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Indeterminacy in Incomplete Market Economies

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  • Mas-Colell, Andreu

Abstract

It is shown that in a two-period economy with a continuum of states and real assets, the following holds: (1) if the asset structure is complete, then equilibria is finite; (2) if there are a finite number of real assets (this can approximate completeness arbitrarily close) then, for a non-empty open set of economies, there are a continuum of distinct equilibria. Asymptotic versions (on the number of states and on the number of assets) of the result are also given. It is argued, therefore, that incompleteness, by itself, may be a leading source of indeterminacy.

Suggested Citation

  • Mas-Colell, Andreu, 1991. "Indeterminacy in Incomplete Market Economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 45-61, January.
    • Handle: RePEc:spr:joecth:v:1:y:1991:i:1:p:45-61
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    Citations

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    Cited by:

    1. Dana, R. A. & Le Van, C., 1996. "Asset Equilibria in Lp spaces with complete markets: A duality approach," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 263-280.
    2. Calvet, Laurent E., 2001. "Incomplete Markets and Volatility," Journal of Economic Theory, Elsevier, vol. 98(2), pages 295-338, June.
    3. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    4. Polemarchakis, H. M. & Siconolfi, P., 1998. "Prices, Asset Markets and Indeterminacy," Journal of Economic Theory, Elsevier, vol. 82(1), pages 46-64, September.
    5. Hervé Crès & Tobias Markeprand & Mich Tvede, 2016. "Incomplete financial markets and jumps in asset prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 201-219, June.
    6. Covarrubias, Enrique, 2011. "The equilibrium set of economies with a continuous consumption space," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 137-142, March.
    7. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    8. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    9. Monteiro, Paulo Klinger & Pascoa, Mario R., 2000. "Discreteness of equilibria in incomplete markets with a continuum of states," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 229-237, March.
    10. Michael Zierhut, 2021. "Indeterminacy of Cournot–Walras equilibrium with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 81-114, February.
    11. Jean-Marc Tallon, 1995. "Théorie de l'équilibre général avec marchés financiers incomplets," Revue Économique, Programme National Persée, vol. 46(5), pages 1207-1239.
    12. Bettzuge, Marc Oliver, 1998. "An extension of a theorem by Mitjushin and Polterovich to incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 285-300, October.
    13. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.
    14. Elvio Accinelli, 1999. "On uniqueness of equilibrium for complete markets with infinitely many goods and in finance models," Estudios de Economia, University of Chile, Department of Economics, vol. 26(1 Year 19), pages 45-61, June.
    15. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.

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