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Delay Effect and Subadditivity. Proposal of a New Discount Function: The Asymmetric Exponential Discounting

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  • Salvador Cruz Rambaud

    (Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain)

  • Piedad Ortiz Fernández

    (Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain)

Abstract

The framework of this paper is intertemporal choice and, more specifically, the so-called delay effect. Traditionally, this anomaly, also known as decreasing impatience, has been revealed when individuals reverse their preferences over monetary or non-monetary rewards. In this manuscript, we will analyze the delay effect by using preference relations and discount functions. The treatment of the delay effect with discount functions exhibits several scenarios for this paradox. Thus, the objective of this paper is to deduce the different expressions of the delay effect and their mathematical characterizations by using discount functions in stationary and dynamic settings. In this context, subadditivity will be derived as a particular case of decreasing impatience. Finally, we will introduce a new discount function, the so-called asymmetric exponential discount function, able to describe decreasing impatience.

Suggested Citation

  • Salvador Cruz Rambaud & Piedad Ortiz Fernández, 2020. "Delay Effect and Subadditivity. Proposal of a New Discount Function: The Asymmetric Exponential Discounting," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:367-:d:329593
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    References listed on IDEAS

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    1. Drazen Prelec & George Loewenstein, 1991. "Decision Making Over Time and Under Uncertainty: A Common Approach," Management Science, INFORMS, vol. 37(7), pages 770-786, July.
    2. Jonathan Baron, 2000. "Can We Use Human Judgments to Determine the Discount Rate?," Risk Analysis, John Wiley & Sons, vol. 20(6), pages 861-868, December.
    3. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    4. Drazen Prelec, 2004. "Decreasing Impatience: A Criterion for Non‐stationary Time Preference and “Hyperbolic” Discounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 511-532, October.
    5. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2007. "Empirical estimation of consistency parameter in intertemporal choice based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 338-342.
    6. Cairns, John & van der Pol, Marjon, 2000. "Valuing future private and social benefits: The discounted utility model versus hyperbolic discounting models," Journal of Economic Psychology, Elsevier, vol. 21(2), pages 191-205, April.
    7. Robert Scharff, 2009. "Obesity and Hyperbolic Discounting: Evidence and Implications," Journal of Consumer Policy, Springer, vol. 32(1), pages 3-21, March.
    8. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    9. Kirby, Kris N. & Marakovic, Nino N., 1995. "Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts," Organizational Behavior and Human Decision Processes, Elsevier, vol. 64(1), pages 22-30, October.
    10. Pender, John L., 1996. "Discount rates and credit markets: Theory and evidence from rural india," Journal of Development Economics, Elsevier, vol. 50(2), pages 257-296, August.
    11. Uri Benzion & Amnon Rapoport & Joseph Yagil, 1989. "Discount Rates Inferred from Decisions: An Experimental Study," Management Science, INFORMS, vol. 35(3), pages 270-284, March.
    12. Salvador Cruz Rambaud & María José Muñoz Torrecillas, 2016. "Measuring Impatience in Intertemporal Choice," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-17, February.
    13. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    14. Ikeda, Shinsuke & Kang, Myong-Il & Ohtake, Fumio, 2010. "Hyperbolic discounting, the sign effect, and the body mass index," Journal of Health Economics, Elsevier, vol. 29(2), pages 268-284, March.
    15. Harrison, Glenn W. & Lau, Morten I. & Rutström, E. Elisabet, 2010. "Individual discount rates and smoking: Evidence from a field experiment in Denmark," Journal of Health Economics, Elsevier, vol. 29(5), pages 708-717, September.
    16. Marc Scholten & Daniel Read, 2006. "Discounting by Intervals: A Generalized Model of Intertemporal Choice," Management Science, INFORMS, vol. 52(9), pages 1424-1436, September.
    17. Angelina Lazaro & Ramon Barberan & Encarnacion Rubio, 2001. "Private and social time preferences for health and money: an empirical estimation," Health Economics, John Wiley & Sons, Ltd., vol. 10(4), pages 351-356, June.
    18. Read, Daniel & Roelofsma, Peter H. M. P., 2003. "Subadditive versus hyperbolic discounting: A comparison of choice and matching," Organizational Behavior and Human Decision Processes, Elsevier, vol. 91(2), pages 140-153, July.
    19. Salvador Cruz Rambaud, 2014. "A New Argument In Favor Of Hyperbolic Discounting In Very Long Term Project Appraisal," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(08), pages 1-17.
    20. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
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    1. Cruz Rambaud, Salvador & Ortiz Fernández, Piedad & Parra Oller, Isabel María, 2023. "A systematic review of the main anomalies in intertemporal choice," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 104(C).

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