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Optimality and monetary equilibria in stationary overlapping generations models with long lived agents: growth versus discounting

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  • S. Rao Aiyagari

Abstract

This paper studies the relationship between the existence and optimality of a monetary steady-state and the nonoptimality of nonmonetary steady-states. We construct a sequence of stationary overlapping generations economies with longer and longer lived generations in which all agents maximize a discounted sum of utilities with a common discount rate. Under some assumptions the following result is established: If the discount rate is greater (less) than the population growth rate, then eventually every nonmonetary steady-state is optimal (non-optimal) and a monetary steady-state does not exist (exists and is optimal).

Suggested Citation

  • S. Rao Aiyagari, 1986. "Optimality and monetary equilibria in stationary overlapping generations models with long lived agents: growth versus discounting," Working Papers 312, Federal Reserve Bank of Minneapolis.
  • Handle: RePEc:fip:fedmwp:312
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    References listed on IDEAS

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    1. 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.
    2. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
    8. 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.
    9. Benveniste, Lawrence M & Cass, David, 1986. "On the Existence of Optimal Stationary Equilibria with a Fixed Supply of Fiat Money: I. The Case of a Single Consumer," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 402-417, April.
    10. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
    11. Cass, David & Okuno, Masahiro & Zilcha, Itzhak, 1979. "The role of money in supporting the pareto optimality of competitive equilibrium in consumption-loan type models," Journal of Economic Theory, Elsevier, vol. 20(1), pages 41-80, February.
    12. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
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    Cited by:

    1. Stefano Lovo, 2000. "Infinitely Lived Representative Agent Exchange Economy with Myopia," Working Papers hal-00598167, HAL.
    2. Dmitri Vinogradov, 2003. "Macroeconomic evolution after a shock: the role for financial intermediation," Macroeconomics 0310007, University Library of Munich, Germany.
    3. Chetty, V. K. & Ratha, Dilip, 1996. "On finite life times and growth," Journal of Macroeconomics, Elsevier, vol. 18(2), pages 353-358.
    4. 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.
    5. Dmitri Vinogradov, 2004. "Macroeconomic evolution aftera shock: the role of financial intermediation," Money Macro and Finance (MMF) Research Group Conference 2003 106, Money Macro and Finance Research Group.

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