Two-Stage Optimal Control Problem Appearing in the Investment Policy Study for Delivery Lag Environment

Recent studies of optimal investment decisions for firms whose capital goods are subject to a delivery lag have shown the need for a solution for a control problem with a time-delay argument in the objective function. Necessary conditions for such problems are obtained by reducing them to a two-stage optimal control problem under a set of simple assumptions. A special case is also studied where a sufficient condition for non-existence of the switching of stages is derived.