Modelling drug market supply disruptions: Where do all the drugs not go?

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Journal of Policy Modeling 30 (2008) 251–270

Modelling drug market supply disruptions: Where do all the drugs not go? Jonathan P. Caulkins ∗ , Haijing Hao Carnegie Mellon University, Qatar Campus and Heinz School of Public Policy, Qatar Received 1 October 2006; received in revised form 1 February 2007; accepted 1 April 2007 Available online 4 May 2007

Abstract Drug producing regions often supply several geographically distinct drug consumption markets. Disruptions of opium cultivation in Afghanistan and cocaine production in Colombia show that consumption reductions can be much smaller in some final markets than are reductions in cultivation. This paper derives a model for predicting how production deficits will be “allocated” across downstream markets in the form of reduced use. Plausible parameterization suggests that for cocaine, markets outside the US may serve as a sort of “shock absorber”, partially shielding US markets from sharp fluctuations in consumption. One implication is that multi-lateral efforts may be appropriate for source country control. © 2007 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved. JEL classification: K14; I12; Q17 Keywords: Drug policy; Source country control; Market disruption; Supply chain modelling

1. Introduction The illicit drugs that cause the biggest problems in many first-world consumer nations come from crops grown in developing nations. This coupled with a natural desire to attack the root of a problem has prompted sometimes aggressive efforts at “source country control”, notably on the part of the US in Colombia (ONDCP, 2004a). Source country control efforts take many forms including crop eradication, crop substitution, precursor chemical control, and law enforcement (Perl, 2005). All can be thought of as shifting back the supply curve of drugs available for export.

∗ Corresponding author at: Carnegie Mellon University, PO Box 24866, Doha, Qatar. Tel.: +974 492 8977; fax: +974 492 8255. E-mail address: [email protected] (J.P. Caulkins).

0161-8938/$ – see front matter © 2007 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.jpolmod.2007.04.003

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Most source zones supply markets in multiple countries. (An exception being Mexican heroin, which is predominantly destined for US markets.) This raises an interesting question. Suppose one drug-using country funds a successful source country control program that halves the quantity of drugs available for export—at any given price. Since drug demand is not perfectly inelastic, global consumption will decline. Which nation or nations will benefit the most from reduced drug use? Presumably the reduction in consumption would be shared in some measure by all consumer countries, but there is no reason the reductions need be the same, proportionally, in each country. In some countries drug use may fall more, in percentage terms, than did exports from the source country. In others, drug use may fall by less. What determines where the consumption reductions are larger or smaller? This is a fairly straightforward question in market modelling, but has not been addressed in the context of illicit drugs, despite its importance in that context. There is a moderately large literature that seeks to model quantitatively the effects of source country control interventions (for a review, see Caulkins, 2004), but to the best of the authors’ knowledge, none of it speaks directly to this question. Most causal or “what if” analyses focus on a single drug distribution pipeline feeding one destination market. These models implicitly assume that parallel pipelines feeding other destination markets can be ignored, a presumption this paper calls into question. There are “accounting” models that synthesize various data in an attempt to capture all drug flows to all destination countries (e.g., Drug Availability Steering Committee, 2002; Reuter, Greenfield, & Paoli, 2005). However, such descriptive models cannot in their present form be used to answer “what if” questions concerning how supply reductions in source countries would differentially affect consumption in different markets. This paper uses basic economics to produce a “what if” model for assessing how reductions in source country supply would differently affect consumption in various downstream markets and parameterizes the model for the international cocaine distribution system. The analysis is timely given what happened with source country control components of Plan Colombia and the Andean Initiative (Perl, 2005).1 These efforts together with the Uribe Administration’s efforts seem to have reduced Colombian coca cultivation. The US Office of National Drug Control Policy (ONDCP, 2004b, Table 51) reports that eradication in Colombia increased from about 45,000 ha/year in 1999–2000 to roughly 130,000 ha/year from 2002 through 2004. Commensurately, Colombian coca cultivation is reported to have declined by one-third, from 169,800 ha in 2001 to about 114,000 ha in 2003 and 2004 (Walters, 2005). Factoring in Peru and Bolivia, the ONDCP data imply cultivation in South America as a whole declined by about 22%. The United Nations (UNODC, 2005) reports a slightly larger reduction in South American coca cultivation (30% reduction from 220,000 to 155,000 ha), but shifted back 1 year, with the declines between 2000 and 2003. This 20–30% reduction in cultivation does not seem to have led to a comparably large reduction in US cocaine consumption. Stronger statements are not possible because several key monitoring systems are unable to trend outcomes over this entire period. The Arrestee Drug Abuse Monitoring (ADAM) system, with its urinalysis testing of arrestees, was phased out for budgetary reasons (Kleiman, 2004), so its data are only available through 2003. Several changes were made to the National Survey on Drug Use and Health in 2002, including offering respondents a $30

1 US drug policy vis a vis Colombia also encompasses interdiction between Colombia and the US; modeling the effectiveness of interdiction in transit is equally important but is not the present topic.

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cash incentive, so comparisons of drug use levels before and after 2002 are not reliable (Kennet & Gfroerer, 2005). Likewise, the Drug Abuse Warning Network (DAWN), which monitors emergency department drug mentions, was redesigned, interrupting trend lines from before and after January 2003. The remaining relevant, but imperfect, data sets show little evidence of dramatic changes in US cocaine consumption. Between 1999 and 2004 high school seniors surveyed by monitoring the future reported stable past-month cocaine prevalence (increasing just from 2.2% to 2.3%) and modest reductions in lifetime prevalence (from 8.6% to 8.1%). Federal cocaine seizures changed little, declining slightly from 106 to 107 metric tonnes in 2000–2001 to 103 metric tonnes in 2002 before edging back up to 116 metric tonnes in 2003. The percentage of arrestees testing positive for cocaine in the ADAM program increased between 2000 and 2003 in more cities than it decreased for both female (9 cities versus 7 cities) and male arrestees (20 versus 9). The proportion of Treatment Episode Data Set records for which cocaine or crack were mentioned at admission continued its long-standing decline, dropping from 32.4% in 1999 to 30.1% in 2002, before rebounding in 2003 to 30.8%. US market indicators are also inconsistent with sharp reductions in supply (Caulkins et al., 2004b). Between 2000 and the second quarter of 2003, retail to mid-level wholesale purity rose for crack (9–13%, depending on market level) and was stable for cocaine powder (−3% to +8%). Purity adjusted prices fell for both crack (by 13–28%) and powder (20–34%). Walters (2005) reports those perverse trends continued through early 2005. They improved during 2005, but have not yet returned to 2003 let alone 2000 levels. In summary, there is considerable uncertainty concerning recent trends in US cocaine markets, but it does not appear that reductions in South American coca cultivation led to proportional reductions in US cocaine supply or consumption. The Taliban’s opium ban in 2000–2001 offers a parallel case. In 1999 and 2000 Afghanistan accounted for 80–90% of global potential opium production. The Taliban cut Afghan production by 94% between 2000 and 2001, leading to a 66% decline in global opium production (UNODC, 2005). Afghanistan was the principal supplier of heroin to Europe (though not to the US), so if European consumption had declined in proportion to the reduction in source country supply, the effects should have been striking. Reuter et al. (2005) traced the effects of this production cut on downstream markets from Pakistan to Europe. Pietchmann (2004) also analyzed this opium drought. There is fairly persuasive evidence that purity-adjusted heroin prices rose and consumption fell in Europe but apparently much less than proportionately. Reuter et al. summarize the evidence as supporting “the hypothesis that in 2002 and probably 2003 there was a perceptible tightening of heroin supplies in Western Europe but that should be regarded as still a preliminary conclusion.” Thus for both of these reductions in source country production, consumption in downstream first world markets (cocaine in the US, heroin in Europe) appears to have fallen much less than proportionately. There are at least two broad explanations that can reconcile dramatic reductions in global production with modest reductions in first-world consumption. The first is that suppliers were holding copious stocks of inventory, and year-long or even multi-year production disruptions can largely be made up by drawing down inventory. There are precious few data on inventory holding practices, so it is difficult to investigate that hypothesis, although Reuter et al. (2005) note that if every stage in an 10-layer distribution network holds 2 weeks of inventory, that adds up to 5 months worth of consumption held in inventory. It is probably safe to say that expert judgment in the field believes inventories are more likely to have played an important role in

