On the indeterminacy of capital accumulation paths

In neoclassical optimal growth models the stability of the accumulation paths depends on the discount parameter. We prove that, for discount factors small enough, the policy function which describes an optimal path can be of any type. The result is achieved using the notion of α-concavity. We adopt a constructive approach. Given any twice differentiable map we show how to construct an optimal growth problem which produces that map as the optimal policy function. A consequence is that "chaos" can appear in these models. We also provide bounds on the values of the discount parameter for which "indeterminacy" is possible.