Topological entropy of policy functions in concave dynamic optimization models

Abstract We derive a simple relationship between the topological entropy of the optimal policy function of a concave dynamic program and the underlying discount factor. It follows from this relationship that solutions that exhibit very complicated dynamics can only occur in models with small discount factors. Our result is, therefore, a converse to the general possibility theorem of Boldrin and Montrucchio ( Journal of Economic Theory , 1986, 40, 26–39).

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