# Investment under Uncertainty

Avinash K. Dixit
Robert S. Pindyck
Pages: 476
https://www.jstor.org/stable/j.ctt7sncv

1. Front Matter
(pp. i-vi)
(pp. vii-x)
3. Preface
(pp. xi-xiv)
Avinash K. Dixit and Robert S. Pindyck
4. Part I. Introduction
• Chapter 1 A New View of Investment
(pp. 3-25)

Economics defines investment as the act of incurring an immediate cost in the expectation of future rewards. Firms that construct plants and install equipment, merchants who lay in a stock of goods for sale, and persons who spend time on vocational education are all investors in this sense. Somewhat less obviously, a firm that shuts down a loss-making plant is also “investing”: the payments it must make to extract itself from contractual commitments, including severance payments to labor, are the initial expenditure, and the prospective reward is the reduction in future losses.

Viewed from this perspective, investment decisions are ubiquitous....

• Chapter 2 Developing the Concepts Through Simple Examples
(pp. 26-56)

Firms make, implement, and sometimes revise their investment decisions continuously through time. Hence much of this book is devoted to the analysis of investment decisions as continuous-time problems. However, it is best to begin with some simple examples, involving a minimal amount of mathematics, in which investment decisions are made at two or three discrete points in time. In this way, we can convey at the outset an intuitive understanding of the basic concepts. In particular, we want to show how the irreversibility of an investment expenditure affects the decision to invest, and how it requires modification of the standard...

5. Part II. Mathematical Background
• Chapter 3 Stochastic Processes and Ito’s Lemma
(pp. 59-92)

This chapter and the next provide the mathematical tools—stochastic calculus, dynamic programming, and contingent claims analysis—that will be used throughout the rest of this book. With these tools, we can study investment decisions using a continuous-time approach, which is both intuitively appealing and quite powerful. In addition, the concepts and techniques that we introduce here are becoming widely used in a number of areas of economics and finance, and so are worth learning even apart from their application to investment problems.

This chapter begins with a discussion of stochastic processes. We will begin with simple discrete-time processes, and...

• Chapter 4 Dynamic Optimization under Uncertainty
(pp. 93-132)

Time plays a particularly important role for investment decisions. The payoffs to a firm’s investment made today accrue as a stream over the future, and are affected by uncertainty as well as by other decisions that the firm or its rivals will make later. The firm must look ahead to all these developments when making its current decision. As we emphasized in Chapter 2, one aspect of this future is an opportunity to make the same decision later; therefore the option of postponement should be included in today's menu of choices. The mathematical techniques we employ to model investment decisions...

6. Part III. A Firm’s Decisions
• Chapter 5 Investment Opportunities and Investment Timing
(pp. 135-174)

With the mathematical preliminaries behind us, we can now turn to the analysis of investment decisions under uncertainty. In this chapter and throughout this book, our main concern will be with investment expenditures that have two very important characteristics. First, the expenditures are at least partly irreversible; in other words,sunk coststhat cannot be recovered. Second, these investments can be delayed, so that the firm has the opportunity to wait for new information to arrive about prices, costs, and other market conditions before it commits resources.

As the simple examples in Chapter 2 suggested, the ability to delay an...

• Chapter 6 The Value of a Project and the Decision to Invest
(pp. 175-212)

The basic model of irreversible investment in Chapter 5 demonstrated a close analogy between a firm’s option to invest and a financial call option. In the case of a call option, the price of the stock underlying the option is assumed to follow an exogenously specified stochastic process, usually a geometric Brownian motion. In our model of real investment, the corresponding state variable was the value of the project,V, for which we stipulated an exogenous stochastic process.

However, as we explained at the beginning of Chapter 5, lettingVfollow an exogenous stochastic process, and particularly a geometric Brownian...

• Chapter 7 Entry, Exit, Lay-Up, and Scrapping
(pp. 213-244)

In the previous chapter we showed how one can first value a project, and then value the option to invest in the project and determine the optimal investment rule. Our starting point was a stochastic process for the evolution of the price of the project’s output, and hence uncertainty over the future flow of operating profits. This flow of profits could sometimes become negative, and we assumed that at such times the firm could suspend operation, and resume it later if the profit flow turned positive, without paying any lump-sum stopping or restarting costs.

For many projects, this assumption of...

7. Part IV. Industry Equilibrium
• Chapter 8 Dynamic Equilibrium in a Competitive Industry
(pp. 247-281)

In chapters 5 through 7, we examined a variety of investment and disinvestment decisions for a single firm. Throughout, we assumed that the firm has a monopoly right to invest in a given project, and we ignored the possibility of other firms entering in competition.¹ The profit flows of an operational project were subject to ongoing shocks. Since we were assuming that the project would yield a fixed output flow, we could model these shocks as an exogenous price process. We found that the textbook Marshallian present value criteria or comparisons of price and cost were very far from the...

• Chapter 9 Policy Intervention and Imperfect Competition
(pp. 282-316)

In the previous chapter we developed a basic model of competitive industry equilibrium in which each firm makes its irreversible investment decisions in an environment of ongoing uncertainty, knowing that all other firms are similarly situated and are making similar decisions. We considered industrywide as well as firm-specific uncertainty, and found that both had the effect of making firms less eager to invest, but for different reasons. With industry-wide uncertainty, each firm knows that others will enter or expand in response to favorable developments just as it does. The resulting increase in supply will dampen the, price increase, thereby reducing...

8. Part V. Extensions and Applications
• Chapter 10 Sequential Investment
(pp. 319-356)

In this and the following chapters we return to the investment decisions of a single firm. In Chapters 5, 6, and 7, we developed a series of models in which the firm must decide when (and whether) to invest in a single project. In Chapter 5 we assumed that the value of that project evolved as an exogenous stochastic process, and we derived the optimal investment rule. In Chapter 6 we allowed the price of the project’s output to evolve as an exogenous stochastic process, and then, given a variable cost of production, we derived both the value of the...

• Chapter 11 Incremental Investment and Capacity Choice
(pp. 357-393)

The models of individual firms’ investment decisions that were developed in Chapters 5-7, and the models of industry equilibrium in Chapters 8 and 9, were based on a simple discrete unit of investment, namely, a single project of a given fixed size. In Chapter 10 we continued to examine a single project, but we accounted for the fact that completion of a project often requires a sequence of steps, each of which increases the sunk cost that is committed to the project. In this chapter, we examine a firm’s investment decisions in a more general context. We allow each firm...

• Chapter 12 Applications and Empirical Research
(pp. 394-428)

We hope that by this point we have made it quite clear that the “options” approach presented in this book is applicable to a broad range of investment problems. Our numerical calculations were guided by numbers typical of some specific industries, for example, copper mining in Chapters 7 and 8, and oil tankers in Chapter 7. However, for the most part our models were simple and stylized. In this chapter we present some examples that illustrate actual applications of the techniques, and their extension to other problems and issues.

We will begin with a problem faced regularly by companies in...

9. References
(pp. 429-444)
10. Symbol Glossary
(pp. 445-468)