Environment, Uncertainty, and Option Values

We analyze in this chapter decision-making when costs and benefits of an action are uncertain, that is, when future preferences are uncertain. We begin, in Section 2, with the classical analysis by Krutilla et al. (1972) of whether the expected consumer's surplus is a correct measure of the net benefits from the action. It turns out that for one individual, the correct measure is the expected consumer's surplus corrected with one term representing the covariance between the state-contingent consumer's surplus and the state-contingent marginal utility of wealth and a second term representing risk aversion. This corrected measure is what Krutilla et al. (1972) called the option value. Thus the difference between option value and expected consumer's surplus is determined by the covariance between preferences and consumer's surplus and risk aversion. The sign of this difference will therefore depend on these factors. We apply this result to a number of cases in order to derive additional useful results. First we look at the aggregate (over a set of individuals) option value and establish a general result. We then apply this result to the allocation of risk in the context of both public and private goods.In Section 3, we introduce relevant dynamic elements to the general problem of decisions under uncertainty. We analyze actions that may have irreversible effects, but where the decision-maker can improve her information about the true future preferences. This problem was first studied by Arrow and Fisher (1974) and Henry (1974), who showed (as we do in Section 3.2) that when the decision-maker has to choose between two actions, of which one is irreversible, and future benefits are uncertain in the first time period, maximizing expected value will result in a biased result: the irreversible action will be chosen too often. However, this result is based on assumptions of linearity. In order to study the problem without this restriction, we rely on Epstein's (1980) framework, which we present in some detail. The result is that convexity (concavity) assumptions are essential to establish the direction of the bias. We also use Epstein's framework to look at issues such as uncertainty about cost of restoration and uncertainty about irreversibility.All of the results to this point are for models with just two time periods. In Section 4, we analyze the many-period case, adopting a somewhat different analytical framework: stochastic dynamic programming, as presented in Dixit and Pindyck (1994). Additional results in continuous time are developed, drawing on the theory of stochastic processes. We look in particular at the "optimal stopping problem," a useful and important special case, and present an empirical application due to Conrad (1997): when, if ever, to cut an old-growth forest that also yields benefits in its natural state.