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

  • S. Rao Aiyagari

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).

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Paper provided by Federal Reserve Bank of Minneapolis in its series Working Papers with number 312.

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Date of creation: 1986
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Publication status: Published in Journal of Economic Theory (Vol. 43, No. 2, December 1987, pp. 292-313)
Handle: RePEc:fip:fedmwp:312
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  1. Cass, David & Okuno, Masahiro & Zilcha, Itzhak., . "The Role of Money in Supporting the Pareto Optimality of Competitive Equilibrium in Consumption-Loan Type Models," Working Papers 242, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. 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.
  3. 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.
  4. 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.
  5. Robert E. Lucas Jr. & Nancy L. Stokey, 1982. "Optimal Growth with Many Consumers," Discussion Papers 518, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. 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.
  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, pages 467.
  8. 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.
  9. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
  10. 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 402-17, April.
  11. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
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