Part II

Legalization and Drug Use: What We Cannot Know

  Jonathan P. Caulkins
H. John Heinz III School of Public Policy and Management
Carnegie Mellon University
5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA

Summary of Results

This note addresses how price changes associated with drug legalization would affect cocaine use in the US. The main substantive conclusion is that it is not possible to make precise predictions; there is no good way to upper bound the magnitude of the possible increase. The uncertainty stems not so much from uncertainty about how much prices would fall or how responsive consumption is to price changes around current prices (which can be measured empirically), but rather from lack of knowledge about the shape of the demand curve for prices below current and recent prices. Alternate plausible models of demand give wildly different predictions concerning legalization-induced consumption changes. Furthermore, there is little prospect for empirically determining the shape of the demand curve at lower prices without letting prices fall. Hence, at least at present, legalization would have to be viewed as a risky experiment in terms of its impact on consumption. 

Overview of Problem

Drug legalization is a contentious topic. Some people approach it from a moral perspective (right to privacy vs. government’s obligation to defend fundamental values), but many are “consequentialists” who focus on the likely benefits and costs. To reduce a complex debate to its bare essence, the principal appeal of legalization to consequentialists is that it could largely eliminate problems associated with black markets and drug control, including most drug-related violence, and the principal fear is that it would lead to large increases in use (Kleiman, 1992). Whether replacing our current drug control problem with a problem of greater use is a net gain depends critically on the question of how much consumption would increase if drugs were legalized (Goode, 1998). 

This note focuses on how legalization-induced price changes would affect consumption of cocaine, the most problematic illicit drug in the US today. Of course price is just one of many determinants of drug use (MacCoun, 1993), but the conclusion that precise predictions are not credible would be reinforced by including non-price considerations. If legalization’s effect on consumption through prices alone is hard to pin down, the total effect is even more uncertain.

Two ingredients are needed to estimate how price changes will affect consumption: estimates of relevant parameters (the elasticity of demand and prices before and after the change) and a model of the demand curve. Although current prices are known fairly precisely, there is uncertainty about the price after legalization and the value of the elasticity of demand, so we carry through the calculations with low, base, and high estimates of those parameters. Likewise, there is not just one plausible model of demand. We perform the calculations with two models and contrast the results.

Parameter Estimates

The Price Elasticity of Demand
Four recent studies estimated the elasticity of demand for cocaine in the US. They use data on various subpopulations (See Table 1.) and produce estimates between -0.72 and -2.0. We take those two values as our low and high estimates, respectively, and -1.3 as our base estimate. (-1.3 is the average of the midpoints of the studies’ ranges of estimates.)

Table 1: Empirical Estimates of the Elasticity of Demand for Cocaine 

Cocaine Prices: Now and After Legalization
The current retail price of cocaine, denoted P_c, is known with a reasonable degree of certainty. The ONDCP (1997) reports that in 1996 it was $93.95 per pure gram. We round that off to $100/gram and do not show sensitivity analyses with respect to this parameter because the results are relatively insensitive to it over plausible ranges. 

The price after legalization, denoted P_L, is less certain. One estimate comes from noting that kilograms of cocaine can be purchased in Colombia for $1,500 (Caulkins and Reuter, 1998). If drugs were legal in the US, presumably they could be shipped like any other commodity. (Smuggling is difficult primarily because the US wants to keep drugs out, not because Colombia wants to keep drugs in.) Kilogram parcels can be overnight expressed from Colombia to the US for about $44 (Caulkins and Reuter, 1998). One-hundred percent markups are common in retail sales. If the retail price were double the wholesale price including transportation costs, that would imply a price of $3.09 per gram. However, if the US legalized cocaine, production costs in South America would likely drop, particularly if the source countries legalized production. So this may be an over-estimate. On the other hand, excise taxes are possible if not likely, though the magnitude of such taxes is limited by the ability of the black market to undercut prices. So we evaluate a range of values for P_L, with $1.50 per gram as the low estimate, $3 per gram as the middle, and $6 per gram as the high estimate, all in 1997 dollars. (See Caulkins (2000) for further discussion of likely post-legalization cocaine prices.) 