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softening the 1-year disruption in opiate production than they did for the multi-year reduction in coca cultivation. Another possibility is that when global production fluctuates moderately, consumption in developing countries may change greatly while consumption in first-world countries changes only modestly. Seeming to support this possibility is the fact that retail prices in affluent countries tend to be much higher, sometimes 10 times higher, than are retail prices in developing countries. It might seem to “make sense” that drug suppliers would “serve first” customers in high-priced markets. However, intuition about market-related phenomenon is sometimes imprecise. That is the case here. It turns out that the results depend directly not on the price in each market but rather on the elasticity of demand for exports to each consumption market. This export demand elasticity in turn depends on price linkages as well as seizure patterns, but not only on price mark-ups. The price mark-up influences the export demand elasticity, but in non-obvious ways. 2. Supply and demand framework for the export market The next section models how the elasticity of demand is reflected up a distribution chain, but first we set down carefully how that export demand elasticity interacts with the export market’s supply elasticity to determine how reductions in supply translate into changes in shipments to each consumption market. We are interested in a textbook economics problem: how does reduction in supply affect consumption in various markets? The answer naturally is an algebraic function of various elasticities. Using mathematical notation helps avoid confusion about exactly which elasticities are involved. Labelling the equations as pertaining to the cocaine export market also lends clarity, but the equations apply equally to the heroin export market. Indeed, we describe the market as having multiple exporters to make clear how the framework would apply for the heroin market; that degree of generality is not really needed for the cocaine example worked below. The international export market for cocaine physically resides primarily in Colombia, even though the coca is also grown in Peru and Bolivia. It has perhaps several hundred cocaine producers selling to organizations that will take responsibility for moving the cocaine out to international markets. Often the smuggling services are provided by contractors, and there are some vertically integrated firms that both produce cocaine powder from cocaine base and sell in foreign markets. Nevertheless, this illicit market functions sufficiently as a market that government documents commonly refer to an “export price” of cocaine, and the mark-up between the export price in Colombia and the import price in the US is sometimes used as a performance indicator for assessing the effectiveness of interdiction. Without making any assumptions about functional forms, we can analyze the effects of a production cut via comparative statics by viewing the cocaine export market as in equilibrium with i = 1, 2, . . ., m suppliers who have individual supply curves QiS (P) with elasticities ηiS and  j market shares ϕi such that m . . ., n customers with demand curves QD (P) i=1 ϕi = 1, and j = 1, 2, j with elasticities ηD and market shares φj such that nj=1 φj = 1. Customers could be thought of as representing individual drug firms, but since data are not available at the firm level, a customer can also be thought of as the collection of all firms shipping to a particular destination market, such as the US. They do not, however, represent individual retail-level consumers in the US e.g., the elasticity of demand for “customer”, ηUS D , represents the percentage change in demand for exports to the US with respect to a change in the export price. We shall show below that this

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is very different than the retail price elasticity of demand. Likewise, applications of the model might view one supplier as the aggregation of all suppliers sharing a given supply elasticity and subject to similar supply disruptions, e.g., the collection of all suppliers in a given geographic region. Suppose 100 × θ% of supplier k’s production capacity is eliminated. That would cut by 100 × θ% the amount this supplier would be willing to bring to market at any given price. Hence, supplier k’s supply curve QkS (P) shifts down by 100 × θ%. Algebraically that means premultiplying it by (1 − θ), yielding a new market equilibrium price P that is determined implicitly as a function of θ by: 

QiS (P) + (1 − θ)QkS (P) =

n 

j

QD (P).

(1)

j=1

i=k

Implicit differentiation yields the rate of change in the market clearing export price P per unit reduction in supply, θ. Near the original market equilibrium (i.e., for θ ≈ 0), this change, expressed as a percentage of the original price P0 , is    1 dP  ϕk ϕk (2) = m = n  j i P dθ θ=0 D j=1 φj ηD i=1 ϕi η − S

m

 j where we use the shorthand D = i=1 ϕi ηiS − nj=1 φj ηD for convenience. Note, since elasticities of demand are customarily negative, D > 0 and the supply reduction increases the market clearing price. Using the definitions of the elasticity of supply and demand we can convert changes in price into percentage changes in quantities supplied and “consumed” (meaning, purchased and passed further down the distribution chain), per unit change in θ as: • % change in quantity supplied by supplier k = ηkS /D − 1, • % change in quantity supplied for all other suppliers = ηiS /D, and j • % change in quantity consumed for each customer = ηD /D. When modelling the effects of the Taliban opium ban, one would consider multiple suppliers because the ban affected only one source of heroin. In contrast, the vast majority of South American coca cultivation feeds one export market. So, the effect of the roughly 25% decline in South American coca cultivation can be modelled as a θ = 25% reduction in production capacity for a single supplier (i.e., m = 1). Note: this does not imply that we model cocaine producers as monopolists; it merely means that there is one supply curve describing production, not separate curves for different regions that have different supply elasticities. In the single supply region case, the percent reduction in shipments to a given customer l (say, the US) per unit reduction in production capacity is    1 dQlD  ηlD = . (3)  n l  dθ  QD j θ=0 ηS − φ j ηD j=1

This expression shows that if the elasticity of supply ηS is negligible and the elasticity of demand is the same in all regions, then the percentage reduction in the quantity supplied to every

