How to eat a cake of unknown size: A reconsideration

The paper revisits the issue of the optimal depletion of an exhaustible resource stock of uncertain size by recasting it in terms of the hazard function. In addition to re-establishing some of the existing results, it obtains a complete, qualitative characterization of the optimal depletion program for a fairly large array of continuous probability distributions that are likely to describe the initial stock distribution. It turns out that an important feature of the optimal program is the eventual monotonicity of the optimal extraction-cum-consumption rate, so characteristic of the certainty scenario. Additional results regarding the duration of the optimal planning horizon and comparison with the situation of perfect certainty provide further insight into the nature of the optimal depletion program for the iso-elastic utility function.