POLICY REFORM AND NATURAL RESOURCE MANAGEMENT
WEEK 2: DAY 1
RESOURCE ECONOMICS AND THE THEORY OF EXHAUSTIBLE RESOURCES
Noman KANAFANI, The Royal Veterinary and Agricultural University of Copenhagen
CONTENTS
1.
1.2.
1.2.
2.
2.1.
2.2.
3.
3.1.
3.2.
4.
5.
5.1.
5.2.
5.3.
6.
INTRODUCTION
Exhaustible versus renewable resources
The political economy of natural resources
THE RESOURCE AVAILABILITY DEBATE:
The “limits to growth” and the “material balance”
The “no problem” thesis
RENT IN ECONOMIC ANALYSIS
The view of the classics
Rent, supply elasticity and user-cost
RESOURCES’ EXTERNAL AND INTERNAL ECONOMIES
THE PURE THEORY OF EXHAUSTIBLE RESOURCES
Inter-temporal resource depletion time-path: Efficiency
Inter-temporal resource depletion time-path: Equity
Inevitable imperfection and lack of future markets
CONCLUSION
REFERENCES
1
1.
INTRODUCTION
Natural resources are primary commodities or non-produced goods, which may be used in
their crude form and are useful to mankind. In order to make them available for consumption
or intermediate use, these commodities must be discovered and extracted, but this is not
production in the true sense of the word. Natural resource economics, or resource economics
for short, studies the extraction of these resources and their allocation on various uses within
different time frames. What makes natural resources a special case is the fact that these
commodities cannot be reproduced in the usual manner as other goods in the economy. In
addition, they cannot be produced by the mere use of labour and capital, as it is usually
assumed in economic theory.
1.1.
Exhaustible versus Renewable Resources
Natural resources are generally divided into two broad categories: renewable and exhaustible
resources. Resources are termed exhaustible when any use pattern makes their supply dwindle
to zero. Simply put, exhaustible resources are available in finite stocks in nature. No matter
how large these stocks or reserves are, once we recognize that they are finite, or that they need
extremely long time to be remade, then the resources would be exhausted at some point of
time. All types of minerals and oil and natural gases are examples of exhaustible resources. On
the other hand, renewable resources have an infinite supply because they are capable of
renewing themselves according to their own natural cycle. Fish in the oceans, forests, and selfcleaning atmosphere are some examples of renewable resources. It is worth noting that both
exhaustible and renewable resources have a common characteristic: their supply is affected by
other factors than the ones usually dealt with when studying reproducible goods. The supply of
reproducible goods is a technical matter and it can be controlled entirely by using various
levels and combinations of labour and capital. When it comes to natural resources, other
detrimental factors must be taken into account, including the fact that current use affect future
supply and that certain biological reproduction time-cycles must strictly be respected.
The line of distinction between exhaustible and renewable resources is not, in fact, totally
permanent or unchanging. It can be easily conceived that over-exploitation of a renewable
resource may reduce its size to a point lower than the critical mass needed to renew itself. In
this case, the resource, although renewable in principle, can be exhausted. The distinction,
nevertheless, remain useful: a resource is renewable if it is possible to find a pattern of use that
makes its supply constant over time. In this chapter, we shall concentrate mainly on
exhaustible resources, leaving renewable resources to another chapter.
1.2.
The Political Economy of Natural Resources
Land, the mother of all natural resources, was seen by the great classical economists as the key
to understand the economic systems: the productivity of land determines nations' wealth, and
land ownership determines income distribution and political powers. Actually, the inevitable
stagnation of the system, as predicted by the classics, was mainly due to the constraint
imposed by land. “To nineteenth-century man”, Dasgupta and Heal (1979) write, “it would
therefore have seemed unthinkable that one could explain the dynamics of an economy, to
analyse the process of production and exchange, without having special attention to the role of
2
natural resources” (p.1).
Yet, this unthinkable situation became quite common among modern economists. As the same
authors have argued, one could read all the extensive literature of the 1950s and 1960s on
long-term economic growth without ever realising that availability of natural resources might
be a determinant of the potential of growth. Why did such a drastic shift take place? Probably
because of the sense of euphoria that prevailed then and made everything, including endless
accelerated economic growth, seem possible. The fact that natural resources were then also
very cheaply available must have played a role as well. Their relatively low or even zero,
prices gave the impression that resources are endless and that the misuse of nature can go on
forever cost-free.
That natural resources in general, and minerals in particular, were relatively cheap and
plentiful is closely connected with the type of relations that prevailed between the producers
and the consumers of these resources. Whether due to geological coincidences or not, the
major deposits of some of the most important minerals in the world are located in the poor,
previously colonised, and underdeveloped countries, while the major centres of consumption
of these resources are in the rich and developed part of the world. It is tempting to claim,
therefore, that by undermining the importance of natural resources in their discipline, the
economists were taking the observed prices as signs of economic fundamentals rather than as
reflection of ignorance and unequal relations between the producers and consumers. Within
this setting, it is not hard to see why resource issue has always been a central theme in NorthSouth relations and why it has always been a highly politically-charged discipline. The
increased awareness of the importance of natural resources and the surge of their prices in the
1970s have been conceived by many as signs of the emerging power of the South and as a step
towards a more balanced international economic order. The close relationships, in the ongoing
debate, between global environmental concerns and issues of inequality and development are
a testimony of the significance of the socio-political aspects of resource economics.1
The chapter starts by discussing the two extreme schools of thought with respect to resource
availability: the first claims that depletion of exhaustible resources will restrain the ability of
the global economy to grow, while the second argues simply that it will not. After shedding
some light on the pros and cons of each school, section 3 will examine one of the central
theoretical concepts within resource economics: rent. The section will follow how the concept
has developed through time and how it affected the modern treatment of exhaustible
resources. Section 4 goes a step further and introduces another basic concept related to
resource economics: external and internal economies. In section 5, the basic themes in the
theory of exhaustible resources will be introduced. We shall deal first with economic
efficiency: the conditions under which as much economic value as possible can be derived
from finite resources. At a second stage, we will turn to the issues of optimality: how to
distribute the efficient outcomes. Both efficiency and optimality will be treated within the so1
Rees (1990) warns against “the common piece of mythology that the bulk of advanced nation consumption is
only made possible by mass imports from the Third World”. She proceeds that “while in no way disputing that
Third World countries do export significant quantities of raw materials, the fact remains that the developed
nations are themselves the chief mineral producers and the chief source of their own mineral consumption”
(pages 85 and 93).
3
called inter-temporal analytical framework: extraction and allocation over several periods of
time, and across several generations. Finally, the stringent conditions under which free
competitive markets can bring about efficient resource use will be highlighted before
presenting an overall summary of the chapter.
2.
THE RESOURCE AVAILABILITY DEBATE
The controversy about the potential effects of human activities on the future of the planet has
never failed to attract great attention and passion since, at least, 1798, when Malthus
published his famous pamphlet on population growth. The question has invariably been, can
past trends continue in the long future? What will be the possible effect of extending past
trends when some variables lack behind, when some necessary inputs are absolutely finite?
Malthus was concerned with the failure of food production to keep up with population growth.
In recent times, the concern has shifted toward the unrestrained and accelerated economic
growth verses the limited ability of nature to renew itself.2
At the core is the question of whether human societies are self-adjusting systems that will
always ensure continuity. If not, then conscious effort should be made to readjust and avoid
paths that are not sustainable, and perhaps catastrophic, in the long run. Those who believe
that societies do not incorporate self-adjusting mechanisms attempt to trace early warning
signals and make ‘prophesies’. These take often the form of passionate cries for a conscious
change before it is too late. Those who believe in the inherent abilities of societies to survive,
question the ‘doom-day prophesies’ and the authenticity of the warning signals. They are
assured that even if the signals were true, the self-adjusting mechanisms will take care of
them. Serious and vital for the future of mankind as it is, the discussion between the two
schools of thought seems sometimes to be fruitless and, in several instances, not very serious.
Some dismiss the need to worry because “all past doom-day prophesies proved to be wrong”.
However, does being wrong in the past justify the claim that one will also be wrong in the
future? Alternatively, does it make one more likely to be right in future?
For some reasons, which may not be difficult to trace, the overwhelming majority of economists find themselves in the so-called ‘optimistic’ front of this age-old confrontation. Let us
start by presenting the point-of-view of the "pessimist" school as expressed by one of its most
prominent representatives in modern times: the Club of Rome. After a short introduction to
the “material balance” thesis, we shall turn to the criticism put forward by the ‘optimistic’
school.
2.1.
The “Limits to Growth” and the “Material Balance”
The “Limits to Growth” thesis, by Meadows et al. (1972), was the first attempt to deploy
modern computing techniques in order to test the future effects of five major global trends:
2
Neither of this issue is actually totally new. W. Jovens, one of the founders of modern economics, tackled some
of these concerns in connection with the possible exhaustion of coal. In a publication in 1865 entitled “The Coal
Question”, Jovens concluded that coal exhaustion may not hinder growth as such, but the corresponding increase
in its price will deprive England from a significant portion of its comparative advantages over other nations.
