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 to the global oil market predicts substantially higher future oil prices and considerably lower global oil production with the more realistic geological constraints set-up than with the Hotelling simulation. While mainly (small) non-OPEC producers 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. High future oil prices therefore, do not necessarily translate to increased oil supplies on global markets. (c) 2015 Elsevier B.V. All rights reserved.