COMMODITY PAIR DESIRABILITY AND THE CORE EQUIVALENCE THEOREM

Abstract

This chapter discusses the core-Walras equivalence in economies with a continuum of agents and with an infinite-dimensional commodity space. It discusses the general importance of infinite-dimensional commodity spaces in economics. Infinite-dimensional commodity spaces arise quite naturally in economics. In particular, an infinite-dimensional commodity space may be desirable in problems involving an infinite time horizon, uncertainty about the possibly infinite number of states of nature of the world, or infinite varieties of commodity characteristics. The chapter discusses core-Walras equivalence results for perfectly competitive economies with an infinite-dimensional commodity space that is sufficiently general to include all of the spaces that have been found most useful in equilibrium analysis. In infinite-dimensional commodity space whose positive cone has a nonempty—norm—interior, core-Walras equivalence results can be obtained under quite mild assumptions. The chapter also reviews notation, definitions, and some results on Banach lattices and the integration of correspondences.