HOW TO DO COMPARATIVE DYNAMICS ON THE BACK OF AN ENVELOPE IN OPTIMAL-CONTROL THEORY

The dynamic primal-dual methodology of Caputo (1988) is extended and applied to a general nonautonomous optimal control problem with a fixed and finite time horizon, a fixed vector of initial states, a free vector of terminal states, a time-independent vector of parameters, and a vector of nondifferential constraints on the state and control variables. A symmetric negative semidefinite matrix subject to constraint is shown to characterize the qualitative properties of the model as implied by the dynamic maximization assertion. © 1990.