Comparative dynamics (sensitivity analysis) in optimal control theory

This paper considers an optimal control problem with a parameter and develops a systematic method for comparative dynamics. A sufficient condition for the optimum solution to be differentiable with respect to the parameter is provided. Formulas for computing the derivative are given in the form of initial-value problems of linear differential equations. The possibility of discontinuous optimal controls is fully taken care of. An example of the comparative dynamics is given in terms of a model of optimal capital accumulation.