Complex solutions of nonconcave dynamic optimization models

Summary In this paper we consider a class of time discrete intertemporal optimization models in one dimension. We present a technique to construct intertemporal optimization models with nonconcave objective functions, such that the optimal policy function coincides with any pre-specifiedC² function. Our result is a variant of the approach presented in a seminal paper by Boldrin and Montrucchio (1986). Whereas they solved the inverse problem for the reduced form models, we address the different question of how to construct both reduced and primitive form models. Using our technique one can guarantee required qualitative properties not only in reduced, but also in primitive form. The fact that our constructed model has a single valued and continuous optimal policy is very important as, in general, nonconcave problems yield set valued optimal policy correspondences which are typically hard to analyze. To illustrate our constructive approach we apply it to a simple nonconcave model.We are grateful for the helpful comments of L. Montrucchio, K. Nishimura, T. Mitra and an anonymous referee. Financial support of the Austrian Science Foundation under contract No. P7783-PHY and No. J01003-SOZ is gratefully acknowledged. This paper was written while M. Kopel was visiting the Department of Economics, Cornell University.