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region will be exactly the same as the percentage reduction in production (namely, θ). However, to the extent that ηS > 0 and/or the elasticity of demand for shipments to a region is less than the weighted average elasticity of demand for all regions, weighting by the regions’ market shares for shipments, then consumption in a region can shrink by less than the percentage reduction in supply. The next two sections argue that both conditions hold vis a vis the US and cocaine. In particular, (1) the elasticity of demand for exports  to the US is small relative to the corresponding figures  j US for other regions (|ηD | <  φj ηD ) and (2) all elasticities of demand for exports are quite a bit smaller than are the retail elasticities of demand for cocaine, making it likely that ηS is not negligible by comparison. Hence, one might expect reductions in US cocaine consumption to be considerably less, in percentage terms, than are reductions in South American coca cultivation. 3. Relating the elasticity of demand at the export and retail market levels Data limitations preclude empirically estimating the elasticity of demand in the export market for shipments to a particular region, such as the US. Fortunately, we can derive and parameterize the relationship between that elasticity and the more familiar retail elasticity of demand. For these purposes, distribution from the export market down to drug users can be thought of as a special type of network called a “tree”, with one root node repeatedly branching out through a multi-level distribution tree. That is, dealers buying cocaine in the Colombian export market do not sell directly to drug users in the US. Rather, they sell to or employ the services of smugglers who typically carry the cocaine to a transhipment country such as Mexico. Local gangs in Mexico move the drugs to the US border. They may transport the drugs over the US border or hire or sell to smugglers who do so. In the US, high-level wholesale dealers buy drug shipments and divide them into smaller packages for resale to other dealers who are one step closer to the customers. That second layer of sellers may sell directly to some retail sellers but more often there are one, two, or even three more layers of branching to lower and lower level wholesale sellers. Finally, each lowest-level wholesale dealer sells to multiple retail sellers, who in turn supply multiple customers (Caulkins, 1997). There are not a fixed number of layers in the distribution tree. Some drugs may reach users after passing through only a handful of distribution layers. Others may change hands 10 or more times before reaching a user. Furthermore, the number of layers and branching factors can be different for drugs distributed to the US, to Europe, and to various markets in the developing world. However, the relationship across just one link turns out to have a particularly simple form that can be replicated and aggregated to cover the entire tree. 3.1. Model relating demand elasticity across a single link in a distribution chain Drugs are lost as they move down the distribution network. The most important type of loss is seizure by law enforcement, but there is also spoilage, in-kind consumption by drug distributors, and disposal or abandonment (e.g., to destroy evidence when arrest is imminent). These other forms of losses and are probably minor compared with seizures, so in the sequel we refer simply to seizures. Let function g() stand for the quantity of drugs that must be shipped down a link in order to get one unit of drugs to arrive at the bottom of the link. For example, if 50% of shipments were

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seized or otherwise lost, then g(x) = 2x. Likewise, if 10 kg are seized regardless of the quantity shipped, then g(x) = x + 10. Just as quantities shrink, prices rise as one moves down the distribution network. Let the function f() stand for the price at the retail end of the link as a function of the price at the wholesale end. If the drug dealers who move drugs from the wholesale to the retail side of the link insist on “doubling their money” then f(p) = 2p. If instead they always demand $10 per unit delivered, then f(p) = p + 10. Given f() and g() we can relate the known demand at the bottom or “retail” end of the link, denoted DR (PR ), to the price, PW , at the top or “wholesale” end of the link. If the price at the top of the link is PW , then the price at the bottom is f(PW ). That means the quantity demanded at the bottom is DR (f(PW )), and the quantity shipped from the top is g(DR (f(PW ))). That expression is the quantity demanded at the top of the link as a function of the price at the top of the link i.e., it is the demand curve at the top of the link, DW (PW ). The elasticity of this demand at the top of a link in the distribution chain is: ηD W =

PW dDW (PW ) PW dg(DR (f (PW ))) = dPW DW (PW ) dPW g(DR (f (PW )))

df (PW ) PW   PW PR D R = g DR f dPW g(DR (f (PW ))) D W PR D R     DR PW  PR f DR = ηg ηf ηD = g R DW PR DR  = g DR

(4)

where ηg is the elasticity of the quantity shipped down the link with respect to the quantity received, ηf the elasticity of the price at the bottom of the link with respect to the price at the top, and ηD R is the elasticity of demand at the bottom of the link with respect to the price at the bottom of the link. In words, the price elasticity of demand reflected up one link is the price elasticity of demand at the bottom of that link times the elasticity of quantity shipped with respect to quantity received times the elasticity of price at the bottom with respect to price at the top of the link. 3.2. Extension to entire distribution tree When reflecting demand over more than one link the elasticities with respect to f() and g() can be chained together, so Eq. (3) still applies. For example, consider the relationship between quantity shipped (QS ) from the top of a three-link pipeline with no branches to the quantity delivered at the bottom of the third link (Q3 ), where Q1 and Q2 denote the quantities delivered at the end of the first and second links of the pipeline, respectively. Let g1 (), g2 (), and g3 () denote the relationships between quantities shipped down a link to quantities received at the bottom of that link for all three links. So QS = g1 (g2 (g3 (Q3 ))). The elasticity of quantity shipped across all three links with respect to quantity delivered at the bottom is just:     dQS (Q3 ) Q3 Q3 Q1 Q2 Q3 g2 g3 = ηg1 ηg2 ηg3 . = g1 g2 g3 = g1 (5) dQ3 QS QS QS Q1 Q2 The same logic applies for combining elasticities with respect to price across links (the f()’s). So, Eq. (3) applies not just over a single link, but over any chain or “pipeline” of links where the functions f() and g() are understood to relate prices and quantities at the top and bottom of the entire chain of links, and ηD R refers to the elasticity of demand at the very bottom of the chain.

