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Optimality of Impulse Harvesting Policies

Author

Listed:
  • Erdlenbruch, Katrin
  • Jean-Marie, Alain
  • Moreaux, Michel
  • Tidball, Mabel

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 policies. 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. Copyright Springer-Verlag 2013
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Suggested Citation

  • Erdlenbruch, Katrin & Jean-Marie, Alain & Moreaux, Michel & Tidball, Mabel, 2010. "Optimality of Impulse Harvesting Policies," IDEI Working Papers 603, Institut d'Économie Industrielle (IDEI), Toulouse.
    • Handle: RePEc:ide:wpaper:22541
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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

    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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