United States
Environmental Protection
Agency
Municipal Environmental Research
Laboratory Se:
Cincinnati OH 45268
Research and Development
xvEPA
Evaluation of
Benefits of Resource
Conservation
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EPA-600/5-78-015
September 1978
EVALUATION OF ECONOMIC BENEFITS OF
RESOURCE CONSERVATION
by
Robert C. Anderson
Environmental Law Institute
Washington, D.C. 20036
Grant No. R803880-01-1
Project Officer
Oscar Albrecht
Solid and Hazardous Waste Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
EPA - RTP LIBRARY
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DISCLAIMER
This report has been reviewed by the Municipal Environ-
mental Research Laboratory, U.S. Environmental Protection Agen-
cy, and approved for publication. Approval does not signify
that the contents necessarily reflect the views and policies
of the U.S. Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement
or recommendation for use.
11
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FOREWORD
The Environmental Protection Agency was created because of increasing
public and government concern about the dangers of pollution to the health
and welfare of the American people. Noxious air, foul water, and spoiled
land are tragic testimony to the deterioration of our natural environment.
The complexity of that environment and the interplay between its components
require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem solu-
tion and it involves defining the problem, measuring its impact, and
searching for solutions. The Municipal Environmental Research Laboratory
develops new and improved technology and systems for the prevention, treat-
ment, and management of wastewater and solid and hazardous waste pollutant
discharges from municipal and community sources, for the preservation and
treatment of public drinking water supplies, and to minimize the adverse
economic, social, health, and aesthetic effects of pollution. This publica-
tion, which addresses the issue of resource conservation, is one of the
products of that research; a most vital communications link between the re-
searcher and the user community.
The question of what value should be placed on resource conservation has
been around for some time. If markets functioned perfectly, the value of
conservation would be appropriately incorporated in the resource prices. But
numerous forces act to distort prices from those which would be socially
optimal. Moreover, it must be recognized that any socially optimal norm must
necessarily be arbitrary when viewed in an intertemporal context. This report
investigates the issue of price and quantity determinations for non-renewable
resources and illuminates the difficulty of measuring biases given to prices
by various forces acting over time.
Francis T. Mayo, Director
Municipal Environmental Research
Laboratory
111
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ABSTRACT
This report addresses the issue of price and quantity de-
termination for non-renewable natural resources in competitive
markets. The issue of natural resource pricing is important
in an overall evaluation of the social desirability of recy-
cling, for the rate of recycling directly affects the quantities
of virgin materials which are conserved. If through the action
of the market mechanism conservation benefits are accorded a
value which is less than the true value of these benefits to
society, there would exist a rationale for greater governmental
support of resource recovery and recycling.
A comprehensive review of the extensive literature on nat-
ural resource economics reveals that many forces may act to
create a divergence between the socially optimal structure of
prices and the prices which are determined in the market for
natural resources. Unfortunately, for the purposes of this re-
port, the forces act in varying directions and with varying in-
tensities over time. It does not appear possible to establish
analytically with any degree of precision the magnitude or even
the direction of bias given to prices through the actions of
supply and demand for natural resources.
This report was submitted in fulfillment of Grant No.
R803880-01-1 by the Environmental Law Institute under the par-
tial sponsorship of the U.S. Environmental Protection Agency.
This report covers the period August 14, 1975 to February 14,
1977 and work was completed as of March 31, 1977.
IV
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CONTENTS
Disclaimer ii
Foreword iii
Abstract iv
Figures vi
Tables vi
Acknowledgments vii
1. Introduction 1
2. Historical Perspectives on Conservation 3
3. Economic Perspective on Resource Scarcity 5
4. Intertemporal Resource Allocation 8
Market allocation 8
Private profit maximizing behavior ... 9
Maximization of social value 10
Distributional considerations 11
Allocations from the original position .... 13
5. Divergence of Prices from Optimality 18
Assessment of market forces 18
Taxation 18
Monopoly 19
Uncertainty 19
Externalities 20
Price effects of taxes, monopoly, uncer-
tainty and externalities 22
Conclusions 27
References 29
Bibliography 32
Appendix 35
v
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FIGURES
Number Page
1 Time profile of benefits and costs 11
2 Time profile of prices and extraction
costs 26
TABLES
Number Paqe
1 Percentage Impact on Market Prices 23
2 Hypothetical Lease Values 25
VI
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ACKNOWLEDGMENTS
This report was prepared by members of the staff of the
Environmental Law Institute with assistance from several out-
side consultants. The project was directed by Robert Anderson.
He was assisted by Roger Dower of ELI, Professor Anthony Fisher
of the University of Maryland, Professor Milton Weinstein of
Harvard, and David Pearce of the University of Aberdeen.
Comments and criticisms offered by a number of individuals
have been helpful and appreciated. In particular, acknowledg-
ment is due to the Project Officer, Oscar Albrecht, Michael Hay
of the Department of the Interior, and Haynes Goddard of the
Environmental Protection Agency.
VI1
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SECTION 1
INTRODUCTION
This report addresses one dimension of recycling---the eco-
nomic evaluation of virgin materials which are conserved when
industrial and consumer goods are recycled. Of key interest,
then, is the value placed on undeveloped virgin natural re-
sources. Do competitive markets for natural resources estab-
lish prices which correspond to the actual social value of the
resource? If there are divergences between market prices and
social values, can the differences be estimated?
The market evaluation of conservation is but one dimension
of recycling. It is one factor which may lead to a difference
between the amount society would like to recycle and the amount
which is actually recycled. Some other factors which could
have a similar impact on recycling but which will not be con-
sidered in this report include the relative amounts of pollu-
tion from primary and secondary industries, the pricing of sol-
id waste disposal, and institutional factors such as freight
rate policies and federal procurement policies.
Fears of increasing resource scarcity have led to recur-
rent demands for greater attention to resource conservation.
For example, the Conservation Movement accepted as basic tenets
that most resources were too cheap, were wastefully exploited,
and would become exhausted soon, thereby depriving future gen-
erations of their use. More recently, attention has been di-
rected to the virtues of energy conservation. Alarming statis-
tics indicating imminent depletion of the world's petroleum re-
sources have been used as a central argument to justify greater
federal involvement in energy resource allocation and conserva-
tion.
This paper begins with a review of the history of resource
conservation. Malthus [20], Ricardo [34], and other early econ-
omists offered some of the first views of the consequences of
population growth and resource exploitation in a finite world.
Later, the leaders of the Conservation Movement espoused the
doctrine, along with supporting evidence, that resources were
being exploited too rapidly. We will be interested in examin-
ing the accuracy of their forecasts of impending resource ex-
haustion and will search for explanations for the source of
their errors. It will be shown that a variety of economic
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forces act to alleviate production and consumption constraints
which otherwise would appear as resources are depleted. Lastly,
we will be interested in the extent to which the forces of price
sensitive demand, technological change, and substitution coun-
teract the effects of resource depletion, thereby helping to en-
sure an adequate supply of exhaustible resources for use by fu-
ture generations.
The conclusion that some resources will remain available
for use by future generations, despite the cumulative effects
of depletion since the arrival of man on this planet, does not
in any way imply that the rate at which resources are being de-
pleted is socially desirable. Although the world may not be in
imminent danger of exhausting an essential resource, competitive
market environments may lead to excessively high rates of con-
sumption and lower standards of living for future generations.
The second section of the paper offers an analysis as to
how the appropriate rate of resource depletion should be deter-
mined. From the perspective of economic efficiency, the com-
petitive market system does a good job, subject to qualifica-
tions that when resources are exploited under conditions of free
and open access or resource development is influenced by forces
such as non-neutral taxation, externalities, uncertainty, and
monopolistic control, some form of governmental regulation may
be necessary. From the perspective of intertemporal equity
among generations, one cannot be certain that the competitive
market mechanism results in a desirable allocation of natural
resources. Neither a single individual nor groups of individu-
als voicing their desires through the market will, in general,
firid it possible to devise resource consumption plans which are
acceptable to those same individuals from every vantage point in
time. One approach which has been advanced to help assure in-
tertemporal fairness is that resource allocation decisions
should be made by a congress of individuals operating from be-
hind a veil of ignorance as to which generation each individual
will belong. It is argued later, however, that this approach
may not be very practical.
In the final section of the report, an attempt is made to
be more specific as to the magnitude of the distortion in mar-
ket prices created by each of several market forces. Because
the effects of the seperate forces are to a degree offsetting
and are uncertain in magnitude, it is not even possible to indi-
cate the qualitative nature of the cumulative bias in natural
resource prices, let alone make an explicit estimate of the size
of the bias.
The appendix to this report contains a non-technical sum-
mary of the principal findings. This summary was delivered as
a paper at the 107th Annual Meeting of the American Institute of
Mining and Petroleum Engineers in March 1978.
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SECTION 2
HISTORICAL PERSPECTIVE ON CONSERVATION
The specter of increasing resource scarcity in industrial
economies has long been a source of concern, both within and
outside the economics profession. The economists Malthus,
Ricardo, and Mill investigated some of the implications of in-
creasing demands for resources in a finite world. Writing near-
ly 200 years ago, Malthus made a persuasive case that resource
scarcity restrains economic growth. Malthus' model, which as-
sumed fixed quantities of homogenous resources, was modified
later by Ricardo to include resources of varying quality and
productivity. Mill added to Ricardo's notion of scarcity noting
that costs for individual mines will begin to rise before the
mines are exhausted since "shafts must be sunk deeper, galleries
driven further" [23, p. 188], etc. Mill also was one of the
first to discuss aesthetic benefits from natural resources. In
the late nineteenth century, the Conservation Movement flour-
ished, partly because of a widely held conviction that the Na-
tion's finite natural resources were being wasted and would soon
be exhausted [4, ch. 4].
Members of the Conservation Movement offered what they felt
was incontrovertible evidence that the Nation ""s physical re-
sources were being wasted needlessly and depleted at rates which
would lead to exhaustion of supplies in the proximate future.
Although a closely reasoned economic analysis at that time might
have reached quite different conclusions about the probability
of impending economic calamities attributable to scarcity of
natural resources, the arguments of those in the Movement did
have a broad popular appeal. They argued, for example, that in-
creasing scarcity was an inevitable consequence of the use of
limited physical resources. The Conservation literature is re-
plete with estimates of the size of the stock of many of the Na-
tion's physical resources along with projections of the exhaus-
tion dates for various future rates of consumption [e.g., 32, p,
43]. The inescapable consequences of resource use were thought
to be aggravated by what was termed "waste." The Conservation
literature identified several types of waste which could be
avoided by "wise use." Some examples of needless waste included
the flaring of natural gas from oil wells, the failure to obtain
maximum productivity from renewable resources such as forests,
cropland, and water, and the mismanagement of non<-renewable rer-
sources (e.g., permitting mines to flood when useful ore re*-
mains).
