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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 - CEMAGREF - Centre national du machinisme agricole, du génie rural, des eaux et forêts - IRD [Occitanie] - Institut de Recherche pour le Développement - CIHEAM-IAMM - Centre International de Hautes Etudes Agronomiques Méditerranéennes - Institut Agronomique Méditerranéen de Montpellier - CIHEAM - Centre International de Hautes Études Agronomiques Méditerranéennes)

  • Alain Jean-Marie

    (MAESTRO - Models for the performance analysis and the control of networks - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique, APR - Algorithmes et Performance des Réseaux - LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique)

  • Michel Moreaux

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université 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. For the cyclical solution, we establish a link with the discrete-time model by Dawid and Kopel (1997). For the steady state solution, we explore the relation to Clark's (1976) continuous control model. Our model can admit convex and concave profit functions and allows the integration of different stock dependent cost functions. We show that the strict convexity of the profit function is only a special case of a more general condition, related to submodularity, that ensures the existence of optimal cyclical policies.

Suggested Citation

  • Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2010. "Optimality of Impulse Harvesting Policies," Working Papers hal-00864187, HAL.
    • Handle: RePEc:hal:wpaper:hal-00864187
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-00864187v1
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    References listed on IDEAS

    as
    1. Tracy R. Lewis & Richard Schmalensee, 1979. "Non-convexity and Optimal Harvesting Strategies for Renewable Resources," Canadian Journal of Economics, Canadian Economics Association, vol. 12(4), pages 677-691, November.
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    6. Dawid, Herbert & Kopel, Michael, 1997. "On the Economically Optimal Exploitation of a Renewable Resource: The Case of a Convex Environment and a Convex Return Function," Journal of Economic Theory, Elsevier, vol. 76(2), pages 272-297, October.
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    9. Hartman, Richard, 1976. "The Harvesting Decision When a Standing Forest Has Value," Economic Inquiry, Western Economic Association International, vol. 14(1), pages 52-58, March.
    10. Akiomi Kitagawa & Akihisa Shibata, 2005. "Endogenous growth cycles in an overlapping generations model with investment gestation lags," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 751-762, April.
    11. Jess Benhabib & Kazuo Nishimura, 2012. "Competitive Equilibrium Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 75-96, Springer.
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    Citations

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    Cited by:

    1. 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.
    2. Grass, D. & Chahim, M., 2012. "Numerical Algorithms for Deterministic Impulse Control Models with Applications," Discussion Paper 2012-081, Tilburg University, Center for Economic Research.
    3. 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.
    4. 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.
    5. 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.

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    More about this item

    Keywords

    optimal control; Impulse control; renewable resource economics; Submodularity;
    All these keywords.

    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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