古典的有限次元財空間経済モデルにおける競争均衡の存在定理について : Nikaido(1956, 57)を中心にして

This paper consides the equilibrium existence theorem obtained in Nikaido(1956) and its supplementary Nikaido(1957). Nikaido(1956) established the existence of competitive equilibrium in exchance economies and that in Leontief world economies based on Gale-Nikaido lemma which is derived from Kakutani fixed point theorem. In the exchange economies, each consumer is assumed to have all goods as his initial endowment, and in the Leontief world economies, each country is assumed to produce all goods. Since these are strong conditions, it is desirable to establish the existence of competitive equilibium in these ecnomies with a weaker condition on initial endowment or production sets. This is indeed the purpose pf the supplementary Nikaido(1957). In the pure exchange ecnomies, each consumer is assumed to some of goods as his initial endowment and consumers are to have all of goods as their aggregate initial endowment. In the Leontief world economies, each country is assumed to produce some goods, but world economy as a whole can produce all goods. This weaker condition prevents demand correspondences of consumers from upper semi-continuou over entire price set. Since every demand correspondence is upper semi-continuou on the set of prices where his income is positive or the country’s income is positive, the demand correspondence drived from the closure of the demand correpondences restricted to thse sets is upper semi-contuous, the fixed point argument of Nikaido(1956) still applies to this situation and the existence of competitive equilibrium is established as well.