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Explain The Economic Rationale Essay, Research Paper

Explain the Economic Rationale for the Supply of Crime, Show the Implications of this Rationale for the Design of Crime Deterrence Policies, and Assess the Empirical Relevance of this Rationale.

The economic rationale for the supply of crime will initially be analysed using Becker s framework. The implications of his findings will then be used as a means of explaining how crime deterrence policies can be devised. The same procedure will then be undertaken for Ehrlich s model, with an assessment of the application of the model in addition to its empirical relevance. There will be a discussion on the merits of both of these frameworks using other papers by other economists.

Gary Becker applied the principles of expected utility theory to explain the individual s decision to commit a crime. This decision to commit an offence is made rationally and is dependent on incentives. This model views crime as an economic activity that has rational, utility-maximising participants who only choose to commit an offence if the expected utility is higher than the utility from a legal activity.

The number of times that an individual commits a crime can be represented by the following function:

Oj = Oj ( pj, fj,uj )

Becker s model showed that the number of crimes committed (Oj) is dependent on the probability of being caught and convicted per offence (pj), the expected severity of the punishment (fj) and other variables such as legal or illegal earning ability (uj).

An increase in either pj or fj would lead to a fall in the expected utility of the criminal offence . A fundamental assumption of this model is that the individuals must be fully responsive to relevant economic incentives and decisions are rational. It then follows that this framework would not be relevant to an insane person (thus the motivation for a criminal to plea insanity ).

A market offence function can now be formed to demonstrate the total number of offences supplied by individuals to a community.

O = O( p, f, u )

This is possible because of the assumption that the market function has the same properties as the individual functions.

The expected utility function can be represented like so:

EU = pU (W-L) + (1-p) U (W+G)

An individual that will not engage in any criminal activity will have a utility function where the expected utility will equal the utility of their initial wealth. The individual will only commit the crime if the expected utility exceeds the utility of abiding by the law. The decision of the individual to supply crime is dependent on their attitude to risk in addition to the magnitude of L, G and p. It is important to note that even if the individual is risk averse, the gamble may still be accepted if the levels of p and L are low enough and the payoff from the risk sufficiently high.

Becker believed that the only means to reduce the amount of crime in order to minimise costs through policies such as the probability of detection and the severity of the sentence. The idea of the social loss function can now be introduced. The imposition of a fine is considered to be a transfer payment thus posing no social cost, however, imprisonment and probation have social costs that are greater than those of the offender as outside resources need to be employed as a means of imposing the punishment. Any action carried out as a result of a crime that is committed imposes costs on society such as the damage from the actual offence as well as the costs of running the legal system as well as the opportunity cost of the punishment. As a result, the design of any crime deterrent policy must take into consideration the costs and benefits of reducing crime (the optimal level of crime is not necessarily zero).

The aim of a deterrent policy ought to be the minimisation of society s loss function:

L = D (O) + C (p, O) + b.f.p.O

Becker concluded that anybody willing to commit a crime must have a risk-loving attitude because crime doesn t pay (between a certain range of p and f). Thus policies need to be implemented that reduce the expected utility of the individual either through an increase in the probability of detection or through the loss if caught and convicted (in order to minimise the social loss). Appendix 1 shows us that for a risk-averse individual at the optimum point, the expected utility of the crime does not exceed the utility of the initial wealth. Becker also observed that the number of offences is more responsive to the probability of being caught rather than the level of punishment.

The expected cost of the crime is independent of the extent of the crime. In order to have an effective deterrent, a marginal cost must be imposed on the criminal (otherwise the criminal may commit a far more serious crime and subjected to the same punishment). The idea of making the punishment fit the crime means that the criminals would face higher costs for the more serious crimes and equate the marginal benefit to the marginal cost. Therefore, the larger the probability of arrest and fine, the greater the marginal cost on the criminal leading to a fall in the supply of crime.

Becker believed that fines ought to be used whenever possible, however this is not realistic due to the regressive nature of the punishment. Also, this may be inappropriate if combined with a small probability of getting caught, as the criminals are likely to misjudge the likelihood of getting caught. However, an increase in the level of police enforcement would soon clear up this misconception. The problem with this is that Carr-Hill and Stern estimated that an increase in police would lead to an increase in crime, as more crimes are likely to be reported.

British legal history shows that there has been significant controversy regarding proposals by Michael Howard to introduce more severe punishments and especially extended sentences to repeat offenders. This suggestion was met with opposition by magistrates and police who believed that the probability of detection had a larger deterrent effect on the supply of crime . In the case that the punishment is too severe, there may be a situation where more crime results as criminals may may as well commit a more serious crime if they will face similar consequences to a smaller crime.

Becker s model ignores the probable deduction that the distribution of income is likely to play a large part on the probability that an individual will offend. Carr-Hill and Stern demonstrate that under the assumptions of risk-aversion and wealth, the less well off were more likely to offend than the wealthy.

Both Smigel (1965) and Ehrlich (1967) have estimated similar market offence functions using seven felonies as reported by the FBI and have discovered the relationship to be relatively stable between the number of offences and p and f with significant negative effect.

