A Note on Competitive Investment under Uncertainty

Uncertainty over future output prices or input costs can affect investment by a riskneutral firm in two opposing ways. First, it can increase the value of the marginal unit of capital, which leads to more investment. This only requires that the stream of future profits generated by the marginal unit be a convex function of the stochastic variable; by Jensen's inequality, the expected present value of that stream is increased. This result was demonstrated by Richard Hartman (1972) and later extended by Andrew Abel (1983) and others. In their models, constant returns to scale and the substitutability of capital with other factors ensure that the marginal profitability of capital is convex in output price and input costs. Even with fixed proportions, however, this convexity can result from the ability of the firm to vary output, so that the marginal unit of capital need not be utilized at times when the output price is low or input costs are high. ' If investment is irreversible and can be postponed, a second effect of uncertainty is to create an opportunity cost of investing now, rather than waiting for new information to arrive before committing resources. This increases the full cost of investing in a marginal unit of capital, which reduces investment.2 Hence the net effect of uncertainty on irreversible investment depends on the size of this opportunity cost relative to the increase in the value of the marginal unit of capital. The sign of the net effect is significant because of its possible policy implications. Pindyck (1988) and Giuseppe Bertola (1989) developed models in which a firm faces a downward-sloping demand curve and found the net effect to be negative. Ricardo Caballero (1991) has recently studied investment by an individual firm facing a stochastically shifting demand curve. He shows that, as returns to scale become constant and the elasticity of demand faced by the firm rises, this opportunity cost of investing now rather than waiting approaches zero. Thus, in the limit of constant returns and an infinitely elastic demand curve, an increase in uncertainty tends to raise rather than decrease current investment, even if that investment is irreversible. It is important to stress that Caballero's limiting result treats the firm in isolation and describes the effect of a meanpreserving increase in price uncertainty, and not an increase in industry-wide demand uncertainty. This note shows that, in a competitive market, the key interactions between irreversibility and uncertainty occur at the industry level and can only be understood by making price and industry output endogenous.3 Doing so restores the positive opportunity cost associated with irreversible investment. In addition, Caballero's result is based on a model with convex adjustment costs. An innovative aspect of the model is that these costs can be asymmetric, thereby allowing for partial or complete irreversibility; complete irreversibility corresponds to a cost of * Massachusetts Institute of Technology, Cambridge, MA 02139. This work was supported by the National Science Foundation under Grant No. SES-8618502, and by MIT's Center for Energy Policy Research. My thanks to Julio Rotemberg and especially Ricardo Caballero for very helpful comments and discussions. 1Then the marginal profit of capital at each time t in the future is max[O,(pt ct)], where ct is variable cost. Thus, a unit of capital represents a set of all options on future production, which are worth more the greater the variance of pt or ct. 2For a detailed discussion of this point and a survey of the recent literature on irreversibility and its implications for investment and market evolution, see Pindyck (1991). 3Studies that make price endogenous include Steven Lippman and Richard Rumelt (1985), Avinash Dixit (1989, 1991), and John Leahy (1990).