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The Paradox Of Punishment: Reflections On The Economics Of Criminal Justice
 3030316947,  9783030316945,  9783030316952

Table of contents :
Preface......Page 6
References......Page 10
Contents......Page 11
List of Figures......Page 13
List of Tables......Page 15
Chapter 1: Prologue: The Paradox of Punishment......Page 16
The Crime-and-Punishment Game......Page 19
Overview of the Book......Page 32
References......Page 35
Part I: Competing Economic Theories of Crime......Page 36
Chapter 2: The Social Cost of Crime: Deterrence......Page 37
The Rational Offender Assumption......Page 39
The Optimal Enforcement Policy......Page 42
Theory and Practice......Page 52
References......Page 57
Chapter 3: Crime As Exchange: Retribution......Page 60
The Competitive Market Paradigm......Page 61
Probability Scaling......Page 64
Moral Costs......Page 68
The Proportionality Norm......Page 69
Differences in Offenders......Page 74
Distinguishing Crimes and Torts......Page 76
References......Page 83
Part II: The Institutional Structure of Punishment......Page 85
Chapter 4: Sentencing Guidelines and Judicial Discretion: Balancing Deterrence and Retribution......Page 86
Sentencing Guidelines......Page 88
Determining the Optimal Degree of Judicial Discretion: Theory......Page 92
Some Evidence......Page 102
References......Page 104
Chapter 5: Plea Bargaining: Negotiated Justice......Page 107
The Operation of the Procedural System......Page 108
Criminal Adjudication and Legal Error......Page 110
An Economic Approach to Plea Bargaining......Page 114
Implications of Plea Bargaining for Corrective Justice and Deterrence......Page 123
References......Page 126
Part III: Other Objectives of Punishment......Page 128
Chapter 6: Repeat Offenders: Marginal Deterrence and Redemption......Page 129
Explaining Escalating Penalties......Page 131
Marginal Deterrence and the Parable of the Prodigal Son......Page 134
A Model of Repeat Offenses and Marginal Deterrence......Page 135
Enforcement by Religious Belief......Page 144
Choosing the Optimal Punishment Regime......Page 148
Expungement......Page 152
References......Page 154
Chapter 7: Individual Versus Collective Responsibility: It Takes a Village......Page 157
Some Examples of Collective Responsibility......Page 158
The Optimal Choice Between Individual and Group Punishment......Page 163
Other Considerations......Page 169
References......Page 171
Chapter 8: The Limits of Punishment: Of Angels and Bad Men......Page 173
The Expressive Function of Law......Page 174
The Emergence of Law: Are Religion and Law Substitutes or Complements?......Page 177
The Optimal Scope of Law......Page 186
The Impact of Morality on the Scope of Law......Page 195
References......Page 203
Part IV: Conclusion......Page 206
Chapter 9: Epilogue: What Have We Learned?......Page 207
Summary of Conclusions......Page 211
References......Page 218
Chapter 2......Page 220
Chapter 4......Page 223
Chapter 7......Page 226
Chapter 8......Page 229
References......Page 232
Index......Page 233

Citation preview

Thomas J. Miceli

The Paradox of Punishment Reflections on the Economics of Criminal Justice

The Paradox of Punishment

Thomas J. Miceli

The Paradox of Punishment Reflections on the Economics of Criminal Justice

Thomas J. Miceli Department of Economics University of Connecticut Storrs Mansfield, CT, USA

ISBN 978-3-030-31694-5    ISBN 978-3-030-31695-2 (eBook) https://doi.org/10.1007/978-3-030-31695-2 © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To my mentor and friend, Richie Adelstein, who inspired me to follow the road less-traveled (and it has made all the difference).

Preface

This book explores the insights that can be gained by looking at the criminal justice system from an economic point of view. Such a perspective, of course, is not new; economists have been thinking about crime and punishment at least since the work of Montesquieu (1748), Beccaria (1764), and Bentham (1780). However, the subject was strangely neglected by economists for 200 years, until finally being revived by Gary Becker in his classic article on the economics of crime and punishment (Becker 1968). Now, as we embark on the second half-century since the publication of that path-breaking work, it would seem to be an opportune moment to assess its influence on both the scholarly literature and the practice of law enforcement. There is no dispute that Becker’s model has had a profound effect on the way economists think about criminal law. Indeed, it has begotten a massive literature that has culminated in a highly polished theory of the optimal structure of law enforcement. Perhaps because Becker’s objective was avowedly normative, however, the resulting insights have been somewhat less successful in describing the actual practice of criminal justice. Although the theory broadly agrees with the observation that greater efforts are devoted to apprehending more dangerous offenders, and more egregious crimes are met with harsher punishments, its more specific prescriptions regarding, for example, how resources should be allocated between apprehension and punishment, and what form those punishments should optimally take, seem to depart rather dramatically from existing policies. The principal reasons for this divergence are likely based on differing views of the purpose of the criminal justice system, and p ­ erhaps on the meaning of “justice” itself, thus raising philosophical issues that are somevii

