Time Inconsistency and the Use of the Maximin Principle as a Criterion for Just Savings

Abstract

Murrell (1980) has considered the implication of the Rawlsian maximin just savings policy when each generation cares for the welfare of the following generation. This approach results in certain attractive features of the maximin path and the author concludes that the of the maximin principle for a just savings policy is consistent with the arguments of A Theory of Justice. This is in stark contrast, as the author points out, to the negative results of Arrow (1973), Calvo (1977), Dasgupta (1974) and Grout (1977). The aim of this note to help clarify certain issues and to raise certain reservations with the general use of utility functions used in Murrell (1980) to solve the Rawlsian problem. In Grout (1978) it is argued that the approach adopted to generate utilities such as in equation (2) of Murrell (1980) is unlikely to represent individual subjective preferences. While one would wish ethical preferences to place a positive weight on every generation one cannot expect an individual's selfish preferences to have this property (or to be more exact one should not rely on this case). Indeed, it is the fact that selfish preferences may well not have this form that is usually used as a defence for the introduction of a concept of justice in intertemporal distribution. Phelps & Riley (1978) have also stated certain reservations with an assumption of utilitarian features for subjective preferences. In the end such a question is an empirical one and will not be considered here. Instead two interrelated points will be made. The general thrust of these points is that the unattractive features of maximin solutions are not necessarily dependent on the fact that any generation may not place a positive weight on all future generations and consequently general approaches of the type given in Murrell (1980) will not solve these problems. Consider firstly the case when each individual's utility is a geometrically weighted infinite utility sum across all future generations (as in (2) below). Then every generation attaches a positive weight to every other generation's consumption and for any e>0 almost all (i.e. all but a finite number) utilities receive a weight less than e. Suppose alternatively that