4
accelerated industrialisation, rapid population growth, widespread malnutrition, depletion of
renewable resources, and deteriorating environment. The model seeks to investigate the
interrelationships among these trends and their overall effects within a time horizon of one
hundred years into the future. The work can be comprehensively summarised by the following
points:
1. The overall model consists of five separate, but interdependent, sub-models for population,
industrial growth, food supply, natural resources and pollution. The model takes the world as
a single unit and is designed to trace the effect of evolution in each of its five sub-models on
the other four and on the state of the world as a whole. The basic variables in the model
increase at an exponential rate throughout time. Exponential growth is a dynamic principle
which leads to positive feed back-loop: the rate of the increase depends on the volume of the
base quantity, and the increase in one period becomes itself a source of a larger increase in the
next period, and so forth.3
2. The dynamic analysis of the future state of the world starts by defining the feed back-loops
of growth in population and industrialization. The feed back-loop of population growth is
clear. As to the industrialization, the model assumes that capital is the only determinant of
output. Industrial capital stock is subject to a negative feed (depreciation) and a positive feed
(investment). The overall effect is cumulative: increases in capital stock create industrial
output, which again lead to net increases in the capital stock.
3. The model then asks: how many people can be provided for on this earth, at what level of
welfare, and for how long? To answer these questions, the model investigates the elements
which are needed to provide the necessary physical support for given population and
industrialisation standards (given the size of the economy). Food production, use of nonrenewable resources and the state of the environment are selected for investigation here. The
study points out that other issues, of socio-political nature, like peace, social stability, and
education, are also important but are not explicitly incorporated into the analysis.
4. As before, the positive and negative effects on food supply and demand, on a global scale,
are identified. The supply of food is a function of arable land, water, and capital. The overall
supply of the first two production factors is assumed to be finite. Incorporating the exponential
population growth into the picture and assuming constant productivity (0.4 ha to feed one
person annually), the model concludes that total arable land on the globe will impose a
constraint on feeding the world population by the year 2000. Even when productivity is
assumed to quadruple, the intersection between demand and supply of arable land will be
3
Exponential growth has fascinated and bewildered human minds throughout times. It is said that the man who
invented the game of chess asked his king for a ‘modest’ prize: one grain of rice on the first square of the chess
board to be doubled on each following square down to the 64th square. The king, wildly in love with the new
game, granted him his wish, only to discover that the wish couldn’t possibly be fulfilled. If one grain of rice
weighs a tenth of a gram, the prize would amount to 1,844,674 million tons (1.8 trillion tons)of rice! For the sake
of comparison only, current world annual production of rice is about 300 million tons. Note that any quantity
increasing at an exponential rate doubles its size at certain number of years equal to 70 divided by the annual
growth rate. Also, exponential growth corresponds with the idea of sudden catastrophic shocks: a quantity which
doubles its size once every day may take years just to occupy half of a given space, but it will take then only one
day to occupy the whole space!
5
delayed by 30 years only. A similar analysis is applied to water-use leading to similar results.
5. The use of non-renewable resources is modeled in the same manner as arable land, although
the effect of the increase in average per-capita consumption is taken into account here. The
exponential growth in resource-use is driven by the growth of population and capital.
Obviously, the size of available reserves is the most critical assumption when dealing with the
supply of non-renewable resources. The model assumes that there are given static reserve
estimates for various minerals. Various scenarios are presented for the possible effects of
production cost, new technologies, and elasticities of demand and of substitutions on the size
of the reserves. However, these hardly alter the basic results. Increasing the size of the
estimated ‘proven’ reserves five times does not even affect the conclusions in a substantial
manner. Given present resource-use rates and the projected increase in these rates, the great
majority of the currently important non-renewable resources will be extremely rare, and
therefore very costly, after 100 years. This remains true even when the most optimistic
assumptions with respect to undiscovered reserves, technological progress, substitution and
recycling are taken into account, as long as the demand for resource continues to grow
exponentially. These conclusions can be found in Meadow et al. (1972, p 67).
6. The book came out with the following three conclusions and recommendations:
a) If the present growth trends in world population, industrialization, pollution, food
production, and resource depletion continue unchanged, the limits to growth on this planet
will be reached sometime within the next one hundred years.
b) If and when these growth trends are altered, it is possible to create conditions for
ecological and economic stability that would be sustainable far into the future. The book’s
message is simple and clear: to promote understanding of and to furnish the ground for a
shift in world’s development path, a transition from growth to global equilibrium.
c) The sooner the world’s people decide on attending global equilibrium, the greater will be
the chance of success (page 23).
Although most of the predictions of the “Limits to Growth”, especially with respect to size of
the world’s reserves of minerals, proved to be quite off the line after two decades, the Club of
Rome has maintained and defended its basic vision. In an update to the old work, entitled
"Beyond the Limits", the scholars of the Club of Rome have revised some of the earlier
estimations but maintained the central thrust of their arguments and recommendations.
The material balance school
The Limits to Growth, as well as “all physical deterministic models”, write Rees (1990), “fail
to take account of the fact that resources are culturally determined, a product of social choice,
technology and the workings of the economic system” (p. 38). We shall shed more light on
this weakness in the following section. There is however another school of thought, the
material balance school, which shares the same concern and arrives at similar conclusions to
the Limits to Growth thesis, but without making arbitrary assumptions about the total physical
availability of resources. The material balance thesis asserts that what is withdrawn from
6
nature should be eventually returned to nature: neither matter in nature is created nor
destroyed, it merely changes form with use. Matter changes form and is returned to the
environmental system at every stage in the production and consumption processes.
Sustainability of the economic system is conditioned, therefore, by maintaining that delicate
material redelivery. Once the balance is upset and residuals from resource use are not
smoothly and harmlessly reintegrated in nature, limits on further use and on growth could
appear (Ayres and Kneese, 1969).
2.2.
The ‘No Problem’ Thesis
Rarely has a single book provoked so much reactions, with so much passion, from politicians,
experts, as well as lay people, as the Limits to Growth. The timing of its publication just
before the break of the first international oil crisis and the soaring of natural resource prices in
the mid-1970s simply could not have been any better. The thesis is frequently referred to, in
an obvious attempt to ridicule it, as “Neo-Malthusian” or “Doom Day”. Many economists,
among whom the book was considered “essentially trivial” and “a significant retrogression in
scientific technique” (Rees, 1990, p.38), were particularly against the call for zero-growth,
which they saw as the logical implication of the Club’s pessimistic analysis. The thrust of the
attack concentrated on the book’s treatment of nonrenewable resources in general, and on its
assumptions with respect to available reserves of minerals in particular.
Critics of the limits to growth model stressed that it is impossible to provide a satisfactory
treatment for the resource depletion problems with the aid of a relatively simple model which
assumes given reserves and constant (or increasing) depletion rates. Such models ignore some
very serious issues on the fronts of supply and demand of resources, issues that may
drastically change the forecaster outcomes (see Kay and Mirrlees, 1975; Robinson, 1975).
On the supply side, there are serious problems in estimating the future size of reserves. This is
not only because improvements in technology will allow us to find more deposits, but also
because ‘proven’ mineral reserves, at any point of time, is defined as the amount which can
be extracted with current technologies and price levels. It is clear that higher prices and better
technology will increase proven reserves. In this sense, reserves should be considered as a
dynamic concept rather than a static figure: better technology increases the reserves by
allowing for the extraction of resources at lower costs. Technological development, on the
other hand, can be affected by higher resource prices. In this sense, the dynamics of resource
extraction implies that price increases, triggered by resource depletion, stimulate intensive
activities for creating additional resources.4
On the demand side, there is the serious issue of demand elasticities: as resource prices
4
An example on the relation between the size of reserves and price and technology is the development of the
North Sea oil and gas. With low oil prices in the 1960s, the search and extraction of oil from the high-seas was
unthinkable, due to the high cost. Exploration activities were not possible with the prevailing technology.
However, this was dramatically changed after the steep rise in oil prices in the 1970's. The technological
development in this area was spurred by the profit margins on basis of higher prices. Even when real oil prices
declined in the 1990s back to their levels in the 1960s, oil extraction from the high-seas continued. In 1996,
Norway was the world’s sixth largest oil producer, ahead of a number of OPEC countries, producing about 3
million barrels each day.
7
increase with depletion, demand will fall and shifts to alternative substitutes will take place. It
is wrong to assume that demand will continue to increase at the same past trends when one
also assumes that resources are being depleted. Higher resource prices will also reduce
demand via inducing more efficient resource use and stimulating resource-augmenting
technical progress. It helps to think of how many kilometers a modern car can drive with one
liter of gasoline compared with the cars of the 1950's.
