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Existence of Equilibria and Core Convergence in Economies with Bads

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  • Hara, C.

Abstract

We consider an exchange economy in which there are infinitely many consumers and some commodities are bads, that is, cause disutility to consumers. We give an example of such an economy for which there is no competitive equilibrium or its variants (quasi- or psuedo-equilibrium). We also give examples of the failure of the so called uniform integrability condition of equilibrium allocations of increasingly populous property.

Suggested Citation

  • Hara, C., 2004. "Existence of Equilibria and Core Convergence in Economies with Bads," Cambridge Working Papers in Economics 0413, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0413
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    1. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, vol. 59(4), pages 678-684, Part I Se.
    2. Robert M. Anderson, 1981. "Core Theory with Strongly Convex Preferences," Cowles Foundation Discussion Papers 578, Cowles Foundation for Research in Economics, Yale University.
    3. Grodal, Birgit & Trockel, Walter & Weber, Shlomo, 1984. "On approximate cores of non-convex economies," Economics Letters, Elsevier, vol. 15(3-4), pages 197-202.
    4. HILDENBRAND, Werner, 1968. "The core of an economy with a measure space of economic agents," LIDAM Reprints CORE 26, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Polemarchakis, H. M. & Siconolfi, P., 1993. "Competitive equilibria without free disposal or nonsatiation," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 85-99.
    6. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-585, October.
    7. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    8. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-623, September.
    9. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    10. W. Hildenbrand, 1968. "The Core of an Economy with a Measure Space of Economic Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 443-452.
    11. Cornet, Bernard & Topuzu, Mihaela & Yildiz, Aysegul, 2003. "Equilibrium theory with a measure space of possibly satiated consumers," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 175-196, June.
    12. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    13. 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.
    14. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457, Elsevier.
    15. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
    16. McKenzie, Lionel W, 1981. "The Classical Theorem on Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 49(4), pages 819-841, June.
    17. Araujo, Aloisio, 1985. "Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience," Econometrica, Econometric Society, vol. 53(2), pages 455-461, March.
    18. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December.
    19. Anderson, Robert M, 1981. "Core Theory with Strongly Convex Preferences," Econometrica, Econometric Society, vol. 49(6), pages 1457-1468, November.
    20. HILDENBRAND, Werner, 1970. "Existence of equilibria for economies with production and a measure space of consumers," LIDAM Reprints CORE 79, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Inoue, Tomoki, 2005. "Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 571-601, August.

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    More about this item

    Keywords

    general equilibrium; bads; existence; core convergence;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • Q21 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Demand and Supply; Prices

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