consumption of inferior goods. Thus, the effects of price and income on demand interact, indicating a complex system of interdependencies between goods, prices, elasticities, and incomes.

Effect of Unit Price on Operant Behaviors

These interrelationships can be addressed using the concept of ► unit price, or cost per unit of a commodity. Unit price is often represented as the schedule requirement or response effort, divided by reinforcer magnitude (quantity of reward commodity) (Hursh et al. 1988). It is formally expressed as:

Response Requirement

Unit price =

Reinforcer Magnitude

where either decreasing the magnitude of the reinforcer (commodity) or increasing the response requirement (cost) can increase the unit price of a commodity. This simple calculation predicts that when a commodity has the same response requirement and magnitude as another their unit prices will be equal. Thus, when represented in unit prices, commodities can be compared to each other despite different levels of magnitude and cost. Behavioral economic researchers have suggested that unit price may be the single construct that underpins both reinforcer-magnitude and schedule-of-reinforcement effects (DeGrandpre and Bickel 1996). For example, Bickel et al. (1991) assessed cigarette smoking under varying response requirements (fixed-ratio 200, 400, and 1,600 level pulls) and reinforcer magnitudes (1, 2, and 4 puffs per bout). For each subject, Bickel et al. found a positive relationship between unit price and responses per session, and a negative relationship between unit price and consumption of puffs. Moreover, the responses per session and the consumption of puffs were generally comparable among subjects at the same unit price; that is, an increase in response requirement is functionally equivalent to a decrease in the number of puffs. This positively decelerating demand curve appears to be a ubiquitous phenomenon: meta-analysis of smoking studies showed positively decelerating demand curves across all reported data sets (DeGrandpre and Bickel 1996).

The positively decelerating function has an implication when response rate rather than consumption is plotted as the dependent variable. During low prices consumption is typically inelastic, with smaller-than-proportional changes in response rate in relation to changes in price. However, as consumption increasingly decelerates with increases in price, the changes in response rate become elastic and response rate declines at a faster rate than the change in price. This causes the response rate to follow a bitonic function (exhibiting both inverse and direct relationships) where response rate increases at low prices and decreases at higher prices.

Unit price has also been applied in characterizing the interaction between commodities in pharmacology and drug consumption. For example, the effects of agonists and antagonists have been modeled using unit price; that is, unit price can describe the specific drug effects of ► methadone and ► naltrexone (DeGrandpre and Bickel 1996). DeGrandpre and Bickel reanalyzed the animal self-administration of opioid antagonists (► naltrexone) and agonists (► methadone) for heroin self-administration. They found, relative to saline, doses of antagonists increased the consumption of heroin at low unit prices, and decreased the consumption of heroin at high unit prices. Similar results have been found using ► morphine administration and cigarette smoking (ibid).

Interrelating Variables Predicting Drug Demand and Consumption

Other behavioral economic concepts also contribute to drug consumption. For example, Bickel et al. (1995) studied the effects of concurrently available alternatives to drug taking. They examined drug consumption using a fixed ratio (FR) response requirement when drug consumption was available and an alternative activity, employment (experiment 1), or another activity such as reading, playing games, etc. (experiment 2), was either available or unavailable. Fig. 1 illustrates these results.

Another variable that affects choice behavior is temporal duration. Elsmore et al. (1980) examined the effects on income when the inter-trial interval, the time between trials, changed. Elsmore et al. found that although there was the same number of choices for heroin and food at low inter-trial intervals, the consumption of heroin decreased to a greater extent than for the food alternative. Thus, temporal effects modify the subjective "value" of a commodity as indicated by choice responses. Similar temporal interactions are also important for another behavioral methodology describing decision-making - temporal discounting.

Discounting of Delayed Reward: Choice and Addiction

Research examining the effect of changing the temporal delay between choice and obtaining the reward has found that ascribed value changes, i.e., the subjective value is discounted. Specifically, the longer the delay that precedes the reward the less the reward is valued. This discounting

process can be represented as a hyperbolic curve, most commonly represented by Mazur's (1987) hyperbolic function:

1 + kD w where V is value, A is the undiscounted reward value, D is delay, and k is a free parameter describing the ► temporal discounting rate. The hyperbolic discounting relation implies that value decreases based on the total delay rather than a constant decline as suggested by other interpretations.

The hyperbolic function of temporal discounting has been used to describe the behavioral phenomena of ► preference reversal, or "switching" between alternatives when the delay to the outcomes changes. For example, given a choice between $100 now and $50 now most people would choose the larger alternative. However, as delays to obtaining the larger alternative increase the subjective value of this alternative declines, and given a long enough delay to reinforcement, organisms will switch their preference from the larger delayed alternative to the smaller immediate alternative. The switching phenomenon is illustrated in Fig. 2.

Behavioral Economics. Fig. 1. Consumption (number of cigarette puffs) is plotted as a function of unit price on log-log coordinates. Redrawn from DeGrandpre and Bickel (1996) Figure 10 (two plots only). The top panel shows consumption for one subject when the opportunity to earn money was and was not concurrently available;and the bottom panel show consumption for the same subject when recreational activities were and were not concurrently available. Data points located crossing the x-axis represent values of 0.0 on the y-axis. Advances in Behavioral Economics Volume 3: Substance Use and Abuse, L. Green and J. H. Kagel. Copyright © 1996 Ablex, Publishing Corporation. Reproduced with permission of ABC-CLIO, LLC. Open circle represents alternative present, filled square represents alternative absent, and dotted line represents best fitting non-linear trend line. The top panel shows the effects of available and unavailable employment, and the bottom panel shows the effects of available and unavailable recreation for one participant (similar curves were obtained for the other participants in these experiments). Drug consumption decreased as a positively decelerating function of unit price in each experiment. Moreover, available alternative reinforcers led to greater decreases in consumption compared to unavailable reinforcers indicating both employment and activities were acting as substitutes to drug consumption.

Behavioral Economics. Fig. 2. Hypothetical discounting curves. Hypothetical discounting curves for $10,000 and $6,000 delayed 5 years and 6 months, respectively. The dotted lines represent the hyperbolic decay of the subjective value of receiving the money as the delay increases. Delay is represented on the x-axis and the two alternatives are represented as vertical bars. The changes in value are represented by the dotted lines for each alternative, and the point where switching occurs is predicted by their intersection.

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