Working Paper No. 572

Welfare Foundations of Discounting

Published: January 23, 2002Pages: 22Keywords: Altruism; Discounting; Dynamic Inconsistency; Time Inconsistency; Welfare JEL-codes: 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.

Interdisciplinary European Studies

The European Union in a Changing World Order

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This book explores how the European Union responds to the ongoing challenges to the liberal international order. These challenges arise both within the EU itself and beyond its borders, and put into question the values of free trade and liberal democracy. 

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