Modeling Peak Oil and the Geological Constraints on Oil Production

We propose a model to reconcile the theory of inter-temporal non-renewable resource depletion with well-known stylized facts concerning the exploitation of exhaustible resources such as oil. Our approach introduces geological constraints into a Hotelling type extraction-exploration model. We show that such constraints, in combination with initially small reserves and strictly convex
exploration costs, can coherently explain bell-shaped peaks in natural resource extraction and hence U-shapes in prices. As production increases, marginal profits (marginal revenues less marginal extraction cost) are observed to decline, while as production decreases, marginal profits rise at a positive rate that is not necessarily the rate of discount.
A numerical calibration of the model to the world oil market shows that geological constraints have the potential to substantially increase the future oil price. While some (small) non-OPEC producers are found to increase production in response to higher oil prices induced by the geological constraints, most (large) producers’ production declines, leading to a lower peak level for global
oil production.