Hotelling Rule Research Articles

Capital-Resource Substitution and the Discount Effect in Depletable Resources

It is a central proposition of the economics of natural resources that an increase in the discount rate will cause an increase in the rate of extraction for depletable minerals. This traditional discount derives from treating the resource stock as a kind of capital, which will be left in unprocessed form only when the opportunity cost of so doing is low (the Hotelling Rule [10]). This relationship is a cornerstone of the contention by some resource economists that a competitive resource industry extracts too fast, for it is held that risk raises the discount rate used by resource firms above the optimal rate for society. The high real discount rates of recent years, in this view, were also seen as a major contributor to the depressed mineral markets of the early 1980s. Mineral extraction and processing is highly capital-intensive, however, and the opportunity cost of capital will be increased by a higher discount rate. When this disinvestment effect is included Gordon [5], in fact, showed that the overall discount is ambiguous. Neher [13] and Farzin [2], employing specialized assumptions concerning the extractive technology, subsequently showed the sign of the to depend on the relative present values of capital and resource costs in overall mineral extraction and processing.' The purpose of this paper is to extend Neher and Farzin's result by analyzing the discount in terms of general resource industry characteristics such as the elasticity of demand and of substitution, as well as the shares of capital and unprocessed resources in overall cost. We then attempt to apply our results in the third section of the paper using parameters estimated by others for a number of resource industries. Given these parameters it appears that the usual effects of discount changes do apply with respect to the value and price of the unprocessed resource, an increase in the discount rate increasing the demand and lowering the value of the raw mineral, but this is not the case with respect to the processed resource. Because of relatively high capital intensity, over half of the mineral industries surveyed appear to behave as non-resource industries in that they can be expected to reduce overall processed mineral output in response to a discount rate increase. 1. Neher, following Gordon, employed a model in which mineral output is identical with the raw resource input, and in which capital cost is a fixed proportion of the total cost of extracting the resource. This implies the average cost of extraction is simply the sum of average capital and resource costs, unlike in the model to follow, and could realistically apply only to the very first stage of mineral processing.

The role of investment in multiple-deposit extraction: Some results and remaining puzzles

Papers by Olsen and by Cairns and Lasserre analyze equilibrium in a resource industry where deposit quality varies and where extraction requires capital investment. The papers substantially qualify the conventional understanding of such matters as the form of Hotelling's rule, the role of deposit size, the simultaneous extraction from deposits of different quality, and the price path. The argumentation, however, à intricate and the crucial role of investment as such à not easily distinguishable. We clarify the intuition behind the results, bring out the role of the various assumptions, and raise important remaining issues.

Exhaustible Resources: A Theory of Exploration

The paper presents a theory of exploration for exhaustible resources. Exploration serves both to find new reserves and obtain information about potential reserves. Although any realized time path of the resource price fails to obey the Hotelling rule, the expected resource price does increase exponentially through time at the rate of discount. We obtain sharper results when the resource is assumed to be distributed randomly throughout the exploration region and follows a Poisson process with parameter λ. Consumption and exploration decisions are investigated for both the case where λ is known and the case where λ is unknown.

The Evolution of Natural Resource Prices under Stochastic Investment Opportunities: An Intertemporal Asset-Pricing Approach

The authors consider the competitive equilibrium of an economy with technological uncertainty in the production of a composite good and in the extraction of a nonrenewable natural resource. The familiar Hotelling-type rule takes the form of the intertemporal asset-pricing equation of portfolio theory. It characterizes the evolution of the resource price. In its so-called consumption-beta formulation, it predicts that the expected excess return to holding the resource in the ground is proportional to the covariance between the return to holding the resource and the rate of change of per capita consumption. This suggests a framework for testing the Hotelling rule. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

New Qualitative Properties in the Competitive Nonrenewable Resource Extracting Model of the Firm

Using the dynamic primal-dual methodology, it is shown that a symmetric negative semidefinite matrix characterizes a set of qualitative restrictions implied by the dynamic maximization assertion and the mathematical structure of the model. All of these results are new and show that this model contains many qualitative properties beyond Hotelling's rule. Just as important, symmetry is shown to be a fundamental property of the model, analogous to static models of producer behavior. Copyright 1990 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Information and exhaustible resources: A Bayesian analysis

We develop a continuous-time, Bayesian model of investment in information about an exhaustible resource. Because of the way that information affects expectations, the deterministic Hotelling rule turns out to be more appropriate as a description of how resource owners forecast the value of their stocks than as a predictor of observed changes in the resource price. A flow of information generates both unanticipated changes in expectations, which cause the mean rate of change in the resource price to deviate systematically from the deterministic Hotelling rule, and reductions in uncertainty, which do not affect the Hotelling prediction.