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what beyond the scope of this book. But they also likely reflect a difference in how economists think about crime in general as compared to ordinary views, a factor that is relevant for the arguments to be developed herein. As an example of these differing viewpoints, consider one notable area where economic theory actually aligns quite well with contemporary views on criminal justice policy—namely, that the United States over-relies on imprisonment as the predominant form of punishment. The reasons for this criticism, however, are very different: whereas economists emphasize the excessive cost of prison compared to alternative modes of punishment, most other critics point to racial disparities in incarceration rates and the social stigma, resulting in impaired employment opportunities, that imprisonment creates. Of course, these are not mutually exclusive arguments, but they highlight the varying perspectives that the commentators take with respect to the objectives of criminal justice policy. Neither view is more correct; they are just different. One goal of this book, in fact, is to use economic theory to examine how alternative objectives with respect to criminal justice can best be achieved, and how they manifest themselves in different policy prescriptions. I want to emphasize at the outset that this book is not intended to be a survey of the economics-of-crime literature. It is instead an economic analysis of the institutional structure and function of the criminal justice system, how its policies are formulated, and how they affect behavior. But it goes beyond an examination of specific policies to address the question of how law influences behavior in a broader sense. In addition to the threat of criminal sanctions, law inculcates principles of acceptable behavior among citizens by asserting that certain acts are “against the law.” This “expressive function” of law, as it is sometimes called, can influence behavior to the extent that at least some people in society are receptive to such a message, whether as a result of religious indoctrination, parental guidance, or some other source of moral instruction. For these people, the moral content of law has more than mere symbolic value, and consequently, it can expand the scope of traditional law enforcement while lowering its cost. Another goal of the book is therefore to use economic theory to assess this dualistic function of law by specifically recognizing how its policies can both internalize an ethic of obedience to the law among some people irrespective of its consequences, while simultaneously threatening to punish those who only respond to external incentives. As an example, we will examine how the possibility of redemption, a concept borrowed from religion, intertwines with law. Does it, for exam-

 PREFACE 

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ple, lower the cost of crime by offering leniency for first-time offenders as an enticement to reform their ways, or does it increase crime by making first offenses cheaper? We will also ask whether individual responsibility, which is the moral basis of criminal punishment under a retributive theory, and a necessary component under a deterrence theory, should be a pre-­ requisite for punishment. Although most people take this linkage for granted, in ancient times the notion of collective responsibility was often the basis for punishing someone other than the guilty party, such as members of the guilty party’s family or community. Is there ever a justification for this sort of group punishment, or was it simply a product of a less civilized era? And if the latter, why do some vestiges of it persist in modern law? Finally, we will ask how the moral content of law influences the optimal structure of its punitive component. Law and morality co-exist as regulators of behavior in most societies, and so we might ask whether societies that are more religious tend to have more or less secular law. In other words, does traditional law enforcement act as a substitute for morality, or is it a complement to it? Methodologically, the book is aimed at a wide and inter-disciplinary audience, and so the arguments are for the most part developed in a non-­ technical way. This does not mean that they are not rigorous, only that they are largely non-mathematical. I have, however, made use of some simple game theory and graphical analysis as an aid in illustrating certain points. I do not expect that these methods will require a lot of heavy lifting on the part of readers, but in any case they are accompanied by intuitive explanations in purely verbal terms aimed at making the concepts clear. For those readers who are interested in more technical details, proofs of the key results are provided in mathematical appendices to the relevant chapters. The arguments developed in this book are the culmination of many years of thinking about criminal law from an economic perspective. I have drawn upon previously published research of my own and many other scholars, but I have endeavored to offer a fresh perspective on these issues by drawing together various ideas and concepts within a coherent framework. I would like to acknowledge here those who have had the most influence on my thinking about these matters. The first is Richard Adelstein, a distinguished scholar, who first introduced me to the field of law and economics and who planted the seeds that gave rise to many of the ideas contained herein. When I took Richie’s law-and-economics course many years ago, I was an uninspired undergraduate economics major, but that class exposed me to a new and exciting way of thinking about eco-

