Breaking the law when others do: A model of law enforcement with neighborhood externalities

A standard assumption in the economics of law enforcement is that the probability of a violator being punished depends only on the resources devoted to enforcement. However, it is often true that the productivity of enforcement resources decreases with the number of violators. In this paper, an individual who violates the law provides a positive externality for other offenders because the probability of being punished decreases with the number of individuals violating the law. This externality explains the existence of correlation between individuals' decisions to break a law. The model evaluates the implications when determining the socially optimal enforcement expenditure, focusing specifically on the case of neighborhood crime. In particular, using a parametrized functional form, I show that neighborhood externalities will enhance or impede enforcement, depending on the crime rate.