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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. Brock, William A. & Scheinkman, JoseA., 1976. "Global asymptotic stability of optimal control systems with applications to the theory of economic growth," Journal of Economic Theory, Elsevier, vol. 12(1), pages 164-190, February.
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    5. 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.
    6. 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.
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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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