explanation for thebeing flied by individuals ratypically higher among unioplored with negative results i

Table A3 shows the FTpositions including informalreasons noted earlier, a direcThe caption "stipulations" irwhich statistics are regularly

RICHARD A. POSNER 243AGENCIES

etween dismissals andr the Commission than

by the Board are sig-the disparity is simplys a complaint when theand resumption is un-issal of a complaint inlifference between thewould expect if Elmanthe Board, that issues

highly sensitivei acknowledgment thating the case, it wouldaction in closing a caseand print in its officialin every case where ito be unnecessary.

several stages of theniarizes the dismissal

bn 1943 and 1947, and

these findings, however, is impaired by the limitations of our sample. Thevolumes of the official decisions of the Board from which it was drawnunderrepresent the number of dismissals because they omit dismissalsby hearing examiners that are not appealed to the Board. We can correctfor this omission and also obtain complete statistics of the Board's actionsrather than statistics based upon a sample by rearranging certain statisticsin the Board's annual reports.30 Table 8 presents the results of thesemanipulations. Also, by being limited to unfair labor practices committedby employers, Table 8 corrects for the principal modifications in the lawadministered by the Labor Board that were made by the Taft-HartleyAct.31

Table 8 overrepresents the number of contested orders enteredagainst defendants by including cases in which the defendant filed ex-ceptions to the trial examiner's recommended decision but did not file abrief—a course of action inconsistent with a serious effort to overturn theexaminer's decision. (Such cases were omitted from the count of con-tested cases in the earlier tables.) At all events, there are marked dis-parities between the results in the previous tables and the results in Table8. In particular, Table 8 indicates a substantial increase in the dismissalrate, however computed, after 1947. But this may not have been the re-suit of separation of functions. The model developed in Part I of this

30. The FTC volumes, in contrast, record all dismissals; and a single volume covers amuch longer period in the Commission's decisional process, thus reducing sampling error.All of the periods shown in Tables 5 and 6 of FTC decisions are a full 12 months, with thefollowing exceptions: 1938 (seven months), 1941 (five months), 1943 and 1945 (six monthseach) and 1946-1947 (18 months).

31. Two related tables are printed in the appendix. Table A2 presents dismissals andwithdrawals (often a charge is withdrawn because the Board's staff advises that it will notrecommend a complaint) of charges, prior to formal issuance of a complaint, as percentagesof total charges pending on the Board's docket. The table is relevant to the possible conten-tion that a higher dismissal rate as a result of separating the prosecutorial and adjudicativefunctions might manifest itself at the precomplaint stage. Although Table A2 does reveal arising precomplaint dismissal-withdrawal rate over time, the rate actually fell in the yearsimmediately following the formal separation effected by the Taft-Hartley Act in 1947. Apossible explanation for the secular rise in the rate—that a rising proportion of charges isbeing filed by individuals rather than unions and the proportion of meritorious claims istypically higher among union-initiated than among individually initiated charges—is ex-plored with negative results in Table A2.

Table A3 shows the FTC's dismissal rate as a percentage of all cases, and of all dis-positions including informal settlements, to permit comparison with Table 8—although, forreasons noted earlier, a direct comparison between the two agencies is extremely difficult.The caption "stipulations" in Table A3 refers to the only mode of informal settlement forwhich statistics are regularly reported. Stipulations were discontinued in the early 1960s.

eriods, when prosecu-first period, when theyhe dismissal rate in thewer than in the previ-'s staff of authority tois. The significance of

(NLRB)

% DismissedDismissed in Entirety

.37

.45

.40

.12

.24

.18

•0

0 '.-.

(I,

'-•'

C',

•0'V0 'I)

0

E

I

• — CC

E

'0C)

C,,

C0ci

•0V'CC

C)

C0c-I

'IC

U

U1-U

CO

CO

00

CO

a.

LLI

-"C>.C

4

I-

00.C,)

article predicts a p0number of cases broiiin dismissal rate if theto the resource changto increasing ii ratherexplanation of the

A simple index operiods covered by TBoard's employees (b:unfair labor practiceand then dividing thepractices enforcementtice charges lodged withe resulting quotientsfirst period, 1935—41,

Table 9 reveals tilabor practices declinethe prior period and ttnumber of contested c;agency's resources increased even more, anboth resources and thecases increases so maragency's productivity

According to Tab]per case in the periodapart from the highermissal rate. Figure 3 sI

N N C' N N N N O\

00—

00 N NN — N

N N N NN N

"C N 00-C — — — Cl

O — C' ('C 00 N — —

N NNN

CC NN NN

N N NC 0NN

N C C 0 N 0 C NCl C N CO

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Cl N '.0N —'.0 N 0'. N N N

Cl

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N

00 NCl N

N CN NN N

N C N N'0 '.0

C '0

0

'0

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C) 0

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0

z -

.1

t

32. The business of thcpractice cases and represetaverage, somewhere betweeaverage unfair labor practic1948, Hearings before the SSess. 866 (1947); Departmetions for 1968, Hearings beCong., 1st Sess, pt. 1 at 83Welfare Appropriations forComm. on Appropriations,unfair labor practice cases atcase. A problem was createwhich bulked large in the Btwo exchange rates—3.5 anc

r- r-l r-i I#-)- 0000

-r- m

N0

N 00 1—-

—)0 r-1 C•'I

I —

0)

0) 0U0

00<

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:-- >.

