open access

https://hdl.handle.net/2115/29913

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

英語

Interiority Problem and Approximated Cone

2007

Graduate School of Economics and Business Administration, Hokkaido University

Economic Journal of Hokkaido University

36

1-22

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.

紀要論文

Version of Record

0916-4650

AA10772967