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An economic perspective on the issues discussed in the
Conservation literature enables one to support some points and
to refute others. Scarce resources are not necessarily being
wasted when natural gas is flared. If the full costs of gas re-
covery exceed its market value, flaring is a welfare-maximizing
policy for those making the decision. Recovery of the gas when
done at an economic loss would be a true waste of resources.
On the other hand, the development of common property resources
often proceeds wastefully as there exist few or no incentives
for individuals engaging in such resource development to consid-
er their impact on the quality of the resource or the costs of
other developers.
The views of the Conservation Movement that many renewable
and non-renewable resources would soon be exhausted have been
echoed by other subsequent writers. In nearly every instance,
these predictions of resource exhaustion have proven to be high-
ly inaccurate. Even when the predictions materialize, dire con-
sequences fail to ensue. Some forty years ago, Leith, a well
known geologist, warned that "depletion is further advanced than
even mining men generally realize" [18]. At that time, Leith
estimated that proven reserves of crude oil, lead, and zinc were
only some 15 to 20 times as large as annual production rates.
Lake Superior iron ore reserves had less than 20 years of sup-
ply remaining and copper reserves were about equal to 40 years
of then current output. Forty years later, the predicted re-
source exhaustion had not occurred. In fact, rather than facing
imminent exhaustion of these resources, the United States in the
1970's had ratios of known reserves to current output far in ex-
cess of those prevailing in the 1930's when Leith wrote. Domes-r-
tic reserves of zinc equalled over 60 times the annual mine out-
put of 1974, lead reserves over 80 times mine output for 1974,
and copper reserves over 50 times 1974 mine output. The Lake
Superior iron ores did become exhausted, but they were replaced
by taconite, an iron-bearing rock not considered to be ore in
Leith's time.
Modeling of the world economy by the Club of Rome repre-
sents a recent example of the continuing attempts to assess the
impact of increased scarcity of physical resources [21]. As
was characteristic of the Conservationist literature, the mag-
nitude of proven reserves of various resources was compared with
annual output and consumption to derive an estimate of the date
of eventual exhaustion. Not surprisingly, limits of physical
resources did place a limit to economic growth and in some
scenarios signaled the impending collapse of the world economy.
It should be noted that more recent modeling by these research-
ers has included some of the resource augmenting factors dis-
cussed in the next section and has reached more sanguine predic-
tions as to the possibility of continued economic expansion with
a fixed endowment of resources [22].
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SECTION 3
ECONOMIC PERSPECTIVE ON RESOURCE SCARCITY
Several factors act to alleviate constraints which other-
wise would appear as physical resources are consumed. Some of
the more obvious of these factors include technical change,
both induced and autonomous, substitution of inputs in produc-
tion as input prices change, and reduced consumption in re-
sponse to higher relative prices for final outputs. Many of
the inaccuracies of previous forecasts of resource exhaustion
can be explained by a failure to consider adequately some or
all of the dynamic process through which supplies of physical
resources are, in effect, augmented or enhanced.
Barnett and Morse investigated the extent to which the
above factors have acted to offset the condition of increasing
scarcity as resources are depleted. By equating increasing
scarcity with rising costs of natural resource outputs in terms
of the labor and capital used as inputs, Barnett and Morse were
able to formulate empirically testable hypotheses on resource
scarcity. With the notable exception of forest products, which
have become noticeably more scarce over the past several de-
cades, nearly all physical resources have become, by this defin-
ition, less scarce. This indicates that technical change and
substitution (and possible economies of scale and imports) have
in most cases compensated fully for the Ricardian scarcity which
otherwise prevails as development proceeds over time from high
grade to successively lower grade materials.
Although Barnett and Morse found that costs for extractive
outputs, in terms of labor and capital inputs used in their pro-
duction, had remained stable or fallen between 1870 and I960,
one could argue quite persuasively that in the long run the rel-
ative price of extractive products will increase [36]. For one
thing, the availability of certain minerals apparently changes
surprisingly little as the grade of ore mined is lowered [6].
Even with technological improvements in mining and processing,
the supply curve for some of these minerals may be highly in-
elastic. Another factor suggestive of higher prices for ex-
tractive outputs is the substantial energy requirement of most
mining operations. Energy prices appear to have reversed a
long-run secular decline and to have begun a steep upward climb
relative to general economy-wide price indexes.
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If the relative prices of many of the extractive outputs
do begin to advance, as a consequence of further scarcity of
mineral deposits which cannot be compensated by falling mining
and processing costs, the same factors which have led to stable
or falling relative prices for extractive products in the past
should act to restrain the upward pressure on resource prices.
Rising resource prices help to render profitable the mining of
low grade ores. Rising resource prices also may induce changes
in technology to permit greater output of consumption and in-
vestment goods per unit of resource input. The exhaustion of
certain mineral ores may induce the development of technologies
capable of extracting minerals from other, previously unex-
ploited, ores and stimulate more intensive research for new
deposits. Rising resource prices may stimulate greater recy-
cling, thereby reducing the requirements for primary ores. Fi-
nally, higher prices for final products attributable to rising
resource prices may induce consumers to substitute services and
other 'goods which use few physical resources as inputs for re-
source intensive goods. In addition to these factors, there is
an upper limit on the price of a given resource whenever there
exists an abundant though more expensive substitute. Nordhaus
[25] has termed this a "backstop technology."
Experiences of the domestic steel industry provide ample
support for the pervasiveness of these factors. In the 1950's,
as the Lake Superior iron ores were nearing exhaustion, tech-
nologies were developed to pelletize taconite ores for use as
a feedstock to blast furnaces. The electric furnaces as a fa-
cility for producing steel came into widespread use during the
1960's, a period of relative abundance of scrap steel (the prin-
cipal input). Steel, itself, represents a technological im-
provement over iron. Because of a higher strength to weight
ratio, steel has replaced iron as the dominant metal in consump-
tion and investment goods. This substitution has permitted an
increase in the output of consumption and investment goods per
unit of iron ore input.
As Goeller and Weinberg [10] argue, iron, or steel, and
aluminum as substitutes for other, scarcer minerals may consti-
tute the most important resources for the backstop technologies.
Taconite ores presently being mined as an iron-bearing mineral
contain about 27 percent iron and 51 percent silica, or about
3.4 times the average crustal abundance of iron. Some bauxite
presently being mined for aluminum production contains concen-
trations of aluminum at about 2.2 times its average crustal
abundance. These figures indicate that supplies of iron and
aluminum ore may be viewed as relatively abundant.
One key question, which remains unanswered, is the price
at which various minerals will be replaced by the backstop tech-
nologies. Although coal liquefaction does not represent a com-
plete backstop for oil, coal certainly is far more abundant than
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oil. Nordhaus estimated that coal liquefaction would represent
an economically viable alternative to oil at seven or eight 1970
dollars per barrel, a price approximately equal to the present
price of crude oil. One true backstop technology for most uses
of oil is solar energy; another miqht be the breeder reactor.
The price at which solar energy would substitute for oil as fuel
varies from below the present price of oil, for some uses such
as heating in sunny climates, to prices considerably higher than
present oil prices for other uses (propelling vehicles, for ex-
ample) .
The relationships between resource use, resource prices,
and the backstop technologies are examined in more detail in
the next section.
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SECTION 4
INTERTEMPORAL RESOURCE ALLOCATION
This section of the report reviews the economic concepts
and models which have been used to analyze how a private free
enterprise economy determines the rate at which exhaustible
resources will be depleted. The fundamental question is wheth-
er the owners of exhaustible resources have the incentives to
develop resources at a socially optimal rate. To answer this
question, one must first define what is meant by socially opti^-
mal., The Pareto test has long been used as a criterion of op^
timality, but this has been in reference to the allocation of
inputs and outputs at one point in time. To apply such a test
in an intertemporal context, one must assign weights to con-
sumption in different time periods. Whether these weights
should be constant across time or decline into the future is an
ethical question, one which cannot be resolved through positive
analysis. Therefore, any comparison of private resource devel-
opment with a norm which is deemed to be socially optimal will
be arbitrary, given that the criterion for intertemporal opti-
mality depends upon arbitrarily determined standards.
Initially, the discussion will focus on the model first
developed by Hotelling [14], In this model, exponentially de-
clining weights are given to future social values. Later, it
is shown that such a weighting system can result in massive
transfers of wealth and income among generations. Finally, we
explore some alternative criteria for resource allocation among
generations.
MARKET ALLOCATION
Initially this discussion will consider resource alloca-
tion decisions which are made by resource developers. The
fundamental differences between open access exploitation and
the development by a sole owner have long been recognized. If
access to a resource is shared, the incentives which are per-
ceived by individuals will differ from those which are exper-
ienced by society. Typically resource development under open
access is premature and excessive from the viewpoint of society
as a whole. Assignment of property rights forces resource de-
velopers to make a continuing comparison between the value of
the resources if extracted and processed today and the future
values which the same resource would command if development
were postponed.
8
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Private Profit Maximizing Behavior
When natural resources are privately held, the owners are
free to determine that path of extraction which maximizes their
private welfare. The basic dynamic model of the mine assumes
that a mine owner seeks to maximize the present value of profits
subject to the obvious constraints that production each year be
non-negative and total production not exceed the initial quan-
tity of minerals in the deposit. It is assumed that future
prices are known with certainty, that the true magnitude of all
reserves is public knowledge, and that there are no externali-
ties. Given these assumptions, the dynamic optimization prob-
lem can be solved to produce the following fundamental results:
(1) When output is unaffected by the stock of resources
remaining, the value of the resource in place must increase at
the market rate of interest. As Solow [37] and others have
suggested, this must hold in order that resource owners will be
indifferent between producing today and holding minerals in
place for sale at a later date. Equilibrium in the market for
mineral assets must produce this result; otherwise resource
owners would have incentives to alter their rates of production.
If resources in place increase in value at rates less than the
going rate of interest, resources owners have an incentive to
accelerate their rate of extraction and invest the proceeds
elsewhere. If the value of minerals in place increases at rates
in excess of the going return on capital, resource owners would
cut back on current output, raising current prices relative to
future prices until the rate of return is brought into equality
with the interest rate.
