Crime and Punishment: An Economic Approach

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1 This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: Essays in the Economics of Crime and Punishment Volume Author/Editor: Gary S. Becker and William M. Landes, eds. Volume Publisher: NBER Volume ISBN: 0-87014-263-1 Volume URL: http://www.nber.org/books/beck74-1 Publication Date: 1974 Chapter Title: Crime and Punishment: An Economic Approach Chapter Author: Gary S. Becker Chapter URL: http://www.nber.org/chapters/c3625 Chapter pages in book: (p. 1 - 54)

2 Crime and Punishment: An Economic Approach Gary S. Becker of Chicago and National Bureau of Economic Research University 1. INTRODUCTION Since the turn of the century, legislation in Western countries has ex- panded rapidly to reverse the brief dominance of laissez faire during the nineteenth century. The state no longer merely protects against viola- tions of person and property through murder, rape, or burglary but also restricts "discrimination" against certain minorities, collusive business arrangements, "jaywalking," travel, the materials used in construction, and thousands of other activities. The activities restricted not only are numerous 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- would like to thank the Lilly Endowment for financing a very productive summer in I 1965 at the University of California at Los Angeles. While there I received very helpful comments on an earlier draft from, among others, Armen Alchian, Roland McKean, Harold Demsetz, 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 of Columbia; assistance and suggestions from Isaac Ehrlich and Robert Michael; and sugges- Robert A. Mundell. Economy, of Political tions from the editor of the Jour,wl

3 CRIME AND PUNISHMENT: 2 AN ECONOMIC APPROACH victed and the nature and extent of punishments differ greatly from person to person and activity to activity. Yet, in spite of such diversity, some common properties are shared by practically all legislation, and these properties form the subject matter of this essay. in the first place, obedience to law is not taken for granted, and public and private resources are generally spent in order both to prevent Crimes against persont offenses and to apprehend offenders. In the second place, conviction is not Crimes against propert generally considered sufficient punishment in itself; additional and some- Illegal goods and times severe punishments are meted out to those convicted. What deter- Some other crimes mines the amount and type of resources and punishments used to enforce Total a piece of legislation? In particular, why does enforcement differ so Public expenditures on greatly among different kinds of legislation? Corrections The main purpose of this essay is to answer normative versions of Some private costs of these questions, namely, how many resources and how much punish- Overall total ment should used to enforce different kinds of legislation? Put be Presidet SOURCE. — equivalently, although more strangely, how many offenses should per- be mitted and how many offenders should go unpunished? The method used all violations, not jus formulates a measure of the social loss from offenses and finds those ex- receive so much new: penditures of resources and punishments that minimize this loss. The white-collar crimes, general criterion of social loss is shown to incorporate as special cases, broadly, "crime" is valid under special assumptions, the criteria of vengeance, deterrence, notwithstanding the rehabilitation compensation, and that historically have figured so evidence recently pu prominently in practice and criminological literature. Enforcement and Adi The optimal amount of enforcement is shown to depend on, among reproduced in Table other things, the cost of catching and convicting offenders, the nature of and local levels on po punishments—for example, whether they are fines or prison terms—and amounted to over $' the responses of offenders to changes in enforcement. The discussion, guards, counsel, and therefore, inevitably enters into issues in penology and theories of lion. Unquestionably criminal behavior. A second, although because of lack of space subsidiary, significantly understa aim of this essay is to see what insights into these questions are provided the course of enforcii by our "economic" approach. It is suggested, for example, that a useful theory of criminal behavior can dispense with special theories of anomie, psychological inadequacies, or inheritance of special traits and simply I. This neglect probat extend the economist's usual analysis of choice. merit any systematic sciei analysis is seen most clearl gambling is an "economic II. BASIC ANALYSIS true that this loss of proba the excitement of gamblin pleasures of gambling are A. THE COST OF CRIME are likely to engender a r for the higher and more Although the word "crime" is used in the title to minimize terminologi- Appendix). cal innovations, the analysis is intended to be sufficiently general to cover

4 3 GARY S. BECKER TABLE 1 reatly from person ECONOMIC COSTS OF CRIMES ch diversity, some slation, and these Costs (Millions of Dollars) Type n for granted, and der both to prevent Crimes against persons 815 conviction is not Crimes against property 3,932 and some- Illegal goods and services 8,075 What deter- Some other crimes 2,036 used to enforce 14,858 Total 'orcement differ so Public expenditures on police, prosecution, and courts 3,178 1,034 Corrections rmative versions of Some private costs of combating crime I ,9 10 how much punish- Overall total 20,980 of legislation? Put SouRcE.—President's Commission (1967d, p. 44). per- should be The method used like all violations, not just felonies — murder, robbery, and assault, which and finds those ex- receive so much newspaper coverage—but also tax evasion, the so-called mize this loss. The white-collar crimes, and traffic and other violations. Looked at this kte as special cases, broadly, "crime" is an economically important activity or "industry," deterrence, notwithstanding the almost total neglect by economists.1 Some relevant have figured so evidence recently put together by the President's Commission on Law Enforcement and Administration of Justice (the "Crime Commission") is depend on, among reproduced in Table 1. Public expenditures in 1965 at the federal, state, pders, the nature of and local levels on police, criminal courts and counsel, and "corrections" terms—and amounted to over $4 billion, while private outlays on burglar alarms, fit. The discussion, guards, counsel, and some other forms of protection were about $2 bi!- and theories of lion. Unquestionably, public and especially private expenditures are space subsidiary, significantly understated, since expenditures by many public agencies in are provided the course of enforcing particular pieces of legislation, such as state fair- that a useful of anomie, 11 traits and simply I. This neglect probably resulted from an attitude that illegal activity is too immoral to merit any systematic scientific attention. The influence of moral attitudes on a scientific analysis is seen most clearly in a discussion by Alfred Marshall. After arguing that even fair gambling is an "economic blunder" because of diminishing marginal utility, he says, "It is true that this loss of probable happiness need not be greater than the pleasure derived from the excitement of gambling, and we are then thrown back upon the induction [sic] that pleasures of gambling are in Bentham's phrase 'impure'; since experience shows that they are likely to engender a restless, feverish character, unsuited for steady work as well as for the higher and more solid pleasures of life" (Marshall, 1961, Note X, Mathematical imize terminologi- Appendix). tly general to cover

5 4 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH employment laws,2 are not included, and a myriad of private precautions over checks in illeg: against crime, ranging from suburban living to taxis, are also excluded. tions) because no rc also lists the Crime Commission's estimates of the direct Table I costs of various crimes. The gross income from expenditures on various kinds of illegal consumption, including narcotics, prostitution, and mainly B. THE MODEL gambling, amounted to over $8 billion. The value of crimes against prop- It is useful in deteri erty, including fraud, vandalism, and theft, amounted to almost $4 bil- develop a model to lion,3 while about $3 billion worth resulted from the loss of earnings listed in Table I. TI due to homicide, assault, or other crimes. All the costs listed in the table between (1) the nun total about $21 billion, which is almost 4 per cent of reported national cost of offenses, (2: income in 1965. If the sizable omissions were included, the percentage out, (3) the number might be considerably higher. penditures on polic Crime has probably become more important during the last forty costs of imprisonme years. The Crime Commission presents no evidence on trends in costs of offenses and the but does present evidence suggesting that the number of major felonies The first four are d. per capita has grown since the early thirties (President's Commission, later section. 1967a, pp. 22—3 1). Moreover, with the large growth of tax and other legislation, tax evasion and other kinds of white-collar crime have pre- 1. DAMAGES sumably grown much more rapidly than felonies. One piece of indirect evidence on the growth of crime is the large increase in the amount of cur- Usually a belief tha rency in circulation since 1929. For sixty years prior to that date, the tion behind outlawi ratio of currency either to all money or to consumer expenditures had de- of harm would tend clined very substantially. Since then, in spite of further urbanization and income growth and the spread of credit cards and other kinds of credit,4 both ratios have increased sizably.3 This reversal can be explained by an with unusual increase in illegal activity, since currency has obvious advantages 2. Expenditures by the thirteen states with such legislation in 1959 totaled almost $2 million (see Landes, 1966). where H, is the harr 3. Superficially, frauds, thefts, etc., do not involve true social costs but are simply concept of harm an transfers, with the loss to victims being compensated by equal gains to criminals. While are familiar to econ these are transfers, their market value is, nevertheless, a first approximation to the direct social cost. If the theft or fraud industry is "competitive," the sum of the value of the ing external disecor criminals' time input—including the time of "fences" and prospective time in prison—plus an important subse the value of capital input, compensation for risk, etc., would approximately equal the with the level of cri market value of the loss to victims. Consequently, aside from the input of intermediate The social valu products, losses can be taken as a measure of the value of the labor and capital input into these crimes, which are true social costs. 4. For an analysis of the secular decline to 1929 that stresses urbanization and the Cagan (1965, cha 6. growth in incomes, see Cagan (1965, chap. iv). 1929 and 1960 to increa 5. In 1965, the ratio of currency outstanding to consumer expenditures was 0.08, com- 7. The ith subscript pared to only 0.05 in 1929. In 1965, currency outstanding per family was a whopping $738. activity is being discusse

6 APPROACH 5 GARY S. BECKER private precautions over checks in illegal transactions (the opposite is true for legal transac- re also excluded. tions) because no record of a transaction remains.6 of the direct on various B. THE MODEL and mainly against prop- It is useful in determining how to combat crime in an optimal fashion to to almost $4 bil- develop a model to incorporate the behavioral relations behind the costs loss of earnings listed in Table 1. These can be divided into five categories: the relations listed in the table between (1) the number of crimes, called "offenses" in this essay, and the of reported national cost of offenses, (2) the number of offenses and the punishments meted the percentage out, (3) the number of offenses, arrests, and convictions and the public ex- penditures on police and courts, (4) the number of convictions and the curing the last forty costs of imprisonments or other kinds of punishments, and (5) the number e on trends in costs of offenses and the private expenditures on protection and apprehension. jer of major felonies The first four are discussed in turn, while the fifth is postponed until a Commission, later section. of tax and other liar crime have pre- 1. DAMAGES piece of indirect Usually a belief that other members of society are harmed is the motiva- in the amount of cur- tion behind outlawing or otherwise restricting an activity. The amount to that date, the of harm would tend to increase with the activity level, as in the relation had de- her urbanization and H,(O,), H, ther kinds of credit,4 be explained by an with (1) advantages 0, 1959 totaled almost S2 where H, is the harm from the ith activity and 0, is the activity level.7 The costs but are simply concept of harm and the function relating its amount to the activity level gains to criminals. While are familiar to economists from their many discussions of activities caus- jroximation to the direct sum of the value of the ing external diseconomies. From this perspective, criminal activities are time in prison—plus an important subset of the class of activities that cause diseconomies, equal the with the level of criminal activities measured by the number of offenses. input of intermediate The social value of the gain to offenders presumably also tends to in- bor and capital input into es urbanization and the 6. Cagan (1965, chap. iv) attributes much of the increase in currency holdings between 1929 and 1960 to increased tax evasion from the increase in tax rates. nditures was 0.08, corn- 7. The ith subscript will be suppressed whenever it is to be understood that only one ly was a whopping $738. activity is being discussed.

7 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH 6 crease with the number of offenses, as in 2. THE COST OF AF G = The more that is equipment, the (2) with can postulate a relal and various input5 G' c), wherefi: f(n7, arts." Given f and The net cost or damage to society is simply the difference between the costly, as summariz harm and gain and can be written as H(0) D(O) = G(0). (3) — If, as seems plausible, offenders usually eventually receive diminish- and ing marginal gains and cause increasing marginal harm from additional offenses, G" < 0, H" > 0, and — (4) 0, It would be cheape which is an important condition used later in the analysis of optimality were policemen,8 jt positions (see, for example, the Mathematical Appendix). Since both H' veloped the state ol and G' > 0, the sign of D' depends on their relative magnitudes. It fol- printing, wiretappin! lows from (4), however, that One approxima ber of offenses cleai D'(O) > 0 for all 0> 0. (5) if D'(Oa) Until Section V the discussion is restricted to the region where D' > 0, the region providing the strongest justification for outlawing an activity. where p, the ratio In that section the general problem of external diseconomies is recon- the overall probabili sidered from our viewpoint, and there D' < 0 is also permitted. stituting (7) into (6) The top part of Table 1 lists costs of various crimes, which have been interpreted by us as estimates of the value of resources used up in these crimes. These values are important components of, but are not identical to, the net damages to society. For example, the cost of murder is and measured by the loss in earnings of victims and excludes, among other things, the value placed by society on life itself; the cost of gambling excludes both the utility to those gambling and the "external" disutility to if p0 0. An some clergy and others; the cost of "transfers" like burglary and em- ber of offenses wo bezzlement excludes social attitudes toward forced wealth redistribu- creased "activity" tions and also the effects on capital accumulation of the possibility of theft. Consequently, the $1 5 billion estimate for the cost of crime in 8. According to the Table 1 may be a significant understatement of the net damages to society, wages and salaries (Presi not only because the costs of many white-collar crimes are omitted, but 9. A task-force rep also because much of the damage is omitted even for the crimes covered. and more efficient usage

8 APPROACH 7 GARY S. BECKER 2. THE COST OF APPREHENSION AND CONVICTION The more that is spent on policemen, court personnel, and specialized equipment, the easier it is to discover offenses and convict offenders. One (2) can postulate a relation between the output of police and court "activity" in. A = and various inputs of manpower, materials, and capital, as is a production function summarizing the "state of the c), wheref f(m, arts." Given f and input prices, increased "activity" would be more between the costly, as summarized by the relation (3) C=C(A) Ily receive diminish- and (6) krm from additional (4) It would be cheaper to achieve any given level of activity the cheaper of optimality were policemen,8 judges, counsel, and juries ana the more highly de- Since both H' veloped the state of the arts, as determined by technologies like finger- magnitudes. It fol- 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 (5) A (7) pO, where D' > 0, an activity. where p, the ratio of offenses cleared by convictions to all offenses, is is recon- the overall probability that an offense is cleared by conviction. By sub- permitted. stituting (7) into (6) and differentiating, one has ês, which have been aC(pO) used up in these =c'o>o cJ,= ap are not identical cost of murder is and (8) among other C0 = C'p> 0 cost of gambling disutility to 0. An increase in either the probability of conviction or the num- if p0 burglary and em- ber of offenses would increase total costs. If the marginal cost of in- wealth redistribu- creased "activity" were rising, further implications would be that the possibility of k cost of crime in all police costs consist of According to the Crime Commission, 85—90 per cent of 8. damages to society, wages and salaries (President's Commission, 1967a, p. 35). es are omitted, but 9. A task-force report by the Crime Commission deals with suggestions for greater he crimes covered. and more efficient usage of advanced technologies (President's Commission, 1967e).