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nomics, and especially its power to illuminate ideas outside of the conventional market setting. As powerful as these new ideas were on their own, however, in retrospect I cannot separate their influence on me from Richie’s passionate and erudite way of presenting them. My debt to him for inspiring me to pursue a career in academics, and then to choose law and economics as my primary area of study, is incalculable. It has been one of the great rewards of my professional life to have been able to collaborate with Richie in writing about some of these topics, and one of the rewards of my personal life to be able to call him my friend. I have also benefited from several other productive collaborations throughout my career. The most important of these has been with my colleague, Kathleen Segerson. Kathy and I came to the field of law and economics from different directions, but we found common interests and a common philosophy about what we could learn by applying economic reasoning to interesting policy questions, principally in the areas of tort law, property law, and criminal law. I have learned much from her careful and penetrating way of thinking about economic problems. Three other long-time co-authors, C. F. Sirmans, Metin Cos¸ gel, and Matthew Baker, have also been extremely influential in my thinking about a variety of topics at the intersection of law, economics, and religion. Several people contributed directly to the completion of this book. Attorney Steven Varney read and offered comments on an early draft of the entire manuscript, as did three anonymous reviewers. I thank them all for their extremely useful inputs. Elizabeth Graber at Palgrave Macmillan expressed enthusiasm for this project when it was merely a vague idea, and along with her assistant, Sophia Siegler, ably shepherded the manuscript through the production process. My sincere thanks go to both of them. I acknowledge the hospitality of the faculty and staff at the University of Connecticut School of Law, where I completed the first draft of this book during a sabbatical leave. The setting was both welcoming and intellectually stimulating. I also want to thank Stanford University Press for granting me permission to use Fig. 5.2, which originally appeared in the most recent edition of my undergraduate law-and-economics textbook (Miceli 2017). Finally, and most importantly, I want to acknowledge the enduring love and support of my family—my wife Ana Maria and my sons Tommy and Nick—without which I would not have had the energy or will to pursue this (or any other) project. Storrs Mansfield, CT, USA Summer 2019

Thomas J. Miceli

 PREFACE 

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References Beccaria, Cesare. 1764 [1986]. On Crimes and Punishments. Indianapolis: Hackett Publishing Company. Becker, Gary. 1968. Crime and Punishment: An Economic Approach. Journal of Political Economy 76: 169–217. Bentham, Jeremy. 1780 [1970]. An Introduction to the Principles of Morals and Legislation. New York: Oxford University Press. Miceli, Thomas. 2017. The Economic Approach to Law. 3rd ed. Stanford: Stanford University Press. Montesquieu, Charles-Louis. 1748 [1977]. The Spirit of Law. Berkeley: University of California Press.

Contents

1 Prologue: The Paradox of Punishment  1 Part I Competing Economic Theories of Crime  21 2 The Social Cost of Crime: Deterrence 23 3 Crime As Exchange: Retribution 47 Part II The Institutional Structure of Punishment  73 4 Sentencing Guidelines and Judicial Discretion: Balancing Deterrence and Retribution 75 5 Plea Bargaining: Negotiated Justice 97

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Contents

Part III Other Objectives of Punishment 119 6 Repeat Offenders: Marginal Deterrence and Redemption121 7 Individual Versus Collective Responsibility: It Takes a Village149 8 The Limits of Punishment: Of Angels and Bad Men165 Part IV Conclusion 199 9 Epilogue: What Have We Learned?201 Appendix215 Index229

List of Figures

Fig. 1.1 Fig. 1.2 Fig. 1.3 Fig. 2.1 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 5.1

Sequential-move game in which the enforcer moves first. (Source: Author’s creation. Note: The equilibrium is indicated by the arrow at the bottom) 9 Sequential-move game in which the offender moves first. (Source: Author’s creation. Note: The equilibrium is indicated by the arrow at the bottom) 11 Game tree with payoffs reflecting general deterrence. (Source: Author’s creation. Note: The equilibrium is indicated by the arrow at the bottom) 14 Iso-crime line and the optimal probability of apprehension given f = A. (Source: Author’s creation) 36 Determination of equilibrium in a competitive market. (Source: Author’s creation) 49 Underdeterrence as a result of less than certain apprehension of offenders. (Source: Author’s creation) 54 Impact of varying the probability of apprehension when the fine is maximal. (Source: Author’s creation) 60 Fairness functions and optimal ex post punishments for two offender types. (Source: Author’s creation based on Miceli 2008) 84 Optimal ex post sentences under binding sentencing guidelines (s  0) when offenders’ gains do not count in welfare. (Source: Author’s creation) Crime rate (crimes per person) in the United States, 1960–2014. (Source: FBI statistics)

