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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.

Suggested Citation

  • Fwu-Ranq Chang, 2004. "Optimal Growth and Impatience: A Phase Diagram Analysis," CESifo Working Paper Series 1359, CESifo.
    • Handle: RePEc:ces:ceswps:_1359
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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, January.
    2. Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, vol. 26(1), pages 45-75, August.
    3. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
    4. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
    5. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-172, January.
    6. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    7. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    8. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    9. Drugeon, Jean-Pierre, 1996. "Impatience and long-run growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 281-313.
    10. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
    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, President and Fellows of Harvard College, 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. Iwasa, Kazumichi & Zhao, Laixun, 2020. "Inequality and catching-up under decreasing marginal impatience," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 99-110.
    5. Akira Maeda & Makiko Nagaya, 2023. "Exhaustible resource use under endogenous time preference," International Journal of Economic Policy Studies, Springer, vol. 17(1), pages 223-248, February.
    6. 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.
    7. Kazumichi Iwasa & Kazuo Nishimura, 2021. "Time preference and international trade," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(1), pages 31-45, March.
    8. 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.
    9. 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.
    10. Kawagishi, Taketo, 2012. "Endogenous time preference, investment externalities, and equilibrium indeterminacy," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 234-241.
    11. Kawagishi, Taketo, 2014. "Investment for patience in an endogenous growth model," Economic Modelling, Elsevier, vol. 42(C), pages 508-515.
    12. 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.
    13. Liutang Gong & Wei Wang, 2020. "Self‐fulfilling patience," Australian Economic Papers, Wiley Blackwell, vol. 59(4), pages 336-357, December.
    14. Kazumichi Iwasa & Kazuo Nishimaura, 2020. "Time Preference and International Trade," Discussion Paper Series DP2020-10, Research Institute for Economics & Business Administration, Kobe University.

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    More about this item

    Keywords

    recursive utility; decreasing marginal impatience; saddle point; bounded slope assumption;
    All these keywords.

    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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