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0— 00 0' 00 —

— ".n — 'C 0 e')Cr—t'C

article predicts a positive correlation between agency resources andnumber of cases brought. A budget increase might produce an increasein dismissal rate if the change in the number of cases was large in relationto the resource change — if in other words the new resources went mostlyto increasing n rather than to increasing c (and hence p). This may be theexplanation of the post-1947 increase in the dismissal rate.

A simple index of changes in the Board's resources during the fourperiods covered by Table 8 can be constructed by first distributing theBoard's employees (by means of a simple weighting factor 32) between itsunfair labor practice business and its other business during the period,and then dividing the number of employees thus allocated to unfair laborpractices enforcement in each period by the number of unfair labor prac-tice charges lodged with the Board during that period. Table 9 translatesthe resulting quotients into an index in which the agency's resources in thefirst period, 1935—4 1, equals 100.

Table 9 reveals that the agency's resources for dealing with unfairlabor practices declined slightly in the period 1943—47 as compared withthe prior period and that this decline was attended by a sharp drop in thenumber of contested cases and in the dismissal rate. In the next period theagency's resources increased, but the number of contested cases in-creased even more, and the dismissal rate rose. In the latest period, whenboth resources and the dismissal rate have fallen, the number of contestedcases increases so markedly as to suggest a profound change either in theagency's productivity or in the character of its unfair labor practice cases.

According to Table 9, the Board actually expended fewer resourcesper case in the period 1948—52 than in the previous period—which, quiteapart from the higher n, would lead us to predict an increase in the dis-missal rate. Figure 3 shows how a reduction in c combined with an even

r'UN0-4 04—

r— oC——C'100 000cr-

I I' II I

)E-) 'C 'C '.0

32. The business of the Board consists primarily of two types of cases—unfair laborpractice cases and representation cases. Representation cases apparently consume, onaverage, somewhere between 20 and 40 per cent of the agency resources required by theaverage unfair labor practice case. See Labor-Federal Security Appropriations Bill for1948, Hearings before the Subcomm. of the S. Comm. on Appropriations, 80th Cong., 1stSess. 866 (1947); Departments of Labor and Health, Education, and Welfare Appropria-tions for 1968, Hearings before a Subcomm. of the H. Comm. on Appropriations, 90thCong., 1st Sess., pt I at 835 (1967); Departments of Labor, and Health, Education, andWelfare Appropriations for Fiscal Year 1969, Hearings before the Subcomm. of the H.Comm. on Appropriations, 90th Cong., 2d Sess. 481 (1968). 1 equated representation tounfair labor practice cases at the rate of 3.5 representation cases to one unfair labor practicecase. A problem was created by a third class of Board cases, union.authorization cases,which bulked large in the Board's activity in the third period covered by Table 8. I usedtwo exchange rates— 3.5 and 4—producing the range shown in the table.


greater increase in n (possible because B has increased) could increasethe agency's expected utility while reducing the average probability ofits winning the cases that it brings.

2. If Elman's thesis is correct, an agency in which prosecution andadjudication are joined should be sensitive to possible criticism of a dis-missal as an acknowledgment that the agency erred at the complaint-issuance stage. If so, we would expect such an agency, when it does dis-miss a complaint, frequently to do so without acknowledging failure toestablish a violation. It may feel compelled to dismiss a complaint thatcannot possibly withstand judicial review but it need not cast its dismissalin the form of a potentially damaging admission. A dismissal in whichthere is no acknowledgment that a violation was not established will becalled a "grudging" dismissal.

I have found no grudging dismissals among the decisions of theBoard. Table 10, which compares ungrudging with significant dismissalsby the FTC, suggests that the grudging dismissal is an important featureof the Commission's decision-making process. That many dismissals ofFTC cases, and none of NLRB cases, are grudging may appear to con-

TABLE 9RESOURCE CONSTRAINT AND DISMISSAL RATE—NLRB UNFAIR

LABOR PRACTICE CASES

Index of Index of % ofAvailable Number of ContestedResources Contested Index (1) ÷ Cases

Period (1) Cases (2) Index (2) Dismissed

1935—41 100 100 1.00 .161943—47 97 80 1.21 .131948—52 102—107 121 .84—.88 .23

1955_698 87 296 .29 .21

SOURCES.—See Table 8, supra; also U.S. Presidents, Bureau of the Budget,Budget of the United States Government, fiscal yrs. 1935—1969; Hearings beforethe Subcomm. of the Senate and House Comms. on Appropriations on NLRBappropriations for fiscal yrs. 1935—1969 (earlier hearings are included with theIndependent Offices Appropriations Bill hearings from the 77th Cong., 2d Sess.(fiscal yr. 1943) and later are included with the Department of Labor Appropria-tions Bill hearings).

aThe years 1955—56, 1959—60, 1961—62, 1965—66,and 1968—69 were usedto figure the average for the period.

