EPA-23 0-12-85-025
September 1985
METHODS DEVELOPMENT FOR ENVIRONMENTAL
CONTROL BENEFITS ASSESSMENT
Volume VII
METHODS DEVELOPMENT FOR ASSESSING ACID
DEPOSITION CONTROL BENEFITS
by
Thomas D. Crocker, John T. Tschirhart, and Richard M. Adams
University of Wyoming
Laramie, Wyoming 82071
Bruce Forster
University of Guelph
Guelph, Ontario NIG 2W 1
USEPA Grant # R8 0697 2-01-0
Project Officer
Dr. Alan Carlin
Office of Policy Analysis
Office of Policy, Planning and Evaluation
U*S. Environmental Protection Agency
Washington, D.C. 20460
OFFICE OF POLICY ANALYSIS
OFFICE OF POLICY, PLANNING AND EVALUATION
US . ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
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OTHER VOLUMES IN THIS SERIES
Volume 1, Measuring the Benefits of Clean Air and Water, EPA-230-12-85-021.
This volume is a nontechnical report summarizing recent research for EPA on
methods development for better estimates of economic benefits from environmental
improvement. The report-presents the basic economic concepts and research methods
underlying benefits estimation as well as a number of case studies, including
several from other volumes of this series. Finally, it offers insights regarding
the quantitative benefits of environmental improvement.
Volume 2, Six Studies of Health Benefits fran Air Pollution Control, EPA-230-
12 - 85 - 02 0~!
This volume contains six statistical epidemiology studies. They show that
large associations between health and current levels of air pollution are not
robust with respect to the statistical model specification either for mortality
or morbidity. They also find that significant relationships, mostly small, oc-
casionally appear.
Volume 3, Five Studies on Non-Market Valuation Techniques, EPA-230-12-85-021.
This volume presents analytical and empirical canparisons of alternative
techniques for the valuation of non-market goods. The methodological base of
the survey approach - directly asking individuals to reveal their preference
in a structured hypothetical market - is examined for bias, replication, and
validation characteristics.
Volume 4, Measuring the Benefits of Air Quality Charges in the San Francisco
Bay Area: Property Value and Contingent Valuation Studies, EPA-230-12-85-022.
This volume replicates a property value study conducted in the Los Angeles
Basin for the San Francisco Bay area. A taxonary series of air quality types
and socioeconomic typoligies are defined for cities in the area to examine how
property values vary with pollution levels. The contingent valuation method
surveys individuals, directly asking their willingness to pay for changes in
air quality. The survey method yields benefit values that are about half the
property value benefits in both the Bay area and Los Angeles.
Volume 5, Measuring Household Soiling Damages from Suspended Particulate:
A Methodological Inquiry, EPA 230-12-85-023.
This volume estimates the benefits of reducing particulate matter levels
by examining the reduced costs of household cleaning. The analysis considers
the reduced frequency of cleaning for households that clean themselves or hire
a cleaning service. These estimates were compared with willingness to pay
estimates for total elimination of air pollutants in several U.S. cities.
The report concludes that the willingness-to-pay approach to estimate parti-
culate-related household soiling damages is not feasible.
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Volume 6, The Value of Air Pollution Damages to Agricultural Activities in
Southern California, EPA-230-12-85-024.
This volume contains three papers that address the economic implications
of air pollution-induced output, input pricing, cropping, and location pat-
tern adjustments for Southern California agriculture. The first paper esti-
mates the economic losses.to fourteen highly valued vegetable and field crops
due to pollution. The second estimates earnings losses to field workers ex-
posed to oxidants. The last uses an econometric model to measure the reduction
of econanic surpluses in Southern California due to oxidants.
Volume 8, The Benefits of Preserving Visibility in the National Parklands of the
Southwest, EPA-230-12-85-026.
This volume examines the willingness-t-pay responses of individuals surveyed in
several U.S. cities for visibility improvements or preservation in several Nation-
al Parks. The respondents were asked to state their willlingness to pay in the
form of higher utility bills to prevent visibility deterioration. The sampled
responses were extrapolated to the entire U.S. to estimate the national benefits
of visibility preservation.
Volume 9, Evaluation of Decision Models for Environmental Management, EPA-230-
12-85-027.
This volume discusses hew EPA can use decision models to achieve the proper role
of the government in a market economy. The report recanmends three models useful
for environmental management with a focus on those that allow for a consideration
of all tradeoffs.
Volume 10, Executive Suimary, EPA-230-12-85-028.
This volume summarizes the methodological and empirical findings of the series.
The concensus of the empirical reports is the benefits of air pollution control ap-
pear to be sufficient to warrant current ambient air quality standards. The report
indicates the greatest proportion of benefits from control resides, not in health
benefits, but in aesthetic improvements, maintenance of the ecosystem for recreation,
and the reduction of danages to artifacts and materials.
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PREFACE
Many individuals have made useful contributions to the preparation of
this report. Drs. Alan Carlin and Dennis Tirpak of the USEPA were
particularly helpful in setting bounds or. the nature of the problem during the
early stages of the research. A meeting in October 1979, with the members of
the Committee on Biological Effects of the National Atmospheric Deposition
Program was also helpful in this respect. Michael Marcus of the Department of
Zoology at the [University of Wyoming has provided written material which has
been used as the basis for several lengthy passages in Chapters II and V.
Intermittent conversations with and written commentaries from Dennis Knight,
William Schulze, and Harold Bergman have been instrumental in shaping some of
what appears in the following pages. None bears any responsibility for any
errors or omissions. Reza Sepassi has contributed in numerous wavs as the
primary research assistant for the research effort. Finally, Carol Steadman
has employed her multiple talents to provide worthy research, editing,
bookkeeping, organizational, and typing services throughout the project.
ii
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ABSTRACT
There has recently been increasing awareness that some environmental
pollutants, because of the broad geographical scope of their effects, impose
not only the direct affronts to human life and property of the traditional
urban pollutants, but also attack the pleasures and the life support services
that the earth's ecosystem scaffolding can provide. Acid precipitation might
be one of these pollutants. The basic purpose of this report is to suggest
those types of natural science research that would be most helpful to the
economist faced with the task of assessing the economic benefits of
controlling acid precipitation. However, while trying to formulate these
suggestions, inadequacies in the supporting material the ecologist could offer
the economist, and in what the economist could do with whatever the ecologist
offered him, became apparent. Therefore part of our effort has been devoted
to initial development of a resource allocation process framework for
explaining the behavior of ecosystems that can be integrated into a broadened
benefit-cost analysis which captures traditional ecological concerns about
ecosystem diversity and stability. Our intent has been to make a start at
providing a basis for the ecological and the economic disciplines to ask
better-defined questions of each other.
Some reasonably well-defined questions have nevertheless been asked and
tentative answers have been provided for a few of them. In particular, most
of the existing techniques for assessing the benefits of pollution control
require knowledge of the magnitude of the response of the entity of interest
to variations in the quantity of pollution to which it is exposed. The entity
that is the object of interest in these estimates of response surfaces or
functions must itself have value to humans or it must contribute in some known
fashion to another entity having value to humans. Otherwise, the economist is
unable to perform his tasks. Additional properties that response surface
research must have to be most valuable for the empirical implementation of the
techniques of benefit-cost analysis are outlined in the text.
The simplest of these available techniques is applied in a first exercise
at using known response surfaces to assess the benefits of controlling acid
precipitation in Minnesota and the states east of the Mississippi River.
Current annual benefits of control are estimated to be $5 x 10 in 1978
dollars, with materials damages constituting the largest portion of these
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benefits. The reader must not treat this estimate as definitive, although the
ordering of current annual control benefits by sector is highly plausible.