Estimating Consumption After Legalization Using Two Models of Demand

To estimate how legalization-induced price changes would affect consumption, one needs a model of the demand for cocaine. What model is correct is not known. We carry through the calculations with two textbook models – a linear and a constant elasticity demand curve – to illustrate the implications of this uncertainty. 

Linear Demand Curve
Suppose one believed the demand curve for cocaine were linear:

Q = a + b P,

where Q = quantity consumed, P = price, and a and b are constants. The elasticity of demand for this demand curve, evaluated at the current price (P_c), is

The percentage change in consumption created by prices moving from P_c to P_L is

Our point estimate of the percentage change in consumption is [($3 - $100) / $100] * (-1.3) = 126.1%, i.e., consumption would slightly more than double. Varying the elasticity of demand and the price after legalization between their low, base, and high estimates generates estimates of consumption changes between 68% and 197%. (See Table 2.) With a linear demand curve, uncertainty about the price after legalization has only limited effect on estimates of the change in consumption. Regardless of the specific estimate of price after legalization, the percentage change in price is always close to 100%. One might be tempted to conclude from Table 2 that legalization-induced price change would no more than triple consumption. Such confidence is unwarranted, however, as we will see next.

	PL = $6.00 per gram	PL = $3.00 per gram	PL = $1.50 per gram
D = -0.72	68 %	70 %	71 %
D = -1.3	122 %	126 %	128 %
D = -2.0	188 %	194 %	197 %

Table 2: Sensitivity of Legalization’s Effect on US Cocaine Consumption with Respect to Uncertainty About Parameter Values for a Linear Demand Curve

Constant Elasticity of Demand Curve
In contrast, suppose the demand curve displayed a constant elasticity of demand, i.e.,

Then, if legalizing drugs changed prices from P_c to P_L, the percentage change in consumption relative to the base year would be

With the constant elasticity of demand model, our point estimate of the change in consumption is (0.03)^-1.3 - 1 = 9,400%, almost a 100-fold increase. Table 3 shows that varying estimates of and P_L between their low and high values generates estimates ranging between a six-and-a-half-fold increase and a 4,000-fold increase.

With the constant-elasticity model the consumption change is very sensitive to the estimate of the price after legalization because it is the ratio of the prices before and after, not the percentage difference in price, that determines the change in consumption.

	PL = $6.00 per gram	PL = $3.00 per gram	PL = $1.50 per gram
D = -0.72	658 %	1150 %	1960 %
D = -1.3	3780 %	9440 %	23400 %
D = -2.0	27700 %	111000 %	444000 %

Table 3: Sensitivity of Legalization’s Effect on US Cocaine Consumption with Respect to Uncertainty About Parameter Values for a Constant Elasticity Demand Curve

Comparison of Two Models’ Predictions
With a linear model of the demand curve, there is a roughly 3:1 ratio between the highest and lowest estimates of legalization’s effect on consumption. That range is large, but it does not swamp other uncertainties about the outcome of legalizing drugs. In contrast, switching to a constant elasticity model increased the base estimate by a factor of 75 (not just 75%), and the lowest estimate with the constant elasticity model is larger than the highest estimate with the linear model. Clearly sensitivity with respect to parameter values does not encompass the full range of uncertainty in that case. 

The extreme sensitivity to the structural assumption concerning the demand curve, and the minimal sensitivity to estimates of the price after legalization, can be illustrated with a stoplight chart. Suppose one would favor legalization if use would no more than double and oppose legalization if use would increase by more than a factor of ten. As a point of reference, there were 3.1 million casual cocaine users and 3.6 million heavy cocaine users in the US in 1995. (ONDCP, 1997) Then the figure below shows the ranges of values of the two uncertain parameters for which one would favor (green), oppose (red), or be agnostic (yellow) concerning legalization with both a linear demand model (top figure) and a constant elasticity model (bottom figure). Readers can experiment with different parameter ranges by downloading the spreadsheet that draws the stoplight chart. 