S

4

C' — — —

0

firm the Elman thesis.Board even before thare a much smaller frthan until then. MostCommission gave nopears to be an aspecreticence about explror exculpatory.33 The1946 and disappearsonly two out of 42 sigJ

33. See, e.g., Gerard'and, with specific referenccU.S. Atty. Gen.'s CommitiU.S. Atty. Gen.'s Cornmimission 63—65 (Monograpl


ased) could increase S

rerage probability of

hich prosecution and,le criticism of a dis-ed at the complaint-LCY, when it does dis-iowledging failure to

a complaint thatnot cast its dismissal

A dismissal in whichot established will be

the decisions of thesignificant dismissalsan important featuremany dismissals of

g may appear to con-

FIGURE 3

firm the Elman thesis. However, grudging dismissals were unknown at theBoard even before the first separation of functions in October 1942, andare a much smaller fraction of all FTC significant dismissals after 1945than until then. Most grudging dismissals are so classified because theCommission gave no reason for its action in dismissing, and this ap-pears to be an aspect of the Commission's early and much criticizedreticence about explaining the basis of its decisions, whether punitiveor exculpatory.33 The practice of "blind" dismissals begins to wane in1946 and disappears after 1952. In the three later periods in Table 10only two out of 42 significant dismissals (24 total dismissals) are grudging.

33. See, e.g., Gerard C. Henderson, The Federal Trade Commission 334—35 (1924),and, with specific reference to the Commission's failure to state the reasons for dismissals,U.S. Atty. Gen.'s Committee on Administrative Procedure, .supra note 24, at 136—37, andU.S. Atty. Gen.'s Committee on Administrative Procedure, The Federal Trade Com-mission 63—65 (Monograph No. 6, 1940).

A

A,

C,

0

B'

-NLRB UNFAIR

—I

n ti'

N

% ofContested

Caseslex (2) Dismissed

1.00 .161.21 .13

4—88 .23.29 .21

Bureau of the Budget,—1969; Hearings beforepropriations on NLRBs are included with thehe 77th Cong., 2d Sess.ent of Labor ApproPria-

and 1968—69 were used


TABLE 10FORM OF FTC DISMISSALS

SOURCES. — See Table 5, supra.a As defined in text.

b Or average.

TotalContest

DiscrimiPeriod tion Ca:

1935—36 421938 29

1946 26

1947 17

Totaib

1956 30

1969 29TotaP' 59

SOURCE. — Decision1, 8,69,72, 115, 178.

a That is, of discrimb Or average.

fair labor practice cas1947; a comparison s

Table 11 also penstages in the Board'ssubstantive law (the rmained unchanged sinAccording to Table 11cessive changes in thefunctions.

4. It should alsowhich prosecution ancequal, dismiss a smaamount of agency resc

cases. Criticism of anbringing an unmeritossuasive when the amc

34. The low rate of di:Consistent with data obtaiTable 5 or 6, from the firsvolume are .06 (significant

DISMISSAL

. GrudgingGrudging Total Dis-Dismissals missals

% of as a % as a %Total % of Un- Total Un- of All of All

Contested grudging a grudging Significant SignificantPeriod Cases Dismissals Dismissals Dismissals Dismissals

1938 60 .10 .03 .50 .71

1941 61 .05 .05 .82 .82

1943 32 .09 .06 .63 .71

1945 43 .07 .05 .73 .78Totalb 196 M8 MS 69

1946—47 70 .20 .16 .22 .27

1949—50 53 .17 .13 .18 .22

1951—52 62 .23 .18 .07 .08

1955—56 36 .28 .19 .00 .00

1959—60 58 .36 .12 .00 .00

1965 34 .29 .24 .17 .20

Totaib 313 A6 Al AS

3. Professor Elman's thesis implies that an agency in which prosecu-tion and adjudication are combined will be less reluctant to dismiss a casein which legal issues predominate than one in which factual issues pre-

dominate. Since the scope of judicial review of administrative action isbroader with respect to questions of law than with respect to questionsof facts, an agency has little to gain by distorting the applicable lawwhereas it may get away with a certain amount of tendentious fact-find-ing.

Table 11 attempts to test this implication of the Elman thesis bycomparing NLRB dismissal rates at various periods for a type of case—cases in which an employer is charged with discriminating against an em-ployee or employees because of union activities — in which factual ques-tions, primarily motive, predominate. If the Elman thesis is correct, thedismissal rate in discrimination cases should be lower than that in all Un-


GrudgingGrudging Total Dis-

Dismissals missalsasa% asa%of All of All

Significant SignificantDismissals Dismissals

.50 .71

.82 .82.63 .71.73 .78

.69 .84

.22 .27

.18 .22

.07 .08

.00 .00.00 .00.17 .20ir

ency in which prosecu-to dismiss a case

ich factual issues pre-dministrative action is;h respect to questionsng the applicable lawtendentious fact-find-

f the Elman thesis byds for a type of case—linating against an em-in which factual ques-n thesis is correct, thewer than that in all Un-

