IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/59126.html
   My bibliography  Save this paper

Local Determinacy of Prices in an Overlapping Generations Model with Continuous Trading

Author

Listed:
  • d'Albis, Hippolyte
  • Augeraud-Véron, Emmanuelle
  • Hupkes, Herman Jan

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

  • d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Herman Jan, 2014. "Local Determinacy of Prices in an Overlapping Generations Model with Continuous Trading," MPRA Paper 59126, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:59126
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/59126/1/MPRA_paper_59126.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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.
    3. 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.
    4. 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.
    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. 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.
    8. 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.
    9. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
    10. 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.
    11. 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.
    12. 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.
    13. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation for Research in Economics, Yale University.
    14. 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.
    15. 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.
    16. 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).
    17. 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.
    18. 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.
    19. Shell, Karl, 1971. "Notes on the Economics of Infinity," Journal of Political Economy, University of Chicago Press, vol. 79(5), pages 1002-1011, Sept.-Oct.
    20. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Levine's Working Paper Archive 122247000000002225, David K. Levine.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.
    2. Shihong Zeng & Xinwei Zhang & Xiaowei Wang & Guowang Zeng, 2019. "Population Aging, Household Savings and Asset Prices: A Study Based on Urban Commercial Housing Prices," Sustainability, MDPI, vol. 11(11), pages 1-21, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    3. Brito, Paulo, 2014. "Interest rates and endogenous population growth: joint age-dependent dynamics," MPRA Paper 58656, University Library of Munich, Germany.
    4. 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.
    5. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    6. Gorokhovsky, Alexander & Rubinchik, Anna, 2022. "Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models," Journal of Economic Theory, Elsevier, vol. 204(C).
    7. 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.
    8. Brito, Paulo, 2008. "Equilibrium asset prices and bubbles in a continuous time OLG model," MPRA Paper 10701, University Library of Munich, Germany.
    9. 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.
    10. 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.
    11. 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.
    12. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & Michael Woodford, 1991. "Gross Substitutes in Large Square Economics," Levine's Working Paper Archive 2057, David K. Levine.
    13. DEMICHELIS, Stefano & POLEMARCHAKIS, Heracles, 2000. "Life-span and the determinacy of equilibrium in economies of overlapping generations," LIDAM Discussion Papers CORE 2000034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. 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.
    15. H. Polemarchakis & S. Demichelis, 2002. "Frequency of Trade and the Determinancy of Equilibrium Paths: Logarithmic Economies of Overlapping Generations Under Certainty," Working Papers 2002-16, Brown University, Department of Economics.
    16. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    17. Kehoe, Timothy J. & Levine, David K., 1984. "Regularity in overlapping generations exchange economies," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 69-93, April.
    18. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Schubert, Katheline, 2010. "Demographic-economic equilibria when the age at motherhood is endogenous," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1211-1221, November.
    19. Fisher, Eric ON., 1997. "A Note on the Core of a Monetary Economy," Journal of Economic Theory, Elsevier, vol. 74(2), pages 425-434, June.
    20. Lakshmi Raut, 2006. "Two-sided altruism, Lindahl equilibrium, and Pareto optimality in overlapping generations models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 729-736, April.

    More about this item

    Keywords

    Overlapping generations models ⋅ Local dynamics ⋅ Existence ⋅ Determinacy ⋅ Functional differential equations;

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:59126. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.