Optimal Law Enforcement: Nuance Between Arrest and Punishment

Abstract

In the economic literature on law enforcement, the distinction between the probability of arrest and the probability of conviction is not explicit. However, detection does not necessarily imply punishment. This paper focuses on proving that punishment cannot be applied without preceding detection. In this context, in the case of non-apprehension, the offender expects a double gain: monetary and non-monetary gains. The result shows that if the probability of arrest is high, the reputation evaporates, which means the arrest has a deterrent effect on crime insofar as it generates a bad reputation for the offender. The monetary sanction has a deterrent effect on the monetary benefit from crime in the sense that this variable is less elastic than punishment cost. The low probability of punishment can be compensated by a maximum punishment.