Testing the Assumptions and Predictions of the Hotelling Model

In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. Using panel data on fourteen nonrenewable natural resources to estimate this empirical Hotelling model, we get qualitatively different results as compared to the related literature. We find evidence of stock-dependent extraction costs for most resources. There is no evidence against the linearity of the optimal extraction rate in the resource stock for almost all resources studied. Furthermore, the Hotelling model may sustain a zero long-run growth rate in resource prices. These results depend on whether firms use different extractive technologies or whether the structural break observed on resource prices is taken into account.     

Endogenous growth with a limited fossil fuel extraction capacity

Campbell (1980) and following authors have discussed a limited resource extraction capacity as an augmentation of the well‐known Hotelling model. We integrate a limited extraction capacity and related investments in the endogenous growth model of Tsur and Zemel (2005) to study its effect on economic development. The capacity constraint gives rise to three effects. On the one hand, higher energy costs and the reallocation of production towards capacity investments decrease production available for consumption, research and/or capital investments (energy costs and reallocation effect). On the other hand, research investments may increase, which boosts available production (research effect). Depending on the capital endowment and the strength of the effects, long‐run consumption may be boosted or depressed. In particular, the capacity constraint may render everlasting consumption growth non‐optimal in a resource‐rich economy. Furthermore, we find that capacity investments may be postponed to later points in time if the capital endowment is high.     

我国矿产资源价格重构中的税收效应分析

现阶段我国矿产资源价格扭曲是导致资源配置效率低下和环境污染的重要诱因。本文在标准的动态霍特林模型分析框架下,对税收与资源价格之间的关系进行理论分析,重点对矿产资源征税应采取从量税还是从价税作出解释。最后针对我国矿产资源价格改革中存在的诸多税收问题,提出资源税收进一步深化改革的政策建议。     

Hotelling and recycling

We study the exploitation of recyclable exhaustible resources such as metals that are crucial for the energy transition or phosphorus that is crucial for agricultural production. We use a standard Hotelling model of resource exploitation that includes a primary sector and a recycling sector. We study two polar cases: competitive and monopolistic extraction. We show that, when the primary sector is competitive, the Hotelling’s rule holds and the price of the recyclable resource increases over time. We then show a new reason why the price of an exhaustible resource may decrease: when the primary sector is monopolistic, the primary producer has incentives to delay its production activities in order to delay recycling. As a consequence, the price path of the recyclable resource may be U-shaped. Numerical simulations reveal that the monopolist has an incentive to delay extraction when the recoverability rate is high (because more recycled goods are produced) or when the recoverability rate is low (when fewer recycled goods are expected to be produced in the future). As a consequence, the date of exhaustion of the virgin resource is further away in time for high and low levels of recoverability than for intermediate levels.     

The Hotelling rule in non-renewable resource economics: A reassessment

Harold Hotelling's 1931 contribution is known for providing a basic principle—the Hotelling rule—to the economics of non-renewable resources. Nearly 90 years later, empirical tests conclude the rule lacks empirical validity, requiring strong amendments to describe the long-term, aggregate behaviour of its target object. On the basis of Hotelling's unpublished archival material, this paper revisits the place given to the Hotelling rule in non-renewable resource economics. Our reconstruction shows that Hotelling's 1931 paper has been misinterpreted: from the outset, the Hotelling rule was not valid for mineral resources. In contrast, the consideration of two inherent geological constraints, alongside exhaustibility, offered the opportunity for an alternative basic framework, capable to generate bell-shaped and U-shaped equilibrium trajectories for supplies and prices, respectively. Inspired by this unknown aspect of Hotelling's work brought to light by our archival investigation, we sketch this alternative basic model, enabling non-renewable resource economics to circumvent the empirical shortfalls of the Hotelling rule.     

