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Optimality of impulse harvesting policies

Author

Listed:
  • Katrin Erdlenbruch

    (UMR G-EAU - Gestion de l'Eau, Acteurs, Usages - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - AgroParisTech - IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture - IRD [Occitanie] - Institut de Recherche pour le Développement)

  • Alain Jean-Marie

    (MAESTRO - Models for the performance analysis and the control of networks - Centre Inria d'Université Côte d'Azur - Inria - Institut National de Recherche en Informatique et en Automatique, LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique)

  • Michel Moreaux

    (LERNA - Economie des Ressources Naturelles - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - INRA - Institut National de la Recherche Agronomique - CEA - Commissariat à l'énergie atomique et aux énergies alternatives, TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Mabel Tidball

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

We explore the link between cyclical and smooth resource exploitation. We define an impulse control framework which can generate both cyclical solutions and steady-state solutions. Our model can admit convex and concave profit functions and allows the integration of different stock-dependent profit functions. We show that the strict concavity of the profit function is only a special case of a more general condition, related to submodularity, that ensures the existence of optimal cyclical pol- icies. We then establish a link with the discrete-time models with cyclical solutions by Benhabib and Nishimura (J Econ Theory 35:284-306, 1985) and Dawid and Kopel (J Econ Theory 76:272-297, 1997). For the steady-state solution, we explore the relation to Clark's (1976) continuous control model.

Suggested Citation

  • Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2013. "Optimality of impulse harvesting policies," Post-Print hal-00862924, HAL.
    • Handle: RePEc:hal:journl:hal-00862924
    DOI: 10.1007/s00199-011-0650-6
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    Cited by:

    1. Grass, D. & Chahim, M., 2012. "Numerical Algorithms for Deterministic Impulse Control Models with Applications," Discussion Paper 2012-081, Tilburg University, Center for Economic Research.
    2. Grass, D. & Chahim, M., 2012. "Numerical Algorithms for Deterministic Impulse Control Models with Applications," Other publications TiSEM 1295ac64-8704-4e47-ae89-b, Tilburg University, School of Economics and Management.
    3. Chahim, Mohammed & Hartl, Richard F. & Kort, Peter M., 2012. "A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 18-26.
    4. Reddy, P.V. & Schumacher, J.M. & Engwerda, J.C., 2012. "Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model," Discussion Paper 2012-001, Tilburg University, Center for Economic Research.
    5. Sadana, Utsav & Reddy, Puduru Viswanadha & Zaccour, Georges, 2021. "Nash equilibria in nonzero-sum differential games with impulse control," European Journal of Operational Research, Elsevier, vol. 295(2), pages 792-805.

    More about this item

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation

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