In this note I consider a family of discrete-time intertemporally separable optimization problems with unbounded horizon in which the objective is parameterized by a finite dimensional vector. Under standard assumptions, I show that optimal solutions vary smoothly with the initial state and the vector of parameters. These results provide a basic framework to develop the familiar methods of comparative analysis in a dynamic setting. Likewise, the local analysis of equilibria set out by Kehoe, Levine, and Romer [ J. Econ. Theory 50 (1990), 1–21] is extended here to economies with general equilibrium dynamics.