9 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH 8 of these felonies anc > C"02 0, C,,,, = either arrests or coi (9) = C"p2 > 0, at least $500 if cond and + C' > 0. C,,0 C,,,, = C"pO 3. THE SUPPLY OF A more sophisticated and realistic approach drops the implication Theories about the i of (7) that convictions alone measure "activity," or even that p and 0 from emphasis on have identical elasticities, and introduces the more general relation bringing and disenc (10) A=h(p,0,a). theories agree, how increase in a perso The variable a stands for arrests and other determinants of "activity," victed would genera and there is no presumption that the elasticity of I, with respect to p bly, the number of c equals that with respect to 0. Substitution yields the cost function C = zation by persons If, as is extremely likely, h,,, h,, and h,, are all greater than C(p, 0, a). ability has a greater C,, are all greater than zero. zero, then clearly C1,, C,,, and punishment,'2 althou. In order to insure that optimality positions do not lie at "corners," it shed any light on thi is necessary to place some restrictions on the second derivatives of the The approach t; cost function. Combined with some other assumptions, it is sufficient that choice and assumes 0, C,,,, utility to him exceed (11) resources at other a fore, not because the and but because their be 0 C,,,, many general impli (see the Mathematical Appendix). The first two restrictions are rather criminal behavior be plausible, the third much less so.'° not require ad hoc c indicates that in 1965 public expenditures in the United Table I like,'4 nor does it ass States on police and courts totaled more than $3 billion, by no means a any of the other can minor item. Separate estimates were prepared for each of seven major This approach ii felonies." Expenditures on them averaged about $500 per offense (re- offenses by any persc ported) and about $2,000 per person arrested, with almost $1,000 being if convicted, and to c spent per murder (President's Commission, l967a, pp. 264—65); $500 is legal and other illega' an estimate of the average cost willingness to comm. A 12. For example, Lc with methods of punish. C,,,, = C"(/i,,)' + C"(h,,)' + C'/i,,; 10. Differentiating the cost function yields C,,,, significance lii than they be negative could or C,,. marginal costs were rising, C,,, C,,,, = Ch,/i,, + C/i,,,,. If C'h,,,,; severity of punishment." would not very likely. However, C,,,, is sufficiently negative, which were or only if h,,, I'm, sightful eighteenth-centur sufficiently negative, which is also unlikely. Note were be approximately zero only if h,,, p. 282). > 0. and h,,,, = I,,,, = 0, that if "activity" is measured by convictions alone, h,,, 13. See, however, thc II. They are willful homicide, forcible rape, robbery, aggravated assault, burglary, 14. For a discussion larceny, and auto theft.

10 GARY S. 9 BECKER of these felonies and would presumably be a larger figure if the number of would either arrests or Convictions were greater. Marginal costs (Ce) be (9) at least $500 if condition (11), C,,0 0, were assumed to hold throughout. 3. THE SUPPLY OF OFFENSES )pS the implication Theories about the determinants of the number of offenses differ greatly, even that p and 0 from emphasis on skull types and biological inheritance to family up- relation eneral bringing and disenchantment with society. Practically all the diverse theories agree, however, that when other variables are held constant, an (10) increase in a person's probability of conviction or punishment if con- nants of "activity," victed would generally decrease, perhaps substantially, perhaps negligi- with respect to p bly, the number of offenses he commits. In addition, a common generali- = cost function C zation by persons with judicial experience is that a change in the prob- all greater than rare ability has a greater effect on the number of offenses than a change in the zero. punishment,'2 although, as far as I can tell, none of the prominent theories lie at "corners," it shed any light on this relation. derivatives of the The approach taken here follows the economists' usual analysis of that 'is, it is sufficient choice and assumes that a person commits an offense if the expected utility to him exceeds the utility he could get by using his time and other resources at other activities. Some persons become "criminals," there- (11) fore, not because their basic motivation differs from that of other persons, but because their benefits and costs differ. I cannot pause to discuss the many general implications of this approach,'3 except to remark that strictions are rather criminal behavior becomes part of a much more general theory and does not require ad hoc concepts of differential association, anomie, and the tures in the United like,'4 nor does it assume perfect knowledge, lightning-fast calculation, or lion, by no means a any of the other caricatures of economic theory. of seven major This approach implies that there is a function relating the number of per offense (re- offenses by any person to his probability of conviction, to his punishment almost $1,000 being if convicted, and to other variables, such as the income available to him in p. 264—65); $500 is legal and other illegal activities, the frequency of nuisance arrests, and his willingness to commit an illegal act. This can be represented as For example, Lord Shawness (1965) said, "Some judges preoccupy themselves 12. with methods of punishment. This is their job. But in preventing crime it is of less C,,, = C"(h0)2 + C'h,,,,; significance than they like to think. Certainty of detection is far more important than could be negative r severity of punishment." Also see the discussion of the ideas of C. B. Beccaria, an in- ly. However, C,,,, would sightful eighteenth-century Italian economist and criminologist, in Radzinowicz (1948, 1, is also unlikely. Note ii p. 282). 0. and 6,,.. > 13. See, however, the discussions in Smigel (1965) and Ehrlich (1967). vated assault, burglary, 14. For a discussion of these concepts, see Sutherland (1960).

11 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH 10 (12) O3(p3, f,, U3), enter illegal activitie shift in the form of the number of offenses he would commit during a particu1ar is where would tend to reducc punishment per his period, p3 his probability of conviction per offense, f, they cannot be comi offense, and u3 a portnianteau variable representing all these other in- This approach fluences.'5 greater response to Since only convicted offenders are punished, in effect there is "price An increase in "C convicted discrimination" and uncertainty: if convicted, he pays f per would not change the offense, while otherwise he does not. An increase in either p, orf3 would the expected utility, reduce the utility expected from an offense and thus would tend to reduce shown that an incre2 the number of offenses because either the probability of "paying" the the number of offens. higher "price" or the "price" itself would increase.'6 That is, has preference for ri: he has aversion to ri <0 neutral.'9 The widesç by the probability of (13) and turns out to imply in ao3 preferrers, at least in < 0, °fj= The total numbe pend on the set of p3, which are the generally accepted restrictions mentioned above. The effect significantly between also be anticipated. For ex- could of changes in some components of 113 education, previous ample, a rise in the income available in legal activities or an increase in simplicity I now cons law-abidingness due, say, to "education" would reduce the incentive to 17. 18. This means that on the judge, jury, depend be considered distributions that f3 might and Both 15. utility and offenses. depends on the p's and prosecutor, etc., that j happens to receive. Among other things, U3 19. From n. 16 f'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 äp3 U1 pjUj(Y3 — EU., = —J) + (1 as Y1 is his income, monetary plus psychic, from an offense; U, is his utility function; where and fi is to be interpreted as the monetary equivalent of the punishment. Then The term on the left is thc <0 = — —f,) greater than, equal to, or le and (J > 0, neutrality by = 20. p can be defined a <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 result and similar definitions hold in conviction.

12 11 GARY S. BECKER APPROACH (12) enter illegal activities and thus would reduce the number of offenses. Or a shift in the form of the punishment, say, from a fine to imprisonment, it during a particular would tend to reduce the number of offenses, at least temporarily, because his punishment per they cannot be committed while in prison. g all these other in- This approach also has an interesting interpretation of the presumed greater response to a change in the probability than in the punishment. effect there is "price An increase in p) "compensated" by an equal percentage reduction in f, convicted per ays change could not change the expected income from an offense would orf1 would either the expected utility, because the amount of risk would change. It is easily Nould tend to reduce shown that an increase in p,, would reduce the expected utility, and thus lity of "paying" the jfj the number of offenses, more than an equal percentage increase inf, 6 is, That would have the greater effect if has preference for risk; the increase in he has aversion to risk; and they would have the same effect if he is risk neutral.15 The widespread generalization that offenders are more deterred p, by the probability of conviction than by the punishment when convicted (13) turns out to imply in the expected-utility approach that offenders are risk preferrers, 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 differ above. The effect significantly between persons because of differences in intelligence, age, anticipated. For ex- education, previous offense history, wealth, family upbringing, etc., for ties or an increase in simplicity I now consider only their average values, p,f, and u,2° and write the incentive to 17. would reduce 18. This means that an increase in "compensated" by a reduction in f, on the judge. jury, ,epend utility and offenses. depends on the p's and 19. From n. 16 g that offenders do substi- —aEU, p, fi {U,(Y,) — U,(Y, = p,UJ(Y, —fj) — U,,< as äp, U,, c'fj U3 U,, as U,,(Y,, U,(Y,,) — —fi) his utility function; is U, U(Y, —f,) ishment. Then fi 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, as U' 0. But risk preference is defined by —f,,) 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 xpand the analysis by in- d trials that do not result and similar definitions hold fcn-f and u.

13 12 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH the market offense function as mission, 1967b). Th came to about l,30C (14) 0 = O(p,f, u). About one-half were This function is assumed to have the same kinds of properties as the the remaining one-si: individual functions, in particular, to be negatively related to p and f and The cost of diffi to be more responsive to the former than the latter if, and only if, offenders parable by converti on balance have risk preference. Smigel (1965) and Ehrlich (1967) esti- which, of course, is cost of an imprisonn mate functions like (14) for seven felonies reported by the Federal Bu- and the value place 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- Since the earnings ft vary of lation coefficients; that there are significant negative effects on 0 p from person to and f; and that usually the effect of p exceeds that of f, indicating duration is not a unit preference for risk in the region of observation. offenders who could fender would be A well-known result states that, in equilibrium, the real incomes of gone earnings and f persons in risky activities are, at the margin, relatively high or low as length of sentences. persons are generally risk avoiders or preferrers. If offenders were risk Punishments afT preferrers, this implies that the real income of offenders would he lower, at the margin, than the incomes they could receive in less risky legal society. Aside from activities, and conversely if they were risk avoiders. Whether "crime as revenue by pays" is then an implication of the attitudes offenders have toward risk as well as offenders:: and is not directly related to the efficiency of the police or the amount guards, supervisory spent on combating crime. If, however, risk were preferred at some values billion is being spent of p and f and disliked at others, public policy could influence whether and institutionalizatic "crime pays" by its choice of p andf. Indeed, it is shown later that the dously from a low ol for juveniles in dete social loss from illegal activities is usually minimized by selecting p and f in regions where risk is preferred, that is, in regions where "crime does pp. 193—94). The total social not pay." cost or minus the ga equals the cost to 4. PUNISHMENTS social cost of fines is Mankind has invented a variety of ingenious punishments to inflict on cost of probation, in] convicted offenders: death, torture, branding, fines, imprisonment, ban- erally exceeds that ti ishment, restrictions on movement and occupation, and loss of citizen- ivation of optimality ship are just the more common ones. In the United States, less serious venient if social cost: offenses are punished primarily by fines, supplemented occasionally by probation, petty restrictions like temporary suspension of one's driver's license, and imprisonment. The more serious offenses are punished by a wheref' is the social combination of probation, imprisonment, parole, fines, and various re- The size of b vane: strictions on choice of occupation. A recent survey estimated for an average day in 1965 the number of persons who were either on probation, 21. In this respect, ii parole, or institutionalized in a jail or juvenile home (President's Corn- also exemplified by queue

14 APPROACH 13 GARY S. BECKER total number of persons in one of these categories The mission, 1967b). came to about 1,300,000, which is about 2 per cent of the labor force. (14) About one-half were on probation, one-third were institutionalized, and the remaining one-sixth were on parole. properties as the of The cost of different punishments to an offender can be made com- elated to p and f and parable by converting them into their monetary equivalent or worth, and only if, offenders which, of course, is directly measured only for fines. For example, the Ehrlich (1967) esti- cost of an imprisonment is the discounted sum of the earnings foregone by the Federal Bu- and the value placed on the restrictions in consumption and freedom. unit of observation. Since the earnings foregone and the value placed on prison restrictions enced by high cone- vary from person to person, the cost even of a prison sentence of given of p ye effects on 0 duration is not a unique quantity but is generally greater, for example, to of f, indicating offenders 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- the real incomes of gone earnings and foregone consumption are positively related to the high or low as length of sentences. (1 offenders were risk Punishments affect not only offenders but also other members of would be lower, society. Aside from collection costs, fines paid by offenders are received in less risky legal as revenue by others. Most punishments, however, hurt other members Whether "crime as well as offenders: for example, imprisonment requires expenditures on have toward risk guards, supervisory personnel, buildings, food, etc. Currently about $1 or the amount billion is being spent each year in the United States on probation, parole, at some values and institutionalization alone, with the daily cost per case varying tremen- Id influence whether dously from a low of $0.38 for adults on probation to a high of $11.00 shown later that the for juveniles in detention institutions (President's Commission, 1967b, ed by selecting p and pp. 193—94). where "crime does The total social cost of punishments is the cost to offenders plus the cost or minus the gain to others. Fines produce a gain to the latter that equals the cost to offenders, aside from collection costs, and so the social cost of fines is about zero, as befits a transfer payment. The social tshments to inflict on cost of probation, imprisonment, and other punishments, however, gen- ban- imprisonment, erally exceeds that to offenders, because others are also hurt. The der- and loss of citizen- ivation of optimality conditions in the next section is made more con- d States, less serious venient if social costs are written in terms of offender costs as nted occasionally by (15) ion of one's driver's es are punished by a wheref' is the social cost and b is a coefficient that transforms fintof'. nes, and various re- The size of b varies greatly between different kinds of punishments: ey estimated for an either on probation, 21. In this respect, imprisonment is a special case of "waiting time'S pricing that is e (President's Corn- also exemplified by queueing (see Becker, 1965, esp. pp. 5 15—16, and Kleinman, 1967).