Some Taxation Theorems in the Hotelling Model

In this paper, we investigate the relationship between the demand ad valorem, cost ad valorem and unit taxes in terms of price, quantity and tax revenue. In particular, we prove that the Musgravian transformation holds in the Hotelling model. In addition, we show that the Suits‐Musgrave theorem must be revised as output in the Hotelling model remains invariant in the presence of different taxes. That is, for a given price instead of a given output, the tax revenue under demand ad valorem tax exceeds that under the corresponding unit tax as long as profit levels for both stores are positive, a very general assumption. The exception is when the two stores are located close to each other and transportation cost is zero. Only in this case, are tax revenues and price under both tax regimes the same. If both stores are symmetrically located, the superiority of the ad valorem tax holds true except when the two stores are located back to back. Finally the farther away the location of a firm from the end point is, the smaller the difference in tax revenues between demand ad valorem and unit tax will be: the effect of the Suits‐Musgrave theorem weakens in the presence of location clustering.     

Hotelling–Downs Competition with Free Entry When Voters Have an Option to Contest

Osborne shows that for almost all distributions of voters’ preferences, a pure strategy Nash equilibrium does not exist in the classical Hotelling–Downs model of electoral competition with free entry. We show that equilibrium is generically possible if in addition one allows voters an option to announce their candidacy to compete side‐by‐side with office‐seeking players. The model studied in this paper renders Osborne and the celebrated citizen‐candidate model à la Osborne and Slivinski as two extreme cases. We characterize the equilibrium set with two central questions: (i) can there be equilibria where only voters contest? and (ii) are equilibria with contesting office‐seeking players possible? We also show that in our general setting, extremists are typically voter‐candidates so that in every two‐party contest, office‐seeking politicians stay out of competition.     

Why do many resource-rich countries have negative genuine saving?: Anticipation of better times or rapacious rent seeking

We investigate the Hartwick rule for saving of a nation necessary to sustain a constant level of private consumption for a small open economy with an exhaustible stock of natural resources. The amount by which a country saves and invests less than the marginal resource rents equals the expected capital gains on reserves of natural resources plus the expected increase in interest income on net foreign assets plus the expected fall in the cost of resource extraction due to expected improvements in extraction technology. Effectively, depletion is then postponed until better times. This suggests that it is not necessarily sub-optimal for resource-rich countries to have negative genuine saving. However, in countries with different groups with imperfectly defined property rights on natural resources, political distortions induce faster resource depletion than suggested by the Hotelling rule. Fractionalised societies with imperfect property rights build up more foreign assets than their marginal resource rents, but in the long run accumulate less foreign assets than homogenous societies. Hence, such societies end up with lower sustainable consumption and are worse off, especially if seepage is strong, the number of rival groups is large and the country does not enjoy much monopoly power on the resource market. Genuine saving is zero in such societies. However, World Bank genuine saving figures based on market rather than accounting prices will be negative, albeit less so in more fractionalised societies with less secure property rights.     

Strategic competition and optimal parallel import policy

Abstract In a two‐country Hotelling type duopoly model of price competition, we show that parallel import (PI) policy can act as an instrument of strategic trade policy. The home firm’s profit is higher when it cannot price discriminate internationally if and only if the foreign market is sufficiently bigger than the domestic one. The key mechanism in the model is that the home firm’s incentive to keep its domestic price close to the optimal monopoly price affects its behavior during price competition abroad. We also analyze the welfare implications of PI policies and show that our key insights extend to quantity competition.     

DID THE GREAT RECESSION REDUCE VISITOR SPENDING AND WILLINGNESS TO PAY FOR NATURE‐BASED RECREATION? EVIDENCE FROM 2006 AND 2009

Outdoor recreation is a large industry that can diversify public land‐based economies that have traditionally relied upon resource extraction. However, what happens to nature‐based recreation visitor spending and benefits during times of national economic recession? To address this question, we replicate a 2006 high mountain recreation study in the same region 3 years later during the 2009 recession. Results indicate that nature‐based public land recreation in this area did not experience reductions in most categories of visitor spending or total number of visits during the recession. These results imply that nature‐based recreation may represent an economically stable industry in public land mountain economies. Total benefits to the visitors are also quite stable, only dropping from $129 per person per trip in 2006 to $120 in 2009. This 7% drop in willingness to pay is not statistically significant at conventional levels. (JEL Q26)     

