Research On The Problems About General Equilibrium Of A Produce-exchange Economy With A Special Taxation

This paper mainly discusses a production-exchange economy with special taxation general equilibrium problems, on the demonstration of the existence of the equilibrium, this equilibrium welfare problems investigated the use of welfare economics. The preference of consumers in the economy of the convexity, monotonicity, unsaturated and production function producer satisfies convexity and the premise of bounded closed set, set a total consumption tax is present in the economy, are extracted in the consumers to buy the product, and then to subsidies to return to consumers; and producers are not taxed, nor subsidies. Then prove the economic production set is a simplex by using the principle and method of mathematical analysis, then the excess demand function will produce and exchange links, proved that the excess demand function in this economy is a unit simplex. Finally, by using the Brouwer fixed point theorem, prove the existence of equilibrium point. Then the properties of the equilibrium point of welfare economics, in the definition of the Pareto optimal, prove the first theorem of welfare economics, and proved the second theorem of welfare economics the hyperplane separation theorem of convex sets in convex analysis. In the function set to measure the total social welfare is a linear function, introduced a transfer price equilibrium and quasi-transfer price to balance these two concepts, to determine the relation between the equilibrium point and Pareto optimal. Finally what circumstances these two kinds of price equilibrium equivalence, using a counterexample that the equilibrium point of this kind of economy is not Pareto optimal.