Two-stage optimal control problems with an explicit switch point dependence: Optimality criteria and an example of delivery lags and investment

Abstract

This paper provides necessary conditions for the solution of two-stage optimal control problems where the switch point is a choice variable and where the switch point appears as an argument of the integrands in each integral which comprise the criterion index to be maximized. Problems of this variety have arisen in the exhaustible resource and neoclassical investment literature. Using the conditions necessary for the solution of these problems, we analyze an example of optimal investment in the presence of delivery lags and show how the optimal switch point (delivery lag) responds to shifts in exogenous parameters.