Optimality of impulse harvesting policies

• DOI: 10.1007/s00199-011-0650-6
• Publication Date: 2011-06-24T17:20:32Z
• Authors: Katrin Erdlenbruch; Alain Jean-Marie; Michel Moreaux; Mabel Tidball
• Keywords: Impulse control; Stock (firearms)

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 pol- icies. 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.