Monique Florenzano () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) Pascal Gourdel (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) Alejandro Jofré (CMM - Centre de Modélisation Mathématique / Centro de Modelamiento Matemático - CNRS : UMR2071)
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In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex economies, a recent result obtained by one of the authors, introduces conditions which, when applied to the convex case, give for Banach commodity spaces the well-known result of decentralization by continuous prices of pareto optimal allocations under an interiority condition. In this paper, in order to prove a different version of the Second Welfare Theorem, we reinforce the conditions on the commodity space, assumed here to be a Banach lattice, and introduce a nonconvex version of the properness assumptions on preferences and the total rpoduction set. Applied to the convex case, our result becomes the usual Second Welfare Theorem when properness assumptions replace the interiority condition. The proof uses a Hahn-Banach Theorem generalization by Borwein-Jofré which allows to separate nonconvex sets in general Banach spaces.
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Length: Date of creation: Nov 2006 Date of revision: Publication status: Published, Economic Theory, 2006, 29, 3, 549-564 Handle: RePEc:hal:cesptp:halshs-00086819_v1
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