The Timing of Land Development: An Invariance Result

The Arrow-Fisher-Henry (AFH) analysis of land development under uncertainty has been conducted in a two-period model. Recently, Capozza and Helsley (1990) and Batabyal (1995) have addressed the question of land development under uncertainty in a many-period setting. In this paper, aspects of this literature are extended by analyzing the land development question in a Markov decision theoretic framework. Inter alia, it is shown that the timing of land development is invariant to the manner in which a landowner uses information about the consequences of development. Key words: development, information, land, timing, uncertainty. Resource and urban economists have been in-terested in the question of land development under uncertainty-with the development deci-sion being potentially irreversible-at least since Weisbrod and Shoup. Since then, Arrow and Fisher, and Henry have shed considerable light on this development question. Inter alia, these researchers have identified a concept known as option value. The so-called Arrow-Fisher-Henry (AFH) concept of option value-also called quasi-option value-tells us that when development is both indivisible and irre-versible, a landowner who ignores the possibil-ity of obtaining new information about the con-sequences of such development will invariably underestimate the benefits of preservation and, hence, skew the binary choice development de-cision in favor of development. This simple and yet powerful result has been shown to hold in its most general form in a two-period setting. However, the result typi-cally does not hold in more general settings. It has already been shown by Epstein and by Hanemann that when the development decision is divisible, this bias toward development need not arise; indeed, it will not arise unless the de-velopment benefit function is of a rather spe-cific form. Similarly, one can ask about the nature of the development decision when this decision i