We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem:...

In this paper we develop a framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results about the existence and uniqueness of solutions to the Bellman equation through a notion of Banach contractions that generalizes known results for Banach and local...

Governments in modern economies devote much policy attention to enhancing productivity and continue to emphasize its drivers such as investment in R&D. This paper analyzes the relationship between productivity growth and levels of R&D investments. The econometric analysis shows that more than 65...