Figure 1: Stoplight chart showing assumptions for which cocaine use would no more than double (Green), increase between 100% and 1000% (Yellow), and increase by more than a factor of 10 (Red)

Evidence Regarding the Two Models of Demand

There is some circumstantial evidence concerning the validity of the two demand models. First, all four elasticity studies mentioned above used a log-linear regression. I.e., they regressed the log of a measure of consumption on log of price, and took the coefficient of logged price as the basis for the elasticity estimate. That procedure makes sense if the demand curve has constant elasticity. If Q = , then log Q = log + log P. If the demand curve were linear (Q = a + bP), then the consumption and price measures should not have been logged, and the coefficient estimated for price should have been multiplied by Q over P to get the elasticity of demand. The mere fact that the studies used log-log regression does not imply that the constant elasticity model is correct. All four studies could have suffered from misspecification error, but none report evidence of such error.

A second piece of circumstantial evidence comes from considering the range of elasticity estimates relative to the range of prices over which they were computed. Prices over the period covered by the four studies varied from $874/gram down to $134/gram (Table 1). If the demand curve displayed constant elasticity then all four studies should have produced the same elasticity estimate. In fact, the midpoints of the studies’ ranges of estimates are all within a factor of two, and some variation is to be expected because of estimation error and differences across subpopulations.

On the other hand, if the demand curve were linear, the point elasticity would have varied by much more than a factor of two over that range of prices. With a linear demand curve the point elasticity is 
= b P / (a + b P) = P / (^a/_b + P). There are no values of ^a/_b for which the point elasticities remain between -0.72 to -2.0 over this price range. Any value of ^a/_b that yields a plausible elasticity for today’s prices yields an implausibly large value for prices that pertained in the early 1980’s and vice versa. Likewise, there are no values of ^a/_b that give arc elasticities that are within a factor of two when starting at the different initial prices listed in Table 1.

Thus the linear model is questionable for prices between $134 and $874/gram, casting doubt on whether it is good model between $1.50 and $100/gram. The constant elasticity model is more plausible for prices between $134 and $874/gram, but most likely does not apply for the entire range between $1.50 and $100/gram. The consumption increases that would imply are not really plausible, at least not for elasticities of -1.3 or larger in absolute value. 

In summary, we simply do not know what the right model of the demand curve is over the range of prices relevant for legalization. Nor can we expect to get much insight from historical analogies. Discussions of drug policy often look to Europe for evidence (Reuter, Falco, and MacCoun, 1993; MacCoun and Reuter, 1997), but cocaine prices in Europe are as high or higher than they are in the US (Farrell, Mansur, and Tullis, 1996). Cocaine prices in the US were lower in the early 1900’s (even adjusting for inflation), but estimates of consumption are weak, estimates of changes in consumption are even weaker, and it would be hard to quantify and account for the substantial formal and informal controls that were in place even before the passing of the Harrison Anti-Narcotics Act in 1914 (Spillane, 1994). That is, in short, an instance of the common but sometimes under-appreciated problem of decision makers needing projections based on extrapolation of relationships beyond the range for which data exist.

Conclusion:  

Estimates of the elasticity of demand for illicit drugs are enormously important. Among other things, they play a crucial role in determining the cost-effectiveness of drug control strategies that influence drug use by driving up price (e.g., Rydell, et al., 1996; Caulkins et al., 1997). 

However, another debate to which the elasticity estimates are applied is that pertaining to legalization. Legalization would reduce the costs of using drugs, creating incentives for greater consumption. As Kleiman (1992) puts it, we can choose between having a drug problem and having a drug control problem. Legalization would get rid of (most of) our drug control problems, including violence associated with black markets, but would likely lead to an increase in use. Estimating the magnitude of that increase is all important for determining whether legalization is a creative solution to a Gordian knot or a foolhardy idea whose primary value is providing intellectual entertainment for the chattering class.

This note shows that having a good estimate of the current price elasticity of demand is not enough to determine how legalization would affect use, even ignoring the many non-price effects. The price-induced change in consumption depends more heavily on the nature or shape of the demand curve over the entire range of relevant prices than it does on the elasticity near current prices. The evidence seems more consistent with a constant elasticity than a linear demand function and, hence, with legalization leading to a large increase in use. However, the evidence is circumstantial at best, and it is likely that some third, as of yet unspecified model of demand may be superior to either of those considered here. Unfortunately, there is little prospect for resolving that question empirically unless prices fall very substantially.

