Demand for cocaine and food over time

Abstract

When reinterpreted, data from Ahmed and Koob [Ahmed, S.H., Koob, G.F., Transition from moderate to excessive drug intake: Change in hedonic set point. Science 1998; 282:298–301.] show that the reinforcing strength of cocaine, an inessential good, increases with experience. However, no such effect obtains with a homeostatically regulated good such as food. The present study evaluated whether this difference could serve to distinguish abused drugs from biologically necessary goods. In Experiment 1, five rats from Christensen, Silberberg, Hursh, Huntsberry and Riley [Christensen, C.J., Silberberg, A., Hursh, S.R., Huntsberry, M.E., Riley, A.L., Essential value of cocaine and food in rats: tests of the exponential model of demand. Psychopharmacology 2008;198(2):221–229.] earned cocaine under a Fixed-Ratio 3 schedule for 7 sessions. Thereafter, in a demand procedure identical to that in Christensen et al., demand was re-assessed by measuring consumption at Fixed Ratios between 3 and 560. In Experiment 2, five different rats from Christensen et al. had their food demand curves re-determined using an identical procedure as the first. When fit with the exponential model, the second determination of cocaine demand in Experiment 1 showed greater essential value than the first, indicating that strength increased with cocaine exposure. In Experiment 2, the re-determined food demand curves showed no change from their initial determination. These results show that the strength of cocaine, but not food, increases with increased experience. Measures of time-based changes in essential value may serve as a basis for distinguishing addictive from non-addictive reinforcers.

Introduction

Economic demand curves can be used to map the relation between an individual's consumption of a good and a good's price. When plotted in price (X axis)-log consumption (Y axis) space, these curves are downward sloping—that is, as the price of a good increases, the demand for it decreases.

Operant-based analogues of these demand curves can be constructed by allowing animals to earn as many units of a good as they desire as the size of a Fixed-Ratio (FR) schedule is varied across sessions. If goods that differ in size, potency or type are to be compared in a single plot, the unit of price (P) for each good is defined as the number of responses needed to produce 1% of that good at the lowest price on its demand curve (Hursh and Winger, 1995). For example, if, as is typically the case, consumption is highest under FR 1; and if the subject earns 200 reinforcers before sating, then each unit of price would equal two responses (i.e., 1% of 200 reinforcers requires 2 responses under an FR 1).

Once demand curves are plotted in this fashion, Hursh and Silberberg (2008) have advanced an exponential equation they believe accommodates these demand curves. It takes the form:

$$logQ=log{Q}_0+k\left(e^{-\alpha \cdot Q_0\cdot C}-1\right)\text{,}$$

where Q, Q₀, and e, respectively, signify units of consumption, units of consumption at the lowest price on the demand curve, and the base of the natural logarithm. The range of the exponential is adjusted so that it accommodates the number of log units (k) spanned by the demand curve with the largest range of consumption. Depending on the goods, k generally assumes a value ranging from 1 to 4 log units. The symbol α defines a free parameter that is adjusted to minimize the difference between the predictions of the equation and each demand curve. It varies inversely with a good's reinforcing strength or, in the terms of Hursh and Silberberg, a good's essential value. C represents the cost requirement (e.g., an FR 10 would have C = 10). The exponential term, Q₀ · C (i.e., normalized price), equals the cost of the reinforcer adjusted for the level of responding required to defend the level of demand at Q₀.

Christensen et al. (2008) recently tested the predictive adequacy of this exponential model with two goods, cocaine and food. They found that it accommodated the variance in demand for these goods, and that food had greater essential value than intravenously (i.v.) administered cocaine. In addition, they showcased the utility of an economic approach in explaining an otherwise paradoxical drug effect: In some studies (e.g., Aigner and Balster, 1978), cocaine seems to evidence remarkable reinforcing power while in others its reinforcing efficacy seems weak (e.g., Foltin and Fischman, 1994). Actually, both sets of data are consistent with the judgment Christensen et al. (2008) reach that, when compared with food, cocaine is a reinforcer of lower essential value. As a demand analysis makes clear, the essential value of a good is defined by an animal's persistence in defending consumption as prices increase. It is this test that shows cocaine is inferior, at least when compared to food.