IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v65y2018i1d10.1007_s00199-016-1005-0.html
   My bibliography  Save this article

Cycles and chaos in the one-sector growth model with elastic labor supply

Author

Listed:
  • Gerhard Sorger

    (University of Vienna)

Abstract

It is shown that the discrete-time version of the neoclassical one-sector optimal growth model with elastic labor supply and standard monotonicity and convexity assumptions on technology and preferences can have periodic solutions of any period as well as chaotic solutions. The optimality of these non-monotonic solutions is traced back to strong income effects. When technology and preferences are parameterized as it is commonly done in quantitative macroeconomic studies, these phenomena cannot occur.

Suggested Citation

  • Gerhard Sorger, 2018. "Cycles and chaos in the one-sector growth model with elastic labor supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 55-77, January.
    • Handle: RePEc:spr:joecth:v:65:y:2018:i:1:d:10.1007_s00199-016-1005-0
    DOI: 10.1007/s00199-016-1005-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-016-1005-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-016-1005-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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

    as
    1. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    2. Kazuo Nishimura & Makoto Yano, 2012. "On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 165-191, Springer.
    3. Takashi Kamihigashi, 2015. "Multiple interior steady states in the Ramsey model with elastic labor supply," International Journal of Economic Theory, The International Society for Economic Theory, vol. 11(1), pages 25-37, March.
    4. Gerhard Sorger, 2000. "Income and wealth distribution in a simple model of growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 23-42.
    5. Sorger,Gerhard, 2015. "Dynamic Economic Analysis," Cambridge Books, Cambridge University Press, number 9781107443792, September.
    6. Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February.
    7. Gerhard Sorger, 1994. "Period Three Implies Heavy Discounting," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 1007-1022, November.
    8. Mitra, Tapan, 1996. "An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models," Journal of Economic Theory, Elsevier, vol. 69(2), pages 281-305, May.
    9. repec:cup:cbooks:9781107083295 is not listed on IDEAS
    10. de Hek, Paul A., 1998. "An aggregative model of capital accumulation with leisure-dependent utility," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 255-276, September.
    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. Iwasa, Kazumichi & Sorger, Gerhard, 2018. "Periodic solutions of the one-sector growth model: The role of income effects," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 59-63.
    2. Goenka, Aditya & Nguyen, Manh-Hung, 2020. "General existence of competitive equilibrium in the growth model with an endogenous labor–leisure choice," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 90-98.
    3. Hashimoto, Ken-ichi & Im, Ryonghun & Kunieda, Takuma & Shibata, Akihisa, 2022. "Financial destabilization," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    4. Antoine Riche & Francesco Magris & Daria Onori, 2020. "Monetary rules in a two-sector endogenous growth model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 1049-1100, June.
    5. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2020. "Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 48-56.
    6. Gori, Luca & Sodini, Mauro, 2020. "Endogenous labour supply, endogenous lifetime and economic development," Structural Change and Economic Dynamics, Elsevier, vol. 52(C), pages 238-259.

    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. Gerhard Sorger, 2018. "Cycles and chaos in the one-sector growth model with elastic labor supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 55-77, January.
    2. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2005. "Incomplete-market dynamics in a neoclassical production economy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 407-438, August.
    3. Ghiglino, Christian & Venditti, Alain, 2007. "Wealth inequality, preference heterogeneity and macroeconomic volatility in two-sector economies," Journal of Economic Theory, Elsevier, vol. 135(1), pages 414-441, July.
    4. Sorger, Gerhard, 2009. "Some notes on discount factor restrictions for dynamic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 435-448, July.
    5. Guerrero-Luchtenberg, C.L., 2000. "A uniform neighborhood turnpike theorem and applications," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 329-357, November.
    6. Iwasa, Kazumichi & Sorger, Gerhard, 2018. "Periodic solutions of the one-sector growth model: The role of income effects," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 59-63.
    7. Goenka, Aditya & Poulsen, Odile, 2004. "Factor Intensity Reversal and Ergodic Chaos," Working Papers 04-13, University of Aarhus, Aarhus School of Business, Department of Economics.
    8. Ghiglino, Christian & Sorger, Gerhard, 2002. "Poverty Traps, Indeterminacy, and the Wealth Distribution," Journal of Economic Theory, Elsevier, vol. 105(1), pages 120-139, July.
    9. Ali Khan, M. & Piazza, Adriana, 2011. "Optimal cyclicity and chaos in the 2-sector RSS model: An anything-goes construction," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 397-417.
    10. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2020. "Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 48-56.
    11. Sorger, Gerhard, 2009. "Some notes on discount factor restrictions for dynamic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 435-448, July.
    12. Mitra, Tapan, 1998. "On the relationship between discounting and complicated behavior in dynamic optimization models," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 421-434, January.
    13. Sorger, Gerhard, 2004. "Consistent planning under quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 118(1), pages 118-129, September.
    14. Calvet, Laurent E., 2001. "Incomplete Markets and Volatility," Journal of Economic Theory, Elsevier, vol. 98(2), pages 295-338, June.
    15. Gerhard Sorger, 2000. "Income and wealth distribution in a simple model of growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 23-42.
    16. d’Albis, Hippolyte & Augeraud-Veron, Emmanuelle & Venditti, Alain, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 295-308.
    17. Mitra, Tapan & Nishimura, Kazuo, 2001. "Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 256-293, January.
    18. Bosi, Stefano & Seegmuller, Thomas, 2010. "On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 475-492, July.
    19. Jean-Paul Chavas, 2004. "On Impatience, Economic Growth and the Environmental Kuznets Curve: A Dynamic Analysis of Resource Management," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 28(2), pages 123-152, June.
    20. Takashi Kamihigashi, 2017. "Regime-Switching Sunspot Equilibria in a One-Sector Growth Model with Aggregate Decreasing Returns and Small Externalities," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 125-146, Springer.

    More about this item

    Keywords

    Optimal growth; Endogenous labor supply; Periodic solutions; Chaotic dynamics;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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:spr:joecth:v:65:y:2018:i:1:d:10.1007_s00199-016-1005-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.