Hence legalization would be an experiment. Furthermore, in an important sense the experiment would be irreversible. To the extent that drug use increased, re-instituting prohibition would not restore current conditions because some of the increased use would create drug dependence, and that dependence would not disappear when drugs were recriminalized.  Thus, a temporary legalization followed by reinstated prohibition could create a bigger black market and a bigger problem than before. That makes legalization risky in the sense that if the experiment turned out badly, it would not be possible to undo the damage done.  This observation that legalization is a risky experiment can be overlooked by commentators who do not conduct formal sensitivity analyses concerning its predicted effects.

References:

Caulkins, J.P. (1995), “Estimating the Elasticities and Cross Elasticities of Demand for Cocaine and Heroin, Carnegie Mellon University,” Heinz School Working Paper 95-13, Pittsburgh, PA.

Caulkins, J.P. and P. Reuter (1997), “Setting Goals for Drug Policy: Harm Reduction or Use Reduction,” Addiction, Vol. 92, pp.1143-1150. 

Caulkins, J.P., C.P. Rydell, W.L. Schwabe, and J. Chiesa (1997), “Mandatory Minimum Drug Sentences: Throwing Away the Key or the Taxpayers’ Money?” RAND, Santa Monica, CA.

Caulkins, J.P. and P. Reuter (1998), “What Price Data Tell Us About Drug Markets,” Journal of Drug Issues.

Caulkins, J.P. (2000) “Do Drug Prohibition and Enforcement Work?” White paper published in the “What Works?” series. Lexington Institute, Arlington, VA.

Chaloupka, Frank J., M. Grossman, and J. A. Tauras (1998), “The Demand for Cocaine and Marijuana by Youth,” National Bureau of Economic Research Working Paper #6411, National Bureau of Economic Research, Cambridge, MA.

Farrell, G., K. Mansur, and M. Tullis. (1996), “Cocaine and Heroin in Europe: A Cross-national Comparison of Trafficking and Prices,” The British Journal of Criminology, Vol. 36, pp. 255-281.

Goode, Erich. (1998), “Strange Bedfellows: Ideology, Politics, and Legalization,” Society. Vol. 35, No. 4, pp.18.

Grossman, M., F.J. Chaloupka, and C.C. Brown (1996), “The Demand for Cocaine by Young Adults: A Rational Addiction Approach,” National Bureau of Economic Research Working Paper #5713, National Bureau of Economic Research, Cambridge, MA.

Kleiman, M.A.R. (1992), Against Excess: Drug Policy for Results. Basic Books, New York, NY.

MacCoun, R.J. (1993), “Drugs and the Law: A Psychological Analysis of Drug Prohibition,” Psychological Bulletin, Vol. 113, pp.497-512.

MacCoun, R.J. and P. Reuter (1997), “Interpreting Dutch Cannabis Policy: Reasoning by Analogy in the Legalization Debate,” Science, Vol. 278, No. 5335, pp.47-52.

Office of National Drug Control Policy (ONDCP) (1997), The National Drug Control Strategy: Budget Summary, The White House, Washington, DC.

Reuter, P., M. Falco, and R. MacCoun (1993), Comparing Western European and North American Drug Policies, RAND, Santa Monica, CA. 

Rydell, C.P., J.P. Caulkins, and S.S. Everingham (1996), “Enforcement or Treatment: Modeling the Relative Efficacy of Alternatives for Controlling Cocaine,” Operations Research, Vol. 44, No.5, pp.687-695.

Saffer, H. and F. Chaloupka (1995), “The Demand for Illicit Drugs,” National Bureau of Economic Research Working Paper #5238, National Bureau of Economic Research, Cambridge, MA.

Spillane, J.F. (1994), “Modern Drug, Modern Menace: The Legal Use and Distribution of Cocaine in the United States, 1880-1920,” Ph.D. Dissertation in History, Carnegie Mellon University, Pittsburgh, PA.