(2) The price of extracted minerals equals marginal ex-
traction cost plus marginal user cost. That is, minerals are
supplied by a competitive mining industry at a price equal to
the sum of extraction costs on the last units removed and an
amount equal to the value of minerals in place (the marginal
user cost). Because price depends on both marginal extraction
and user costs, it is to be expected that changes in technology,
the rate of new discovery, and demand would affect price.
(3) The first two results can be combined to yield the
proposition that the optimal time profile for extraction pro-
ceeds from high-grade, low-cost, to low-grade, high-cost depos-
its. High-cost producers cannot serve the market when low-cost
deposits are known to exist. At a price level which supports
production from high-cost resources, the low-cost producer
would have a strong incentive to undercut the price. More fun-
damentally, prices'could not be high enough initially to sus-
tain production from the high-cost sources because at those
prices, user cost on both grades of desposits could not continue
to rise at the same rate of compound interest. High-grade de-
posits would increase in value more slowly than the going rate
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of interest, thereby stimulating production from high-grade
sources. These concepts have been developed more rigorously
by Heal [13].
A more formal and precise development of these basic re-
sults is given in the appendix. Having established the basic
results under profit maximization in a dynamic context, we now
turn to the maximization of social value.
Maximization of Social Value
Hotelling and others [14, 35, 41, 43] have investigated
the conditions which maximize societal welfare. Generally
speaking, social values are assumed to be the sum of producer
and consumer surpluses. The critical question is how social
values in different periods are to be weighted. Is a unit of
consumption today worth more, less, or the same as a unit next
year or one hundred years from now? As noted in the introduc-
tion to this section, Hotelling assumed that present and future
social values could be compared by discounting future values at
the market rate of interest. This convention dates at least as
far as the work of Irving Fisher in the late nineteenth century.
More recently, Koopmans [16] has lent further theoretical sup-
port to the notion that it is quite rational for existing mem-
bers of society to discount future values.
The maximization of social welfare is thus defined as the
maximization of the present value of producer and consumer sur-
pluses, with all future values discounted at the market rate of
interest. When the objective function is expressed in function-
al form and the indicated operations performed, it can be shown
that the equilibrium conditions are identical to those for pri-
vate profit maximization. In this way, it has been demonstrated
that the decisions of profit maxmizing individuals are entirely
consistent with the intertemporal maximization of aggregate so-
cial welfare.
Two aspects of the demonstration that profit maximization
leads to a socially optimal allocation of resources across time
deserves further discussion. First, the demonstration requires
that a number of assumptions regarding production be satisfied.
Some of these assumptions include (1) competition must prevail,
(2) there must be no uncertainty, and (3) there must be no dis-
tortions between private and social cost (such as caused by tax-
ation or externalities). The second important aspect which
should be noted is that maximization of the present value of
profits, or equivalently, the present value of producer and con-
sumer surpluses, can result in significant impacts on the dis-
tribution of income and wealth over time. We will discuss this
latter point in the next few pages and reserve consideration of
the first point until later.
10
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DISTRIBUTIONAL CONSIDERATIONS
Several economists have questioned the desirability of per-
mitting market forces to determine resource allocation over long
time spans. Essentially, these arguments share a common theme,
that when decisions involve transfers of wealth among genera-
tions the best course of action will vary depending upon one's
perspective in time. It is as if we were evaluating a project
with undiscounted future benefits and costs as illustrated in
Figure 1. From the perspective of to, a present value calcula-
tion which discounts future benefits and costs may indicate a
positive value for net present benefits. Using to as the van-
tage point for its calculations, the market process signals that
the project should be undertaken. If one were to compute the
present value of future benefits and costs at a later date, say
t]_, the calculations would show present costs exceeding present
benefits and market forces would signal to decision makers that
the project should not be undertaken. The immediate gains from
undertaking the project at date to are followed by net costs to
succeeding generations.
Undiscounted
Benefits and
Costs Each Year
Time
Figure 1. Time profile of benefits and costs.
11
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One important refinement of present value maximization by
members of existing generations has been offered by Arrow and
Fisher [3]. They show that in situations where decisions are
basically irreversible and the magnitude of future benefits and
costs is uncertain, waiting to make a decision can often in-
crease the magnitude of the expected net benefits when waiting
reduces the uncertainty of benefits and costs. In the example
of Figure 1, one can take the benefit and cost values as ex-
pected values, assuming that there is a wide band of uncertainty
about each expected value. Any delay in decision-making will,
in this example, increase the likelihood that the computed value
of expected net benefits will be negative.
A related finding was first offered by Strotz [40] . He
showed that the plan (specifically a consumption plan) which is
optimal for an individual from one vantage point, often will not
be optimal (in the sense of present value maximization for that
individual) from another vantage point. Page [26, 27, 28] has
argued that this so-called "dynamic inconsistency" should give
present members of society further pause for thought when they
selfishly maximize net present benefits of projects which have
the potential for large intertemporal transfers of wealth. The
arguments of Strotz and Page appear to have limited bearing upon
economic decision-making by members of the present generation.
Economists have attempted repeatedly to tackle questions of
wealth and income distribution, and by now have apparently
reached a consensus that economics, per se, has little to offer
in the way of guidance. Nonetheless, when the use of nuclear
power, fluorocarbons, and pesticides by members of the present
generation threatens a massive transfer of wealth away from mem-
bers of future generations, a basic appeal to intertemporal
fairness dictates that we proceed with great caution. Moreover,
the tremendous uncertainties associated with the estimates of
future costs for these projects may, according to the Arrow-
Fisher analysis, necessitate delays in such investments if ex-
pected net present benefits are to be maximized.
The typical decision to deplete a particular nonrenewable
resource deposit does not involve such a clearcut transfer of
wealth among generations. Occasionally, these decisions may in-
volve the irreversible loss of scenic natural environments. In
such a case, one may appeal to the Arrow-Fisher [3] argument
that the present value of benefits can often be increased by
postponing the development decision and attempting to resolve
the uncertainties which accompany estimates of future benefits
and costs. In most other situations, the decision by members
of the present generation to develop a non-renewable natural
resource has both plusses and minuses with respect to the wel-
fare of future generations. Assuming net present benefits of
development, such decisions increase the income of the present
generation and, assuming a positive marginal rate of saving out
12
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of income, such development decisions also increase the wealth
of future generations unless some resource essential to future
income is exhausted. When prices for non-renewable resources
dictate development today, this is because capital which embod-
ies the resource is more productive than is the resource in its
undeveloped state.
If all resources (including natural environments) are
priced correctly in the market place, the typical development
decision should benefit future as well as present generations.
In those cases where resource development is expected to en-
hance the welfare of the present generation, but damage the in-
terests of future generations, an alternative to market-deter-
mined allocations may be deemed desirable.
The next few pages explore one possible alternative to mar-
ket-determined allocations.
ALLOCATIONS FROM THE ORIGINAL POSITION
The original position provides an alternative to market
determinations for resource allocation both over extended time
horizons and at one point in time. In contrast to decisions by
members of existing generations, which in a competitive market
setting are consistent with the maximization of these indivi-
duals' self-interest, decisions in the original position result
from the thought experiment of soliciting a consensus from hypo-
thetical individuals who are unaware of the generation they will
be born into and the abilities they will possess.
Although clearly not the originator of the concept of an
original position, Rawls [33] has developed a rich exposition
of decision-making from this perspective. Rather than debate
what is a fair allocation of resources given one's present po-
sition in life and society, Rawls suggests that a fair resolu-
tion of distributional issues can be had by resorting to what
he terms the "veil of ignorance" in an original position. From
this position of ignorance as to one's eventual position in so-
ciety, preferences, abilities, and the like, one is asked to
evaluate alternative allocations of resources. Rawls concludes
that from this original position one would opt to reallocate
within a generation until an equal share is available to all.
The Rawlsian utility function, which places liberty above all
else in importance, and the generalized difference principle,
which is that societal welfare within a generation is increased
only by increasing the welfare of the least well-off member of
society, are of less interest to us than is the basic concept
of decision-making from the original position.
The generalized difference principle, subsequently termed
the "maximin principle" (maximizing welfare at its minimum lev-
el) , has been severely criticized by economists. This principle
13
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implies that any benefit to the worst-off member of society out-
weighs any loss to other individuals, provided the latter do not
become the worst-off in the process. As Arrow has noted, by
this principle one would support the use of medical procedures
which serve to keep terminally ill patients alive, even if the
procedures were so expensive as to reduce the rest of the pop-
ulation to poverty levels. Apparently Rawls was aware of this
problem with the strict interpretation of maximin, for he de-
veloped the modification of "close knittedness" of society
through which individuals consider not only their own welfare
but also the welfare of others in evaluating their own level of
satisfaction. Some inequality in the distribution of resources
is to be tolerated, particularly if the inequality can be shown
to produce incentives for improved performance from the most
able members of society.
The maximin principle represents a basic alternative to
the utilitarian approach of welfare economics. The fact that
a fundamental alternative to utilitarian welfare economics has
surfaced has sparked inquiry into the feasibility of using max-
imin as an intertemporal allocation rule; in fact, he specifi-
cally rejected it because "there is no way for later genera-
tions to improve the situation of the least fortunate first gen-
erations." Despite such a disclaimer by Rawls, the implications
of maximin have been investigated in some detail. For example,
Solow [38] shows that the maximim criterion calls for equal con-
sumption in all generations. With stationary technology there
would be zero net saving and with technological progress there
would be, of necessity, negative net saving.
Rather than use maximin as an intergenerational savings
criterion, Rawls argued that as each "generation cares for its
immediate descendants, as fathers care for their sons, a just
savings principle . . . would be adopted." The economic impli-
cations of this principle were investigated by Dasgupta [7].
He interpreted the savings rule as a Nash equilibrium where each
generation's strategy consisted in the choice of its own savings
rate. Compared to the savings implied by the Utilitarian prin-
ciples, the Rawlsian savings rule was found to be Pareto ineffi-
cient. That is, some members of society could be made better
off while none were worse off if one were to deviate from the
Rawlsian savings plan.
Finding a fair and defensible rule for allocating resources
across generations is a problem which has attracted only limited
attention from economists. Generally, it is conceded to be more
difficult than the problem of allocating resources within one
time period, and the latter problem has not been solved com-
pletely. As Rawls has noted,
the question of justice between genera^-
tions . . . subjects any ethical theory
14
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to severe if not impossible tests . . .
I believe that it is not possible, at
present anyway, to define precise limits
on what the rate of savings should be.
How the burden of capital accumulation
and of raising the standard of civili-
zation is to be shared between genera-
tions seems to admit of no definite
answer.
