IDEAS home Printed from
   My bibliography  Save this article

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.
(This abstract was borrowed from another version of this item.)

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.
  • Handle: RePEc:bla:ijethy:v:5:y:2009:i:2:p:245-255

    Download full text from publisher

    File URL:
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    1. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, March.
    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, Oxford University Press, vol. 95(2), pages 375-382.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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. Kawagishi, Taketo, 2012. "Endogenous time preference, investment externalities, and equilibrium indeterminacy," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 234-241.
    4. Kawagishi, Taketo, 2014. "Investment for patience in an endogenous growth model," Economic Modelling, Elsevier, vol. 42(C), pages 508-515.
    5. 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.
    6. 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.
    7. 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.

    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


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:ijethy:v:5:y:2009:i:2:p:245-255. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.