Abstract
This paper considers a strategy for the extraction and production of non-renewable resources that are finite in quantity. Specifically, we illustrate empirical data on reserves, production, consumption, and price evolution for fossil fuel. Our model is an intertemporal model of a short decision time horizon with a monopolistic resource producer extracting non-renewable resources. The model is solved numerically using a finite horizon solution method called Nonlinear Model Predictive Control (NMPC), which approximates well models with a longer decision time horizon. Consistent with the results of recent empirical studies, our numerical solution method shows a U-shaped path for the price and an inverted U-shaped path for the extraction rate, in the case of modest initial stock of proved reserves.
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