A Stochastic Model of Rational Addiction

Zaifu Yang () and Rong Zhang ()
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Zaifu Yang: Department of Economics and Related Studies, University of York
Rong Zhang: College of Economics and Business Administration, Chongqing University

Annals of Economics and Finance, 2022, vol. 23, issue 2, 223-251

Abstract: We propose a new model of addictive behavior that takes as a starting point the classic model of Becker and Murphy (1988), but incorporates uncertainty. We model uncertainty through the Brownian motion process. This process is used to capture both random events such as exposure to harmful substances, anxiety, tensions and environmental cues which can precipitate and exacerbate addictions, and those sober and thought-provoking episodes that discourage addictions. We derive closed-form formulas for optimal addictive consumption and capital trajectories and examine their global and local properties. Our theory provides plausible explanations for several typical patterns of addiction and has novel policy implications.

Keywords: Rational Addiction; Uncertainty; Health Issue; Stochastic Optimization; Ito Lemma (search for similar items in EconPapers)
JEL-codes: C61 D01 D11 I10 I18 K32 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:cuf:journl:y:2022:v:23:i:2:yang:zhang

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