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A Stochastic Model of Rational Addiction

Author

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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)

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.

Suggested Citation

  • Zaifu Yang & Rong Zhang, 2022. "A Stochastic Model of Rational Addiction," Annals of Economics and Finance, Society for AEF, vol. 23(2), pages 223-251, November.
    • Handle: RePEc:cuf:journl:y:2022:v:23:i:2:yang:zhang
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    References listed on IDEAS

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    1. Marcus, Jan & Siedler, Thomas, 2015. "Reducing binge drinking? The effect of a ban on late-night off-premise alcohol sales on alcohol-related hospital stays in Germany," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 0, pages 55-77.
    2. Jody Overland & Christopher D. Carroll & David N. Weil, 2000. "Saving and Growth with Habit Formation," American Economic Review, American Economic Association, vol. 90(3), pages 341-355, June.
    3. Olekalns, Nilss & Bardsley, Peter, 1996. "Rational Addiction to Caffeine: An Analysis of Coffee Consumption," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 1100-1104, October.
    4. Orphanides, Athanasios & Zervos, David, 1995. "Rational Addiction with Learning and Regret," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 739-758, August.
    5. Gary S. Becker & Kevin M. Murphy, 1993. "A Simple Theory of Advertising as a Good or Bad," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 941-964.
    6. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    7. Jonathan Gruber & Botond Köszegi, 2001. "Is Addiction "Rational"? Theory and Evidence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(4), pages 1261-1303.
    8. Dockner, Engelbert J & Feichtinger, Gustav, 1993. "Cyclical Consumption Patterns and Rational Addiction," American Economic Review, American Economic Association, vol. 83(1), pages 256-263, March.
    9. Jérôme Adda & Francesca Cornaglia, 2006. "Taxes, Cigarette Consumption, and Smoking Intensity," American Economic Review, American Economic Association, vol. 96(4), pages 1013-1028, September.
    10. Fenn, Aju J. & Antonovitz, Frances & Schroeter, John R., 2001. "Cigarettes and addiction information: new evidence in support of the rational addiction model," Economics Letters, Elsevier, vol. 72(1), pages 39-45, July.
    11. Bakshi, Gurdip S & Chen, Zhiwu, 1996. "The Spirit of Capitalism and Stock-Market Prices," American Economic Review, American Economic Association, vol. 86(1), pages 133-157, March.
    12. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    13. David Laibson, 2001. "A Cue-Theory of Consumption," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(1), pages 81-119.
    14. Iannaccone, Laurence R., 1986. "Addiction and satiation," Economics Letters, Elsevier, vol. 21(1), pages 95-99.
    15. Grossman, Michael & Chaloupka, Frank J., 1998. "The demand for cocaine by young adults: a rational addiction approach," Journal of Health Economics, Elsevier, vol. 17(4), pages 427-474, August.
    16. Becker, Gary S & Grossman, Michael & Murphy, Kevin M, 1994. "An Empirical Analysis of Cigarette Addiction," American Economic Review, American Economic Association, vol. 84(3), pages 396-418, June.
    17. Keeler, Theodore E. & Hu, Teh-Wei & Barnett, Paul G. & Manning, Williard G., 1993. "Taxation, regulation, and addiction: A demand function for cigarettes based on time-series evidence," Journal of Health Economics, Elsevier, vol. 12(1), pages 1-18, April.
    18. Grossman, Michael & Chaloupka, Frank J & Sirtalan, Ismail, 1998. "An Empirical Analysis of Alcohol Addiction: Results from the Monitoring the Future Panels," Economic Inquiry, Western Economic Association International, vol. 36(1), pages 39-48, January.
    19. Becker, Gary S & Murphy, Kevin M, 1988. "A Theory of Rational Addiction," Journal of Political Economy, University of Chicago Press, vol. 96(4), pages 675-700, August.
    20. Chaloupka, Frank, 1991. "Rational Addictive Behavior and Cigarette Smoking," Journal of Political Economy, University of Chicago Press, vol. 99(4), pages 722-742, August.
    21. Carbone, Jared C. & Kverndokk, Snorre & Rogeberg, Ole Jorgen, 2005. "Smoking, health, risk, and perception," Journal of Health Economics, Elsevier, vol. 24(4), pages 631-653, July.
    22. B. Douglas Bernheim & Antonio Rangel, 2004. "Addiction and Cue-Triggered Decision Processes," American Economic Review, American Economic Association, vol. 94(5), pages 1558-1590, December.
    23. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    24. Suranovic, Steven M. & Goldfarb, Robert S. & Leonard, Thomas C., 1999. "An economic theory of cigarette addiction," Journal of Health Economics, Elsevier, vol. 18(1), pages 1-29, January.
    25. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    Cited by:

    1. Teresa Perry, 2024. "Why Don’t You Leave? A Household Bargaining Model with a Household Preference of Addiction," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 50(3), pages 307-336, June.

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    More about this item

    Keywords

    Rational Addiction; Uncertainty; Health Issue; Stochastic Optimization; Ito Lemma;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • I10 - Health, Education, and Welfare - - Health - - - General
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • K32 - Law and Economics - - Other Substantive Areas of Law - - - Energy, Environmental, Health, and Safety Law

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