The counter-attack to the Limits to Growth thesis is summarised by Feige and Blau (1980): “It
is our view that the application of neoclassical economic theory to the natural resource area
provides a much more powerful and illuminating framework ... and allows consideration of
factors that will be powerful determinants of future resource use but which have been
consistently underestimated in the forecasts of doom throughout the years. The most
significant of these factors are surely the extraordinary substitution possibilities (in both
consumption and production) induced by changes in the relative prices of resources” (page
110).
Another level of criticism against the Club of Rome stresses that the thesis divert attention
away from the real and truly urgent problem, the need for a fair international economic order
to all world’s inhabitants. It was argued that the call for a zero growth, if it is not accompanied
by a large scale income transfers on a global scale, would result in perpetuating the disastrous
world income inequality and maintenance of poverty for the majority of the world’s
population (Surrey and Page, 1975). This criticism of the Club of Rome is, actually, not totally
fair. Meadows et al. explicitly pointed out that the state of global equilibrium, which they
recommended, can be designed in a way that secures every man and woman on earth with the
basic resource whereby each person can get equal opportunity to attain his or her aspirations.
It must have become clear by now that the origin of the difficulties and confusion in the
debate is rooted in the uncertainties surrounding the involved issues. Uncertainty about the
world’s ultimate endowments of natural resources, uncertainty about how demand will react
to changes in prices, and uncertainty about the potential substitution possibilities. Risk also
corresponds with the type of the technical progress: some new or currently known
technologies, which can ease the problem of resource shortages, may turn to be socially and
politically unacceptable. This has happened recently in Sweden, where public pressure forced
the government to introduce a plan to close down the nuclear electricity-generating reactors.
As much as the limits to growth thesis seems gloomy and restrictive by underestimating the
abilities of human beings, via individual and collective choices, to control and affect their
future, the alternative school undermines the importance of the serious risks and uncertainties
with respect to technical advancement and future demand and supply of resources. This makes
the “optimistic” school no less extremist than its “pessimistic” counterpart. It rests totally on
the proper working of the price mechanism and that free markets will certainly solve all
problems. The evidence of its claim is that shortages did not happen in the past, thus why
should they happen in future? On the other hand, stated somewhat differently, technology has
solved the problems in the past and so will it in the future.
The “optimistic” school is also neither impressed nor worried about the material balance
thesis, although this does not assume particular physical limits on resource availability. Once
8
again, we are promised that higher prices will save the world: the induced technical progress
will reduce waste (Robinson, 1975). Neither the possible correlation between new
technologies and non-recycled residuals, nor the somewhat speculative nature of the
‘prescription’ seem to be reasons for worry.
As pointed out earlier, resource economics is closely related with the issues of distribution.
Advocates of the material balance suggest that the current pattern of resource uses have been
so far maintained because the majority of the world’s population is excluded. In the 1970s,
when the US population represented less than 6% of world population, their share of world
consumption of aluminium was 42%, copper and oil was 33%, zinc, lead and silver was 25%
and natural gas was 50%. Can the world’s environment be sustainable if, say, every Chinese
and Indian consume resources and produce as much waste as the average American?
Obviously, some far fetching assumptions about future technologies would have to be made if
global balance is to be maintained while the deprived 70% of the world’s population
approaches the consumption level and pattern of the affluent 30%.
3.
RENT IN ECONOMIC ANALYSIS
3.1.
The View of the Classics
The rent theory was a cornerstone in the structure of the classical economics. The classics
dealt almost exclusively with land rent associated with agricultural activity. Rent in their
terminology refers, therefore, only to the income paid to landlords in return for the right to use
land productively. In modern economic terminology, rent is synonymous with surplus and
refers to any amount realized over actual cost of production. Land, according to the classical
economists, has two intrinsic characteristics that distinguish it from other production factors:
being limited physically and exhibiting diminishing returns at the margin. It is interesting to
point out that the “law of diminishing returns”, which is central in modern microeconomics,
was first observed in connection with agriculture: the horizontal extension of cultivated area
implies that less and less fertile land would be taken into production with consequent
decreases in yield.
The classical rent theory has wide implications, from determining income distribution to
providing an ethical base for taxation. The classics considered rent to be ‘qualitatively’
different from wages and profit. Rent was morally condemned, because it was seen as a
payment to a social class that does not make a real contribution to production. This is in
contrast to labourers who extend work in return of their wages. It is also in contrast with the
capitalists who extend capital (which is ‘recycled’ into the products themselves) and earn
profit. The classicists anticipated also that rent would eventually lead to the overall stagnation:
as, increasingly, marginal land areas are brought under cultivation, rent would inevitably
increase at the expense of the rate of profit. Population increase will accelerate the pressure on
land and the long-term declining trend of profit will bring the whole economic system to a
halt. Let us concentrate here on the classics’ view concerning the reasons behind the existence
of rent and on its particular properties.
The advantages enjoyed by one firm over other firms, in certain type of activities, may emerge
9
from a pure natural advantage rather than from better application of labour and capital. This is
particularly the case of production activities which incorporate land as a basic factor of
production, like agriculture and mining, For instance, a mining company with easy accessible
iron ore would have cost advantages over another company with poorer mines and deeper iron
deposits.
Suppose that (average) production cost (and thus market price in the classic treatment) perunit of output from the superior firms is P1. Suppose also that the production of these firms
falls short of meeting the demand. Therefore, production from less-advantageous firms would
be needed. Assume that production cost in the latter firms is P2, which is higher than P1. Now,
since only one single price would exist for the same product at the market, then P2 will
necessarily be that price. Otherwise the less productive firms will not be able to produce and
demand will not be met. This implies that the advantageous firms will earn an extra profit
equal to the difference between P2 (the market price) and their own average cost P1. This extra
earning, according to the classics, is captured by the landowners and is called rent, the
‘Ricardian rent’. The Ricardian rent will exist whenever natural advantages play a role in
production processes. In the example of mining, the owners of the easily accessible mines will
capture the rent.5
Landlords would capture the rent because the competition among those who want to lease the
superior plots of land would secure that all the surplus earning go to landowners. The
maximum rent the operators would be ready to pay is the difference between the production
cost on the marginal land (which equals the market price) and the production cost on the plot
of land in question. Given this general background, the classics stressed on two particular
aspects of rent.
First, the least fertile land (or mine) drawn into production to meet the demand or the
marginal land does not earn any rent. The marginal land is, by definition, the land for which
current market price is just high enough to cover the average cost (the cost of all material
inputs, labour, and the average rate of profit on the invested capital). So long as any of the
land of a country, which is fit for cultivation is not cultivated, the worst land in actual
cultivation pays no rent. This was important in a conceptual manner for the economics of the
classics. For, if the marginal land does not pay rent then a standard would then be available for
estimating the amount of rent paid by any other plot of land. Also, and by introducing a
number of other assumptions, the classics were able to calculate the overall rate of profit in
the economy on basis of what was calculated as profit (after paying for material inputs and
wages) on the marginal land.6
5
Along with the Ricardian rent, Karl Marx introduced, in part IV of the third volume of “Capital”, a second type
of rent in his reasoning. He labeled the first the ‘differential’ rent and introduced the “absolute” rent. Absolute
rent is the amount that should be paid to landlords in order to lease land for productive use regardless of its
fertility: even if the fertility of a plot of land is worse than all those hitherto under cultivation, there is no reasons,
Marx argued, to suppose that landlords will lease it freely because the market price is just enough to bring about
the average rate of profit for the person who is exploiting it. Thus, rent should also be paid on the marginal land.
Absolute rent, unlike differential rent, takes the form of a unified per hectare payment on all land under
cultivation and is a component of the production cost.
6
This refers to the circular problem that the classics faced with respect to the rate of profit and prices: one needs
prices to calculate the rate of profit, and one needs the rate of profit to determine the prices. Ricardo ‘solved’ the
10
Second, rent is ‘qualitatively’ different from other payments to factors of production: high or
low wages and profits are the cause of high or low prices, high or low rent is the effect of it. In
his famous opposition to the ‘Corn Law’, Ricardo maintained that the price of corn is not high
because a rent is paid, but a rent is paid because the price of corn is high. Rent, in other words,
is determined by demand side and it is not a genuine component of production cost.
Moreover, since it is embodied in the value of the produced commodities, rent was seen as a
payment against which no real contribution in the production was rendered. Clearly then,
classical economics portrayed the landlords as a parasitic social class.7
3.2.
Rent, Supply Elasticity, and User-Cost
Neoclassical economists have generalised the concept of rent by extending the concept of
diminishing returns to all other production factors, and by introducing the principle of
marginal pricing. Leon Walras (1954) concluded, “Thus all that remains of Ricardo’s [rent]
theory after rigorous critical analysis is that rent is not a component part, but a result of the
price of production. But the same thing can be said of wages and interest” (page 292). Walras
also quoted Wickstead, who arrived at a similar conclusion: “It is equally correct to say that
wages are not the reason but the effect of the exchange value of commodities, and this is also
true for interest”.
