Working Paper No. 572

Welfare Foundations of Discounting

Publicerad: January 23, 2002Antal sidor: 22Nyckelord: Altruism; Discounting; Dynamic Inconsistency; Time Inconsistency; Welfare JEL-koder: D11; D64; D91; E21

Welfare Foundations of Discounting María Sáez-Martí and Jörgen W. Weibull

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 in 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 they are biased in favor of the current self, and 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.

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