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On the continuity of the walras correspondence for distributional economies with an infinite dimensional commodity space

Author

Listed:
  • Sebastián Cea-Echenique

    (UC - Pontificia Universidad Católica de Chile)

  • Matías Fuentes

    (UNSAM - Universidad Nacional de San Martin)

Abstract

Exchange economies are defined by a distribution on the space of characteristics where the commodity space is an ordered separable Banach space. We characterize the continuity of the equilibrium correspondence and a stability concept associated. We provide a positive answer to an open question about the continuity of the Walras correspondence in infinite dimensional spaces. Regarding the stability concept, differentiability assumptions are not required as it is usual in the literature on regularity. Moreover, since distributional economies do not specify a space of agents, our setting encompass several results in the literature on large economies.

Suggested Citation

  • Sebastián Cea-Echenique & Matías Fuentes, 2020. "On the continuity of the walras correspondence for distributional economies with an infinite dimensional commodity space," Working Papers hal-02430960, HAL.
    • Handle: RePEc:hal:wpaper:hal-02430960
    Note: View the original document on HAL open archive server: https://hal.science/hal-02430960v3
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    References listed on IDEAS

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    1. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August.
    2. Back, Kerry, 1986. "Concepts of similarity for utility functions," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 129-142, April.
    3. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    4. Ram Sewak Dubey & Francesco Ruscitti, 2015. "A remark on the continuity of the Walras correspondence in pure exchange economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 33-41, April.
    5. Mas-Colell, Andreu, 1977. "On the Continuous Representation of Preorders," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 509-513, June.
    6. Sofía Correa & Juan Torres-Martínez, 2014. "Essential equilibria of large generalized games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 479-513, November.
    7. Khan, M. Ali & Sagara, Nobusumi, 2016. "Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 95-107.
    8. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    9. Graciela Chichilnisky, 1980. "Continuous Representation of Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(5), pages 959-963.
    10. Hildenbrand, W & Mertens, J F, 1972. "Upper Hemi-Continuity of the Equilibrium-Set Correspondence for Pure Exchange Economies," Econometrica, Econometric Society, vol. 40(1), pages 99-108, January.
    11. Mas-Colell, Andreu, 1977. "Indivisible commodities and general equilibrium theory," Journal of Economic Theory, Elsevier, vol. 16(2), pages 443-456, December.
    12. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    13. HILDENBRAND, Werner, 1970. "On economies with many agents," LIDAM Reprints CORE 61, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    15. Hildenbrand, Werner, 1970. "On economies with many agents," Journal of Economic Theory, Elsevier, vol. 2(2), pages 161-188, June.
    16. Noguchi, Mitsunori, 1997. "Economies with a continuum of consumers, a continuum of suppliers and an infinite dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 1-21, February.
    17. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    18. Hildenbrand, Kurt, 1972. "Continuity of the equilibrium-set correspondence," Journal of Economic Theory, Elsevier, vol. 5(1), pages 152-162, August.
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    Keywords

    Essential Stability; Walras Correspondence; Infinitely Many Commodities; Large Economies; Nowhere Equivalence;
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