On the Economically Optimal Exploitation of a Renewable Resource: The Case of a Convex Environment and a Convex Return Function

We investigate optimal policies for the exploitation of a renewable resource subject to a concave growth function and a convex return function. We prove an important result on the elasticity of the objective function and apply it to give a characterization of the optimal harvesting paths in this class of models. In particular, we derive conditions such that all optimal programs converge to a fixed point or to a cycle of finite period, and hence result in the conservation of the resource. We also show which assumptions guarantee that extinction of the stock is optimal. That nonconvex preferences or technologies cause problems for economic theory is well-known. As our model can formally be interpreted as an optimal growth model with nonconcave utility function, our results are a further contribution on the dynamics of optimal paths in the general class of economic models with nonconcavities. Journal of Economic Literature Classification Numbers: C61, E32, Q20. 1997 Academic Press