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Nonmonetary steady states in stationary overlapping generations models with long lived agents and discounting: multiplicity, optimality, and consumption smoothing

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  • S. Rao Aiyagari

Abstract

We construct a sequence of pure exchange, stationary OLG economies in which generations have longer and longer life spans and all agents maximize a discounted sum of utilities with a fixed, positive, and common discount rate. Period utility functions and endowment patterns are subject to mild restrictions and within generation heterogeneity is permitted. We show that: (i) Every sequence of equilibrium interest rates converges to the discount rate. (ii) Eventually every nonmonetary steady state is optimal and a monetary steady state will never exist. (iii) For any agent consumption at any fixed age converges to permanent income evaluated using the utility discount rate.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Minneapolis in its series Working Papers with number 325.

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Date of creation: 1987
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Publication status: Published in Journal of Economic Theory (Vol. 45, No. 1, June 1988, pp. 102-127)
Handle: RePEc:fip:fedmwp:325

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  1. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
  2. Spear, Stephen E., 1985. "Rational expectations in the overlapping generations model," Journal of Economic Theory, Elsevier, vol. 35(2), pages 251-275, August.
  3. Timothy J. Kehoe & David K. Levine, 1982. "Comparitive Statics and Perfect Foresight in Infinite Horizon Economies," UCLA Economics Working Papers 259, UCLA Department of Economics.
  4. Wilson, Charles A., 1981. "Equilibrium in dynamic models with an infinity of agents," Journal of Economic Theory, Elsevier, vol. 24(1), pages 95-111, February.
  5. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
  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.
  7. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
  8. Shell, Karl, 1971. "Notes on the Economics of Infinity," Journal of Political Economy, University of Chicago Press, vol. 79(5), pages 1002-11, Sept.-Oct.
  9. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
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Cited by:
  1. D'ALBIS Hippolyte & AUGERAUD-VÉRON Emmanuelle, 2009. "Continuous-Time Overlapping Generations Models," LERNA Working Papers 09.15.291, LERNA, University of Toulouse.
  2. 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.
  3. Colucci, Domenico, 2003. "Steady states in the OLG model with seignorage and long-lived agents," Research in Economics, Elsevier, vol. 57(4), pages 371-381, December.
  4. S. Rao Aiyagari, 1988. "Can there be short-period deterministic cycles when people are long lived?," Staff Report 114, Federal Reserve Bank of Minneapolis.
  5. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.

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