Two economists, Vickrey [42] and Harsanyi [11, 12], pre-
date Rawls in the use of a construct which removes men from
their station in life as a perspective for making ethical judg-
ments. Vickrey focused on the question of optimality of an in-
come distribution. Building upon ideas of Ramsey, von Neuman,
and Morgenstern, that choice in risky situations can be de-
scribed as the maximization of expected utility, Vickrey argued
that from a position of ignorance as to their station in life,
individuals would want to maximize the sum of expected utilities
accruing to members of society. if there are n members of so-
ciety and the utility accruing to the ith individual is Uj_, the
value of a particular distribution is 1/n (2Ui). The expecta-
tion for an individual is maximized by making the sum of utili-
ties as large as possible.
Vickrey established the connection between utility and the
distribution of income by assuming that the marginal utility of
income declines with increasing income. If one could treat the
aggregate amount of income to be distributed as independent of
the distribution income, the sum of utilities would be maximized
with an equal share for all. But the distribution of income
can affect the incentives for production and in turn the total
aggregate income. Therefore, Vickrey suggests that some degree
of inequality is needed to create the incentives which would
maximize the sum of expected utilities, which in turn maximizes
the expected utility of an individual in the original position.
Rawls and Vickrey are very close to agreement in how one would
distribute fairly a given quantity of income among members of
one generation.
Extending Vickrey's model to cover more than one generation
is quite difficult. One then needs to be concerned with the
rate of savings, for savings have a profound effect on future
incomes. In its barest form, the intertemporal version of
Vickrey's model would say that one should maximize the sum of
all present and future utilities, thereby maximizing the ex-
pected utility of an individual in the original position. De-
pending upon how severely the marginal utility of income de-
clines with increasing income, this approach appears to suggest
that savings should be made as high as possible, constrained
only by that minimal level of consumption necessary for surviv-
al.
15
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The principal difficulty with the criterion of maximizing
the sum of future utilities is that it would require great sac-
rifices by the present generation and would benefit individuals
not yet born. It seems obvious that the present generation
would be unwilling to agree to such a proposition. Because the
future promises to be wealthier than we are, we may anticipate
that they will view our failure to save more as justifiable.
It does appear though, that when the present generation engages
in activities which can be expected to make future generations
far poorer, future generations will not view our actions kindly.
The relationships between intertemporal and intratemporal
resource allocation was addressed recently by Mishan [24]. He
argued that the failure of economics to provide reasonable cri-
teria for intratemporal allocation need not preclude the analy-
sis of intertemporal distributional issues. For intratemporal
allocations of income, Mishan considers two plausible perspec-
tives. One is that the income distribution is generated by ran-
dom chance, that chance encounters, the friends one has, and the
abilities one is born with, largely determine one's income.
From this perspective, an equal distribution within a genera-
tion would be deemed just. On the other hand, one may argue
plausibly that income is the fruit of one's efforts and, there-
fore, to encourage that effort, incomes should be distributed
according to effort. Both views have merit, but unfortunately
economic criteria do not enable one to decide which is more
important. The distributional question is essentially an ethi-
cal problem to be resolved from the original position.
For intertemporal allocations, Mishan argues that no mat-
ter which view one has on a just income distribution, one is
led to advocate an equal share for each generation. Clearly,
those who believe that variation in income is generated by
random chance would advocate an egalitarian distribution across
generations. Those who believe that income should be distri-
buted according to effort would be led to the same conclusion,
Mishan argues, because the effort by each generation is proba-
bly constant, at least as a first approximation.
In his commentary, Fisher [8] pointed out that an equal
distribution for the members of each generation has the same
deficiencies noted by Solow for the maximin criterion. That
is, income would be constrained for all time by the low income
level of the first generation. Fisher argued that one may es-
cape this unhappy dilemma if one postulates benevolence toward
future generations. If each generation attempts to "make the
world a better place for its having been there," one can have
rising incomes over time as the equal incomes which are roughly
proportional to effort by each generation are augmented by the
benevolence motive.
Despite the progress which has been made to date in assess-
16
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ing the basic issue of fairness to existing and future genera-
tions, the original position and related constructs face formid-
able obstacles before they can truly be deemed workable as tools
for intertemporal resource allocation. No matter how hard we
may try to place ourselves in the original position, the fact
remains that we are members of a current generation and have es-
tablished tastes, preferences, and abilities. Any decisions we
make would no doubt reflect these inherent sources of bias.
17
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SECTION 5
DIVERGENCE OF PRICES FROM OPTIMALITY
ASSESSMENT OF MARKET FORCES
This section is directed to the assessment of the nature
and magnitude of deviations between actual market prices and
a "socially optimal" norm. While we have reviewed two methods
for deriving the "socially optimal" norm, the original position
method appears to be so severely limited in practicality that
we must use Retelling's definition of optimality. That is, we
must maximize the present value of producer and consumer sur-
pluses. Using this as the criterion for social optimality,
Hotelling demonstrated that the price and consumption patterns
which result from the competitive exploitation of resources by
profit-maximizing firms are optimal, from the viewpoint of so-
ciety, provided certain assumptions are satisfied. The assess-
ment here centers upon establishing the direction and magnitude
of biases in market price which result when Hotelling's strict
assumptions are relaxed to reflect real-world considerations
of taxation, monopolies, externalities, and uncertainty.
Most of the literature relevant to this problem investi-
gates a somewhat different question, that of the impact of
various market forces on the rate of resource depletion. Know-
ing that resources are being depleted too fast or too slowly
does not tell one immediately that prices today are either too
low or too high. For example, when development is stimulated
by a force such as uncertain tenure of ownership, resources
are extracted and consumed at an earlier date than would be
deemed socially optimal. Initially, prices for the mineral will
be depressed as production exceeds the optimal rate. Later,
however, when the deposit is exhausted, less of the mineral will
be available than would be socially optimal, and prices may well
be higher than would prevail under an optimal plan. Later, we
attempt to deal more fully with this problem of assessing im-
pacts on the time profile of prices. Below, we review the lit-
erature on production biases caused by various market forces.
Taxation
The extractive sector which develops natural resources is
subject to an unusually large number of taxes and tax deductions
including depletion allowances, expensing of exploration and
18
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development outlays, bonus bidding for lease rights, production
royalty payments, and severance taxes, as well as ordinary
sales, income, and property taxes. Some of these taxes and tax
subsidies are easily incorporated into an economic model of pro-
duction from a mineral deposit. For example, Sweeney [41] and
Peterson [29] have shown that lump sum and pure profits taxes
would not distort production decisions. Included in this cate-
gory would be bonus bids, as well as ideal income taxes. Among
those forces which may accelerate production are depletion de-
ductions and expensing of exploration and development {though
the latter has not been analytically demonstrated in the liter-
ature) . When property taxes are based on the value of mineral
remaining in the ground, they too can accelerate production.
Forces which serve to slow the pace of mineral extraction in-
clude royalty payments and severance taxes.
Monopoly
The effects of monopolistic ownership of resources on the
time profile of production were first analyzed by Hotelling.
He showed that monopolistic control of resources served to de-
lay production, in essence concluding that the monopolists may
be doing more to promote the interests of conservation than the
Conservation Movement was ever able to do. Subsequent investi-
gation by others has revealed that monopolists do not always
maximize the present value of their profits by holding resources
off the market. Sweeney [41] and Lewis [19] have shown that
certain patterns of demand growth and certain configurations of
stable demand curves can lead the monopolist to extract at a
faster rate than would a competitive group of owners. On the
other hand, Stiglitz [39] and Peterson and Fisher [31] have
concluded that the most likely effect of monopolistic control
over resource exploitation is to slow the rate of extraction.
To date, there has been no analysis of the impacts of oligopo-
listic resource development on resource prices and production
rates.
Uncertainty
Although Sweeney claims that the effects of uncertainty on
the production decisions of the natural resource sector are
still largely unresolved, there is substantial agreement that
one general impact is the acceleration of production from known
deposits. At least three important cases of uncertainty have
been discussed: uncertain tenure of resource ownership, uncer-
tain price (demand) expectations, and uncertainty over future
technology and factor costs. To this list could be added un-
certainty over future taxes and royalties which may be levied
on output. Assuming resource owners are risk averse, each
source of uncertainty will, other things equal, create an in-
centive to accelerate the rate of production.
19
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Perhaps this effect is most clearly illustrated in the
case of uncertain tenure of ownership. A profit-maximizing
firm operating a mineral concession in a politically volatile
region has a tremendous incentive to extract ore at a rate far
in excess of that which would maximize profits on a similar do-
mestic deposit. One common method of accelerating mineral pro-
duction on these foreign concessions is to extract and process
only the highest grade ores. This often has the effect of ren-
dering uneconomic much of the lower grade ore which would have
been mined had tenure been more certain.
A second probable impact of uncertainty has been noted by
Peterson and Fisher. In their view, uncertainty would diminish
incentives for exploration, leading to smaller reserve holdings,
especially relative to production rates. The related problem
of optimization in exploration has been addressed recently by
Gilbert [9]. Preliminary results show that private firms may
invest excessive amounts (.from society's view) to eliminate
uncertainty over the quality and quantity of mineral deposits
available for development.
Kay and Mirrlees [15] sketched a preliminary analysis of
the likely effects of uncertainty over future prices on pro-
duction decisions of resource owners. In their view, current
prices for resources whose exhaustion is not imminent should
approximate the marginal cost of extraction. Because resources
cannot be sold at prices which fall short of extraction costs,
at least in the long run, the general level of resource prices
is more likely to exceed than to fall short of the true marginal
cost of extraction. If prices are too high, this is just anoth-
er way of saying that production is delayed relative to the so-
cially optimal path (that which would maximize the present value
of producers' plus consumers' surpluses).
Externalities
The interest of the economics profession in the problems
of environmental externalities dates at least as far back as
Pigou's smoke nuisance example. Only relatively recently have
natural resource economists examined in any detail mineral ex-
ploration and production for evidence of such market failures.
Peterson [30] investigated two sources of externalities to the
petroleum industry. His results, which apply equally to other
extractive industries, indicate that the discovery of a new oil-
producing site typically involves two externalities, a so-called
"Easter egg" externality and an information externality. By re-
moving one more "Easter egg" from the field of search, each new
discovery raises the cost of finding new deposits. Since the
unclaimed mineral deposits have no market price (at least on
open access federal lands in the U.S.), scarcity value is re-
flected only in the expenditures individual economic units must
incur in order to find each new deposit. Such common property
20
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resources become overdeveloped because of a divergence between
private and social costs of acquiring additional resources.