15 14 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH there are a fairly Ia > 1 for torture, probation, parole, imprisonment, 0 for fines, while b b directly subject to and most other punishments. It is especially large for juveniles in deten- offenses, C; the pui tion homes or for adults in prisons and is rather close to unity for torture form of punishment or for adults on parole. via the D, C, and 0 f the loss L. III. OPTIMALITY CONDITIONS Analytical cony a decisionvariabje. A The relevant parameters and behavioral functions have been introduced, a given constant gn and the stage is set for a discussion of social policy. If the aim simply variables, and their were deterrence, the probability of conviction, p, could be raised clOse to the two first-order o 1, and punishments,f, could be made to exceed the gain: in this way the number 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 the does an increase inf if b > 0 through cost of combating offenses, C, as and the effect on the cost of punishments, bf. At relatively modest values of p and f, these effects might outweigh the social gain from increased L deterrence. Similarly, if the aim simply were to make "the punishment fit the crime," p could be set close to 1, and f could be equated to the If and are not harm imposed on the rest of society. Again, however, such a policy ig- recombine terms, to nores the social cost of increases in p andf. What is needed is a criterion that goes beyond catchy phrases and gives due weight to the damages from offenses, the costs of apprehending and convicting offenders, and the social cost of punishments. The social- and welfare function of modern welfare economics is such a criterion, and one might assume that society has a function that measures the social D loss from offenses. If (16) where is the function measuring social loss, with presumably (17) abf>°' and 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, to The term on the assume that the loss function is identical with the total social loss in real income from offenses, convictions, and punishments, as in increasing the numbe infand in (22) throu L=D(0)+C(p, 0)+bpfo. (18) to be in a region whe: The term bpfo is the total social loss from punishments, since bf is the 22. The Mathematica loss per offense punished and p0 is the number of offenses punished (if

16 GARY S. 15 BECKER APPROACH there are a fairly large number of independent offenses). The variables role, imprisonment, directly subject to social control are the amounts spent in combating rjuveniles in deten- offenses, C; the punishment per offense for those convicted, f; and the to unity for torture form of punishments, summarized by b. chosen, these variables, Once via the D, C, and 0 functions, indirectly determine p, 0, D, ultimately and the loss L. Analytical considered convenience suggests that p rather than C be a decision variable. Also, the coefficient b is assumed in this section to be Lye been introduced, a given constant greater than zero. Then p and fare the only decision y. If the aim simply variables, and their optimal values are found by differentiating L to find Id be raised close to the two first-order optimality conditions,22 gain: in this way the nih. However, an in-. (19) ugh its effect on the infif b > 0 through and rely modest values of from increased (20) àke "the punishment be equated to the through by them, and are If 0, 0,, and not equal to zero, one can divide ver, such a policy ig- recombine terms, to get the more interesting expressions catchy phrases and =_bpf(1 _!) (21) D' + C' of apprehending ishments. The social- and such a criterion, and measures the social (22) (16) where 5ly f Cj Of = (17) (23) and ly b that minimize L. p Lv = 0,,. to , develop the dis- milation, namely, to The term on the left side of each equation gives the marginal cost of tal social loss in real increasing the number of offenses, 0: in equation (21) through a reduction as in > is assumed infand in (22) through a reduction in p. Since C' 0 and 0 (18) > through 0, the marginal cost of increasing 0 to be in a region where D' ents, since bf is the 22. The Mathematical Appendix discusses second-order conditions. ffenses punished (if

17 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH 16 that the marginal re' pointed out earlier, Marginal cost that offenders have Marginal pay." Consequently, revenue selected from those MC,= D' + ferrers. Although oi directly determine wi insures that "crime d I indicated earlic United States genera by elasticity) of p on C —!) risk preferrers and Moreover, both elast !) therefore, actual pub optimality analysis. If the supply of Number of offenses neutral—a reduction i inf would leave FIGURE 1 loss, because the cost by the reduction in p. be positive. A reduction in p partly reduces the cost of combating f must ing p arbitrarily clos( offenses, and, therefore, the marginal cost of increasing 0 must be less product pf would md when p rather than when f is reduced (see Figure 1); the former could offenders were risk a were sufficiently large. Average "revenue," given even be negative if arbitrarily close to ze by —bpf, is negative, but marginal revenue, given by the right-hand side of only C but also 0 an equations (21) and (22), is not necessarily negative and would be positive There was a ten if the elasticities €,, and e,were less than unity. Since the loss is minimized tunes in Anglo-Saxon when marginal revenue equals marginal cost (see Figure 1), the optimal underdeveloped couni value of Cf must be less than unity, and that of e,, could only exceed unity rather severely, at thc is a reversal of the usual equilibrium This sufficiently large. were if C,, condition for an income-maximizing firm, which is that the elasticity of 24. If b < 0, the optini demand must exceed unity, because in the usual case average revenue is Optimal social policy woul assumed to be 25. Since Since the marginal cost of changing 0 through a change in p is less conditions given by eqs. (2 than that of changing 0 throughf, the equilibrium marginal revenue from p must also be less than that fromf. But equations (21) and (22) indicate From this condition and ft of value Ej Thus if b < 0, average revenue would be positive and the optimal 23. be determined. I only if C,, were sufficiently would be greater than 1, and that of a,, could be less than 26. If b < 0, the optil large. are either risk neutral or nt

18 APPROACH 17 GARY S. BECKER that the marginal revenue from p can be less if, and only if, e,, > As pointed out earlier, however, this is precisely the condition indicating that offenders have preference for risk and thus that "crime does not are pay." Consequently, the loss from offenses is minimized if p and f selected from those regions where offenders are, on balance, risk pre- ferrers. Although only the attitudes offenders have toward risk can D' + C' directly determine whether "crime pays," rational public policy indirectly D' + C' + insures that "crime does not pay" through its choice of p and f.24 indicated earlier that the actual p's andf's for major felonies in the I United States generally seem to be in regions where the effect (measured by elasticity) of p on offenses exceeds that off, that is, where offenders are MR,=.—bPf(t —!) risk 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 the optimality analysis. If the supply of offenses depended only on pf—offenders were risk umber of offenses a reduction in p "compensated" by an equal percentage increase neutral — inf would leave unchanged pf, D(0), and bpfo but would reduce the 0, loss, because the costs of apprehension and conviction would be lowered by the reduction in p. The loss would be minimized, therefore, by lower- of combating the cost ing p arbitrarily close to zero and raisingf sufficiently high so that the 0 must be less product pf would induce the optimal number of offenses.25 A fortiori, if 1); the former could offenders were risk avoiders, the loss would be minimized by setting p page "revenue," given arbitrarily close to zero, for a "compensated" reduction in p reduces not the right-hand side of only C but also 0 and thus D and bpf0.2° would be positive There was a tendency during the eighteenth and nineteenth cen- the loss is minimized turies in Anglo-Saxon countries (and even today in many Communist and figure 1), the optimal underdeveloped countries) to punish those convicted of criminal offenses only exceed unity rather severely, at the same time that the probability of captute and con- the usual equilibrium that the elasticity of the optimality condition is that e,. < that offenders are risk avoiders. < 0, 24. If b €1' or tse average revenue is pay." does be to select p and fin regions where "crime Optimal social policy would then if 0 depends only on pf, and C = 0 if p = 0, the two equilibrium 25. Since €, = e,, = a change in p is less conditions given by eqs. (21) and (22) reduce to the single condition arginal revenue from .J) D' =_bPf(l (21) and (22) indicate From this condition and the relation 0 = O(pj), the equilibrium values of 0 and pf could optimal value of €, the Ld be determined. C,, were sufficiently nly if 26. If b < 0, the optimal solution is p about zero and f arbitrarily high if offenders are either risk neutral or risk preferrers.

19 18 CRiME AND PUNISHMENT: AN ECONOMIC APPROACH viction was set at rather low values.27 A promising explanation of this tendency is that an increased probability of conviction obviously absorbs IV. SHIFTS iN T public and private resources in the form of more policemen,judges,juries, This section analyz and so forth. Consequently, a "compensated" reduction in this proba- tions—the damage, bility obviously reduces expenditures on combating crime, and, since the mal values of p and, expected punishment is unchanged, there is no "obvious" offsetting matical Appendix, h increase in either the amount of damages or the cost of punishments. proofs Ti The result can easily be continuous political pressureto keep police and why more damaging other expenditures relatively low and to compensate by meting out strong sive offenders less s punishments to those convicted. An increase in th Of course, if offenders are risk preferrers, the loss in income from D', increases the mai offenses is generally minimized by selecting positive and finite values of p or f (see Figures p and f, even though there is no "obvious" offset to a compensated necessarily decrease, reduction in p. One possible offset already hinted at in footnote 27 is increase. In this case that judges or juries may be unwilling to convict offenders if punishments values of p and fmo' are set very high. Formally, this means that the cost of apprehension and An interesting a, Conviction, C, would depend not only on p and 0 but also on If C of offenses. Althougt were more responsive tofthan to p, at least in some regions,29 the loss in done by most offens income could be minimized at finite values of p and f even if offenders that offenses like mu were risk avoiders. For then a compensated reduction in p could raise, larceny or auto theft. rather than lower, C and thus contribute to an increase in the loss. Risk avoidance might also be consistent with optimal behavior if v increases monotonically the loss function were not simply equal to the reduction in income. For =0. p example, suppose that the loss were increased by an increase in the ex If the loss function eq post "price discrimination" between offenses that are not and those that are cleared by punishment. Then a "compensated" reduction in p would the optimality conditions v increase the "price discrimination," and the increased loss from this could more than offset the reductions in C, D, and bpf0.3° For a discussion of English criminal law in the eighteenth and nineteenth cen- 27. and turies, see Radzinowicz (1948, Vol. 1). Punishments were severe then, even though the death penalty, while legislated, was seldom implemented for less serious criminal offenses. 0' -f 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 have Since the term çV(dv/dp)(: either been executed or given severe prison sentences for economic crimes. I 1 owe the emphasis on this point to Evsey Domar. 28. 31. 1 stress this prima, 29. This is probably more likely for higher values off and lower values of p. that "the more deficient in 30. if p is the probability that an offense would be cleared with the punishment f, ii of section entitled "Of is the probability of no punishment. The expected punishment would be then I — p = pf. (orf) were exogenously de the variance and the coefficient of variation — p)ft, = p(l for then the optimal value c (see the Mathematical Apr IT::-;; v =— = frequently they move in thi 'p

20 19 BECKER GARY S. APPROACH g explanation of this IV. SHIFTS IN THE BEHAViORAL RELATIONS rn obviously absorbs emen, judges, juries, This section analyzes the effects of shifts in the basic behavioral rela- iction in this proba- tions—the damage, cost, and supply-of-offenses functions—on the opti- crime, and, since the mal values of p andf Since rigorous proofs can be found in the Mathe- "obvious" offsetting matical Appendix, here the implications are stressed, and only intuitive :ost of punishments. proofs are given. The results are used to explain, among other things, re to keep police and why more damaging offenses are punished more severely and more impul- by meting out strong sive offenders less severely. An increase in the marginal damages from a given number of offenses, loss in income from D', the marginal cost of changing offenses by a change in either increases and finite values of p or f (see Figures 2a and b). The optimal number of offenses would et to a compensated necessarily decrease, because the optimal values of both p and f would in footnote 27 is increase. In this case (and, as shortly seen, in several others), the optimal if punishments values of p and f move in the same, rather than in opposite, directions.3' of apprehension and An interesting application of these conclusions is to different kinds If C also on of offenses. Although there are few objective measures of the damages regions,29 the loss in done by most offenses, it does not take much imagination to conclude id I even if offenders that offenses like murder or rape generally do more damage than petty in p could raise, larceny or auto theft. If the other components of the loss in income were base in the loss. optimal behavior if increases monotonically from a low of zero when p = I to an infinitely high value when t' Iction in income. For p = ci. increase in the ex If the loss function equaled not and those that in p would the optimality conditions would become loss from this (21) D'+C'=_bpf(l and nineteenth cen- and re then, even though the serious criminal offenses. (22) allegedly for "specula- n the Soviet Union have is positive, it could more than offset the negative term Since the term ic crimes. 1 stress this primarily because of Bentham's famous and seemingly plausible dictum 31. wer values of p. that "the more deficient in certainty a punishment is, the severer it should be" (1931, chap. with the punishment f, ii of section entitled "Of Punishment," second rule). The dictum would be correct if p shment would be = pf, (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, then frequently they move in the same direction. - —

21 20 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH Marginal Marginal cost = cost Marginal Marginal c + c revenue revenue a 0 -J MR 0 Number of offenses b. a. 2 FIGuRE the same, the optimal probability of apprehension and conviction and the punishment when convicted would be greater for the more serious offenses. Table 2 presents some evidence on the actual probabilities and H punishments in the United States for seven felonies. The punishments are simply the average prison sentences served, while the probabilities are ratios of the estimated number of convictions to the estimated number of 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 punishments are positively related, one should find that the more serious felonies have — higher probabilities and longer prison terms. And one does: in the table, < lists the felonies in decreasing order of presumed seriousness, which the actual probabilities and the prison terms are positively related both seriousness. to Since an increase in the marginal cost of apprehension and convic- tion for a given number of offenses, C', has identical effects as an increase in marginal damages, it must also reduce the optimal number of offenses and increase the optimal values of p andf. On the other hand, an increase in the other component of the cost of apprehension and conviction, has no direct effect on the marginal cost of changing offenses with f and reduces the cost of changing offenses with p (see Figure 3). It therefore reduces the optimal value of p and only partially compensates with an increase in f, so that the optimal number of pifenses increases. Accord- and ingly, an increase in both C' must increase the optimaif but can C,. either increase or decrease the optimal p and optimal number of offenses, depending on the relative importance of the changes in C' and C,..

