Optimal Capital Policy With Irreversible Investment

Abstract : The paper analyzes investment policy for a firm which cannot disinvest faster than its capital depreciates. The model discussed assumes that there is a single capital good and that the firm's profit is a time-varying function of the size of the capital stock. Using methods of mathematical control theory it is shown that the optimal policy consists of alternating regimes in which positive gross investment is or is not undertaken; prices are derived which can be used as a guide to correct policies. These results are contrasted with the case where disinvestment is allowed (that is, where capital goods can be bought or sold by the firm at a fixed price). An alogrithm for finding the intervals where investment will take place is presented.