The known response surfaces used to construct the above estimate
sometimes displayed two properties that could impart "all-or-nothing" and
"now-or-never" features to the acid precipitation control decision problem,
These two features arise because the marginal benefits of reducing acid
precipitation appear to be increasing over a substantial interval of
increasing pH values, and because the effects of acid precipitation upon
ecosystem buffering capacities are less than fully reversible, both
technically and economically.
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CONTENTS
Preface ii
Abstract iii
Figures vi
Tables vi
I. Introduction 1
II. A First Exercise in Assessing the Benefits of Controlling
Acid Precipitation 19
III. Decision. Problems in the Control of Acid Precipitation:
Nonconvexities and Irreversibilities 65
IV. Valuing Ecosystem Functions: The Effects of Acidification ... 84
V. Natural Science Research Useful to the Economist 12.0
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FIGURES
Number Page
1.1 Evolution of the Resource Stock 6
1.2 Equilibrium Pollution and Resource Stock 7
3.1 The Standard Representation 66
3.2 The Nonconvexity Problem 69
3.3 Possible Time Path of Acid Precipitation Effects 71
4.1 ThePhysiologySet 91
4.2 Effect of Environmental Conditions 91
4.3 Attainable Stored Energy 92
4.4 The Maximizing Solution 92
4.5 An Unbounded Physiology Set 94
4.6 A Diversity Possibilities Frontier 104
4.7 The Compensating Function 104
4.8 Consumer Preferences 113
4.9 ANatural State Optimum 113
4.10 An Interventionist Optimum 113
5.1 AResponse Surface 124
5.2 Convexity and Concavity 124
5.3 Effect of Air Pollution Risk Upon Yields 144
TABLES
2.1 Average Acreage, Production and Gross Value for Selected
Commodities, by Region and Total, 1975-77 Crop Year 25
3.1 Sections with Fish at Various pH Levels for a Sample of
Pennsylvania-Streams Suffering from Acid Mine Drainage 68
3.2 Variation of Numbers of Fish Species with Respect to pH
Levels for a Sample of Pennsylvania Streams Suffering
from Acid Mine Drainage 68
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I. INTRODUCTION
It is now widely accepted that the average pH of the annual precipitation
in nearly the entire United States east of the Mississippi River was below 5.0
in 1972-73 [Glass (1978, pp. vii, 19)]. Only northern Wisconsin and southern
Florida were exempted. Since 1972-73, no increase in rainfall pH is believed
to have occurred. With the likely increased combustion of coal in Canada and
the United States, most commentators expect further reductions in pH levels
and a further spreading of the geographical areas subjected to acid
precipitation and acidifying depositions. This expectation persists even
though doubts have been publicly expressed about whether some of the
instrumentation used to measure precipitation acidity is accurate [Galloway,
et al. (1.979)] , and whether current measures actually represent a decline from
historical pH levels TPerhac (1979) 1 .
Substantial concern has been expressed in both scientific and lay circles
about the impacts of increasingly acidic precipitation upon the flows of
material resources and amenity and life support services provided by forest
and aquatic ecosystems. Because of these potential impacts, policymakers in
the U.S. and Canada are now being asked to weigh the benefits provided by
these resources and services against the costs of controlling emissions of
acid precursors from fossil fuel combustion. Allied with these concerns are
numerous proposals for more research on the biological and economic effects of
acid precipitation. In this report we attempt to provide policymakers with
some of the information they need to choose intelligently from among these
proposals and to prepare adequately for the findings of whatever research
programs are ultimately adopted. Although researchers have made considerable
progress in identifying those features of different ecosystems that render
their economically valuable components and processes more-or-less vulnerable
to disruption as s. consequence on long-term acid precipitation, the goal of
providing consistently dependable guidance to policymakers has not yet been
reached.
Toward this end, we have, after this introduction, structured this report
in four chapters. The next chapter provides an economist's review of the
existing literature on the biological and physical effects of acid
precipitation. The overview content is combined with limited information on
the market values of the affected material resources and amenity and life
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support services to arrive at no better than order-of-ma.gnitude assessments of
the current annual economic losses to existing activities caused by acid
precipitation in the eastern United States (Minnesota and the states east of
the Mississippi River). The emphasis in this second chapter is on identifying
the economic sectors that appear to be suffering the greatest damages from
acid precipitation. Only the simplest of economic methods are used to perform
this first exercise in assessment. A third chapter raises two plausible
special features, nonconvexities and irreversibilities, of the ecosystem
effects of acid precipitation that are likely to cause special, difficulties
for control decisionmaking as well as difficulties for the application of both
the simple and more sophisticated methods of assessing the economic benefits
of control. In a fourth chapter, we present a somewhat broader framework for
assessing the economic benefits of control than the framework that underlies
traditional assessment methods: we provide a start in the development of a
framework which, in principle, allows one to assess the economic impact of
pollution or anv source of stress upon ecosystem yields and ecosystem
diversity. This framework has been developed because of the inattention given
by traditional economic assessment procedures to questions of fundamental
concern to ecologists, and because of our perceived lack of an
ecological-theoretical. framework which could guide the questions the economist
asks of the ecologist. Finally, while drawing upon the information generated
in the previous parts, we develop and try to defend a set of recommendations
for natural science research on the biological effects of acid precipitation.
Our recommendations assume that without exception all natural science research
into these effects is directed toward the provision of information for assess-
ing the economic benefits of acid precipitation control. This last chapter is
the culmination of our current efforts. The reader should therefore view the
report not as an assessment of the economic benefits of specific control
alternatives but rather as a prelude to that assessment.
The Tasks of the Economist
We divide into six tasks the role of the economist in providing decision-
makers with information to assess the benefits of controlling acid precipita-
tion. Since attempts to treat these tasks, within the limits of research time
and resources, compose the bulk of this report, we offer only the briefest
treatment here: -
1.) To enumerate a set of economic indicators capable of communicating
national, and regional, economic benefits of alternative types and degrees of
control of acid precipitation.
2) To identify those features of acid precipitation that when altered
have direct implications for the aforementioned indicators. These features
may affect directly the components of ecosystems and the economic activities
that depend upon them. Alternatively, they may alter the behavior of these
components, resulting in changes in ecosystem processes and the economic
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activities which employ them. An example of a direct effect is a reduction in
the yield of a vegetable due to acid precipitation-induced inhibition of
photosynthesis in the standing stock of vegetable plants. An indirect effect
might consist of the changes in successional Patterns of a forest due to the
differential effects of acid precipitation upon particular tree, understory,
and soil microbe species.
3) To identify and, where appropriate, develop a theoretical framework
for assessing the potential national and regional economic benefits of
alternative acid precipitation control strategies. This framework should
generate refutable hypotheses about the causal relationships between the
features of various control strategies and the responses in economic terms of
relevant ecosystem processes and components. In short, the framework should
make easier the appropriate specification and estimation of the economic and
ecosystem parameters needed to explain and to make predictions of the magni-
tudes and the timing of the potential benefits of alternative control strat-
egies .
A) To identify the data required to estimate the aforementioned para-
meters. The data requirements should be as parsimonious as the theoretical
framework will allow.
5) Given the current state-of-the-world, to estimate the current values
of the relevant economic and ecosystem parameters, while employing properly
constructed variables, applicable statistical and numerical tools, and an
appropriate sample of ecosystems.
6) To incorporate the estimated parameters into a body of knowledge that
will predict the values of the economic indicators resulting from adoption of
alternative acid precipitation control strategies.
Generally speaking, each of these tasks is served by an analytical
framework or model encompassing a greater range of phenomena than did previous
models. Of the six tasks, however, the third and the fourth are most likely
to be of greatest relative interest to the professional researcher, while the
other four tasks assume greatest relative importance for the decisionmaker.
