Crime and Punishment: An Economic Approach · tly general to cover TABLE 1 ECONOMIC COSTS OF CRIMES...

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)

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

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

Crime and Punishment:An Economic Approach

University of Chicago and National Bureau of Economic Research

Gary S. Becker

1. INTRODUCTION

2 CRIME AND PUNISHMENT: AN ECONOMIC APPROACH

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

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

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

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

II. BASIC ANALYSIS

A. THE COST OF CRIME

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

Crimes against persontCrimes against propertIllegal goods andSome other crimes

TotalPublic expenditures onCorrectionsSome private costs of

Overall total

SOURCE. — Presidet

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

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

GARY S. BECKER 3

reatly from personch diversity, someslation, and these

n for granted, andder both to prevent

conviction is notand some-

What deter-used to enforce

'orcement differ so

rmative versions ofhow much punish-

of legislation? Putshould be per-

The method usedand finds those ex-

mize this loss. Thekte as special cases,

deterrence,have figured so

depend on, amongpders, the nature of

terms—andfit. The discussion,

and theories ofspace subsidiary,

are providedthat a useful

of anomie,11 traits and simply

imize terminologi-tly general to cover

TABLE 1ECONOMIC COSTS OF CRIMES

TypeCosts

(Millions of Dollars)

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

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

Overall total 20,980

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

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

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


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

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

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

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

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

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

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

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

The social valu

6. Cagan (1965, cha1929 and 1960 to increa

7. The ith subscriptactivity is being discusse

over checks in illeg:tions) because no rc

B. THE MODEL

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

1. DAMAGES

Usually a belief thation behind outlawiof harm would tend

with

APPROACH

private precautionsre also excluded.

of the directon various

and mainlyagainst prop-

to almost $4 bil-loss of earnings

listed in the tableof reported national

the percentage

curing the last fortye on trends in costsjer of major felonies

Commission,of tax and other

liar crime have pre-piece of indirect

in the amount of cur-to that date, the

had de-her urbanization andther kinds of credit,4

be explained by anadvantages

1959 totaled almost S2

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

time in prison—plusequal the

input of intermediatebor and capital input into

es urbanization and the

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

GARY S. BECKER 5

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

B. THE MODEL

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

1. DAMAGES

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

H, H,(O,),

0,

(1)with

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

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

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

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


crease with the number of offenses, as in

with

G =

G'

(2)

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

D(O) = H(0) — G(0). (3)If, as seems plausible, offenders usually eventually receive diminish-

ing marginal gains and cause increasing marginal harm from additionaloffenses, G" < 0, H" > 0, and

— 0, (4)

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

D'(O) > 0 for all 0> if D'(Oa) 0. (5)Until Section V the discussion is restricted to the region where D' > 0,the region providing the strongest justification for outlawing an activity.In that section the general problem of external diseconomies is recon-sidered from our viewpoint, and there D' < 0 is also permitted.

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

2. THE COST OF AF

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

and

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

One approximaber of offenses cleai

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

and

if p0 0. Anber of offenses wocreased "activity"

8. According to thewages and salaries (Presi

9. A task-force repand more efficient usage

APPROACH GARY S. BECKER 7

2. THE COST OF APPREHENSION AND CONVICTION

(2)

between the

(3)

Ily receive diminish-krm from additional

(4)

of optimalitySince both H'

magnitudes. It fol-

(5)

where D' > 0,an activity.

is recon-permitted.

ês, which have beenused up in theseare not identical

cost of murder isamong other

cost of gamblingdisutility to

burglary and em-wealth redistribu-the possibility of

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

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

and

C=C(A)(6)

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

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

A pO, (7)

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

and

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

ap

C0 = C'p> 0(8)

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

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

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


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

3. THE SUPPLY OF

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

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

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

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

13. See, however, thc14. For a discussion

C,,,, = C"02 > 0,= C"p2 > 0, (9)

andC,,0 C,,,, = C"pO + C' > 0.