22 C-) 0 > 2.8 15.1 15.0 18.8 28.4 Felonies Combined All These C) .4- r 2.1 13.7 11.5 21.3 20.6 Auto Theft 9.8 2.2 19.8 16.2 10.7 Larceny 0 0 C 0 2.4 13.0 10.2 24.6 26.2 Burglary Bureau of Investigation (1960, Table 10); 2(c), 3.0 16.1 25.0 27.1 27.3 vated Aggra- Assault Federal 8.4 17.8 25.1 42.4 56.1 Robbery TABLE 2 37.7 44.8 63.6 26.9 . 22.7 Rape Forcible 57.9 39.8 40.7 CD 121.4 Man- 111.0 Murder negligent slaughter and Non- , —• (P (P (P (pC#iO O OF CoNvIcTIoN AND AVERAGE PRISON TERM FOR SEVERAL MAJOR FELONIES, 1960 CD (P CD F- C) ° 0 < CD CD entering federal found guilty of institutions If) CD PROBABILITY CD and state prisons (excludes many juveniles) offenses charged offenses known . C-> CD —c" SOURCE.— I, Bureau of Prisons (1960, Table 3); 2 (a) and (b), c) Those b) State Average time served (months) before first release: a) Federal civil institutions b) Those and conviction (per cent): Probabilities of apprehension a) Those found guilty of CD 1. 2. - C- Federal Bureau of Investigation (1961, Table 2), Bureau of Prisons (n.d.,Table Al; 1961, Table 8). -.:i • If) P

23 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH 22 offenses observed in: Marginal tion between C,, (or cost C if b 0, a red > Marginal increases the margil revenue Figure 4a). The resu a decrease in the opi the optima! p. Simi respect top also in 4b), decreases the 0; MR An equal f. the optimal number If b = 0, - both marg Number of offenses and changes in thes FIGURE 3 p andf The income of The cost of apprehending and convicting offenders is affected by a little cost, its total i variety of forces. An increase in the salaries of policemen increases both ferent elasticities of while and C' C,,, improved police technology in the form of fingerprinting, markets having low ballistic techniques, computer control, and chemical analysis, or police offenses could be and court "reform" with an emphasis on professionalism and merit, the elasticities of suç would tend to reduce both, not necessarily by the same extent. Our anal y- the total loss would sis implies, therefore, that although an improvement in technology and lower p's and f's — ii reform may or may not increase the optimal p and reduce the optimal Sometimes it is number of offenses, it does reduce the optimalf and thus the need to rely offense into groups on severe punishments for those convicted. Possibly this explains why the example, unpremedi secular improvement in police technology and reform has gone hand in impulsively and, the hand with a secular decline in punishments. significantly between different differ and to a lesser extent C', C,,, Marginal kinds of offenses. It is easier, for example, to solve a rape or armed rob- cost bery than a burglary or auto theft, because the evidence of personal identi- Marginal fication is often available in the former and not in the latter offenses.32 \ revenue This might tempt one to argue that the p's decline significantly as one moves 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's would increase as one moved across the table, which is patently false. Consequently, the positive correlation between p,f, and the severity of Nu 32. "If a suspect is neither known to the victim nor arrested at the scene of the crime, a- 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.

24 GARY S. BECKER 23 APPROACH offenses observed in the table cannot be explained by a negative correla- (or severity. C') and tion between > 0, a reduction in the elasticity of offenses with respect to f If b increases the marginal revenue of changing offenses by changing f (see Figure 4a). The result is an increase in the optimal number of offenses and a decrease in the optimalf that is partially compensated by an increase in the optimal p. Similarly, a reduction in the elasticity of offenses with respect to p also increases the optimal number of offenses (see Figure the optimal p. and partially compensates by an increase in decreases 4b), f An equal percentage reduction in both elasticities a fortiori increases the optimal number of offenses and also tends to reduce both p and f If b both marginal revenue functions lie along the horizontal axis, = 0, and changes in these elasticities have no effect on the optimal values of p andf The income of a firm would usually be larger if it could separate, at tders is affected by a little cost, its total market into submarkets that have substantially dif- increases both ferent elasticities of demand: higher prices would be charged in the sub- of fingerprinting, markets having lower elasticities. Similarly, if the total "market" for àl analysis, or police offenses could be separated into submarkets that differ significantly in and merit, > the elasticities of supply of offenses, the results above imply that if b 0 extent. Our analy- the total loss would be reduced by "charging" lower "prices" —that is, nt in technology and lower p's and f's—in markets with !owei- elasticities. I recuce the optimal Sometimes it is possible to separate persons committing the same the need to rely offense into groups that have different responses to punishments. For this explains why the example, unpremeditated murderers or robbers are supposed to act rrn has gone hand in impulsively and, therefore, to be relatively unresponsive to the size of y between different Marginal Marginal rape or armed rob- cost cost of personal identi- MC Marginal Marginal latter offenses.32 revenue revenue significantly as one sig- are se the the left than for the implies that the f's cli is patently false. —bpf (i and the severity of Number of offenses Number of offenses at the scene of the crime, b. a- )fflmiSSiOn, l967e, p. 8). FIGURE 4 les during January, 1966.

25 24 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH punishments; likewise, the insane or the young are probably less affected of the payment "b' than other offenders by future consequences and, therefore,33 probably society, and a net si less deterred by increases in the probability of conviction or in the pun- offenses then becon ishment when convicted. The trend during the twentieth century toward ditions, because it relatively smaller prison terms and greater use of probation and therapy change in punishme for such groups and, more generally, the trend away from the doctrine of Although trans: "a given punishment for a given crime" is apparently at least broadly today, the other is consistent with the implications of the optimality analysis. Communist countri An increase in b increases the marginal revenue from changing the other punishments a number of offenses by changing p orf and thereby increases the optimal waiting-time forms number of offenses, reduces the optimal value off, and increases the opti- ing (see Becker, 196 mal value of p. Some evidence presented in Section II indicates that b is conditions. It is mt especially large for juveniles in detention homes or adults in prison and optimality conditior is small for fines or adults on parole. The analysis implies, therefore, that assumptions about t other things the same, the optimal f's would be smaller and the optimal p's larger if punishment were by one of the former rather than one of the B. OPTIMALITY Co latter methods. If b = 0, say, becau hending and convic V. FINES conditions (21) and A. WELFARE THEOREMS AND TRANSFERABLE PRICING Economists generall The usual optimality conditions in welfare economics depend only on the such as factories thl levels and not on the slopes of marginal cost and average revenue func- land, should be taxe tions, as in the well-known condition that marginal costs equal prices. external harm equal. The social loss from offenses was explicitly introduced as an application net damages equaled of the approach used itt welfare economics, and yet slopes as incorporated harm always exceed into elasticities of supply do significantly affect the optimality conditions. sumed to be zero, a: Why this difference? The primary explanation would appear to be that suitable inequality cc it is almost always implicitly assumed that prices paid by consumers are of apprehending, con fully transferred to firms and governments, so that there is no social loss offense caused more from payment. offenses would be If there were no social loss from punishments, as with fines, b would eliminate all offenses equal zero, and the elasticity of supply would drop out of the optimality with the criterion 01 If b > 0, as with imprisonment, some condition given by equation high.35 Equation (24) d 33. But see Becker (1962) for an analysis indicating that impulsive and other "irra- may be as deterred from purchasing a commodity whose price has risen the fine and probabi tional" persons as more "rational" persons. ordinarily prices do not affect because 34. It remains in eq. (22), through the slope 35. "The evil of the marginal costs, while they do here through the influence of p on C. (Bentham, 1931, first rule

26 APPROACH 25 GARY S. BECKER obably less affected the payment "by" offenders would not be received by the rest of of herefore,33 probably society, and a net social loss would result. The elasticity of the supply of iction or in the pun- offenses then becomes an important determinant of the optimality con- tieth century toward ditions, because it determines the change in social costs caused by a obation and therapy change in punishments. from the doctrine of Although transferable monetary pricing is the most common kind tly at least broadly today, the other is not unimportant, especially in underdeveloped and Communist countries. Examples in addition to imprisonment and many alysis. other punishments are the draft, payments in kind, and queues and other e from changing the increases the optimal waiting-time forms of rationing that result from legal restrictions on pric- increases the opti- and from random variations in demand and supply ing (see Becker, 1965) is II indicates that b conditions. it is interesting, and deserves further exploration, that the in prison and optimality conditions are so significantly affected by a change in the nplies, therefore, that assumptions about the transferability of pricing. and the optimal rather than one of the B. OPTEMALITY CoNDITIoNs say, because punishment was by fine, and if the cost of appre- If b = 0, hending and convicting offenders were also zero, the two optiniality conditions (21) and (22) would reduce to the same simple condition D'(O) 0. (24) CING Economists generally conclude that activities causing "external" harm, only on the depend such as factories that pollute the air or lumber operations that strip the tverage revenue func- land, should be taxed or otherwise restricted in level until the marginal costs equal prices. I external harm equaled the marginal private gain, that is, until marginal ced as an application net damages equaled zero, which is what equation (24) says. If marginal opes as incorporated harm always exceeded marginal gain, the optimum level would be pre- ptimality conditions. sumed to be zero, and that would also be the implication of (24) when appear to be that suitable inequality conditions were brought in. In other words, if the costs by consumers are of apprehending, convicting, and punishing offenders were nil and if each there is no social loss offense caused more external harm than private gain, the social loss from offenses would be minimized by setting punishments high enough to would s with fines, b eliminate all offenses. Minimizing the social loss would become identical )ut of the optimality with the criterion of minimizing crime by setting penalties sufficiently imprisonment, some high.35 Equation (24) determines the optimal number of offenses, O, and npulsive and other "irra- the fine and probability of conviction must be set at levels that induce ity whose price has risen narily prices do not affect of the punishment "The evil 35. must be made to exceed the advantage of the offense" C. (Bentham, 1931, first rule).

27 26 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH If the economists' usual theory of offenses. offenders to commit just O choice is applied to illegal activities (see Sec. II), the marginal value of In other words, off these penalties has to equal the marginal private gain: them as well as for I (25) ization of the usual V= G'(O), The optimality V is the monetary value is the marginal private gain at O and where G '(O) of the marginal penalties. Since by equations (3) and (24), D'(O) = H'(O) D' - one has by substitution in (25) G'(O) — = 0, would replace equal V= H'(O). (26) conviction were fixe The monetary value of the penalties would equal the marginal harm > 0,39 and thus that caused by offenses. number when costs Since the cost of apprehension and conviction is assumed equal to Victjon increase or d zero, the probability of apprehension and conviction could be set equal pends, therefore, on to unity without cost. The monetary value of penalties would then simply fine or in the probabj equal the fines imposed, and equation (26) would become control, the optimal j: to zero, unless the sc H'(Ô). (27) f = the discussion in Sec. Since fines are paid by offenders to the rest of society, a fine determined by (27) would exactly compensate thelatter for the marginal harm suf- C. THE CASE FOR F fered, and the criterion of minimizing the social loss would be identical, Just as the probabiljt3 if the harm at the margin, with the criterion of compensating "victims." subject to control by s to victims always exceeded the gain to offenders, both criteria would usually specifies whei reduce in turn to eliminating all offenses. institutionalization or If the cost of apprehension and conviction were not zero, the optimal- ity condition would have to incorporate marginal costs as well as marginal 38. Since equilibrium ri damages and would become, if the probability of conviction were still assumed to equal unity, then (29) follows directly (28) D'(O)+C'(O, 1)=0. by 39. That is, if, as seems Since C' > 0, (28) requires that D' < 0 or that the marginal private gain exceed the marginal external harm, which generally means a smaller It is easy to show that equation number of offenses than when D' = then (28) would be satisfied if the fine equaled the sum of marginal harm and marginal costs: and the rest of society and not just the persons actually harmed. is meant 36. By "victims" in the Mathematical of the results case derived as a special 37. This result can also be Appendix on the effects of increases in C'.

28 GARY S. BECKER 27 APPROACH (29) f= H'(O) + C'(O, l).38 sts' usual theory of e marginal value of In other words, offenders have to compensate for the cost of catching them as well as for the harm they directly do, which is a natural general- ization of the usual externality analysis. (25) The optimality condition monetary value the H(O) (24), D'(O) = (30) =0 D'(O) + C'(O, j5) + CP(O, j5) would replace equation (28) if the fine rather than the probability of (26) Conviction were fixed. Equation (30) would usually imply that D'(O) the marginal harm > and thus that the number of offenses would exceed the optimal number when costs were zero. Whether costs of apprehension and con- assumed equal to viction increase or decrease the optimal number of offenses largely de- equal be set could pends, therefore, on whether penalties are changed by a change in the would then simply fine or in the probability of conviction. Of course, if both are subject to kome control, the optimal probability of conviction would be arbitrarily close to zero, unless the social loss function differed from equation (18) (see (27) the discussion in Sec. III). a fine determined marginal harm suf- C. THE CASE FOR FINES would be identical, Just as the probability of conviction and the severity of punishment are 'ctims." 36 the harm If subject to control by society, so too is the form of punishment: legislation tboth criteria would usually specifies whether an offense is punishable by fines, probation, institutionalization, or some combination. Is it merely an accident, or z.ero, the optimal- Ls as well as marginal since from (28) 38. Since equilibrium requires thatf= G'(O), and :onviction were still 0(O) = 1), — C'(O, H'(O) = — G'(O) directly then (29) follows by substitution. (28) 39. That is, if, as seems plausible, private gain > 0, ± = dp ap ly means a smaller show that equation then f marginal harm and + <0, C, and persons actually harmed. suits in the Mathematical > 0. c,. D'(O) = _(c' +

29 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH 28 they are no worse 01 have optimality considerations determined that today, in most countries, other punishments fines are the predominant form of punishment, with institutionalization re- spend additional res served for the more serious offenses? This section presents several argu- prising, therefore, th ments which imply that social welfare is increased if fines are used it'hen- fact have not "paid ever feasible. punishments,43 inclu the first place, probation and institutionalization use up social re- In opportunities and sources, and fines do not, since the latter are basically just transfer pay- absen ments, while the former use resources in the form of guards, supervisory "rehabili otherwise personnel, probation officers, and the offenders' own time.4° Table 1 indi- therapy, and other pi about cates that the cost is not minor either: in the United States in 1965, much additional cost $1 billion was spent on "correction," and this estimate excludes, of sons do not easily d course, the value of the loss in offenders' time.41 usually levied again Moreover, the determination of the optimal number of offenses and habilitate" them. severity of punishments is somewhat simplified by the use of fines. A One argument n wise use of fines requires knowledge of marginal gains and harm and of in effect, they permit marginal apprehension and conviction costs; admittedly, such knowledge bread or other gooth is not easily acquired. A wise user of imprisonment and other punish- the price of an offem ments must know this too, however; and, in addition, must know about example, the "price' the elasticities of response of offenses to changes in punishments. As the only difference is in bitter controversies over the abolition of capital punishment suggest, it in monetary units, in has been difficult to learn about these elasticities. If anything, monetar I suggested earlier that premeditation, sanity, and age can enter into preferred iii pricing a the determination of punishments as proxies for the elasticities of re- Optimal fines d sponse. These characteristics may not have to be considered in levying marginal harm and cc fines, because the optimal fines, as determined, say, by equations (27) ers. This has been ci or (29), do not depend on elasticities. Perhaps this partly explains why economists discussing externalities almost never mention motivation or 42. Bentham recognii intent, while sociologists and lawyers discussing criminal behavior in- another useful quality in a variably do. The former assume that punishment is by a monetary tax or punishing an offense and fine, while the latter assume that nonmonetary punishments are used. to alarm. This is a charact Fines provide compensation to victims, and optimal fines at the mar- 43. In the same way. gin fully compensate victims and restore the status quo ante, so that society, has led to addit, bonuses, hospitalization ri 44. See Sutherland (I Several early writers on criminology recognized this advantage of fines. For ex- 40. 45. The very early Et ample. "Pecuniary punishments are highly economical, since all the evil felt by him who it has been said that "eve pays turns into an advantage for him who receives" (Bentham, 1931, chap. vi), and "Im- price, and much of the ju as a useless prisonment would have been regarded in these old times Ica. tenth these preappointed prices' punishment; it does not satisfy revenge, it keeps the criminal idle, and do what we may, The same idea was p ii is cost/v' (Pollock and Maitland, 1952, p. 516; my italics). police car carrying a sign 41. On the other hand, some transfer payments in the form of food, clothing, and speed limit—pick Out spee shelter are included.