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Thus Eq. (3) is a simple and general expression which relates the elasticity of demand generated by the customers of any specific retail drug seller reflected all the way back to Colombia. We next want to aggregate the demand reflected back to the export market from all retail sellers in a region such as the US. Fortunately, in a graph theoretic sense, a tree can be thought of as a summation of all the paths (chains) linking the root to the leaves. Furthermore, the elasticity of demand summed across several entities is just the weighted sum of the elasticity of demand for each individual entity, weighted by the quantity demanded by each entity. So, suppose there are N retail sellers in the US, each of whom reflects demand Qi (PS ) back to the US source country. Then the total demand at the source generated by US drug users is QD S (PS ) = N US = Qi (PS ), and the elasticity of that total demand reflected up from the US is ηD S i=1 N D i=1 ηi pi , where pi is the proportion of demand at the source stemming from customers of retail seller i. Hence, the expression for quantity demanded at the top of one link as a function of demand at the bottom of that link can be extended to an arbitrarily complicated distribution tree, producing a parsimonious way of thinking about how total demand from a region (e.g., total US demand) is perceived in the export market. The elasticity of demand felt in the export market that is reflected up from a consumption market is the weighted average taken over submarkets, weighting by the quantity shipped to each submarket, of the product of three elasticities: the elasticity of demand of drug users with respect to retail price, the elasticity of the quantity shipped with respect to the quantity delivered, and the elasticity of the retail price with respect to the export price in the source country. 4. Estimating the three elasticities This section parameterizes the model for cocaine, which should be understood to refer to cocaine in all its consumption forms, including crack and, where relevant, coca leaf. The following section explores implications of these elasticity estimates. 4.1. The elasticity of demand There is a growing literature estimating the elasticity of demand for cocaine in the United States. Grossman, Chaloupka, and Shim (2002) summarized this literature as finding a price elasticity of participation of −0.4 to −1.0 and a price elasticity of consumption given participation of −0.4, suggesting a total elasticity of demand of −0.8 to −1.4. However, that summary may be high for two reasons. First, it seems to be a “simple average” of the literature’s findings. Estimates pertaining to youth and estimates based on survey self-reports tend to be on the higher side, and those populations account for a modest share of cocaine demand. The weighted average, weighting by amounts consumed, might be lower, particularly since recent estimates (Dave, 2004a,b) based on measures of heavier use are substantially lower. Second, some studies did not control for state or regional fixed effects, and Desimone and Farrelly (2003) find that omission can overstate price responsiveness for cocaine. Hence, we take −0.75 as a point estimate and consider the range from −0.5 to −1.0 in sensitivity analysis. There are few comparable estimates for other countries. Econometric estimates for hard drugs in other countries primarily pertain to heroin and amphetamines. It is possible, though, to consider qualitatively factors that may suggest differences in cocaine demand elasticity across countries. One’s first impulse might be that the elasticity should be the same all over the world because

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consumption is dominated by the minority of users who are dependent, dependence is a medical condition (a “brain disease”), and brain wiring is much the same for all people. However, one can identify several contextual issues that may both vary from country to country and affect the elasticity of demand. The first is the availability of substitutes. One expects higher elasticity of demand when close substitutes are available, ceteris paribus. Pharmacologically, amphetamine type stimulants (ATS) might be the closest substitute for cocaine. Relative to cocaine, ATS are less commonly used in the US than elsewhere. UNODC (2005) reports that globally there are almost two ATS users for every cocaine user, whereas in the Western Hemisphere the ratio is reversed. Strikingly, the ratio of ATS to cocaine users is lower in North America even than in South America (0.46:1 versus 0.57:1). Furthermore, there is considerable “social distance” between US methamphetamine users (west and mid-west, white, not urban) and dependent cocaine/crack users (nationally distributed, but more common in the east, urban, and – to an extent that is a matter of some dispute – disproportionately African-American) (cf., Brownsberger, 1997; Caulkins, 2003). People who use only cocaine might reduce consumption less in response to a price increase than would polydrug users who could alter the mix of drugs they are already using. Leaving aside cannabis, cocaine is the dominant drug in the Western Hemisphere, whereas it is secondary to heroin in much of the rest of the world. Hence, more cocaine demand in the Eastern Hemisphere may come from people for whom cocaine is a secondary drug than is the case for the US or South America. Another factor is the availability of treatment, which is in some sense another substitute for continued cocaine use. As a gross generalization, treatment is more widely available in other affluent countries than it is in the US, but more available in the US than in developing countries. Since European cocaine demand is dominated by relatively affluent Western European nations (DASC, 2002), this suggests higher elasticity of demand for cocaine in Europe than in the US. A fourth factor is the proportion of demand stemming from dependent, heavy, or “hard core” users as opposed to their counterparts (non-dependent, light, or occasional). Those proportions can vary dramatically over the course of a cocaine epidemic, with light users dominating demand early on and heavy users dominating demand later (Everingham & Rydell, 1994; Caulkins, Behrens, Knoll, Tragler, & Zuba, 2004a). One might guess that dependent users are less price-responsive than are occasional users. The US cocaine epidemic is mature, with stable demand stemming primarily from dependent users. Epidemic modelling has not been done for cocaine elsewhere, but cocaine became popular in Europe more recently than in the US, and there are indications of considerable hidden consumption outside the pool of dependent users known to authorities (e.g., Zuccato et al., 2005). Also, UNODC (2005, p. 79) notes that cocaine consumption is still increasing throughout Europe and South America and also in much of the rest of the world, whereas it is stagnant in North America. Table 1 summarizes these speculations and offers a guess as to what they collectively imply for the elasticity of demand in Europe, Latin America, and the rest of the world. For the sake of establishing a base case, we presume the elasticity of demand for cocaine in Latin America is three-quarters that in the US, in Europe it is 1.5 times as large, and in the rest of the world it has the same value as in the US. It is important to emphasize the word “speculation”. Although the literature concerning the elasticity of demand for cocaine in the US is not definitive, those estimates do have some empir-

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Table 1 Factors that might make the elasticity of cocaine demand higher or lower in other parts of the world relative to the US Factor

Europe

Latin America

Rest of the World

Availability of ATS Polydrug use Treatment availability Stage in epidemic Cumulative effect

Higher Higher Higher Higher Higher

– Lower Lower Higher? Lower

– Higher Lower Maybe higher??? Same???

ical grounding. The speculations here concerning relative magnitudes in other regions are just educated guesses. To the extent that their implications are provocative, that might be construed as demonstrating that research on the elasticity of cocaine demand outside the US would be valuable as much as it is a demonstration of any particular policy conclusion.

4.2. The elasticity of quantities shipped with respect to the quantity delivered It is a bit foreign to think about g(x), the quantity that must be shipped in order to deliver x units of drugs. It is more intuitive to think about the quantity seized as a function of the quantity shipped, which we denote by s(). One would expect that s(0) = 0 (nothing will be seized if nothing is shipped), s ≥ 0 (shipping more will not reduce the quantity seized), s < 1 (the more that is shipped the more that will be received, so seizures rise by less than shipments do), and s < 0 (seizures are a concave function of the quantity shipped, for any given enforcement effort). These properties together with the accounting identity shipments = deliveries + seizures (g(x) = x + s(g(x))), imply that g(x) is also concave by the following argument. Totally differentiating g(x), g = 1 + s g , so g = 1/(1 − s ). Since 0 ≤ s < 1, we have g > 1 and, hence, g > 0. Differentiating again, g = s g + s g , so g = s g /(1 − s ). Since 0 ≤ s < 1 and g > 1, sign(g ) = sign(s ). By assumption s < 0, so g < 0 and g(x) is concave. Hence, ηg = g x/g ≤ 1 since concavity plus the fact that g(0) = 0 implies that g x ≤ g for all x ≥ 0. Likewise, since g > 1 it follows that ηg > x/g. We reach the limiting case of ηg = 1 when seizures are a fixed proportion of shipments, s(y) = φy. Then g(x) = x + φg(x), implying g(x) = x/(1 − φ), and an elasticity of ηg = 1 even if φ = 0 (there are no seizures). Since s ≥ 0, the opposite extreme occurs when s(x) = K for any x > 0 and some non-negative constant K. In that case, g(x) = x + K for x > 0 so ηg =

dg(x) x x x =1 = . dx g(x) g(x) x+K

So the larger K is, the lower is this elasticity ηg . Both extremes are special cases of seizures being a linear function of quantity shipped, s(x) = K + φx, for which ηg = φx/(K + φx). So large quantities seized reduce this elasticity when those seizures are independent of the quantity shipped and delivered. There are no data that allow estimation of s(x) or g(x). Trafficking and enforcement patterns change faster than does consumption, so variation over time in seizures and consumption cannot

