Reconciling Gray and Hotelling: Lessons from Early Exhaustible Resource Economics

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CONSIDERABLE TIME AND ENERGY have been devoted into the economic study of exhaustible resources (ER) since the early 20th century. The results of these efforts provide a basis for a modern field in ER economics. Like progress in many scholarly fields, ER economics research is characterized by waves in which efforts increase, peak, decrease, bottom out, and then rise again. One such peak of effort came shortly after the 1973 oil embargo of the United States. During this peak, the paper by Harold Hotelling (1931) was identified as the seminal work from earlier periods that had stood the test of time and provided a solid foundation for ER economics: "Hotelling's elegant and comprehensive analysis, his wide ranging conjectures and asides, make the 1931 analysis very nearly the sole source of work in a vigorously growing branch of economics" (Devarajan and Fisher 1981: 71).

The contribution of Lewis Cecil Gray (1913, 1914) to the field of ER economics has only recently begun to be more fully recognized by economists (see, for example, Crabbe 1983 and Smith 1986). The acknowledgment of Gray's work, however, comes at a cost: the literature often bundles and characterizes his contributions as similar to Hotelling's contributions. Nevertheless, the contributions of Gray and Hotelling, other than focusing on ER economics, are significantly different and cannot, except perhaps in special cases, be thought of as a unified economic argument. As a result, the potential for applying ideas elucidated by these respective frameworks that support empirical applications of the economics of ER has not been fully developed in previous research. In this paper, we submit that Gray's and Hotelling's frameworks have the potential to provide primarily distinct contributions, and that this awareness could influence empirical research or the search for evidence in support of Hotelling's r-percent rule. Hotelling's r-percent rule states that during a period of continuous extraction, the price of a resource over time would follow an equilibrium path equivalent to the value society places on the remaining resource stock. Thus, the price gap between the price and the marginal cost of extraction over time would rise with the discount rate. Cairns (1994) notes that Gray's work, by contrast, is quantity, or output, focused, and incorporates a possibility of a firm's adjusting its rate of production, so the difference between the anticipated price and the marginal cost, assuming a U-shaped cost curve, would increase with the rate of interest.

The aim of this paper is twofold: first, to explore a reevaluation of Gray's relative value to Hotelling's and, second, to use a model as an illustration that helps establish key distinctions between Gray and Hotelling. The remainder of the paper is structured as follows. In Section II, conceptual issues in the economics of ER associated with Gray and Hotelling are surveyed, and general differences between the works by Gray and Hotelling are highlighted. A model, formally examining the implications of Gray's assumptions in contrast to Hotelling's assumptions, which have not been explored before, is introduced. This model, presented in Section III, is in fact Gray's example of spatially identifiable, heterogeneous deposits with fixed costs. Results and policy implications are presented in Section IV.


Concepts in Economics of Exhaustible Resources: Gray and Hotelling

GRAY'S WORK has been associated more with classical economics, although his contribution is mostly neoclassical due to the marginal analysis presented and the emphasis of economic substitution in input use (Crabbe 1983). The literature refers to one or both authors, and only a few contributions have contrasted differences between the analyses presented by Gray and Hotelling (Crabbe 1983, 1986; Smith 1986; Cairns 1994). Hotelling's theoretical framework had a major impact in the early 1970s, about 40 years after its publication, at a time when economists were focused on global resource issues and the management of natural resources was on the verge of becoming a full-fledged research field (for example, see Meadows et al. …