30 29 GARY S. BECKER APPROACH they are no worse off than if offenses were not committed.42 Not only do y, in most countries, other punishments fail to compensate, but they also require "victims" to stitutionalization re- spend additional resources in carrying out the punishment. It is not sur- resents several argu- prising, therefore, that the anger and fear felt toward ex-convicts who in fines are used when- "paid fact have not their debt to society" have resulted in additionaf punishments,43 including legal restrictions on their political and economic use up social re- tion and informal restrictions on their social acceptance. opportunities ily just transfer pay- Moreover, the absence of compensation encourages efforts to change and I guards, supervisory psychiatric "rehabilitate" counseling, through offenders otherwise Table 1 mdi- therapy, and other programs. Since fines do compensate and do not create in 1965, about much additional cost, anger toward and fear of appropriately fined per- estimate excludes, of sons do not easily develop. As a result, additional punishments are not usually levied against "ex-finees," nor are strong efforts made to "re- of offenses and habilitate" them. the use of fines. A One argument made against fines is that they are immoral because, and harm and of in effect, they permit offenses to be bought for a price in the same way that such knowledge considered be bread or other goods are bought for a price.45 A fine can and other punish- the price of an offense, but so too can any other form of punishment; for on, must know about example, the "price" of stealing a car might be six months in jail. The As the only difference is in the units of measurement: fines are prices measured suggest, it in monetary units, imprisonments are prices measured in time units, etc. If anything, monetary units are to be preferred here as they are generally d age can enter into preferred in pricing and accounting. the elasticities of re- Optimal fines determined from equation (29) depend only on the in levying marginal harm and cost and not at all on the economic positions of offend- by equations (27) ers. This has been criticized as unfair, and fines proportional to the in- partly explains why ention motivation or 42. Bentham recognized this and said, "To furnish an indemnity to the injured party is criminal behavior in- another useful quality in a punishment. It is a means of accomplishing two objects at once— by a monetary tax or punishing an offense and repairing it: removing the evil of the first order, and putting a stop tishments are used. to alarm. This is a characteristic advantage of pecuniary punishments" (1931, chap. vi). ma! fines at the mar- 43. In the same way, the guilt felt by society in using the draft, a forced transfer to s quo ante, so that has led to additional payments to veterans in the form of education benefits, society, bonuses, hospitalization rights, etc. 44. See Sutherland (1960, pp. 267—68) for a list of some ut these. vantage of fines. For cx- 45. The very early English law relied heavily on monetary fines, even for murder, and the evil felt by him who it has been said that "every kind of blow or wound given to every kind of person had its 1931, chap. vi), and "Im- price, and much of the jurisprudence of the time must have consisted of a knowledge of nth century] as a useless these preappointed prices" (Pollock and Maitland, 1952, p. 451). le, and do what we may, The same idea was put amusingly in a recent Mutt and Jeff cartoon which showed a police car carrying a sign that read: "Speed limit 30 M per H—$5 fine every mile over rn of food, clothing, and speed limit—pick out speed you can afford."

31 30 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH comes of offenders have been suggested.46 If the goal is to minimize the felonies and other c social loss in income from offenses, and not to take vengeance or to inflict quently observed an harm on offenders, then fines should depend on the total harm done by 139—53), 1 do not kn offenders, and not directly on their income, race, sex, etc. In the same recognition that the way, the monetary value of optimal prison sentences and other punish- quence of the nature ments depends on the harm, costs, and elasticities of response, but not Another argumc directly on an offender's income. Indeed, if the monetary value of the murder or rape, are punishment by, say, imprisonment were independent of income, the pensate the harm related length of the sentence would be inversely to income, because the special case of the n value placed on a given sentence is positively related to income. exclusively wheneve: We might detour briefly to point out some interesting implications then victims could no for the probability of conviction of the fact that the monetary value of a have to be supplemer given fine is obviously the same for all offenders, while the monetary to discourage equivalent or "value" of a given prison sentence or probation period is probation, and parole generally positively related to an offender's income. The discussion in ies; considerable han Section 11 suggested that actual probabilities of conviction are not fixed resources to compen to all offenders but usually vary with their age, sex, race, and, in particu- need for a flexible lar, income. Offenders with higher earnings have an incentive to spend fines more readily an more on planning their offenses, on good lawyers, on legal appeals, and This analysis im even on bribery to reduce the probability of apprehension and conviction given offense and oth' for offenses punishable by, say, a given prison term, because the cost to by fine and the latte them of conviction is relatively large compared to the cost of these ex- these methods penditures. Similarly, however, poorer offenders have an incentive to fore the cry is raised ti use more of their time in planning their offenses, in court appearances, and consider the follOwin1 the like, to reduce the probability of conviction for offenses punishable Those punished by a given fine, because the cost to them of conviction is relatively large agreed to by their " compared to the value of their time.47 The implication is that the prob- for which su ability of conviction would be systematically related to the earnings of creditors. Moreover, offenders: negatively for offenses punishable by imprisonment and pos- voluntary market trat itively for those punishable by fines. Although a negative relation for "debtors" and others. one, the former is co when apprehended. Y For example, Bentham said, "A pecuniary punishment, if the sum is fixed, is in the 46. subsequently profit of the . Fines have been determined without regard to the . highest degree unequal. . . Pecuniary punishments should al- offense, to its evil, or to the wealth of the offender. . the poor man, in effec ways be regulated by the fortune of the offender. The relative amount of the fine should be Whether a punis fixed, not its absolute amount; for such an offense, such a part of the offender's fortune" offenders lacking suffi (1931, chap. ix). Note that optimal fines, as determined by eq. (29), do depend on "the profit of the offense" and on "its evil." 48. In one study, abou 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; (see President's Commissk likewise, the incentive to use money to reduce the probability of a given fine is also unrelated 49. The "debtor priso to earnings, because the punishment is fixed in monetary, not time, units. repay loans.

32 31 APPROACH GARY S. BECKER al is to minimize the felonies and other offenses punishable by imprisonment has been fre- engeance or to inflict quently observed and deplored (see President's Commission, 1967c, pp. total harm done by 1 39—53), I do not know of any studies of the relation for fines or of any ex, etc. In the same recognition that the observed negative relation may be more a conse- and other punish- quence of the nature of the punishment than of the influence of wealth. of response, but not Another argument made against fines is that certain crimes, like onetary value of the murder or rape, are so heinous that no amount of money could com- lent of income, the pensate for the harm inflicted. This argument has obvious merit and is a income, because the special case of the more general principle that fines cannot be relied on d to income. exclusively whenever the harm exceeds the resources of offenders. For eresting implications then victims could not be fully compensated by offenders, and fines would monetary value of a have to be supplemented with prison terms or other punishments in order while the monetary to discourage offenses optimally. This explains why imprisonments, fr probation period is probation, and parole are major punishments for the more serious felon- The discussion in ies; considerable harm is inflicted, and felonious offenders lack sufficient riviction are not fixed resources to compensate. Since fines are preferable, it also suggests the and, in particu- need for a flexible system of instalment fines to enable offenders to pay in incentive to spend fines more readily and thus avoid other punishments. legal appeals, and This analysis implies that if some offenders could pay the fine for a and conviction given offense and others could not,48 the former should be punished solely because the cost to by fine and the latter partly by other methods. In essence, therefore, cost of these ex- these methods become a vehicle for punishing "debtors" to society. Be- aye an incentive to fore the cry is raised that the system is unfair, especially to poor offenders, urt appearances, and consider the following. offenses punishable Those punished would be debtors in "transactions" that were never Ion is relatively large agreed to by their "creditors," not in voluntary transactions, such as is that the prob- loans,48 for which suitable precautions could be taken in advance by to the earnings of creditors. Moreover, punishment in any economic system based on prisonment and pos- voluntary market transactions inevitably must distinguish between such kegative relation for "debtors" and others. If a rich man purchases a car and a poor man steals one, the former is congratulated, while the latter is often sent to prison when apprehended. Yet the rich man's purchase is equivalent to a "theft" the sum is fixed, is in the subsequently compensated by a "fine" equal to the price of the car, while regard to the profit of the y punishments should al- the poor man, in effect, goes to prison because he cannot pay this "fine." ount of the fine should be Whether a punishment like imprisonment in lieu of a full fine for f the offender's fortune" offenders lacking sufficient resources is "fair" depends, of course, on the ,do depend on 'the profit 48. In one study, about half of those convicted of misdemeanors could not pay the fines ity of a given prison sen- (see President's Commission, 1967c. p. 148). me, not monetary, units; iven fine is also unrelated 49. The "debtor prisons" of earlier centuries generally housed persons who could not e, units. repay loans.

33 32 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH length of the prison term compared to the fine.50 For example, a prison larger than $1,000 a term of one week in lieu of a $10,000 fine would, if anything, be "unfair" months or a fine nc to wealthy offenders paying the fine. Since imprisonment is a more costly 1030, Arts. 70 and punishment to society than fines, the loss from offenses would be reduced excessive prison sei by a policy of leniency toward persons who are imprisoned because they imprisonment in liet cannot pay fines. Consequently, optimal prison terms for "debtors" would often must "choose', not be "unfair" to them in the sense that the monetary equivalent to them of the prison terms would be less than the value of optimal fines, which in D. COMPENSATION' turn would equal the harm caused or the "debt." 51 It appears, however, that "debtors" are often imprisoned at rates of Actual criminal proc exchange with fines that place a low value on time in prison. Although I of deterrence, comf have not seen systematic evidence on the different punishments actually that these goals are offered convicted offenders, and the choices they made, many statutes in simultaneously achi the United States do permit fines and imprisonment that place a low value minimizing the soda on time in prison. For example, in New York State, Class A Misde- sating "victims" fu. meanors can be punished by a prison term as long as one year or a fine no partially pursued. Tb ishment by optimal criminal law would 50. \'et without any discussion of the actual alternatives offered, the statement is made that "the money judgment assessed the punitive damages defendant hardly seems compara- First and forem ble in effect to the criminal sanctions of death, imprisonment, and stigmatization" ("Criminal become the same: n 1967). Safeguards ment of the "harm" SI. A formal proof is straightforward if for simplicity the probability of conviction is would become a bral taken as equal to unity. For then the sole optimality condition is the public would coIl (1') would be defined fun \ the inability of a per Since D' = H' — C', by substitution one has Thus an action woulc pensated "harm" to (2') while tort law would As a practical e and since equilibrium requires that C' =f, wrought, consider th (3') 1= H' + C' + bf(l classic demonstratior and reduce econom; or 52. "Violations," H'+C' , (4') days or fines no larger — b(I — 11€,) I imposed by the courts can (see Sec. 111), and hence by eq. (4'), punish by imprisonment, b If b > 0, €, < I 53. "The cardinal (5') compensation for the injul where the term on the right is the full marginal harm. If p as well asfis free to vary, the James, 1956, p. 1299). analysis becomes more complicated, but the conclusion about the relative monetary values 54. Of course, many I of optimal imprisonments and fines remains the same (see the Mathematical Appendix). be criminal under this app

34 33 GARY S. BECKER APPROACH larger than $1,000 and Class B Misdemeanors, by a term as long as three or example, a prison months or a fine no larger than $500 (Laws of New York, 1965, chap. nything, be "unfair" 1030, Arts. 70 and 80).52 According to my analysis, these statutes permit nent is a more costly excessive prison sentences relative to the fines, which may explain why es would be reduced imprisonment in lieu of fines is considered unfair to poor offenders, who •isoned because they often must "choose" the prison alternative. for "debtors" would y equivalent to them ptimal fines, which in D. COMPENSATION AND THE CRIMINAL LAW nprisoned at rates of Actual criminal proceedings in the United States appear to seek a mixture in prison. Although I of deterrence, compensation, and vengeance. I have already indicated 1punishments actually that these goals are somewhat contradictory and cannot generally be çade., many statutes in simultaneously achieved; for example, if punishment were by fine, 'that place a low value minimizing the social loss from offenses would be equivalent to compen- tate, Class A Misde- sating "victims" fully, and deterrence or vengeance could only be one year or a fine no partially pursued. Therefore, if the case for fines were accepted, and pun- ishment by optimal fines became the norm, the traditional approach to criminal law would have to be significantly modified. the statement is made cred, hardly seems corn First and foremost, the primary aim of all legal proceedings would ('Criminal become the same: not punishment or deterrence, but simply the assess- ment of the "harm" done by defendants. Much of traditional criminal law probability of conviction is would become a branch of the law of torts,53 say "social torts," in which the public would collectively sue for "public" harm. A "criminal" action (1') would be defined fundamentally not by the nature of the action but by the 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, (2') while tort law would cover all other (civil) actions. As a practical example of the fundamental changes that would be wrought, consider the antitrust field. Inspired in part by the economist's classic demonstration that monopolies distort the allocation of resources (3') and reduce economic welfare, the United States has outlawed con- however, can only be punished by prison terms as long as fifteen 52. "Violations," (4') days or fines no larger than $250. Since these are maximum punishments, the actual ones imposed by the courts can, and often are, considerably less. Note, too, that the courts can York, 1965, chap. 1030, Art. 60). of punish by imprisonment, by fine, or by both(La,i's 53. "The cardinal principle of damages in Anglo-American law [of torts] is that of (5') conzpensatiolz for the injury caused to plaintiff by defendant's breach of duty" (Harper and James, 1956, p. 1299). II asfis free to vary, the 54. Of course, many traditional criminal actions like murder or rape would still usually relative values monetary be criminal under this approach too. Mathematical Appendix).

