Hyperbolic discounting and exponentiated demand: Modeling demand for cigarettes in three dimensions

Behavioral economics has been a fruitful area of research in substance use. Mathematical descriptions of how individuals temporally discount the value of a commodity have been correlated with substance use and mathematical descriptions of drug consumption decreasing as a function of price (i.e., demand) predict maladaptive substance use. While there is a logical assumption that temporal factors affect demand for a drug, little has been done to merge these models. Thus, the purpose of this study was to combine models of discounting and demand, extending Howard Rachlin's work and contributions to novel areas of study. Data from 85 participants from Amazon Mechanical Turk (MTurk) who completed a hypothetical cigarette purchase task that included price of and delay to cigarettes were analyzed. Multilevel modeling was used to determine descriptive accuracy of combined additive and multiplicative models of discounting and demand. Of the discounting models used in conjunction with the exponentiated demand equation, the Rachlin hyperboloid best described the delay dimension of consumption. The multiplicative version of the Rachlin equation applied to both delay and price outperformed other models tested. Therefore, existing models of discounting and demand can be extended to modeling consumption data from complex multidimensional experimental arrangements.