The Economic Journal, 109 (Apn'l), 179-189. 0 Royal Economic Society 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 lJF, UK and 350 Main Street, Malden, MA 02148, USA. A MARKUP INTERPRETATION OF OPTIMAL INVESTMENT RULES* Avinash Dixit, Robert S. Pindyck and Sigbjlm Sldal We reexamine the basic investment problem of deciding when to incur a sunk cost to obtain a stochastically fluctuating benefit. The optimal investment rule satisfies a trade-off between a larger versus a later net benefit; we show that this trade-off is closely analogous to the standard trade-off for the pricing decision of a firm that faces a downward sloping demand curve. We reinterpret the optimal investment rule as a markup formula involving an elasticity that has exactly the same form as the formula for a firm's optimal markup of price over marginal cost. This is illustrated with several examples. Consider what is probably the most basic irreversible investment problem: a project can be undertaken that requires a sunk cost C and yields a benefit V. The cost is known and constant over time, but the benefit (measured as the present value at the time the cost is incurred) fluctuates as an autonomous Markov process {Vt) with continuous sample paths.1 Time is continuous, and at each point the firm must decide whether to invest or to wait and reconsider later. The firm's objective is to maximise the expected present value of net benefits, with a discount rate that is constant and equal to p. At time t, all of the information about the future evolution of V is sum- marised in the current value Vt. Therefore the optimal decision rule must be of the form: invest now if Vt is in a certain subset of possible values, otherwise wait. Also, because the process is autonomous and the discount rate is constant, the optimal rule is independent of time. As long as the process has positive persistence-i.e., a higher current value Vt shifts the distribution of the random value V, at any future time s to the right in the sense of first-order stochastic dominance-the rule will be of the form: invest now if Vt is at or above a critical threshold v*, otherwise wait.2 The problem therefore boils down to determining the optimal choice for the threshold v*. As first shown by McDonald and Siege1 (1986), the optimal V* exceeds C by a 'markup', or premium, that reflects the value of waiting. One can think of the firm as having an option to invest that is akin to a financial call option, and, like the call option, is optimally exercised only when 'deep in the money', i.e., when the stock price is at a premium over the exercise price. Thus one can solve the firm's investment problem (and determine the optimal markup) by finding the value of the firm's option to invest and the optimal exercise rule.3 * This research was supported by the National Science Foundation through grants to Dixit and Pindyck, and by M.I.T.'s Center for Energy and Environmental Policy Research. Our thanks to John Leahy and an anonymous referee for helpful comments. ' V may itself be explained in terms of other more basic economic variables like prices of output and/or inputs; we work simply with the end result. See Dixit and Pindyck (1996), pp. 104, 128-9 The option is valued assuming it is exercised optimally, so the valuation of the optiorl yields the optimal exercise rule. See Dixit and Pindyck (1996).