Teaching the Economics of Non- renewable Resources to Undergraduates

fallenleafblackbeansOil and Offshore

Nov 8, 2013 (3 years and 9 months ago)


Teaching the Economics of Non
renewable Resources to Undergraduates

William L. Holahan

Charles O. Kroncke

International Review of Economics Education
, volume 3, issue 1 (2004), pp. 77


Harold Hotelling’s path
breaking article in 1931 used hi
gher mathematics to
explain the economics of non
renewable resources. In that article, Hotelling
asserted that conventional static models were inadequate to illustrate his ideas,
and presumably he would have extended that opinion to the many technical
rs that his work spawned.

The purpose of this paper is to show how to extend the conventional static
model to enable instructors of economics to present to undergraduates at least
some of the ideas of Hotelling and later research economists. By making such

presentations, these introductory courses can make a great improvement in
economic understanding at precisely the time in our history that energy policy
in general, and oil dependence in particular, are front
page news.


Classification: A22


With the recent release of the
NEPDG (National Energy Policy Development Group)
, teachers of basic economics courses have an excellent opportunity to
demonstrate how a proper understanding of economic principles is essential when
making and analys
ing public policy. The NEPDG Report notes that domestic oil
production declined for most years after 1970, offsetting increases in the production of
coal, natural gas, nuclear and renewable energy. The report calls for significant
departures from the marke
t outcome, including several methods of subsidising the
extraction of petroleum, such as modification of federal oil and gas leases, royalty
reductions and more development offshore as well as in Alaska’s National Petroleum
Reserve. It concludes that the U
nited States needs such a change in order to reduce its
dependence on foreign suppliers. Given the instability in the Middle East and the ability
of OPEC to manipulate world prices, a policy that claims to reduce US vulnerability to
these forces plays well

with the American public.

The economics of oil must take into account that it is a depletable non
(note 1)

In his path

(note 2)

Harold Hotelling recognised that
the marginal cost of extraction of a non
renewable re
source depends not only on the
current rate of production but also on the amount of cumulative production (or
equivalently, the stock remaining in the ground); however, he discounted the ability of
economists to explain the economics of non
renewable resou
rces without recourse to
higher mathematics. He wrote:‘The static
equilibrium type of economic theory which is
now so well developed is plainly inadequate for an industry in which the indefinite
maintenance of a steady rate of production is a physical impo
ssibility, and which is
therefore bound to decline.’ An almost exclusive reliance on this static model in
principles and intermediate microeconomics courses has laid a weak foundation for the
presentation of the economics of depletable nonrenewable resourc
es. Only a few
students take the math required to read Hotelling’s work or the literature it has
(note 3)

This paper is an effort to show how a properly reworked version of the static model can
indeed introduce students to the problems of depletabl
e non
renewable resources and
equips them, at an early stage in their study of economics, to understand the economics
of oil. We suggest that the instructor introduce a new curve that rests both on the
standard family of average and marginal cost curves, a
nd on the ‘Hotelling Rule’ that
describes how those costs are rising over time as the resource is extracted.
(note 4)

slightly extending the lectures on cost curves, the instructor’s presentation can
demonstrate historic misunderstandings and help to ide
ntify the steps necessary for
achieving a more market
oriented approach to energy policy.


In order to explain the economics of oil and establish the way a market would allocate it
over time, the material in this paper could be inserted in th
e course after the standard
treatment of the ATC, AVC and MC curves, and the treatment of static competition. Many
texts omit the equal
cost principle, which the instructor should also present
first. We present a summary here.

Figure 1 is the stan
dard supply and demand picture illustrating the equal
principle. Each firm is a price taker, taking as given the price determined by market
supply and demand. In a competitive market, each faces the same price and sets output
so that marginal

cost equals price. Since price is the same for all firms, they all have the
same marginal costs. All of these principles are key to understanding the oil market.

Figure 1










Total industry cost is minimised w
hen marginal costs are equated.
(note 5)

The proof is by
contradiction: suppose one firm had a higher marginal cost than another. A
rearrangement of a unit of output from the higher marginal cost firm to the lower
marginal cost firm would result in no chang
e in total output, but a reduction in total cost.
To minimise total industry cost, all such opportunities to squeeze costs out must be
seized until the marginal costs of all firms are the same. In a price system, this happens
automatically when all firms f
ollow the incentive to set marginal cost equal to the same

To model the world market as it would be if competitive, the student must understand
the horizontal summation of marginal cost curves. Panel (a) of Figure 1 shows the
marginal cost of the fi
rm. Price is determined by supply and demand. Because each firm
accepts price as given, the individual firm marginal cost curves can be summed to derive
the country’s supply curve in panel (b). In panel (c), the supply curves in individual
countries are su
mmed to derive the supply curve for the world. In a price
taking world,
output is produced at minimum cost.

