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Optimal enforcement policies (crackdowns) on an illicit drug market
Author(s) -
Kort Peter M.,
Feichtinger Gustav,
Hartl Richard F.,
Haunschmied Josef L.
Publication year - 1998
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199805/06)19:3<169::aid-oca625>3.0.co;2-a
Subject(s) - enforcement , illicit drug , business , point (geometry) , saddle point , microeconomics , law enforcement , economics , law , drug , mathematics , psychology , geometry , psychiatry , political science
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. © 1998 John Wiley & Sons, Ltd.