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Optimal growth and impatience: A phase diagram analysis

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  • Fwu‐Ranq Chang

Abstract

When the time preference exhibits decreasing marginal impatience, the rate at which the discount function decreases plays a central role in the stability analysis. This paper shows that if the discount function is strictly decreasing, strictly convex and has a uniform bound on its first derivative, then the continuous‐time, one‐sector optimal growth problem has a unique steady state that exhibits the saddle‐point property. Moreover, the phase diagram analysis is geometrically similar to the case of a constant discount rate. The proposed bounded slope assumption is inspired by and in direct contrast with Magill and Nishimura's “division of countries” example.

Suggested Citation

  • Fwu‐Ranq Chang, 2009. "Optimal growth and impatience: A phase diagram analysis," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 245-255, June.
  • Handle: RePEc:bla:ijethy:v:5:y:2009:i:2:p:245-255
    DOI: 10.1111/j.1742-7363.2009.00107.x
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    References listed on IDEAS

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    1. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947.
    2. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-172, January.
    3. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
    4. Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, vol. 26(1), pages 45-75, August.
    5. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    6. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    7. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    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. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
    10. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
    11. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 375-382.
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    Citations

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    Cited by:

    1. Taketo Kawagishi & Kazuo Mino, 2016. "Time Preference and Income Convergence in a Dynamic Heckscher–Ohlin Model," Review of International Economics, Wiley Blackwell, vol. 24(3), pages 592-603, August.
    2. Kazumichi Iwasa & Laixun Zhao, 2013. "Inequalities and Patience for Tomorrow," KIER Working Papers 847, Kyoto University, Institute of Economic Research.
    3. Been-Lon Chen & Yunfang Hu & Kazuo Mino, 2016. "Stabilization Effects of Taxation Rules in Small-Open Economies with Endogenous Growth," KIER Working Papers 946, 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. Kirill Borissov, 2013. "The Existence of Equilibrium Paths in an AK-model with Endogenous Time Preferences and Borrowing Constraints," EUSP Department of Economics Working Paper Series 2013/01, European University at St. Petersburg, Department of Economics.
    6. Akihiko Yanase & Yukio Karasawa-Ohtashiro, 2019. "Endogenous time preference, consumption externalities, and trade: multiple steady states and indeterminacy," Journal of Economics, Springer, vol. 126(2), pages 153-177, March.
    7. Kawagishi, Taketo, 2012. "Endogenous time preference, investment externalities, and equilibrium indeterminacy," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 234-241.
    8. Kawagishi, Taketo, 2014. "Investment for patience in an endogenous growth model," Economic Modelling, Elsevier, vol. 42(C), pages 508-515.
    9. Kirill Borissov, 2013. "The Existence of Equilibrium Paths in an AK-model with Endogenous Time Preferences and Borrowing Constraints," EUSP Department of Economics Working Paper Series Ec-01/13, European University at St. Petersburg, Department of Economics.
    10. Kazumichi Iwasa & Kazuo Nishimaura, 2020. "Time Preference and International Trade," Discussion Paper Series DP2020-10, Research Institute for Economics & Business Administration, Kobe University.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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