TABLE 11DISMISSAL RATE— NLRB DISCRiMINATiON CASES

Total

Period

ContestedDiscrimina-tion Cases

Dis-missals

C

in

ompleteDis-issals a

%Dismissed

%Dismissedin Entirety

1935—36 42 16 2 .38 .051938 29 23 . 8 .79 .281946 26 1 8 .42 .311947Total b

17

114

6

56

2

20

.35

A9.12.18

1956 30 14 5 .47 .171969 29 9 6 .31 .21Totalb 59 23 11 39 .19

SOURCE. — Decisions and Orders of the National Labor Relations Board, vols.1, 8,69,72, 115, 178.

a That is, of discrimination count or counts.b Or average.

fair labor practice cases prior to the separations of functions in 1942 or1947; a comparison with Table 6 shows that it is not.34

Table 11 also permits a comparison among dismissal rates at differentstages in the Board's evolution that is unaffected by changes either insubstantive law (the prohibition against employer discrimination has re-mained unchanged since the Wagner Act) or in the agency's mix of cases.According to Table lithe dismissal rate has not been affected by the suc-cessive changes in the Board's structure with respect to the separation offunctions.

4. It should also follow from the Elman thesis that an agency inwhich prosecution and adjudication are combined will, other things beingequal, dismiss a smaller fraction of major cases, so classified by theamount of agency resources consumed in their prosecution, than of minorcases. Criticism of an agency for having wasted the taxpayer's money bybringing an unmeritorious case is more apt to be forthcoming and per-suasive when the amount squandered is substantial.

34. The low rate of dismissals in the first year of the Board's operations, 1935—36, isconsistent with data obtained for all unfair labor practice cases, but not reported inTable 5 or 6, from the first volume of the Board's decisions. The dismissal rates in thatvolume are .06 (significant dismissals) and .00 (significant total dismissals).


Unfortunately other things are not equal. Although the FTC doesdismiss a higher proportion of its larger cases (the statistics were pre-sented in Table 3), the model developed in Part I of this article suggeststhat there are reasons for this that have nothing to do with the presenceor absence of bias. Table 3 can be made to bear on the present question,however, if another column is added — one showing the percentage of allcases, settled as well as litigated, that are dismissed (Table 12). It appearsthat in many periods a large fraction of the Commission's antitrustprosecutions, and hence in resource terms a large fraction of the Com-mission's entire enforcement activity, have not resulted in the entry ofremedial orders. So marked a propensity to rule in favor of the defendantis difficult to reconcile with the Elman thesis.

5. The Elman thesis would seem to imply that the members of anagency in which prosecution and adjudication are combined would be lessreluctant to dismiss a complaint that had been authorized by their prede-cessors in office than one they themselves had authorized. In the formercase they could not properly be criticized for having initiated a case thatlacked merit; in the latter case they could. The low rate of ungrudging

TABLE 12DISMISSAL RATE—FTC ANTITRUST CASESa INCLUDING SETTLED CASES

Percentage

Period Total Cases Dismissed b

1938 19 .051941 26 .351943 8 .381945 9 .22

1946—47TotaIc

11

73

.27

25

1949—50 16 .251951—52 15 .07

1955—56 32 .09

1959—60 21 .10

1965 34 .26

Totaic 118 16

SOURCE.—See Table 3, supra.a Excluding cases brought exclusively under one of the minor Robinson-Pat-

man Act amendments. See note 10, supra.

b Significant total dismissals only, as defined in text.C Or average.

dismissals disclosed 1'support thisdecided by thevery same members.members of the Corn

But an inference,'dismiss complaints olnot in fact be drawnthe proportion of giadoption of a policythan the length of sethey decide. If we igungrudging and cons.dismissal rate is no Ii

missioners' average l

Further

analyze the later peri

13 shows the percent

the Commission whocomplaint was issuedwho decided the castissued, and so onbers of theperiods. If members o

complaints but less rpercentage of dismiss;

If dismissals areor fewer commissioncmission when the cchigher in the secondstatistically significan

from the Elman thesismembers of the Comisued (the number ofthe rate of dismissal iswhen the case was decas it is where only oimember when the cot

35. In 1938 the mostonly two cases decided thaimost junior member had sat


hough the FTC doese statistics were pre-

this article suggestsdo with the presencethe present question,the percentage of all

(Table 12). It appears)mrnlSSiofl'S antitrustfraction of the Corn-

suited in the entry offavor of the defendant

at the members of anbmbined would be less

by their prede-horized. In the former

initiated a case that)W rate of ungrudging

DING SETTLED CASES

PercentageDismissed

.05

.35

.38

.22.27.25

.25

.07

.09

.10.26.16

dismissals disclosed by Table 10 for the period up to 1945 may appear tosupport this hypothesis, for it was a period in which nearly all the casesdecided by the members of the Commission had been authorized by thevery same members.35 In subsequent periods the average tenure of themembers of the Commission is much shorter.

But an inference that members of the Commission are more prone todismiss complaints of their predecessors than their own complaints ëan-not in fact be drawn from these data. As explained earlier, the decline inthe proportion of grudging dismissals appears to reflect the gradualadoption of a policy of stating reasons for dismissing a complaint ratherthan the length of service of the commissioners in relation to the casesthey decide. If we ignore, therefore, whether a dismissal is grudging orungrudging and consider only whether it is significant, we find that thedismissal rate is no higher after 1945, despite the reduction in the com-missioners' average length of service.

