Ex Post Welfare Economics and the Theory of Merit Goods

Abstract

In recent years a number of papers have questioned the extension of the main theorems of welfare economics to a world of uncertainty stemming from the work of Arrow (1953) and Debreu (1959). The Arrow-Debreu extension is based on the idea that consumer preferences may be defined on state contingent commodities; as a special but important case, these preferences may be represented by von Neumann-Morgenstern utilities. With this interpretation of the commodity space the main theorems of weltare economics remain valid in a world of uncertainty. A competitive equilibrium is a Pareto optimum, a Pareto optimum can be sustained as a competitive equilibrium, and the diagnosis of the causes of market failure remains as before. There are several reasons why one may feel uneasy about this construction. A good deal of attention has been paid to the assumption of universality of markets necessary to establish the connection between equilibrium and optimum. On a deeper level perhaps are the doubts that one may have about the criterion of welfare or efficiency. First, should social welfare be a function of individuals' expected utilities, or should the appropriate concept be that of expected welfare? Second, if probability beliefs are not identical across individuals, whose probabilities, if any, should be used for welfare evaluation? In the next section we review some concepts and results in the recent literature on ex post welfare economics, and in Section II it is argued that this literature can provide the foundations for a more satisfactory theory of merit goods, a concept originally introduced by Musgrave (1959). This idea is applied in Section III to a model with a complete set of markets in the Arrow-Debreu sense, and in Sections IV and V to an incomplete markets model, which provides the most natural framework for the study of merit goods. Various remarks on further aspects of the problem are collected in the concluding section of the paper.