Optimal dynamic law enforcement

In this paper we present an intertemporal extension of Becker's static economic approach to crime and punishment. For a dynamic supply of offenders we determine the optimal dynamic trade-off between damages caused by offenders, law enforcement expenditures and cost of imprisonment. By using Pontryagin's maximum principle we obtain interesting insight into the dynamical structure of optimal law enforcement policies. It is found that inherently multiple steady states are generated which can be saddle points, unstable points and boundary solutions. As in other non-linear control models there exists a threshold (a so-called Skiba point) which makes the optimal enforcement policy dependent on the initial conditions. It turns out that above the Skiba point the optimal trade-off between social costs implies a steady state with a high level of offences, while below the threshold the optimal law enforcement should eradicate crime.