Interest rates and metal price movements: Further evidence

We offer a theory about the relationship between interest rates and metal price movements. The theory is a version of the Hotelling rule Eq. (8). The results obtained from prices of four different metals based on seasonally and unadjusted quarterly data over the period 1968:2–1982:2 suggest that a reformulated Hotelling rule which has a dynamic structure can explain the relationship between metal prices and interest rates. In view of this result, it appears that the return on exhaustible resources is related to changes in, rather than the levels of, interest rates. This result also confirms the results of G. M. Heal and M. M. Barrow [ Rev. Econom. Stud. 48, 161–181 (1979); Econom. Lett. 7, 95–103 (1981)].

Uncertainty and the joint extraction of helium and natural gas

In this paper a model of joint natural resources is developed in order to examine particular aspects of the helium industry. The importance of helium demand for the equilibria in the markets for natural gas and helium, the joint resources, is analyzed. This analysis is pursued under both conditions of certainty and helium demand uncertainty. A modified Hotelling rule is derived under conditions of uncertainty in the timing of demand for the residual resource.

A note on uncertainty and the hotelling rule

In this paper we derive the Hotelling rule of optimal natural resource depletion, modified to account for uncertainty in rates of return. It is shown that in the presence of risk aversion, the rule implies that the expected equilibrium rate of increase of net resource price must equal the expected rate of interest if and only if there exists a zero covariance between the marginal utility of consumption and the difference between the rate of net price increase and the rate of interest. The sign of this covariance is an empirical question, as an example illustrates.

The hazard rate and the hotelling rule

The hazard rate and the hotelling rule

Harold Hotelling 1895-1973

Harold Hotelling was a leading mathematical economist at a time when that subject was in its infancy; he also enjoyed a world-wide reputation as a mathematical statistician. In both fields he was renowned for his theoretical prowess and as a most effective and caring teacher. His wide influence upon the professions is felt not only through his publications (a large number of which are seminal contributions), but also through his students, among whom one can count many of the next generation's leading economists and statisticians. Hotelling's career spans a most creative period in the disciplines of both mathematical economics and mathematical statistics, and few figures have displayed his originality and flair: fewer still have publication records that bear comparison. Most importantly, his published papers are today seen as the starting point of much contemporary research. Indeed, his name is familiar to a remarkably wide range of professionals, a range that runs from economists to statisticians but also includes educationalists and psychologists. In economics there is Hotelling's Lemma and Hotelling's Rule and in statistics he is particularly known through the Hotelling T2 statistic. In 1985 his widow donated the collection of Harold's correspondence and professional manuscripts to the Butler Library of Columbia University. It comprises a very large and impressive source of material for the historian of economic and statistical thought. This fascinating figure has never been the subject of any systematic study and the primary material at Columbia affords an exciting opportunity to examine the life and career of this most revered, distinguished and influential man. Harold Hotelling was born on September 29, 1895 in Fulda, Minnesota, of ancestors long American but originally of English and Dutch extraction. When he was nine the family moved to Seattle. The Church became a focus of the lives of the newcomers, providing both a place of religious worship and a most hearty welcome. Hotelling records that he was stimulated as a very young man by Methodist interest in social justice and race equality, and the family tradition of active concern with public problems. (This and other nonattributed quotations are from original

Pricing Policies of an Oil Cartel with Expectation of Substitute Producers

The proposition that the net price in a competitive market and the net marginal revenue in a monopolistic market rise at the rate of interest was first demonstrated by Hotelling (1931) for a non-durable exhaustible resource. However, Levhari and Liviatan (1977) and Fisher (1981) have shown that Hotelling's r-percent rule is not valid when extraction costs rise with cumulative production. This r-percent rule also applies to a perfectly durable resource when the resource is produced in a competitive market. It does not apply in the case of a monopolistic market.

Auctioning Incentive Contracts

This paper draws a remarkably simple bridge between auction theory and incentive theory. It considers the auctioning of an indivisible project among several fi rms. The firms have private information about their future cost at th e bidding stage, and the selected firm ex post invests in cost reduct ion. The authors show that (1) the optimal auction can be implemented by a dominant strategy auction that uses information about both the first bid and the second bid; (2) the winner faces a (linear) incenti ve contract; (3) the fixed transfer to the winner decreases with his announced expected cost and increases with the second lowest announce d expected cost; and (4) the share of cost overruns borne by the winn er decreases with the winner's announced expected cost. Copyright 1987 by University of Chicago Press.

