Optimal Enforcement Policies (Crackdowns) on a Drug Market

In this paper an optimal control model is presented to design enforcement programs minimizing the social costs from both the market and crackdown.By using the maximum principle we show that performing an enforcement policy that leads to a collapse of the drug market is more likely to be optimal when the sales volume depends on the number of dealers.In case of a buyer's market the optimal enforcement policy leads to a saddle point equilibrium where the enforcement rate is fixed such that the number of dealers is kept constant at a positive level.