Working Paper No. 575

Discounting and Future Selves

Publicerad: February 21, 2002 Antal sidor: 23Nyckelord: Altruism; Discounting; Dynamic Inconsistency; Welfare JEL-koder: D11; D64; D91; E21

Discounting and Future Selves María Sáez-Martí and Jörgen W. Weibull

Is discounting of future instantaneous utilities consistent with altruism towards future selves? More precisely, can temporal preferences, expressed as a sum of discounted instantaneous utilities, be derived from a representation in the form of a sum of discounted total utilities? We find that a representation in the quasi-exponential (ß,d)-form in Phelps and Pollak (1968) and Laibson (1997) correspond to quasi-exponential altruism towards one's future selves. For ß=1/2, these 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 instantaneous-utility weights and apply this equation to a number of examples. We also postulate five desiderata for instantaneous-utility discounting. None of the usual discount functions satisfy all desiderata, but we propose a simple class of discount functions which does.

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