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

Mark J. Rzeszutek, Christopher T. Franck, Haily K. Traxler, Brent A. Kaplan, Mikhail N. Koffarnus

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)57-71
Number of pages15
JournalPsychology of Addictive Behaviors
Issue number1
StatePublished - Nov 28 2022

Bibliographical note

Funding Information:
This work was funded by institutional funds at Virginia Tech to Mikhail N. Koffarnus. Mark J. Rzeszutek’s time was supported by the National Institute on Alcohol Abuse and Alcoholism of the National Institutes of Health Grant R01 AA026605 awarded to Mikhail N. Koffarnus. Haily K. Traxler’s time was supported by the National Institutes of Health Grant TL1 TR001997 awarded to Craig Rush. This research was solely supported by federal or state money with no financial or nonfinancial support from nongovernmental sources. The content of this article is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The funding source did not have a role in writing this article or in the decision to submit it for publication

Publisher Copyright:
© 2022 American Psychological Association


  • Alcohol purchase task
  • Behavioral economics
  • Demand
  • Discounting
  • Hyperbolic modeling

ASJC Scopus subject areas

  • Medicine (miscellaneous)
  • Clinical Psychology
  • Psychiatry and Mental health


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