Symbiotic transfer, arbitrage, and equilibrium

We lay a unified foundation for a theory of general equilibrium by proving the existence of an equilibrium for a grand model which covers all the well-known general equilibrium models under the convexity and continuity assumptions. The grand model allows an economy to have an extended list of commodities including assets which can be traded on unlimited short sales. The conceptual framework we develop for the existence problem is simple. Consider an economy consisting of two agents. If there were a commodity bundle which is always desirable to one agent and always undesirable to the other agent, the economy could not reach an equilibrium because they can increase their utility through an indefinite give-and-take process. What we need for the existence of an equilibrium is to exclude the presence of commodity bundles that can bring an economy into this state of "economic symbiosis." We proceed further by taking the Closedness Hypothesis that the utility possibility set is compact. The finite dimensional findings do not hold for an economy with an infinite dimensional commodity space so that we investigate under what circumstances the Closedness Hypothesis holds. We develop sufficient conditions for the Closedness Hypothesis to hold and prove the existence of an equilibrium of an infinite dimensional economy under some spanning conditions on consumption sets