**Working Paper Series**
# No 572:

Welfare Foundations of Discounting

*María Sáez-Martí *()

* and Jörgen W. Weibull *()

**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 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.

**Keywords:** Altruism; Discounting; Dynamic Inconsistency; Time Inconsistency; Welfare ; (follow links to similar papers)

**JEL-Codes:** D11; D64; D91; E21; (follow links to similar papers)

22 pages, January 23, 2002

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