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.

Following a peak in US crude oil production nearly 30 years ago, more and more non-OPEC producers have seen their production decline as a result of resource depletion. OPEC on the other hand has extracted a comparatively smaller proportion of its reserve base. Given that non-OPEC discoveries are growing ever limited, we explore the role of reserve additions and OPEC in determining future crude oil supply: we formulate a model that embodies a weak and strong OPEC for varied rates of reserve additions in mature crude oil provinces. Using this geo-economic partial equilibrium model that generates a peak in crude oil production, we show that although potential conventional crude oil resources may seem abundant, OPEC strategy could cause substantial crude oil reserve depletion in non-OPEC countries by 2050 (or even earlier) given likely depletion rates. In addition, we find that reducing reserve decline levels in mature crude oil provinces discourages OPEC from engaging in an overly strategic extraction behavior.

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