Further evidence is presented in Tables 13 through 15, whichanalyze the later periods in detail. The last column in each box in Table13 shows the percentage dismissed of cases in which all five members ofthe Commission who decided the case had also been members when thecomplaint was issued, cases in which four members of the Commissionwho decided the case had also been members when the complaint wasissued, and so on down to zero (i.e., none of the incumbents were mem-bers of the Commission when the complaint was issued), in variousperiods. If members of the Commission are reluctant to dismiss their owncomplaints but less reluctant to dismiss those of their predecessors thepercentage of dismissals should increase as we move down the columns.

If dismissals are grouped according to whether three or more or twoor fewer commissioners deciding the case were members of the Com-mission when the complaint was issued, the dismissal rate is indeedhigher in the second group (Table 14). The difference, however, is notstatistically significant. Moreover, contrary to the prediction derivedfrom the Elman thesis, the highest rate of dismissal is found where all fivemembers of the Commission were members when the complaint was is-sued (the number of cases, however, is too small to be significant); andthe rate of dismissal is the same where three members of the Commissionwhen the case was decided were members when the complaint was issuedas it is where only one present member of the Commission was also amember when the complaint was issued.

he minor Robinson-Pat-35. In 1938 the most junior member of the Commission had sat for three years and

only two cases decided that year had been instituted prior to his appointment. In 1941 themost junior member had sat for six years; the figure is eight years for 1943 and ten for 1945.

DIS

MIS

SA

L

° RA

TJ

m C — C —

IN

DE

CID

ING

CA

SE

WI 0 — — ' — I

I

_______________________

— II N

o.ofCornm

jssjc

Who

Were

Mem

bersU I

the

Com

plaint

Was

IsIL.I W

hen

the

Case

Was

I

— — — r'.l

I —I —.

— —

10

0

5

I,;

N I 0 00 0 0

4

I I 'I'i 3I 2I V

oc;

o 0 0 N C — .

C C CIN - 3_5

0—200

V V0 00 00'-

C — N C C

I '.0U SOU

RC

E

—T

able

13

4,— a "Ungrudging"

N C

bExcluding

mem

be.

Z

—

mission's

decision.

c Or average.

U- m T

ables

13 and

I

c.e.—

'.0 jority,

either

to dismi

— N C'l

— C C C — Oft-

senters

are

treated

sei

were

more

reluctant

t

V sors',

then

we

wouldI-

0 quently

when

the

maj

majority

voted

to ent

U mem

bers

voted

to disiE

times

when

the

major

— four

times

to enter

an

plaint.36

QV

0:

..0 V U 36.

It is of course

pos1

dissented

from

the

origina

event

his

later

vote

would

1

252

00

N

00

'1

'I)

03.

U)

0

0

U0)

E

0

0

0)

0

0

0)

0.0)

0

U)

0

0

CO

a

RICHARD A. POSNER

TABLE 14DISMISSAL a RATE AS A FUNCTION OF WHETHER COMMISSIONERS

DECIDING CASE WERE MEMBERS WHEN COMPLAINT WAS ISSUED—SUMMARY OF TABLE 13

253

No. of CommissionersWho Were Members Both Whenthe Complaint Was Issued andWhen the Case Was Decided0

All Periods

Order Dis. Total % Dis.

5 2 4 6 .674 61 15 76 .203 36 6 42 .142 30 13 43 .301 32 8 40 .200 11 5 16 .31

172 51 223 .23

3.-S 99 25 124 .200—2 73 26 99 .26

— 01 0 — N—

o — 0 'roiQo

2 0

0000 V'I —

00.0

'.0 0 0 0 oir-

C'-. 0'. r'l 00 0'.C__C

C". 0'. N 00

0 '.0 )F'.—-

0 — OIN

0 2 2

C'4 0I-

SOURCE. —Table 13, supra.a "Ungrudging" total dismissals as defined in the text.b Excluding members who dissented from or did not participate in the Com-

mission's decision.c Or average.

Tables 13 and 14 count only commissioners voting with the ma-jority, either to dismiss or to enter a remedial order. The votes of dis-senters are treated separately in Table 15. If members of the Commissionwere more reluctant to dismiss their own complaints than their predeces-sors', then we would expect old members (members both when the com-plaint was issued and when the case was decided) to dissent more fre-quently when the majority voted to dismiss the complaint than when themajority voted to enter an order. Table 15 indicates, however, that oldmembers voted to dismiss the complaint — their complaint, as it were — 13

times when the majority voted to enter a remedial order, and voted onlyfour times to enter an order when the majority voted to dismiss the com-plaint.36

36. It is of course possible for an "old" member voting against the complaint to havedissented from the original action of the Commission in issuing the complaint, in whichevent his later vote would be no evidence of open-mindedness. Unfortunately, data on vot-


ing at the complaint-issuance stage are unavailable. It should be noted, however, thatunder the Elman view the commissioner who voted against issuing the complaint in the firstplace would still feel considerable pressure to enter a cease and desist order after the trialin order to protect the agency against charges of having wasted the taxpayer's money and inorder to prevent the demoralization of the staff.