Alfred Marshall, who explicitly introduced short- and long-run considerations in economic
analysis, formally generalised the idea of rent and connected it with the supply elasticities of
all production factors. He distinguished between two types of rent: quasi-rent and rent. Quasi
rent is the extra earning of any production factor, due to demand increases, whose supply is
fixed in the short-run. The latter refers to the extra earning of any production factor whose
supply is absolutely fixed. Since Marshall’s exposition, rent has been understood as the extra
earning of any factor of production over its marginal cost: the difference between the market
price and the “Marshallian supply price”.8 Within this modern interpretation, rent became
closely associated with supply elasticities. A persistent difference between market price and
the Marshallian supply price implies that long-term supply curve is not perfectly elastic, i.e.
higher prices are needed to increase supply. This may result either from increasing cost at the
margin (diminishing returns) or from presence of monopoly elements in the supply
institutions. Rent resulting from the former is called “diminishing returns rent” and that from
the second is “monopoly rent”.
problem by introducing the ‘wheat economy’: wheat is used as seed (material input), wages for labour and wheat
is the output (harvest). By deducting inputs and wages from the quantity harvested on the marginal land, the
surplus would equal the profit. This profit matches with the average rate of profit in the economy as a whole!
7
The essence of “Ricardian rent” is still alive in modern economics. Here, the stress is placed on other types of
advantages than land’s natural fertility. The proximity of plot of land to major markets may be a source of rent.
Lower transportation cost to the market and other natural advantages are usually capitalised in the price of land
itself. North Sea oil, for example, has a substantial competitive edge over Nigerian oil in the European markets
with respect to transportation costs, which gives rise to rent in the classical manner.
8
Marshall’s supply price is the price required to call forth the exertion necessary for providing any given amount
of a certain good or commodity. If market price is higher then some producers would earn higher income than
they would have been ready to settle for in a more competitive environment.
11
Along with generalizing the concept of rent, the neoclassical analysis also ‘legitimized’ the
diminishing returns type of rent: in the presence of less than perfect elastic supply, rent must
exist to secure equilibrium. Excess demand triggers a price increase over production costs in
order to eliminate the excess, and this is true with respect to all production factors. Rent can
therefore be captured by any social class and it is not a ‘trademark’ of landlords.
The true enrichment of the concept of rent came about in connection with investigating the
conditions of Inter-temporal equilibrium (i.e., market equilibrium at successive time-intervals)
of resources with finite stocks. Let us take a natural resource, say oil, which is available in a
finite stock. Let us also ignore the more efficient producers (who earn rent) and concentrate on
the marginal producer, who finds the market price of oil just high enough to cover his
marginal extraction cost. Now, since the overall stock of oil is finite, the above Marshallian
analysis suggests that future prices of oil will be higher than current prices: a price increase in
future may be needed since supply is not perfectly elastic in the long-run. The marginal oil
producer, who stands ready to extract oil, faces a zero net price (price minus marginal cost)
now but positive net price in future. The marginal producer has, in other words, an incentive
to postpone extracting oil. As we shall see later, inter-temporal efficient equilibrium requires
that deposit owners find the present value of the net price of their oil the same throughout the
time horizon. This perfectly simple and logical insight implies that:
First, current oil net price should be positive even for the marginal oil producer. This is
necessary to make producers indifference towards extracting their oil now or in future. The net
price should be positive even if scarcity of the finite resources is not felt yet but is expected in
future.
Second, to secure the indifference toward current or future extraction, it is necessary not only
to ensure that the absolute value of the net price is the same, but also that the present value of
this net price is constant, i.e. that the net price should increase at the rate of interest
throughout time.
An excess of market price over marginal extraction cost, is an inherent element in the pricing
of all natural resources that are available in finite stocks. This excess takes account of future
profit that is foregone due to extracting a unit from the deposit now rather than later. Said in
other words, any unit currently extracted has an opportunity value equal to the value of any
other unit that will be extracted at any other point in time. The exact value of this “margin”
depends largely on the way in which deposit owners perceive factors such as future cost,
future demand, and relative scarcity. The difference between the price and marginal extraction
cost has different names in the literature, including user cost, scarcity rent, shadow price, net
price, and royalty. This is dealt with, in more detail, later in this chapter.
4.
RESOURCES’ EXTERNAL AND INTERNAL ECONOMIES
It is generally acknowledged that the economic activities associated with natural resources are
especially associated with various types of externalities and/or economies of scale. The
externalities are particularly reflected with respect to the environmental effects of utilizing
natural resources. Many extractive industries are also characterised by strong economies to
12
scale, a feature which, sometimes, is used to justify monopolistic trends in resource markets.
We shall deal briefly with these concepts before concentrating on the theory of exhaustible
resources.
It is well established in economic theory that a free market mechanism can lead to an efficient
allocation of resources for various uses under a number of restrictive assumptions. The
conditions needed to substantiate that hypothesis are usually bundled together and is referred
to as “perfect competitive” environment. One of the conditions of a perfect competitive
market is that the cost or benefit born by any individual from his/her own economic activity
must match the cost and benefit born by the society as a whole. In other words, the cost born
by an individual (and by the society) when producing a unit of output must exactly match the
benefits gained from consuming it. These costs and benefits are faithfully expressed by the
marginal cost born by the producer and the price paid by the consumer. If the producer does
not bear all the cost of production, then neither marginal cost nor the market price will be an
honest reflection of the true cost and benefits. When social production cost is larger than the
private cost, and when the concerned commodity is sold at its (private) marginal production
cost, then, the consumer would be deriving larger benefits from consuming it than expressed
by its price. The cost in this case is not ‘internal’ to the economic agents, but ‘external’. In the
opposite situation, when social cost is lower than private cost, some of the benefits of
producing and consuming the concerned goods would be ‘external’ to the private economic
agent. This implies the market price is lower than (private) production costs and so the goods
or services in question would not be provided by profit-seeking firms. An obvious example of
this is a firm’s expenditure on research and training. Since the firm’s own returns from this
expenditure are usually lower than the returns to society as a whole, free market forces would
lead to lower expenditure on training than is socially desirable and optimal.
When private costs and benefits of any economic activity diverge from the social costs and
benefits, it is said that externality exists. Free market forces are unable to deal with
externalities. Once the signals, on basis of which free markets will allocate resources, are
‘wrong’, then the market mechanism can hardly be expected to bring about an efficient
allocation. Usually, a system of taxes and subsidies are needed in order to ‘internalize’
externalities and to create balance between private and social costs and returns.
There are different types of externalities. A particular type refers to the situation where
exclusive provision of goods and services to only those who pay for them is not possible:
Provision of clean, non-polluted air is an example of this type of externality, which is known
as the ‘public goods’ case. Another type of externality refers to the situation where the action
of one agent inflicts extra cost that is born by other agents. This type of externality usually
arises in common property areas with open or free access, such as fishing in high seas.
Solving such problems are, therefore, closely connected with the way property rights are
defined. Having defined property rights does not always remove the problem. Of particular
interest relates to extractive activities. For example, a natural resource (e.g., oil or natural gas)
reservoir under a large surface area of land owned by different people. Although property
rights of the land surface may be perfectly defined, extraction of one unit by one owner would
reduce the stock for all other owners and would increase their extraction cost.
The above-mentioned externalities, which could be either positive or negative, are referred to
13
in the literature as ‘external economies’ and ‘external diseconomies’. These are distinct from
‘economies of scale’. Economics of scale refers to the inverse relation between the per-unit
cost of production and the volume of production. Certain economic activities are characterised
by very strong economics of scale. For example, once the initial huge investment for starting a
cable-tv transmission is in place, registering a new subscriber will add nothing to the fixed
cost, leading thus to a reduction in the per-viewer transmission cost. Thus the more viewers
there are, the lower would be the price of the service. These types of economic activities are
sometimes referred to as ‘natural monopolies’ in the sense that there is little room for
competition.
The idea of strong scale economies has been used to rationalise the monopolistic tendencies in
the world markets for minerals in general and for crude oil in particular. For example, in the
mid-1950s, the world oil market was effectively monopolised by seven giant multinational oil
companies, the famous “Seven Sisters”. A theory suggested then that the oil industry is a
perfect example of a decreasing cost (or increasing revenue) type, which makes it a typical
candidate to turn into a ‘natural monopoly’ industry. Once initial investments in oil
exploration, extraction, and transportation are made, the larger the production, the lower the
per-unit cost will be. Thus, taking the entire market will give the lowest per-unit cost.
Producing an extra barrel of oil would reduce the per-barrel extraction cost of all output and
would therefore increase revenues. This would motivate the oil companies to increase supply
without a limit. However, as this is done, the market will suffer from “inherent surplus” and
prices will decline. Oil producers, if they are acting individually, must therefore eventually
operate at a loss. Such a situation, of course, cannot be sustained in the long run. In natural
monopoly industries, only a single producer is allowed for in the market to cartelise output.
Otherwise, some kind of collaboration is needed among producers to regulate supply and keep
up the price. This is what the “Seven Sisters” did long before OPEC was founded (see UN,
1955).
5.
