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Competitive Equilibrium Cycles for Small Discounting in Discrete-Time Two-Sector Optimal Growth Models

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  • Alain Venditti

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, EDHEC - EDHEC Business School)

Abstract

We study the existence of endogenous competitive equilibrium cycles under small discounting in a two-sector discrete-time optimal growth model. We provide precise concavity conditions on the indirect utility function leading to the existence of period-two cycles with a critical value for the discount factor that can be arbitrarily close to one. Contrary to the continuous-time case where the existence of periodic-cycles is obtained if the degree of concavity is close to zero, we show that in a discrete-time setting the driving condition does not require a close to zero degree of concavity but a symmetry of the indirect utility function's concavity properties with respect to its two arguments.

Suggested Citation

  • Alain Venditti, 2018. "Competitive Equilibrium Cycles for Small Discounting in Discrete-Time Two-Sector Optimal Growth Models," Working Papers halshs-01934842, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01934842
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01934842
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    References listed on IDEAS

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    1. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.
    2. Benhabib, Jess & Nishimura, Kazuo, 1981. "Stability of Equilibrium in Dynamic Models of Capital Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 275-293, June.
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    7. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    8. Boldrin, Michele & Deneckere, Raymond J., 1990. "Sources of complex dynamics in two-sector growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 627-653, October.
    9. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    10. Montrucchio, Luigi, 1995. "A turnpike theorem for continuous-time optimal-control models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 599-619, April.
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    More about this item

    Keywords

    small discounting; two-sector optimal growth model; strong and weak concavity; period-two cycles;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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