Faced with the choice between preserving and developing a natural resource in the presence of uncertain environmental externalities, the social return to undertaking development is stochastic. When development is irreversible and the decision-maker can defer commencement, there is value to new information that is revealed over time which reduces the uncertainty about the externalities. The assessment is therefore one of how much to develop and when to begin development. This approach to the problem differs from conventional cost benefit analysis and optimal extraction models. The former asks the question of whether to invest a given amount and the latter asks how much is optimal to invest. In this paper a model is developed which identifies both the level and timing of investment which are socially optimal. The solutions are found using optimal stopping techniques a single stochastic state variable, environmental cost and two control variables, timing and scale of development. Initially, the problem is solved for an omnipotent social planner, who makes the time and scale decisions. This is followed by consideration of cases in which one or both decision variables are controlled by private decision-makers. As expected, it is shown that private optimal level of investment exceeds that which is socially optimal. We find that if the social planner can control only investment timing then for levels, which exceed the social optimum, it will pay to wait for environmental costs to fall below the level corresponding to the social optimum. Conversely, level of investment which are low relative to the social optimum, may never generate sufficient private returns to offset the increment to environmental cost. The antecedents to this work are found in the environmental economics literature on quasi-option value and in the finance literature on options and investment.
Decision under uncertainty Environmental externalities