108 129 133 137 176 181 186 191 193 208

List of Tables

Table 1.1 Payoff matrix for the enforcement game Table 5.1 Criminal convictions by guilty plea, by offense (U.S. District Courts, 2015) Table 5.2 Conviction rates and expected sentences for various crimes (U.S. District Courts, 2015) Table 8.1 Payoffs for the prisoners’ dilemma game

6 105 108 169

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CHAPTER 1

Prologue: The Paradox of Punishment

What is the purpose of criminal punishment? As a first approximation, the answer seems straightforward: namely, to make those convicted of crimes pay for the harm they have done to their victims, and concomitantly to discourage others from committing the same harmful acts in the future. These twin rationales, which we might loosely call corrective justice (or retribution), and deterrence, respectively, would seem to liken punishment to a price and, by extension, criminal acts to economic exchanges, which is in fact the perspective that forms the foundation for the economic approach to crime. According to this paradigm, party A receives (or takes) something of value from party B, and A is then required (by the forceful intervention of the state) to pay the cost of the thing that he has taken. In an exchange of this sort, the price serves both to deter some transactions (those for which the gain perceived by A is less than the price he will have to pay), and to allow others to go forward (those for which the reverse is true). In the latter case, the price compensates society (and party B indirectly) for loss of the good in question. When framing a criminal act in this way, however, the “price” analogy will seem to many to have been stretched a bit too far because, unlike a true market exchange, a crime is by its very nature non-consensual; that is, the victim of a crime, in contrast to the supplier of a good or service, is not a legally willing participant in the “transaction.” For this reason, the punishment-­as-price metaphor, as I will call it, would seem to “legitimize”

© The Author(s) 2019 T. J. Miceli, The Paradox of Punishment, https://doi.org/10.1007/978-3-030-31695-2_1

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the criminal act, which is clearly not consistent with the popular c­ onception of the role of criminal punishment. Indeed, for most people punishment is specifically aimed at de-legitimizing the criminal act as a way of discouraging it altogether, or at least of expressing society’s strong disapproval of it. In this view, it would seem to be more appropriate to characterize criminal punishment as a penalty rather than as a price, perhaps reflecting a primitive urge for vengeance or retaliation rather than serving as compensation. The preceding discussion raises the question of what we can learn about the criminal justice system by viewing it from an economic perspective, which clearly has as its core the idea of “punishment-as-price.” Indeed, one of the themes of this book will be to examine how far this metaphor can carry us, both in terms of thinking about how criminal justice policy is actually implemented, and in revealing what the goals are that society is trying to pursue by this mechanism. A necessary first step in this exercise is to think about the justifications that are most commonly offered for imposing criminal punishment. These include the two already mentioned, deterrence and retribution, to which we must also add rehabilitation and incapacitation.1 The economic approach to punishment places a priority on deterrence, but we shall argue that an economic perspective on the other functions can be offered as well. In addition, we will see that the various rationales are not mutually exclusive categories in the sense that, in different circumstances, criminal punishment can be justified as pursuing all or a subset of these objectives. In other words, the economic approach to crime need not be one-­dimensional but can accommodate a multi-faceted approach very much in the spirit of Hart (1982, p. 3). As noted, the economic view of criminal punishment likens crime to a market transaction between the offender and a victim, notwithstanding the troubling recognition that the crime victim is an unwilling participant. Still, it is useful to think of the threatened punishment as sending a signal to would-be offenders of the cost of contemplated acts with the belief that it can thereby serve as an optimal deterrent. It is important to recognize at the outset, however, that optimal deterrence does not mean complete deterrence. Rather, it means that some acts will be discouraged because the price exceeds the offender’s gain, while others will be committed because the reverse is true. In the latter case, the offender commits the act and then pays the price in the same way that a buyer pays for the goods or 1

 See, for example, Hart (1982, Chap. 1), and Shavell (2004, Chaps. 20–24).

