Periodic and chaotic programs of intertemporal optimization models with non-concave net benefit function

In this paper we address the so-called 'inverse optimal problem,' that is the question, given a time path, is it optimal for some intertemporal optimization problem? Whereas in the existing literature the inverse problem is solved for the reduced form models, we consider the more difficult question of how to construct a model in both, the reduced and the primitive form. Using our technique one can guarantee required qualitative properties, not only in reduced, but also in primitive form. To illustrate our constructive approach we apply it to a well-known advertising model. We show that the resulting optimal advertising policy is topologically conjugated to the well-known quadratic map, and hence exhibits topological and ergodic chaos