Climate policy and the optimal extraction of high‐ and low‐carbon fossil fuels

Abstract. We study how restricting CO₂ emissions affects resource prices and depletion over time. We use a Hotelling‐style model with two non‐renewable fossil fuels that differ in their carbon content (e.g., coal and natural gas) and in addition are imperfect substitutes in final good production. We show that an economy facing a CO₂ flow‐constraint may substitute towards the relatively dirty input. As the economy tries to maximize output per unit of emissions it is not only carbon content that matters: productivity matters as well. With an announced constraint the economy first substitutes towards the less productive input such that more of the productive input is available when constrained. Preliminary empirical results suggest that it is cost‐effective to substitute away from dirty coal to cleaner oil or gas, but to substitute from natural gas towards the dirtier input oil.     

ASYMMETRIC INFORMATION AND EXCHANGE OF INFORMATION ABOUT PRODUCT DIFFERENTIATION

We introduce asymmetric information about consumers’ transportation costs (i.e., the degree of product differentiation) in the model of Hotelling. When transportation costs are high, both firms have lower profits with asymmetric information than with perfect information. Contrarily, if transportation costs are low, both firms may prefer the asymmetric information scenario (the informed firm always prefers the informational advantage, while the uninformed firm may or may not prefer to remain uninformed). Information exchange is ex‐ante advantageous for both firms, but ex‐post damaging if transportation costs turn out to be low. If the information is unverifiable, the informed firm does not represent a reliable source of information, since it always prefers to announce that transportation costs are high and there is no contract that induces truthful revelation.     

Modeling Nonrenewable Resources Use with Multiple Demands and Multiple Sources

The theoretical literature following Hotelling (J Polit Econ 39:137–175, 1931) assumed that all nonrenewable resource needs are satisfied by one type of resource (e.g. “oil”), extractible at different per-unit costs. This formulation implicitly assumes that all users are the same distance from each resource pool, that all users can switch costlessly from one type of resource to another (e.g. liquid fossil fuels to coal or vice-versa), and that all users are subject to the same regulations. These assumptions imply, as Herfindahl (Extractive resources and taxation. University of Wisconsin Press, Madison, pp 63–90, 1967) showed, that in competitive equilibrium all users will exhaust a lower-cost resource completely before beginning to extract a higher-cost resource: simultaneous extraction of different grades of oil or of oil and coal should never occur. In trying to apply the single-demand curve model during the last twenty years, several teams of authors have independently found a need to generalize it to account for users differing in their (1) location, (2) resource needs, or (3) regulatory environment. Each research team found that Herfindahl’s strong, unrealistic conclusion disappears in the generalized model; in its place, a weaker Herfindahl result emerges. Since each research team focussed on a different application, however, it has not always been clear that everyone has been describing the same generalized model. The goal in this paper is to integrate the findings of these teams and to present an easily accessible generalization of the nonrenewable resource model to multiple demand curves.     

Spatial Competition with an Outside Good and Distributed Reservation Prices

In this paper, we analyze spatial competition within the framework of a Hotelling model with quadratic transportation costs and an outside option. The new feature of our approach is that consumers are uniformly distributed not only along the Hotelling line but also with regard to reservation prices. It turns out that in this particular model, duopolists always locate their shops exactly at the first and third quartile of the consumer distribution – i.e., at the socially optimal locations. Moreover, with uniformly distributed reservation prices, less than seventy percent of the consumers buy the good, and profits are less than fifteen percent of those in the standard model without an outside option. Received February 7, 2001; revised version received March 27, 2002 Published online: November 11, 2002     

A nearly complete test of a capital accumulating,vertically integrated,nonrenewable resource extracting theory of a competitive firm

