Approximation of excess demand on the boundary and euilibrium price set资料.pdfVIP

Adv. Math. Econ. 9, 99-107 (2006) Advances in MATHEMATICAL ECONOMICS ©Springer-Verlag 2006 Approximation of excess demand on the boundary and equilibrium price set* Manabu Toda^ School of Social Sciences, Waseda University, 169-8050, Tokyo, Japan, (e-mail: mtoda@waseda.jp) Received: December 1, 2004 Revised: January 6, 2005 JEL classification: D50 Mathematics Subject Classification (2000): 91B50 Abstract. When preferences may not be homothetic but satisfy other regularity con- ditions such as monotonicity, the market excess demand function is characterized by continuity and Walras law on almost entire region of the price simplex. In particular, Mas-Colell (1977) shows that for a continuous function / defined on the interior of the price simplex satisfying Walras law and the boundary condition, there exists an exchange economy f whose excess demand function is approximately equal to / and the equilibrium price set of i is exactly equal to the one of / . This paper shows that if / may be finite on the boundary of the price simplex, ^ can be chosen so that the equilibrium price set of ^ is approximately equal to the one of / . Theorem 3 in Wong (1997), showing the equivalence between Brouwers fixed-point theorem and Arrow- Debreus equilibrium existence theorem, follows from this result. Key words : excess demand, decomposition theorem, fixed-point theorem 1. Introduction The classical theorem of Eisenberg (1961) show s that when preference s are homothetic and the incom e distribution is independent of prices , the market excess deman d function be