Why present-oriented societies undergo cycles of drug epidemics

Musto (The American Disease, Yale University Press, New Homen, 1987) hypothesizes that cycles of drug use arise when the current generation of youth no longer remembers the adverse experiences of their forebears. This paper underlines this hypothesis through the results of an optimal control model of drug epidemics that incorporates an endogenous initiation function, models the reputation of a drug as being determined by memories of past use, and finds the optimal drug treatment strategy. Interestingly, unless the societal discount rate is quite low, if memories of past users decay moderately quickly, the optimal strategy is cyclic. Hence, not only do we find that ‘those who forget the past are condemned to repeat it’, but also that ‘for those who forget the past and over-value the present it may even be optimal to have their future recreate the past’. These findings are illustrated by numerical analysis based on empirical data from the current US cocaine epidemic.

[1]  David F. Musto,et al.  The American Disease , 1973 .

[2]  A. Skiba,et al.  Optimal Growth with a Convex-Concave Production Function , 1978 .

[3]  Gustav Feichtinger,et al.  Optimale Kontrolle ökonomischer Prozesse : Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften , 1986 .

[4]  C. Peter Rydell,et al.  Enforcement or Treatment? Modeling the Relative Efficacy of Alternatives for Controlling Cocaine , 1996, Oper. Res..

[5]  Phillippe Michel,et al.  On the Transversality Condition in Infinite Horizon Optimal Problems , 1982 .

[6]  W. Davis Dechert,et al.  Increasing returns to scale and the reverse flexible accelerator , 1983 .

[7]  Ngo Van Long,et al.  Optimal control theory and static optimization in economics: Bibliography , 1992 .

[8]  Jonathan P. Caulkins,et al.  Optimal Control of Drug Epidemics: Prevent and Treat--But Not at the Same Time?: Prevent and Treat--But Not at the Same Time? , 2000 .

[9]  C. P. Rydell,et al.  Controlling Cocaine: Supply Versus Demand Programs , 1995 .

[10]  Kazuo Nishimura,et al.  A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function , 1983 .

[11]  J. Caulkins,et al.  Cocaine consumption in the United States: Estimating past trends and future scenarios , 1995 .

[12]  D. Rice,et al.  Estimates of economic costs of alcohol and drug abuse and mental illness, 1985 and 1988. , 1991, Public health reports.

[13]  Kevin M. Murphy,et al.  A Theory of Rational Addiction , 1988, Journal of Political Economy.

[14]  P. Andreas,et al.  Clinging to Failure: The Rise and Continued Life of U. S. Drug Policy@@@Drug War Politics: The Price of Denial@@@The Return of the Dangerous Classes: Drug Prohibition and Policy Politics , 1998 .

[15]  Franz Wirl,et al.  Limit cycles in intertemporal adjustment models: Theory and applications , 1994 .

[16]  Daniel Leonard,et al.  The signs of the co-state variables and sufficiency conditions in a class of optimal control problems , 1981 .

[17]  C. P. Rydell,et al.  Modeling the Demand for Cocaine , 1995 .

[18]  Gustav Feichtinger,et al.  Cyclical Consumption Patterns and Rational Addiction , 1993 .

[19]  Jonathan P. Caulkins,et al.  Optimal Dynamic Allocation of Treatment and Enforcement in Illicit Drug Control , 2001, Oper. Res..

[20]  C. Peter Rydell,et al.  An Ounce of Prevention, a Pound of Uncertainty , 1999 .

[21]  Jonathan P. Caulkins,et al.  Optimal Control of Drug Epidemics , 2000 .

[22]  Gustav Feichtinger,et al.  On the optimality of limit cycles in dynamic economic systems , 1991 .

[23]  J. Caulkins,et al.  A dynamic model of drug initiation: implications for treatment and drug control. , 1999, Mathematical biosciences.