Modifying the diagram to explain the
oil market

To understand energy policy, this analysis needs to be modified to reflect the
nonrenewable nature
of oil resources. The market would induce firms to extract oil in a
maximising pattern: with the lowest marginal extraction cost first, and then to
proceed to tap higher marginal cost reserves. (Marginal cost differs because oil reserves
lie in geol
ogical structures that vary in location, weather, depth, pressure and other
characteristics that impact on their extraction. Even within a single structure, different
reserves may differ in marginal extraction costs.) Extraction continues until marginal
st rises to price. Reserves that could be extracted profitably at higher prices, but not
current prices, remain in the ground, available in the future should prices rise or
technological change reduce costs. That is, at all times, the decision to extract o
r store
for the future depends on the comparison of marginal cost and price.

In Figure 2, we introduce a cumulative marginal cost curve that reflects the economics of
oil extraction. The three panels of Figure 2 permit us to see how the marginal cost
s shift as oil is depleted from a geological structure. Panel (a) shows the family of
cost curves in period 1, and panel (b) shows the family of cost curves in period 2. Note
that these panels seem to depict a static family of curves at a point in time. Ho
taken in sequence, (a) first, then (b), they are actually depicting a dynamic process of
extraction. Extraction causes the curves to rise due to depletion. Thus, in period 2, the
curves have risen to positions higher than they were in period 1. We a
re deploying static
figures to depict the choice of output at a moment in time, where the rate of output, in
turn, determines the rate at which costs are rising

slow depletion causes the cost
curves to rise slowly; rapid depletion causes the curves to ri
se rapidly.

Standard economic principles tell us that a firm will select its output to set marginal cost
equal to price, or produce no output if price lies below minimum average variable costs.
Thus, referring once again to Figure 2, the firm in period 1
will not operate if price lies
below point
, and in period 2 will not operate if price lies below point
.When the firm
has depleted a portion of its in
ground oil, it cannot get that oil a second time, and it
cannot get its replacement at the same cost a
s it did in prior periods (cet. par., i.e. same

Figure 2




Period 1

output of firm A

Period 2

output of firm A



In panel (c), we have horizontally summed the marginal cost curves shown in panels (a)
and (
b) for periods 1 and 2. Point
' corresponds to point
in panel (a), therefore the
height of
' is the minimum AVC in period 1. Point
' corresponds to point
in panel (b)
and therefore the height of
' is the minimum AVC in period 2. Just as depletion r
the family of cost curves, it also makes portions of the cumulative marginal cost curve
disappear. For example, as we make the transition from period 1 to period 2, the portion
' disappears. Although when we use paper we are forced to depict only
discrete time
periods, the process of oil depletion is steady rather than discrete.
(note 6)

The cumulative
marginal cost curves show this steady rise in marginal cost better than the time
families of cost curves. Students should learn that the ste
ady elimination of the lower
portion of the cumulative marginal cost curve (as if being chewed up by Pac Man) occurs
because oil is being depleted.

Since the cumulative marginal cost is a function of all oil depleted from a structure
up to
a point in time
, it is different in character from the conventional marginal cost curve,
which is a function of the rate of output
at a given point in time
. The cumulative
marginal cost curve is derived from conventional curves, but unlike the conventional
curves, which
a firm can ride up and down, the cumulative curve has a sense of
direction: the firm can climb up the curve, but not back down as oil is depleted, precisely
because oil is non
renewable. As a reminder of this fact, we place small upward
arrows on
the cumulative marginal cost curve. For example, once the oil whose marginal
extraction cost is shown by point
' has been extracted, that portion of the cumulative
marginal cost curve disappears. As depletion proceeds, the firm must pay higher and
marginal costs to extract more oil. The upward
sloping cumulative marginal cost
curve expresses the reality that the ‘easy oil is taken first’.
(note 7)

