NDLI: Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Content Provider	Springer Nature Link
Author	Anderson, Robert M. Zame, William R.
Copyright Year	1998
Abstract	Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L 1, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices.
Starting Page	331
Ending Page	377
Page Count	47
File Format	PDF
ISSN	09382259
Journal	Economic Theory
Volume Number	11
Issue Number	2
e-ISSN	14320479
Language	English
Publisher	Springer-Verlag
Publisher Date	1998-02-05
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Economics and Econometrics

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