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Core Convergence Without Monotone Preferences or Free Disposal

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  • Alejandro Manelli

Abstract

We prove some core convergence theorems for finite economies without monotone preferences or free disposal of commodities. When these assumptions are relaxed, the relationship between the continuum and the large finite economies is lost. Extra conditions are needed, in general, to obtain convergence results.

Suggested Citation

  • Alejandro Manelli, 1990. "Core Convergence Without Monotone Preferences or Free Disposal," Discussion Papers 891, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:891
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, January.
    2. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    3. Hart, Oliver D. & Kuhn, Harold W., 1975. "A proof of the existence of equilibrium without the free disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 335-343, December.
    4. Robert M. Anderson, 1981. "Core Theory with Strongly Convex Preferences," Cowles Foundation Discussion Papers 578, Cowles Foundation for Research in Economics, Yale University.
    5. Grodal, Birgit & Trockel, Walter & Weber, Shlomo, 1984. "On approximate cores of non-convex economies," Economics Letters, Elsevier, vol. 15(3-4), pages 197-202.
    6. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    7. Rader, Trout, 1972. "Theory of General Economic Equilibrium," Elsevier Monographs, Elsevier, edition 1, number 9780125750400.
    8. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
    9. Gerard Debreu, 1961. "New Concepts and Techniques for Equilibrium Analysis," Cowles Foundation Discussion Papers 129, Cowles Foundation for Research in Economics, Yale University.
    10. Anderson, Robert M, 1985. "Strong Core Theorems with Nonconvex Preferences," Econometrica, Econometric Society, vol. 53(6), pages 1283-1294, November.
    11. Gabszewicz, Jean Jaskold & Mertens, Jean-Francois, 1971. "An Equivalence Theorem for the Core of an Economy Whose Atoms Are Not 'Too' Big," Econometrica, Econometric Society, vol. 39(5), pages 713-721, September.
    12. Trockel, Walter, 1976. "A limit theorem on the core," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 247-264, December.
    13. Bewley, Truman F, 1973. "Edgeworth's Conjecture," Econometrica, Econometric Society, vol. 41(3), pages 425-454, May.
    14. Brown, Donald J. & Robinson, Abraham, 1974. "The cores of large standard exchange economies," Journal of Economic Theory, Elsevier, vol. 9(3), pages 245-254, November.
    15. Dierker, Egbert, 1975. "Gains and losses at core allocations," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 119-128.
    16. Karl Vind, 1965. "A Theorem on the Core of an Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(1), pages 47-48.
    17. Anderson, Robert M, 1988. "The Second Welfare Theorem with Nonconvex Preferences," Econometrica, Econometric Society, vol. 56(2), pages 361-382, March.
    18. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    19. M. Ali Khan, 1974. "Some Equivalence Theorems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(4), pages 549-565.
    20. Anderson, Robert M, 1981. "Core Theory with Strongly Convex Preferences," Econometrica, Econometric Society, vol. 49(6), pages 1457-1468, November.
    21. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
    22. Ali Khan, M., 1976. "Oligopoly in markets with a continuum of traders: An asymptotic interpretation," Journal of Economic Theory, Elsevier, vol. 12(2), pages 273-297, April.
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