A more sophisticated and realistic approach drops the implicationof (7) that convictions alone measure "activity," or even that p and 0have identical elasticities, and introduces the more general relation

A=h(p,0,a). (10)The variable a stands for arrests and other determinants of "activity,"and there is no presumption that the elasticity of I, with respect to pequals that with respect to 0. Substitution yields the cost function C =C(p, 0, a). If, as is extremely likely, h,,, h,, and h,, are all greater thanzero, then clearly C1,, C,,, and C,, are all greater than zero.

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

C,,,, 0,

(11)and

C,,,, 0

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

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

A

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

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

GARY S. BECKER 9

(9)

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

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

(10)

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

rare all greater thanzero.

lie at "corners," itderivatives of the

'is, it is sufficient that

(11)

strictions are rather

tures in the Unitedlion, by no means a

of seven majorper offense (re-

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

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

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

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

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

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

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


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

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

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

and

APPROACH

(12)

it during a particularhis punishment per

g all these other in-

effect there is "priceays per convictedeither orf1 would

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

(13)

above. The effectanticipated. For ex-

ties or an increase inthe incentive to

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

g that offenders do substi-

as

U, is his utility function;ishment. Then

GARY S. BECKER 11

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

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

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

17.18. This means that an increase in

p,

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

19. From n. 16

as

fi—aEU, p, {U,(Y,) — U,(Y, = p,UJ(Y, —fj) —äp, U,, U,,< c'fj U,, U3

U,(Y,,) — U,,(Y,, —fi) U(Y, —f,)fi

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

The term on the left is the average change in utility between Y3 —j5 and Y,. It would begreater than, equal to, or less than U(Y, —f,,) as U' 0. But risk preference is defined by

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

iTh

i-I

and similar definitions hold fcn-f and u.


the market offense function as

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

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

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

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

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

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

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

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

wheref' is the socialThe size of b vane:

21. In this respect, iialso exemplified by queue


(14)

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

enced by high cone-ye effects on 0 of p

of f, indicating

the real incomes ofhigh or low as

(1 offenders were riskwould be lower,

in less risky legalWhether "crimehave toward risk

or the amountat some values

Id influence whethershown later that the

ed by selecting p andwhere "crime does

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

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

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

e (President's Corn-

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

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

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

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

(15)

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

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


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

III. OPTIMALITY CONDITIONS

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

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

(16)

is the function measuring social loss, with presumably

abf>°' (17)the aim would be to select values off, C, and possibly b that minimize L.

It is more convenient and transparent, however, to develop the dis-cussion at this point in terms of a less general formulation, namely, toassume that the loss function is identical with the total social loss in realincome from offenses, convictions, and punishments, as in

L=D(0)+C(p, 0)+bpfo. (18)The term bpfo is the total social loss from punishments, since bf is theloss per offense punished and p0 is the number of offenses punished (if

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

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

and

L

If and are notrecombine terms, to

and

D

where

and

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

22. The Mathematica


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

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

from increasedàke "the punishment

be equated to thever, such a policy ig-

catchy phrases andof apprehending

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

(16)

(17)

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

as in

(18)

ents, since bf is the

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

there are a fairly large number of independent offenses). The variablesdirectly subject to social control are the amounts spent in combatingoffenses, C; the punishment per offense for those convicted, f; and theform of punishments, summarized by b. Once chosen, these variables,via the D, C, and 0 functions, indirectly determine p, 0, D, and ultimatelythe loss L.

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

(19)

and

(20)

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

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

and

(22)

where

fCj = Of

and (23)

pLv = 0,,.

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

5ly

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


Marginalcost

Marginalrevenue

FIGURE 1

—!)

!)

Number of offenses

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

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

23. Thus if b < 0, average revenue would be positive and the optimal value of Ejwould be greater than 1, and that of a,, could be less than I only if C,, were sufficientlylarge.

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

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

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

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

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

25. Sinceconditions given by eqs. (2

From this condition and ftbe determined.

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

MC,= D' +


D' + C'

D' + C' +

MR,=.—bPf(t —!)

umber of offenses

the cost of combating0 must be less

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

would be positivethe loss is minimized

figure 1), the optimalonly exceed unity

the usual equilibriumthat the elasticity of

tse average revenue is

a change in p is lessarginal revenue from

(21) and (22) indicate

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

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

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

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

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

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

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

D' =_bPf(l .J)

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

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

18 CRiME AND PUNISHMENT: AN ECONOMIC APPROACH

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

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

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

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

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

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

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

IT::-;;v =— = 'p

IV. SHIFTS iN TThis section analyztions—the damage,mal values of p and,matical Appendix, hproofs Tiwhy more damagingsive offenders less s

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

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

v increases monotonicallyp =0.

