Intertemporal Preferences and Utility (Infinite Horizon, Time Preference, Generations).

Abstract

The question of whether future utility should be discounted has a long history, dating back to early in this century. This debate has been rekindled in the more recent literature on exhaustible resources. Here a critique of the literature on infinite horizon preference orderings and optimality criteria is provided and an alternative is suggested. Three undesirable properties of such preferences are defined: limit dependence, eventually strong myopia and non-substitution. It is shown that the commonly employed criteria have one of these properties. A new axiom for intertemporal preferences is suggested as an alternative to the impatience axiom and the equal treatment of generations axiom. It says, roughly, that given two alternative programs which are not getting better as time passes, the one with the better future is better. This axiom is incorporated into a discrete time recursive utility function. The result is a criterion which has none of the above properties. For a special case the criterion orders improving economies identically to discounted utility and yet orders declining economies like maximin. Furthermore preferences are intertemporally consistent. This allows the optimal path in pessimistic resource models to be bounded away from zero, but permits growth in more productive economies. Given that the utility function is necessarily not additive across time, a set of axioms, including a weakened version of the independence axiom and a state contingent separability axiom, is provided which allows preferences to be represented by a utility function which is not additive across time.