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services he or she obtains in a market transaction. In a true market setting, the result of a completed transaction is that the buyer obtains a positive net benefit (the consumer surplus), while the seller is fully reimbursed for his or her costs, possibly with some profit (producer surplus) leftover. In theory, this same logic applies to a criminal transaction. However, in contrast to the market setting, the “price” of a crime is not assessed by the seller (victim), nor is it directly “paid” to him or her. Rather, it is set and collected by the government, ostensibly acting as an agent of the victim and of society in general. In addition, the price is not a mere transfer payment from the buyer to the seller, as is true of a market price, because it is costly to impose, even if in the form of a monetary fine, precisely because the offender does not willingly pay it but must be coerced into doing so. And if punishment is prison, it is also costly to carry it out. Thus, the punishment process involves the expenditure of resources, first to apprehend the offender and then to establish his or her guilt and possibly to impose punishment (depending on its form), all of which involve very costly procedures. And then, once an offender is convicted, the assessed “payment” is not transferred to the victim as compensation for the harm he or she has incurred (as would be true of a market price). This is necessarily true when the payment takes a non-monetary form, but even when punishment is a fine, the revenue is not handed over to victims.2 At most, therefore, the latter may derive some indirect benefit or satisfaction from the knowledge that the offender was caught and punished. Whether or not this provides sufficient “compensation” for the harm the victim has suffered is dubious—probably it depends on the form and magnitude of the punishment. Though significant, these various departures of a “criminal transaction” from an ordinary market transaction do not, I will argue, detract from the insights that can be gained by maintaining the punishment-as-price metaphor, at least as regards the role of punishment as a deterrent. As long as the anticipated punishment accurately reflects the harm of a criminal act to would-be perpetrators, the latter, assuming they are acting rationally, will only commit “efficient crimes,” defined to be those for which the benefit exceeds the perceived cost. This is the basis of optimal deterrence as embodied in the economic theory of crime, as will be elaborated on in the next chapter. 2  Crime victims sometimes can, however, seek compensation for harm through the tort system—see Shavell (2004, Chap. 8).

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As for the enforcement of the criminal penalties, an implicit assumption in the economic approach to crime is that the relevant governmental authority (variously embodied by the legislature, the police, prosecutors, and courts) stands ready to impose the punishment once an offender commits the illegal act. Another theme of this book will be that this is not always a reasonable assumption, precisely because the required processes are costly, and because they involve various decision makers operating at different points in the punishment process and with different and possibly conflicting objectives. Before providing an illustration of this last point, it is worth noting why no such concerns arise in a true market setting. It is principally because the seller of the good or service, as a willing participant in the transaction, will not part with the demanded item or provide the requested service until payment has either been tendered or credibly promised by the buyer. Indeed, in most ordinary transactions, the exchange of goods or services for payment happens instantaneously. In the criminal context, in contrast, we have noted that the “seller” (victim) is neither a willing participant nor the ultimate recipient of the offender’s “payment.” Instead, the government both assesses and collects the punishment from the offender after the act has been committed, and the process of doing so is costly. In the remainder of this chapter, we demonstrate, in a very simple law-­ enforcement “game,” the consequences of this difference between criminal and market transactions as it relates to the potential credibility problem with respect to the imposition of punishment after the fact. Although highly stylized, the example will set the stage for the examination of more realistic enforcement regimes in later chapters. The point here is simply to illustrate the fundamental nature of the problem, which I will term the “paradox of punishment.”

The Crime-and-Punishment Game Consider a simple game that depicts the interaction between a potential criminal offender and a third-party enforcer (the government). Suppose that the offender expects to derive a monetary gain of $150 from committing the act in question. Further, suppose that act is deemed to be a crime precisely because it is socially undesirable in the sense that it imposes a cost on society of $200. (For purposes of the example, the particular nature of the crime and the identity of the victim or victims are immaterial.) Let the dollar cost to the offender of the threatened sanction, whether in the form

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of a fine or imprisonment, be s, so that he will only commit the crime if $150 > s. (We will assume that when indifferent, the offender refrains from committing the act.) Let us also suppose that the administrative cost of imposing s is just s, the same as the cost borne by the offender. This cost includes the costs of apprehension and adjudication of guilt, and, in the case of imprisonment, the cost of detention before and after conviction. Thus, any sanction s  −200/(1 + r), or that r  p ( f + wt ) .