Cumulative marginal cost curves can be summed horizontally just as conventional
marginal cost curves ca
n. At any given price, the firms set output so that marginal cost
equals price, so long as price is at least as great as minimum ATC. In Figure 3, we have
a three
panel diagram that shows two representative firms in an industry and the
industry summation m
arginal cost curve. In the figure, firm 1 will not produce output
because the price is too low. Its oil will be preserved for the future when prices rise. Firm
2 will produce q
at price P
and the industry output is shown by the summation curve (of
a larg
e number of firms) with industry output of Q
.Thus some firms are not producing,
the rest are, and a rise in price will increase not only the total output of the industry but
also the number of producing firms. Similarly, if price falls, perhaps due to dis
coveries of
oil in Azerbaijan, then some firms will stop producing while others continue to produce,
but at a lower rate of production.
(note 8)

Figure 3




Firm 1


Firm 2



If technological change occurs that reduces costs,

the cumulative marginal costs fall and
the industry marginal cost shifts to the right. More firms can produce at any given price.
Similarly, if technological change occurs in the production of a substitute, such as natural
gas liquefaction, the demand for

oil will fall, reducing the price of oil and causing some
firms to stop production and others to produce at a reduced rate.
(note 9)

US oil policy in light of oil’s non
renewable character

For years, US energy policy has subsidised the extraction of domes
tic oil, resulting in
artificially low prices, more consumption and less public concern for the efficient use of
oil and its substitutes. Worse, by skewing energy use to subsidised oil, the artificially low
prices have deterred technological innovations an
d removed the motivation for research
and development into energy alternatives, making the country even more dependent on
oil. Higher
cost domestic oil that should have remained in the ground until world prices
dictated otherwise was instead exhausted even

though lower
cost oil could have been
imported. The NEPDG recommendations continue this tradition. Using the cumulative
cost curve in Figure 4, the instructor can demonstrate that such subsidies are an
incentive to extract oil sooner than would be the cas
e if competitive markets were
allowed to prevail in the domestic oil industry.

In Figure 4, a cumulative marginal cost curve is shown in which the price is less than the
marginal cost (
). From the previous analysis of Figure 2, we know that the firm will

choose to shut down. Now suppose that the energy subsidies called for by NEPDG are
available to the firm. Geometrically, this drives down the marginal cost that the firm
perceives and so the operative curve is

minus subsidy.

Figure 4

The m
inimum average variable cost at the cumulative depletion point q
is now driven
down to point
.Since point

lies well below price, the firm will now deplete oil that it
would not have had the market price not been subsidised. The producer will extract oi
l at

minus subsidy is driven up to point
. The subsidy policy will
result in extra oil produced equal to

.That is the amount that would be left in the
ground without the subsidy.

Without NEPDG incentives in effect, US ma
rginal cost at
is above the world marginal
cost. However, due to NEPDG subsidies, firms are encouraged to extract their more
costly reserves. Consumers enjoy artificially reduced prices for petroleum
based energy,
but as a nation, because of diminished d
omestic reserves, the United States actually
becomes more dependent on foreign suppliers. Moreover, it is less able to react to the
price spikes induced by supply disruptions. This analysis would imply that
implementation of the NEPDG proposals will produc
e the opposite of their intended
rather than reducing the United States’ dependence on foreign oil, the policy
would increase its dependence

Because oil is a non
renewable resource, the United States actually becomes less
dependent, not more depe
ndent, when it imports. When price is less than domestic
extraction costs, consuming another country’s oil is the correct decision. Dependency
should not be defined as how much the United States is importing at a given moment,
but rather how costly and how

rapidly it could respond to price spikes caused by cartel
price manipulations or war. The United States becomes less dependent when it lets the
market dictate the pace at which the country uses domestic and foreign oil.
(note 10)

The impact of Russian oil

on the world

The best way to force a cartel to reduce its price is for additional oil to come on to the
market. In recent years, Russia, long the owner of huge oil reserves but unable to bring
much of it to market, has greatly improved its pipeline

network and cooperates little with
OPEC to keep prices high by restricting output. What does the cumulative marginal cost
curve teach us about an efficient policy response to the emergence of Russia as a major
oil exporter? Answer: as always, consult the
marginal cost and the world price. If
Russian oil is available for less than the unsubsidised marginal cost, it should be
imported. Domestic reserves that cost more should remain in the ground.