The information externality arises when the spatial orien^-
tation of deposits is such that the discovery of one deposit
conveys valuable information to those searching for deposits on
nearby lands. If the value of the information cannot be recov-
ered by those making the initial discovery, insufficient expen-
ditures will be forthcoming in the resources sector (private
cost exceeds the social cost for new discoveries). Another ex-
ternality in exploration, which may produce too much informa-
tion, arises when firms are permitted to perform their own inde-
pendent evaluations of properties prior to leasing. Expensive
exploratory programs are duplicated as each firm attempts to
gain an advantage in the ultimate bidding for lease rights.
Under the General Mining Law of 1872, which governs hard<-
rock mineral development on U.S. federal lands, the actions of
individual mining operators to protect their own interests serve
to increase development costs for all [1]. One example of this
is the absence of a comprehensive claim reporting system, the
result being thousands of cases of overlapping and conflicting
claims,* In developing such properties, a claimant bears the
risk that another claimant will seek to invalidate his rights
in court. Such uncertainties over title to a property should
serve to inhibit development. These uncertainties differ im-
portantly from those faced by the owner of an operating mine.
In the latter case, fears of higher taxes, expropriation, and
the like definitely serve to hasten the rate of extraction. A
second example of inefficiency in mineral development, especial-
ly common now that lower grade deposits are being mined in
large-scale, capital intensive operations, is the difficulty of
amalgamating several small claims into large properties under
one owner. Individual claim owners have an incentive to hold
out for all of the potential gains from consolidation under
the present system and this often serves to block development.
This implies that properties which would be developed under al-
ternative systems for the disposal of mineral rights on public
lands (e.g., a leasing system) are not developed under the dis-
covery system of the 1872 law. In turn, these inefficiencies
under the present system of mineral development lead to higher
costs for the mining industry and a slower rate of extraction
than would occur in a system free of such externalities.
Yet another form of externality, one which is perhaps more
obvious to all, are the residuals which are produced in mining,
smelting, and refining operations. These residuals are left in
* It should be noted that a comprehensive claim reporting sys-
tem is called for in the Federal Land Policy and Management
Act of 1976. How well it will work in practice remains an
unknown.
21
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the form of tailings, discharges into the atmosphere, and on
occasion, discharges into waterways. When such discharges im-
pose costs on other economic units and these costs are not paid
by the mineral firm making the discharges, there is said to ex-
ist an externality. Again, social costs of production exceed
private costs of production. In such situations, the quantity
of output exceeds that which is socially optimal.
Finally, as noted earlier, the environment serves as a
source of valuable amenity services. Typically, private re-
source developers are not rewarded by the market when they pre-
serve scenic natural environments. In some instances, state
and federal environmental statutes force private developers and
public resource managers to consider the value of the amenity
services which would be foregone as a result of development.
Nonetheless, Krutilla and Fisher [17] argue that insufficient
attention continues to be given to the values of environmental
preservation.
PRICE EFFECTS OF TAXES, MONOPOLY, UNCERTAINTY AND
EXTERNALITIES
In the Retelling model, the optimal price for a resource
is the sum of lease value and marginal social cost of extrac-
tion. Deviations from optimal prices arise when lease values
are computed incorrectly (as is the case when private operators
view their operations as subject to uncertainties that a social
planner would not perceive), when privately computed costs di-
verge from social costs (as in the case of preferential taxa-
tion, information externalities, and the like), when monopoly
rents are earned, and when regulation needlessly increases pri-
vate marginal cost (as in the case of our federal mining laws).
It becomes apparent that to answer the questions posed at the
outset of this report, that is, whether or not non-renewable
resources are indeed too cheap, one must analyze in detail the
determination of optimal price and the impact of each of these
separate influences on market price.
In the appendix, it is shown that the optimal price for a
resource equals marginal social costs of extraction, plus lease
value. It is also shown that when there is no stock effect
(that is, when output does not depend upon the amount of miner-
als remaining in place), the lease value grows at compound in-
terest. When there is a stock effect, lease values no longer
need rise at the rate of interest; in fact, they may actually
fall with the passing of time.
As a very general proposition, it appears that taxes may
be characterized as affecting private marginal costs of extrac-
tion. Taxation creates a divergence between private and social
costs of extraction. Now all corporate activities are subject
to taxation, so the divergence between private and social costs
22
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cuts across all industries. The real issue from the standpoint
of resource allocation, both natural and otherwise, is whether
or not the mining sector experiences significantly different
tax rates from other sectors of the economy. From the availa-
ble evidence, one can conclude that, on balance, the mining
sector does benefit from special provisions of the income tax
laws. A recent report [2] contains estimates of the impacts of
taxation and tax subsidies on the price of final outputs of the
extractive sector. The more significant of these effects are
listed in Table 1. It should be noted that the most likely im-
pacts may be as little as half of the reported upper limits.
TABLE 1. PERCENTAGE IMPACT ON MARKET PRICE
Expensing of explora-
Mineral Depletion Severance taxes tion and development
Pig Iron -3% + 3% Unknown
Copper -6% +1.5% "
Lead -3% +1%
Aluminum -2% +0.2% "
* The severance tax on iron extraction in Minnesota can be off-
set to a considerable extent by credits for labor employed.
The true impact on price is less than 3%. Severance taxes
for other minerals are averages of effective rates in the two
or three states with the largest share of domestic output.
Expensing of exploration and development, another tax de-
duction which lowers the burden on mining firms, is unlikely to
have an impact as large as depletion deductions. Our detailed
examination of financial statements for over a dozen mining con-
cerns revealed that expensing was listed infrequently as a fac-
tor which lowered effective tax rates by more than 1 percent,
whereas depletion typically reduced effective income tax rates
by from 5 percent to 15 percent or more.
Two factors suggest that the price impacts of monopolistic
control over resources are negligible for most minerals. First,
few mineral producers have an actual monopoly position (the De
Beers diamond cartel and the OPEC oil cartel being two notable
exceptions); world markets for most resources are highly compe-
titive. Second, the rates of return on mining investments, af-
ter adjustment for risk, appear to be no higher than for compar-
23
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able investments in manufacturing.*
One of the basic results of the Hotelling model is that in
a competitive market there are two components to resource
prices, marginal extraction cost and lease values. A condition
for equilibrium in the market for mineral deposits is that the
owners of the deposits must be offered a return equal to the
going rate of return on alternative investments. Uncertainty,
whether it be over future prices, technology, or ownership
rights, is reflected as an increase in the rate of return which
must be earned on ore deposits left in their undisturbed state
[13, 37]. The greater the uncertainties, the more likely it is
that mining firms would behave pretty much as if price equalled
the marginal cost of extraction. However, one can easily demon-
strate that lease values are small relative to extraction costs
so long as exhaustion of a particular grade of ore does not appear
imminent in the immediate future. Therefore, uncertainty, per
se,-is unlikely to exert a significant effect on most renewable
resource prices.
As an illustration, assume that at a price of $6 above
the current market price of copper (all in real terms) substi-
tutes which are more abundant (e.g., aluminum) will have com-
pletely replaced copper as an input to industry. Suppose fur-
ther that this substitution will occur in 100 years and that in
the intervening 100 years copper will be obtained at constant
marginal cost. Then the pricing equation would read:
P(2077) = C'(1977) +Xe100r
Substituting in $6 for the difference between price in 2077 and
the marginal cost of extraction from deposits being mined, one
Xe100r = $6.00, solving for the lease value, A,
one obtains X= $6.00 e'"1001'
The table below presents more details of the relationship be-
tween the rate of discount r, the time remaining until complete
substitution occurs, and the imputed value of the deposit. Giv-
en reasonable real rates of discount and the assumptions con-
* Fortune reports summary statistics of rates of return for var-
ious industrial groupings among the largest 500 industrial
corporations. These summaries indicate that over the past
decade mining firms have averaged a rate of return approxi-
mately 1 percent in excess of that in general manufacturing,
a difference which may be attributable entirely to differences
in risk.
24
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earning quantities available and eventual substitution possi-
bilities, the lease value of copper deposits today is quite
small.
TABLE 2. HYPOTHETICAL LEASE VALUES
Years remaining Lease value,
Rate of discount before substitution $ per Ib.
r = .05 10
20
30
40
50
60
70
100
200
r = .10 10
20
30
40
50
100
r = .20 10
20
50
3.64
2.21
1.34
.80
.49
.30
.18
.04
.0003
2.21
.80
.30
.11
.04
.0003
.80
.11
.0003
The inclusion of deposits of varying quality gives the
example a greater correspondence to reality. Suppose as before
that exhaustion occurs in 100 years and that substitution will
be at a price of $6 above the current market price of 60 cents
per pound. Instead of a single quality of copper available at
a constant cost of 60 cents per pound for the next 100 years,
assume that 60-cent copper will satisfy demand for 40 years and
that copper with a marginal extraction cost of $1 per pound will
be used thereafter. Figure 2 depicts the approximate pattern
of marginal extraction cost, market price, and lease value over
the next 100 years. Lease values are computed by working back-
ward from the year 2077, assuming a discount rate of 10 percent.
Lease values for $1 copper in the year 2017 equal $.01388 per
pound, and for 60-cent copper in 1977 lease values are $.00758
per pound. Compared to the previous example, where all copper
for the next 100 years had a marginal extraction cost of 60
cents, lease values in 1977 have increased by some 25 fold. The
60-cent copper will be depleted 40 years hence, and not held off
the market beyond that date, because beyond that date the lease
25
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Prices
Costs
Price
$1.00
$ .60
Marginal Cost
of Extraction
40
100
Time in years past 1977
Figure 2. Time Profile of Prices and Extraction Costs.
value on 60-cent copper ceases to increase as fast as the in-
terest rate. It is interesting to note that $1 copper has a
lease value today ($.00025 per pound) even though it will not
be mined for 40 years.
Although sufficient data on reserves, demand, and so forth
are not available to enable one to compute precise mineral lease
values, a reasonably accurate estimate can be obtained for cop-
per. Bennett [5] has compiled data on all known and inferred
copper deposits and coupled this with an analysis of the cost
structure of mining. He concluded that known and inferred de-
posits available at $.50 per pound (1973) prices totaled about
82 million tons or approximately 50 years of output at present
production rates. Even with a 6% compound rate of growth in de-
26
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mand, these reserves would be adequate for more than 25 years of
production. At a price of $.75 per pound, another 30 years of
reserves become available. Given the tendency of the industry
to underestimate reserves and the absence of any correction for
future technological change which could lower the cost of min-
ing, it may be assumed that reserves at $.75 per pound would be
significantly larger than the figure reported by Bennett.
