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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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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