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Table 2 DASC-based lower bounds on ηg , the elasticity of amounts shipped with respect to amounts delivered, by country/region

Latin America US US less federal domestic seizures Canada Europe total Middle East, Africa, Asia, Oceania

Consumption (metric tonnes)

Seizures (metric tonnes)

x/(x + K), lower bound on ηg

183 259 259 17 129 36

75.8 161.0 145.0 1.4 48.9 2.9

0.71 0.62 0.64 0.92 0.73 0.92

be used to identify these functions.2 One can, however, compute the plausible range of elasticities, x/(x + K) ≤ ηg ≤ 1, where x and K are the quantities consumed and seized, respectively, in a given country or region. This range is relatively narrow for final market countries, so inaccuracies in estimating this elasticity are not terribly problematic. DASC (2002) estimates cocaine consumption by country and region in 2000. It acknowledges openly the frailties of its estimates, but they are at present the only ones available, and their methodology is straightforward and sensible. The DASC also provides data on all seizures from throughout the world in 2001 that are known to the US government. Conveniently, it distinguishes seizures outside the US that were destined for the US from those destined for other markets.3 However, DASC data exclude state and local seizures in the US and presumably also exclude domestic seizures in many other countries. The UNODC (2005) provides data on seizures in 2003 from throughout the world as reported by those countries, so presumably usually including domestic seizures, but it does not distinguish between seizures meant for domestic consumption versus transhipment to third countries. So these two data sources have complementary strengths and weaknesses. Table 2 estimates x/(x + K) from DASC data. These lower bounds on ηg are lowest for the US, even when (federal) domestic seizures are excluded. Table 3 estimates are based on UNODC seizure and DASC consumption estimates.4 Countryspecific results are broadly consistent with Table 2, but Table 2 figures are preferred for Europe since so much of the cocaine destined for Europe is seized in Spain, Portugal, and The Netherlands. Table 3’s main lesson is that countries outside the US, Latin America, and Europe (specifically Canada, Nigeria, Russia, and South Africa) have lower bounds on ηg that are quite large, approaching their upper bound of one, meaning their ηg values are known fairly precisely. For base case parameter values, we set ηg equal to the midpoint between its lower and upper bounds for each region, specifically 0.82 for the US, 0.87 for Europe, 0.89 for Latin America, and 0.96 for the rest of the world. Sensitivity analyses with respect to these parameters are not reported because variation within plausible ranges has only a modest effect on the conclusions.

2 Simply adding right-hand side control variables for enforcement effort or spending is not an adequate control because there is so much adaptation over time in tactics and technologies. 3 We assume that seizures in Latin America that were being shipped overseas to someplace other than the US were destined for Europe, since Europe is by far the largest market in the Eastern Hemisphere. 4 Source and transhipment countries are excluded because their K values are inflated, skewing x/(x + K) ratios. E.g., the Dutch seized 17.56 mts of cocaine versus consumption of 4.72 mts. It is theoretically possible that the Dutch seize 17.56/(17.56 + 4.72) = 79% of all cocaine entering The Netherlands, but more likely that additional cocaine enters The Netherlands but is sent on to other European countries.

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Table 3 UNODC- (and DASC-) based lower bounds on ηg , the elasticity of amounts shipped with respect to amounts delivered, by country Country

Metric tonnes of consumption in 2000 (DASC, 2002)

Metric tonnes seized (UNODC, 2005)

x/(x + K)

US Brazil UK Germany Canada Italy Argentina France Chile Australia Russia South Africa Nigeria

259.08 47.3 25.75 20.42 16.46 15.83 14.24 11.23 7.37 6.42 6.06 5.81 5.4

117.0 9.6 3.6 1.0 0.5 3.5 2.0 4.2 2.4 0.3 0.1 0.8 0.2

0.69 0.83 0.88 0.95 0.97a 0.82 0.88 0.73 0.75 0.96a 0.99a 0.88a 0.97a

a x/(x + K) is biased downward (is conservative) because seizures are based on the region not just the country, e.g., all of Oceania for Australia.

4.3. The elasticity of retail price with respect to export price There is a literature concerning f(x), the retail price as a function of the export price in Colombia (Boyum, 1992; Caulkins, 1990, 1994; Crane, Rivolo, & Comfort, 1997; DeSimone, 1998; Rhodes, Johnson, Han, McMllen, & Hozik, 2000). The brief summary is that there are two extreme models (the “additive” and “multiplicative” models) that anchor a spectrum, with the actual relations likely falling somewhere in between. In the additive model, the price difference between the lower and upper market level is always a fixed constant, presumably equal to the costs of moving drugs from the upper to the lower level. In the multiplicative model it is the price ratio that is constant. For example, if dealers always seek to “double their money” the price per unit at the lower market level (PR ) would be twice that at the higher level (PW ). Both are special cases of the linear relationship PR = α + βPW , for which the elasticity of demand is ηf = βPw /(α + βPW ). In the multiplicative model α = 0 and β > 1, so ηf = 1. In the additive model α > 0 and β = 1, so ηf = PR /PW , or, for the entire chain, ηf = export price/retail price. The conventional wisdom prior to 1990 was that a variation on the additive model applied (Reuter, Crawford, & Cave, 1988). Certainly a pure multiplicative model cannot hold from Colombia all the way to retail levels because (1) there is no evidence that prices in the US are highly correlated with prices in South America and (2) prices in the US and Europe are only moderately correlated, whereas if the multiplicative model held everywhere then all downstream prices would be highly correlated. However, the additive model might be more applicable upstream (closer to Colombia), and the multiplicative model applicable further downstream (Caulkins, 1990). The reason is that the additive model should apply when distribution costs are driven by the weight of what is being distributed, as is typical in conventional commerce. The multiplicative model should apply when distribution costs depend on the goods’ value (e.g., paying couriers a percentage of the drug’s value to discourage them from absconding). Lower in the distribution chain, drugs are so valuable per unit weight that distribution costs related to weight may become secondary.

