Analysis of competitive equilibrium in an infinite dimensional commodity space

Abstract

This paper considered the cost of allocated goods and attaining maximal utility with such price in the finite dimensional commodity space and observed that there exist an equilibrium price. It goes further to establish that in an infinite dimensional commodity space with subsets as consumption and production set there exist a price system. The compactness and convexity properties of these two disjoint sets enables us to establish this price system in this infinite dimensional space via the existence of set of continuous linear functional. This price system becomes the competitive equilibrium price and allocation which maximizes and minimizes the cost function for producers and consumers respectively

Keywords: Competitive equilibrium, commodity space, functional, agents and price system