IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_1359.html
   My bibliography  Save this paper

Optimal Growth and Impatience: A Phase Diagram Analysis

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp1359.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    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. 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.
    4. 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.
    5. 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.
    6. Kawagishi, Taketo, 2012. "Endogenous time preference, investment externalities, and equilibrium indeterminacy," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 234-241.
    7. Kawagishi, Taketo, 2014. "Investment for patience in an endogenous growth model," Economic Modelling, Elsevier, vol. 42(C), pages 508-515.
    8. 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.
    9. Iwasa, Kazumichi & Zhao, Laixun, 2020. "Inequality and catching-up under decreasing marginal impatience," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 99-110.
    10. 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.
    11. 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.
    12. Liutang Gong & Wei Wang, 2020. "Self‐fulfilling patience," Australian Economic Papers, Wiley Blackwell, vol. 59(4), pages 336-357, December.
    13. Kazumichi Iwasa & Kazuo Nishimaura, 2020. "Time Preference and International Trade," Discussion Paper Series DP2020-10, Research Institute for Economics & Business Administration, Kobe University.
    14. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ingmar, SCHUMACHER, 2006. "On optimality, endogeneous discounting and wealth accumulation," Discussion Papers (ECON - Département des Sciences Economiques) 2006058, Université catholique de Louvain, Département des Sciences Economiques.
    2. Takashi Hayashi, 2020. "Investment in time preference and long-run distribution," The Japanese Economic Review, Springer, vol. 71(2), pages 171-190, April.
    3. Zhang Wei-Bin, 2013. "Habit Formation and Preference Change with Capital and Renewable Resources," Business Systems Research, Sciendo, vol. 4(2), pages 108-125, December.
    4. Hashimzade, Nigar & Kirsanov, Oleg & Kirsanova, Tatiana, 2023. "Distributional effects of endogenous discounting," Mathematical Social Sciences, Elsevier, vol. 122(C), pages 1-6.
    5. ZHANG, Wei-Bin, 2013. "Habit Formation And Preference Change In A Twosector Growth Model With Elastic Labor Supply," Academica Science Journal, Economica Series, Dimitrie Cantemir University, Faculty of Economical Science, vol. 1(2), pages 3-20, May.
    6. Kawagishi, Taketo, 2014. "Investment for patience in an endogenous growth model," Economic Modelling, Elsevier, vol. 42(C), pages 508-515.
    7. Wei-Bin Zhang, 2013. "Dynamic Interactions among Growth, Environmental Change, Habit Formation, and Preference Change," The International Journal of Economic Behavior - IJEB, Faculty of Business and Administration, University of Bucharest, vol. 3(1), pages 3-25, December.
    8. Harashima, Taiji, 2016. "The Cause of the Great Recession: What Caused the Downward Shift of the GDP Trend in the United States?," MPRA Paper 69215, University Library of Munich, Germany.
    9. Le Kama, Alain Ayong & Schubert, Katheline, 2007. "A Note On The Consequences Of An Endogenous Discounting Depending On The Environmental Quality," Macroeconomic Dynamics, Cambridge University Press, vol. 11(2), pages 272-289, April.
    10. Schumacher, Ingmar, 2009. "Endogenous discounting via wealth, twin-peaks and the role of technology," Economics Letters, Elsevier, vol. 103(2), pages 78-80, May.
    11. Tom Kompas & Omar Abdel-Razeq, 2001. "A Simple Monetary Growth Model with Variable Rates of Time Preference," International and Development Economics Working Papers idec01-10, International and Development Economics.
    12. Ken-ichi Hirose & Shinsuke Ikeda, 2012. "Decreasing marginal impatience in a two-country world economy," Journal of Economics, Springer, vol. 105(3), pages 247-262, April.
    13. Ken-Ichi Hirose & Shinsuke Ikeda, 2015. "Decreasing Marginal Impatience and Capital Accumulation in a Two-Country World Economy," Metroeconomica, Wiley Blackwell, vol. 66(3), pages 474-507, July.
    14. Schumacher, Ingmar, 2011. "Endogenous discounting and the domain of the felicity function," Economic Modelling, Elsevier, vol. 28(1-2), pages 574-581, January.
    15. Wei-Bin Zhang, 2016. "Population Growth And Preference Change In A Generalized Solow Growth Model With Gender Time Distributions," Oradea Journal of Business and Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 7-30, September.
    16. Erol, Selman & Le Van, Cuong & Saglam, Cagri, 2011. "Existence, optimality and dynamics of equilibria with endogenous time preference," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 170-179, March.
    17. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    18. Luis Alcalá & Fernando Tohmé & Carlos Dabús, 2019. "Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience," Dynamic Games and Applications, Springer, vol. 9(2), pages 314-365, June.
    19. Harashima, Taiji, 2009. "Depression as a Nash Equilibrium Consisting of Strategies of Choosing a Pareto Inefficient Transition Path," MPRA Paper 18953, University Library of Munich, Germany.
    20. Ken-Ichi Hirose & Shinsuke Ikeda, 2013. "Time Preference and Dynamic Stability in an N-Country World Economy," ISER Discussion Paper 0887, Institute of Social and Economic Research, Osaka University.

    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

    Statistics

    Access and download statistics

    Corrections

    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:ces:ceswps:_1359. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.