THE PURE THEORY OF EXHAUSTIBLE RESOURCES
The fundamental issue in the theory of exhaustible resources is to determine the conditions
under which exploitation of finite resource is economically efficient. Economic efficiency is a
concept that incorporates two distinct elements: technical efficiency and allocative efficiency.
Technical efficiency ensures that the economy is producing the maximum attainable level of
output for given levels of inputs and given technology. Allocative efficiency, on the other
hand, refers to the utilization side and ensures that resources, including factors of production,
and goods and services, are utilized by those agents who value them most.
Economic efficiency does not say anything about equity or fairness of distribution of resources
among members of a society. Economic theory maintains that while it is possible to
objectively define the conditions under which the resource base of a society is as large as
possible, the issue of how these resources are distributed is a normative or subjective one. In
other words, defining the conditions under which economic efficiency can be attained is the
business of economists, but defining distribution is a moral issue and is everybody’s business.
Many social scientists, including some economists, do not accept this isolation between
‘science’ and ‘values’, but we shall not dwell on that here. It is important to stress however
14
that both efficiency and equity are equally important concepts and societies cannot afford
concentrating on one at the expense of the other, especially in the area of exhaustible natural
resources.
Efficiency and equity can be investigated in either a static or a dynamic manner. However, due
to the inherent characteristics of depletable resources, economists concentrate on the dynamic
aspect of efficiency and equity. The theory aims, therefore, at defining the efficient extraction
programme over the life span of the resources rather than within a single period of time. The
same is true with respect to equity: it is not the distribution among members of a single
generation, but rather the distribution among various generations, which is the focal of
concern. The theory, in other words, assumes that static efficiency (and equity) is acquired and
directs its attention on efficiency across successive periods of time, the so-called
intertemporal efficiency. Let us deal first with efficiency conditions in exhaustible resource
markets before turning our attention to the equity issues.
5.1.
The Inter-temporal Depletion Time-Path: Efficiency
The basic insights of the theory of exhaustible resources were laid down in the early 1930s by
the seminal works of H. Hotelling. Hotelling (1931) observed that equilibrium between the
flows of supply and demand of a natural and finite resource implies that resource owners must
be indifferent as to when they extract and sell from their deposit. If this were not the case, then
resource owners would extract either too much or too little relative to demand. Based on this
observation, he made a postulation about the price movement:
“Since it is a matter of indifference to the owner of the mine whether he
receives for a unit of his product a [net] price P0 now or a [net] price P0ert
after time t, it is not unreasonable to expect that the [net] price will be a
function of the time of form P = P0ert, r being the force of interest” (page
140).
Hotelling, in other words, suggested that equilibrium of the flows of supply and demand in
resource markets requires the net price (i.e., price minus marginal extraction cost) to be the
same at any point in time. No other price time-path would secure supply to regulate itself in
order to clear the markets of finite resources. This net price is the scarcity rent component that
we referred to earlier as ‘user cost’. It is inherent in the pricing of all exhaustible natural
resources.
The same line of reasoning was also suggested by Solow (1974), but in connection with
equilibrium conditions in asset markets: under which condition will a resource owner be
persuaded to hold on to his resource assets? Only if he is made indifferent towards holding the
resource underground or in any other capital asset: “A pool of oil or vein of iron or deposit of
copper in the ground is a capital asset to society and to its owner, much like printing press or a
building or any other reproducible capital assets” (p.1). As capital assets, Solow argues,
natural resources underground should produce returns to their owners, and these returns would
match with the prevailing interest rate in equilibrium. Yet, since these returns cannot be
collected before the resources are extracted and sold, then their net price should grow at the
rate of interest while they are buried beneath the surface.
15
This rule, stipulating that equilibrium net prices of exhaustible resources are positive and
increase exponentially at the rate of interest, is called Hotelling Rule. “It is hard to
overemphasise the importance of this tilt in the time profile for net price”, wrote Solow, and
added that this is “the fundamental principle of the economics of exhaustible resources” (page
3). Hotelling Rule sets out the necessary condition for efficiency or for securing that an
extraction time-path is economically efficient. By ensuring that each unit of the reserve brings
about the same net price to the owner as any other unit, regardless of when it is extracted, the
rule guarantees that more will be extracted from any given stock than under any other price
path. Box 1 presents two approaches for deducing the necessary condition for efficiency in a
more formal manner.
Box 1. Hotelling Rule
As pointed out in the text, the fundamental principle in exhaustible resource economics, or
Hotelling Rule, can be deduced either on basis of stock equilibrium in the assets market or
flow equilibrium in the resource market. Let us take the first and present it within the
framework of partial equilibrium.
Assume that time is measured in equal intervals, such that if the current period is t, then the
following period is (t+1). Assume also that there is an exhaustible natural resource whose
extraction cost is zero and spot price per unit is pt at time t. Assume finally that there is an
asset in this economy whose unit price is pt also and that this asset gives a positive rate of
return rt at each time interval (t, t+1).
Now, any individual in that economy with pt money holding at time t can either choose to buy
a unit of the asset or a unit of the resource. Under the condition of competitive equilibrium,
individuals should be indifferent between these two options, i.e. the gains from either of them
must match with the gains from the other. If an individual chooses the asset option, she will
end up with (1+ rt )pt at time (t+1). This implies that a resource unit whose price at time t is pt
should appreciate at time (t+ 1) to a price equal to pt+1 =(1+ rt)pt. When time is taken as
continuos, the previous equation can be rearranged as ∆pt/pt = rt. Now, since the only way for
unextracted resources to yield returns is by appreciating in value, the price of the natural
resource should increase over time at the rate of return on other assets. By assuming that r is a
positive constant, integrating both sides of ∆pt/pt = rt with respect to t gives:
pt = p0 ert
(1)
This is the equation that was cited from Hotelling’s article in the body of the text. The
equation describes the movement of the spot price of an exhaustible resource. If extraction
cost is zero, the present value of the price will remain constant, i.e., the price will compound
at the rate r, which must equal the overall rate of interest in the economy.
The proof of the same idea on basis of flow equilibrium is also straightforward. Assume that
the reserve stock of a natural resource at time t is Rt, and the spot price per unit is pt. The spot
16
value of the total reserve would then be Rt*pt. Under competitive conditions, the spot value of
total reserve must equal the sum of present values of the resource when it is extracted in
portions over time in future. If the spot value were larger than the discounted future values
then nobody would wish to hold the stock, and if it were the opposite then nobody would wish
to extract from the stock now. This implies that the present value of the resource price must be
constant, i.e., the price must increase at the rate of interest. Note finally that, in equilibrium,
the rate of return on all forms of capital assets in the economy must equal the rate of interest.
Another more frequently used approach to deduce Hotelling Rule is to find the conditions
under which an extractive company maximizes the present value of all its future profits. The
maximization problem is subject to a number of constraints, including the finite reserve. It is
easy to demonstrate that overall profit will be at maximum when the marginal revenue of
extraction increases at a rate equal to the rate of return on capital. Under a perfect competitive
environment, marginal revenue is synonymous with the price, and the return on capital is the
rate of interest9. This technique is dealt with in Box 3.
The fact that the net price or user cost rises exponentially does not mean that the market price
would necessarily rise too. This would be the case only when extraction cost is ignored. In
general, resource price to the consumer consists of two components, marginal extraction cost
and the user cost. If marginal extraction cost is positive, then equilibrium market prices may
actually decline if the decline in marginal extraction cost more than offset the exponential
increase in the user cost. It may also increase at a slower or faster rate than the interest rate:
with positive and non constant extraction cost, market price will increase at the weighted
average of the interest rate and the change in extraction cost.
Hotelling rule, important as it is, provides only the necessary but not the sufficient condition
for securing efficient extraction time-path. The rule defines the pace at which the net price
should increase in order to insure that the present value of every unit extracted throughout the
time-path is constant. This will allow more output to be extracted from the fixed available
deposits, but it does not necessarily secure that all available reserve will be extracted. It is
clear that any time-path, which fails to extract all the reserve, will be inefficient. To insure
efficiency, the sufficient condition should be added to the necessary one. Efficiency requires
also that total available (and known) stock under the ground should be completely extracted.
The sufficient condition can be inserted in different ways into the model. The basic aim here
9
In the other extreme form of the market, monopoly, the maximization condition would be the same: marginal
revenue should grow at the rate of return on capital. However, marginal revenue here would be different from the
price: the monopolist is not a price-taker but will take into account the effect of higher prices on demand and the
resulting impacts on his revenues. There are conflicting views among economists as to whether a monopoly
produces at a faster or a slower rate than competitive firms. Hotelling suggested the latter, in line with the
standard treatment of monopoly. Solow supported the former view. The question depends, in fact, on demand
elasticities and extraction cost. If the demand elasticity is constant and extraction cost is zero, then the time-path
of resource use will be identical under the two extreme market forms. If elasticity is increasing over time and/or
extraction cost is positive, then the monopoly price will be above the competitive price (and the monopoly will
produce less) at the initial stages. The monopoly price will be below the competitive rice and the monopolist
will produce more than competitive firms at the latter stages of the resource life. In general, however, it is argued
that the life time of the resource might be longer under the monopoly. (Cf. Heal, 1977).