In those parts of economics relevant to the assessment of the benefits of air
pollution control, there has frequently been inadequate attention by
analytical investigators to possibilities for improved empirical
implementation. Analytical investigators have on occasion indulged in illicit
intercourse with beautiful models, as at least one economist has remarked. On
the other hand, economists having some interest in empirical implementation
have occasionally been too ready to indulge requests to generate estimates of
the benefits of air pollution control. From some perspectives, this report
might accomplish the unusual act of being culpable on both counts. The second
chapter of the report engages in an empirical exercise that is not solidly
embedded in a theoretical framework. The fourth chapter goes through a
theoretical exercise which could be empirically implemented. Nevertheless, in
this report any beauty it has must be judged as an abstraction; it is provided
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little empirical flesh. Only the third chapter makes a limited attempt to
clothe the abstract in the empirical. We nevertheless feel that these rather
disparate chapters do result in a set of natural science research
recommendations, that when accomplished, are likely to be useful and inputs
for assessing the economic benefits of alternative acid precipitation control
strategies.
A Dynamic Economic Sketch of the Ecosystem Effects of Acid Precipitation
In order to frame our discussion, we present in this section a model
which outlines the economic nature of the problem of preventing ecosystem
damages from acid precipitation. As will be near-universal throughout this
report, knowledge of the dose-response function relating ecosystem effects to
acid precipitation is central to any empirical application of the model.
Assume an industrial region, I, that generates a constant waste flow, W,
per time period. Some of these wastes are carried and transformed by
atmospheric processes to a lake region, L. The waste that travels the
distance, x , from I to L each period is given by:
L
^ w fX Li
TJ(x ) = — - f ^(x>dx, (1)
Hu I
J o
where H is the mixing or scavenging height of the air column and u is the wind
speed. H and u are assumed constant over [o,x ]. W/Hu = W/k is then the
initial pollution concentration at I. ^(x) is a pollution^oss or trans-
formation function which is assumed constant over distance. - Thus
W(x^) = W/k - Lx* (2)
is the waste concentration arriving each period at 1 as a result of W being
generated in I.
Atmospheric processes cause the waste to be deposited and accumulated in
L as a stock of pollution, P. This accumulation is:
dP Lx .
— = g(W(x )) - aP, (3)
where g(*) measures the waste concentration in the lake region, and aP
measures the abilities of the region'^ forest and aquatic ecosystems, R, to
cleanse themselves of the pollutant. - We assume that a is constant and
independent of pollution. Forster (1975) discusses a model in which a is a
decreasing function of P.
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The dynamic evolution of R is governed by a pollution version of the
Lotka (1925) biological growth function:
d"- F(R-P) ¦ ,4)
where, for a given P, the F function has the usual Lotka shape. Increases in P
will shift the entire curve downward in Figure 1. The environmental carrying
capacity, R, is thus an inverse function of the level of pollution. That is:
R = R(P); R'<0 (5)
Expression (5) is an example of what is commonly called a dose-response
function. The loss in R may be thought of as the ecosystem damages caused by
a change in the pollution level. Its critical importance to system behavior
and thus human welfare can be illustrated by introducing a harvesting function
relating man's harvest, H, from the system to his harvesting effort, a, and
the size of the lake region's forest and aquatic ecosystem resources.
H = aR (6)
For a given level of effort, the harvest will be larger if the resources are
more plentiful. Using (6) and the previous expressions, the dynamic structure
of the lake region ecosystem is governed by:
dP - L
— = g (W/k - z,x ) - aP.
dR
\
dt
F(R,P) - aR.
(7)
(8)
The limiting solution for pollution, PB, depends upon meteorological
factors, the level of waste emissions in I, and the self-cleansing abilities
of the lake region's ecosystems:
P°° = a g(W/k - ixL) . (9)
This solution, which is globally stable, can be substituted into (9) to
examine the limiting solution for R. The result of doing so is illustrated
in Figure 2.
In Figure 2, pollution reduces the growth rate of the lake region's
resources and thereby reduces the region's environmental carrying capacity
from R(0) to R(P°°). With a given level of harvesting effort, the bioeconomic
equilibrium stock size is reduced from R* to R00 and the equilibrium harvest
suffers a decline from H* to H°°. The equilibrium resource stock size is
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Figure 1.1
Evolution of the Resource Stock
F(R,P)
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Figure 1.2
Equilibrium Pollution and Resource Stock
aR
H*
00
E
RCO)
F(R,0)
Rao
dR
dt
Roo
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stable. Efforts to enhance the resource base by restocking fish or fert-
ilizing forest soils may offer temporary respites by raising the resource
stock above R00. However, with P continuing at pc^ the stock must over time
decline again to R°°.
The Meaning of Economic Benefits
Everything said in this report unequivocally assumes that man is the
measure of all things. As Adams and Crocker (forthcoming) point out, whatever
a person does must be the best thing for him to do, given his knowledge of his
circumstances of the moment--otherwise, he would not do it: thus theperson's
autonomous preferences are revealed by his behavior. This is the perspective
of value that pervades economic analysis. Contrary, however, to much common
usage, "economics" and "pecuniary" are not viewed as synonymous. For example,
human behavior and the health, production, or aesthetic effects of a pollutant
on that behavior are directly "economic." The effects of a pollutant on
vegetation are "economic" only insofar as that vegetation contributes to human
health and happiness.
The preceding perhaps conveys the stance of economics with respect to the
basis of values. It fails, however, to state the units in which values are to
be measured or the context that bestows meaning on these units. Assume, for
example, that a person derives satisfaction from an aesthetic phenomenon, such
as lush vegetation. Tf there is a local decline in the lushness of
vegetation, the person will possibly feel he has been raade worse off,
However, if there are other worldly things capable of providing him
satisfaction, then some additional provision of these other things may cause
him to feel as well off as he would without the decline in vegetation
lushness. Finally, if these things can be secured by the expenditure of
income, or time that can be used to earn income, then there is some additional
income that in the face of the lushness decline, would make the person feel no
worse off. The unit, therefore, in which economics would have us measure
value is money stated in terms of income. Implicit in the acceptance of this
unit is the presumption that, even if the thing being valued cannot be secured
in the marketplace, there are in this marketplace collections of other things
from which the person receives equal satisfaction. These other things, which
have market prices attached, can under a quite wide range of well-specified
conditions, serve as vehicles to infer the "values" of entities and services
for which no directly observable pecuniary prices exist.
In spite of the common sense approach to valuation sketched above, it
will often yield, depending on the conditions adopted for the analysis,
different values for the same quantity variation in the entity being valued.
For example, if one is interested in the control of a pollutant that is
damaging vegetation, the value that a person will attach to the reduction of
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the pollutant can depend on whether one is measuring what the person is
willing to pay for the reduction or what the person would have to be paid in
order not to have the reduction. Tn the latter case, because the person is
viewed as holding the legal right to stop the pollution, his revelation of
preferences is not limited by his income. However, his income does limit what
he can do when he nnis£ buy a cessation of pollution from someone else. As his
money becomes scarce, he becomes reluctant to trade money for goods. Thus ,
the two measures would be identical only when variations in income play a
trivial role in determining the quantity of the good that the person will
choose to hold.
Other sources of variations in values of identical changes in the quan-
tity of a particular good include whether, in an original and in a new state,
the original is the most preferred or the least preferred quantity; whether
the valuation in the new state is independent of adjustments in overall
patterns of consumption in moving from the original quantity of the good to
the new quantity; and whether the person can by his own actions adjust his
consumption of the good in question or, as with many pollutants, must become
resigned to an externally imposed fate. In short, to be meaningful and
communicable, the exact context of a particular economic valuation measure
must be explicitly and fully stated. The criteria for judging which of the
several analytically correct valuation measures to apply to a particular real
problem must often come from outside economics.
