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Optimality of greedy and sustainable policies in the management of renewable resources

Author

Listed:
  • A Rapaport

    (ASB - Analyse des Systèmes et Biométrie - INRA - Institut National de la Recherche Agronomique)

  • S Sraidi

    (ASB - Analyse des Systèmes et Biométrie - INRA - Institut National de la Recherche Agronomique)

  • Jean-Philippe Terreaux

    (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 consider a discrete-time modelling of renewable resources, which regenerate after a delay once harvested. We study the qualitative behaviour of harvesting policies, which are optimal with respect to a discounted utility function over infinite horizon. Using Bellman's equation, we derive analytically conditions under which two types of policies (greedy and sustainable) are optimal, depending on the discount rate and the marginal utility. For this particular class of problems, we show also that the greedy policy is attractive in a certain sense. The techniques of proof lie on concavity, comparison of value functions and Lyapunov-like functions.

Suggested Citation

  • A Rapaport & S Sraidi & Jean-Philippe Terreaux, 2003. "Optimality of greedy and sustainable policies in the management of renewable resources," Post-Print hal-04210849, HAL.
    • Handle: RePEc:hal:journl:hal-04210849
    DOI: 10.1002/oca.718
    as

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