LU

0

0

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LU

00z

LUCd,

LU

U

F-.

zU-0

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>LU

L)

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TABLE 15VOTES OF DISSENTING FTC COMMISSIONERS— 1946-65

I.

Nature of Vote

For Issuance of For Dismissal ofRemedial Order Complaint

By By By ByCommissioner Commissioner Commissioner Commissioner

Who Was Who Was Not Who Was Who Was NotMember Member Member Member

When Corn- When Corn- When Corn- When Com-plaint Was plaint Was plaint Was plaint Was

Period Number Issued Issued Issued Issued

1946—47 3 3 — — —

1949—50 — — — — —

1951—52 3 — — 3 —

1955—56 9 — — 9 —

1959—60 — — — — —

1965

Total12

2714 6 13 4

SouRcE.—See Table 13, supra.

6. If the combination of prosecution and adjudication makes anagency reluctant to dismiss unmeritorious complaints and thus prone toenter unjustified orders, one would expect the orders of such an agencyto be reversed more frequently on judicial review than the orders of anagency in which the functions are separated. Table 16 seeks to test thishypothesis by comparing, for a few randomly selected periods, the re-suits of judicial review of FTC cease and desist orders and orders inNLRB unfair labor practice cases. Employer discrimination cases arereported separately to facilitate comparison between the preseparatedand the separated Board.

Table 16 shows not only that the FTC has fared consistently betteron judicial review than the Board, but also (and more pertinently, sinceaccording to our model many factors apart from bias must influence an

D

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1946—65

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255


agency's p On judicial review) that the Board's record has actuallyworsened since separation, both generally and with respect to discrimina-tion cases alone. However, Table 16 also reveals secular changes in theoutcome of judicial review of agency action that cannot be ascribed tothe combination or separation of functions and that may conceal theeffect of separation.

7. Finally, an agency in which prosecution and adjudication arecombined is, under the Elman thesis, one much concerned about beingcriticized for dismissing complaints but relatively unconcerned aboutits record on judicial review. (Were it greatly concerned about its courtrecord 'it would dismiss all doubtful cases in order to minimize the dangerof being reversed by a reviewing court.) This model would be more per-suasive were there evidence that an agency like the FTC or NLRB wasjudged, by those with power over the agency, more by its internal battingaverage than by its success or failure in the courts. Some places to lookfor such evidence are the agencies' annual reports, where the agencyboasts of its successful performance, presumably using criteria of successpersuasive to its intended audience; the agencies' annual appropriationhearings before the House and Senate appropriation subcommittees; andappraisals of the agencies' performance by critics or supporters. A searchof these sources reveals, however, many more references to the agency'srecord on judicial review than to the rate at which either the FTC or theNLRB dismisses complaints.

In one respect, though, dismissals clearly could affect an agency'sperformance. Congress, the agencies, and their critics all seem greatlyconcerned with the size of the agency's work load as measured by suchquantitative indicia as the number of charges filed with the agency, thenumber of complaints issued, and the number of decisions. The routineargument advanced for a larger appropriation is that the agency's workload has grown faster than its budget, and an increase in work load isdifficult to demonstrate unless some quantitative change can be pointedto. The routine criticism of an agency is that its budget is excessive inrelation to its present quantity of work. The effect of a dismissal may beto compel the agency's staff, in similar future cases, to investigate morethoroughly before recommending a complaint and to present more evi-dence of violation at trial — in short, to expend additional resources in theprosecution of the case. This will reduce the number of cases it can bringwith reasonable prospect of success.

Such a process can be seen at work in the FTC in the middle and late1960s. As Table 3 shows, in 1965 the Commission dismissed 60 per centof its contested antitrust cases. Many of these decisions establishedhigher standards for proving violations of law than had previously been

applied by the Comntion's Commission tcCommission for a pinumber of investigat:criteria of activity.37of the reasons for thcchange of policy, ref..direction of more

This history rnwhether or not to disiwould increase the dsignificant, in appraimission in 1965 wasmissing major cases'

D. WI-tv WERE PROTHE BOARD AND N

The results of our inand adjudication bia:finitive, suggest thateffected a limited septized the separation, ahow the FTC has es

The congression;Act developed no fircombination of funccombination was thoithe combination of ficaped sustained conti

The probable ex1in the merits of the is:community to the

37. SeeABAComm'r38. Which the ABA

Statistical Study of Antitri39. See 2 Kenneth C40. See id. at § 13.0541. This opposition ü

Wagner Act to Taft-Hartle91(1950).

