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Article Excerpt
Markets for illicit drugs are frustratingly resilient, but periodically there are significant disruptions, such as the recent Australian heroin drought during which purity-adjusted prices at least tripled and overdoses fell by as much as 80% (Moore, Caulkins, Potter, Dietz, Monagle, & Pruden, 2005). There is a modest literature debating whether supply control programs can create such events (e.g., Weatherburn, Jones, Freeman, & Makkai, 2003; Degenhardt, Reuter, Collins, & Hall, 2005a; Wood, Stoltz, Li, Montaner, & Kerr, 2006), and a somewhat larger literature documenting resulting effects on outcomes such as overdose, crime, and use of other substances (Longo, Henry-Edwards, Humeniuk, Christie, & Ali, 2004; Degenhardt, Conroy, Gilmour, & Collins, 2005b; Baker, Lee, Claire, Lewin, Grant, Pohlman, Saunders et al., 2004).
Here we raise a different question. How, if at all, should drug policy or drug control efforts change during a market disruption, where by disruption we mean any unanticipated, substantial, and temporary shift in supply, not necessarily only a situation where the market literally does not clear? Consider treatment as an example. Is a drought a particularly good time to expand treatment programs, e.g., because users have an extra incentive to quit, or is it more valuable to expand treatment programs during a glut, because easy availability can lead to greater use and. hence, greater need for treatment? At first blush, either answer seems plausible. Parallel questions can be asked about enforcement. Is it more valuable to eliminate a seller or selling organization when the market is flush or when it is already weakened? If dealers with excess supply stimulate recruitment of new users it might be the former, but Kleiman 1993's "enforcement swamping" argument for increasing returns to enforcement intensity suggests the latter. At a more general level, during a supply disruption for one drug, should extra efforts be devoted to that drug, in effect attacking when the market is weak, or is that the time to focus on other drugs to which users might switch?
How drug policy ought to respond to market disruptions is a difficult question, and we only try to address one very simple special case. For one particular model of drug use dynamics, we use optimal control theory to investigate what the optimal trajectory of drug control effort is when prices suddenly rise by a known amount for a given length of time and the principal effect of that effort is to induce current users to cease using. Hence, our main contribution may come simply from asking the question.
There is considerable interest in understanding the effectiveness and even the cost-effectiveness of various drug control policies and programs (e.g., Cartwright, 2000). Yet none of the literature of which we are aware speaks directly to the present question in the sense that none draw conclusions such as, "This program's cost-effectiveness is X during normal times, but if and when the drug is temporarily in short supply, that cost-effectiveness rises [or falls] to Y."
The present question is a cousin of questions pertaining to how drug policy ought to evolve as a drug epidemic progresses from early stages, typically of explosive growth, to a more stable, endemic pattern of use. (See Caulkins, 2004, 2005 for overviews.) Both look at markets that are changing dynamically, in contrast with classic comparative statics analysis that compares two stable equilibria (cf. Reuter & Kleiman, 1986).
Substantively the difference is what is driving the dynamic change. In most of the existing literature change in the state variables is driven by the natural or endogenous evolution of patterns of drug use over the course of a drug epidemic, so the conclusions are of the ilk, "enforcement is relatively more effective early in a drug epidemic" (Tragler, Caulkins, & Feichtinger, 2001) or "treatment and harm reduction are relatively more effective later" (Behrens, Caulkins, Tragler, & Feichtinger 2000; Caulkins, Feichtinger, Tragler, & Wallner (Forthcoming)). Here we recognize the ongoing epidemic dynamics, but the proximate event to which policy may or may not wish to adapt is an exogenous market disruption.
This implies the present model addresses a different time scale and, hence, models market supply differently. Epidemic models have explored how numbers of users have grown or ebbed over many years. Since drug production and distribution are relatively low-tech activities with low capital requirements and few barriers to entry, it has typically been tacitly assumed that supply can keep up with these changes in demand with price remaining stable at some long-run average value, so the number of suppliers or network throughput capacity is not modeled explicitly. Here, in contrast, we focus on those times when there is too much or too little supply relative to demand. That is, we are looking exactly at the points in time when long-run equilibrium models, such as Reuter & Kleiman 1986"s classic risks and prices model of drug markets, do not apply.
Admittedly supply shocks and disequilibrium are the exceptional case. At any given time, in most drug markets prices are stable or exhibit some long- run trend (Caulkins, Pacula, Arkes, Reuter, Paddock, Iguchi et al., 2004b) and usually the great majority of users report success at being able to locate a supplier who has drugs (National Institute of Justice, 2003). However, there are enough exceptions that they merit study. In the U.S., every major drug has witnessed significant market disruptions, including the 1969 marijuana shortage (McGlothlin, Jamison & Rosenblatt, 1970; Gooberman, 1974; Craig, 1980); the heroin drought of the early 1970s associated with the Turkish opium ban and French connection case (DuPont & Greene, 1973); the cocaine shortage of 1989-1990 and possibly a briefer one in 1995 associated with the Peruvian air bridge interdiction (Crane, Rivold, & Comford, 1997); and multiple rounds of methamphetamine shortages associated with precursor controls (Cunningham & Liu, 2003; 2005). It is less clear how often there are true market gluts, but some authors have mentioned the possibility with respect to heroin (Dietze & Fitzgerald, 2002) and MDMA (Hall, Spillane, & Camejo, 2000).
Overview of model
Underlying dynamics
Tragler et al. (2001) proposed what is in some sense the simplest of all possible dynamic models of drug prevalence because it tracks just the total number of users, not differentiating between lower- and higher-frequency users as in Behrens and colleagues (1999; 2000; 2002) or between different substances as in Caulkins et al. (2007). Furthermore, there are just three flows: initiation, natural desistance, and desistance induced via drug control. We adopt Tragler et al.'s model here, just modifying initiation to follow the more familiar logistic function, rather than a power function. This modification allows for a behavior thought to be common in drug markets, namely the possibility of having both a low-use equilibrium and a high-use equilibrium, separated by a...
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