# Nikaido, Hukukane (1923–2001)

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_2621

## Abstract

Hukukane Nikaido graduated from the Department of Mathematics, University of Tokyo, in 1949. While he was a university student he became interested in economics and studied Marx’s *Das Kapital*, Hicks’s *Value and Capital* and Samuelson’s *Foundations of Economic Analysis*. After graduating from the University of Tokyo and becoming an Associate Professor of Mathematics at the Tokyo College of Science, he wrote papers concerning the von Neumann growth model and the minimax theorem (1954a, b; 1955). He also worked on the existence of equilibria in the general equilibrium model with many firms and many consumers. His paper had been completed independently of Arrow and Debreu (1954) and McKenzie (1954), and was published in *Metroeconomica* (1956a). One of his results in the existence proof is now known as Gale–Nikaido lemma. These achievements led him to visit Stanford in 1955–6 at the invitation of Kenneth Arrow. At Stanford, Nikaido started to work on the existence of general equilibria for an economy with infinitely many commodities (1956b; 1957), and then published in the *Journal of the Mathematical Society of Japan* (1959a). His contributions on the existence of general equilibria in the infinite dimensional space had long remained unknown.

## Keywords

Existence of general equilibria Factor substitution Gale–Nikaido lemma Harrod–Domar model Imperfect competition Knife-edge property Minimax theorem Monopolistic competition Morishima, M. Nikaido, H. Objective demand functions Solow, R. Turnpike theorems von Neumann growth model## JEL Classifications

B31## Bibliography

- Arrow, K., and G. Debreu. 1954. Existence of an equilibrium for a competitive economy.
*Econometrica*22: 265–290.CrossRefGoogle Scholar - McKenzie, L. 1954. On equilibrium in Graham’s model of world trade and other competitive systems.
*Econometrica*22: 147–161.CrossRefGoogle Scholar - Morishima, M. 1961. Proof of a turnpike theorem: The ‘no joint production case’.
*Review of Economic Studies*28: 89–97.CrossRefGoogle Scholar - Radner, R. 1961. Paths of economic growth that are optimal states: A turnpike theorem.
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