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


  • 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

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    References listed on IDEAS

    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. Nishimura, Kazuo & Yano, Makoto, 1996. "On the Least Upper Bound of Discount Factors That Are Compatible with Optimal Period-Three Cycles," Journal of Economic Theory, Elsevier, vol. 69(2), pages 306-333, May.
    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.
    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.
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    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.

    More about this item


    Optimal growth; Endogenous labor supply; Periodic solutions; Chaotic dynamics;

    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


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