On Gray's Rule and the Stylized Facts of Non-Renewable Resources

Cairns, Robert D., Journal of Economic Issues

The economics of non-renewable resources is composed of at least two branches. The better-known branch owes much to a famous paper by Harold Hotelling [1931], which most economists consider to be the first modern article in the field. Hotelling's main concern was with the unfolding of equilibrium through time in the market for a resource. Price at any instant of time was viewed as responding to the total resource stock available to society. As Robert Solow [1974] pointed out, this response was a consequence of the fact that the resource was an asset to society and would in equilibrium have the same rate of return (through capital gains) as other assets. Price would adjust in intertemporal equilibrium so that the divergence between price (or marginal revenue if the market had market power) and marginal cost of extraction would rise at the rate of interest through time. (This follows because, if extracted and sold, a unit of resource would yield the going rate of interest. Only if the value of the resource rose by a like amount would it be left in the ground.) This result has come to be known as Hotelling's r-per-cent rule. Frederick Peterson and Anthony Fisher [1977] have set out clearly the factors that are important to the Hotelling theory. These include the level of aggregate consumption, the level and rate of increase of price as The author is Professor of Economics, Megill University, and a member of the Centre de Recherche et Developpement Economique, Universite de Montreal and of the Laboraloire d'Economie Quantitative d'Aix-Marseille. The author wishes thank Carl Calantone, Gdrard Gaudet, John Hartwick, Anne Mayhew, Nguyen van Quyen, and a referee for comments and the FCAR and SSHRC for financial support. determinative of aggregate consumption, and the evolution of aggregate extraction costs as an influence on price, among others.

What is less often observed is that there is another tradition that abstracts from market equilibrium and deals with the "micromicro" aspects of production from deposits of non-renewable resources. This approach explains the effects of taxation and other public policies, investment, the physical and economic characteristics of the deposit, the size of the firm, and so on, on the rate of production from the individual mine or well. This branch looks into the black box of details neglected in the Hotelling branch. Almost a generation before Hotelling wrote, Lewis C. Gray [1913; 1914] discussed the relation between the two branches. He attempted to integrate the theory of the mine and the theory of optimal usage, optimal pricing, and the role of the interest rate.(1) His use of micro-micro considerations from the theory of the mine as the basis for the study of optimality and of market equilibrium provides a fugue for the present paper. Gray concluded that a (price-taking) firm facing u-shaped costs would adjust its rate of production (its marginal cost) so that the divergence between anticipated price and marginal cost would rise at the rate of interest. This would occur whatever the anticipated equilibrium path of price, the benchmark being a constant price through the life of a mine. This result could justifiably be called Gray's r-per-cent rule.

Meanwhile, in the Hotelling branch of the theory, an impasse has developed. Empirical studies have had (at best) mixed success in reconciling observation and theoretical predictions. As a result, several modifications--one might call them epicycles-have been proposed in an attempt to force observations to be consistent with theory. The object of the economics of non-renewable resources has been to describe what one observes by a series of stylized facts and then to explain these stylized facts in a way that is both sophisticated and interesting in the context of neoclassical economics. The thesis of the present paper is that three of the stylized facts need to be rethought.

What needs recognition is first that non-renewable resources are heterogeneous; this is a fundamental aspect to the rate of their exploitation, rather than exhaustibility. Among other things, heterogeneity renders the marginal cost of production and the very level of reserves endogenous to economic decision making. Attention to such decisions is central to greater understanding of the nature of the market equilibrium. Heterogeneity also implies that there are methodological difficulties whenever one attempts to study aggregations of these resources. Conceptual, as well as statistical, biases pervade the more common types of aggregation that have been used to tty to detect the influence of Hotellings r-per-cent rule. Second, investment is a central, but almost neglected, aspect of resource supply. Non-renewability exerts an influence mainly through the choice of capacity. Technically, capacity constraints and non-convexities affect the optimal conditions of exploitation at the mine level.

Third, largely because of heterogeneity, strong informational asymmetries affect policymaking for these industries.

After an overview of some of the problems that have afflicted the Hotelling branch, the three stylized facts will be discussed. An important part of the discussion is how the micro-micro aspects of production can affect public policy in ways not emphasized in much of the theoretical economic literature.

The Impasse

Let us begin with an informal tour d'horizon. The Hotelling model, as modified to date, almost always predicts that prices of non-renewable resources will increase through time; in the simplest models, the rate of increase is society's rate of discount. But 10 years before the first major increase in the price of oil by OPEC, Harold Barnett and Chandler Morse [1963] found that the price of forest products had increased, but that the price of minerals had diminished since the beginning of the century and even before.

Following a general line of argument inspired by Solow [1957], the explanation seemed evident: technological change had reduced the cost of production so that, even with the diminution of reserves, and even as aggregate consumption increased, price remained the same or decreased. Margaret Slade [1982] formulated a model in which technological progress could account for the price of metals falling for fairly long periods before rising. Her results were consistent with an updated investigation by Barnett [1977], who found that the prices of metals seemed to have begun to rise in the United States.

However, a study of the path of metal prices by Geoffrey Heal and Michael Barrow [1980] found no regularity in the behavior of prices across metals. Jeff Frank and Mark Babunovic [1985], too, found that different metals had different price paths. Moreover, naive, time series models performed as well as or better than more sophisticated ones in the Hotelling tradition [V. Kerry Smith 1981]. Slade [1988] found that prices of metals were well described as martingales, i.e., that there was no significant trend and all changes could be viewed as essentially random.

But why did prices rise in the forest sector? There had been rapid increases in demand for wood products, but there had been at least comparable increases in demand for mineral products [Gavin Wright 1990]. Was it possible to believe that technological progress had been so rapid in the mining sector as to overcome the non-renewability of the resource but so slow in the forest sector, with its more renewable resources, to produce such a striking difference of performance?

One could …

Questia, a part of Gale, Cengage Learning. www.questia.com
Publication information: Article title: On Gray's Rule and the Stylized Facts of Non-Renewable Resources. Contributors: Cairns, Robert D. - Author. Journal title: Journal of Economic Issues. Volume: 28. Issue: 3 Publication date: September 1994. Page number: 777+. © 1999 Association for Evolutionary Economics. COPYRIGHT 1994 Gale Group.

This material is protected by copyright and, with the exception of fair use, may not be further copied, distributed or transmitted in any form or by any means.