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Frequency of trade and the deterrminacy of equilibrium in economies of overlapping generations

Author

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  • Hippolyte d'Albis

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Emmanuelle Augeraud-Véron

    (MIA - Mathématiques, Image et Applications - EA 3165 - ULR - La Rochelle Université)

Abstract

In a recent article, Demichelis and Polemarchakis (2007) highlighted the role played by the frequency of trade on the degree of indeterminacy of equilibrium in economies of overlapping generations. Assuming that time has a finite starting point and extends into the infinite future, they prove that the degree of indeterminacy increases with the number of periods in the life-span of individuals, which is assumed to be certain. We show that this result does not hold when individual longevity is uncertain. We build a discrete time model that uniformly converges to a standard continuous time overlapping-generation model when the frequency of trade is infinite. Deriving the equilibrium prices, we demonstrate that the degree of indeterminacy is independent of the frequency of trade and is always equal to one.

Suggested Citation

  • Hippolyte d'Albis & Emmanuelle Augeraud-Véron, 2012. "Frequency of trade and the deterrminacy of equilibrium in economies of overlapping generations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717158, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00717158
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00717158
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    References listed on IDEAS

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    1. Hippolyte d'Albis & Emmanuelle Augeraud-véron, 2009. "Competitive Growth In A Life-Cycle Model: Existence And Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 459-484, May.
    2. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    3. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    4. Farmer, Roger E.A. & Nourry, Carine & Venditti, Alain, 2011. "Debt, deficits and finite horizons: The stochastic case," Economics Letters, Elsevier, vol. 111(1), pages 47-49, April.
    5. Weil, Philippe, 1989. "Overlapping families of infinitely-lived agents," Journal of Public Economics, Elsevier, vol. 38(2), pages 183-198, March.
    6. Kehoe, Timothy J. & Levine, David K., 1984. "Intertemporal separability in overlapping-generations models," Journal of Economic Theory, Elsevier, vol. 34(2), pages 216-226, December.
    7. Buiter, Willem H, 1988. "Death, Birth, Productivity Growth and Debt Neutrality," Economic Journal, Royal Economic Society, vol. 98(391), pages 279-293, June.
    8. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    9. Théophile T. Azomahou & Raouf Boucekkine & Bity Diene, 2009. "A closer look at the relationship between life expectancy and economic growth," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 201-244, June.
    10. S. Demichelis & H. Polemarchakis, 2007. "The determinacy of equilibrium in economies of overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 461-475, September.
    11. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    12. Polemarchakis, H. M., 1988. "Portfolio choice, exchange rates, and indeterminacy," Journal of Economic Theory, Elsevier, vol. 46(2), pages 414-421, December.
    13. Raouf Boucekkine, 2009. "Overlapping-Generations Models," Mathematical Population Studies, Taylor & Francis Journals, vol. 16(1), pages 1-1.
    14. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Woodford, Michael, 1991. "Gross substitutability in large-square economies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 1-25, June.
    15. Hippolyte d’Albis & Emmanuelle Augeraud-Véron, 2007. "Balanced cycles in an OLG model with a continuum of finitely-lived individuals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 181-186, January.
    16. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    17. Tomoyuki Nakajima & Herakles Polemarchakis, 2005. "Money and Prices Under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 223-246.
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    1. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2015. "Local determinacy of prices in an overlapping generations model with continuous trading," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 16-24.

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    More about this item

    Keywords

    discrete time; Overlapping generations; perpetual youth model; determinacy; continuous time; Générations imbriquées;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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