Notes on Demand: Conceptual and Empirical Benefits of Applying Rachlin’s Discounting Equation to Demand Data

Objective: Howard Rachlin wrote extensively on how value diminishes in a hyperbolic form, and he contributed to understanding choice processes between different commodities as a molar pattern of behavior. The field of behavioral economic demand has been dominated by exponential decay functions, indicating that decreases in consumption of a commodity are best fit by exponential functions. Because of the success of Rachlin’s equation at describing how hyperbolic decay affects the value of a commodity across various factors (e.g., delay, probability, social distance), we attempted to extend his equation to behavioral economic demand data for alcohol and opioids. Method: Rachlin’s discounting equation was applied to estimate consumption on alcohol purchase task data and nonhuman drug demand data. We compared results of his equation to the exponentiated demand equation using both a mixed-effects modeling approach and a twostage approach. Results: Rachlin’s equation provided better fits to consumption data than the exponentiated equation for both mixed-effects and two-stage modeling. We also found that traditional demand metrics, such as Pmax, can be derived analytically when using Rachlin’s equation. Certain metrics derived from Rachlin’s equation appeared to be related to clinical covariates in ways similar to the exponentiated equation. Conclusions: Rachlin’s equation better described demand data than did the exponentiated equation, indicating that demand for a commodity may decrease hyperbolically rather than exponentially. Other benefits of his equation are that it does not have the same pitfalls as the current exponential equations and is relatively straightforward in its conceptualization when applied to demand data.