17
is to define the current price level at any point of time. Since the movement of this price is
already defined by Hotelling Rule, defining its absolute level at any point determines the price
along the time-path. Once a demand function for the resource is introduced, the sufficiency
condition would be expressed by a current resource price, which would secure that the
accumulated demand matches exactly with the total available reserve stock. In other words,
the sufficient condition of efficiency is expressed in terms of the initial absolute price of the
resource. To ensure extraction of the entire stock, the initial price must be at a specifically
defined level. As it increases, in accordance with Hotelling Rule, it should reach its maximum
at exactly the same time when the last unit of the reserve is demanded. Beyond that point, the
demand will fall to zero and the reserve will be totally used up.
If the initial price is set higher than the efficient level, extraction would be slower and the
maximum price, beyond which demand would fall to zero, would be reached while there is
still some reserve under the ground. Obviously, this would not be an efficient extraction timepath. If the price was set lower, then extraction will be too fast and exhaustion would take
place before demand vanishes. Box 2 presents the above exposition in a more formal fashion.
Box 2. The Necessary and Sufficient Conditions for Efficiency
As pointed out in the text, Hotelling Rule defines the shape of the efficient price time-path of
exhaustible resources, but not the level of the price, which is a sufficient condition. To define
that price, we need some information about the relationship between the price of the resource
and the corresponding demand. Let us assume a simple demand function Dt(pt) and that
annual extraction from the reserve (Et) matches the annual demand. Thus, Et = Dt(pt). Assume
further that the demand does not shift over time and Dt (pt,t) = pt -1/α, where α is the price
elasticity of demand (α > 0)10.
Now substituting (1), from Box 1, into the demand equation gives the following expression:
E t = p o−1 / α e − ( r / α ) t
(2)
The above equation suggests that the rate of resource extraction would decline at a constant
base equal to (r/α). As the equilibrium price increases at the rate r, demand would decline as
prescribed by the price elasticity α.
Now, if R0 is the initial reserve of an exhaustible natural resource (the accurately known
reserve at present time, t = 0), feasibility condition requires that the accumulated amount to be
extracted from the reserve should not exceed total available stock. Assuming a contentious
extraction path through time Et, the feasibility condition can be expressed in the following
inequality:
10
Strictly speaking, this relation implies that the demand is positive irrespective of the price. This implicitly
means that the resource will not be exhausted in a finite time along the equilibrium extraction path. This
simplification, however, does not affect the results.
18
∞
E t dt ≤ R 0
(3)
0
This implies that extraction from an exhaustible reserve must necessarily decline to zero in the
long run, i.e., limt → ∞ Et = 0.
Let us integrate Et over the horizon of t (from 0 to ∞) to find out the price level that would
secure the maximum utilization of available reserve. By substituting Et from (2) into (3) and
integrating the expression we get:
∞
∞
E t dt = P0
0
−1 / α
e −( r / α ) t dt = (α / r )Po−1 / α ≤ R 0
(4)
0
Thus an initial price p0 = (r R0/α)-α would secure that total accumulated output would exactly
match total available reserve, R0. Only at this initial price level, which must increase at the
rate of interest, would the extraction time-path be efficient. Note that, the price that secures
current equilibrium in the resource market may not lead to an efficient extraction time-path.
The system needs some definite signals to prod the economy in a direction to be able to select
the ‘correct’ current price in order to achieve an efficient time-path.
5.2.
The Intertemporal Depletion Time-Path: Equity
Efficient outcomes, as pointed out earlier, may be unattractive from the society’s point of
view. Efficiency is actually only one of the concerns that a society has when considering
extraction of exhaustible resources. Given that efficient use of available resources is made, the
question then is how should the maximum producible output be distributed? Which of the
numerous efficient time-paths is socially optimal and should, therefore, be selected? We are
clearly here in the realm of social choices, for “choosing an optimal path means choosing who
is to be made better off at the expense of whom because, given the efficiency, there is no way
to make one individual or generation better off without making another worse off” (Feige and
Blau 1980, p. 123). By concentrating on producing the largest possible output, efficiency
analysis is relatively simple and straightforward compared with equity analysis. Equity is
concerned with securing that the efficient extraction time-path is also socially ‘desirable’. The
very use of this word implies making postulations about the aspirations, needs, tastes, and
values not only of current generation but of the generations to come as well.
The standard application of optimality analysis to exhaustible resources concentrates on
intergenerational optimality rather than optimal distribution within a single generation. To
simplify treatment, the models presume that the question of distribution within each
generation is resolved, say, by assuming all individuals in each generation have identical
tastes and receive equal shares of current output. Thus, the models can focus on comparing the
welfare of “typical” individuals in different generations.
The aim of the analysis is to select the “best” distribution of aggregate welfare among all
generations. To the extent that welfare is derived from consumption of goods and services,
19
optimality refers to the intergenerational allocation of these goods and services. Furthermore,
since production of these goods and services requires natural resources, optimality analysis
gives certain indications about the “best” way to share these finite resources among different
generations.
The usual technique here is to assume the existence of a social welfare function, which
represents the aggregate social utility of current and future generations. Utility is measured by
consumption of a composite good whose production requires both reproducible and
exhaustible inputs. The aim is to select the particular demand curve, which maximises the
social welfare function. The maximization is bound by a number of constraints:
•
•
•
A production function that accounts for the output of the composite good. The production
function specifies that some inputs, including natural resources and capital, are necessary
in the production process.
Total output in each period is split between consumption, which is the argument in the
target social welfare function, and investment, which is needed for production and
increases output in the following periods.
Finite reserves of natural exhaustible resources.
The results of the exercises along these lines, not surprisingly, depend crucially on the
assumptions with respect to:
•
•
•
The elasticity of substitution between reproducible and natural resources in the production
function and the effect of technical progress.
The population growth rate.
The discount rate on basis of which the present value of the utility of future generations is
calculated.
It is easy to understand that no clear-cut results are agreed upon when one recognises the high
degree of uncertainty that exists with the above-mentioned parameters. The central message of
the analysis, however, is that one should not look at equity in the narrow sense of simply
looking at the division of finite natural resources within a particular generation. Under certain
assumptions, it may turn out to be perfectly ‘fair’ to leave fewer natural resources to future
generations provided that they are also given better technology and/or more capital. Actually,
as affirmed by Stiglitz (1974), the question of whether an economy is able to sustain a
constant per-capita income while resources are being exhausted, can be answered in the
affirmative if one of the following three conditions are satisfied: whether the elasticity of
substitution between capital and natural resources is greater than one; whether the elasticity is
one and the share of capital is greater than the resources in production; or whether there is
resource augmenting technical change.
However, Dasgupta and Heal (1974), assuming constant population, infinite time horizon, and
positive social time preference, concluded that it is optimal to deplete only a constant
percentage of the stock at each period if the resource is “essential” for production of output.
The model, in other words, suggests that it is not optimal to exhaust the resource stock
entirely. Dasgupta and Heal concluded that the higher the social discount rate the larger is this
percentage. Other models have also stressed the effect of the chosen discount rate (relative to
20
the rate of technical progress) on the optimal path, e.g., Stiglitz (1974). In fact, one of the
standard conclusions of the theory is that the optimal time-path will exhibit a slower rate of
extraction the smaller the social discount rate is. Also, when capital is allowed to substitute
for exhaustible resources, the optimal path will dictate a higher rate of capital accumulation
the smaller the discount rate is.
The Social Discount Rate. The importance of the social discount rate in intertemporal
optimality analysis demands an extra treatment here. The discount rate used for calculating
present values of future consumption is the rate which the society considers “desirable” for
inter-temporal substitution: how much of the next generation’s consumption (welfare) weighs
relative to ours? This is a measure of the marginal rate of transformation between
consumption at different dates: if the rate is s, then a given generation will be indifferent
towards consuming C now or leaving C(1+s) for the consumption of the following generation.
The discount rate s is called the social rate of time preference. Much of the ethical values in
the area of intergenerational equity are in fact coded into the social rate of time preference.
Under the usual strict assumption of perfect competitive markets, it can be proved that the
social welfare function reaches its maximum value when the social rate of time preference, s,
equals the social rate of return to capital, r. The logic of this equilibrium is quite simple: the
satisfaction derived from consuming a unit today would equal the satisfaction derived from
consuming 1+ s in the following period and investing a unit today will bring about 1+r units in
the next period. Then, if s > r, the society will lose from transferring one unit of consumption,
which has the same value of 1+s for the consumers in the next period, to investment, which
will become only 1+ r in the following period. In this case, the welfare of the society will be
higher if the unit was consumed rather than invested. The opposite will be the case when s < r.
Note also that the social rate of return on capital coincides, under certain conditions, with the
market interest rate.
