We consider dynamic optimization problems on one-dimensional state spaces. Un- der standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation...

We modify the growth model with horizontal innovations from Romer (1990) and Jones (1995) by assuming that researchers can determine the quality of the products they invent. Because research effort increases with product quality, the researchers face a tradeoff between the quantity and the...

The authors derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be...