(2.1)

We assume that the gain, g, varies across potential offenders, reflecting different criminal opportunities relative to an individual’s best alternative (legal) activity. Thus, among those individuals who would consider committing crimes, condition (2.1) will hold for some, and not hold for others. Aggregating across the number of potential offenders for whom the condition does hold yields the overall crime rate, R(p,f,t), which we write as a function of the three policy levers that the government can control: the probability of conviction, the fine, and the prison term.

6

 See, for example, the survey by Levitt and Miles (2007).

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Now observe that because the expected punishment expression on the right-hand side of (2.1) is increasing in all of these policy variables, the government can reduce the crime rate at the margin by raising any one of them. In other words, if the marginal offender finds that g > p0(f0 + wt0) for some initial combination of variables (p0, f0, t0), but the government then raises the fine, say, to f1 > f0 such that g  h—that is, for which the gain to the offender exceeds the harm to society—are efficient and should be allowed. Note that this condition allows the possibility that for some acts, h is so large that it exceeds g for all offenders, in which case no instances of this particular act can be efficient. As Stigler’s criticism of the Becker model implied, this would seem applicable to certain violent crimes like murder or rape, but it would not be true of speeding or other potentially beneficial but harmful acts. In any case, efficiency is assured if the expected fine is set at a level that assures that would-be offenders are confronted with the full cost of their acts—that is, if pf = h. In other words, the expected fine effectively becomes an externality (Pigovian) tax. Solving this equation for f yields the optimal fine:

f ∗ = h / p.



(2.2)

According to this formula, convicted offenders should be assessed a fine equal to the harm caused by their act, appropriately adjusted to reflect the 9  This includes the direct cost to the victim plus the broader costs felt by sympathizers with the victim and anyone else who suffers moral outrage. The measurement of the cost of crime will be discussed in greater detail in Chap. 3.

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uncertain probability of apprehension. As a result, those offenders who are actually convicted end up paying more than the harm that their crime actually caused given p  1). In essence, those offenders who are punished pay for the harms they caused, but also, implicitly, for the harms caused by those who go unpunished (including, perhaps, themselves at other times). This adjustment is referred to as probability scaling. For example, if a criminal act imposes harm of $10,000, and only one in three offenders is caught and punished, optimal deterrence requires that the fine paid by that one person should be set at $30,000. This ensures that prospectively, all would-be offenders expect to pay $10,000. One practical objection to this policy is that many offenders will lack the resources to pay the required fine, especially if p is small. This so-called “judgment proof problem” provides the economic rationale for combining fines with the possibility of imprisonment as a means of punishing offenders (Polinsky and Shavell 1984). However, because prison is costly to impose, whereas we have assumed that fines are costless, it would never be optimal in the Becker model to use prison unless a fine alone is an inadequate deterrent. Thus, in the previous example, the possible use of prison should be limited to those offenders who are unable to pay the $30,000 fine. It is important to emphasize this point, as it is one of the key prescriptions of the economic model of crime; namely, that it is optimal to use fines up to the maximum ability-to-pay of offenders before considering the use of prison as a deterrent. To be more specific, suppose that an offender’s maximum ability to pay is limited by his or her wealth level, denoted by A. Then, the optimal fine in (2.2) would be adjusted as follows:



h / p if h / p ≤ A f∗ = .  A if h / p > A

(2.3)

As a result, offenders who can afford to pay the optimal fine, h/p, will be efficiently deterred because they will expect to pay h (the first line), while offenders who cannot afford to pay it (the bottom line) will be underdeterred because they will expect to pay less than h. That is, absent further punishment, they will commit some inefficient crimes for the simple reason that they know their punishment is limited. It is only the threat of possible imprisonment on top of the fine that potentially overcomes this problem.

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The difficulty with imprisonment is that, because it is costly to impose, it will not generally be desirable to use it to the point where all inefficient crimes are deterred. To illustrate, return to the above numerical example where h = $10,000 and p = 1/3, which yielded an optimal fine of $30,000. Now consider two potential offenders, one whose benefit of committing the act in question is $12,000 and one whose benefit is $7000. Thus, it is efficient for the first offender to commit the act (because $12,000 > $10,000), but it is not efficient for the second offender to commit it (because $7000  h were committed. When p can be chosen along with f, however, the outcome is different because now crime can also be deterred by raising p. However, because raising p is costly, it will no longer be optimal to raise it to the point where only efficient crimes occur. In fact, it is desirable for there to be some under-deterrence under the optimal policy. Specifically, with f = A as prescribed above, the optimal p should be chosen so that pA