Forschungsgruppe ORCOS
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Control of Drug Consumption

Illicit drug consumption and drug related crimes (e.g., property crime) pose serious challenges for societies around the world. (According to Rydell & Everingham, 1994, the social costs of cocaine consumption in the U.S. in 1992, say, amount to at least $ 33 billion.) A variety of drug control interventions (e.g., prevention, enforcement, treatment, etc.) are available, and the question arises, how scarce resources should be allocated amongst these interventions.
In a research project, which is partly financed by the Austrian Science Foundation (FWF) under contract No. P11711-SOZ ("Dynamic Law Enforcement"), dynamic optimization models (optimal control models, differential games) deal with this and related questions. The models are developed, analysed, and empirically validated with data of the U.S. cocaine epidemic (the only useful data available at this time) in a fruitful cooperation with Jonathan Caulkins (Carnegie Mellon University, H. John Heinz III School of Public Policy and Management and RAND Drug Policy Resarch Center).

The basic structure of the (continuous time) optimal control models is as follows. The decision maker (e.g., the U.S. government) wants to find those levels of prevention, enforcement, treatment, etc., spending, which minimize the total social costs over a given (sometimes infinite) planning horizon (cf. the static approach to crime and punishment by Becker, 1968) subject to a differential equation constraint which describes the dynamics of the number of users (in Tragler et al., 1997, we have one group of -- "average" -- users, whereas in Behrens et al., 1997, we distinguish between so-called "light" and "heavy" users, respectively). The models are analysed with the help of the maximum principle (see, e.g., Feichtinger & Hartl, 1986) and Wolfram's software system Mathematica.

These models generate a variety of insights. E.g., from our first model (Tragler et al., 1997; one state: average users; two controls: treatment, enforcement) we conclude, among other things, that (1) detecting the onset of a drug epidemic quickly is valuable because total costs are much lower if control begins early, when the number of users is small; (2) people who perceive drug use to be costly for society should favor greater drug control spending per user and allocating a greater proportion of that spending to enforcement; (3) sharp price declines, such as those observed in the 1980s for cocaine in the U.S., do not necessarily imply a policy failure; indeed, it can be optimal to have such declines; and (4) under certain conditions it can be optimal to spend a very large amount per user -- primarily on treatment -- in a manner that prevents the epidemic from ever expanding beyond its initial, low use state.

In Dworak et al. (1998) and Popovic et al. (1998) these first approaches to the optimal control of illicit drug consumption have been extended by taking into account the drug related social problem of property crimes. For the future, we plan to include also prostitution and infectious diseases related to injecting drug users (like, e.g., HIV and Hepatitis). Apart from that, a social network approach is planned for a better understanding of drug initiation.

In co-operations with the EMCDDA (European Monitoring Centre for Drugs and Drug Addiction, Rua da Cruz de Santa Apolonia 23-25, P-1100 Lisbon, Portugal) and with the UNDCP (United Nations International Drug Control Programme, Vienna International Centre, A-1400 Vienna, Austria; UNDCP, 1997) it is our aim to extend our analyses by using data on specific European drug phenomena.