Time Invariant Decision Rules and Land Development: A Dynamic and Stochastic Analysis *

The Arrow-Fisher-Henry (AFH) analysis of land development under uncertainty has been conducted in a two period model. In contemporary times, Capozza and Helsley (1990), Batabyal (1996, 1997, 2000), and others have analyzed the question of land development under uncertainty in a multi-period setting. We extend aspects of this literature by examining the role that bid values play in the decision to develop land over time and under uncertainty. We first delineate a simple decision rule for a landowner who wishes to obtain, at the very least, a minimal level of revenue from land development. Next, we compute the expected value of the bid that results in land development when this decision rule is followed by the landowner. L'analyse Arrow-Fisher-Henry (AFH) du developpement foncier sous des conditions de l'incertitude fut poursuivie en utilisant un modele base sur deux periodes temporelles. Recemment, Capozza et Helsley (1990), et Batabyal (1996, 1997, 2000) entre autres ont analyse la question du developpement foncier sous des conditions d'incertitude dans un contexte multi-temporel. Nous poursuivons quelques aspects de cette litterature en analysant le role que joue les valeurs offertes dans la decision a developper le terrain dans le temps et sous des conditions de l'incertitude. D'abord, nous definissons une regle decisionnelle simple pour un proprietaire de terrain qui voudrait obtenir, au moins, un revenu minimum du developpement de son terrain. Puis, nous calculons la valeur attendue de l'offre qui donne lieu au developpement du terrain quand cette regle est suivie par le proprietaire. Introduction Natural resource and environmental economists have been interested in the question of (potentially irreversible) land development under uncertainty at least since Weisbrod (1964). Since then, Arrow and Fisher (1974) and Henry (1974) have shed considerable light on this development question. Specifically, these researchers have identified a notion known as option value. The so called Arrow-Fisher-Henry (AFH) notion of option value--sometimes called quasi-option value (QOV)--tells us that when development is both indivisible and irreversible, a landowner who disregards the possibility of procuring new information about the effects of such development will invariably underestimate the benefits of preservation and hence skew the binary choice develop/preserve decision in favour of development. Does this AFH result hold when the development decision is divisible? Epstein (1980), Hanemann (1989), and Batabyal (1999) have studied various aspects of this question and have shown that when the development decision is divisible, the AFH result will not hold in general. One can also inquire about the nature of the development decision when this decision is made in a multi-period setting. Because the AFH analysis is conducted in a two period model, the pertinent development question is "Do I develop today or tomorrow?" In contrast, in a multi-period setting, the pertinent question is "When do I develop?" This follows from the fact that a landowner's decision problem now is not over two periods but over n > 2 periods. Markusen and Scheffman (1978), Arnott and Lewis (1979), and Capozza and Helsley (1989) have all studied this question in a deterministic environment. However, when the pertinent development decision is irreversible, the use of a certainty framework will bias results about when land ought to be developed. In fact, as we have learned from the investment under uncertainty literature, (1) uncertainty will typically impart an option value to undeveloped land and delay the development of land from, say, agricultural to urban use. Therefore, if we are to comprehend when land ought to be developed in the presence of an irreversibility, it is essential that we explicitly account for uncertainty. Recently, Titman (1985), Capozza and Helsley (1990), and Batabyal (1996, 1997, 2000) have examined the question of land development under uncertainty. …