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Linear and non-linear price decentralization

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  • Aliprantis, Charalambos D.
  • Florenzano, Monique
  • Tourky, Rabee

Abstract

The present paper provides compendious and thorough solutions to the price equilibrium existence problem, the second welfare theorem, and the limit theorem on the core of an economy for exchange economies whose commodity space is an arbitrary ordered Frechet space. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory commodity spaces that are not vector lattice ordered and whose positive cones have empty interior, a typical situation in models of portfolio trading with incomplete markets. Our assumptions are made on the primitive objects fo the economy. Remarkably, the assumptions that we make on the order structure of the commodity space are indispensable. For w-proper economies, these assumptions are both sufficient and necessary for the existence of equilibrium, the second welfare theorem, and the Edgeworth-Walras equivalence theorem. We take advantage of new developments in the theory of ordered vector spaces, in particular the possibility of embedding the price cone into a lattice cone called the super-order dual of the ordered vector space. Therefore, even though the commodity price duality has no lattice structure important lattice theoretic techniques can be applied outside this duality.
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  • Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2005. "Linear and non-linear price decentralization," Journal of Economic Theory, Elsevier, vol. 121(1), pages 51-74, March.
  • Handle: RePEc:eee:jetheo:v:121:y:2005:i:1:p:51-74
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    1. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
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    Cited by:

    1. Carlos Hervés-Beloso & V. Martins-da-Rocha & Paulo Monteiro, 2009. "Equilibrium theory with asymmetric information and infinitely many states," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 295-320, February.
    2. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    3. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques b04116, Université Panthéon-Sorbonne (Paris 1).
    4. V. Martins-da-Rocha & Frank Riedel, 2006. "Stochastic equilibria for economies under uncertainty with intertemporal substitution," Annals of Finance, Springer, vol. 2(1), pages 101-122, January.
    5. Achille Basile & Maria Gabriella Graziano, 2012. "Core Equivalences for Equilibria Supported by Non-linear Prices," CSEF Working Papers 309, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
    7. Klishchuk, Bogdan, 2015. "New conditions for the existence of Radner equilibrium with infinitely many states," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 67-73.
    8. Roko Aliprantis & Monique Florenzano & Daniella Puzzello & Rabee Tourky, 2006. "The wedge of arbitrage free prices : anything goes," Cahiers de la Maison des Sciences Economiques b06070, Université Panthéon-Sorbonne (Paris 1).

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