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Generalized equilibrium in an economy without the survival assumption

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Abstract

It is well known that an equilibrium in the Arrow-Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satisfied. We study two approaches that allow for the relaxation of this condition. Danilov and Sotskov (1990), and Florig (2001) developed a concept of a generalized equilibrium based on a notion of hierarchic prices. Marakulin (1990) proposed a concept of an equilibrium with non-standard prices. In this paper, we establish the equivalence between non-standard and hierarchic equilibria. Furthermore, we show that for any specified system of dividends the set of such equilibria is generically finite. We also provide a generic characterization of hierarchic equilibria and give an easy proof of the core equivalence result.

Suggested Citation

  • Konovalov, A. & Marakulin, V., 2002. "Generalized equilibrium in an economy without the survival assumption," Econometric Institute Research Papers EI 2002-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:537
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    References listed on IDEAS

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    1. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    2. Konovalov, A., 1998. "Core Equivalence in Economies With Satiation," Discussion Paper 1998-80, Tilburg University, Center for Economic Research.
    3. Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
    4. Dreze, Jacques H. & Muller, Heinz, 1980. "Optimality properties of rationing schemes," Journal of Economic Theory, Elsevier, vol. 23(2), pages 131-149, October.
    5. Kajii, Atsushi, 1996. "How to discard non-satiation and free-disposal with paper money," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 75-84.
    6. Florig, Michael, 2001. "Hierarchic competitive equilibria," Journal of Mathematical Economics, Elsevier, vol. 35(4), pages 515-546, July.
    7. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
    8. Danilov, V. I. & Sotskov, A. I., 1990. "A generalized economic equilibrium," Journal of Mathematical Economics, Elsevier, vol. 19(4), pages 341-356.
    9. Makarov, V. L., 1981. "Some results on general assumptions about the existence of economic equilibrium," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 87-99, March.
    10. Konovalov, A., 2001. "Essays in general equilibrium theory," Other publications TiSEM fece7269-5d1e-47b9-a21c-6, Tilburg University, School of Economics and Management.
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