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Optimal growth and impatience: A phase diagram analysis

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  • Fwu-Ranq Chang

Abstract

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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Bibliographic Info

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. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947.
  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. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
  4. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-72, January.
  5. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
  6. 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.
  7. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
  8. Drugeon, Jean-Pierre, 1996. "Impatience and long-run growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 281-313.
  9. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-94, March.
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Cited by:
  1. Kawagishi, Taketo, 2012. "Endogenous time preference, investment externalities, and equilibrium indeterminacy," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 234-241.
  2. Kirill Borissov, 2013. "The existence of equilibrium paths in an AK-model with endogenous time preferences and borrowing constraints," EUSP Deparment of Economics Working Paper Series Ec-01/13, European University at St. Petersburg, Department of Economics.
  3. Taketo Kawagishi & Kazuo Mino, 2013. "Time Preference and Income Convergence in a Dynamic Heckscher-Ohlin Model," KIER Working Papers 880, Kyoto University, Institute of Economic Research.
  4. Borissov, Kirill, 2013. "Growth and distribution in a model with endogenous time preferences and borrowing constraints," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 117-128.
  5. Kazumichi Iwasa & Laixun Zhao, 2013. "Inequalities and Patience for Tomorrow," KIER Working Papers 847, Kyoto University, Institute of Economic Research.

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