Scandinavian Working Papers in Economics

Working Paper Series,
Research Institute of Industrial Economics

No 572: Welfare Foundations of Discounting

María Sáez-Martí () and Jörgen W. Weibull ()
Additional contact information
María Sáez-Martí: The Research Institute of Industrial Economics, Postal: P.O. Box 55665, SE-102 15 Stockholm, Sweden
Jörgen W. Weibull: The Research Institute of Industrial Economics, Postal: P.O. Box 55665, SE-102 15 Stockholm, Sweden

Abstract: We investigate whether temporal preferences expressed as a sum of discounted consumption utilities can be derived from a welfare representation in the form of a sum of discounted total utilities. We find that a consumption-based representation in the usual exponential form corresponds to one-period "altruism" towards one's future selves: the current self gives positive weight to her total utility in the next period, and weight zero to her total utility in all subsequent periods. We also find that a consumption-based representation in the quasi-exponential (ß,d)-form suggested by Phelps and Pollak (1968) and Laibson (1997) correspond to quasi-exponential altruism towards one's future selves. For ß=1/2, the welfare weights are exponential, while for ß 1/2 in favor of one's future selves. More generally, we establish a functional equation which relates welfare weights to consumption-utility weights. We also postulate five desiderata for consumption-utility weights. None of the usual formalizations satisfy all desiderata, but we propose a simple formalization which does.

Keywords: Altruism; Discounting; Dynamic Inconsistency; Time Inconsistency; Welfare

JEL-codes: D11; D64; D91; E21

22 pages, January 23, 2002

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