Learning buyers' valuation distribution in posted-price selling

Summary. For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution. Received: July 22, 1997; revised version: December 11, 1997     

On the difficulty of combining actual and potential criteria for an increase in social welfare

Summary. This paper examines two problems associated with the use of potential Pareto criteria in welfare economics. The first problem is the well-known intransitivity of the compensation criteria à la Kaldor-Hicks-Scitovsky. The second problem is the possible incompatibility between the Chipman-Moore-Samuelson criterion and the Pareto principle. The main result of this paper is that, in order to avoid either of these problems, it is necessary and sufficient that the domain to which these criteria are used is such that the Chipman-Moore-Samuelson criterion encompasses completely the Pareto criterion. When interpreted in a standard economic environment, this result is shown to be equivalent to Gorman's requirement of non-crossing between utility possibility frontiers. Received: June 18, 1998; revised version: March 2, 2000