Ehrlich s model of the supply of crime assumes that the gains from the illegal activity and the level of punishment are both dependent on the amount of time devoted to that activity. Unlike Becker s model, Ehrlich allows for an individual to participate in both activities in a specific time period. The individual is expected to choose an amount of time spent on illegal activities (t c) by maximising expected utility. Time spent on legitimate work is denoted by t L , where t c + t L = T. Income earned from both forms of work is Wc (t c) + WL(T- t c). Wo is the level of unearned income and Fc (t c) is the size of the fine, then the level of income would be dependent on the level of t c like so:

X0 = Wo + Wc (t c) + WL(T- t c) if the criminal is not caught

X1 = Wo + Wc (t c) + WL(T- t c) Fc(T- t c) if the criminal is caught

Thus the expected utility function would be:

EU = p.U(X1) + (1-p).U(X0) = 0

The diagram in Appendix 2 shows that the equilibrium arises where the marginal rate of substitution between X0 and X 1 is equal to the marginal rate of transformation between the two. If an individual has allocated an optimal amount of time to crime (where t c | T*), s/he would be a specialist in this field at Tc. However, if the optimal point is t c 0, the individual would specialise in legal activities At equilibrium, the time spent on crime would equal zero if the slope of the indifference curve is greater than the slope of the opportunity boundary. From this we can deduce that crime does pay as the gain form crime is smaller than the expected punishment. The agent would only devote all of his/her time to crime if the slope of the indifference curve at t c is less than the slope of the boundary at that point . We can see that whether or not crime will pay is dependent on the risk attitude of the offenders, as the expected returns are wholly dependent on the slope of the individual indifference curves. Thus when considering any policies it is essential to change the preferences of the criminals.

As a means of deterring criminals, there could be a forced increase in either p or f as this would reduce the attractiveness of participating in criminal activity (as the expected marginal cost of the punishment would increase). The result of this is that the new equilibrium would be shifted to the right meaning that any increase in punishment ought to lead to a fall in the supply of crime.

If the criminal was a risk lover and spending some time on legitimate activities, an increase in the average penalty per offence may be ineffective in deterring him/her from the crime.

A change in the punishment or return is unlikely to affect an individual who is at a corner solution i.e. has devoted all available time to that specific activity. This change would only affect the probability that the individual remains at these points. Therefore, it is the hardcore criminals who are do not participate in the labour force that policies should be aimed at.

If policies were devised so as to increase the probability of conviction, the amount of time an individual spends on crime would be expected to decrease (unless at a corner solution). Looking at Appendix 3, we see that an increase in p will lead to less crime, as the new equilibrium will lie to the right of the old equilibrium .

Factors such as the probability of unemployment have ambiguous effects on the supply of crime. This is because an increase in the probability of the most undesirable state would increase the demand for money and decrease the incentive to participate in additional illegal activities. If the results had shown that unemployment is strongly correlated with the supply of crime, policies to reduce unemployment would have been a useful tool to reduce the crime rate.

Wealth effects also affect the time spent on illegal activities, this is because illegitimate activities are likely to have higher returns than legal activities, thus increasing the incentive for the less wealthy to participate in these operations.

Ehrlich s model of murder supply is based on similar assumptions as Becker s model of the supply of crime. Ehrlich concluded that the number of murders was far more responsive to changes in the probability of being caught rather than the probability of conviction and of executions.

This rationale was used by Ehrlich to create a recorded murder rate equation and run a regression on US annual time series data between 1933 and 1969.

log Om = a + bX + epa log pa + e p c/a log p c/a + e p e/c log p e/c

This has been derived from an estimation of the murder supply function for an individual. Ehrlich included permanent income, unemployment, labour force participation as well as the percentage of the population in the 14-24 age group in his X vector. Ehrlich s conclusion confirmed that epa > e p c/a > e p e/c and that the execution rate was significantly negatively correlated with the supply of murders.

Ehrlich also found that the participation in the labour force had a negative effect (although this was frequently insignificant), however the level of permanent income was positively correlated whilst the age effect had strong positive correlation with the murder rate. The implications of these findings do not really help us to form policies to deter crime, as these variables are not under control. However, Ehrlich did estimate that one additional execution would result in reduction of the murder rate by 8 . These results may lead to those devising the anti-crime policies to consider the idea of increasing the incarceration rate.

However, the problem with this is that these figures are not reliable and the real effects additional murders are likely to be unanticipated. Passel and Taylor made the observation that an increase in the execution rate may have the result of fewer criminals being convicted than before. This is because they are likely to want more proof of guilt if the consequence of a guilty verdict is so much harsher.

In 1975, Passell used a different set of data and included an additional variable- the sentence of criminals who were found to be guilty but not executed. Passell found that the length of the sentence had an effect on the murder rate whilst the execution variable did not. Thus it would not be advisable to reintroduce capital punishment based on this evidence but think of alternative measures.

We can thus conclude that when deciding on policies to deter crime, it is important not to rely heavily on econometric evidence but mainly on common sense. This is because although the evidence does help to provide an analytical framework to explain some of the rationality behind the supply of crime, the majority of the time criminal behaviour is in no way governed by logical thought. The main tools of deterrence policies (the level of punishment and the fine imposed) have varying effects on the level of crime, this may indicate that underlying contributory factors to the supply of crime are unaffected if these factors are insignificant.


Becker, G. Crime and Punishment: An Economic Approach

Carr-Hill, R. A. and Stern N. H. An Econometric Model of the Supply and Control of

Recorded Crime in England and Wales

Cooter, R. and Ulen, T. Law and Economics

Ehrlich, I. Participation in Illegal Activities: a Theoretical and Empirical


Grogger, J. Certainty vs. Severity of Punishment

Gibbons, T. The Utility of Economic Analysis of Crime

Polinsky, A.M. and Shavell, S The Optimal Use of Fines and Imprisonment

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