Optimal enforcement policies (crackdowns) on an illicit 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. The model is built around a dynamic equation proposed by Caulkins in which the development of the number of dealers in a particular illicit drug market depends on market sales and police enforcement. By using the maximum principle we show that, due to the positive feedback effect hypothesized by Kleiman, 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 buyers' market, which means that the total of sales completely depends on the number of buyers, 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.