Existence of equilibria with infinitely many commodities. Banach lattices reconsidered

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The purpose of this paper is twofold. The first aim is to present an extension of the results on the existence of Walrasian equilibrium to the infinite dimensional setting. The result depends on two crucial assumptions. These are the compactness of the collection of feasible allocations and the non-emptiness of the interior of the production set. The proof is a direct generalization of Bewley's (1972) proof for the L case. The second purpose of this paper is to show that the recent result of Mas-Colell (1986) on the existence of equilibrium for exchange economies on Banach lattices can be obtained through an argument based on the result outlined above. That is, exchange economies on Banach lattices with 'uniformly proper' preferences behave as though they were production economies in which the production sets have non-empty interior.

Original languageEnglish (US)
Pages (from-to)89-104
Number of pages16
JournalJournal of Mathematical Economics
Issue number2
StatePublished - 1987

Bibliographical note

Funding Information:
*I would like to thank Andreu Mas-Cole11 both for his generous comments and his encouragement. Financial assistance from the National Science Foundation in the form of a grant number SES-8308446 is gratefully acknowledged. Finally, I would like to thank the Institute for Mathematics and Its Applications at the University of Minnesota for providing an environment conducive to fruitful interaction. It was from the conversations that I had with Chalambros Aliprantis, Don Brown, Darrel Dufflie, Andreu Mas-Colell, Nicholas Yanelis, and William Zame while visiting at the Institute that this work was derived.

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