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

A Rapaport (), S Sraidi and Jean-Philippe Terreaux ()
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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

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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.

Keywords: optimal control; discrete time; infinite horizon; dynamic programming; sustainability; renewable resource management; harvest policies (search for similar items in EconPapers)
Date: 2003-01
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Published in Optimal Control Applications and Methods, 2003, 24, pp.23 - 44. ⟨10.1002/oca.718⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04210849

DOI: 10.1002/oca.718

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