Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities

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Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities

Authors

Rustichini, Aldo

Yannelis, Nicholas C.

Published Date

1987-04

Publisher

Center for Economic Research, Department of Economics, University of Minnesota

Type

Working Paper

Abstract

This paper contains the following results for economies with infinite dimensional commodity spaces. (i) He establish a core-Walras equivalence theorem for economies with an atomless measure space of agents and with an ordered separable Banach commodity space whose positive cone has a non-empty norm interior. This result includes as a special case the Aumann (1964) and Hildenbrand (1974) finite dimensional theorems. (ii) We provide a counterexample which shows that the above result fails in ordered Banach spaces whose positive cone has an empty interior even if preferences are strictly convex, monotone and weak* continuous and initial endowments are strictly positive. (iii) After introducing a new assumption on preferences called "commodity pair desirability," (which is automatically satisfied whenever preferences are monotone and the positive cone of the commodity space has a non-empty interior), we establish core-Walras equivalence in any arbitrary separable Banach lattice whose positive cone may have an empty (norm) interior. (iv) We provide a proof that in some concrete spaces whose positive cone may have an empty interior, the assumption of an extremely desirable commodity or uniform properness suffices for core-Walras equivalence. Finally, (v) we indicate how our methods can be used to obtain core-Walras equivalence results for the space M(~) of measures on a compact metric space.

Keywords

Core allocations

Walrasian allocations

Extremely desirable commodity

Commodity pair desirability

Bochner integral

Banach lattice

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Center for Economic Research Discussion Papers

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Discussion Paper
238

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Previously Published Citation

Rustichini, A. and Yannelis, N.C., (1987), "Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities", Discussion Paper No. 238, Center for Economic Research, Department of Economics, University of Minnesota.

Suggested citation

Rustichini, Aldo; Yannelis, Nicholas C.. (1987). Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/55508.

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