RICHARD A. POSNER 2575ENCIES

ecord has actuallyspect to discrimina-

changes in thennot be ascribed tott may conceal the

adjudication areicerned about beingunconcerned about

med about its courtminimize the dangerwould be more per-FTC or NLRB was

py its internal battingplaces to look

s, where the agencycriteria of success

knnual appropriation

Isubcommittees; and

kupporters. A searchto the agency'sthe the

Id affect an agency'slics all seem greatlys measured by such

Lith the agency, theThe routine

the agency's workease in work load islange can be pointeddget is excessive ina dismissal may beto investigate more

o present more evi-nal resources in theof cases it can bring

the middle and lateismissed 60 per centecisioris establishedhad previously been

applied by the Commission. By 1969 we find the American Bar Associa-tion's Commission to Study the Federal Trade Commission blasting theCommission for a precipitous decline in its work load as measured bynumber of investigations, decisions, and other conventional quantitativecriteria of activity.37 The causation is complex but it would seem that oneof the reasons for the Commission's decline38 in number of cases was itschange of policy, reflected in the dismissals of the middle 1960s, in thedirection of more exacting standards of proof.

This history may influence the Commission's future decisionswhether or not to dismiss complaints, in circumstances where a dismissalwould increase the difficulty of proving a violation. But it is at least assignificant, in appraising the Elman thesis, to observe that the Com-mission in 1965 was apparently not deterred by such a prospect from dis-missing major cases with great frequency.

D. WHY WERE PROSECUTION AND ADJUDICATION SEPARATED ATTHE BOARD AND NOT AT THE

The results of our inquiry into whether the combination of prosecutionand adjudication biases an agency's adjudication, although hardly de-finitive, suggest that it does not. If so, one may wonder why the Boardeffected a limited separation in 1942, why Congress extended and formal-ized the separation, apparently at some cost in efficiency,39 in 1947, andhow the FTC has escaped serious pressure for some form of separation.

The congressional hearings preceding enactment of the Taft-HartleyAct developed no firm evidence of bias in adjudication traceable to thecombination of functions.4° And if separation was legislated becausecombination was thought inherently unfair, it is hard to understand whythe combination of functions in the FTC has not only persisted but es-caped sustained controversy.

The probable explanation for separation at the Labor Board lies notin the merits of the issue but in its politics. The opposition of the businesscommunity to the Wagner Act and its enforcing agency4' was better or-

37. See ABA Comm'n to Study the Federal Trade Commission, supra note 9, at 16—26.38. Which the ABA Commission, however, overstated. See Richard A. Posner, A

Statistical Study of Antitrust Enforcement, supra note 10, at 370.39. See 2 Kenneth Cuip Davis, Administrative Law Treatise § 13.05, pp. 206—1 1.40. See id. at § 13.05, pp. 204—5.41. This opposition is described in Harry A. Millis & Emily Clark Brown, From the

Wagner Act to Taft-Hartley—A Study of National Labor Policy and Labor Relations 381—91(1950).


ganized, more vocal, and more tenacious than the business community'sopposition to the FTC and the statutes it enforces has ever been. Thecosts imposed by the Board on business were probably greater than thoseimposed by the FTC—this might explain why greater resources weremarshaled against the Board than against the Commission. Probably, too,it is easier to organize employers as an effective political pressure groupthan the diffuse victims of FTC prosecution. At all events, within 12years of the passage of the Wagner Act the opponents of that Act and ofthe Board were able, in the Taft-Hartley Act, to effect a major overhaul ofthe law. Charges of unfairness are a conventional refrain in the litany ofpolitical controversy and once the Wagner Act was up for a thoroughoverhaul it was relatively easy to amend the provisions of the Act relatingto the structure of enforcement as well as the substantive law provisions;

has never been a comparable overhaul of the Federal Trade Corn-Act. That the separation of functions apparently imposed at least

short-term costs in the form of lowered efficiency due to problems of co-ordination between the Board and the General Counsel provides a suffi-cient explanation why the Board's opponents should have wanted tobring about a separation of the functions regardless of the actual meritsof such a step.

What the last point may suggest is that administrative regulation canperhaps best be understood when elements of the effective-political-group and rational-utility-maximizing models of administrative agencybehavior are combined.

APPENDIX

PROOF THAT THE CONDITION FOR LITIGATIONCANNOT BE SATISFIED IF S = S', k> 1, AND r

so

ec+

e'c'c+c, c1+c

—e')+e'.

Substituting this equation into inequality (15), the condition for litigation becomes

— e') s'e' rc' /1 — 1+e'>—I—I 1+2——.s Ls'\\Q/ k

Since s = s', this can be simplified to

Subtracting the first ternwe have

Since k > 1, the right skdition for litigation cann

RATIo OF SIGNIFICAN:OF JUSTICE ANTI:

Penin WICase

Agency Brou

AntitrustDivision 1935-

1940.1945-1950.1955.1960-Total

FTC 1935-1940-194 5-

1950-1955-1960.Total

S0URCE.—Richard iment, 13 J. Law & Econ.(Table 12).

a Excluding cases brcamendments. See note 1(

b Or average.


— e') — e') / I

\ k

Subtracting the first term on the left-hand side of the inequality from both sides,we have

e' > e'

Since k> 1, the right side must exceed the left for any value of e', and the con-dition for litigation cannot be satisfied.

