Ex-Post Efficiency and Resource Allocation Under Uncertainty

Abstract

Ross Starr (1973) has recently pointed out that under uncertainty about the future an ex-ante optimal allocation of resources over time or an optimal allocation of risk bearing , following the terminology of Arrow (1964), does not necessarily imply an ex-post optimal allocation of resources over time. Starr's general result is that an ex-ante optimum will not be an ex-post optimum unless individuals' subjective probability distributions over states of nature are identical.' The conflict between ex-post and ex-ante Pareto efficiency of intertemporal resource allocation under uncertainty is an example of the problems caused by changing tastes. The problem has serious implications for making welfare judgements, as there may well be a divergence between ex-ante choice and ex-post preference. This casts doubt on the validity of the principle of consumer sovereignty as a means of evaluating resource allocations. Suppose it has been decided by government or society that the desirability of alternative resource allocations, when there is uncertainty about the future, is to be judged in the Pareto sense relative to the ex-post preferences of the consumers in the economy. Note that this is an explicit value judgement on the part of society in that they respect individual preferences, but only ex-post preferences. Some economists have expressed the opinion that it is only these preferences which should count . Starr states that the achievement of an Arrow (ex-ante) optimum is a normative dead end. After all, we are not so much interested in expectations as in results .'2 We do not propose to discuss whether ex-ante or ex-post optimality is to be ethically preferred, but rather to examine the logical implications of accepting the ex-post view. Even if welfare judgements are made from an ex-post viewpoint, any actual allocation of resources will continue to be made ex ante. Furthermore, individuals may make ex-ante choices with respect to ex-ante preferences. We will assume in particular that these choices are made in accordance with the Von Neumann-Morgenstern-Savage axioms of behaviour under uncertainty, and that individuals' subjective probabilities are not necessarily the same. Two questions then arise. Can an ex-ante decentralized resource allocation mechanism be found, such that when ex-ante choices are made within the context of this mechanism, all equilibrium allocations are ex-post Pareto efficient? Secondly, given an ex-post efficient allocation, can an ex-ante decentralized resource allocation mechanism be found which attains that allocation as an equilibrium? It should be evident that these are natural analogues to the usual welfare questions which use ex-ante Pareto efficiency as the welfare criterion. In this paper we propose a resource allocation mechanism which is market like as consumers use prices to guide decision making. Arrow-Debreu markets have the feature that ex-ante marginal rates of substitution are equated as all consumers face the same set of prices. When a state of the world is realized, however, the actual intertemporal marginal rates of substitution will differ across individuals unless all individuals have the same ex-ante beliefs. The resource allocation mechanism proposed in this paper corrects for these ex-post divergences among marginal rates of substitution by quoting to each