If the loss function eq

the optimality conditions v

and

0' -f

Since the term çV(dv/dp)(:I

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

GARY S. BECKER 19APPROACH

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

loss in income fromand finite values of

et to a compensatedin footnote 27 is

if punishmentsof apprehension and

also on If Cregions,29 the loss in

id I even if offendersin p could raise,

base in the loss.optimal behavior if

Iction in income. Forincrease in the exnot and those that

in p wouldloss from this

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

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

wer values of p.with the punishment f,

shment would be = pf,

IV. SHIFTS IN THE BEHAViORAL RELATIONS

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

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

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

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

If the loss function equaled

the optimality conditions would become

and

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

(22)

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

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

— -


Marginal Marginalcost cost =

Marginal Marginal c + crevenue revenue

a0-J

0

b.

FIGuRE 2

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

Table 2 presents some evidence on the actual probabilities andpunishments in the United States for seven felonies. The punishments Hare simply the average prison sentences served, while the probabilitiesare ratios of the estimated number of convictions to the estimated numberof offenses and unquestionably contain a large error (see the discussions i—in Smigel, 1965, and Ehrlich, 1967). If other components of the loss func-tion are ignored, and if actual and optimal probabilities and punishmentsare positively related, one should find that the more serious felonies havehigher probabilities and longer prison terms. And one does: in the table, —which lists the felonies in decreasing order of presumed seriousness, <both the actual probabilities and the prison terms are positively relatedto seriousness.

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

MR

a.

Number of offenses

If) -.:i

CD

(P

- C

-.

CD

°F

-—

c"C

D If)<

C)

PC

->C

D0

•

CD

CD

CD

CD

r .4- C)

TAB

LE 2

PRO

BA

BIL

ITY

OF

CoN

vIcT

IoN

AN

D A

VE

RA

GE

PR

ISO

N T

ER

M F

OR

SE

VE

RA

L M

AJO

R F

ELO

NIE

S, 1

960

Mur

der

and

Non

-ne

glig

ent

Agg

ra-

All

Thes

eM

an-

Forc

ible

vate

dA

uto

Felo

nies

slau

ghte

rR

ape

Rob

bery

Ass

ault

Bur

glar

yLa

rcen

yTh

eft

Com

bine

d

1.A

vera

ge ti

me

serv

ed (m

onth

s).

befo

re fi

rst r

elea

se:

a) F

eder

al c

ivil

inst

itutio

ns11

1.0

63.6

56.1

27.1

26.2

16.2

20.6

18.8

b) S

tate

inst

itutio

ns12

1.4

44.8

42.4

25.0

24.6

19.8

21.3

28.4

2.Pr

obab

ilitie

s of a

ppre

hens

ion

and

conv

ictio

n (p

er c

ent):

a) T

hose

foun

d gu

ilty

ofof

fens

es k

now

n57

.937

.725

.127

.313

.010

.713

.715

.1b)

Tho

sefo

und

guilt

y of

offe

nses

cha

rged

40.7

26.9

17.8

16.1

10.2

9.8

11.5

15.0

c) T

hose

ente

ring

fede

ral

and

stat

e pr

ison

s(e

xclu

des m

any

juve

nile

s)39

.822

.78.

43.

02.

42.

22.

12.

8

SOU

RC

E.—

I, B

urea

u of

Pris

ons (

1960

, Tab

le 3

); 2

(a) a

nd (b

),F

eder

alB

urea

u of

Inve

stig

atio

n (1

960,

Tab

le 1

0); 2

(c),

Fede

ral B

urea

u of

Inve

stig

atio

n (1

961,

Tab

le 2

), B

urea

u of

Pris

ons (

n.d.

,Tab

le A

l; 19

61, T

able

8).

