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

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  • Hippolyte D'Albis

    ()
    (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne)

  • Emmanuelle Augeraud-Véron

    ()
    (MIA - Mathématiques, Image et Applications - Université de La Rochelle : EA3165)

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.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00717392.

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Date of creation: Jun 2012
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Handle: RePEc:hal:cesptp:halshs-00717392

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Keywords: Overlapping generations; perpetual youth model; determinacy; continuous time; discrete time.;

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  1. Polemarchakis, H. M., 1988. "Portfolio choice, exchange rates, and indeterminacy," Journal of Economic Theory, Elsevier, vol. 46(2), pages 414-421, December.
  2. S. Demichelis & H. Polemarchakis, 2007. "The determinacy of equilibrium in economies of overlapping generations," Economic Theory, Springer, vol. 32(3), pages 461-475, September.
  3. D. K. Levine & T. J. Kehoe, 1982. "Intertemporal Separability in Overlapping Generations Models," Working papers 315, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. 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.
  5. Hippolyte D'Albis & Emmanuelle Augeraud-Véron, 2011. "Continuous-Time Overlapping Generations Models," Post-Print hal-00424799, HAL.
  6. Roger E.A. Farmer & Carine Nourry & Alain Venditti, 2009. "Debt, deficits and finite horizons: the stochastic case," Working Papers halshs-00439336, HAL.
  7. Raouf Boucekkine & Bity Diene & Theophile Azomahou, 2007. "A closer look at the relationship between life expectancy and economic growth," Working Papers 2007_24, Business School - Economics, University of Glasgow.
  8. 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, 05.
  9. Hippolyte d’Albis & Emmanuelle Augeraud-Véron, 2007. "Balanced cycles in an OLG model with a continuum of finitely-lived individuals," Economic Theory, Springer, vol. 30(1), pages 181-186, January.
  10. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
  11. Olivier J. Blanchard, 1984. "Debt, Deficits and Finite Horizons," NBER Working Papers 1389, National Bureau of Economic Research, Inc.
  12. Weil, Philippe, 1989. "Overlapping families of infinitely-lived agents," Journal of Public Economics, Elsevier, vol. 38(2), pages 183-198, March.
  13. 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.
  14. Tomoyuki Nakajima & Herakles Polemarchakis, 2005. "Money and Prices Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 223-246.
  15. Raouf Boucekkine, 2009. "Overlapping-Generations Models," Mathematical Population Studies, Taylor & Francis Journals, vol. 16(1), pages 1-1.
  16. Buiter, Willem H, 1988. "Death, Birth, Productivity Growth and Debt Neutrality," Economic Journal, Royal Economic Society, vol. 98(391), pages 279-93, June.
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