Inter-temporal optimality analysis needs a generally accepted ethical standard for weighting
the welfare of future generations. A 5% rate implies that the welfare generated from the
consumption of one unit of the resource today is equivalent to the welfare generated by the
consumption of 11.4 units in 50 years time. Judged on a superior ethical ground, one may
argue that the 5% rate assigns far too little importance to future consumption. When this rate
is used in the maximisation exercise, the result would therefore be biassed: more resources
will be devoted to current consumption at the expense of future generations. It is generally
recognised in the literature that the market interest rate is, in fact, much higher than the social
rate of time preference. That is, future consumption would be excessively discounted if the
market rate were used. In fact, one of the standard conclusions of the theory is that the optimal
time path will dictate a slower rate of extraction the smaller the social discount rate is. When
capital is allowed to substitute for the use of exhaustible resources in production, then the
optimal path will dictate a higher rate of capital accumulation the smaller the discount rate is.
However, a number of economists argue that there is no ethical justification for weighting the
utility of future generations at less than that of the current generation. Some economists have
even judged the whole idea of discounting the utilities of future generations as “morally
objectionable, ethically indefensible, and arises merely from the weakness of the
21
imagination”.11
Solow (1974a) constructed a model that adopts an alternative ethical criterion for
intergenerational distribution, the so-called Rawls’ max-min standard: consumption per head
should be the same for all generations.12 With no technological change, infinite horizon,
constant population, Solow concluded that Rawls’ standard requires that each generation
should have the same initial capital stock as any other. The problem then is to “find the largest
constant consumption per head which can be maintained forever with account taken of the
finiteness of the pool of exhaustible resources” (page 35). When the elasticity of substitution
between natural resources on the one hand and capital and labour on the other is assumed to
be one, the model suggests that a constant output can be maintained through time provided
that each generation creates enough capital stock to replace the resources it has used up.
Solow concluded then that “earlier generations are entitled to draw down the pool (optimally,
of course!) so long as they add (optimally, of course!) to the stock or reproducible capital”
(page 41).
5.3.
Inevitable Imperfection and Lack of Future Markets
Economic theory postulates that free mechanism, under perfect competitive environment, can
automatically secure efficiency, but no such claim is made with respect to optimality. This is
simply because the allocation of resources in a society, at any point, determines the
distribution of income and wealth in the following periods. That is, each competitive
equilibrium is contingent on the initial distribution of endowments. If endowments are
unequally distributed then the distribution of the welfare, resulting from the efficient
equilibrium, may not be equal.
The aim of this section is to find out the conditions under which the free market mechanism
can guarantee efficient use of the exhaustible resources. The goal is not to discuss whether the
ideal conditions of perfect competition can be found in the real world. Our interest lies rather
in pointing out the particular forms of market imperfections that arise from the inherent
characteristics of natural exhaustible resources.
We have already identified the characteristics of the efficient time-path of resource extraction.
Competitive owners of finite natural resources should design their extraction programme in
such a way that market price matches with marginal extraction cost plus user cost. The
necessary condition for inter-temporal efficiency, the Hotelling Rule, dictates that the user
11
These are the words of Ramsey as cited in Dasgupta and Heal (1979) p.261. The Utilitarian school argues
strongly against the “myopic” view of using a positive rate for discounting the utility of future generations. The
school maintained that “...the time at which a man exists cannot affect the value of his happiness from a universal
point of view”. Therefore the utility of each and every person within a single generation and/or across all
generations should be “weighed in ideal scales against any other”. Other economists argue, that the existence of a
positive return on capital justifies a positive discount rate otherwise the current generation would not invest.
Others have also suggested that the mere possibility that life may cease on earth calls for the use of some positive
discount rate.
12
Rawls’ max-min standard postulates that social welfare (utility) of any generation equals the utility level of the
least well-off generation.
22
cost should increase exponentially at the rate of interest. Furthermore, the sufficient condition
ensures that the entire deposit is extracted. The sufficient condition can be expressed in terms
of certain specifications about the initial price. The question then is under what conditions can
free market forces be entrusted to make such a stringent selection? There are serious reasons
for doubting the ability of the free market mechanism in this area. An aspect of this was
expressed clearly by Hotelling in his seminal article: “There are in extractive industries
discrepancies from our assumed conditions leading to particularly wasteful forms of
exploitations which might well be regulated in the public interest” (page 143).
Let us first examine in detail the concept of user cost. This sacristy rent measures the effect
that another unit of current extraction has on the present value of the stock. Now, when
deciding how much to extract in the current period, a resource manager sets marginal
extraction cost equal to price minus user cost, “but user cost” as Peterson and Fisher (1977)
pointed out, “depends on expectations of future prices and costs” (page 711). This circularity
can very easily lead to erratic and mistaken extraction decisions. On the other hand, since
marginal extraction cost is not the same in different mines, then user cost should actually vary
from one mine to another. Along with making the efficiency conditions far more complex
than suggested by the simple models, this also intensify the erratic nature of user-cost. Being
the reflection of the future cost of present extraction, as perceived by various managers, user
cost became an even more illusive concept to observe: it is a component which “moves in no
particular direction as resources are depleted” (ibid., page 705).13
However, the most important precondition needed to give individual decision-makers any
chance of approaching efficiency is the existence of future markets for natural resources. For,
in order to calculate the correct price today, deposit owners must know and be certain of how
and where the price will move in the long run. Future markets are needed to provide
trustworthy signals about future supply and demand so that owners can hedge against various
forms of uncertainty. The existence of such markets turns, therefore, to be a precondition for
efficiency. Yet, this condition is plagued by the worst of market imperfections in the real
world. They are absent. Absence of future markets implies that resource owners would be
forced to make decisions in a state of total uncertainty and resources would be exhausted
faster or slower than the efficient rates, depending on the owners’ perceptions of the state of
the world and their personal attitudes to risk.
Accurate signals about future prices are needed for competitive equilibrium in all types of
economic activities, including resource markets. This is because markets may settle for a long
time on a short-run stable time-path even when this does not secure an efficient long-run
equilibrium. Signals about future prices are also needed for the sake of making correct
investment decisions. Extractive industries require usually huge investments in highly
specialised and irreversible capital goods with a long gestation period and strong economies to
scale. Furthermore, demand for resources is largely, inelastic. All of these imply that relatively
13
It is interesting to point out that some economists, as a reaction to the illusiveness of user-cost concept, argue
that resource owners behave in fact just like any producer of reproducible goods, i.e. they produce up to the point
where marginal extraction cost equals the price (with user-cost equal zero). Resource owners, in other words, aim
at maximising their current profit from current extraction rather than future profits. This, actually, implies that
final exhaustion will never take place and exhaustible resources are, after all, non-exhaustible!
23
small errors in anticipating the price may lead to dramatic effects on future supply. In the
dynamic setting of resource economics, the decisions of current consumers and producers
about current supply and demand are also decisions about future supply and demand.
Many economists have also argued that resource markets are permeated with many types of
risks. Feige and Blau (1980) pointed out that "uncertainty and risk permeate most aspects of
natural resource industries to a greater degree than in many other areas" (page 127). Stiglitz
(1975) stressed the particular difficulties of anticipating demand and supply of energy
resources in particular. The risks about possible technical progress and future demand are
indeed real: the decisions on how much to explore and extract require some precise ideas
about when (or if!) and at what cost synthetic substitutes will be discovered. Along with these,
there are the risks associated with estimating the overall available reserve stocks and
estimating the effect of each unit extracted on the future marginal extraction cost.
Another interesting issue refers to the relation between market price and extraction cost. In
order to secure a smooth increase in the price, as depletion accelerates and scarcity increases,
one needs to assume that deposits that are cheaper to extract must be exploited before those
with higher extraction costs. If this was not the case, then market prices may fluctuate and
create further confusion in the market. The requirement of exploiting cheaper deposits first is
not totally consistent with the occasional discoveries of extra ordinary favourable deposits.
Finally, one ought also to keep externalities in mind. Economic theory maintains that markets
cannot allocate resources efficiently in the presence of externalities. This, of course, is true in
all markets. Yet, many economists have stressed that externalities may in fact be more serious
in the inter-temporal resource allocation of natural resources than in most other areas of
investment. Externalities are witnessed during all the stages of resource industries, from
exploration to consumption. Peterson (1975) referred to two externalities in this respect:
external economies resulting from any explorative activity, which provides free information
about the potentials of finding deposits in nearby areas, and external diseconomies where
exploratory activities and new discoveries increase the cost of future explorations. A number
of other economists identified numerous forms of externalities, including environmental
degradation, concerning the extraction, transportation and consumption of natural resources.
In short then, competitive market economy leads to economic efficiency in resource use only
under very specific conditions. The most important of these are (Stiglitz, 1975 p.55):
•
•
•
the existence of a full set of futures market;
the existence of a full set of risk (insurance) markets; and
absence of all forms of externalities.
Economists are (almost) in agreement with respect to the following three propositions:
•
•
•
that these basic conditions are less readily available in exhaustible resource markets than
in other markets;
that imperfections in resource markets are closely related to the inherent nature of finite
natural resources; and
that these market imperfections have much more significant consequences on the
24
performance of resource markets than other types of activities.
