Indivisibility and divisibility in land development over time and under uncertainty

The quasi-option value (QOV) literature originated by Arrow et al. (Arrow, K.J., Fisher, A.C., 1974. Environmental preservation, uncertainty, and irreversibility. Quarterly Journal of Economics 88, 312-319) and by Henry (Henry, C., 1974. Option values in the economics of irreplaceable assets. Review of Economic Studies 41, 89-104) is largely concerned with the analysis of two-period models of land development. Our paper extends this literature by analyzing two scenarios in which the decision to develop land is made in a multi-period and stochastic framework. In the first scenario, the development decision is indivisible. In contrast, in the second scenario, the development decision is divisible. Specifically, we study the properties of the indivisible development decision when there is a time constraint on when land is to be developed. We then analyze the ways in which the divisible land development decision depends on the extent of a landowner's landholding and on the number of development opportunities awaiting this landowner.