A new approach to testing a generalized Hotelling theory of a nonrenewable resource extracting firm is developed. In contrast to approaches extant, it (i) permits empirical testing of all the refutable implications of the theory, (ii) does not require estimates of, or data on, the shadow value of the resource stock, (iii) does not require estimation of the feedback control functions or the necessary conditions associated with the underlying optimal control problem, and (iv) treats the capital stock in a theoretically sound manner in the econometric model. Because of certain limitations in the data, most, but not all, of the refutable implications of the theory are tested using a Bayesian approach. Other limitations in the data mean that the paper is better viewed as an illustration of how one would go about rigorously testing the extended Hotelling theory, rather than as one which presents convincing empirical evidence that supports or refutes it.     

A test of the Hotelling rule using old‐growth timber data

Abstract.  The paper tests Hotelling's prediction that scarcity rent for a non‐renewable resource will rise at the rate of discount in a market equilibrium. We perform the test using data for old‐growth timber, a resource that is effectively non‐renewable. In contrast to previous studies, for this resource a measure of scarcity rent is directly observable in the form of stumpage price bids in timber auctions. We construct a model that allows for replanting and captures the institutional framework of the western U.S. timber market. The modified Hotelling rule that we derive is not rejected in several of our specifications.     

Human capital and the time-profile of human fertility revisited

This paper examines a model of the intertemporal distribution of births recently proposed by Cigno that concludes 1) the optimal time profile will satisfy the Hotelling rule of natural resources depletion, and 2) women with high initial endowments of human capital will have all their children early in married life while those with low initial endowments will spread childbearing more evenly over the fertile period. This paper argues that Cigno's model is inconsistent with the empirical evidence. Specifically, it is claimed that: 1) the natural resource analogy has been misapplied; 2) the stated 1st order conditions are incorrect; 3) optimal birth profiles do not satsify the Hotelling rule; and 4) the optimal time profile is for all women, regardless of their human capital, to concentrate births at the end of the fertile period. Since the discounted opportunity cost of a birth declines over time, it always pays to postpone a birth as long as possible. However, again, the theoretical prediction of delayed childbirth is not consistent with available evidence, suggesting that important factors have been omitted from this model.     

A Model of Resource Depletion with Multiple Grades*

The standard extension of the Hotelling model of resource depletion to consider multiple grades leads to sequential development of successively poorer grades. However, this is not what is observed, and this paper formalises one reason for simultaneous exploitation—the existence of overhead costs in the preparation of a mine. It is shown that the structure of rents which is obtained in the simple model of multiple grades still applies in this more complex situation.     

Sustainability or Ruin of a Common Resource Economy with Random Jump

We consider a common resource economy in which agents exploit the common resource, and use it to produce goods and consume the goods produced. Also the agents can invest in private and productive capital. The resource extracted from the common resource is non‐renewable and the common pool is under uncertainty in the sense that it could have a sudden increase or decrease in the course of extraction. In this model we shall explore the probability of sustainability or ruin of the economy. We compare and discuss the optimal extraction rules and the probabilities under cooperative and non‐cooperative regimes.     

On the Cost of Opportunistic Behavior in the Public Sector: A General‐Equilibrium Approach

This paper studies the wasteful effect of bureaucracy on the economy by addressing the link between opportunistic behavior of government bureaucrats and the public sector wage bill. In particular, public officials are modeled as individuals competing for a larger share of those public funds. A simple extraction technology in the government administration is introduced in a standard real‐business‐cycle setup augmented with detailed public sector. The model is calibrated to German data for the period 1970–2007. The main findings are: (i) the model performs well vis‐à‐vis the data; (ii) due to the existence of a significant public sector wage premium and the high public sector employment, a substantial amount of working time is spent in opportunistic activities, which, in turn, leads to significant losses in terms of output; and (iii) the model‐based loss measures obtained for the EU‐12 countries are highly correlated to indices of bureaucratic inefficiency.