Optimality of impulse harvesting policies

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, <CitationRef CitationID="CR1">1985</CitationRef>) and Dawid and Kopel (J Econ Theory 76:272–297, <CitationRef CitationID="CR6">1997</CitationRef>). For the steady-state solution, we explore the relation to Clark’s (<CitationRef CitationID="CR3">1976</CitationRef>) continuous control model. Copyright Springer-Verlag 2013