Economic Theory

, Volume 52, Issue 2, pp 429–459 | Cite as

Optimality of impulse harvesting policies

  • Katrin Erdlenbruch
  • Alain Jean-Marie
  • Michel Moreaux
  • Mabel Tidball
Research Article

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.

Keywords

Optimal control Impulse control Renewable resource economics Submodularity 

JEL Classification

C61 Q2 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Katrin Erdlenbruch
    • 1
  • Alain Jean-Marie
    • 2
  • Michel Moreaux
    • 3
  • Mabel Tidball
    • 4
  1. 1.Cemagref and UMR G-EAUMontpellier Cedex 5France
  2. 2.INRIA and UMR LIRMMMontpellier Cedex 5France
  3. 3.Toulouse School of Economics at Université Toulouse 1 Capitole, (IDEI and LERNA)ToulouseFrance
  4. 4.INRA and UMR LAMETAMontpellier Cedex 1France

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