The Relationship between Illegal Drug Prices at the Retail User and Seller Levels

I. INTRODUCTION The hierarchical nature of illegal drug markets is well known. Drugs such as marijuana and cocaine reach consumers through multi-level distribution networks. Typically, a dealer at a given market level buys a quantity of drugs, repackages that quantity into a number of smaller units, and sells these repackaged units at a markup to either lower-level dealers or users. As drugs move down the distribution chain, therefore, their per unit prices increase. Price markups are much greater for illegal drugs than for legal goods. Little is known, however, about the underlying determinants of these markups. The two main competing theories hold that markups are either a fixed amount or a fixed percentage of the original price. These theories correspond to a price change at one market level passing through to lower market levels either additively or multiplicatively, respectively, prompting Caulkins (1990) to label the theories as the additive and multiplicative models. The important distinction between the two models is in their predictions regarding the effect of a change in the wholesale price of an illegal drug on the retail price. Suppose, for example, that retail seller (i.e., low-level wholesale) and user prices for cocaine are $50 and $100 per pure gram, respectively (roughly their mean values during the 1990s), and that a reduction in enforcement efforts lowers the retail seller price to $25. The additive model implies that the retail user price will also fall by $25, to $75, representing a decrease of 25%. Meanwhile, the multiplicative model implies a retail user price reduction of 50%, to $50. Restrictive drug policy that increases wholesale prices is thus more effective when the relationship between wholesale and retail prices is multiplicative rather than additive. Suppose that the price elasticity for past year participation in cocaine use is -0.4 (from DeSimone and Farrelly 2003). The above retail seller price decline would then increase the number of cocaine users by 10% if the additive model holds but by 20% if the multiplicative model holds. According to the Office of National Drug Control Policy (ONDCP 2001c) estimate that 5.74 million individuals were cocaine users in 2000, the difference in the two predictions represents 574,000 users, or about 0.2% of the U.S. population. In light of their differing implications for the potential impact of successful wholesale level drug enforcement on drug demand, information on which of the two models more accurately describes illegal drug markets is highly relevant for illegal drug policy. The recent report of the National Academy of Sciences Committee on Data and Research for Policy on Illegal Drugs (Manski et al. 2001) acknowledges that little is known about the effectiveness of current drug policy in general and drug law enforcement in particular (p. xi) and specifically notes that evidence regarding how changes in wholesale prices affect retail prices would be useful to illegal drug policy makers (p. 161). The only published study that conducts direct empirical tests of the additive and multiplicative models is Caulkins (1994), who analyzes 1977-91 data on median cocaine prices in eight U.S. cities. (1) Estimates from regressions of gram-level prices on ounce-level prices, as well as those for regressions of gram and ounce prices on kilogram prices, strongly reject the implications of the additive model but correspond closely with those of the multiplicative model. These results support the observation by Kleiman (1992) that the ratio of retail to wholesale cocaine prices remained approximately constant during the 1980s even as prices at both levels fell dramatically. Similarly, ONDCP (2001a) estimates a correlation of 0.46 between monthly retail and wholesale cocaine prices, with a $1 retail price increase associated with a wholesale price increase of just 7 cents. However, Caulkins and Reuter (1998) point out that the multiplicative model seems implausible closer to the origins of the distribution chain, because large variations in monthly coca leaf prices are not paralleled in retail price series. …