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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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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 1359.

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Date of creation: 2004
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Handle: RePEc:ces:ceswps:_1359

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Keywords: recursive utility; decreasing marginal impatience; saddle point; bounded slope assumption;

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  1. Drugeon, Jean-Pierre, 1996. "Impatience and long-run growth," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 20(1-3), pages 281-313.
  2. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521541947.
  3. Robert E. Lucas Jr. & Nancy L. Stokey, 1982. "Optimal Growth with Many Consumers," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 518, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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, MIT Press, vol. 95(2), pages 375-82, September.
  5. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 27(10), pages 1881-1898, August.
  6. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 353-94, March.
  7. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 31(1), pages 133-152, October.
  8. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, Econometric Society, vol. 56(1), pages 147-72, January.
  9. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 81, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Kazumichi Iwasa & Laixun Zhao, 2013. "Inequalities and Patience for Tomorrow," KIER Working Papers 847, Kyoto University, Institute of Economic Research.
  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, European University at St. Petersburg, Department of Economics Ec-01/13, European University at St. Petersburg, Department of Economics.
  3. Kirill Borissov, 2011. "Growth and Distribution in a Model with Endogenous Time Peferences and Borrowing Constraints," DEGIT Conference Papers c016_073, DEGIT, Dynamics, Economic Growth, and International Trade.
  4. 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.
  5. Kawagishi, Taketo, 2012. "Endogenous time preference, investment externalities, and equilibrium indeterminacy," Mathematical Social Sciences, Elsevier, Elsevier, vol. 64(3), pages 234-241.

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