Optimal Magnitude & Probability of Fines when Courts Dislike Punishment

Nuno Garoupa

The proposition that crime rates respond to risks and benefits is called the deterrence hypothesis in the economic literature. It asserts that individuals respond significantly to the incentives created by the criminal justice system. If so, increasing the resources that society devotes to the arrest, prosecution, conviction, and punishment of criminals will reduce the amount and social cost of crime. Suppose that there is a particular offense that we wish to deter, say, illegal parking or a specific unlicensed activity. It might be possible to eliminate them, or very nearly eliminate them, by imposing a severe punishment with high probability. However, deterring illegal parking or unlicensed activities in this way may run into a cost problem. Apprehending, prosecuting, and punishing offenders can be significantly expensive. Policy-makers need to balance these costs against the advantages of reducing illegal parking (Garoupa 1997, Polinsky and Shavell 2000).

In this essay, we reconsider the high fine-low probability result by Becker (1968): When deciding whether or not to commit an act, an individual compares the benefit from the act with the expected punishment. The expected punishment is given by the probability of detection and punishment times a monetary sanction. A fine is a costless transfer from the convicted offender to the government. In contrast, detection is expensive. Consequently, the government should set the fine equal to an offender’s entire wealth and complement it with the appropriate probability in order to achieve optimal deterrence. This high fine-low probability result suggests the following corollary: If the agents’ wealth goes up, the government should increase the sanction and, at the same time, reduce the probability of detection. That way the government still provides for optimal deterrence, but saves resources on law enforcement.

I have already shown that this intuitive corollary (the substitutability between fine and probability) only holds if the social optimum involves nearly or is close to full deterrence. If there is substantial under-deterrence (the expected fine is significantly less than the social damage caused by the offense), then there is a complementary relationship between the two variables. When the fine goes up, so should the probability of detection. In order to understand this result, consider a rather extreme case where the agent’s wealth is zero. In this case, fines are zero and the deterrent value is zero. Thus, it makes absolutely no sense to spend money on enforcement. When wealth goes up, so do fines. Now it becomes worthwhile for the government to engage in some detection and punishment. As a consequence, we have a complementary relationship between fine and probability when there is substantial under-deterrence (alternatively, when offenders are poor and monetary sanctions are very low). This contrasts with the conventional substitutability which holds if the expected sanction is close to the social damage caused by the offense (that is, when offenders are wealthy and monetary sanctions are severe).

The standard analysis implicitly assumes that courts are willing to implement Beckerian fines. Suppose, however, that courts dislike severe punishment. Maximal sanctions could induce a countervailing effect. Courts might opt for acquittal rather than punishment with an extremely severe punishment. They could also consider conviction for a less severe crime in order to modulate the magnitude of punishment. Clearly, in these situations, severe punishment is no longer effective. Fines should be lower to take into account court preferences. The impact on the probability follows the analysis of 2001 study.

A numerical example can illustrate the insight of the present analysis. Suppose a particular crime generates harm of 100. The maximal sanction is 2,000. Under the multiplier principle (which eliminates under-deterrence), the probability should be 5%. However, notice that the optimal probability should be less than 5% due to enforcement costs. In a world where courts dislike punishment and can opt for acquittal rather than conviction, the maximal sanction cannot be effectively implemented. Let us assume that the maximal sanction courts are willing to implement is 500. Under the multiplier principle, now the probability should be 20%. We show in this essay, following my 2001 study, that the optimal probability could be less than 10% due to enforcement costs. When such result occurs, not only the severity of punishment goes down due to court preferences, but the probability also goes down in order to maximize social welfare. As a consequence, we can say that when courts dislike punishment, substantive under-deterrence can take place.

The essay is organized as follows: the result is formally derived in section two; applications and final remarks are addressed in sections three and four respectively.

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