A theory of spatial general equilibrium in a fuzzy economy

Abstract

Let an economic space be characterized by the existence of a given distribution of locations, i.e. consumers' residential locations and producers' plants. It is equipped with a system of prices. The economy is fuzzy because the economic behaviors of agents are imprecise. In this context, spatial partial equilibria theories are applications of a fuzzy economic calculation model. The aim of the present paper is to study the conditions which must be fulfilled in order that the compatibility of consumers' equilibria and producers' equilibria be verified. Mathematical tools are Butnariu's theorems which extend the Brouwer's and Kakutani's theorems to the cases of fuzzy functions and fuzzy point-to-set mappings. Economic results are the extension of the Walras Law to a fuzzy economic space and the formulation of a theorem which states the conditions for the existence of a spatial general equilibrium in a fuzzy economy. This theorem is a generalization of a classical Debreu's result.