If one assumes the lease value of $.75 ore will be nominal
(say less than $.05 per pound) 50 years hence, the lease value
of deposits being mined today would be $.025 per pound using a
5 percent discount rate and $.002 using a 10 percent discount
rate. If one assumes that the $.50 ore deposits will be ex-
hausted in only 25 years, the lease value at a 5 percent dis-
count rate is $.086. Although this latter figure is fairly
large relative to the price of copper, a more reasonable set of
assumptions would produce significantly lower figures for lease
values.
To date relatively little attention has been devoted to
the measurement of the last of the four market forces, external-
ities in mineral exploration and production, yet these forces
are potentially the most significant in terms of creating a di-
vergence between market prices and the social costs of produc-
tion. Sufficient information is not available with which to es-
timate quantitatively any of the externality impacts; we are
left with the qualitative conclusions discussed earlier.
CONCLUSIONS
This paper has reviewed some of the evidence as to how
severely prices are affected by the various market forces which
are assumed away in the Hotelling model. For those forces for
which price effects could be estimated, the distortion between
actual and optimal prices appears to be rather small in most
cases. Furthermore, forces which stimulated premature develop-
ment and lower prices many years ago may act to increase prices
today, particularly if the size of the remaining resource stock
affects the amount of mineral which can be extracted for a given
application of labor and capital. Therefore, we find that at
any point in time many of the forces act in opposing directions
and over time a force may change in terms of the direction of
its impact on price.
However, even if it were found that the various market
forces effectively cancel one another leaving no net effect on
price, one could not say that resources were being allocated
properly. Just because prices are approximately correct does
not mean that goods are produced at the least total cost to so-
ciety. When governmental controls are poorly designed, costs
of an activity such as mineral development may be needlessly in-
creased. Thus we may find that outlays attributable to legal
27
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uncertainties, court costs, and searches for rightful owners
are higher under existing systems of mineral exploration and de-
velopment than they would be under some alternative systems. At
the same time, the U.S. government and no doubt other govern-
ments, too, subsidize the mineral industry through the tax code,
leading to a divergence in social rates of return in different
industrial sectors. The consequence is too much investment in
mining relative to other, more heavily taxed sectors. Conse-
quently, mineral prices do not reflect the full cost of the la-
bor and capital used in mineral production.
A second cautionary note is also in order. Even if miner-
al markets act in some approximate fashion to allocate resources
over time in a manner deemed optimal today by existing members
of society, there is no guarantee that these same individuals
will not wish for an alternative allocation when the decisions
are viewed from other perspectives in time. When the decisions
on,natural resource development have the potential for effecting
massive transfers of wealth and income among generations, the
development decisions which are deemed optimal by living indi-
viduals may be highly undesirable from the viewpoint of unborn
generations. Because these future generations can never be
fully represented today, there will always be an inherent bias
in development toward those projects which favor the present
generation. Just as the discipline of economics offers little
guidance as to how assets should be distributed among indivi-
duals today, so too does economics offer little as to the
weights which should be attached to the satisfaction derived by
members of unborn generations. Nonetheless, by making planners
aware of the intertemporal income effects of various decisions,
economists help to make planners aware of the impacts of their
decisions.
28
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REFERENCES
1. Anderson, R. "Federal Mining Policy: The General Mining
Law of 1872." Nat. Res. J., 16(3) July 1976, pp. 601-19.
2. Anderson, R., and Spiegelman, R. "The Impact of the Tax
Code on Resource Recovery." Washington, D.C.: EPA-600/2-76-
009 U.S. Dept. of Commerce, NTIS PB264 886/AS, 1976.
3. Arrow, K., and Fisher, A. "Environmental Preservation, Un-
certainty, and Irreversibility." Q. J. Econ., 88(2) May,
1974.
4. Barnett, H. and Morse, C. Scarcity and Growth. Baltimore:
Johns Hopkins, 1963.
5. Bennett, H. et al. "An Economic Appraisal of the Supply of
Copper from Primary Domestic Sources." Washington, D.C.:
U.S. Dept. of the Interior, Information Circular 8598, 1973.
6. Cook E. "Limits to Exploitation and Nonrenewable Re-
sources." Science, 191(4220) Feb. 20, 1976, pp. 677-82.
7. Dasgupta, P. "On Some Alternative Criteria for Justice Be-
tween Generations." J. Public Econ., 3(4) Nov. 1974, pp.
405-423.
8. Fisher, A. Unpublished commentary on "Economic Criteria
for Intergenerational Comparisons," 1976.
9. Gilbert, R. "Resource Extraction with Differential Infor-
mation." Am. Econ. Rev., 67(1) Feb. 1977, pp. 250-54.
10. Goeller, H. and Weinberg, A. "The Age of Substitutability."
Science, 191(4229) Feb. 20, 1976, pp. 683-89.
11. Harsanyi, J. "Cardinal Utility in Welfare Economics in the
Theory of Risk-Taking." J. Polit. Econ., 61(5) October
1953, pp. 434-35.
12. Harsanyi, J. "Cardinal Welfare, Individualistic Ethics,
and Interpersonal Comparisons of Utility." J. Polit. Econ.,
63(4) August 1955, pp. 309-21.
13. Heal, G. "The Relationship Between Price and Cost for a
Resource with a Backstop Technology." Bell Journal of
29
-------
Economics, 7(2) Autumn 1976, pp. 371-78.
14. Hotelling, H. "The Economics of Exhaustible Resources."
J. Polit. Econ., 39(2) April 1931, pp. 137-75.
15. Kay, J. and Mirrlees, J. "The Desirability of Natural Re-
source Depletion." in D. Pearce (ed.) , The Economics of
Natural Resource Depletion. New York: J. Wiley, 1975.
16. Koopmans, T. "Stationary Ordinal Utility and Impatience."
Econometrica, 28(2) April 1960, pp. 287-309.
17. Krutilla, J., and Fisher, A. The Economics of Natural En-
vironments. Baltimore: Johns Hopkins, 1975.
18. Leith, C. Science, 1935, reprinted in Man and His Physical
Environment, McKenzie and Utgard (eds.)~Minneapolis:
- Burgess, 1975, pp. 168-71.
19. Lewis, T. "Monopoly Exploitation of an Exhaustible Re-
source." J. Env. Econ. and Mgt., 3(3) Oct. 1976, pp. 198-
204.
20. Maithus, T. An Essay on Population. London: Ward Lock and
Co., 1826.
21. Meadows, D. et al. The Limits to Growth. New York: Uni-
verse Books, 1972.
22. Mesarovic, M. and Pestel, E. Mankind at the Turning Point.
New York: E. P. Dutton, 1974.
23. Mill, J. Principles of Political Economy. London: Augustus
Kelly, 1965.
24. Mishan, E. "Economic Criteria for Intergenerational Com-
parisons." Presented at meeting of AEA, Atlantic City,
Sept. 16-18, 1976.
25. Nordhaus, W. "The Allocation of Energy Resources."
Brookings Papers on Economic Activity, 3, 1973.
26. Page, T. "Equitable Use of the Resource Base." Environ-
ment and Planning, 9(1) January 1977, pp. 15-22.
27. Page, T. "Selecting Welfare Criteria on the Basis of In-
tertemporal Equity." Presented at meeting of AEA, San
Francisco, Dec. 28-30, 1974.
28. Page. T. "Intertemporal and International Aspects of Sev-
erance Taxes." Mimeo, Nov. 2, 1976.
30
-------
29. Peterson, F. "Intergenerational Transfers of Natural and
Reproducible Resources." Unpublished manuscript, 1974.
30. Peterson, F. "Two Externalities in Petroleum Exploration."
In Brannon (ed.), Studies^ in Energy Tax Policy. Cambridge,
Mass.: Ballinger, 1975, pp. 103-113.
31. Peterson, F. and Fisher, A. "The Economics of Natural Re-
sources." Econ. J., forthcoming.
32. Pinchot, G. The Fight for Conservation. New York: Double-
day, Page & Co., 1910.
33. Rawls, J. The Theory of Justice. Cambridge, Mass.:
Harvard, 1971.
34. Ricardo, D. Principles of Political Economy. New York:
Longmans, Green, 1929.
35. Schulze, W. "The Optimal Use of Non-Renewable Resources:
The Theory of Extraction." J. Env. Econ. and Mgt., 1(1)
May 1974, pp. 53-73.
36. Smith, V. K. "Re-Examination of the Trends in the Prices
of Natural Resource Commodities, 1870-1972." Working Paper
No. 44, SUNY, Binghamton, N.Y., 1974.
37. Solow, R. "The Economics of Resources or the Resources of
Economics." Am. Econ. Rev., 64(2) May 1974, pp. 1-14.
38. Solow, R. "Intergenerational Equity and Exhaustible Re-
sources." Rev. Econ. Stud.; Symposium onjthe Economics of
Exhaustible Resources, Nov. 1974, pp. 29-45.
39. Stiglitz, J. "Monopoly and the Rate of Extraction of Ex-
haustible Resources." Am . Econ. Rev., 66(4) Sept. 1976,
pp. 655-61.
40. Strotz, R. "Myopia and Inconsistency in Dynamic Utility
Maximization." Rev. Econ. Stud., 23(3) 1955-56, pp. 165-80.
41. Sweeney, J. "Economics of Depletable Resources: Market
Forces and Intertemporal Bias." Re v. Econ. Stud., 44(1)
Feb. 1977, pp. 125-41.
42. Vickrey, W. "Measuring Marginal Utility by Reactions to
Risk." Econometrica, 13(4) Oct. 1945, pp. 319-33.
43. Weinstein, M., and Zeckhauser, R. "Use Patterns for De-
pletable and Recyclable Resources." Rev. Econ. Stud.: Sym-
posium on the Economics of Exhaustible Resources, Nov. 1974,
pp. 67-88.
31
-------
BIBLIOGRAPHY
Anderson, K. "Optimal Growth When the Stock of Resources is
Finite and Depletable." J. Econ. Theory, 4(2) April, 1972,
pp. 256-67.
Anderson, R., and Spiegelman, R. "Tax Policy and Secondary Ma-
terial Use." J. Env._Econ. and Mgt., 4(1) March 1977, pp.
68-82.
Arrow, K. "Some Ordinalist-Utilitarian Notes on Rawl's Theory
of Justice." J. Philosophy, 70(9) May 1973, pp. 245-63.
Baumol, W. "On the Social Rate of Discount." Am. Econ. Rev.,
58(4) Sept. 1968, pp. 788-802.
Baumol, W. and Gates, W. The Theory of Environmental Policy.
Englewood Cliffs: Prentice Hall, 1975.
