(1) Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan;(2) Department of Mathematics, National Taiwan Normal University, 88 Sec. 4, Ting Chou Road, Taipei, 116, Taiwan
Abstract:
This paper studies the equilibrium of an exchange economy with the same number of agents and commodities. It is shown that
under rather mild conditions on demand the market have a price equilibrium—independently of the divisibility of the commodities.
The result extends Gale’s equilibrium theorem for indivisible commodities to the case where some commodities are perfectly
divisible. The proof is based on a topological lemma contained in previous paper of one of the authors.