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Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies

Listed author(s):
  • Monique Florenzano


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Pascal Gourdel

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Alejandro Jofré

    (CMM - Centre de Modélisation Mathématique / Centro de Modelamiento Matemático - CNRS - Centre National de la Recherche Scientifique)

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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00086819.

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Date of creation: Nov 2006
Publication status: Published in Economic Theory, Springer Verlag, 2006, 29 (3), pp.549-564. 〈10.1007/s00199-005-0033-y〉
Handle: RePEc:hal:cesptp:halshs-00086819
DOI: 10.1007/s00199-005-0033-y
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  1. Anderson, Robert M, 1988. "The Second Welfare Theorem with Nonconvex Preferences," Econometrica, Econometric Society, vol. 56(2), pages 361-382, March.
  2. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Valuation equilibrium and pareto optimum in non-convex economies," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 293-308, April.
  3. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
  4. Monique Florenzano & Pascal Gourdel & Alejandro Jofré, 2006. "Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 549-564, November.
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