35 34 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH realize that difficult ju spiracies and other constraints of trade. In practice, defendants are often simply required to cease the objectionable activity, although sometimes policy, such as decidir they are also fined, become subject to damage suits, or are jailed. tive or that certain rn if compensation were stressed, the main purpose of legal proceedings and compensation wot would be to levy fines equal to the harm inflicted on society by con- attention on the infor straints of trade. There would be no point to cease and desist orders, imprisonment, ridicule, or dissolution of companies. If the economist's Vi. PRIVATE EXPI theory about monopoly is correct, and if optimal fines were levied, firms would automatically cease any constraints of trade, because the gain to A variety of private them would be less than the harm they cause and thus less than the fines number and incidence expected. On the other hand, if Schumpeter and other critics are correct, employed, locks and al and certain constraints of trade raise the level of economic welfare, and neighborhoods av fines could fully compensate society for the harm done, and yet some list and so on. Table I constraints would not cease, because the gain to participants would ex- and this undoubtedly i ceed the harm to others.56 is private action esr One unexpected advantage, therefore, from stressing compensation economies, where freq and fines rather than punishment and deterrence is that the validity of the his person, to the "car classical position need not be judged a priori. If valid, compensating If each person tn fines would discourage all constraints of trade and would achieve the crimes, optimal privat classical aims. If not, such fines would permit the socially desirable discussion of optimal constraints to continue and, at the same time, would compensate society similar to that given b for the harm done. H = Of course, as participants in triple-damage suits are well aware, the harm done is not easily measured, and serious mistakes would be inevit- represer The term able. However, it is also extremely difficult to measure the harm in many while C,, repr against j, civil suits,57 yet these continue to function, probably reasonably well on tion of p,, for offenses the whole. Moreover, as experience accumulated, the margin of error positively related to 0 would decline, and rules of thumb would develop. Finally, one must tures on crime, and persons.58 fines should exceed the harm done if the probability of conviction were 55. Actually, The term conviction is the intellectual justification for unity. The possibility of avoiding less than of offenders committir punitive, such as triple, damages against those convicted. in a net loss to society The classical view is that D'(M) always 56. measures is greater than zero, where M victims. For example, the different constraints of trade and D' measures the marginal damage; the critic's view is D'(M) < 0. It has been shown above that if D' always is greater than that for some Al, just a transfer paymen zero, compensating fines would discourage all offenses, in this case constraints of trade, is less than zero, some offenses would remain (unless sometimes the while if D' 58. An increase in C1 marginal cost of detecting and convicting offenders, were sufficiently large relative to D'). againstj, because more of i 57. Harper and James said, "Sometimes [compensation] can be accomplished with 59. The expected a fair degree of accuracy. But obviously it cannot be done in anything but a figurative siderable variance because and essentially speculative way for many of the consequences of personal injury. Yet it is any single person. 1ff were the aim of the law to attain at least a rough correspondence between the amount awarded as dude a term that dependec damages and the extent of the suffering" (1956, p. 1301).

36 35 GARY S. BECKER C APPROACH are often , defendants realize that difficult judgments are also required by the present antitrust ',although sometimes policy, such as deciding that certain industries are "workably" competi- s, or are jailed. tive or that certain mergers reduce competition. An emphasis on fines se of legal proceedings and compensation would at least help avoid irrelevant issues by focusing on society by con- attention on the information iftost needed for intelligent social policy. ise and desist orders, es. If the economist's VI. PRIVATE EXPENDITURES AGAINST CRIME nes were levied, firms e, because the gain to A variety of private as well as public actions also attempt to reduce the hus less than the fines number and incidence of crimes: guards, doormen, and accountants are ler critics are correct, employed, locks and alarms installed, insurance coverage extended, parks economic welfare, and neighborhoods avoided, taxis used in place of walking or subways, rn done, and yet some 1 965, and so on. Table 1 lists close to $2 billion of such expenditures in participants would ex- and this undoubtedly is a gross underestimate of the total. The need for highly interdependent modern private action is especially great in tressing compensation economies, where frequently a person must trust his resources, including the validity of the his person, to the "care" of employees, employers, customers, or sellers. valid, compensating If each person tries to minimize his expected loss in income from would achieve the crimes, optimal private decisions can be easily derived from the previous socially desirable discussion of optimal public ones. For each person there is a loss function tid compensate society similar to that given by equation (18): (3 1) + + C)(p), C, Us are well aware, the would be inevit- The term the 0) offenses committed from represents the harm to j sure the harm in many againstj, while C, represents his cost of achieving a probability of convic- ly reasonably well on tion of for offenses committed against him. Note that C2 not only is the margin of error positively related to 0,, but also is negatively related to C, public expendi- p. Finally, one must set of private expenditures by other the tures on crime, and to Ck, persons.58 bability of conviction were The term measures the expected loss toj from punishment justification for of offenders committing any of the 0,,. Whereas most punishments result in a net loss to society as a whole, they often produce a gain for the actual zero, where M measures victims. For example, punishment by fines given to the actual victims is damage; the critic's view is D' always is greater than just a transfer payment for society but is a clear gain to victims; similarly, case constraints of trade, remain (unless C'[M], the ently large relative to D'). solve offenses 58. constant—presumably helps An increase in C1, — 0,, and C held can be accomplished with againstj, because more of those against k would be solved. anything but a figurative 59. The expected private loss, unlike the expected social loss, is apt to have con- f personal injury. Yet it is siderable variance because of the small number of independent offenses committed against een the amount awarded as any 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

37 36 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH probability of apprel punishment by imprisonment is a net loss to society but is a negligible able, and in treating loss to victims, since they usually pay a negligible part of imprisonment well as by monetary costs. This is why is often less than or equal to zero, at the same time analytically from an that b, the coefficient of social loss, is greater than or equal to zero. when crimes are pun are determined primarily by public policy on punish- Since vanish. ments, the main decision variable directly controlled by j is p,. If he Discussions of chooses a p,, that minimizes the optimality condition analogous to fectly symmetrical to equation (22) is / analogues to the law 1\60 a u' i_ c" c' — 1 lAj T — — cannot be collected €)Pj caused, and no publi elasticity measures the effect of a change in on the number of The torneys apprehend at b, < 0, and if the left-hand side of equa- offenses committed against j. If course, there is publi tion (32), the marginal cost of changing were greater than zero, then other, privileges (32) implies that > 1. Since offenders can substitute among victims, officials, scientists, is probably much larger than E,,, the response of the total number of private bodies. Amor offenses to a change in the average probability, p. There is no incon- the Congressional sistency, therefore, between a requirement from the optimality condi- these are piecemeal > 1. tion given by (22) that ç < I and a requirement from (32) that and lack the guidanc ferent kinds of advan Possibly the exp VII. SOME APPLICATIONS developed at the tim A. OPTIMAL BENEFITS vantages, or possibly considered too prone Our analysis of crime is a generalization of the economist's analysis of metry in the law do external harm or diseconomies. Analytically, the generalization consists formal analysis of ad' in introducing costs of apprehension and conviction, which make the that is quite symmetr ers. A function A(B 1 have assumed that 60. from B benefits in th offenses. Likewise, äCk — = — = 0, rewarding benefactoi 3p, and > 0; B(p1, a other words, that j is too "unimportant" to influence other expenditures. Although in award per benefit an usually reasonable, this does suggest a modification to the optimality conditions given by eqs. (21) and (22). Since the effects of public expenditures depend on the level of private aB/aa> 0; and b1 ca ones, and since the public is sufficiently "important" to influence private actions, eq. (!2) stead of a loss func has to be modified to offenses, there can 1 from benefits: (22') and similarly for eq. (21). "The" probability p is, of course, a weighted average of the If 11 is maximiz p,. Eq. (22') incorporates the presumption that an increase in public expenditures would be optimality condition: partially thwarted by an induced decrease in private ones.

38 37 GARY S. BECKER APPROACH probability of apprehension and conviction an important decision vari- y but is a negligible able, and in treating punishment by imprisonment and other methods as art of imprisonment well as by monetary payments. A crime is apparently not so different ro, at the same time analytically from any other activity that produces external harm and tr equal to zero. when crimes are punishable by fines, the analytical differences virtually lic policy on punish- vanish. p3. If he is led by j Discussions of external economies or advantages are usually per- ridition analogous to fectly symmetrical to those of diseconomies, yet one searches in vain for 60 analogues to the law of torts and criminality. Generally, compensation (32) cannot be collected for the external advantages as opposed to harm caused, and no public officials comparable to policemen and district at- on the number of torneys apprehend and "convict" benefactors rather than offenders. Of ft-hand side of equa- course, there is public interest in benefactors: medals, prizes, titles, and eater than zero, then other privileges have been awarded to military heroes, government titute among victims, officials, scientists, scholars, artists, and businessmen by public and f the total number of private bodies. Among the most famous are Nobel Prizes, Lenin Prizes, p. There is no incon- the Congressional Medal of Honor, knighthood, and patent rights. But the optimality condi- these are piecemeal efforts that touch a tiny fraction of the population > 1. rom (32) that and 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 law developed at the time when external harm was more common than ad- vantages, or possibly the latter have been difficult to measure and thus considered too prone to favoritism. In any case, it is clear that the asym- )nomist's analysis of metry in the law does not result from any analytical asymmetry, for a neralization consists formal analysis of advantages, benefits, and benefactors can be developed on, which make the that is quite symmetrical to the analysis of damages, offenses, and offend- ers. A function A(B), for example, can give the net social advantages from B benefits in the same way that D(O) gives the net damages from 0 offenses. Likewise, K(B, can give the cost of apprehending and rewarding 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 the expenditures. Although r award per benefit and v represents other determinants, with aB/ap1 and timality conditions given äB/3a > end on the level of private 0; and b1 can be the fraction of a that is a net loss to society. In- e private actions, eq. (!2) stead of a loss function showing the decrease in social income from offenses, there can be a profit function showing the increase in income from benefits: (22') €p / — K(B, b1p1aB. (33) A(B) II = Pi) — weighted average of the If [I is maximized by choosing appropriate values of p1 and a, the blic expenditures would be optimality conditions analogous to equations (21) and (22) are

39 38 CRIME AND PUNISHMENT: AN EcoNoMIc APPROACH (i +1) marginal income of c A' — = K' b,p,a (34) less risky legal activi and "benefits do pay"—i: factors would this sense it "pays" I (35) As an illustratio inventors for their ii where value of B invention one. The function K( a tors; if a patent syste preparing applicatior and in patent litigation.62 inventors to changes Pi = b, measures the a patent system, the than would otherwis are both greater than zero. The implications of these equations are related Equations (34) a to and yet differ in some important respects from those discussed earlier the smaller the elasti for (21) and (22). the probability and n For example, if b, > 0, which means that a is not a pure transfer but changed, for exampit costs society resources, clearly (34) and (35) imply that e5 > since the controversy both > 0 and ap1/3B > 0. This is analogous to the implication of(21) from a basic desire and (22) that > e,, but, while the latter implies that, at the margin, from the prospects of offenders are risk preferrers, the former implies that, at the margin, bene- on systematic inves factors are risk avoiders.6' Thus, while the optimal values of p and f quite consistently ust would be in a region where "crime does not pay"—in the sense that the equally consistently Even if A', the r 61. The relation e9 > e0 holds if, and only if, optimal decision wou aEUa 3EUp, if is, to set p, = 0, (1') e,, and Ca sufficiently where or greatly alter the p costliness, large K oi (2') example, Plant, 1934 (see the discussion on pp. 177—78). By differentiating eq. (2'), one can write (I') as If a patent syster p,[U(Y+a)— U(Y)] > a), (3') ticities of response or 62. These costs are i U(Y+a)—U(Y) U'(Y+a). (4') alone spent $34 million (s spent in preparing applicat But (4') holds if everywhere U" < 0 and does not hold if everywhere U" 0, which was to 63. Presumably one r' be proved. (that is, cost) of discoverir

40 APPROACH GARY S. BECKER 39 marginal income of criminals would be less than that available to them in (34) less 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. In this sense it "pays" to do "good" and does not "pay" to do "bad." (35) As an illustration of the analysis,.consider the problem of rewarding inventors for their inventions. The function A(B) gives the total social value of B inventions, and A' gives the marginal value of an additional one. 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, of preparing applications, and of the lawyers, judges, and others involved the response of measure e0 and in patent litigation.62 The elasticities e,, inventors to changes in the probability and magnitude of awards, while b1 measures the social cost of the method used to award inventors. With a patent system, the cost consists in a less extensive use of an invention than would otherwise occur, and in any monopoly power so created. equations are related Equations (34) and (35) imply that with any system having b1 > 0, rose discussed earlier the smaller the elasticities of response of inventors, the smaller should be the probability and magnitude of awards. (The value of a patent can be a pure transfer but changed, for example, by changing its life.) This shows the relevance of ily that e,, > e11, since the controversy between those who maintain that most inventions stem implication of(21) from a basic desire "to know" and those who maintain that most stem that, at the margin, from the prospects of financial awards, especially today with the emphasis at the margin, bene- on systematic investment in research and development. The former nal values of p and f quite consistently usually advocate a weak patent system, while the latter the sense that the equally consistently advocate its strengthening. Even if A', the marginal value of an invention, were "sizable," the optimal decision would be to abolish property rights in an invention, that sufficiently large and/or the elasticities were if b1 and K 63 is, to set Pt = 0, (I') and sufficiently small. Indeed, practically all arguments to eliminate ea or greatly alter the patent system have been based either on its alleged (see, e(, costliness, large K or b1, or lack of effectiveness, low e,) or for (2') example, Plant, 1934, or Arrow, 1962). e can write (I') as If a patent system were replaced by a system of cash prizes, the elas- (3') 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 Office (4') alone spent $34 million (see Bureau of the Budget, 1967), and much more was probably spent in preparing applications and in litigation. ere U' 0, which was to 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.

