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Life-span and the determinacy of equilibrium in economies of overlapping generations

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  • DEMICHELIS, Stefano
  • POLEMARCHAKIS, Heracles

Abstract

Equilibrium paths in an economy of overlapping generations are determinate. Time is either discrete or continuous; in either case, it extend into the infinite future and, possibly, the infinite past. There is one, nonstorable commodity at each date. The economy is stationary; intertemporal preferences are logarithmic; the endowments and discount factors of individuals need not depend continuously on time. With continuous time, equilibrium paths of prices are smooth; this, even for endowments and discount factors of individuals that do not depend continuously on time. With discrete time, as the number of periods in the life-span of individuals increases, equilibrium paths converge to the continuous time solutions. If time extends infinitely into the infinite past as well as into the infinite future, in continuous time, all non-stationary equilibrium paths of prices are time-shifts of a single path; in addition, there are two stationary solutions; in discrete time, there is a one dimensional family of non-stationary solutions, up to time-shift; however the indeterminacy vanishes as the number of periods in the life-span of individuals tends to infinity. If, alternatively, time has a finite starting point, in discrete time the degree of indeterminacy increases with the life-span of individuals, and, in continuous time, it is infinite; however these are families of exponentially decreasing oscillations which, although they may exhibit pseudo-chaotic behaviour for a while, as time tends to infinity they all get damped, and asymptotic behaviour is that of the economy that originates in the infinite past.

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:2000034
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    References listed on IDEAS

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    1. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
    2. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    3. Chris Shannon, 1996. "Determinacy of Competitive Equilibria in Economies with Many Commodities," GE, Growth, Math methods 9610002, University Library of Munich, Germany.
    4. 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.
    5. 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.
    6. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    7. 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.
    8. J. D. Geanakoplos & H. M. Polemarchakis, 1986. "Walrasian Indeterminacy and Keynesian Macroeconomics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 755-779.
    9. 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.
    10. Geanakoplos, J. D. & Polemarchakis, H. M., 1984. "Intertemporally separable, overlapping-generations economies," Journal of Economic Theory, Elsevier, vol. 34(2), pages 207-215, December.
    11. 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.
    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. 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.
    14. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & William Zame, 1989. "Determinacy of Equilibrium in Large Square Economies," Levine's Working Paper Archive 46, David K. Levine.
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    1. Molina-Abraldes, Antonio & Pintos-Clapés, Juan, 2008. "Pareto optimality in continuous-time OLG economies," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 933-950, September.

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    More about this item

    Keywords

    life-span; continuous time; overlapping generations; determinacy.;
    All these keywords.

    JEL classification:

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

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