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

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  • Hippolyte D'Albis

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

  • Emmanuelle Augeraud-Véron

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

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://halshs.archives-ouvertes.fr/halshs-00717158
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    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    5. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    6. 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, pages 467-467.
    7. Polemarchakis, H. M., 1988. "Portfolio choice, exchange rates, and indeterminacy," Journal of Economic Theory, Elsevier, vol. 46(2), pages 414-421, December.
    8. 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.
    9. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," Review of Economic Studies, Oxford University Press, vol. 32(2), pages 137-150.
    10. Raouf Boucekkine, 2009. "Overlapping-Generations Models," Mathematical Population Studies, Taylor & Francis Journals, vol. 16(1), pages 1-1.
    11. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    12. 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.
    13. 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.
    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. Buiter, Willem H, 1988. "Death, Birth, Productivity Growth and Debt Neutrality," Economic Journal, Royal Economic Society, vol. 98(391), pages 279-293, June.
    16. Tomoyuki Nakajima & Herakles Polemarchakis, 2005. "Money and Prices Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 223-246.
    17. Weil, Philippe, 1989. "Overlapping families of infinitely-lived agents," Journal of Public Economics, Elsevier, vol. 38(2), pages 183-198, March.
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    Cited by:

    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.

    More about this item

    Keywords

    continuous time; perpetual youth model; determinacy; discrete time; Overlapping generations; Générations imbriquées;

    JEL classification:

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

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