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Part IIIa 

Case Assignment Concerning Legalization and Drug Use

Problem Statement:

Drug legalization is a contentious topic. To reduce a complex debate to its bare essence, the principal appeal of legalization is that it could largely eliminate problems associated with black markets and drug control, including most drug-related violence. The principal fear is that it would lead to large increases in use. Whether replacing our current drug control problem with a problem of greater use is a net gain depends critically on the question of how much consumption would increase if drugs were legalized. Legalization would affect drug use through many factors, some tending to increase drug use, some tending to decrease it. The most important, however, would likely be the change in price.

By most measures, cocaine is the most problematic of the currently illicit drugs in the US. Imagine you have been hired by a senior national policy maker to predict how legalization-induced price changes would affect consumption of cocaine. What would you say? Prepare both a concise, bottom-line summary that the official can understand and a supporting technical report for the official’s staff. Some background information that you might find useful follows. (Assume for the sake of this assignment that your report will be kept strictly confidential. You do not need to censor the report to delete material that could be damaging to you or the client if it were leaked and “spun” by the media or political opponents.)

Background Information:

Illicit cocaine currently retails in the US for about $100 per gram. (All prices are adjusted for purity, so you can ignore dilution.) The price after legalization is uncertain, but $3 per gram is a reasonable point estimate with values between $1.50 per gram and $6 per gram being quite plausible. 

The function relating quantity consumed to price is called a “demand curve.” Two simple models of the demand curve used in textbook examples are a linear demand curve:

Q = a + b P,

where Q = quantity consumed, P = price, and a and b are constants, and a constant elasticity demand curve:

where and are constants. The true form of the demand curve for illicit drugs is not known, particularly for prices below current levels. (In recent decades prices in the US have been at least as high as $100 per gram. Indeed, in real terms they fell by 75% during the 1980s and have drifted down further in the 1990s.)

Economists summarize how responsive consumption is to price changes with a parameter known as the “price elasticity of demand,” often denoted by the symbol . The elasticity of demand is the percent change in consumption associated with a one percent increase in price or, more formally, 

= dQ / dP * (P / Q).

Several studies have estimated the elasticity of demand for cocaine in the US using historical data, producing estimates that range between -0.72 and -2.0 with –1.3 being representative of their central tendency.

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Part IIIb   

Case Assignment Concerning Legalization and Drug Use (with citations)

Problem Statement:

Drug legalization is a contentious topic (see, e.g., Trebach and Inciardi, 1993). To reduce a complex debate to its bare essence, the principal appeal of legalization is that it could largely eliminate problems associated with black markets and drug control, including most drug-related violence. The principal fear is that it would lead to large increases in use (Kleiman, 1992). Whether replacing our current drug control problem with a problem of greater use is a net gain depends critically on the question of how much consumption would increase if drugs were legalized (Goode, 1998, among others). Legalization would affect drug use through many factors, some tending to increase drug use, some tending to decrease it (MacCoun, 1993). The most important, however, would likely be the change in price.

By most measures, cocaine is the most problematic of the currently illicit drugs in the US. Imagine you have been hired by a senior national policy maker to predict how legalization-induced price changes would affect consumption of cocaine. What would you say? Prepare both a concise, bottom-line summary that the official can understand and a supporting technical report for the official’s staff. Some background information that you might find useful follows. (Assume for the sake of this assignment that your report will be kept strictly confidential. You do not need to censor the report to delete material that could be damaging to you or the client if it were leaked and “spun" by the media or political opponents.) 

Background Information:

Illicit cocaine currently retails in the US for about $100 per gram (ONDCP, 1998). (All prices are adjusted for purity, so you can ignore dilution.) The price after legalization is uncertain, but $3 per gram is a reasonable point estimate with values between $1.50 per gram and $6 per gram being quite plausible (Caulkins and Reuter, 1998). 

The function relating quantity consumed to price is called a “demand curve.” Two simple models of the demand curve used in textbook examples are a linear demand curve:

Q = a + b P,

where Q = quantity consumed, P = price, and a and b are constants, and a constant elasticity curve:

where and are constants. The true form of the demand curve for illicit drugs is not known, particularly for prices below current levels. (In recent decades prices in the US have been at least as high as $100 per gram. Indeed, in real terms they fell by 75% during the 1980s and have drifted down further in the 1990s. Caulkins and Reuter, 1998.)

