Econometric Modelling of World Oil Supplies: Terminal Price and the Time to Depletion

This paper develops a novel approach by which to identify the price of oil at the time of depletion; the so-called "terminal price" of oil. It is shown that while the terminal price is independent of both GDP growth and the price elasticity of energy demand, it is dependent on the world real interest rate and the total life-time stock of oil resources, as well as on the marginal extraction and scarcity cost parameters. The theoretical predictions of this model are evaluated using data on the cost of extraction, cumulative production, and proven reserves. The predicted terminal prices seem sensible for a range of parameters and variables, as illustrated by the sensitivity analysis. Using the terminal price of oil, we calculate the time to depletion, and determine the extraction and price profiles over the life-time of the resource. The extraction profiles generated seem to be in line with the actual production and the predicted prices are generally in line with those currently observed.