Delivery lags and buffer stocks in the theory of investment by the firm

Abstract

This paper contains a dynamic model of a firm holding a stock of unfilled orders for output while facing a fixed delivery lag attached to acquiring new capital goods. The model leads to a two-stage optimal control problem where the initial time interval corresponds to the Marshallian short-run and the second interval is the period during which deliveries of capital goods may arrive. Optimality criteria are provided for both time intervals and the behavior of the firm is characterized along both adjustment paths. The short-run decisions of the firm are shown to be tied to long-run decisions planned by the firm.