On optimal cycles in dynamic programming models with convex return function

In this paper we study the behavior of optimal paths in dynamic programming models with a strictly convex return function. Such a model has been inves tigated in Dawid and Kopel (1997) who assume that the growth of a renewable resource is governed by a piecewise linear function. We prove that in thei r model the optimal cycles undergo the following qualitative changes or bif urcations: a cycle of period n "bifurcates" into a cycle of period n + 1 fo r increasing elasticity of the return function. We also show that under the assumption of a concave differentiable growth function the qualitative pro perties of the optimal policy remain valid: oscillating behavior is optimal . Furthermore, we demonstrate numerically that the period of a cyclic optim al path increases if the convexity of the return function (measured by the elasticity) increases.