Brown, G., and Field, B. "Implications of Alternative Meas-
ures of Natural Resource Scarcity." Presented at meeting
of AEA, Atlantic City, Sept. 16-18, 1976.
Buchanan, J. "A Hobbesian Interpretation of the Rawlsian Dif-
ference Principle." Kyklos, 29(1) 1976, pp. 5-23.
Dasgupta, P., and Heal, G. "The Optimal Depletion of Exhausti-
ble Resources." Rev. Econ. Stud.; Symposium on the Eco-
nomics of Exhaustible Resources, Nov. 1974, pp. 3-28.
Doilney, J. "Equity, Efficiency, and Intertemporal Resource
Allocation Decisions." Unpublished dissertation, Univ.
Maryland, 1974.
Fisher, A., Krutilla, J. and Cicchetti, C. "Economics of En-
vironmental Preservation." Am. Econ. Rev., 62(4) Sept.
1972, pp. 605-19.
Fisher, A.', and Krutilla, J. "Valuing Long Run Ecological Con-
sequences and Irreversibilities." J. Eny. Econ. and Mgt.,
1(2) August 1974, pp. 96-108.
Fisher, A., and Krutilla, J. "Resource Conservation, Environ-
mental Preservation and the Rate of Discount." Q. J.
Econ., 89(3) August 1975, pp. 358-70.
32
-------
Garg, P. "Optimal Growth with Exhaustible Resources." Unpub-
lished Ph.D. dissertation, Stanford Univ., 1974.
Georgescu-Roegen, N. "Energy and Economic Myths." S. Econ. J.,
41(3) January 1975, pp. 347-81.
Hanson, D. "Second Best Pricing Policies for an Exhaustible
Resource." Am. Econ. Rev., 67(1) Feb. 1977, pp. 351-54.
Herfindahl, 0. "Depletion and Economic Theory." In: Gaffney
(ed.), Extractive Resources and Taxation. Madison: Univ.
of Wisconsin, 1967.
Koopmans, T. Some Observations on Optimal Economic Growth and
Exhaustible Resources. Cowles Foundation Paper No. 396,
Yale Univ., 1973.
Krutilla, J. "Conservation Reconsidered." Am. Econ. Rev., 57
(4) Sept. 1967, pp. 777-86.
Lecomber, R. Economic Growth Versus the Environment. New York:
J. Wiley, 1975.
Lusky, R. "Conservation of Natural Resources and the Theory of
Recycling." Ph.D. dissertation, MIT, 1972.
Malinvaud, E. "The Analogy Between Atemporal and Intertemporal
Theories of Resource Allocation." Rev. Econ. Stud., 28(3)
June 1961, pp. 143-46.
Marglin, S. "The Social Rate of Discount and the Optimal Rate
of Investment." Q. J. Econ., 77(1) Feb. 1963, pp. 95-112.
Neher, P. "Democratic Exploitation of a Replenishable Re-
source." J. Public Econ. , 5(3-4) April-May 1976, pp. 361-
71.
Page, T. C_ons_eryatig_n and Economic Efficiency. Baltimore:
Johns Hopkins Press, 1977.
Pearce, D. The Economics of Natural Resource Depletion. New
York: J. Wiley, 1975.
Pitchford, J. Population in Economic Growth. New York: North
Holland, 1974.
Sampson, A. "A Model of Optimal Depletion of Renewable Re-
sources." J. Econ. Theory, 12(2) April 1976, pp. 315-23.
Sandier, T., and Smith, V. Kerry. "Intertemporal and Intergen-
erational Pareto Efficiency." J. Env. Econ. and Mgt., 2
33
-------
(3) Feb. 1976, pp. 151-59.
Scott, A. "The Theory of the Mine under Conditions of Certain-
ty." In Mason Gaffney (ed.), Extractive Resources and
Taxation. Madison: Univ. Wisconsin Press, 1967.
Smith, V. "Dynamics of Waste Accumulation: Disposal Versus
Recycling." Q. J. Econ., 86(4) Nov. 1972, pp. 601-16.
Solow, R., and Wan, F. "Extraction Costs in the Theory of Ex-
haustible Resources." Bell J. Econ., 7(2) Autumn 1976,
pp. 359-70.
Weinstein, M., and Zeckhauser, R. "The Optimal Consumption of
Depletable Natural Resources." Q. J. Econ., 89(3) Aug.
1975, pp. 371-392.
Vqusden, N. "Basic Theoretical Issues of Resource Depletion."
J. Econ. Theory, 6(2) April 1973, pp. 126-43.
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APPENDIX: VALUING THE BENEFITS OF RESOURCE CONSERVATION: THE
DOMESTIC COPPER INDUSTRY AS A CASE STUDY*
INTRODUCTION
The fundamental question which we address may be stated as
follows: Under the resource development policies of the United
States are non-renewable resources, particularly non-fuel miner-
als, extracted at rates which maximize overall societal well-
being? This is an important question in that rapid development
and exhaustion of our minerals would endanger our own well-being
as well as that of future generations. Conversely, if we with-
hold too much from the market today, we risk lowering the cur-
rent standard of living as well as the future stock of accumu-
lated wealth.
The Environmental Protection Agency (EPA), the sponsor of
this research, is particularly concerned with the rate of devel-
opment of U.S. non-fuel minerals. The EPA is mandated by Con-
gress to perform research, promulgate regulations, establish
standards, and make legislative recommendations concerning the
recovery and reuse of recyclable materials. Now, the context
of resource recovery is typically one of competition between
primary, virgin-based materials and secondary materials recover-
ed from the industrial and post-consumer waste streams. The
extent to which existing governmental policies and other market
forces operate either to stimulate or retard virgin material
development will affect the prices of virgin materials. Shifts
in virgin material prices affect recycling and, moreover, impact
overall societal well-being.
HISTORICAL PERSPECTIVE ON CONSERVATION
The historical literature on resource conservation reveals
that present concerns with the rate of resource depletion, the
level of non-renewable resource prices, and the maximization of
societal welfare were also felt in the past. The nineteenth
century economists, Malthus, Mill, and Ricardo noted the effects
of increasing resource scarcity. They observed that economic
growth may be curtailed or restrained as resources become more
expensive to locate and extract. Mill further noted that pri-
vate mining concerns do not typically consider aesthetic bene-
fits to society. We will return to this point later.
The Conservation Movement, as its name implies, advocated
the preservation and conservation of the nation's finite re-
sources and argued that these resources were being needlessly
*Presented at the 107th annual meeting of the AIME, Denver
Colorado, March 2, 1978.
35
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wasted and would soon be exhausted. One of the more notable
successes of the Movement was the creation of several National
Forests under President Theodore Roosevelt. The views of the
Conservation Movement have been echoed by many other writers.
In 1935, the well-known geologist C.K. Leith warned that "deple-
tion is further advanced than even mining men generally realize."
He estimated that reserves of crude oil, lead, and zinc were
only 15 to 20 times that of the annual consumption rate.
It should come as no surprise to us to learn that known
reserves of most of these minerals have increased even faster
than consumption with the consequence that the nominal date of
exhaustion has been pushed still farther into the future. An
examination of some of the factors which have acted to allevi-
ate, at least temporarily, the predicted resource scarcity will
help us to focus on the determinants of the optimal rate of re-
source depletion.
One of the effects we should expect is that resources
should exhibit a secular pattern of increasing price. However,
as examination of trends in resource prices reveals that, con-
trary to predictions, resources have generally become cheaper in
terms of the labor and capital required to extract them. The
only noteworthy exceptions appear to be forest products and
fisheries. One need not be reminded of the low prices of some
materials today. The price of copper, for example, is actually
lower in real terms than it was 10, 20, or even 30 years ago.
Another observed effect of resource scarcity, especially
when scarcity affects relative prices, is the substitution of
more abundant resources for those which become relatively scarce.
For example, the depletion of the rich iron ore deposits near
Lake Superior drove up the price of high-grade ores relative to
the low grade taconite ores. Over time the change in relative
prices stimulated the development of technologies to concentrate
the taconite ore as a feedstock to the steel industry.
Substitution, however, may occur even when a resource is
relatively abundant. For instance, although copper is not con-
sidered paricularly scarce today - with stocks of refined copper
on hand worldwide equal to more than one year's rate of consump-
tion - substitution of cheaper materials and better technologies
threaten the markets once dominated by copper. For example, it
is generally acknowledged that glass fibers will make inroads
into markets now held by copper wire, particularly those for the
transmission of information, and there is little that the copper
industry can do if glass can perform the same functions at a
lower cost.
Does the fact that resources, at least the non-fuel miner-
als, appear to be no more expensive or even less expensive than
they were decades ago indicate that private markets are develop-
36
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ing minerals too rapidly and that we are conserving too few re-
sources for the future? In order to answer this question we
have to examine more closely what is meant by the optimal rate
of development and consider how governmental policies and market
forces affect this rate.
OPTIMALITY IN RESOURCE EXTRACTION
Some forty years ago, Retelling sought to define the opti-
mal rate of natural resource depletion. Hotelling's definition
in essence is that society should produce resources so as to
maximize the present value of what consumers would be willing to
pay for the resource over and above what it costs producers to
deliver the resource. Using this definition of optimality,
Hotelling was able to show that a privately owned, profit-maxi-
mizing resource sector would produce with a time profile which
just matched that for social optimality. It is important to
note, however, that a number of conditions must be satisfied in
order for private decisions to lead to maximum societal well-
being. The following are the most important of these conditions:
1. Competition must prevail.
2. There must be no uncertainty regarding future demand, re-
source availability, and the tenure of ownership.
3. The relationships between private costs and societal costs
must not be distorted by externalities and diverse forms
of taxation.
Although the first of these conditions may be satisfied
approximately for many of the non-fuel minerals, especially when
foreign competition is considered, it is clear that the second
and third conditions are not satisfied. Using copper as a
sample case, we may explore some forces which distort the pro-
duction of the industry away from the rate which would be con-
sidered optimal.
1. Uncertainty
Several classes of uncertainty have affected production de-
cisions of the domestic copper industry, probably to a far
greater extent than is the case for the average U.S. industry.
In the 1960's a major source of uncertainty to the copper in-
dustry was the prospect that foreign properties, most notably
in Chile, would be expropriated. A second source of uncertain-
ty, that of future demand conditions, is a matter of much con-
cern to the industry today (e.g., potential loss of telecom-
munications markets to glass fibers). A third source is asso-
ciated with regulation and taxation. Will the industry be for-
ced to comply with EPA1s latest environmental regulations or
will the standards be relaxed somewhat for non-ferrous smelters?