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Table 4 Estimates of the elasticity ηf of US retail cocaine prices with respect to mid-level wholesale prices (∼200 g) Path

Resulting elasticity

Constituent elasticities

Direct from 1 to 4 1–3 and 3–4 1–2 and 2–4 1–2 and 2–3 and 3–4

0.81 0.76 0.75 0.70

=0.64 × 1.18 =0.84 × 0.90 =0.84 × 0.71 × 1.18

There has been some empirical testing of the two models, primarily between the kg-level and gram-level within the US. Caulkins (1994) found evidence for a mixed model leaning toward multiplicative. Rhodes, Hyatt, and Scheiman (1994), Crane et al. (1997), and DeSimone (1998) argue more for a multiplicative model, while DeSimone (2006) finds evidence for a primarily additive model. New and potentially better price series are now available for the US. Caulkins et al. (2004b) estimated quarterly cocaine prices from 1981 through the second quarter of 2003 for four market levels: <2 g, 2–10 g, 10–50 g, and >50 g. The >50 g observations are almost all less than 2 kg and might be thought of as representing the ∼200 g market level. For each of the six pairs of levels, price at the lower level (PR ) was regressed on price at the higher level (PW ). For these data, it appears that β > 1 and (in all but one case) α > 0, indicating a mixed model. (Parallel analyses with city-level price series likewise suggest a mixed model.) The overall elasticity of prices at the lowest level (<2 g) with respect to prices at the highest level (∼200 g) can be computed directly by regressing level #1 prices on level #4 prices, or indirectly by chaining together the elasticity obtained in different steps, e.g., #1 on #3 and then #3 on #4. The results are summarized in Table 4. They suggest a price elasticity between level #4 and level #1 of between 0.70 and 0.81, with 0.75 being perhaps the single best point estimate of the elasticity ηf between the gram and ∼200 g levels in the US. Price transmission should tend toward the additive model, with a lower elasticity, as one moves up the chain. The more additive it is, the more dramatic are our primary conclusions below. Hence, to be conservative we presume that the elasticity is also 75% between the ∼200 g level in the US and the ∼40,000 g (40 kg) import level, where the price is about $15,000/kg. (Both stages, import to ∼200 g and ∼200 g to retail, have about the same number of intermediate layers.) There are no data that allow one to estimate the elasticity of the US import price with respect to the Colombian export price. It seems likely that the price mark ups at those levels are primarily additive, but one cannot be sure. Hence, we analyze results below as a function of γ, the proportion of the increase from the ∼$1500/kg export price in Colombia to the ∼$15,000/kg US import price that is due to the additive term. For example, if γ = 67%, then the intercept of the linear relationship is 67% × ($15,000 − $1500) = $9000 and the multiplicative coefficient β = 4, so US import price = $9000 + 4 × Colombian export price. A simple argument suggests focusing on 0.5 ≤ γ ≤ 1. Prices increase from ∼$15,000/kg to ∼$100,000/kg ($100/g) between the US import and retail market levels. To get ηf = 0.752 over that range with a linear model implies retail price = 3.75 × import price + $43,750, for which $43,750/$85,000 = 51.5% of the price increase is due to the additive term. Since the proportion of mark ups due to additive factors should be higher further up the chain, it seems likely that 0.5 ≤ γ ≤ 1. Regressions were also done with UNODC’s (2005) European wholesale and retail prices from 1990 to 2004. Using UNODC’s weighted average price for Europe as a whole, the resulting elas-

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ticity is 0.83. Using country-specific wholesale and retail series gives widely divergent elasticity estimates whose simple average is 0.66. These values are in the same range as the US estimate of 0.75, but given the divergence in country-specific European estimates, any aggregation or average for Europe is necessarily imprecise. To avoid making policy conclusions below depend excessively on such a poorly measured parameter, we set the elasticity of European retail price with respect to Colombian export price equal to the corresponding elasticity for the US retail price. This is at least partially justified by the observation that the UNODC reports that US and European retail prices are roughly similar ($77 and $88/g in 2003) as are wholesale prices in the US and the average for The Netherlands, Spain, and Portugal, the three European countries that dominate continental imports and so presumably have the high-level wholesale markets. We use the same elasticity of retail demand with respect to Colombian export prices for the other, non-Latin American markets. This assumption is relatively innocuous since other, nonLatin American markets account for less than 7% of global consumption. It is justified in part by the observation that retail cocaine prices elsewhere in the world are comparably high as in the US and Europe. The main regional difference in ηf is with respect to Latin American consumption. UNODC (2005) reports retail cocaine prices in Latin America that are far lower than elsewhere in the world, averaging about $6/g. We model the price increases within Latin America the same way we model the price increase between Colombia and the US in the sense that we make the proportion of the price increase attributable to additive factors be γ. Because retail price/g in Latin America is below the wholesale (and even import) prices elsewhere, this means that ηf is lower in Latin America than elsewhere. To see this, note   (6000 − 4500γ) P, Latin American retail price = 4500γ + 1500 where P = the Colombian export price. So for Latin America ηf =

(6000 − 4500γ) = 1 − 0.75γ. 6000

The corresponding elasticity for US import prices is (15,000 − 13,500γ)/15,000 = 1 − 0.9 γ. Factoring in the elasticity from the other two levels (import to wholesale and wholesale to retail) yields an overall elasticity of US retail prices with respect to Colombian export prices of ηf = 0.75 × 0.75 × (1 − 0.9γ). 5. Results Table 5 summarizes the implications of the discussion above for the elasticity parameters. We define our base case to be a retail elasticity of demand in the US of ηUS D = 0.75 and γ = 75% of upstream price mark-ups being due to additive factors, but perform sensitivity analysis with respect to these parameters. The aggregate elasticity of demand for exports to non-US regions is the weighted average of constituent export demand elasticities e.g., for the base case it is (19.5% × −0.179 + 2.0% × −0.197 + 28.3% × −0.221 + 4.3% × −0.132)/(19.5% + 2.0% + 28.3% + 4.3%) = −0.198, or about 75% larger than for exports to the US. As discussed, if aggregated non-US export demand elasticity is larger, in absolute magnitude, than the demand elasticity for exports to the US, then reductions in the quantity supplied to US markets will be smaller than would be predicted by a na¨ıve model that focused only on the

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Table 5 Components of export demand elasticity for five market regions

ηRetail D ηg ηf Overall base case η Consumption Seizures Shipments % of Shipments

US

Europe

Canada

Latin America

Elsewhere

−0.75 (range of −0.5 to −1.0) 0.82 0.75 × 0.75 × (1 − 0.9γ) −0.112

1.5 × US value 0.87 =US value −0.179

1.5 × US value 0.96 =US value −0.197

0.75 × US value 0.9 (1 − 0.75γ) −0.221

=US value 0.96 =US value −0.132

259 161.0 420.0 45.9%

129 48.9 177.9 19.5%

17 1.4 18.4 2.0%

183 75.8 258.8 28.3%

36 2.9 38.9 4.3%

Table 6 Difference between elasticity of demand for exports to the US and non-US markets as a function of US retail cocaine demand elasticity (ηUS D ) and proportion of upstream price mark-ups due to additive factors (γ), base case in bold γ, proportion of upstream mark up due to additive factors