Benefits Assessment Methodologies
Schulze, et al. (forthcoming) provide an informative and succinct common
theoretical basis for the alternative economic methodologies available to
assess the benefits o acid precipitation and other plausible
environmental insuits '-/coiffiWlfff^t their analysis with the recognition that
all assessment methodologies presume that there exist marketplace collections
of things other than the entity being valued from which the representative
individual could receive equal satisfaction. These substitution possibilities
are said to exist across alternative activities and locations, both of which
are denoted A . • ,A #,... ,A . Each of these activities and/or locations is
associated with § level @f §f\Vlronmental quality, 50n,
Increases in the represent environmental quality improvements.
The individual's weakly separable, quasi-concave utility function is
written as:
U(Ai,Qi,X), (l0)
where X is a composite commodity the magnitude of which is unaffected by A^
and Qj. Utility is assumed to be increasing in A^, Q., and X. The
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individual' ^decision problem is then to maximize (1) subject to a budget
constraint:—
y-£pa-X=0,
i=l
where Y is current period income, P is the price of the ith activity, and X
is assumed to have a price of unity. The necessary conditions for solution of
the problem include
aU/aA^ 9U/3A.
au/ax' - 1' and 3U/3X " 1 i " 'i " 0, (12)
assuming that A. is consumed in some positive quantity. This says that the
individual will equate the marginal rate of substitution of the ith activity
for X to the price, P , of that activity.
i
To determine the marginal willingness-to-pay for the environmental
quality associated with a particular activity, i=l, Schulze et al. set (10)
equal to a constant and then totally differentiate this expression as well as
expression (11). When dA =0 for ifl, and by using (12), they obtain:
i
f f A. !Z^i (13)
d0l L, 1 dQ 3TJ/3X
i=l M
This represents the additional income that in the face of an environmental
quality change would make the individual feel no worse off. Considering only
the total differential of (11), while continuing to assume that dQ, =0 for ifl,
they obtain another expression for dY/dQ^:
dY ^ A dP. r—* dA.
i = Z < — + L i —
h dQi h dQi
When one equates (13) and (14), and cancels similar terms, the result is:
dX (14)
y P ^ + « - -8U/3°1 us)
£—• 1 dQ. dQ. au/ax
i= 111
In short, the last two terms in (14) are negative.
Schulze, et al. suggest that (14) and (15) provide a common and easily
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grasped basis for interpreting the substantive analytical content and the data
requirements of alternative economic methodologies for assessing marginal
willingnesses-to-pay for changes in environmental quality. Consider, for
example, an air pollutant which reduces the yield of an agricultural crop.
One expedient method to assess the economic value of a quality improvement is
simply to ask individual producers and consumers what their magnitudes of
dY/dO^ are. This approach, probably because of the ready availability of
price, yield, and location data, has not to our knowledge vet been used to
assess agricultural damages from air pollution. under the label of "bidding
games" or "contingent valuations" it has been widely used to value environmen-
tal quality improvements where there is little or no historical experience
with the potential improvement and where directly observable price and
quantity data are unavailable to either the researcher or the individual
producer and consumer. These circumstances aptly describe many aesthetic and
health effects of air pollution. Schulze et al. thoroughly review and
evaluate several of the existing contingent valuation studies, and provide a
listing of many more. Brookshire and Crocker (forthcoming) provide further
discussion of the real-world circumstances under which contingent valuation
approaches are especially appropriate. Although the natural science
informational requirements of these methods might appear to be minimal or
nonexistent, all commentaries insist that great care must be taken in
describing the state-of-the-world to which the interviewee is to be asked to
respond. Otherwise, biases can be introduced that make interviewee responses
uninterpretable. Thus , although natural science information is not an
integral part of the analytical exercise involved in contingent valuation
methods, it does play an important role in establishing the scenario that is
to be valued.
If agricultural settings have seen but infrequent application of the
contingent valuation methods that capture the right-hand-side of (14), they
have experienced numerous applications of methods that focus on no more than
the middle term, SP (dA./dQ ). on its left-hand-side. Examples are Benedict,
et al. (1973) and Millecan (1976) . When the P. are readily observable, the
role the economist need play is minimal; the role of the natural scientist
dominates because, by assumption, only the activities change in response to
changes in environmental quality. Thus the natural scientist must translate
alternative air pollution states into changes in plant growth, and changes in
this growth into changes in useful yield. Given that crops and crop varieties
display different tolerances to pollution, numerous dose-response functions
similar to those established for alfalfa by Oshima and his colleagues (1976)
may be required. Having obtained these dose-response functions for the list
of activities in question, the determination of dY/dO^ is a simple matter of
multiplying the changes in yields by the observed'or inferred market prices.
If the scope of the analysis extends beyond yield effects upon existing
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cropping and location patterns, the role of the economist for evaluating
P.(dA./dQ^) need not be quite so limited as the previous paragraph implies.
In particular, a change in pollution may make alternative cropping and
location patterns more appealing. Economic contributions are then useful in
specifying those among the set of feasible grower alternatives that are worthy
of detailed investigation. Nevertheless, the core of the exercise remains the
estimation by natufal'scientists of the yield responses of individual crops to
pollution under a variety of environmental conditions and in a variety of
locations.
Two terms remain on the right-hand-side of (5) that we have not yet
discussed: EA^dP_^/dO^, the change in the price of the ith activity due to a
change in the environmental quality parameter; and dX/dQi, the change in
expenditures on the composite commodity due to a change in the quality para-
meter. Here the relative importance of the roles of the natural scientist and
the economist is reversed from the earlier discussion. Cropping and location
patterns are treated as being utterly unresponsive to changes in the quality
parameter. All adjustments to variations in the quality parameter are
reflected in inferred or market prices alone. Thus, for example, as Johnson
and Hough (1970) and Crocker (1971) have done, one might estimate dY/dQ by
holding the levels of all agricultural activities constant, the prices all
other commodities except land constant, and the magnitude of expenditures on
other goods constant, and then estimate the effect of variations in the
quality parameter upon the market prices of agricultural sites. In this
extreme case, the only role of the natural scientist would be to identify the
sites that are subjected to a variety of levels of pollution. If thenumber
of activities whose price responsivenesses to pollution was of interest were
to be expanded for study purposes, the natural scientist's role would continue
to be limited to specifying the existing levels of these activities. Just as
with contingent valuation methods, the natural scientist's expertise on the
behavior of organisms under stress has no role to play.
The importance of considering these dP /dQ and dX/dQ, terms is readily
1,1.1 , 1
perceived by considering a simple analytical model of price determmati.on
frequently used by agricultural economists. Specifically, the equilibrium
price of agricultural commodities, in the aggregate or individually, may be
derived from the intersection of the relevant supply and demand curves. The
effects of air pollution may be viewed as a supply phenomenon, shifting the
supply curve. Given the generally inelastic demand for agricultural com-
modities, the supply-demand model indicates that shifts in the supply curve
will translate into rather large shifts in the equilibrium price of food.
Thus, following from the nature of the demand-supply relationships, one may
hypothesize changes in commodity prices if air pollution affects the position
of the supply curve.
12
-------
The significance of these price movements is that agricultural prices
cannot necessarily be assumed to be static or stable. Further, changes in
agricultural prices do not occur in isolation but rather work their way
through the system, affecting the welfare of consumers, producers, input
suppliers, resource owners, and other parties. For example, given the gen-
erally inelastic demand for agricultural commodities, reductions in supply may
actually increase farmers total net revenue, as the attendant price rise may
be greater than the percentage reduction in quantity supplied or produced.
Conversely, the increase in prices from a supply reduction will reduce con-
sumers' welfare. Thus , if air pollution alters yield of a substantial pro-
portion of a given crop or causes a reduction in planted acreage of that crop,
then the overall change in supply may result in changes in the price at the
farm level which will ultimately be felt at the consumer level. Alter-
natively, if farmers employ mitigative measures to adjust for the presence of
air pollution, then any additional costs of such measures may also affect
consumers through shifts in supply caused by changes in producers' cost
functions.