TABLE AlRATIO OF SIGNIFICANT DSMISSALS TO REMEDIAL ORDERS, DEPARTMENT

OF JUSTICE ANTITRUST DIVISION AND FTC ANTITRUST a CASES

(Contested Cases Only)

Period

Agency

in WhichCase WasBrought

RemedialOrder

Dis-missal Total

% Dis-missed

Antitrust .

Division 1935—391940—441945—491950—541955—591960—64Totalb

15

51

26385863

251

1250282218

31

161

2710154607694

412

.44

.50

.52

.37

.24.33

.39

FTC 1935—391940—441945—49

1950—541955—59

1960—64

504820143523

190

362312

10

2214

117

867132245737

307

.42.32.38.42.39.38

.38

business community'ss has ever been. The

ably greater than those-eater resources werenission. Probably, too,olitical pressure groupall events, within 12

ents of that Act and ofect a major overhaul ofrefrain in the litany of'as up for a thorough

ions of the Act relatingantive law provisions;

e Federal Trade Corn-rently imposed at least

to problems of co-unsel provides a suffi-

have wanted toss of the actual merits

strative regulation can

the effective-political-administrative agency

1

)fl for litigation becomes

2——k

SOURCE. — Richard A. Posner, A Statistical Study of Antitrust Enforce-ment, 13 J. Law & Econ. 365, 376 (Table 6), 379 (Table 9), 381 (Table 11), 382(Table 12).

a Excluding cases brought exclusively under the minor Robinson-Patman Actamendments. See note 10, supra.

b Or average.

U,

=ova'

a'ooE

5) a)

a) U,.—

o

C,

0a)


TABLE A2NLRB EMPLOYER UNFAIR LABOR PRACTICE CASES CLOSED AT

PRECOMPLAINT STAGE

(I,

a'C,,

C,,

CCa

C-5)

I-C

% With-drawn or

Dismissed —Excluding % of

% With- Charges ChargesCases drawn or Filed by Filed by

Period Pending Dismissed individuals Individuals

1935—36 865 .32 N.A. N.A.1936—37 3,124 .21 N.A. N.A.

8,213 .31 .29 .081938—39 7,132 .25 .24 .091939—40 6,836 .33 .30 .111940—41 6,981 .30 .28 .09

Total a 33,151 .29 .28 .09"

1943—44 3,896 .42 N.A. .09

1944—45 3,633 .42 N.A. .09

1945—46 5,126 .40 N.A. .06

1946—47 6,457 .45 N.A. .06

Total a 19,112 .42. — .07

1948—49 5,543 .43 N.A. .38

1949—50 6,635 .43 N.A. .331950—51 8,504 .35 N.A. .331951—52 6,676 .45 N.A. .27Total a 27,358 .41 — .33

1955—56 5,326 .57 N.A. .361959—60 11,121 .54 N.A. .461961—62 12,186 .50 N.A. .38

1965—66 15,632 .44 N.A. .29

1968—69 17,559 .47 N.A. .34

Total a 61,824 A9 — .36

Cd,

Cd,

UU

a'.

a.U,

C

CU,a,

a's)- C,,

C

0I-

SouRcE.—See Table 8, supra.a Or average."Excluding 1935—1937.

——

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l0 tn >

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t'.)

UJ

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0 0

0 0

0 —

00

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TA

BLE

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DIS

POSI

TIO

N O

F FT

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ASE

S

Ord

er a

ndD

ism

issa

ls

% O

fC

onte

sted

% o

f A

llSt

ipu-

Con

-%

Con

-D

is-

% D

is-

Cas

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ispo

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riod

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tions

t)T

otal

test

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sted

mis

sed

Cm

isse

dD

ism

isse

dD

ism

isse

d•

•.0

1519

3831

314

860

.41

7.0

5.1

219

4120

417

961

.34

17.0

9.2

8.0

4419

4317

362

32.5

27

.11

.22

.030

1945

188

9443

.46

9.1

0.2

1.0

3219

46—

47T

otal

ci

202

1,08

015

6

639

70 266

.45

.42

15 55

.10

.09

.21

.21

.042

.032

1949

—50

164

106

53.5

09

.08

.17

.033

1951

—52

151

154

62.4

012

.08

.19

.039

1955

—56

158

180

36.2

07

.04

.19

.021

1959

—60

104

352

58.1

67

.02

.12

.015

1965

Total d

— 577

136

928

34 243

.25

.26

10 45.0

7.0

5.2

9.1

9—

.026

e

S0U

RC

E.—

See

Tab

le 5

, sup

ra.

°A

ll12

mon

ths

exce

pt 1

938

(7 m

onth

s),

bTeI

.mex

plai

ned

inno

te31

, sup

ra.

c"S

igni

fican

t"to

tal d

ism

issa

ls, a

s de

fine

d in

text

.d

Or

aver

age.

Exc

ludi

ng 1

965.

1941

(5

mon

ths)

, 194

3 (6

mon

ths)

, 194

5 (6

mon

ths)

and

194

6-47

(18

mon

ths)

.

BECKER, Gary S., LANDES, William Gary Becker-Essays in the Economics of Crime and Punishment

Documents

e t o t i

n o r e s e

e s e c r e t

o n i t o

c r e s e

t r s e c r e t

t i o n i n t h e r

n e c o n o