Will new royalties on mineral production be imposed by state or
Federal governments (as proposed, for example, in H.R. 9292)?
Assuming resource owners are averse to risk, each source of un-
37
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certainty will tend (other things equal) to stimulate production
from existing mines and diminish the incentives for new explora-
tion. During the short run life of existing mines, which in the
case of copper may be several decades, output may be larger than
optimal. In the long run industry output will be adversely af-
fected by diminished incentives for exploration and output may
fall short of what is socially optimal.
2. Distortions Between Private and Social Cost
(a) Taxation
Like all non-fuel mineral industries, the copper industry
faces a large number of taxes and tax subsidies which affect the
private cost of production and may in fact distort that cost
relative to the true cost borne by society. Mineral prices will
be distorted relative to other commodities to the extent that
the taxes specific to mining affect the private costs of mineral
production. The most significant of the mineral taxes are
severance taxes and royalties. Tax deductions specific to the
minerals industry include percent depletion deductions and ex-
pensing of exploration and development. Examination of some of
these taxes and tax sudsidies in the copper industry revealed
that in 1973 the deductions were approximately four times larger
than the extra taxes and the net effect in that year was to low-
er the cost of producing copper by some 3 to 6 percent. In more
recent years depletion deductions in the industry have been con-
strained well below the theoretical maximum by the 50 percent of
net income limitation; thus the net impact on prices has no
doubt been diminished and in fact may have been eliminated. Of
course, whether the present situation of excess supply will per-
sist is problematic. The future impact of taxes and tax sub-
sidies on the industry is therefore difficult to assess.
(b) Externalities
Externalities are outputs of productive processes which
impose costs or confer benefits which are not received by those
engaged in the productive process. Since external diseconomies
are not recognized as costs by individual mining firms, the de-
cisions of these firms do not reflect these costs. Output is
therefore stimulated and prices tend to be lower relative to a
situation in which all of these costs are borne by the firm.
One of the more obvious externalities of the copper indus-
try is air pollution from copper smelters. This particular
externality has been recognized and is being internalized in the
industry cost function by current EPA air pollution regulations.
Perhaps less recognizable as externalities are the workplace
injuries and illnesses in the mining industry, a portion of whose
cost is now paid from general social insurance systems of wel-
fare and social security. A third category of externalities
38
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arises from the discovery system for metallic minerals on public
lands. Because this particular class of externality is both
more subtle and of greater potential interest to this audience
than are the others just noted, we will examine it in somewhat
greated detail.
The General Mining Law of 1872 and Department of Interior
regulations and rulings govern the development of hardrock min-
erals on public lands. Individuals are permitted free and open
access to prospect for and claim any unclaimed valuable showings
of hardrock and certain other minerals. A claim then gives the
individual the right to extract the mineral. Under a system of
open access the individual prospectors have little if any incen-
tive to share their knowledge with potential rivals. The con-
sequence is that some effort is duplicated and the search pro-
cess is not conducted efficiently. Secondly, one individual's
discovery of valuable minerals in an area typically stimulates
others to file preemptive claims in the adjoining area. Until
very recently only fragmented and incomplete records on the
location of each claim were maintained by the regional offices
of the Department of Interior. The result was considerable un-
certainty as to who, if anyone, had prior claim to a particular
tract of land. Although no comprehensive study has been con-
ducted on the impact of the provisions of the General Mining Law
on the cost of locating and producing minerals, we conjecture
that the net effect has been to increase costs relative to those
of other methods under which access is controlled (e.g., leas-
ing) .
Yet another form of externality arises when mining pre-
cludes alternative uses of the land. The Department of Interior
has traditionally accorded mining priority over alternative
(perhaps less socially valuable) uses of public lands, and min-
ing firms have not had to include in their cost functions any of
the opportunity costs associated with other activities which are
foregone once mining has commenced. This situation is in marked
contrast to arrangements under which private developers must bid
against one another for the rights to use private lands, the
winning bidder making a payment at least equal to the profits
which could have been earned in the next most profitable acti-
vity.
EVALUATION
1. From The Perspective of Present Generations
The Hotelling approach asks that nonrenewable resources be
extracted at a rate which maximizes the present value of social
gains from production. Using the present value welfare test, we
have identified several factors which distort production deci-
sions away from that which would be socially optimal. We be-
lieve that two factors deserve to be singled out for their ef-
39
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feet on production decisions of the mining industry. The first
is the Federal tax code which confers a significant tax subsidy
to the mining industry. This subsidy permits mining firms to
acquire capital at lower rates than those enjoyed by the general
class of manufacturing firms. Consequently, investment in min-
ing is stimulated (at least historically), relative to what
would produce optimal societal welfare. The second factor is
the subsidy accorded mining by virtue of the fact that mining
firms need not pay the opportunity costs of the public lands
they aquire for mining purposes. This factor also serves to
subsidize mining firms, making prices lower and output higher
than would otherwise be the case.
2. From The Perspective of Future Generations
Decisions by current generations to produce and consume
nonrenewable resources affect future generations in two ways;
the future availability of these resources is diminished and,
to the extent current production leads to increased wealth and
saving the stock of capital which is inherited by future gener-
ations is augmented. Whether the future generations are made
better off or worse off by our decisions today depends largely
on the substitutability of capital for resources in the future.
Decisions to produce and consume resources to maximize the pre-
sent value of economic welfare may be quite compatible with the
desires of future generations. There is no reason to believe
that capital and other more abundant minerals (glass and alum-
inum) cannot fully substitute for copper as it becomes more
scarce.
It is possible, however, to envision situations where the
decision to maximize the present value of economic welfare will
not be consistent with the desires of future generations. Were
we to focus on the production of uranium ore, for example, we
might conclude that future generations are being made worse off
by our use of uranium and creation of long-lived, high-level
radioactive waste.
CONCLUSION
The current Federal policy of permitting private firms to
determine the rate of extraction of nonrenewable resources is,
in most cases, fully compatible with the maximization of welfare
of current and probably future generations. However, several
important exceptions to this principal have been noted. Tax
subsidies to mining distort capital and labor resource alloca-
tion in the economy and cause excessive activity to occur in the
mining sector. Mining firms do not always pay the full social
costs of their activities on the public lands. Finally, some
forms of nonrenewable resource development have the potential
for creating significant transfers of wealth away from future
generations.
40
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APPENDIX
This appendix presents the basic theory of the mine as de-
veloped in Peterson and Fisher [31]. With this basic theory the
results of Section 4 were derived.
Using the notation of Peterson and Fisher, the production
function for mineral output can be represented as:
Y = f(E,X,t)
where Y is extractive output, E is an index of labor and capi-
tal devoted to extraction, X is the resource stock, and t is
time. Output and the resource stock are linked by the relation-
ship that output is the time derivative of the resource stock.
The mining firm's problem is to maximize the present value of
profits from sales of extractive outputs, or:
max
i
\[Pf(E,X,t) - WE]e~rtdt
where P is the price of the resource, W is the cost of a unit of
the composite capital and and labor input, and r is the rate of
discount. From this expression one forms the Hamiltonian:
H = [Pf(E,X,t) - WE - qY]e~rt
where q is the shadow price (lease value) attached to a unit of
the stock of the resource at time t. By the maximum principle,
the partial derivative of the Hamiltonian with respect to the
control variable is set equal to zero.
H£ = PYE - W - qYE = 0
Rearranging terms in this last expression one obtains:
P = W/YE + q
The first term, W/YE, is just the marginal cost of extraction.
This can be seen by noting that marginal cost is the partial
derivative of cost with respect to output, or Cy. Using the
chain rule for derivatives, this may be expressed as CEEy> or
equivalently, CE/YE. But, CE, the rate at which costs change
with respect to the use of the composite capital and labor in-
put, is just equal to the cost of a unit of the composite input,
or W. Thus W/YE is equal to the marginal cost of extraction,
Cy. As noted, the second term is the shadow price or lease
41
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value attached to a unit of resource in place. Therefore, at
any point in time, price equals the marginal cost of extraction
plus the lease value of the mineral in place.
Another condition which is necessary for a maximum of the
profit expression is that lease values (others have termed this
rent, net price, marginal user cost, and royalty) have a time
profile described by:
q = rq - Hx
where q is the time derivative of q. Substituting for HX and
rearranging terms one obtains:
q/q = r + (1 - P/q)Yx
That is, the lease values increase at the rate of interest plus
an adjustment which is zero whenever there is no stock effect
(YX = 0) or there is a zero marginal cost of extraction (P = q) ,
42
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TECHNICAL REPORT DATA
(Please read Inslructions on ihc reverse before completing)
1. REPORT NO, 2.
EPA-60Q/5-78-015
4. TITLE AND SUBTITLE
EVALUATION OF ECONOMIC BENEFITS OF RESOURCE
CONSERVATION
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
September 1978 (Issuinq Date
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Robert C. Anderson
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Law Institute
1346 Connecticut Avenue, N.W., Suite 620
Washington, D.C. 20036
10. PROGRAM ELEMENT NO.
IDA312
1 1. CONTRACT/GRANT NO.
R803880
12. SPONSORING AGENCY NAME AND ADDRESS . ,
Municipal Environmental Research Laboratory—Cm. ,OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF RE PORT AND PERIOD COVE RED
Final
14. SPONSORING AGENCY CODE
EPA/600/14
1-5. SUPPLEMENTARY NOTES
Project Officer: Oscar Albrecht (513) 684-7886
16. ABSTRACT
The forces that determine prices of non-renewable natural resources are an import
ant consideration in an evaluation of the social desirability of conservation through
recycling. If prevailing market prices accord conservation benefits a value less
than their true value to society, the prices are suboptimal and the solution may re-
quire governmental support of resource recovery and recyling.
A comprehensive review of the literature on natural resource economics reveals
that numerous external forces can cause divergencies between the socially optimal
prices and the prices that are actually determined in the market place. The forces
act in varying directions and with varying intensities over time. It is, however,
difficult to establish with any degree of precision the magnitude or even the direc-
tion of bias given to the prices acting on supply and demand. Moreover, the socially
optimal level of resource conservation is likely to be viewed differently by individ-
uals of different generations.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Materials recovery
Extraction
Scrap
Availability
Conservation
Mining
Taxes
b. IDENTIFIERS/OPEN ENDED TERMS
Solid waste management
Solid waste recycling
Tax subsidies
c. COSATl l-'iclcl/Ciroup
5C
3. DISTRIBUTION STATEMENT
Unrestricted
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
51
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1
43
af.U. 19/8— , •;', - \ -iL.,' i •»•}-.
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