Fortunately, the alternative methods available to assess the benefits of
controlling pollution such as acid precipitation are not limited only to those
which ask hypothetical questions of supposedly knowledgeable interviewees,
consider the activity effects but not the price effects, or consider the price
effects but not the activity effects, of a pollution change. Consider the
following quadratic programming model, with which Adams, et al. (1979) have
recently assessed the economic impact of air pollution upon southern
California agriculture, as an example of the ability of many economic method-
ologies to capture both the price and the activity effects of pollution-
induced damages. Again, however, the viability of the methodology is utterly
dependent upon the availability of accurate dose-response functions.
Assume that the effect of acid precipitation upon a set of annual agri-
cultural crops in a number of regions is of concern. The markets for each of
the included crops in each region operate so as to solve the following
problem:
Max: tt = C 0 + 1/2QTDQ-HTQ (16)
Subject to: AQ <_ b
Q _> 0
The symmetric matrix D in the objective function is negative definite,
and the constraints are convex. The terms of (16) are defined as follows.
A is a m x n matrix of production coefficients indicating the
13
-------
invariant amount of each of a variety of inputs required to produce
any single unit of a particular output.
Q is a n x 1 column vector of crop outputs.
D is a m x ra matrix representing slope values of the linear demand
structure for"thg fourteen included crops.
H is a n. x 1 column vector of invariant unit costs of production
for the included crops.
C is a n x 1 column vector of constants,
b is a m x 1. column vector of inputs.
As advocated by Harberger (1971.), it is the sum of ordinary consumer
surpluses and producer quasi-rents. The supply functions for all producer
inputs purchased in the current period (seeds, labor, fertilizer, etc.) can be
assumed to be perfectly price-elastic. In addition, one can invoke Willig's
(1976) results and presume any differences between ordinary and compensated
consumer surpluses to be trivial. Since neither income elasticizes nor
ordinary consumer surpluses or expenditures as a percentage of incomes are
likely to be large for most crops or other entities affected by acid
precipitation, this invocation seems reasonable.
The left-hand-side of the objective function in (16) can be stated in
terms of observable by introducing a price forecasting expression:
P = C + 1/2 DQ, (17)
where P is a n x 1 vector of farm level crop prices. In matrix form, the
objective function may then be expressed as:
PTQ - HtQ = CT0 + 1/2 QTDQ - HTQ (18)
In order to capture the impact of acid precipitation upon crop yields, we
define a variable. Z* (0
-------
Z* is a n x 1 column vector of indicies of yield reduction for the n
crops.
I is a n x 1 column vector of unity.
L is a n x 1 column vector of the land acreage used for cultivating
the n crops. The total land area available for all crops can be
assumed to be fixed.
Y is a n x 1 column vector of yields per acre of the n crops in the
absence of acid precipitation.
Given L and Y constant, the value of Q* varies inversely with the value
of z*. Thus regions with higher acid precipitation will have higher values of
Z* and consequently lower values for Q*. The yield price effects of these
reductions in 0* are then predicted by (17), the price forecasting expression.
Impacts of these predicted price changes upon consumer surpluses, producer
quasi-rents, and cropping patterns within and across regions can then be
calculated by solving the quadratic programming problem.
The immediately preceding formulation is meant to be illustrative of what
economic analysis can do in assessing the benefits of controlling acid
precipitation. It by no means exhausts the techniques that might be applied
to the various aspects of the acid precipitation issue, although it is
representative of the most robust and economically meaningful of the available
techniques. With the sole exception of contingent valuation techniques which
employ stated answers to hypothetical questions as data, all these techniques
use observed decisionmaker behavior as data. The economic interpretation of
these data on observed behavior is generally unable to proceed unless believ-
able and,useful dose-response functions can be provided by the natural sci-
entist.—' In the last chapter, we shall have a great deal to say about what a
dose-response function must include if it is to be useful to the economist.
For the next two chapters, we try to employ the knowledge the natural
scientist has thus far accumulated on dose-response functions to gain some
insights into the economic benefits of controlling acid precipitation.
15
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REFERENCES
1/ This is adapted from Hamlen (1978), bearing in mind that emissions
are generated in I only.
2/ Note that this formulation deals with deposition of sulfur or NO ,
— X
as such, rather than, acidity. The United States - Canada Research
Consultation Group (undated, p.11) states that this is common to all
models in the area.
3/ See Freeman (1979) and Maler (1974) for additional treatments grounded
upon an internally consistent theoretical framework.
if Further generality can be easily obtained by introducing a time con-
straint. At the level of abstraction used in this section, no additional
insights would be gained by doing so.
5_/ It should be mentioned that, at least in principle, the duality between
cost and production (dose-response) functions that the envelope theorem
provides means that the economist, without any dose-response data what-
soever, can use data on observed behavior to perform analyses of the
benefits of controlling acid precipitation. For a clear treatment of the
envelope theorem, see Silberberg (1978, pp. 309-312). Most interestingly
perhaps, the theorem implies that one could estimate dose-response functions
using only data on cost function parameters. This would permit the
services of the natural scientist to be dispensed with entirely! However,
given the somewhat disturbing findings of Appelbaum (1978) and others on
the empirical reality of this dualism, we prefer to refrain, for now,
from stating that the research of the natural sciences into dose-response
functions is irrelevant. Nevertheless, a careful inventory of practical
opportunities for empirical applications of duality principles to the
valuation of pollution impacts would be worthwhile.
16
-------
BIBLIOGRAPHY
Adams, R.M., and T.D. Crocker, "Analytical Issues in Economic Assessments
of Vegetation Damages," Crop Toss Assessment, University of Minnesota
Press, 1980. (forthcoming).
Adams, R.M., T.D. Crocker, and N. Thanavibulchai, An Economic Assessment
of Air Pollution Damages to Selected Crops in Southern California, a
report to the U.S. Environmental Protection Agency for Grant #R805059010,
Resource and Environmental Economics Laboratory, University of Wyoming
Laramie, Wyoming, (October 1979).
Appelbaum, E., "Testing Neoclassical Production Theory," Journal of Eco-
nometrics 7(1978), 87-102.
Benedict, H.M., C.J. Miller, and J.S. Smith, Assessment of Economic Impact
of Air Pollutants on Vegetation in the United States, Washington, D.C.:
National Technical Information Service Publication Number PB-224-818,
(1973) .
Brookshire, D.S., and T.D. Crocker, "The Advantages of Contingent Valuation
Methods for Benefit-Cost Analysis," Public Choice (forthcoming).
Crocker, T.D., "Externalities, Property Rights, and Transaction Costs: An
Empirical Study," Journal of Law and Economics 14(0ctober 1971),
451-464.
Forster, B.A., "Optimal Pollution Control with a Non-Constant Exponential
Decay Rate," Journal of Environmental Economics and Management 2
(September 1975), 186-194.
Freeman, A.M. Ill, The Benefits of Environmental Improvement, Baltimore:
Johns Hopkins University Press, (1979).
Galloway, J.N., et al. "Acid Precipitation: Measurement of pH and Acidity,"
Limnology and Oceanography 2(1979), 1161-1165.
Hamlen, W.A. Jr., "The Optimality and Feasibility of Uniform Air Pollution
17
-------
Controls," Journal of Environmental Economics and Management 5 (December
1978), 301-312.
Harberger, A.C., "Three Basic Postulates for Applied Welfare Economics: An
Interpretative Essav," Journal of Economic Literature 9 (September
1971), .785-797. . . .
Johnson, S.R. and P.A. Hough, "Agricultural Price Differentials and Their
Relationship to Potentially Modifiable Aspects of the Climate." Review
of Economics and Statistics 52(May 1970),' 173-180.
Lotka, A.J., Elements of Physical Biology , Baltimore: Williams and
Wilkens.
Maler, K.G., Environmental Economics: A Theoretical Inquiry, Baltimore:
The Johns Hopkins University Press (1974) .