What economists are still arguing about is whether all of these provide sufficient ground for
abandoning free market mechanism in the area of natural resources? One answer is eloquently
formulated and rigorously argued for by Dasgupta and Heal (1979): “A competitive process,
even if it were to sustain an equilibrium at each instant in time, cannot be relied upon to coordinate flows and stocks of an exhaustible resource in such a manner as to result in an
efficient outcome. This requires either a complete set of forward markets or a conscious effort
of a planning board” (p. 166). The standard model of exhaustible resource market can be
easily adjusted to accommodate for social rather than private management. This is done in
Box 3. Another school of thought maintains, however, that a social manager may be able to
reduce some market imperfection and able to bring resource market closer to efficiency. This
is particularly with respect to elimination of some forms of externalities and of certain types
of risks associated with decisions which involve only a small segment. However, the
conscious effort of a social manager in attaining efficiency via maximizing some sort of social
utility function would eventually confront the same problems as individual private decision
makers. The advocates of this school argue further that there is no reason to assume that a
social manager will have better foresight of the future than private managers (see, for
example, Peterson and Fisher (1977) page 703).
Box 3. Social Management of Resource Market
Economic efficiency can be acquired by an administrative body appointed by the society. Such
a body or a planning board would look into the future and fix a (shadow) price, λ, which
would co-ordinate the resource flow and stock and secure an efficient extraction time-path.
Let us look at the resource extraction problem from a social point of view. Assume that the
social utility of consuming an exhaustible resource is U(Et). The aim now is to define the
extraction time-path that would maximize the present value of total social utility from
consuming the resource. Find Et that brings about the highest possible value for the following
problem:
∞
max U(E t )e − rt dt
(5)
0
The maximization should be undertaken subject to the following conditions: that total
accumulated extraction may not exceed the available reserve,
∞
E t dt ≤ R 0 , which is the same equation as (3) in Box 2 above; and that
0
Et, Rt ≥ 0 for t≥0 (t=0 is the present time).
The above problem can be solved by realizing that efficiency necessitates that the extraction
time path Et should satisfy the following:
25
∞
E t dt = R 0
(6)
0
On the other hand, optimality requires that the present value of social marginal valuation of
the resource or marginal utility of society from consuming the resource is constant over the
time horizon of the resource life:
U ′(E t )e −rt = λ
(7)
Hotelling rule can be easily deduced from (7), by noticing that the derivative of the utility
function (the marginal utility) equals the resource price.
6.
CONCLUSION
The chapter started with a review of the debate on current and future availability of
exhaustible natural resources. The important issues here are the possible implications of
resource exhaustion on economic growth and standards of living. Some economists are
optimistic and perceive resources other than as deposits that are static and fixed. However, the
issues are blurred with uncertainty and risks. The view that exhaustion of some, or even of all,
essential resources is not necessarily catastrophic rests on substitution possibilities between
exhaustible and inexhaustible inputs and the powerful incentives of the prices.
The chapter proceeded then to deal with two the basic concepts in resource economics: rent
and externalities. The view of classical economists, stressing the peculiarity and immorality of
rent compared with the returns received by other production factors, was presented.
Neoclassical extension of rent to other production factors was also examined. The peculiarity
of natural resources was revived when it was realized that present extraction of a unit from
any finite reserve corresponds with an opportunity cost of extracting it in future. The
equilibrium market price of such a resource should, therefore, be higher than its marginal
extraction cost: the difference between the two accounts for the scarcity rent.
Thereafter, the chapter turned to concentrate on the theory of exhaustible resources. The
conditions under which a resource extraction time-path qualifies as an efficient path were
singled out: the necessary condition or Hotelling Rule and the sufficient condition, which
ensures that total available reserve would be demanded and extracted. Then we turned to
optimality analysis: which of the efficient time-paths should be selected? It was stressed that
the selection of the “best” depends on the criteria agreed upon in the society. The significance
of the social rate of time preference as a code of society’s values was stressed with respect to
inter-temporal analysis.
Our investigation of the theory of exhaustible resources revealed that popular analysis of
physical availability of natural resources and the necessarily catastrophic implications of
resource exhaustion are rather simplistic. This is particularly true with respect to the role of
the prices and the potential of resource-augmenting technologies. Resource stock is certainly a
dynamic concept and this is correlated with the price levels and the state-of-the-art: resources
26
cannot be identified without reference to mankind future wealth and technological
possibilities. This, however, hardly justifies the equally simplistic and naive attitude of the No
Problem school: total reliance on the price mechanism of free market. The last section in the
chapter was devoted to a discussion on why the free market mechanism may fail to secure the
selection of an efficient time-path of resource extraction. The theory of exhaustible resources
casts serious doubts on the claims of the enthusiasts about the magical abilities of the price
mechanism. Dasgupta and Heal (1979) make this point clear: “the forces of supply and
demand will ensure that natural resources are utilised efficiently over time. It is undoubtedly
the case that there are many who will make this claim and will at the same time be totally
innocent of what precisely the claim is, or at the very least, be ignorant of the conditions under
which such a claim can be defended. There must be many whose faith in the market
mechanism is abiding, but who would be surprised if they were to learn of the features that
need to be instituted for that faith to be justified” (p. 111).
27
REFERENCES
Adelman, M. (1972). The World Petroleum Market. John Hopkins University Press.
Ayres, R.U. and Kneese, A.V. (1969). Production, consumption, and externalities. American
Economic Review 59(3):282-97.
Dasgupta, P. and Heal, G. (1974). The optimal depletion of exhaustible resources. Review of
Economic Studies 42:3-28
Dasgupta, P. and Heal, G. (1979). Economic Theory and Exhaustible Resources. Cambridge
Economic Handbooks.
Feige, E.L. and Blau, D.M (1980). The economics of natural resource scarcity and implication
for development policy and international co-operation. In P. Dorner and M. El-Shafie
(eds.). Resource and Development. Croom-Helm, London. 109-148.
Heal, G. (1977). The long-run movement of the prices of exhaustible resources. In Economic
Growth and Resources- Proceedings of the Fifth World Congress of the International
Economic Association. Vol. I: The Major Issues. Tokyo. 89-107.
Hotelling, H. (1931). The economics of exhaustible resources. Journal of Political Economy
39:137-73.
Kay, J. and Mirrlees, J. (1975). The desirability of natural resource depletion. In Pearce D.W.
and J. Rose (eds.). The Economics of Natural Resource Depletion. New York: Wiley, 14076.
Meadows, D.H., Meadows, D.L., Randers, D., and Beherns III, W. (1972). The Limits to
Growth- A report for the Club of Rome’s Project on the Predicament of Mankind.
Universe Books, NY.
Meadows, D.H., Meadows, D.L., and Randers, J. (1992). Beyond the Limits-Global Collapse
or Sustainable Future. London: Earthscan Publications.
Pearce, I. (1975). Resource conservation and the market mechanism. In D.W. Pearce and J.
Rose (eds.). The Economics of Natural Resources Depletion. New York: Wiley. 191-203.
Peterson, F. (1975). Two externalities in petroleum extraction. In G.M. Brannon (ed.). Studies
in Energy Tax Policy. Cambridge, Massachusetts: Ballinger Publishing Company. 101113.
Peterson, F. and Fisher, A. (1977). The exploitation of extractive resources- a survey.
Economic Journal 87:681-721.
Rees, J. (1990). Natural Resources- Allocation, Economics and Policy. Routledge.
Robinson, C. (1975). The depletion of energy resources. In D.W. Pearce and J. Rose (eds.).
The Economics of Natural Resources Depletion. New York: Wiley. 21-55.
Solow, R. (1974). Richard Ely Lecture: The economic of resources or the resources of
economics. American Economic Review 46(2):1-14.
Solow, R. (1974a). Intergenerational equity and exhaustible resources. Review of Economic
Studies 42: 29-45.
Surrey, J. and Page, W. (1975). Some issues in the current debate about energy and natural
resources. In D.W. Pearce and J. Rose (eds.). The Economics of Natural Resource
Depletion. New York: Wiley. 56-74.
Stiglitz, J. (1974). Growth with exhaustible natural resources- the competitive economy.
Review of Economic Studies 139-152.
Stiglitz, J. (1975). The efficiency of market price in the long-run allocation in the oil industry.
In G.M. Brannon (ed.). Studies in Energy Tax Policy. Ballinger Publishing Company,
Cambridge Mass. 55-99.
28
UN (1955). The Price of Oil in Western Europe. E/ECE 1205. Geneva.
Walras, L. (1954). Elements of Pure Economics or the Theory of Social Wealth. Allan
Uniwin, London.
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by Noman Kanafani
Department of Economics and Natural Economics
The Royal Veterinary and Agricultural University
Rolighedsvej 26
DK-1871 Frederiksberg C
Copenhagen, Denmark
E-mail: [email protected]
30