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

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)169-191
Number of pages23
JournalJournal of the Experimental Analysis of Behavior
Issue number1
StatePublished - Jan 2023

Bibliographical note

Funding Information:
This work was funded by institutional funds at Virginia Tech awarded to Mikhail Koffarnus. Mark Rzeszutek's time was supported by the National Institute on Alcohol Abuse and Alcoholism of the National Institutes of Health under award number R01 AA026605 to Mikhail Koffarnus. Haily Traxler's time was supported by a fellowship under the Clinical and Translational Science of the National Institutes of Health award number TL1 TR001997. This research was entirely supported by federal or state money with no financial or nonfinancial support from nongovernmental sources. The content of this manuscript 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 manuscript or in the decision to submit it for publication. Mark Rzeszutek played a lead role in writing of original draft, review and editing, and formal analysis. Brent Kaplan played a lead role in data curation and conceptualization and a supporting role in writing of review and editing. Haily Traxler played a supporting role of writing of original draft and review and editing. Chris Franck played a supporting role in review and editing. Mikhail Koffarnus played a lead role in funding acquisition and conceptualization and a supporting role in review and editing.

Publisher Copyright:
© 2022 Society for the Experimental Analysis of Behavior.


  • behavioral economics
  • cigarette purchase task
  • hyperbolic discounting
  • quantitative modeling
  • substance use

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Behavioral Neuroscience


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