Convexity, Fixed Point Theorems and Walrasian Equilibrium

In this thesis, I will deal with an application of fixed-point theorem of set valued map [Let X and Y be two subsets of Rⁿ: A set-valued map F from X to Y, is a map that associates with any x є X a subset F(x) of Y, A fixed point x for F exists if x є F(x) ], and convexity to prove the existence of Walrasian Equilibrium under sufficient conditions for both pure exchange economy and private ownership economy. Then I will show how to modify these theorems in more general cases under uncertainty and externalities.