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Existence of Equilibria and Core Convergence in Economies with Bads

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Author Info
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.

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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0413.

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Length: 38
Date of creation: Feb 2004
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Handle: RePEc:cam:camdae:0413

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Related research
Keywords: general equilibrium; bads; existence; core convergence;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D41 - Microeconomics - - Market Structure and Pricing - - - 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 (the Commons)

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  1. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November. [Downloadable!] (restricted)
  2. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-85, October. [Downloadable!] (restricted)
  3. 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 678-84, Part I Se. [Downloadable!] (restricted)
  4. Polemarchakis, H. M. & Siconolfi, P., 1993. "Competitive equilibria without free disposal or nonsatiation," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 85-99. [Downloadable!] (restricted)
  5. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January. [Downloadable!] (restricted)
  6. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-23, September. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Anderson, Robert M, 1981. "Core Theory with Strongly Convex Preferences," Econometrica, Econometric Society, vol. 49(6), pages 1457-68, November. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. Robert M. Anderson, 1981. "Core Theory with Strongly Convex Preferences," Cowles Foundation Discussion Papers 578, Cowles Foundation, Yale University. [Downloadable!]
  11. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July. [Downloadable!] (restricted)
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  12. McKenzie, Lionel W, 1981. "The Classical Theorem on Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 49(4), pages 819-41, June. [Downloadable!] (restricted)
  13. Grodal, Birgit & Trockel, Walter & Weber, Shlomo, 1984. "On approximate cores of non-convex economies," Economics Letters, Elsevier, vol. 15(3-4), pages 197-202. [Downloadable!] (restricted)
  14. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
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