41 40 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH the effectiveness. Th optimal policies, because b1 would then be approximately zero.64 A sys- ferent kinds of offen tem of prizes would, moreover, have many of the same other advantages rape, or crimes of y that fines have in punishing offenders (see the discussion in Sec. V). One sive to changes in p significant advantage of a patent system, however, is that it automatically like embezzlement, "meters" A', that is, provides an award that is automatically positively estimated by Smigel related to A', while a system of prizes (or of fines and imprisonment) has do differ considerabi to estimate A' (or D') independently and often somewhat arbitrarily. theft, and assault tha Probably effecti' B. THE EFFECTIVENESS OF PUBLIC POLICY ferences in the ticities of response. The anticipation of conviction and punishment reduces the loss from that varies greatly, offenses and thus increases social welfare by discouraging some offenders. offense.67 For the eai What determines the increase in welfare, that is "effectiveness," of public be brought in and tF efforts to discourage offenses? The model developed in Section III can identify the offender. be used to answer this question if social welfare is measured by income bery than for a relat and if "effectiveness" is defined as a ratio of the maximum feasible in- fair-employment legi crease in income to the increase if all offenses causing net damages were antitrust and public-u abolished by fiat. The maximum feasible increase is achieved by choosing optimal values of the probability of apprehension and conviction, p, C. A THEORY OF C and the size of punishments, f (assuming that the coefficient of social loss from punishment, b, is given). 65 The theory develope. so defined can vary between zero and unity and de- Effectiveness dude certain kinds ( pends essentially on two behavioral relations: the costs of apprehension "unlawful." As an e and conviction and the elasticities of response of offenses to changes in lude in order to obtai p andf. The smaller these costs or the greater these elasticities, the smaller theory of the determ the cost of achieving any given reduction in offenses and thus the greater industry, a theory competitive, monopo and the optimality vanish, and (35) would conditions side of both (34) The right 64. would emerge. One b: would be a theory is of collusic (34') A' — K' = 0 The gain to firms and of their marginal cosi (35') A' — K' — K,, 0. 66. A theoretical argu Since these equations are not satisfied by any finite values of Pi and a, there is a difficulty offenders are less responsi and a (see the similar discussion for fines in Sec. V). 67. A study of crimes in allocating the incentives between 65. In symbols, effectiveness is defined as than half the arrests were made within the first week 68. Evidence relating b13JO] D(0,)—[D(O)+ C(13, Ô)+ E= penalties for these white-c D(0,) — D(02) and Johnson (1967). where j3,f, and O are optimal values, 0, offenses would occur ifp=f= 0, and 0, is the 69. Jacob Mincer value of 0 that minimizes D.

42 GARY S. BECKER 41 APPROACH the effectiveness. The elasticities may well differ considerably among dif- zero.64 A sys- ferent kinds of offenses. For example, crimes of passion, like murder or me other advantages rape, or crimes of youth, like auto theft, are often said to be less respon- sian in Sec. V). One sive to changes in p and f than are more calculating crimes by adults, that it automatically like embezzlement, antitrust violation, or bank robbery. The elasticities ornatically positively estimated by Smigel (1965) and Ehrlich (1967) for seven major felonies d imprisonment) has do differ considerably but are not clearly smaller for murder, rape, auto ewhat arbitrarily. theft, 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 one duces the loss from that varies greatly, is the time between commission and detection of an some offenders. offense.67 For the earlier an offense is detected, the earlier the police can bctiveness," of public be brought in and themore likely that the victim is able personally to ed in Section III can identify the offender. This suggests that effectiveness is greater for rob- by income bery than for a related felony like burglary, or for minimum-wage and Tiaximum feasible in- fair-employment legislation than for other white-collar legislation like net damages were antitrust and public-utility regulation.68 achieved by choosing and conviction, p. C. A THEORY OF COLLUSION coefficient of social The theory developed in this essay can be applied to any effort to pre- ro and unity and de- clude certain kinds of behavior, regardless of whether the behavior is osts of apprehension "unlawful." As an example, consider efforts by competing firms to col- ifenses to changes in lude in order to obtain monopoly profits. Economists lack a satisfactory lasticities, the smaller theory of the determinants of price and output policies by firms in an and thus the greater industry, a theory that could predict under what conditions perfectly competitive, monopolistic, or various intermediate kinds of behavior the optimality conditions would emerge. One by-product of our approach to crime and punishment is a theory of collusion that appears to fill a good part of this lacuna.6" (34') The gain to firms from colluding is positively related to the elasticity of their marginal cost curves and is inversely related to the elasticity of (35') A theoretical argument that also casts doubt on the assertion that less "calculating" 66. nd a, there a difficulty is offenders are less responsive to changes in p andf can be found in Becker (1962). ssion for fines in Sec. V). 67. A study of crimes in parts of Los Angeles during January, 1966, found that "more than half the arrests were made within 8 hours of the crime, and almost two-thirds were made 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). p=f= 0, and 02 is the 69. Jacob Mincer first suggested this application to me.

43 42 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH their collective demand curve. A firm that violates a collusive arrange- tries have an incentiv ment by pricing below or producing more than is specified can be said to firms producing illega commit an "offense" against the collusion. The resulting harm to the col- tion, and abortion. Th lusion would depend on the number of violations and on the elasticities successful collusion tI of demand and marginal cost curves, since the gain from colluding de- like the United States pends on these elasticities. would seem to have an If violations could be eliminated without cost, the optimal solution could be used against would obviously be to eliminate all of them and to engage in pure monop- course. On the other F. oly pricing, in general, however, as with other kinds of offenses, there ized collusions, those are two costs of eliminating violations. There is first of all the cost of cause violators discovering violations and of "apprehending" violators. This cost is c greater, the greater the desired probability of detection and the greater lusions in illegal indu the number of violations. Other things the same, the latter is usually prewar Germany. positively related to the number of firms in an industry, which partly explains why economists typically relate monopoly power to concentra- tion. The cost of achieving a given probability of detection also depends VIII. SUMMARY A on the number of firms, on the number of customers, on the stability of This essay uses econo customer buying patterns, and on government policies toward collusive policies to combat ille arrangements (see Stigler, 1964). its expenditures on po Second, there is the cost to the collusion of punishing violators. The bility (p) that an offens most favorable situation is one in which fines could be levied against convicted, the size of violators and collected by the collusion. If fines and other legal recourse form of the punishme are ruled out, methods like predatory price-cutting or violence have to values of these variabl be used, and they hurt the collusion as well as violators. the constraints impost Firms in a collusion are assumed to choose probabilities of detection, damages caused by a g punishments to violators, and prices and outputs that minimize their loss another the cost of ack from violations, which would at the same time maximize their gain from in p andf on 0. colluding. Optimal prices and outputs would be closer to the competitive "Optimal" decisioi position the more elastic demand curves were, the greater the number of the social loss in incon sellers and buyers, the less transferable punishments were, and the more costs of apprehension hostile to collusion governments were. Note that misallocation of re- ishments imposed, and sources could not be measured simply by the deviation of actual from p, f, and the form of competitive outputs but would depend also on the cost of enforcing collu- strained by "outside" sions. Note further, and more importantly, that this theory, unlike most from the minimization I theories of pricing, provides for continuous variation from purely com- illustrated by a few petitive through intermediate situations to purely monopolistic pricing. If carrying out thc These situations differ primarily because of differences in the "optimal" imprisonment, or paro number of violations, which in turn are related to differences in the spect to a change in p' elasticities, concentrations, legislation, etc., already mentioned. These ideas appear to be helpful in understanding the relative success of collusions in illegal industries themselves! Just as firms in legal indus- 70. An interpretation of

44 APPROACH GARY S. BECKER 43 a collusive arrange- tries have an incentive to collude to raise prices and profits, so too do ecifled can be said to firms producing illegal products, such as narcotics, gambling, prostitu- Llting harm to the cot- tion, and abortion. The "syndicate" is an example of a presumably highly nd on the elasticities successful collusion that covers several illegal products.7° In a country in from colluding de- like the United States that prohibits collusions, those in illegal industries would seem to have an advantage, because force and other illegal methods the optimal solution could be used against violators without the latter having much legal re- ngage in pure monop- course. On the other hand, in countries like prewar Germany that legal- tds of offenses, there ized collusions, those in legal industries would have an advantage, be- irst of all the cost of cause violators could often be legally prosecuted. One would predict, olators. This cost is therefore, from this consideration alone, relatively more successful col- ction and the greater lusions in illegal industries in the United States, and in legal ones in the latter is usually prewar Germany. which partly power to concentra- etection also depends VIII. SUMMARY AND CONCLUDING REMARKS ers, on the stability of his essay uses economic analysis to develop optimal public and private toward collusive policies to combat illegal behavior. The public's decision variables are its expenditures on police, Courts, etc., which help determine the proba- violators. The bility (p) that an offense is discovered and the offender apprehended and be levied against convicted, the size of the punishment for those convicted (f), and the other legal recourse form of the punishment: imprisonment, probation, fine, etc. Optimal g or violence have to values of these variables can be chosen subject to, among other things, tators. the constraints imposed by three behavioral relations. One shows the babilities of detection, damages caused by a given number of illegal actions, called offenses (0), minimize their loss another the cost of achieving a given p, and the third the effect of changes timize their gain from in p andf on 0. to the competitive "Optimal" decisions are interpreted to mean decisions that minimize greater the number of the social loss in income from offenses. This loss is the sum of damages, were, and the more costs of apprehension and conviction, and costs of carrying out the pun- misallocation of re- ishments imposed, and can be minimized simultaneously with respect to of actual from p, f, and the form of f unless one or more of these variables is Con- st of enforcing collu- strained by "outside" considerations. The optimality conditions derived theory, unlike most from the minimization have numerous interesting implications that can be )n from purely corn- illustrated by a few examples. nonopolistic pricing. If carrying out the punishment were costly, as it is with probation, ces in the "optimal" imprisonment, or parole, the elasticity of response of offenses with re- .0 differences in the spect to a change in p would generally, in equilibrium, have to exceed its mentioned. g the relative success firms in legal indus- 70. An interpretation of the syndicate along these lines is also found in Schilling (1967).

45 SI 44 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH cies. The small amoL response to a change inf. This implies, if entry into illegal activities can amined certainly be explained by the same model of choice that economists use to explain cies. For example, it entry into legal activities, that offenders are (at the margin) "risk pre- States that more dan ferrers." Consequently, illegal activities "would not pay" (at the margin) elasticity of response in the sense that the real income received would be less than what could f, and that both are u be received in less risky legal activities. The conclusion that "crime would mality analysis. There not pay" is an optimality condition and not an implication about the effi- the actual tradeoff be ciency of the police or courts; indeed, it holds for any level of efficiency, is frequently less, rati, as long as optimal values of p and! appropriate to each level are chosen. prisoned. Although m: If costs were the same, the optimal values of both p and f would be are seriously hampere greater, the greater the damage caused by an offense. Therefore, offenses quantity and quality like murder and rape should be solved more frequently and punished more the analytical side by severely than milder offenses like auto theft and petty larceny. Evidence sion-making. on actual probabilities and punishments in the United States is strongly Reasonable men consistent with this implication of the optimality analysis. fits caused by different Fines have several advantages over other punishments: for example, tive labor markets are they conserve resources, compensate society as well as punish offenders, minimum are violatioi and simplify the determination of optimal p's and f's. Not surprisingly, and even abortion shc fines are the most common punishment and have grown in importance market price, while tc over time. Offenders who cannot pay fines have to be punished in other These differences are ways, but the optimality analysis implies that the monetary value to them public policy but have of these punishments should generally be less than the fines. sus on damages and Vengeance, deterrence, safety, rehabilitation, and compensation are optimal implementatic perhaps the most important of the many desiderata proposed throughout The main contribi history. Next to these, minimizing the social loss in income may seem optimal policies to cot narrow, bland, and even quaint. Unquestionably, the income criterion can tion of resources. Sinc be usefully generalized in several directions, and a few have already been allocation, an "econol suggested in the essay. Yet one should not lose sight of the fact that it is enrich, the analysis of more general and powerful than it may seem and actually includes more aspects of the latter e dramatic desiderata as special cases. For example, if punishment were by as imprisonments, are an optimal fine, minimizing the loss in income would be equivalent to as well as to offender compensating "victims" fully and would eliminate the "alarm" that so that enters both the re worried Bentham; or it would be equivalent to deterring all offenses Lest the reader be causing great damage if the cost of apprehending, convicting, and punish- framework for illegal ing these offenders were relatively small. Since the same could also be tributors to criminolot demonstrated for vengeance or rehabilitation, the moral should be clear: Beccaria and Benthan minimizing the loss in income is actually very general and thus is more tunately, such an appi useful than these catchy and dramatic but inflexible desiderata. and my efforts can I This essay concentrates almost entirely on determining optimal thereby I hope impro\ policies to combat illegal behavior and pays little attention to actual poli-

46 45 GARY S. BECKER C APPROACH cies. The small amount of evidence on actual policies that I have ex- O illegal activities can amined certainly suggests a positive correspondence with optimal poli- iomists use to explain cies. For example, it is found for seven major felonies in the United margin) "risk pre- States that more damaging ones are penalized more severely, that the t pay" (at the margin) elasticity of response of offenses to changes in p exceeds the response to less than what could f, and that both are usually less than unity, all as predicted by the opti- ion that "crime would mality analysis. There are, however, some discrepancies too: for example, ication about the effi- the actual tradeoff between imprisonment and fines in different statutes ny level of efficiency, is frequently less, rather than the predicted more, favorable to those im- ach level are chosen. prisoned. Although many more studies of actual policies are needed, they oth p and f would be are seriously hampered on the empirical side by grave limitations in the e. Therefore, offenses quantity and quality of data on offenses, convictions, costs, etc., and on tly and punished more the analytical side by the absence of a reliable theory of political deci- Evidence sion-making. States is strongly Reasonable men will often differ on the amount of damages or bene- haiysis. fits caused by different activities. To same, any wage rates set by competi- hments: for example, tive labor markets are permissible, while to others, rates below a certain as punish offenders, minimum are violations of basic rights; to some, gambling, prostitution, Not surprisingly, and even abortion should be freely available to anyone willing to pay the grown in importance market price, while to others, gambling is sinful and abortion is murder. be punished in other These differences are basic to the development and implementation of bnetary value to them public policy but have been excluded from my inquiry. I assume consen- the fines. sus on damages and benefits and simply try to work out rules for an nd compensation are optimal implementation of this consensus. proposed throughout The main contribution of this essay, as I see it, is to demonstrate that income may seem optimal policies to combat illegal behavior are part of an optimal alloca- income criterion can tion of resources. Since economics has been developed to handle resource w have already been allocation, an "economic" framework becomes applicable to, and helps t of the fact that it is enrich, the analysis of illegal behavior. At the Same time, certain unique tually includes more aspects of the latter enrich economic analysis: some punishments, such were by as imprisonments, are necessarily nonmonetary and are a cost to society ruld be equivalent to as well as to offenders; the degree of uncertainty is a decision variable the "alarm" that so that enters both the revenue and cost functions; etc. eterring all offenses Lest the reader be repelled by the apparent novelty of an "economic" ivicting, and punish- framework for illegal behavior, let him recall that two important con- same could also be tributors to criminology during the eighteenth and nineteenth centuries, oral should be clear: Beccaria and Bentham, explicitly applied an economic calculus. Unfor- ral and thus is more tunately, such an approach has lost favor during the last hundred years, desiderata. and my efforts can be viewed as a resurrection, modernization, and letermining optimal thereby I hope improvement, of these much earlier pioneering studies. to actual pofi-

