On the optimal control of an animal-vegetation ecological system

This paper studies the optimal control of an animal-vegetation system where growth in the animal stock is density independent. The ecological system is shown to have a limit cycle, under certain parameter values, but can also be stabilized by a simple harvesting rule. The managing unit maximizes profits from selling the meat, over an infinite planning horizon. With a domestic animal stock, costs are related to keeping a large animal stock, and not to harvesting. An optimal steady state is described, and the effects of parameter changes is discussed, in particular the discount rate. The effect of discounting on the optimal stock size is demonstrated to be ambiguous. The optimal approach path is derived analytically, and is shown to be a saddle path in state-state space. The model is exemplified with a numerical analysis that compares the discounted profit from the optimal harvest regime to a management regime implying a constant harvest ratio. Finally, a postitive stock effect is discussed. JEL Codes: C61, C62, C63, Q24, Q57