Two time-consistent Paretian solutions to the intertemporal resource allocation problem

Abstract

We study the problem of aggregating individual geometric discounting (GD) preferences over infinite streams of consumption profiles into a system specifying, for each consumption history, a social ranking of the streams that follow that history. Such a system is time-consistent if and only if it is generated by a single underlying preference ordering over the lifetime streams. Under the Weak Pareto Principle, Neutrality, Anonymity, and Discounting Irrelevance (individual discount factors do not affect the ranking of constant streams), lifetime streams must be ranked by applying a fixed monotonic and symmetric ordering to the profiles of range-normalized GD utilities they yield (Theorem 1). History Independence singles out the range-normalized utilitarian rule (Theorem 2) whereas the range-normalized Nash rule is characterized by Independence of Infeasible Consumptions (the ranking of streams delivering consumption profiles in an interval from the origin does not depend on individual valuations outside that interval) or Valuation Irrelevance (the ranking of pure timing streams is independent of individual valuations) (Theorem 3).