Transaction Cost And General Equilibrium

The general equilibrium model developed by Arrow and Debreu in the 1950's is one of the greatest works in economic science. They axiomatized their model, under some basic assumptions (preference, technology, endowments), they established an axiomatic theory of the existence, optimality, stability of the equilibrium of the market economy, thus completed a modern explanation of the "invisible hand" of Adam Smith. It is the foundation of later general equilibrium theory.The main thrust of recent work in equilibrium theory has been the relaxation of the assumptions of the Arrow-Debreu model. Since it has been repeatedly argued that its assumptions are not realistic. It visualizes the process of the economic equilibrium taking place at a single point in time, in one large market without externalities, without returns to scale, without interactions among consumers or producers and without information or transaction cost. The sensitivity of the results of the theory to these assumptions has always been an important issue among economic theorists. The systematic relaxation of the "classical "assumptions will probably clarify some of the deeper issues emerging from the theory of a competitive equilibrium.In the present paper we contribute to the extension to the classical Arrow-Debreu model to include transaction cost. We restrict our attention to a pure exchange economy with transaction cost. Under quite weak assumptions we proved the existence, the optimality of the equilibrium. We have two very important conclusions (1) if transaction costs exists, the feasible transaction set is bounded, or people may not be able to exchange some commodities on the market i.e some markets will not be open due to high transaction costs. This is quite different to the complete markets assumptions in the classical equilibrium theory; (2) if the initial endowments of every consumer is strictly positive, (wh >> 0,h), then equilibrium exists, i.e, if transaction cost is taken into account, under classical assumptions of the equilibrium theory( wh∈R1, h), equilibrium may not exists.