The qualitative structure of a class of infinite horizon optimal control problems

Many papers in economics have been written using optimal control theory with what appear to be diverse models. The qualitative results developed in the papers have been related only to the specific model at hand. This paper shows that most of the useful qualitative results occur because the same small number of crucial assumptions are being made about the mathematical structure of the integrand and/or state equation. The taxonomy of models is examined and the seemingly diverse results are unified in this research for the class of one-dimensional, discounted infinite horizon optimal control problems. This is achieved by explicitly linking the local stability of the steady state, the steady state comparative statics and the local comparative dynamics of the optimal control problem.