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Buying and selling price for risky lotteries and expected utility theory with gambling wealth

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  • Michal Lewandowski

Abstract

I analyze two expected utility models which abandon the consequentialist assumption of terminal wealth positions. In the expected utility of gambling wealth model, in which initial wealth is allowed to be small, I show that a large WTA/WTP gap is possible and the (Rabin in Econometrica, 68(5), 1281–1292, 2000 ) paradox may be resolved. Within the same model the classical preference reversal which allows arbitrage is not possible, whereas preference reversal (involving buying prices in place of selling prices), which does not allow arbitrage, is possible. In the expected utility of wealth changes model, in which there is no initial wealth, I show that both a WTA/WTP gap as well as the classical preference reversal are possible due to loss aversion, both in its general as well as some specific forms. Copyright The Author(s) 2014

Suggested Citation

  • Michal Lewandowski, 2014. "Buying and selling price for risky lotteries and expected utility theory with gambling wealth," Journal of Risk and Uncertainty, Springer, vol. 48(3), pages 253-283, June.
    • Handle: RePEc:kap:jrisku:v:48:y:2014:i:3:p:253-283
    DOI: 10.1007/s11166-014-9191-2
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    1. Jack L. Knetsch & J. A. Sinden, 1984. "Willingness to Pay and Compensation Demanded: Experimental Evidence of an Unexpected Disparity in Measures of Value," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 99(3), pages 507-521.
    2. David K. Levine & Drew Fudenberg, 2006. "A Dual-Self Model of Impulse Control," American Economic Review, American Economic Association, vol. 96(5), pages 1449-1476, December.
    3. Zvi Safra & Uzi Segal, 2008. "Calibration Results for Non-Expected Utility Theories," Econometrica, Econometric Society, vol. 76(5), pages 1143-1166, September.
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. Ulrich Schmidt & Chris Starmer & Robert Sugden, 2008. "Third-generation prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 203-223, June.
    6. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    7. Ariel Rubinstein, 2006. "Dilemmas of an Economic Theorist," Econometrica, Econometric Society, vol. 74(4), pages 865-883, July.
    8. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    9. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    10. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    11. W. Viscusi & Joel Huber, 2012. "Reference-dependent valuations of risk: Why willingness-to-accept exceeds willingness-to-pay," Journal of Risk and Uncertainty, Springer, vol. 44(1), pages 19-44, February.
    12. Grether, David M & Plott, Charles R, 1979. "Economic Theory of Choice and the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 69(4), pages 623-638, September.
    13. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    14. Hanemann, W Michael, 1991. "Willingness to Pay and Willingness to Accept: How Much Can They Differ?," American Economic Review, American Economic Association, vol. 81(3), pages 635-647, June.
    15. Cox, James C. & Sadiraj, Vjollca, 2006. "Small- and large-stakes risk aversion: Implications of concavity calibration for decision theory," Games and Economic Behavior, Elsevier, vol. 56(1), pages 45-60, July.
    16. Michał Lewandowski, 2013. "Risk Attitudes, Buying and Selling Price for a Lottery and Simple Strategies," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 5(1), pages 1-34, March.
    17. Palacios-Huerta, Ignacio & Serrano, Roberto, 2006. "Rejecting small gambles under expected utility," Economics Letters, Elsevier, vol. 91(2), pages 250-259, May.
    18. Horowitz, John K. & McConnell, Kenneth E., 2002. "A Review of WTA/WTP Studies," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 426-447, November.
    19. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    20. Susan Chilton & Michael Jones-Lee & Rebecca McDonald & Hugh Metcalf, 2012. "Does the WTA/WTP ratio diminish as the severity of a health complaint is reduced? Testing for smoothness of the underlying utility of wealth function," Journal of Risk and Uncertainty, Springer, vol. 45(1), pages 1-24, August.
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    Cited by:

    1. Giuseppe Coco & Daniele Simone & Laura Serlenga & Sabrina Molinaro, 2023. "Risk awareness and complexity in students’ gambling," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 40(3), pages 971-994, October.
    2. Krzysztof Kontek & Michal Lewandowski, 2018. "Range-Dependent Utility," Management Science, INFORMS, vol. 64(6), pages 2812-2832, June.
    3. Stivender Carol O. & Gaggl Paul & Amato Louis H. & Farrow-Chestnut Tonya E., 2016. "The Impact of Education Earmarking on State-Level Lottery Sales," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 16(3), pages 1473-1500, September.
    4. Michał Lewandowski, 2017. "Prospect Theory Versus Expected Utility Theory: Assumptions, Predictions, Intuition and Modelling of Risk Attitudes," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(4), pages 275-321, December.
    5. Emilia Tomczyk, 2013. "End of sample vs. real time data: perspectives for analysis of expectations," Working Papers 68, Department of Applied Econometrics, Warsaw School of Economics.
    6. Krzysztof Kontek & Michal Lewandowski, 2013. "Range-Dependent Utility," Working Papers 69, Department of Applied Econometrics, Warsaw School of Economics.

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    More about this item

    Keywords

    Expected utility; Narrow framing; Rabin (2000) paradox; Preference reversal; WTA/WTP disparity; Buying and selling price for a lottery; D81; D03; C91;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

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