OPTIMAL PUNISHMENT SCHEMES WITH STATE‐DEPENDENT PREFERENCES

I. INTRODUCTION It is well known in the economics of crime literature that both the certainty and severity of punishment can be manipulated to deter criminal behavior. As Polinsky and Shavell [1979] show, when punishment takes the form of a fine, the optimal combination of the probability of punishment and the magnitude of the fine depends on the risk attitudes of offenders and on the costs of catching and convicting offenders. This paper examines how the optimal combination of certainty and severity are affected if offenders' preferences are state-dependent. State-dependent utility is commonly used in situations in which the state of the world affects how well individuals are able to enjoy the consumption of their wealth. Death of the individual is an obvious example, and Hirschleifer and Riley [1992] also suggest the death of a child, the loss of use of a limb, or the loss of a precious heirloom. There are many reasons to add conviction for a crime to this list.(1) First, if the individual is sent to prison, his consumption opportunities are obviously diminished. Even without a prison sentence, though, utility might best be modeled as being state-dependent. For utility to be state-independent, there must exist some decrease in wealth that has the same effect on the utility function as being convicted of the crime. If the offender is risk averse and has state-independent utility, a loss of wealth reduces the level of utility but increases marginal utility. It is easy to imagine why being convicted of a crime would reduce the level of utility, but it is difficult to imagine why it would increase the individual's marginal utility of wealth. For example, drivers who are caught speeding are angered beyond the level consistent with the expected loss of income. But, this additional anger does not lead to an additional increase in the marginal utility of wealth. In addition to these considerations, Lott [1992a,b] provides evidence that conviction leads to increased divorce rates and constrained job opportunities. The former reduces the level of utility but is unlikely to increase marginal utility, and should therefore be modeled as a shift in the utility function. Constrained job opportunities reduce both income and job satisfaction, and the reduction in job satisfaction is again best modeled as a shift in the utility function. As a final argument supporting the use of state-dependent preferences, Neilson and Winter [1997] show that if offenders' preferences are state-dependent, it is possible for them to be both risk averse and more sensitive to changes in the certainty of punishment than to proportional changes in the severity of punishment. Becker [1968] notes this empirical finding,(2) and concludes that if offenders are expected utility maximizers, they cannot be risk averse.(3) Polinsky and Shavell [1979] demonstrate that when offenders are risk averse and have state-independent utility, increasing the fine increases social loss by increasing the amount of risk borne by offenders. Consequently, in the extreme case in which it is costless to catch and convict offenders, the optimal policy has a relatively low fine but punishes criminals with probability one. This paper shows that if preferences are state-dependent, there is an additional social cost associated with setting a high probability of punishment, because it makes it more likely that criminals are on their lower utility functions. To avoid the additional social cost, the certainty of punishment should be reduced. II. THE MODEL The model presented below is identical to that in Polinsky and Shavell [1979], except for the addition of state-dependent preferences. Identical individuals choose whether to commit a crime or not.(4) Gains from crime are random: with probability q the individual gains a, and with probability 1-q he gains b [greater than] a. Even though the gains are random, it is assumed that the individual knows the true value of the gain before any decision must be made. …