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

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Title: Gale-Nikaido's Lemma in Infinite Dimensional Spaces: Early Attempts by Prof. Nikaido
Authors: Kubota, Hajime Browse this author →KAKEN DB
Keywords: Gale-Nikaido's Lemma
Infinite Dimensional Commodity Space
Existence of Competitive Equilibrium
Interiority Problem and Approximated Cone
Issue Date: 2007
Publisher: Graduate School of Economics and Business Administration, Hokkaido University
Journal Title: Economic Journal of Hokkaido University
Volume: 36
Start Page: 1
End Page: 22
Abstract: As shown in Debreu(1959, Ch.5), Gale-Nikaido'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 Gale-Nikaido'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 Gale-Nikaido's lemma is generalized to the infinite dimensional spaces just after Gale-Nikaido'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 Peleg-Yarri(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 Gale-Nikaido's lemma in infinite dimensional spaces from the present state of general equilibrium theory of infinite dimensional spaces.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/29913
Appears in Collections:Economic Journal of Hokkaido University > Vol. 36

Submitter: 久保田 肇

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