‘Doesn’t this make the US more dependent on Russian oil?’ No m
ore than we are
dependent on their caviar! If they dramatically raised the price of caviar, we would find
substitutes. Similarly, if we efficiently extract oil, leaving the efficient amount in the
ground, the opportunity to substitute domestic oil exists i
f Russia decided to join OPEC.
Again, the key consideration is that we are dependent on oil. Our dependence on foreign
sources is home grown: by depleting our low
cost reserves, we have become more
reliant on foreign sources than we would have been if we h
ad let the market work. The
proper response to lower
cost Russian oil

that is, import it as long as it is cheap

completely at odds with the NEPDG policy recommendations. By expanding its sales on
the world market, Russia has replaced some of the oil

that OPEC withheld from the
market and frustrated its efforts to boost prices. Now is the time to import this cheap
foreign oil and to preserve the United States’ domestic reserves. We become less
dependent when we let the market dictate the pace at which

we use domestic and
foreign oil.

What of ANWAR?

One of the NEPDG recommendations is to slate a tiny portion of the Alaskan Wildlife
Refuge for exploration and oil production. Not surprisingly, this recommendation raises
the ire of environmentalists who ex
press concern for the pristine wilderness and for the
animal life that may be disrupted. The cumulative marginal cost curve shows why, even
if there were no environmental concerns, this oil should not be extracted: because such
extraction can only occur if

subsidised, it is too soon to extract it now. When extraction
of such oil requires a subsidy, it cannot compete with cheap foreign oil. Simply put, it
should remain in the ground. Environmental concerns are a separate issue.


The United States
is dependent on oil, not foreign oil. Since oil is non
renewable, one
must be careful in analysing that dependence. We should use foreign oil when it is
cheap, and domestic oil during those periods when domestic oil is cheaper than the
world price. To smoo
th the effects of sudden spikes in the world price of oil, the
Strategic Petroleum Reserve should be full and ready to counter sudden production cuts.
The rule for filling the SPR is the same as for any other use of oil: fill it with domestic oil
when that

is the cheaper source; fill it with foreign oil when that is cheaper.

Energy policy promises to be a hot topic for years to come. By presenting the issue in
terms of cumulative marginal cost curves, we offer economics teachers another tool to
help clarif
y their students’ economic understanding of this issue.


Deshmukh, S. and Pliska, S. (1980) ‘Optimal consumption and exploration of
nonrenewable resources under uncertainty’,
, vol. 48, no. 1, pp. 177


Devarajan, S. and Fisher, A
. (1981) ‘Hotelling’s ‘Economics of exhaustible resources’:
fifty years later’,
Journal of Economic Literature
, vol. 19, no. 1, pp. 65


Gilbert, R. (1979) ‘Optimal depletion of an uncertain stock’,
Review of Economic Studies
vol. 46, no. 1, pp. 47


Hotelling, H. (1931) ‘The economics of exhaustible resources’,
Journal of Political
, vol. 39, no. 2, pp. 137


Mann, C. (2002) ‘Getting over OIL’,
Technology Review
, January/February, pp. 32


National Energy Policy Development Group (2001)
onal Energy Policy: Reliable,
Affordable, and Environmentally Sound Energy for America’s Future
, Washington, DC:

Pesaran, M. (1990) ‘An econometric analysis of exploration and extraction of oil in the
UK continental shelf’,
Economic Journal
, vol. 10
0, no. 401, pp. 367


Pindyck, R. (1980) ‘Uncertainty and exhaustible resource markets’,
Journal of Political
, vol. 88, no. 6, pp. 1203


Pindyck, R. (1984) ‘Uncertainty in the theory of renewable resource markets’,
Review of
Economic Studies
vol. 51, no. 2, pp. 289


Stiglitz, J. (1976) ‘Monopoly and the rate of extraction of exhaustible resources’,
American Economic Review
, vol. 66, no. 4, pp. 655




The distinction between ‘non
renewable’ and ‘exhaustible’ resources should be m
at the outset. Exhaustible resources are those that can be all used up, but need not be.
For example, steer and bison are exhaustible in the sense that, if they are all killed, no
replacement is possible. If properly managed, however, these herds can g
row: steer
through market incentives and private property rights, and bison through government
intervention, unless a market comes into existence sufficient to create similar
renewable’ adds an extra meaning to ‘exhaustible’: a unit of a no
renewable resource cannot be replaced and at any positive rate of use this resource will
eventually be gone.


