A Unified Model of Investment Under Uncertainty

Abstract

This paper extends the theory of investment under uncertainty to incorporate fixed costs of investment, a wedge between the purchase price and sale price of capital, and potential irreversibility of investment. In this extended framework, investment is a non-decreasing function of q, the shadow price of installed capital. There are potentially three investment regimes, which depend on the value of q relative to two critical values. For values of q above the upper critical value, investment is positive and is an increasing function of q, as is standard in the theory branch of the adjustment cost literature. For intermediate values of q, between two critical values, investment is zero. Although this regime features prominently in the irreversibility literature, it is largely ignored in the adjustment cost literature. Finally, if q is below the lower critical value, gross investment is negative, a possibility that is ruled out by assumption in the irreversibility of literature. In general, however, the shadow price q is not directly observable, so we present two examples relating q to observable varieties.