Optimal control analysis of a simple criminal prosecution model

This paper analyzes an optimal control model dealing with a problem in criminal justice policy. It is assumed that a society generates criminals at a constant rate. The size of the criminal population at any time depends on the criminal generation rate and the number of criminals prosecuted and imprisoned. Optimal prosecution rate over time is found by using Pontryagin's principle. The objective is to minimize the total discounted cost of the damages inflicted by the criminals plus the cost of law enforcement. Explicit forms of the optimal trajectories are found in both the finite and infinite horizon cases. In the latter case, a stability analysis of the optimal steady‐state is also presented. The paper concludes with a comparative statics analysis of the equilibrium and a description of the optimal control of a more detailed criminal justice system model.