Equilibrium Prices and Quasiconvex Duality
Given an economy in which there is a commodity trading between two Sectors A and B. For a given vector of prices Sector B is interested in getting a maximal commodity worth under an expenditure constraint. Sector A is interested in finding a feasible vector of prices such that the level of trade allowance per one unit of commodity worth is maximized. The problem under consideration is a quasiconvex minimization. Using quasiconvex duality we obtain a dual problem and a generalized Karush-Kuhn-Tucker condition for optimality. The optimal vector of prices can be interpreted as equilibrium and as a linearization of the commodity worth function at the optimal dual’s solution.
KeywordsQuasiconvex Duality Price Equilibrium
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- Luenberger, D.G. (1995), Microeconomic Theory, McGraw-Hill, Inc., New York.Google Scholar
- Crouzeix, J.P. (1981), A Duality Framwork in Quasiconvex Programming, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W.T. Ziemba, Academic Press, New York, New York, pp. 207–225.Google Scholar
- Diewert, W.E. (1982), Duality Approaches to Microeconomic Theory, Handbook of Mathematical Economics 2, Edited by K. J. Arrow and M. D. Intriligator, North Holland, Amsterdam, Holland, pp. 535–599.Google Scholar
- Diewert, W.E. (1981), Generalized Concavity and Economics, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W.T. Ziemba, Academic Press, New York, New York, pp. 511–541.Google Scholar
- Oettli, W. (1982), Optimality Conditions for Programming Problems Involving Multivalued Mappings, Applied Mathematics, Edited by B. Korte, North Holland, Amsterdam, Holland, pp. 196–226.Google Scholar
- Stoer, J., and Witzgall, C. (1970), Convexity and Optimization in Finite Dimensions I, Springer Verlag, Berlin, Germany.Google Scholar