47 46 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH MATHEMATICAL APPENDIX Since D'+C'>O a This Appendix derives the effects of changes in vanous parameters on the E1> I Therefore optimal 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. Suppose that D' ac , ac ap , aD ofachangeinaon/c the analysis could easily be extended to cover negative values of b and of this marginal cost term. The conclusion in the text (Sec. II) that D" + C" > 0 is relied on here. I take it to be a reasonable first approximation that the elastici- or ties of 0 with respect to p or fare constant. At several places a sufficient condi- tion for the conclusions reached is that a2c a2c Cpo — Cop Since a is "small" relative to some other terms. This condition is utilized in the form although I cannot claim any supporting of a strong assumption that = 0, intuitive or other evidence. In a similar way it The social loss in income from offenses has been defined as enous variable (Al) LD(O)+C(0,p)+bpf0. fixed, the value off that minimized L would be found from the If b and p were necessary condition . If b is positively re (A2) (D"+C") or or 0D'+C'+bpf(l—E1), (A3) if 0, Since 1 — < 0, and b = where —af 0 E1— y Note that since lIE1 < I The sufficient condition would be that a2L/af2 > 0; using aLl af = 0 and E1 is constant, this condition becomes If E, is positively re (A4) = (D" + C")0,2 + bp(1 — E1)01> 0, or

48 GARY S. BECKER 47 APPROACH (AS) Since D' + C' > 0, and b is not less than zero, equation (A3) implies that us 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(l D" + C"> 0 is that da ation that the elastici- or aces a sufficient condi- — df (A6) > < Since 0, and by assumption 0, then 0, is utilized in the form — + df > (A7) 0. claim any supporting — T In a similar way it can be shown that, if C' is positively related to an exog- med as enous variable /3, (Al) df — — ± 0. (A8) be found from the wid ;> If b is positively related to then E1O (A2) —Ei) —E1)by=0, or (A3) df —b7pf( I — E,)( I — (A9) < 0, > Since 1 — and by assumption 0, df — — <0. (AlO) Note that since lIE, < 1, is and E, 0 d(pfO) g <0. (All) dy If Ef is positively related to &, then (A4) 0, df — — =;<0. (A12)

49 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH 48 Since the elasticity of 0 with respect to f equals were constant, If would (32p/aOap) be i f — a value of p satisfy: and O=E' The effects of cha by (A12), a reduction in E1woulcl reducef. already derived for/an Then the effect of a Suppose that p is related to the exogenous variable r. shift in r on/can be found from a! a! + C")01 + (D" + C")OpPr + Cp0Pr + bp(1 — — — + bf(1 — Ei)Pr = 0, (D" ar dr or and dJ_—(D"+ C")Op(l/Ot)pr bf(1 — Ei)pr(l/0i) (A 13) — dr Since 0,, < 0, and (D" + C") > 0, since by assumption C,,0 = 0. If E0 is positively• C—) + (—) — — (Al4) + dr 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 15) (A long as as 1ff were related to j5 would be given by 1 82L +C,,0+C,, +C P PPQ dji—(D"+C")O,,f,(l di + bf(l — (A16) > 0. (A 16) would hold if Since C,,0 = 0, = since all (with C,,0 = 0), + bf(1 — (A 17) 0. + D" + C" + C C,, If both p and ,,,, 71. If E,, and Er are co is suggested in Section II that C,,,, is generally greater than zero. If, as as- It su med, Then >0, + C' + D' OP 1 and thus that (A 15) implies that equation .and bf(1 — E,,) > o. op

50 APPROACH 49 BECKER GARY S. were constant, a2p/aOap would be negative," and, therefore, If would be positive. Hence, none of the terms of (A 17) are negative, (a2p/aOap) 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 those already derived forf and can be written without comment: r. Then the effect of a dp —= (A18) >0, , da dj3 —= , (A19) >0, and r(lIOi) d/3—b-),pf(l —E1)(l/O,,) (A13) (A20) <0. is positively related to 8', If c45 (A 14) < (A21) 0. d6' L, j5, could be [nimizes If C,. were positively related to the parameter s, the effect of a change in s on j5 would equal (Al5) (A22) .ds were related to the exogenous parameter i, the effect of a change in t on 1ff j5 would be given by d13 —(D" + C")O,.f,(l/O,.) — bf(l = — — E,,)j(l/O,,) 0 di (A16) —E,.)]O,.>0. (A23) since all the terms in the numerator are negative. = 0), (with - E,,)5-> (A 17) 0. If both p and f were subject to control, L would be minimized by choosing 71. If E,. and E,are constants, 0 = and b = where a = 1/E,. l/E,, er than zero. If, as as- Then = ao ka a21) —((1+1) = afb<() aOap ka

51 50 AND PUNISHMENT: AN ECONOMIC APPROACH CRIME optimal values of both variables simultaneously. These would be given by the solutions to the two first-order conditions, equations (A2) and (A 15), assuming or that certain more general second-order conditions were satisfied. The effects of changes in various parameters on these optimal values can be found by differen- tiating both first-order conditions and incorporating the restrictions of the second-order conditions. It can be shown that The values of p andf satisfying (A2) and (A 15), j5 andf, minimize L if 0, Lif> 0, (A24) and and, therefore, (A35) i = (A25) It has now been p conditions (A2) and (i and and since both But have been shown and L,,= parameters change the be greater than zero, (A24) is proved already, and only (A25) remains. By to be found from the two differentiating Lf with respect to p and utilizing the first-order condition that one has = 0, = 26) (A + C" + bf( 1 — E1)p0] where I equals the term in brackets. Clearly I > 0. and By substitution, (A25) becomes > (A27) By Cramer's rule, > are means that and both greater than I. and (A27) holds if I a! E1)p0, > D" + C" + bf(l — Ef)f0 D" + C" + bp(I — (A28) t3z or bfp bpf E1)E,,. — (A29) (1 — E,)E, < and the signs of both de (A29) implies that Since 1 — < 0, Consider the effect E1> E,,, (A 30) eter It is apparent th which necessarily holds given the assumption that b > 0; prove this by combin- > I means that ing the two first-order conditions (A2) and (A 15). and (A3 1) > D" + C" + bf(1 — E1)p0. + bf(1 — D" + C" + + this necessarily holds if < 0, Since and 0, > (A32) < bpf(l — Ef). + bpf(1 — since 0, and 0,, < 0, D By eliminating D' + C' from the first-order conditions (A2) and (A15) and by Similarly, if C' is ci combining terms, one has C,p0 — = 0. (A33) — and By combining (A32) and (A33), one gets the condition

52 51 GARY S. BECKER APPROACH (A34) < Cpp0, C,,ppQ,) 'ould be given by the and (A 15), assuming or tisfied. The effects of ibefoundbydifferen- P3Po> (A35) e restrictions of the Po ap = It can be shown that minimize 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 different have been shown parameters change these optimal values, and the direction and magnitude can ly (A25) remains. By be found from the two linear eqUations t-order condition that (A26) and (A37) a13 af — + = C2 — (A27) By Cramer's rule, I means that C20p1 — C21), L E1)p0, C1014' (A28) (A38) + az — — — CIO1I — C11) (A39) — (A 29) + — and the same as the signs of the numerators. the signs of both derivatives are Consider the effect of a change in D' resulting from a change in the param- (A30) = eter a. It is apparent that C1 = and by substitution C2 prove this by combin- — + af I) 0 (A40) + aa and bf(1 — E1)p0. (A31) I) — — + — (A41) + (A32) since and and > 0, and < 0, > I. 2) and (A15) and by Similarly, if C' is changed by a change in f3, C1 = C2 — — +> I) 0 (A42) (A33) + and

53 AND PUNISHMENT: AN EcoNoMic APPROACH 52 CRIME If is changed + — >0. (A43) + + 8/3 C1 =E,,3bpf, C2 =0, changed by a change in If and (A44) =—<0, + + and —O1E1bpf — = ±> (A45) 0. + + REFERENCES = changed by a change in C1 is 0, = C2 Similarly, if Arrow, Kenneth J. "E. + — — aj tion," in National I (A46) > + — — Direciion of Inve,. NJ.: Princeton and Becker, Gary S. "Irrat — cal Economy 70 (F (A47) <0. + = — 88' "A Theory of ber - 1965). — E,j, —b7pf( I — Ef), C2 = —b7pf( 1 changed by a change in y, C1 is If b Bentham. Jeremy. and Bureau of the Budget. — —(1 — — — dix. Washington: U (A48) < 0, + Bureau of Prisons. Pri ("National Prisone > also, > > 1 and since E, Characieristics. U.S. Dept. of Justii — (1 — Ef)I] — — 8/3 (A49) o, Federal —. Prisons + — + Cagan, Phillip. Deter,ni that when f is held con- Note > (I — for it can be shown that (1 — 1875)960 New Y stant the optimal value of p is decreased, not increased, by an increase in y. Res.), 1965. "Criminal Safeguards Chicago Law Revk if would be greater than (1 — 72. The term (1 — Ehrlich, Isaac. "The S + bf(1 — + E,)(l — E,)f0> bp(I — + Ef) (D" + C')(l — C")(i — (D' script, Columbia Ut or Federal Bureau of Washington: U.S. t p0' fO bpf [(1— E,) > ——b— (1— E1) (I— (D"+ Ibid., 1961. —p— Harper, F. V., and Jam bpf & Co., 1956. —(1 — — E1)[(1 — E,,)(E,) > (D"+ C")(E1— Johnson, Thomas. "The bpf Columbia Univ., N —E,)(E,—E9). KJeinman, E. "The Chc Criminal Sentencin€ Since the left-hand side is greater than zero, and the right-hand side is less than zero, the 1967. inequality must hold.

54 GARY 53 S. BECKER APPROACH changed by a change in s, is If C2 = C1 = 0, (A43) (A50) 0, + + + as and (A44) <0. (A51) (A45) REFERENCES = Arrow, Kenneth J. "Economic Welfare and Allocation of Resources for Inven- tion," in National Bureau Committee for Economic Research. The Rate and (A4 6 of Inventive Activity: Economic and Social Factors. Princeton, Direction N.J.: Princeton Univ. Press (for the Nat. Bureau of Econ. Res.), 1962. Becker, Gary S. "irrational Behavior and Economic Theory." Journal of Politi- (February 1962). cal Economy 70 (A47) "A Theory of the Allocation of Time." Economic Journal 75 (Septem- ber 1965). —Er), Es). - Bentham, Jeremy. Theory of Legislation. New York: Harcourt Brace Co., 1931. Budget of United States Government, /968, Appen- Bureau of the Budget. The dix. Washington: U.S. Government Printing Office, 1967. : 0 (A48) < ' Bureau of Prisons. Prisoners Released from State and Federal Insthurions. + ("National Prisoner Statistics.") Washington: U.S. Dept. of Justice, 1960. of State Prisoners, 1960. ("National Characteristics Prisoner Statistics.") U.S. Dept. of Justice, n.d. (A49) 0, . Federal Prisons, 1960. Washington: U.S. Dept. of Justice, 1961. Cagan, Phillip. Deterininamus and Effects of Changes in the Stock of Money, whenf is held con- that 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, Columbia Univ., New York, 1967. script, Federal Bureau of Investigation. Uniform Crime Reports for the United States. Washington: U.S. Dept. of Justice, 1960. . Ibid., 1961. II. Boston: Little-Brown F. V., and James, F. The Harper, Law of Torts. Vol. 1956. & Co., 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 Criminal Sentencing." Unpublished manuscript, Hebrew Univ., Jerusalem, side is less than zero, the 1967.

55 54 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH Landes, William. "The Effect of State Fair Employment Legislation on the Economic Position of Nonwhite Males." Ph.D. dissertation, Columbia Univ., New York, 1966. Vol. 11(1965). New York. Laws of The Opti Marshall. Alfred. Principles of Economics. 8th ed. New York: Macmillan Co., 1961. of Laws for Inventions." Patents Plant, A. "The Economic Theory concerning 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. George J. The Challenge of Crime in a Free Society. Washington: U.S. Government Printing Office, 1967(a). University of Chi Corrections. ("Task Force Reports.") Washington: U.S. Government Printing Office, 1967(b). The Courts. ("Task Force Reports.") Washington: U.S. Government Printing 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 from 1750. \'ol. 1. London: Stevens & Sons, 1948. All prescription Schilling, T. C. "Economic Analysis of Organized Crime," in President's Com- Usually the obligati mission on Law Enforcement and Administration of Justice. Organized voluntarily by expli Crime. ("Task Force Reports.") Washington: U.S. Government Printing Office, 1967. teach certain Shawness, Lord. "Crime Does Pay because We Do Not Back Up the Police." which 1, and possibi New York Times Magazine, June 13, 1965. negotiation, and in ti Smigel, Arleen. "Does Crime Pay? An Economic Analysis." M.A. thesis, ployer seek to enfor Columbia Univ., New York, 1965. tures from the promi Stigler, George J. "What Can Regulators Regulate? The Case of Electricity." is difficult or impos Journal of Law and Economics 5 (October 1962). noble, or steadfast i "A Theory of Oligopoly." Journal of Political Economny 72 (February are either not made. 1964). flagrant violation. 1 "The Economic Effects of the Antitrust Laws." Journal of Law and organization generali Economnics 9 (October 1 966). has received virtuall: Sutherland, E. H. Principles of Criminology. 6th ed. Philadelphia: J. B. Lippin- tial explanatory pow cott Co., 1960. When the presci vidual agreement, these unilateral rule: actual from prescril could wish for a les

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