(P

—•

O (P(P

(pC

#iO ,

CD

C 0 0 0

0 > C-)


offenses observed in:tion between C,, (or

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

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

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

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

Marginalcost

Marginalrevenue

C

MR

Number of offenses

FIGURE 3

The income oflittle cost, its total iferent elasticities ofmarkets having lowoffenses could bethe elasticities of suçthe total loss wouldlower p's and f's — ii

Sometimes itisoffense into groupsexample, unpremediimpulsively and, the

Marginalcost

Marginalrevenue \

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

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


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

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

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

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

Marginalcost

Marginalrevenue

tders is affected by aincreases both

of fingerprinting,àl analysis, or police

and merit,extent. Our analy-

nt in technology andI recuce the optimal

the need to relythis explains why therrn has gone hand in

y between differentrape or armed rob-of personal identi-

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

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

Marginalcost

MC Marginalrevenue

a-

Number of offenses

—bpf (i

b.Number of offenses

FIGURE 4


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

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

V. FINES

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

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

B. OPTIMALITY Co

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

A. WELFARE THEOREMS AND TRANSFERABLE PRICING

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

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

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

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

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

Equation (24) dthe fine and probabi

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


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

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

B. OPTEMALITY CoNDITIoNs

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

D'(O) 0. (24)

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

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

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

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

alysis.e from changing the

increases the optimalincreases the opti-

II indicates that b isin prison and

nplies, therefore, thatand the optimal

rather than one of the

CING

depend only on thetverage revenue func-

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

appear to be thatby consumers are

there is no social loss

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

npulsive and other "irra-ity whose price has risen

narily prices do not affectC.


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

V= G'(O), (25)

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

V= H'(O). (26)The monetary value of the penalties would equal the marginal harmcaused by offenses.

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

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

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

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

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

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

Appendix on the effects of increases in C'.

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

The optimality

- D'

would replace equalconviction were fixe> 0,39 and thus thatnumber when costsVictjon increase or dpends, therefore, onfine or in the probabjcontrol, the optimal j:to zero, unless the scthe discussion in Sec.

C. THE CASE FOR FJust as the probabiljt3subject to control by susually specifies wheiinstitutionalization or

38. Since equilibrium ri

then (29) follows directly by39. That is, if, as seems

then

and


sts' usual theory ofe marginal value of

(25)

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

(26)

the marginal harm

assumed equal tocould be set equalwould then simply

kome

(27)

a fine determinedmarginal harm suf-would be identical,

'ctims." 36 If the harmtboth criteria would

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

(28)

private gainly means a smallershow that equation

f marginal harm and

persons actually harmed.suits in the Mathematical

f= H'(O) + C'(O, l).38 (29)In other words, offenders have to compensate for the cost of catchingthem as well as for the harm they directly do, which is a natural general-ization of the usual externality analysis.

The optimality condition

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

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

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

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

0(O) = H'(O) — G'(O) = — C'(O, 1),then (29) follows directly by substitution.

39. That is, if, as seems plausible,

then

and

= ± > 0,dp ap

C, + 0.


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

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

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

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

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

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

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

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

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

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

Optimal fines dmarginal harm and ccers. This has been ci

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

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

44. See Sutherland (I45. The very early Et

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

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


y, in most countries,stitutionalization re-

resents several argu-fines are used when-

tion use up social re-ily just transfer pay-

I guards, supervisoryTable 1 mdi-

in 1965, aboutestimate excludes, of

of offenses andthe use of fines. A

and harm and ofsuch knowledge

and other punish-on, must know about

As thesuggest, it

d age can enter intothe elasticities of re-

in levyingby equations (27)

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

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

rn of food, clothing, and

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

Those punishedagreed to by their "

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

Whether a punisoffenders lacking suffi

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

49. The "debtor prisorepay loans.


al is to minimize theengeance or to inflicttotal harm done by

ex, etc. In the sameand other punish-

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

fr probation period isThe discussion in

riviction are not fixedand, in particu-

in incentive to spendlegal appeals, and

and convictionbecause the cost to

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

Ion is relatively largeis that the prob-

to the earnings ofprisonment and pos-kegative relation for

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

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

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

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

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

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

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

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

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

32 CRIME AND PU

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