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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 - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université, 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://halshs.archives-ouvertes.fr/halshs-01934842
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    References listed on IDEAS

    as
    1. 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.
    2. Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 371-382, May.
    3. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
    4. 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.
    5. Tyrrell Rockafellar, R., 1976. "Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate," Journal of Economic Theory, Elsevier, vol. 12(1), pages 71-113, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    small discounting; two-sector optimal growth model; period-two cycles; strong and weak concavity;

    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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