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 EconTheory76:272–297, 1997). For the steady-state solution, we explore the relation to Clark’s (1976) continuous control model.
Optimality of impulse harvesting policies
14 January 2014