Abstract
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.
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References
Debreu, G. (1959), Theory of Value, John Wiley and Sons, New York.
Schaible, S., and Ziemba, W.T., Editors (1981), Generalized Concavity in Optimization and Economics, Academic Press, New York, New York.
Avriel, M., Diewert, W.E., Schaible, S., and Zang, I. (1988) Generalized Concavity, Plenum Press, New York, New York.
Luenberger, D.G. (1995), Microeconomic Theory, McGraw-Hill, Inc., New York.
Crouzeix, J.P. (1974) Polaires Quasi-Convexes et Dualité, Compte Rendus de l’Académic des Sciences de Paris, Vol. A279, pp. 955–958.
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.
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.
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.
Greenberg, H.J., and Pierskalla, W.P. (1973), Quasi-conjugate functions and surrogate duality, Cahiers Centre Études, Rech. Opér., Vol. 15, pp. 437–448.
Martinez-Legaz, J.E. (1988), Quasiconvex Duality Theory by Generalized Conjugation Methods, Optimization, Vol. 19, pp. 603–652.
Oettli, W. (1982), Optimality Conditions for Programming Problems Involving Multivalued Mappings, Applied Mathematics, Edited by B. Korte, North Holland, Amsterdam, Holland, pp. 196–226.
Singer, I. (1986), A General Theory of Dual Optimization Problems, Journal of Mathematical Analysis and Applications, Vol. 116, pp. 77–130, 1986.
Passy, U., and Prisman, E.Z. (1985), A Convex-Like Duality Scheme for Quasiconvex Programs, Mathematical Programming, Vol. 32, pp. 278–300, 1985.
Penot, J.P., and Volle, M. (1990), On Quasiconvex Duality, Mathematics of Operations Research, Vol. 4, pp. 597–625.
Thach, P.T. (1995), Diewert-Crouzeix Conjugation for General Quasiconvex Duality and Applications, Journal of Optimization Theory and Applications, Vol. 86, pp. 719–743.
Stoer, J., and Witzgall, C. (1970), Convexity and Optimization in Finite Dimensions I, Springer Verlag, Berlin, Germany.
Rockafellar, R.T. (1970), Convex Analysis, Princeton University Press, Princeton, New Jersey.
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Thach, P.T. (2005). Equilibrium Prices and Quasiconvex Duality. In: Eberhard, A., Hadjisavvas, N., Luc, D.T. (eds) Generalized Convexity, Generalized Monotonicity and Applications. Nonconvex Optimization and Its Applications, vol 77. Springer, Boston, MA. https://doi.org/10.1007/0-387-23639-2_20
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DOI: https://doi.org/10.1007/0-387-23639-2_20
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