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Optimal growth and impatience: A phase diagram analysis

  • Fwu-Ranq Chang

In this paper we show that we can replace the assumption of constant discount rate in the one-sector optimal growth model with the assumption of decreasing marginal impatience without losing major properties of the model. In particular, we show that the steady state exists, is unique, and has a saddle-point property. All we need is to assume that the discount function is strictly decreasing, strictly convex and has a uniformly bounded first-derivative.

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1742-7363.2009.00107.x
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Article provided by The International Society for Economic Theory in its journal International Journal of Economic Theory.

Volume (Year): 5 (2009)
Issue (Month): 2 ()
Pages: 245-255

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Handle: RePEc:bla:ijethy:v:5:y:2009:i:2:p:245-255
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  1. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
  2. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
  3. repec:cup:cbooks:9780521834063 is not listed on IDEAS
  4. Becker, Robert A, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, MIT Press, vol. 95(2), pages 375-82, September.
  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. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-94, March.
  7. Drugeon, Jean-Pierre, 1996. "Impatience and long-run growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 281-313.
  8. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-72, January.
  9. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
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