Hotelling employed calculus of variations, not commonly understood by economists
in 1931, but now common in graduate curricula. However, so
seldom does an
undergraduate understand such methods when taking principles or intermediate
microeconomics that the course cannot utilise that mathematical analysis. Hence the
topic is not presented at all in the majority of texts.


Many papers have bee
n written in the last two decades of an even more difficult
nature. The simple technique provided here can only enable the instructor to whet
students’ appetite for the intriguing economics of non
renewable resources. A fine review
article by
Devarajan and

Fisher (1981)

appeared 50 years after Hotelling’s article. The
review manages to make his work a bit more understandable, but still does not help
much to explain the analysis to students who will take only principles courses or perhaps
intermediate micro.

Additional articles on this topic include
Deshmukh and Pliska (1980)
Gilbert (1979)
Pesaran (1990)
, Pindyck (
) and
Stiglitz (1976)


The ‘Hotelling Rule’ emerged naturally from his reasoning: the market will extract a
renewable resource

so that the price rises at the rate of interest. Proof: if not, then
the price will rise either faster or slower than the rate of interest. If slower, then it is
better to decrease extraction and invest in financial instruments that will by definition
w at the rate of interest. If faster, then it is better to invest in increased extraction,
since the oil price is growing faster than the value of financial instruments. So, the
equilibrium rate of extraction will keep the price rising at the rate of inter


The average total cost curve would be employed to illustrate the production at
minimum cost to the firm. Here, however, since we are discussing the minimum cost to
the industry, we use marginal cost and follow the usual proof by contradiction.


art graphic packages could be developed to show the smooth
progression of these curves over time.


The cumulative marginal cost curve is a function of all past extraction, not of time. It
differs from the standard textbook marginal cost cu
rve, which assumes continuous
combination of complementary inputs, usually capital and labour, purchased by the firm
at constant prices per unit. The bottom part of the cumulative marginal cost curve
disappears with extraction because the entrepreneur extr
acts the low
marginal cost oil
first; and, since it is a depletable resource, no more oil can be extracted at that marginal
cost again. The disappearance of the bottom portion of the cumulative marginal cost
curve as extraction takes place is our graphical

depiction of what Hotelling stated could
only be shown mathematically.


The oil retail business is comprised of local monopolies, but the oil extraction
business consists of a very large number of small sellers, with the world price greatly

by Middle Eastern sellers. The non
OPEC sellers are so numerous that it is
reasonable to use the price
taking model to discuss what would happen if the US
government did not have a policy of subsidy and trade restrictions. We are assuming
taking beh
aviour by non
OPEC sellers. They take price as a given, not as a variable
they can influence. They set marginal cost equal to that price.


For a highly readable account of the substitutes for oil that are available but only at a
much higher cost of oil
usage, see
Mann (2002)
. That article makes the point that as the
production technology improves for these substitutes, the price will fall, making them
competitive with oil. Thus another problem with the NEPDG is that by artificially reducing
the oil price
, it reduces the incentive to invest in the improvement of production
technologies of substitutes because their use is further delayed into the future.


The instructor should at some point in the discussion of non
renewable resources
make clear to the
students that the time dimension is critical. The use of nonrenewable
oil has a time dimension just as financial assets have. A rational seller of oil will sell it at
a rate that recognises that financial assets are substitutes for oil ownership. As long a
oil owners see that the value of oil is rising faster than the market rate of interest on
financial assets of similar risk, it is profit
maximising to retain ownership of the oil, i.e.
hold it off the market for the price to go up higher at a faster rate

than the rate of
interest. If the value of oil is rising slower than the rate of interest, it is time to sell.

Naturally, an increase in sales reduces the rate of price increase; a decrease in sales
increases the rate of price increase. So, we have an int
ertemporal equilibrium in which
the rate of price increase (net of cost) equals the rate of interest. It is an equilibrium
rate of price increase since if the rate of price increase were greater than the rate of
interest it would fall, and vice versa. Hote
lling’s article was path breaking in part because
he was the first to point out this relationship between the value of durable resources and
financial assets: they both rise and fall at the rate of interest.

Contact details

William L. Holahan

Professor of

Chair, Department of Economics

University of Wisconsin



email: holahan@uwm.edu

Charles O. Kroncke

Professor of Finance

School of Business Administration

University of Wisconsin



email: kroncke@uwm.edu