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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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    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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