Millecan, A.A., A Survey and Assessment of Air Pollution Damage to California
Vegetation, 1.970 through 1974, Sacramento, California: California
Department of Food and Agriculture (April 1976).
Oshima, R.J., M.P. Poe, R.K. Braegelmann, D.W. Baldwin, and V.W. Way,
"Ozone Dosage-Crop Loss Function for Alfalfa: A Standardized Method
for Assessing Crop Losses from Air Pollutants," Journal of the Air
Pollution Control Association 26(September 1976), 861-865.
Perhac, R.M., Transcript of testimony before the National Commission on Air
Quality, Washington, D.C., (October 5, 1979).
Schulze, W.D., R.C. d'Arge, and D.S. Brookshire, "Valuing Environmental
Commodities: Some Recent Experiments," Land Economics (forthcoming).
Silberberg, E. The Structure of Economics, New York: The McGraw-Hill Book
Company (1978).
United States - Canada Research Consultation Group on the Long-Range Trans-
port of Air Pollutants, The LRTAP Problem in North America: A Pre-
liminary Overview, A Report from meetings held in Research Triangle park,
North Carolina, on July 26-27, 1?78, and Downsview, Ontario, on March
6-7, 1979 (undated).
Willig, R.D., "Consumers' Surplus Without Apology," The American Economic
Review 66(September 1976), 589-597.
18
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II. " A"FIRST EXERCISE IN ASSESSING THE BENEFITS
OF CONTROLLING ACID PRECIPITATION
Introduction
In this chapter we undertake a first exercise in assessing the economic
impacts of acid precipitation or acidifying deposition, given that it occurs
at above-background levels. The main benefit of the construction, from the
authors' perspective, has been to serve as a learning and organizing device
about the state of natural science knowledge of acid precipitation effects
upon life and property. We have concluded that the state of this knowledge is
very incomplete, both in terms of empirically testable propositions derived
from a broadly encompassing analytical structure as well as in quantitative
bits of information that have been related to or associated with each other.
Under these circumstances, it is tempting for the economist to plead the
near-impossibility of his task, as if the natural scientist were responsible
for any failings of the economist's attempts to value the effects. On some
occasions, the plea is valid. On this occasion, "it is, on balance, invalid.
The reasons are two.
First, whatever the available research time and resources, economic
analysis generally does not yet know how to assess quantitatively disruptions
in ecosystem functions having major and broad economic impacts. [Building
upon Scarf's (1973) work, Shoven and Whalley (1977), King (1980), and a few
others show that the truth of this statement could be short-lived]. If the
impacts of acid precipitation upon ecosystem nutrient storage, detrital decay,
succession patterns, genetic pools, etc., are as dire as some natural
scientists predict, and if alterations in these functions can legitimately be
viewed as changes in natura 1 transformation processes (production
technologies), then a full economic assessment may be analogous to comparing
the welfare of the 18th century Jeffersonian yeoman farmer with his modern
agricultural corporate clone: the worlds in which the two live(d) are so
vastly different that neither the modern nor the Jeffersonian man could
comprehend most of the opportunities and dangers familiar to the other. It is
questionable whether the comparison would be economically meaningful.
19
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The second reason why the blame for the economic limitations of the
content that follows cannot be shifted to the natural scientist is because, in
principle, it is both possible and practical to value many, perhaps most, of
the effects of acid precipitation. The task is substantial but nevertheless
accomplishable. Economists who read this chapter will recognize that only the
most elementary economic analysis has been performed. In particular, we have
generally resorted" to'an assumption throughout that acid precipitation affects
only the yields from existing sets of economic activities. We, therefore,
have, with only a few exceptions, disregarded any potential price effects, as
well as changes in activity and location patterns. Finally, we have nothing
to say for now about the economic implications of larger questions on changes
in lifestyle, possibly unacceptable risks due to the destruction of life
support systems, and the welfare of future generations. Effects on these
larger questions, as well as those involving changes in activity and location
patterns, are most likely to be generated by the buffering stock depletion
impacts of acid precipitation. It is these stock depletion effects that, as
was indicated in Chapter 1, economically distinguish acid precipitation
effects from traditional analyses of pollution effects. In a later
theoretical chapter, we will view these stock depletion effects as analogous
to drawdowns in the biogeochemical energy available to a geographic location.
In this chapter, so as to remind the reader that we do not view effects on the
yields of current economic activities as the sole effect of acid precipitation
worthy of economic attention, we present a brief treatment of the impact of
acid precipitation on the buffering capacities of natural ecosystems.
Depletion of the Stock of Buffering Capacity
After deposition, the effects of acidifying components depend on sensi-
tivities of the environments where the deposition occurs. This sensitivity is
largely determined by the abilities of the depositional surface to buffer
hydrogen ion additions. In turn, environmental buffering abilities initially
depend on the bedrock and geological, history of the region. Bedrock of
volcanic or igneous origin tend to be low in most minerals important in
buffering [Dillion and Kirchner, (1975)]. Over geologic time, the importance
of the bedrock is moderated by glaciation, weathering and other soil building
processes.
Buffering in soil systems is primarily accomplished through cation ex-
changes between soil solutions and colloidal clay and humus particles, also
called micelles [Buckman and Brady, (I960)] . These micelles are negatively
charged and, therefore, attract positively charged cations which enter soil
solutions during soil mineralizati.on, for example. Cations which are commonly
adsorbed onto micelles in order of increasing affinity for micelle adsorption
are: sodium, potassium, magnesium, calcium, aluminum and hydrogen. Increas-
ing concentrations of hydrogen ions in soil solutions, as would occur with
20
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incident acidifying depositions, shift the equilibrium between the soil
solution and the micelles such that additional hydrogen ions become adsorbed
onto micelles, thus displacing cations having less affinity. Adding lime to
soils causes concentrations of hydrogen, ions in soil solutions to decrease as
they react with the calcium ions. This shifts the equilibrium between soil
solution and micelles: hydrogen ions desorb and calcium ions adsorb onto
micelles.
The second major environmental buffering system, the primary buffering
mechanism for aquatic environments, is the carbonate-bicarbonate system.
While this system is also present in soil environments, it is generally of
relatively minor importance [Buckman and Brady, (I960)]. In aquatic environ-
ments, the abilities of the carbonate-bicarbonate buffering system are
normally measured by alkalinity determinations [Sawyer and McCarty, (1967)].
Buffering capabilities develop as carbon dioxide dissolves in water. The
carbon dioxide reacts with water to form carbonic acid which dissociates to
form bicarbonates and hydrogen ions. Bicarbonates can then further dissociate
to carbonate and hydrogen ions. Additions of hydrogen ions to the aquatic
environment will reverse this process and, with continued additions, carbon
dioxide can eventually be released from the water.
Continued deposition of acidifying substances in ecosystems will cause
buffering capacities to decrease as exchangeable ions, carbonates, bicarbonates
and, eventually, pH values decrease. Simultaneously, titratable acidity,
hydrogen ion concentrations and associated anions such as sulfates and
nitrates increase. Also, mineralization rates of soil particles will increase
with hydrogen ion additions and counter, at least for short periods, the
effects of acidification [Maimer, (1.976)].
The frequencies and durations of acidifying depositional events will
affect the severity and rate of ecosystem changes. However, as eposodic acid
contributions continue, a system's buffering capacity is continually reduced
and its hydrogen ion concentration increased. As the pH continues to
decrease, the impacts on the ecosystem increase and the importance of the
episodic frequency of the acidifying contributions in defining ecosystem
impacts decreases.
Sufficient additions of acidic water to soil systems can cause the cation
released through ion exchange buffering to leach from the system. The
decreased PH can have additional effects on soil chemistry [Buchman and Brady,
(1960), Maimer, (1976)]. As soil pH decreases below 8.0, the amounts of
aluminum, iron, and manganese increase in soil solutions. At low pH levels,
concentrations of these compounds can become toxic; and as concentrations of
these dissolved compounds increase, they can react to fix phosphates as
insoluble hydroxyl-phosphates. In such a complex this valuable nutrient is
21
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not available for plant use.
