Crime and punishment: Does it pay to punish?

Abstract

Crime is the result of a rational distinctive balance between the benefits and costs of anillegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]).In this paper, we simulate a simple artificial society, in which agents earn fixed wages andcan augment (or lose) wealth as a result of a successful (or not) act of crime. The probabilityof apprehension depends on the gravity of the crime, and the punishment takes the formof imprisonment and fines. We study the costs of the law enforcement system requiredfor keeping crime within acceptable limits, and compare it with the harm produced bycrime. A sharp phase transition is observed as a function of the probability of punishment,and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing adeteriorated situation might be much higher than that of maintaining a relatively low levelof delinquency. Besides, we analyze economic consequences that arise from crimes underdifferent scenarios of criminal activity and probabilities of apprehension.