Some Notes on Time Inconsistency and Rawls' Maximin Criterion

Abstract

In a recent paper Dasgupta [3] has neatly demonstrated that the Rawlsian maximin criterion may be inadequate for problems of intergenerational justice by showing that, under some specific utility functions exhibiting altruism towards future generations, plans which are optimal from the standpoint of a given generation will not be continued by future generations even when the latter are true believers in the virtues of maximin, i.e. time inconsistency would arise. This is undoubtedly an alarming result which, if proved to be a common feature of maximin, would give us sufficient grounds to dismiss it altogether as a principle of intergenerational justice. In this paper we present some results aimed at furthering our understanding of that issue. In Section 2 we analyse the question of whether time inconsistency is possible if we make generations choose between arbitrary pairs of consumption sequences. The answer to that question is a resounding yes; in the presence of altruism-defined in a rather general way which includes as a special case the utility function employed by Dasgupta-not only is it possible to find pairs of consumption sequences where maximin proves to be time inconsistent, but we are able to show that there are infinitely many of them. On this account the results of Dasgupta get further support. In Section 3 we constrain the set of consumption sequences to be feasible according to a neoclassical technology and study time consistency of optimal plans when a generation's utility can be represented by a discounted sum of (instantaneous) utilities. This is akin to the problem analysed by Dasgupta, except that the utility function is changed as indicated above. Here the picture is drastically different: for every relevant initial capital stock, k, there is a time-consistent optimal plan. Furthermore, if k is smaller than, or equal to, Golden-Rule capital the optimum is unique. The conclusions are briefly stated in Section 4.