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On Impossibility of Limit Cycles in Certain Two-Dimensional Continuous-Time Growth Mode

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  • Slobodyan Sergey

    (CERGE-EI)

Abstract

This article proves that periodic trajectories are generically impossible in a class of continuous-time growth models that allow a locally indeterminate steady state. Those models reducible to the two-dimensional Lotka-Volterra system of equations constitute the class considered here. Knowledge of the presence or absence of the limit cycles allows a global phase diagram of the system to be constructed. In particular, an explosive steady state implies that all perfect-foresight trajectories diverge to infinity and that the model cannot be used even locally.

Suggested Citation

  • Slobodyan Sergey, 2001. "On Impossibility of Limit Cycles in Certain Two-Dimensional Continuous-Time Growth Mode," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(1), pages 1-9, April.
    • Handle: RePEc:bpj:sndecm:v:5:y:2001:i:1:n:3
    DOI: 10.2202/1558-3708.1069
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    References listed on IDEAS

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    1. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448, Elsevier.
    2. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    3. Guo, Jang-Ting, 1999. "Multiple equilibria and progressive taxation of labor income," Economics Letters, Elsevier, vol. 65(1), pages 97-103, October.
    4. Guo, Jang-Ting & Lansing, Kevin J., 1998. "Indeterminacy and Stabilization Policy," Journal of Economic Theory, Elsevier, vol. 82(2), pages 481-490, October.
    5. Sergey Slobodyan, 1999. "Sunspot Fluctuations: A Way Out of a Development Trap?," Computing in Economics and Finance 1999 922, Society for Computational Economics.
    6. Schmitt-Grohe, Stephanie & Uribe, Martin, 1997. "Balanced-Budget Rules, Distortionary Taxes, and Aggregate Instability," Journal of Political Economy, University of Chicago Press, vol. 105(5), pages 976-1000, October.
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    Cited by:

    1. Slobodyan, Sergey, 2005. "Indeterminacy, sunspots, and development traps," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 159-185, January.
    2. Jonathan P. Caulkins & Gustav Feichtinger & Josef Haunschmied & Gernot Tragler, 2006. "Quality Cycles and the Strategic Manipulation of Value," Operations Research, INFORMS, vol. 54(4), pages 666-677, August.

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    Keywords

    indeterminacy; limit cycles;

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