TITLE:
Existence of Competitive Equilibria without Standard Boundary Behavior
AUTHORS:
Francesco Ruscitti
KEYWORDS:
Excess Demand Function, Competitive Equilibrium, Set-Valued Functions, Selections, Fixed Points, Maximal Elements
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.11,
November
30,
2011
ABSTRACT: We study the existence of competitive equilibria when the excess demand function fails to satisfy the standard boundary behavior. We introduce alternative boundary conditions and we examine their role in proving the existence of strictly positive solutions to a system of non-linear equations (competitive equilibium prices). In addition, we slightly generalize a well-known theorem on the existence of maximal elements, and we unveil the link between the hypothesis of our theorem and one of the boundary conditions introduced in this work.