Recursive utility and optimal capital accumulation II: sensitivity and duality theory

Summary This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where preferences belong to a class of recursive objectives. We combine the topology used by Becker, Boyd and Sung (1989) with a controllability condition to demonstrate that optimal paths are continuous with respect to changes in both the initial capital stock, and the rate of time preference. Under convexity and an interiority condition, we find the value function is differentiable, and derive a multiplier equation for the supporting prices. Finally, under some mild additional conditions, we show that supporting prices obeying the transversality and multiplier equations are both necessary and sufficient for an optimum.Robert Becker acknowledges the research support of National Science Foundation Grant SES 85-20180. We also thank Gerhard Sorger and the participants at the Northwestern Summer Workshop in Capital Theory and Monetary Economics for their helpful comments and suggestions.