Acidifying depositions enter aquatic ecosystems directly through surface
deposition and indirectly through watershed runoff. Increases in the acidity
of rivers and lakes occurs with acid precipitation events. But, depending on
the buffering ability., of the water, such changes may be relatively small and
short in duration. More substantial acidity increases of longer duration can
accompany spring snowmelt. These changes can be particularly dramatic when
the snowpack melts rapidly [Likens et al., (1977)]. At such times, the pH of
surface waters can decline to about 3.0 [Shaw, (1979)]. Gjessing et al.
(1976) noted that when spring meltwaters are less dense than lake waters
(water has a maximum density at 4 C), the meltwaters tend to flow over the
surface waters of the lake and therefore do not mix with lake waters. During
such times, waters having elevated acidities are discharged from lakes to
produce maximum impacts on stream ecosystems. Runoff to lakes at other times
of the vear generally mixes with lake waters, lessening the impacts on
streams.
The influences of acidifying depositions on the chemistries of natural
waters are similar to the effects produced on soils. Increasing the hydrogen
ion concentration reduces the aquatic system's buffering abilities, increases
solubilities of metals, complexes phosphates, etc. Continued addition of
hydrogen ions causes carbonates and bicarbonates to be converted to carbon
dioxide and water [Lewis and Grant, (1979)]. Carbon dioxide can then be lost
to the atmosphere or dissolved concentrations can accumulate to levels which
are directly lethal to aquatic organisms [EIFAC, (1969)]. Precipitation of
normal suspended silt loads has also been noted for streams having increased
hydrogen ion loading rates [Parsons, (1965)].
Studies of effects from acidifying depositions have shown the importance
of buffering capacities in determining the constituents flushed out of water-
sheds. Often the input of hydrogen ions is adsorbed by the watershed eco-
system and no significant increase in hydrogen ion or other cation concentra-
tions is observed in aquatic system outputs (e.g., Lewis and Grant, 1979). In
other cases, the uptake of hydrogen ions by the watershed results in an
increase in the output of other cations from the watershed. For example,
Gjessing et al. (1976) report that outputs of calcium, magnesium, and aluminum
ions from nine watersheds in Norway were proportional to inputs of hydrogen
ions. In contrast, Lewis and Grant (1979) noted no significant change in
outputs of calcium, magnesium, sodium, potassium, phosphate, or hydrogen ions
accompanying increased hydrogen ion inputs to a Colorado, USA, watershed.
Increased outputs were observed for sulfate, nitrate, ammonia and dissolved
organic matter, while decreased outputs of bicarbonate were proportional to
increased hydrogen ion inputs. Variations in output responses among the
Norway and Colorado watersheds suggest that different buffering systems are
22
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responding to the hydrogen ion inputs. The Norway watersheds appear to buffer
primarily through cation exchange, primarily a terrestrial system, while the
Colorado watershed appears to buffer primarily through reactions with
bicarbonate. As both the Norway and Colorado watersheds are of granitic
origin, variations in the buffering systems may reflect the relatively longer
time which Norway has been exposed to acidifying depositions. with continued
additions of- acids-,• bicarbonate buffering systems become exhausted causing
buffering to become increasingly dependent on cation exchange.
Knowledge of buffering capacities is helpful in sorting out habitat
impacts of hydrogen ion inputs from impacts of other chemical constituents
associated with acidifying depositions. Taken together, variabilities in
depositional composition and mode as well as receptor buffering can be used to
discriminate among these effects. In poorly buffered systems, depositional
impacts tend to be more related to pH effects because of the low masses of SO
and NO required to generate pH changes. Tn well buffered systems, the masses
of SO "and NO necessary to generate pH changes are relatively larger and,
consequently, influences of other compounds tend to be enhanced. Thus, well
buffered systems tend to respond more to components other than hydrogen ions
in both wet and dry acidifying depositions; this relationship will tend to be
maintained until the buffering capacity of the system is exhausted. With
poorly buffered terrestrial systems, wet depositions will tend to have
confounded responses to both hydrogen ion concentrations and other
depositional contents until pH effects overwhelm other responses. Dry
depositions to poorly buffered terrestrial systems will tend to cause
responses primarily attributable to the depositional. compound (e.g., SO or
NO ): in some instances biochemical transformation and utilization of "the
compounds will generate accumulations of hydrogen ions causing pH effects to
predominate eventually. Needless-to-say, poorly buffered aquatic systems will
have similar responses to both wet and dry depositions as dry depositions
essentially become wet deposition upon entrance into the aquatic system.
These responses will be similar to wet depositions in poorly buffered
terrestrial systems.
Agricultural Effects
Low-pH precipitation can affect crop yields in two ways. First, as it
percolates through the soil column it accelerates the natural tendency of
water to leach organic and mineral soil components from the root zone. At the
same time, it reduces the so il pH level in this zone, thus making nutrients
less available and toxic metals, such as soluble aluminum and iron, more
available to plants. In addition, reduced soil pH levels can cause declines
in microbe populations that break organic matter down into forms useful for
plants. In the absence of this breaking down, the organic matter can accum-
ulate and seal the upper layers of the surface while permitting various plant
23
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toxins to be formed from the matter. The result for all these impacts is
reduced growth and yields for plants located on the acidified soils [Buchman
and Brady (I960)]. According to Schwartz and Follett, (1979, p. 2) the
"preferred soil pH range for maximum growth" varies between 5.5 and 7.0 for
most commercially important crops, e.g., clover, barley, corn, grasses, and
soybeans. However., this is by no means universal across crops, since the
interval for alfalfa is 6.2 - 7.5; for asparagus and lettuce, it is 6.0 - 7.0;
for blueberries and sweet potatoes, it is 5.0 - 5.7; for white potatoes, it is
5.0 - 5.4; and for cotton, it is 5.5 - 6.5. In the agricultural regions east
of the Mississippi River, soil acidity levels frequently fall below these
"maximum growth" intervals because of the region's high rainfall and because
of grower soil additions of inorganic fertilizers. Consequently, it is a
standard1 -r FpM&dice calcitic or dolomitic ground limestone with
the s°il periodically..— 'Thiisc practice returns the soil to something
resembling its original state in terms of the availability of nutrients and
toxic metals to plants. It also increases the sizes and the variety of
microbe populations. We have found no evidence that the economics of liming
causes farmers to fail to return soils to an approximation of the aforemen-
tioned state.
Tn a verbal communication, N.R. Glass (1979) of the United States
Environmental Protection Agency has stated that if all the sulfur dioxide
emitted annually east of the Mississippi River were to fall as acid
precipitation on the agricultural soils of the region, ". . .a five percent
increase in liming would be required." According to a verbal report on
January 17, 1980, from Dr. Ed Strobe, Professor of Agronomy at Ohio State
University, the 1979 cost of liming, including spreading, in the Ohio Valley
region is $6 to $8 per ton. Raising soil pH to 6.0 for most cropping systems
(e.g., alfalfa, clover, corn) on average mineral soils requires the
application of 2 to 3 tons of lime per acre every 4 to 5 years. There is
substantial variation across soil types, however, as Buchman and Brady (1960,
p. 419) show. In the 1970's according to the U.S. Department of Agriculture
(various issues), the annual consumption of pulverized lime in the United ^
States varied from a low of 26.7 x 10 tons in 1972, to a high of 39.8" x 10
tons in 1976. In real terms, its price, independent of the cost for
spreading, was consistently around $3 per ton in 1978 dollars, with the 1972
price being $3.14 and the 1976 price being $3.08. It seems unlikely,
therefore, that a five percent increase in biological liming requirements
would have much of an effect on either the cost of liming or on the farmer's
perceptions of the economically optimal amounts of lime to spread.