US retail cocaine demand elasticity

−0.5 −0.6 −0.7 −0.75 −0.8 −0.9 −1

0%

25%

50%

75%

100%

0.1147 0.1376 0.1606 0.1721 0.1835 0.2065 0.2294

0.0955 0.1146 0.1337 0.1433 0.1528 0.1719 0.191

0.0763 0.0916 0.1069 0.1145 0.1222 0.1374 0.1527

0.0572 0.0686 0.08 0.0858 0.0915 0.1029 0.1143

0.038 0.0456 0.0532 0.057 0.0608 0.0684 0.076

distribution network from South America to the US. In other words, markets elsewhere would act as a shock absorber partially insulating US consumption from fluctuations in cocaine supply. That turns out to be so not only for the base case but also for any 0 ≤ γ ≤ 1 and any non-zero elasticity of US retail cocaine demand. Table 6 illustrates this for a range of parameter values. Tables 5 and 6 establish that reductions in South American cocaine supply will generate smaller percentage reductions in quantities shipped to US markets than to markets elsewhere. What is not yet clear is whether the reductions everywhere will be almost as large as, or a lot smaller than, the reductions in supply. Eq. (3) answers that question by giving the reduction in quantity supplied to the US per unit reduction in cocaine supply. Given the parameter estimation above, the numerical magnitude is principally a function of three imperfectly known parameters: the elasticity of supply (ηS ), the proportion of upstream mark-ups that are due to additive factors (γ), and the US retail cocaine demand elasticity (ηUS D ). The result is least dependent on the third, so Table 7 presents the range of values traced out by varying the retail US demand elasticity for each combination of the other two values. This paper does not estimate the elasticity of supply, but it shows that the supply elasticity should be compared to the magnitude of the elasticity of demand reflected up to the export market, which is only about one-fifth or one-sixth of the retail demand elasticity (−0.11 versus −0.75 for the US; −0.16 versus −0.78 worldwide). Hence, even a modest supply elasticity of ηS = 0.2 coupled with our base case γ = 75% implies that cutting South American production capacity by 1% will only reduce shipments to the US by 0.25–0.36% (read from the second column, second row of Table 7). Even if the supply elasticity and the proportion of upstream mark-ups due to

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Table 7 Reduction in shipments to US markets per unit reduction in South American supply, ranges of values indicate range produced by varying US retail cocaine demand elasticity (ηUS D ) form −0.5 to −1.0 γ, proportion of upstream mark up due to additive factors

Elasticity of supply (ηS)

0.1 0.2 0.3 0.4

50%

75%

100%

0.47–0.58 0.34–0.47 0.27–0.40 0.22–0.34

0.36–0.48 0.25–0.36 0.18–0.29 0.15–0.25

0.16–0.25 0.09–0.16 0.07–0.12 0.05–0.09

additive factors were both almost implausibly small (ηS = 0.1 and γ = 50%), the US reductions would only be about half as great as the reduction in South American production capacity. Thus, we conclude that reductions in US cocaine consumption are likely not only to be smaller than reductions in consumption elsewhere, but also to be substantially smaller than are the reductions in production capacity. 5.1. Special case of constant elasticity supply and demand curves The analysis so far refrained from making any assumptions about the shape or functional form of the supply or demand curves. This has been accomplished by focusing on derivatives (slopes) around the original market equilibrium. It is also of interest to project the consequences of sizable reductions in supply, such as the ∼25% reduction in coca cultivation between 2000 and 2004. Extrapolating away from the original equilibrium requires making an assumption about the shape of the supply and demand curves. Here, we assume constant elasticity curves. Analysis for other functional forms, such as linear curves, is conceptually similar but more cumbersome. To understand how non-US demand might buffer US consumption for that case, we take advantage of the aggregation of non-US demand to adapt Eq. (1) as  ηS  ηUS  ηelsewhere D D P World P US P World US (1 − θ)Q0 = Q0 + (Q0 − Q0 ) (1 ) P0 P0 P0 and QUS where QWorld 0 0 are baseline global cocaine production and shipments to the US, respectively. Letting f = fraction of baseline global cocaine production that is shipped to the US, we can rewrite this to highlight the two “shock absorbers” between the supply reduction, (1 − θ), and the reduction in shipments to US markets:  −ηS  ηelsewhere −ηUS  ηUS D D D P P P (1 − θ) = f + (1 − f ) (6) P0 P0 P0 If the elasticity of supply (ηs ) is zero and the elasticity of demand for exports to markets outside ηUS D , the US equals that for exports to the US (ηelsewhere = ηUS D D ) this reduces to (1 − θ) = (P/P0 ) leaving no buffer between reductions in supply and effects on US markets. However, both “shock absorbers” are less than one, so reductions in US consumption will be smaller than θ. The supply elasticity does not need to be large in order for supply flexibility to serve as a significant buffer. For example, if the elasticity of supply √ is merely ηWorld = 0.16, then a 100 × θ% D reduction in supply reduces global exports by only 1 − 1 − θ.

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Fig. 1. Effects on cocaine shipments to various markets of a 25% reduction in South American cocaine supply with constant elasticity export supply and demand curves, ηS = 0.25, and price transmission mechanism is mixed, not purely additive.

Such productivity gains could come from harvesting more leaf per ha, extracting more coca paste per kg of leaf, producing more cocaine base per kg of paste, and/or refining more cocaine from each kg of base. Presumably the capacity to “make up” for supply reductions via increased processing yields is greater when the supply reduction is in coca cultivation (the furthest stage upstream) than if it were denominated in a reduction in coca paste or coca base i.e., the elasticity of supply ηs may be greater when modelling crop eradication than when modelling intermediate or finished product seizures in the source country.5 The second “shock absorber” shows, for any given value of (1 − θ)pηS , how large the reduction in shipments to the US would be relative to what they would have been if the elasticity of demand for exports to the US were the same as for exports to the rest of the world. For base case values, the answer is about 27% smaller, with the specifics depending on the values of ηUS D and γ. What do the two shock absorbers together imply for how reductions in South American supply affect US markets? For 0.5 ≤ γ ≤ 1, it turns out that −0.025 ≤ ηUS D ≤ −0.25 and the ratio US ≥ 1.6. So we can look conservatively at the attenuation by taking ηelsewhere /ηUS = /η ηelsewhere D D D D 1.6 (larger values give even greater attenuation) for −0.025 ≤ ηUS D ≤ −0.25. We pay particular attention to −0.075 ≤ ηUS D ≤ −0.15, which is the range covered by varying the US retail cocaine demand elasticity from −0.5 to −1 with γ = 0.75. Since the qualitative results are robust with respect to the elasticity of supply, we fix ηS = 0.25. That value is not empirically estimated but seems to be modest. We focus on a θ = 25% reduction in South American supply. Fig. 1 summarizes the results. Over the entire range of parameter values considered here, exports to the US fall by less than half the reduction in South American cocaine supply. Reductions in exports to other markets are consistently 1.5–1.6 times greater, in percentage terms, than are reductions in exports to the US. For the parameter range of greatest interest (−0.075 ≤ ηUS D ≤ −0.15), exports to the US fell by between 6.0% and 9.2%, or roughly one-third the 25% reduction in South American 5 Consistent with this, UNODC (2005) reports that between 2000 and 2003 cultivation declined by 30%, dry leaf production capacity by 27%, and potential cocaine manufacture declined by just 22%.

