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Non-existence of Optimal Programs in Continuous Time

Author

Listed:
  • Giorgio Fabbri

    (Aix-Marseille Univ. (Aix-Marseille School of Economics), CNRS & EHES, France)

  • Silvia Faggian

    (Department of Economics, University Of Venice CÃ Foscari, Italy)

  • Giuseppe Freni

    (Department of Business and Economics, University of Naples "Parthenope", Naples, Italy.)

Abstract

We report an example of a two-dimensional undiscounted convex optimal growth model in continuous time in which, although there is a unique "golden rule", no overtaking optimal solutions exists in a full neighbourhood of the steady state. The example confirms a conjecture advanced in 1976 that the minimum dimension for non-existence of overtaking optimal programs in continuous time is 2.

Suggested Citation

  • Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2016. "Non-existence of Optimal Programs in Continuous Time," Working Papers 2016:21, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2016:21
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    References listed on IDEAS

    as
    1. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2015. "On the Mitra–Wan forest management problem in continuous time," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1001-1040.
    2. W. A. Brock & A. Haurie, 1976. "On Existence of Overtaking Optimal Trajectories Over an Infinite Time Horizon," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 337-346, November.
    3. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    4. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 275-280.
    5. Khan, M. Ali & Piazza, Adriana, 2010. "On the non-existence of optimal programs in the Robinson-Solow-Srinivasan (RSS) model," Economics Letters, Elsevier, vol. 109(2), pages 94-98, November.
    6. Arie Leizarowitz, 1985. "Existence of Overtaking Optimal Trajectories for Problems with Convex Integrands," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 450-461, August.
    7. Kurz,Heinz D. & Salvadori,Neri, 1997. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521588676.
    8. Peleg, Bezalel, 1973. "A Weakly Maximal Golden-Rule Program for a Multi-Sector Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 574-579, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Optimal growth; Overtaking; Continuous time models;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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