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Local determinacy of prices in an overlapping generations model with continuous trading

Author

Listed:
  • 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)

  • Hermen Jan Hupkes

    (Mathematical institute - Universiteit Leiden = Leiden University)

Abstract
We characterize the determinacy properties of the intertemporal equilibrium for a continuous-time, pure-exchange, overlapping generations economy with logarithmic preferences. Using recent advances in the theory of functional differential equations, we show that the equilibrium is locally unique and that prices converge to a balanced growth path and are determined.

Suggested Citation

  • Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2015. "Local determinacy of prices in an overlapping generations model with continuous trading," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01175922, HAL.
    • Handle: RePEc:hal:cesptp:hal-01175922
    DOI: 10.1016/j.jmateco.2015.03.001
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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. Jean-François Mertens & Anna Rubinchik, 2013. "Equilibria in an overlapping generations model with transfer policies and exogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 537-595, November.
    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. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Stability and determinacy conditions for mixed-type functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 119-129.
    5. Kehoe, Timothy J. & Levine, David K., 1990. "The economics of indeterminacy in overlapping generations models," Journal of Public Economics, Elsevier, vol. 42(2), pages 219-243, July.
    6. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717412, HAL.
    7. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
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    9. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Levine's Working Paper Archive 122247000000002225, David K. Levine.
    10. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    11. 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.
    12. Balasko, Yves & Cass, David & Shell, Karl, 1980. "Existence of competitive equilibrium in a general overlapping-generations model," Journal of Economic Theory, Elsevier, vol. 23(3), pages 307-322, December.
    13. Edmond, Chris, 2008. "An integral equation representation for overlapping generations in continuous time," Journal of Economic Theory, Elsevier, vol. 143(1), pages 596-609, November.
    14. 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.
    15. Hippolyte d'Albis & Emmanuelle Augeraud-Véron, 2013. "Frequency of trade and the determinacy of equilibrium in economies of overlapping generations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 85-100, March.
    16. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
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    18. Brito, Paulo & Dilão, Rui, 2010. "Equilibrium price dynamics in an overlapping-generations exchange economy," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 343-355, May.
    19. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Zame, William R., 1989. "Determinacy of equilibrium in large-scale economies," Journal of Mathematical Economics, Elsevier, vol. 18(3), pages 231-262, June.
    20. Jochen Mierau & Stephen Turnovsky, 2014. "Capital accumulation and the sources of demographic change," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(3), pages 857-894, July.
    21. repec:hal:pseose:hal-00759208 is not listed on IDEAS
    22. 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.
    23. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1991. "Overlapping generations," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 35, pages 1899-1960, Elsevier.
    24. 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.
    25. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation for Research in Economics, Yale University.
    26. Burke, Jonathan L., 1996. "Equilibrium for Overlapping Generations in Continuous Time," Journal of Economic Theory, Elsevier, vol. 70(2), pages 364-390, August.
    27. Jochen Mierau & Stephen Turnovsky, 2014. "Demography, growth, and inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 29-68, January.
    28. MERTENS, Jean-François & RUBINCHIK, Anna, 2009. "Regularity and stability of equilibria in an overlapping generations model with exogenous growth," LIDAM Discussion Papers CORE 2009005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    1. Eugene Bravyi & Vladimir Maksimov & Pyotr Simonov, 2020. "Some Economic Dynamics Problems for Hybrid Models with Aftereffect," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
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    More about this item

    Keywords

    overlapping generations models; local dynamics; existence; determinacy; functional differential equations;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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