GaleNikaido's Lemma in Infinite Dimensional Spaces: Early Attempts by Prof. Nikaido

 Hajime Kubota
 Hokkaido University
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Abstract
As shown in Debreu(1959, Ch.5), GaleNikaido's lemma of Gale(1955) and Nikaido(1956a) is the key in proving the existence of a competitive equilibrium in classical economies with a finite number of commodities. Nikaido(1956b, 57b, 59) extend the GaleNikaido's lemma in economies with a finite number of commodities to the one in some infinite dimensional spaces such as normed spaces and locally convex topological vector spaces. This is surprising since GaleNikaido's lemma is generalized to the infinite dimensional spaces just after GaleNikaido's lemma in economies with a finite number of commodities is established. Since the literature on the existence of competitive equilibrium in economies with infinite number of commodities stars after PelegYarri(1970) and Bewley(1972) and it was one of the main topics for 80's in general equilibrium theory, Nikaido(1956b, 57b,59) precedes to the literature as Debreu(1954) does. The purpose of this paper is to reconsider the Nikaido(1956b, 57b, 59)'s generalization of GaleNikaido's lemma in infinite dimensional spaces from the present state of general equilibrium theory of infinite dimensional spaces.
Journal

 Economic Journal of Hokkaido University

Economic Journal of Hokkaido University (36), 122, 2007
Graduate School of Economics and Business Administration, Hokkaido University
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Details

 CRID
 1570854177305660544

 NII Article ID
 110006394198

 NII Book ID
 AA10772967

 ISSN
 09164650

 Web Site
 http://hdl.handle.net/2115/29913

 Text Lang
 en

 Data Source

 CiNii Articles