Hotelling Meets Darcy: A New Model of Oil Extraction

Abstract

For decades resource economists have relied on the seminal Hotelling paper to model extraction and price paths, despite overwhelming evidence of the empirical limitations of the approach. Particularly in oil markets, the shortcomings of the Hotelling approach are evident: for over 100 years real oil prices were basically constant, in marked contrast to the prediction that rents should rise at the rate of interest. A number of explanations have been offered, including the steady ow of newly found deposits and technological advances that might have continually shifted the price path out, thereby obscuring what otherwise would have been the trend towards higher prices. While these aspects are no doubt important the conventional explanation misses what we believe to be a crucial ingredient, namely production constraints that inhibit agents' ability to shift production forward in time. These constraints are rooted in the physical constraints associated with subterranean uid ows, as articulated by Darcy. In particular, Darcy's approach predicts that output from any given well decline exponentially, at an exogenous rate that is dictated by geological features. As such, the only variable under the extractor's control is the number of deposits to open up for extraction. We articulate a model that incorporates these features, use it to generate a predicted market equilibrium price path, and discus the impact of breakthrough innovations upon the price path.