OPTIMAL ENFORCEMENT POLICIES (CRACKDOWNS) ON AN ILLICIT DRUG MARKET

In this paper an optimal control model is presented to design enforcem ent programs minimizing the social costs from both the market and crac kdown. The model is built around a dynamic equation proposed by Caulki ns(1) in which the development of the number of dealers in a particula r illicit drug market depends on market sales and police enforcement. By using the maximum principle we show that, due to the positive feedb ack effect hypothesized by Kleiman(2), performing an enforcement polic y that leads to a collapse of the drug market is more likely to be opt imal when the sales volume depends on the number of dealers. In case o f a buyers' market, which means that the total of sales completely dep ends on the number of buyers, the optimal enforcement policy leads to a saddle-point equilibrium where the enforcement rate is fixed such th at the number of dealers is kept constant at a positive level. (C) 199 8 John Wiley & Sons, Ltd.