A Markup Interpretation of Optimal Investment Rules

Abstract

We re-examine the basic investment problem of deciding when to incur a sunk cost to obtain a stochastically¯uctuating bene®t. The optimal investment rule satis®es a trade-off between a larger versus a later net bene®t; we show that this trade-off is closely analogous to the standard trade-off for the pricing decision of a ®rm 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 ®rm's optimal markup of price over marginal cost. This is illustrated with several examples.

Smooth pasting as rate of return equalization

“…This allows a larger audience to appreciate and implement smooth pasting techniques in a wider variety of situations. We also relate results to the elasticity-based rules introduced by Dixit et al (1999) and Sødal (1998). The results are illustrated here using geometric Brownian motion but are also valid for other diffusions.…”

“…The popular real options introduction by Dixit and Pindyck (1994) saves the discussion of smooth pasting for a quite technical appendix, and no simple rules of thumb seem to exist for practitioners. Dixit et al (1999) bridged some of the gap between theory and practice using an analogy between optimal exercise of investment options of the McDonald and Siegel (1986) type and application of standard market power models. Optimal investment can be characterized by an elasticity-based premium, analogous to the markup price chosen by a profit-maximizing monopolist.…”

Factors Affecting Delay Discounting—The Real Option Approach

“…Furthermore, this option vanishes once it is exercised. Therefore, subjects demand a compensation (Dixit et al, 1999).…”

Transport Infrastructure Investment and Demand Uncertainty

“…There is the option theory that attaches an extra value to any project that can be adjusted or postponed until more is known about demand. This theory is now the basis for investments in …rms (Dixit and Pindyck [4]) and is also used in cost bene…t assessments (Graham [7]). Another related debate is the use of a higher discount rate in function of the riskiness of the project.…”

“…The combination of a high …xed cost and a constant marginal capacity cost allows us to approximate cost functions with increasing returns to scale 4 . For air, we assume that the …xed costs can be neglected and that the variable costs per passenger (l a ) are constant.…”