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cocaine supply. Hence, the results of a 25% supply reduction with constant elasticity curves are very similar to those that pertain at the margin (for the first incremental reduction in supply) for arbitrary supply and demand curves. 6. Conclusions Given the considerable efforts invested in source country control, it is important to understand how such efforts affect drug consumption. There is no reason to presume the effects will be the same, proportionally, in all downstream markets. This paper presents a simple model for estimating by how much global exports will fall (a function of the elasticity of supply and demand in the export markets) and how those reductions will be allocated across markets (a function of the relative magnitude of the elasticity of demand for exports to the different markets). The elasticity of demand for exports to a market is the product of three distinct elasticities: (1) the retail elasticity of cocaine demand in that market, (2) the elasticity of the quantity delivered with respect to quantity shipped to that market, and (3) the elasticity of retail prices in that market with respect to changes in the export price. When aggregating across several markets, the aggregate export demand elasticity is the weighted average of the constituent elasticities, weighting by quantities shipped to those markets, not the quantities consumed there. This model implies that three things can combine to attenuate reductions in consumption in a given market relative to the reduction in supply in the source country: (1) the elasticity of supply, which reflects source country suppliers’ ability to make available for export more kg per ha under cultivation when export prices rise, (2) the fact that export demand elasticities are much lower than are retail demand elasticities, and (3) the possibility that a given market’s export demand elasticity might be smaller than the elasticity of demand for exports to other markets around the world. Consumption in those other “shock absorber” markets would fluctuate more in response to upstream supply shocks than would consumption in markets whose export demand elasticity is lower. The model was parameterized for global cocaine distribution. The results strongly suggest that reducing cocaine supply in South America would induce a less than proportional reduction in US cocaine consumption. In particular, it seems likely that reductions in shipments to the US are no more than half as great, proportionally, as the reductions in supply, with reductions one-third as great being perhaps the single best guess. That is, a 25% reduction in coca cultivation in South America might be more likely to lead to a 8% reduction in shipments to the US than a 25% reduction. Reductions would be even smaller if the “additive price transmission model” extended further down the distribution chain than is assumed here. The obvious policy implication is to avoid assuming that reductions in cultivation in source countries will translate one for one into reductions in downstream use, even if there are not large stocks of inventory. A more subtle implication is to quantify the externalities enjoyed by other consumer countries when one country pursues source country control operations. For cocaine, more than half of the reduction generated by US-funded source country control efforts would seem to manifest outside the US. This might be an argument for the US favoring multi-lateral rather than unilateral or bilateral source country control efforts. The modelling framework introduced here is insightful. The parameterization is shaky. Hence, a practical implication is that organizations such as the US federal government that pursue source country control might consider investing more in research to improve some of the parameter estimates. Estimating the elasticity of demand for cocaine in Europe and major Latin American

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markets and also estimating better the elasticity of retail prices with respect to variations in upstream prices would be prime candidates for further research. The elasticity of quantity shipped with respect to quantity delivered is no better estimated at present, but the range of plausible variation for that parameter is much smaller. The model structure applies to any sub-tree of the overall distribution network. Hence, one could use it to understand better how reductions in supplies to the US would affect different US submarkets, such as the markets for casual versus dependent users or for users who do and do not also consume other drugs. Another extension would be to model distribution markets for multiple drugs. Parameterization would require cross-elasticity of demand estimates, of which there are currently few empirical estimates, but it may be that the structure of the model, even without detailed parameterization, could yield interesting insights. Acknowledgment This research was supported in part by the Robert Wood Johnson Foundation and the Qatar Foundation. References Boyum, D. (1992). Reflections on economic theory and drug enforcement, doctoral dissertation in public policy, Harvard University, Cambridge, MA. Brownsberger, W. N. (1997). Prevalence of frequent cocaine use in urban poverty areas. Contemporary Drug Problems, 24(2), 349–371. Caulkins, J. P. (1990). The distribution and consumption of illicit drugs: Some mathematical models and their policy implications. Doctoral Dissertation, MIT, Cambridge, MA. Caulkins, J. P. (1994). Developing price series for cocaine. Santa Monica: RAND. Caulkins, J. P. (1997). Modeling the domestic distribution network for illicit drugs. Management Science, 43(10), 1364–1371. Caulkins, J. P. (2003). Methamphetamine epidemics: An empirical overview. Law Enforcement Executive Forum, 3(4), 17–42. Caulkins, J. P. (2004). Drug policy: Insights from mathematical analysis. In M. L. Brandeau, F. Sainfort, & W. P. Pierskalla (Eds.), Operations research and healthcare (pp. 297–332). Boston: Kluwer. Caulkins, J. P., Behrens, D. A., Knoll, C., Tragler, G., & Zuba, D. (2004). Modeling dynamic trajectories of initiation and demand: The case of the US cocaine epidemic. Health Care Management Science, 7(4), 319–329. Caulkins, J. P., Pacula, R. L., Arkes, J., Reuter, P., Paddock, S., Iguchi, M., & Riley, K. J. (2004). The price and purity of illicit drugs: 1981 through the second quarter of 2003. Santa Monica: RAND. Crane, B. D., Rivolo, A. R., & Comfort, G. C. (1997). An empirical examination of Counterdrug Interdiction Program Effectiveness. Alexandria, Virginia: Institute for Defense Analysis. Drug Availability Steering Committee (DASC). (2002). Drug availability estimates in the United States. Washington, DC: USGPO. Dave, D. (2004a), The effects of cocaine and heroin price on drug-related emergency department visits. NBER Working Paper, No. 10619, National Bureau of Economic Research, Cambridge, MA. Dave, D. (2004b). Illicit drug use among arrestees and drug prices, NBER Working Paper, No. 10648, National Bureau of Economic Research, Cambridge, MA. DeSimone, J. (1998). The relationship between marijuana prices at different market levels. Paper available at http://www.ecu.edu/econ/wp/99/ecu9915.pdf. DeSimone, J. (2006). The relationship between illegal drug prices at the retail user and seller levels. Contemporary Economic Policy, 24(1), 64–73. doi:10.1093/cep/byj004 Desimone, J., & Farrelly, M. C. (2003). Price and enforcement effects on cocaine and marijuana demand. Economic Inquiry, 41(1), 98–115. Everingham, S. S., & Rydell, C. P. (1994). Modeling the demand for cocaine. Santa Monica, CA: RAND.

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