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A New Approach to the Lmit Theorem on the Core of an Economy in Vector Lattices

Author

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  • Rabee Tourky

    (Department of Economics and Finance, La Trobe University)

Abstract

We consider economies with general consumption sets in a vector lattice commodity space. We show, by adapting the techniques of Mas-Colell and Richard (8) and Richard (10), the Edgeworth equilibria can be supported as pseudo-equilibria by continuous prices. A corollary of this result is that continuous equilibrium prices support those allocations supported by discontinuous equilibrium prices. Hence, we improve and provide an alternative proof to Mas-Colell and Richard's hypothesis on the relationship between continuous and discontinuous equilibrium prices in models with a vector lattice commodity space and a vector lattice price space.

Suggested Citation

  • Rabee Tourky, 1997. "A New Approach to the Lmit Theorem on the Core of an Economy in Vector Lattices," Working Papers 1997.03, School of Economics, La Trobe University.
    • Handle: RePEc:ltr:wpaper:1997.03
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    Cited by:

    1. 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.
    2. De Simone, Anna & Graziano, Maria Gabriella, 2004. "The pure theory of public goods: the case of many commodities," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 847-868, November.
    3. 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.
    4. 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.
    5. MONIQUE FLORENZANO & ELENA L. Del MERCATO, 2006. "Edgeworth and Lindahl–Foley equilibria of a General Equilibrium Model with Private Provision of Pure Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(5), pages 713-740, December.
    6. Khan, M. Ali & Tourky, Rabee & Vohra, Rajiv, 1999. "The supremum argument in the new approach to the existence of equilibrium in vector lattices," Economics Letters, Elsevier, vol. 63(1), pages 61-65, April.
    7. Allouch, N. & Florenzano, M., 2000. "Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy," Papiers d'Economie Mathématique et Applications 2000.119, Université Panthéon-Sorbonne (Paris 1).
    8. 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.
    9. Bogdan Klishchuk, 2018. "Multiple markets: new perspective on nonlinear pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 525-545, August.
    10. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2000. "Cone Conditions in General Equilibrium Theory," Journal of Economic Theory, Elsevier, vol. 92(1), pages 96-121, May.
    11. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    12. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2004. "General equilibrium analysis in ordered topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 247-269, June.
    13. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 353-370, January.
    14. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers 1396, Econometric Society.
    15. Aliprantis, C. D. & Florenzano, M. & Martins-da-Rocha, V. F. & Tourky, R., 2004. "Equilibrium analysis in financial markets with countably many securities," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 683-699, September.
    16. 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.
    17. Claudia Meo, 2015. "Cooperative Solutions for Large Economies with Asymmetric Information," Metroeconomica, Wiley Blackwell, vol. 66(1), pages 71-90, February.
    18. 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).
    19. repec:dau:papers:123456789/2346 is not listed on IDEAS
    20. 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.
    21. 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.
    22. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
    23. 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.
    24. Aliprantis, C. D. & Tourky, R. & Yannelis, N. C., 2000. "The Riesz-Kantorovich formula and general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 55-76, August.

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