Economists summarize how responsive consumption is to price changes with a parameter known as the “price elasticity of demand,” often denoted by the symbol . The elasticity of demand is the percent change in consumption associated with a one percent increase in price or, more formally, 

= dQ / dP * (P / Q).

Several studies have estimated the elasticity of demand for cocaine in the US using historical data, producing estimates that range between -0.72 and -2.0 with –1.3 being representative of their central tendency (Saffer and Chaloupka, 1995; Grossman, Chaloupka, and Brown, 1996; Chaloupka, Grossman, and Taurus, 1998; Caulkins, 1995. See also Chaloupka and Pacula, forthcoming, for a review).

References:

Caulkins, J.P. (1995), “Estimating the Elasticities and Cross Elasticities of Demand for Cocaine and Heroin,” Heinz School Working Paper 95-13, Carnegie Mellon University, Pittsburgh, PA. 

Caulkins, J.P. and P. Reuter (1998), “What Price Data Tell Us About Drug Markets,” Journal of Drug Issues, Vol. 28, No. 3, pp.593-612.

Chaloupka, Frank J., Michael Grossman, and John A. Tauras (1998), “The Demand for Cocaine and Marijuana by Youth,” National Bureau of Economic Research Working Paper #6411, National Bureau of Economic Research, Cambridge, MA.

Chaloupka, F.J. and R.L. Pacula. Forthcoming. “Economics and Anti-Health Behavior: The Economic Analysis of Substance Use and Abuse,” in W. Bickel and R. Vuchinich (eds) Reframing Health Behavior Change with Behavioral Economics, Lawrence Earlbaum Associates, Hillsdale, NJ.

Grossman, M., F.J. Chaloupka, and C.C. Brown (1996), The Demand for Cocaine by Young Adults: A Rational Addiction Approach, National Bureau of Economic Research Working Paper #5713, National Bureau of Economic Research, Cambridge, MA. 

Kleiman, M.A.R. (1992), Against Excess: Drug Policy for Results. Basic Books, New York, NY.

MacCoun, R.J. (1993), “Drugs and the Law: A Psychological Analysis of Drug Prohibition,” Psychological Bulletin, Vol. 113, pp.497-512.

Office of National Drug Control Policy (1998), The National Drug Control Strategy. The White House, Washington, DC.

Saffer, H. and F. Chaloupka (1995), “The Demand for Illicit Drugs,” National Bureau of Economic Research Working Paper #5238, National Bureau of Economic Research, Cambridge, MA.

Trebach, A. and J. Inciardi. (1993), Legalize It? American University Press, Washington, DC.

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Part IV

Associated Homework Problems

Rydell and Everingham (1994) estimated that cutting enforcement spending by $3B per year (roughly a 25% cut) would lead to a 20% reduction in retail price.

1) If health and crime costs associated with cocaine were proportional to cocaine consumption and those costs were initially $30B per year, would cutting enforcement in the manner described by Rydell and Everingham improve social welfare? (Assume that social welfare comprises only health costs, crime costs, and control spending.)

2) Much of the crime associated with cocaine is driven by the amount users spend on cocaine, not the quantity consumed, so a better model of cocaine-related health and crime costs might be the sum of a term proportional to spending on cocaine plus a term proportional to consumption; i.e. health and crime costs = c₁PQ + c₂Q, where P and Q stand for price and consumption, respectively. Opinions about the wisdom of cutting enforcement often hinge on beliefs about what proportion of health and crime costs are driven by cocaine spending vs. cocaine consumption. Assuming that the elasticity of demand around the current price is = -1.3, for what proportions would the cut in enforcement modeled by Rydell and Everingham improve social welfare?

3) Prepare a sensitivity analysis that shows the combinations of demand model (linear vs. constant elasticity), demand elasticity, and proportions of health and crime costs that are driven by spending vs. consumption for which the enforcement cut modeled by Rydell and Everingham would improve social welfare. (Visual displays are preferred.)

4) Describe other types of sensitivity analyses that would inform judgments about the likelihood that cutting drug enforcement spending would raise or lower social welfare.

References:

Rydell, C.P. and S.S. Everingham (1994), “Controlling Cocaine. Supply Versus Demand Programs,” MR-331-ONDCP/A/DPRC, RAND, Santa Monica, CA. 

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