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. For the cyclical solution, we establish a link with the discrete-time model by Dawid and Kopel (1997). For the steady state solution, we explore the relation to Clark's (1976) continuous control model. Our model can admit convex and concave profit functions and allows the integration of different stock dependent cost functions. We show that the strict convexity 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.