Advances in Decision Sciences
Volume 2011 (2011), Article ID 960819, 7 pages
doi:10.1155/2011/960819
Research Article

A Constructive Analysis of Convex-Valued Demand Correspondence for Weakly Uniformly Rotund and Monotonic Preference

Yasuhito Tanaka1 and Atsuhiro Satoh2

1Faculty of Economics, Doshisha University, Kamigyo-ku, Kyoto 602-8580, Japan
2Graduate School of Economics, Doshisha University, Kamigyo-ku, Kyoto 602-8580, Japan

Received 23 December 2010; Accepted 14 February 2011

Academic Editor: Chenghu Ma

Copyright © 2011 Yasuhito Tanaka and Atsuhiro Satoh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Bridges (1992) has constructively shown the existence of continuous demand function for consumers with continuous, uniformly rotund preference relations. We extend this result to the case of multivalued demand correspondence. We consider a weakly uniformly rotund and monotonic preference relation and will show the existence of convex-valued demand correspondence with closed graph for consumers with continuous, weakly uniformly rotund and monotonic preference relations. We follow the Bishop style constructive mathematics according to Bishop and Bridges (1985), Bridges and Richman (1987), and Bridges and Vîţă (2006).