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 re source subject to a concave growth function and a convex return functi on. We prove an important result on the elasticity of the objective fu nction and apply it to give a characterization of the optimal harvesti ng 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 resourc e. We also show which assumptions guarantee that extinction of the sto ck is optimal. That nonconvex preferences or technologies cause proble ms for economic theory is well-known. As our model can formally be int erpreted as an optimal growth model with nonconcave utility function, our results are a further contribution on the dynamics of optimal path s in the general class of economic models with nonconcavities. (C) 199 7 Academic Press.