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

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  • DEMICHELIS, Stefano
  • POLEMARCHAKIS, Heracles
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    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.

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    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000034.

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    Date of creation: 00 Jun 2000
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    Handle: RePEc:cor:louvco:2000034

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    Related research

    Keywords: life-span; continuous time; overlapping generations; determinacy.;

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    References

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    1. 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.
    2. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-53, March.
    3. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    4. Chris Shannon, 1996. "Determinacy of Competitive Equilibria in Economies with Many Commodities," GE, Growth, Math methods 9610002, EconWPA.
    5. Timothy J. Kehoe & David K. Levine, 1984. "Regularity in Overlapping Generations Exchange Economies," Levine's Working Paper Archive 2184, David K. Levine.
    6. D. K. Levine & T. J. Kehoe, 1982. "Intertemporal Separability in Overlapping Generations Models," Working papers 315, Massachusetts Institute of Technology (MIT), Department of Economics.
    7. DEBREU, Gérard, . "Economies with a finite set of equilibria," CORE Discussion Papers RP -67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. 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.
    9. 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.
    10. 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.
    11. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
    12. repec:fth:louvco:9131 is not listed on IDEAS
    13. Geanakoplos, J. & Polemarchakis, H., 1991. "Overlapping generations," CORE Discussion Papers 1991031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:
    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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