ISSUES IN THE APPLICATION OF COST-BENEFIT ANALYSIS TO ENERGY PROJECTS IN DEVELOPING COUNTRIES *

THE THEORY behind cost-benefit analysis is relatively well developed [see Little and Mirrlees (1968), (1974); Dasgupta, Marglin and Sen (1972); Mason and Merton (1984)], but its application to real world problems is not always easy. This paper considers the application of cost-benefit analysis to energy problems in oil-importing developing countries (OIDCs). The results are divided into four parts: Section 2 presents a methodology for handling uncertainty; Section 3 studies the implications of exhaustibility; Section 4 examines the externalities associated with exploration; Section 5 applies these tools in an analysis of the costs associated with importing oil. In Section 2 we begin with a discussion of the theoretical issues involved in cost-benefit analysis in the presence of uncertainty. Problems arise when there are conflicting estimates of a project's chance of success. The analysis must consider how the range of possible outcomes affects both the total risk borne in the economy and the income distribution. Uncertain future returns have to be appropriately discounted to the present. Projects which deplete exhaustible resources are irreversible and therefore the cost-benefit analysis must take into account the value of current reserves. In Section 3 Hotelling's rule is presented as the starting point for forming expectations about the price path of oil and other exhaustible energy resources. All project appraisals for programs ranging from new energy development to conservation or stockpiling are strongly influenced by the expected future price of energy, and oil in particular. Energy prices today and in the future depend on estimates of total world hydrocarbon reserves, their extraction costs, and the predicted availability of backstop technologies. Uncertainty about future reserves leads to variability in supplies and price, and causes an inefficiency in the intertemporal allocation of oil; depletion takes place more slowly in order to maintain flexibility in the event of worse-case scenarios. The gains from developing new energy supplies (and conservation) include lower prices, reduced vulnerability, and

Oil pricing policies and macroeconomy for an oil-based economy

This paper analyses the oil pricing policies for an oil-based economy within a national planning framework. It contains a total asset maximization problem in the non-oil sector and a macroeconomic model. The main conclusion is that Hotelling's r-percent rule fails to apply for an oil-based nation if the minimum-import constraint becomes binding. Therefore, the difference between the marginal revenue growth rate and the yield on domestic investment turns down when the import constraint is binding and then it goes through several cycles before it turns up as the constraint is non-binding over the planning horizon.

Intergenerational Equity and Heterogeneous Resources

As Ricardo observed, mines vary in quality, and this variation gives rise to a rent. Even within a mine, units of ore vary significantly in quality, and the mining engineer must determine a cut-off grade. The implications for optimal extraction (in the Rawls-Solow sense) are analyzed in a two-sector model with a resource for which an irrevocable cut-off grade decision must be made in each time period. The grade configuration of the orebody is found to have important implications for the allocation of factors between sectors. The Hotelling rule is modified in relation to an alternative definition of social optimum. Harwick's rule is also found to apply.

A note on Hotelling's rule

In 1931, Hotelling developed a rule which became a central efficiency criterion in natural resource economics. It states that in a competitive world the rate of capital gains due to resource use must equal the rate of return on any other asset. Here, the author presents a modification for easier handling of discrete time models taking capital depreciation into account.

The Effect of the Discount Rate on the Optimal Exploitation of Renewable Resources

In a recent paper, Farzin (1984) has shown that the impact of the discount rate on the optimal rate of depletion of an exhaustible resource is ambiguous. This is so because not only is the discount rate an expression of time preference, it also reflects the opportunity cost of capital. As the extraction of an exhaustible resource typically requires investment in buildings, equipment, etc. , a higher discount rate will raise the cost of extraction. In terms of the Hotelling rule, dP/dt = r(P c ) where P is the price of the extracted product, c is the unit cost of extraction, and r is the discount rate, a higher r will be associated with a higher c, and so the implication for the rate of price increase is ambiguous. Furthermore, a higher discount rate is likely to affect the backstop price of the resource. What, then, about renewable resources? Ever since Clark's famous paper on the discount rate and the extinction of animal species (Clark, 1973), it has been recognized that a higher dis-

Set-up costs and the theory of exhaustible resources

Let there be several identical deposits of an exhaustible, non-renewable resource, the working of each deposit entailing a set-up cost but no other costs. It is found that the optimal path of extraction dictates that the deposits must be removed in strict sequence with discontinuities of marginal benefit at transition points. Moreover, the average rate of increase of marginal benefit is less than the rate of interest. These results embellish Hotelling's rule relating to optimal methods of resource extraction.

Deregulation as a switch of regime: Price effects using a modified Hotelling rule

Concern over rising energy prices has led to support for government intervention to regulate the price of domestic non-renewable energy resources. However, US policy makers appear to be looking more towards competition, rather than regulation, to decide who will provide energy resources and how these will be priced. This paper models possible dynamic price effects occasioned by the removal of a regulatory constraint. The analysis focuses on a government decision to eliminate binding price ceilings on a non-renewable (energy) substitute when the incumbent resource is monopolistically controlled (using deregulation of natural gas as an illustration). Under certain conditions it is shown that one will get continuity of marginal revenue and a fall in the world price following decontrol (the expiration of a patent or a decision to grant mineral rights on federal land). In general, however, the model suggests that both marginal revenue and prices will be discontinuous and that the discontinuity is likely to result in a fall in price.