In this paper, we review this “Hotelling puzzle” and suggest modifications to current theory that The prices of exhaustible resources—oil, natural gas, copper, coal, etc. . Review of Economics and Statistics 92 (2), Oil is an exhaustible resource. The economics of exhaustible resources is expressed through Hotelling’s rule. Hotelling’s rule states that the. Hotelling’s rule defines the net price path as a function of time while maximizing economic rent in the time of fully extracting a non-renewable natural resource. ” Hotelling’s ‘Economics of Exhaustible Resources’: Fifty Years Later”. Journal of.

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Economists have long been concerned with the extraction of natural resources. The paper presents a model of the Hotelling rule and examines its applicability to real life phenomena. The paper finds that while the Hotelling theory had contributed to the economics of nonrenewable resources and the rise of the conservationism movement, the assumptions laid out by the theory are not applicable to the real world.

In conclusion, the paper suggests the need to relax the assumptions in order to exhaustuble the real-world phenomena. The efficient use of scarce natural resources, both renewable and non-renewable sources, resourcss long been a concern of natural resource economics Shogren In a similar vein, Ricardo explored on the significance of land quality on economic rent.

Similarly, Jevons raised concern about the consequences of coal depletion on population growth Shogren A feature shared by all these economists is their treatment of natural resources as a free factor of production. That is, they all treat natural resources as provided freely by nature.

But towards the beginning of the 21st century, a shift in mindset occurred as economists began treating natural resources as something more distinct than just a free factor of production Shogren Theorists such as Hotelling and Gray particularly pointed out to the additional intertemporal cost of extracting natural resources Shogren InEfonomics used differential calculus to derive the optimal extraction of a fixed resource over economivs Bradley He began by recognizing the inadequacy of the standard economic analysis in the industry in which production was bound to decline Bradley Hotelling then asserted that if the total resource base and capital investments were fixed and efficient extraction methods used, then the marginal net revenue of extraction of non-renewable resource would rise at the rate of interest over time Hotelling In other words, under a perfectively competitive market, the market price of a non-renewable resource minus the marginal costs must grow in tandem with the interest rate.

As such, the price of the natural resource should increase with time, provided that the marginal costs are kept constant Chakravorty et al. The theory thus proposed the time track of natural resource extraction that most increases the value of the resource reserve. But at the time, his analysis was way ahead of time as mathematics had not yet been incorporated into economics. As a result, his seminal analysis was originally rejected for this reason.

The utility of consumption would be denoted by U Rt. The objective is to maximize the marginal net revenue of extraction of the non-renewable resource. Assuming that the extraction is carried out with constant unit costs. Then the optimal path of extraction of the natural resource would be found by the hotellinv equation.


Assuming that private and social discount rates are the same and that there are no externalities Gaitan et al. But conditions require the optimal extraction path to fulfill the following relation Gaitan et al. The opportunity cost or rather the shadow price at time t, Yt, is in the present case constant. And given that in a market economy, then it can be seen that equation iv reflects the Hotelling rule that the marginal price of the natural resource increases with increase in the rate of discount.

The selfish exploitation of natural resources at a rapid rate gave rise to the conservation movement Rothband This theory has formed the basis of the conservationist movement and has been influential to the point that prohibitions against oil and exhausitble mining and deforestation in certain government lands have been justified on this ground Hotelling An exhhaustible point to emphasize in the Hotelling model is that the market price of non-renewable resources must increase with time, provided that costs remain time-invariant Chakravorty et al.

However, in reality such an increase in the price of non-renewable sources may not persist as many short-run factors such as regulation and speculation in commodity markets may come into play resulting in alternative phases of upward and downward price movements Chakravorty et al. For example, if the Kyoto Treaty was to impose a target of PPM of carbon, energy prices would hktelling expected to rise but fall soon after the constraint becomes binding Chakravorty et al.

But when there is a fall below the ppm level, the prices are bound to rise again Chakravorty et al.

Hotelling’s “Economics of Exhaustible Resources”: Fifty Years Later

Such a cyclical behaviour in the prices of non-renewable resources is not covered under the Hotelling model. Also, economic rseources do not provide evidence of an increase in scarcity of these ehxaustible Krautkraemer Although the popuplar view among the general public is that exhaustion of non-renewable resources is resoutces at a faster rate, this view is highly debatable.

In fact, economic indicators have shown that there has been growth in nonrenewable resource supply as new deposits continue to be discovered and the extraction technology continues to progress Krautkraemer This has been argued to mitigate the scarcity effect Krautkraemer Nonetheless, the popular view that the world is likely run out of natural resources in the near future may not necessarily be true.

Resourdes resources are considered to be scarce, then there is a higher likelihood of its real price rising Braddley In the event of an increase in real price, producers are likely to be induced by the high prices to explore for more reserves resulting in an increase in resource stock Braddley The lifetime measures of most resources can thus be assumed to remain constant over time.

Another error that Hotelling made was linking his highly conditional analysis to the real world Braddley Hotelling faulted laissez-faire for deviating from his derived optimality in extraction of non-renewable resources, stating that the extractive industries had discrepancies which resulted in wasteful forms of exploitation Braddley He also argues that such wasteful forms of exploitation would have been regulated in the interest of the general public Braddley Whilst Hotelling was quick to recognize market failure, he failed to account for what is currently known as government failure Braddley As can be seen with the long history of petroleum regulation in the US, government intervention has generally been lacking in information and has been highly problematic in practice Adelman Only an omniscient planner would know the specifics of demand, supply, price, cost, interest rates, and entreprenurial alertness needed to arrive at an optimal extraction solution Braddley According to the hotelling theory, the most profitable extraction is one in which the price of the resource, determined by the marginal net revenue from sale of the resource, increases at the rate of interest.


In this respect, to reduce on the marginal cost of extraction, it would require that an industry be located close to the extraction point. This would not only decrease the transport costs, but will also increase efficiency in the supply chain and logistics. Logistics thus has an important role to play in determining the optimal extraction solution. The lower the transport costs, the more likely are the returns to scale. Whilst the transport costs are account for a small percentage of the total costs, the optimal extraction solution must also take into account the total logistics costs.

In Summary, the Hotelling theory has contributed to the economics of nonrenewable resources. It has formed the conceptual and theoretical framework used by economists to model the supply and the prices of nonrenewable resources.

More so, it has contributed to the conservationist movement. However, the Hotelling theory, though elegant, seem somewhat misplaced. The model points out to a rise in trajectory of net prices of non-renewable resources along with the rate of interest yet there is a lack of empirical evidence to back this pricing behaviour. Moreover, the assumption of an increase in scarcity of non renewable resources is highly debatable. These assumptions seem not applicable to the real world.

Perhaps, to explain the real-world phenomena, it would be helpful to relax these assumptions. For example, in order to explain the price of oil, it would be necessary to discard all assumptions of inevitable increase in price and the assumption of a fixed stock.


Rev Austrian Econ Oil, gas, and government: School of Business and department of Economics. The Economic Journalvol. Journal of Political Economy 39 2— Egalitarianism as a revolt against nature and other essays, Auburn, AL: Ludwig von Mises Institute, pp.

The Hotelling rent and the Hotelling rule

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