Table 1 gives the average acreages, yields, and values of eight major
field crops for 1975-77. In addition to Minnesota and the states east of the
Mississippi River, Iowa and Missouri are included. With the exception of
potatoes, the eight crops listed are the major field crops produced in the
24
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TABLE 2.1
Average Acreage, Production and Gross Value for Selected Commodities, by Region and Total, 1975-77 Crop Year.
USDA Production Regions
A alachiait^ Delta—^ Corn Belt—^ Northeast—^ Southeast^ Total
Acres
Prod.
Value
Acres"
Prod.
Value
Acres
Prod.
Value Acres
Prod.
Value
Acres
Prod.
Value
Acres
Total
(Millions)
heat
1.09
35.50
95.50
0.72
25.20
63.20
6.41
254.80
713.70
0.71
24.80
17.11
0.34
9.50
26.90
9.26
973.40
3 rn
4.35
284.50
715.50
0.26
12.30
27.20
36.10
3513.80
7740.30
2.59
218.90
500.00
3.30
172.80
390.70
46.60
9373.70
irley
0.20
8.60
12.75
0.04
1.62
2.38
2.62
12.50
19.41
0.04
1.01
1.44
2.90
36.00
Drghum
0.14
7.12
14.70
0.31
14.80
29.30
0.79
50.20
93 .50
-
0.08
2.93
6.34
1.32
143.90
Dtton
0.40
0.31
78.30
2.60
2.60
696.80
0.24
0.20
51.50
-
0.73
0.58
160,70
4.00
987.30
ugar Beets
0.03
0.62
15.50
0.01
0.02
0.34
0.03
15.80
abacco
0.80
1623.30
1792.10
6/
0.09
0.11
0.02
46.10
50.90
0.04
366.65
52.28
0.16
324.00
356.90
1.01
2252.30
Dybeans
4.83
116.70
683.60
10.20
230.40
1370.80
11.84
113.90 ¦
4978.70
0.74
18.80
107.20
3.10
87.80
508.20
30.20
"7648.40
lfalfa
0.47
1.22
67.50
0.09
0.23
12.80
4.02
12.50
692.50
2.08
5.46
305.70
6.66
78.50
Dtal
12.30
7/
3460.00
14 .20
7/
2200.30
59.50
7/ 14339.00
8.80
7/
1002.10
7.80
2/
1451.20
102.60
22452.60
Source: USDA Agricultural Statistics, 1978. Washington, D.C. 1979
-^Includes states of Kentucky, North Carolina, Tennessee, Virginia and West Virginia.
2/
— " " " Arkansas, Mississippi and Louisiana.
3/
— " " ' " Illinois, Indiana, Iowa, Missouri and Ohio.
— " " " Delaware, Maine, Maryland, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania , Rhode Island and Vermont.
— " " " Alabama, Florida, Georgia and South Carolina.
-^Less than one thousand acres.
-^Different units of measurement for production preclude aggregation. Specifically, wheat, corn, barley, sorghum and soybeans are measured
in bushels, tobacco In pounds, sugar beets and alfalfa in tons and cotton in bales (500 pounds) .
25
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indicated subregions. The range of tolerances to acidified soils for these
crops varies from highly sensitive (alfalfa) to moderately tolerant (corn) .
Potatoes are not included because of their relatively high tolerance for
acidified soils (pH = 5.0 - 5.4, as previously noted). Table 1 indicates the
substantial magnitude of agricultural activity in these five subregions,
individually and in the aggregate. The eight field crops in the subregions
account for 38 percent of the total harvested acreage of nearly all crops in
the United States, with the Corn Belt subregion comprising the single largest
area of crop land. Furthermore, these eight crops assume a dominant role in
United States agricultural exports. In terms of gross "on-farm" value, the
$24 x IT) in receipts represents 25 percent of the total value of all agri-
cultural commodities, including livestock, produced in the United States. In
terms of individual crops, corn represents the single largest component of
gross value, followed by soybeans.
Assuming that the 117.35 x 106acres of the field crops in Table 1 would
annually require the application of 0.40 to 0.75 tons per acre of pulverized
lime^in the absence of acid precipitation, anywhere from 46.94 x 106to 88.01
x 10 tons would be used each v,ear. The lower bound of this interval exceeds
"6
the maximum amount (39.83 x 10 tons) ever used for agricultural purposes m
the entire United States. We, therefore, assume that annual use in the region
of interest in the absence of acid precipitation would be 35 x 106 tons.
Thu s , if acid precipitation were to add 5 percent to the quantities of lime
farmers in the region choose to use, an additional 1.7 x 1 0 tons would be
applied. At S6 to $8 per ton in 1978, the annual. cost60f purchasing and
applying the lime would be $10.50 x 106to $14.00 x 10 . This estimate, which
is probably exaggerated for several obvious reasons, should , however, be
contrasted with the estimate of the Commission on Natural Resources of the
National Academy of Sciences (197 , p. 178). The latter employed a 197 cost ,
including spreading, of $14 to $18 per ton for an additional 12 x 10 tons of
lime to counter only the effects of acidifying atmospheric depositions.
Implicitly, this presumes that from farmers' decisionmaking perspectives,
one-third as much lime is required to counter the soil-acidifying effects of
these depositions as is required to counter the soil-acidifying effects of
inorganic fertilizers and reasonably pristine precipitation.
In addition =to its soil acidifying effects, acid precipitation can
directly harm plants by causing foliar necrosis, reduction of leaf area,
leaching of leaf surface minerals, and cuticular erosion as the plant foliage
intercepts the precipitation [Cowling (1978, pp. 49-50)]. The seriousness of
these effects in terms of yields is thought to differ widely across plant
species and across different life stages of the same plant. However, unless
one is willing to make rather tenuous analogies with the well-known effects of
sulfur oxides [Committee on Sulfur Oxides (1978, pp. 80-129)], there appears
to be only minimal knowledge about the effects of acid precipitation upon crop
26
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yields. The two most commonly cited studies referring specifically to acid
rain effects on yields seem to be Ferenbaugh's (1976) research on pinto beans,
and a degradation in the exterior appearance of Yellow Delicious apples that
Cowling (1978, p.59) mentions. These results are hardly a sufficient basis
for any analysis, sophisticated or otherwise, of the economic impact of the
direct effects of acid precipitation upon agricultural yields. Dose response
functions on a greater variety of crops are expected to be available soon,
however. The United States-Canada Research Consultation Group on the
Long-Range Transport of Air Pollutants (undated, p. 19) reports that results
from studies of the sensitivity of field crops to simulated acid precipitation
were to be made public in the spring of 1980. In the meantime, the
Consultation Group (p. 19) states that "... there is every indication that
acid rainfall is deleterious to crops," and that there is "... the potential
for widespread economic damage to a number of field crops."
In spite of the current absence of dose-response data to do either an
unsophisticated or a sophisticated economic analysis of the direct effects of
acid precipitation upon crop yields, one might hazard a guess about the
magnitude of the "potential" for widespread economic damage by drawing anal-
ogies with other cropping systems that are known to have been exposed to
continuing high levels of air pollution. If the forms of representative plant
responses and representative farmers' decisions based on these responses are
roughly similar across types of air pollutants, combinations of crop types,
and geographical areas, the hazarded guess would have some basis in reality.
Adams, et al. (1979) have studied the economic effects of photochemical
oxidants in southern California upon twelve vegetable and two field crops.
Their study took into account differences in the tolerances of the yields of
the various included crops to oxidant exposures, changes in cropping patterns,
input substitutions, and locational changes. For many of the included vege-
table crops, southern California has a seasonal near-monopoly. Major adjust-
ments in cropping patterns and cropping locations were predicted and observed
within the region in response to increasing ambient oxidant levels. After all
these adjustments, a 3.01 percent decline in the sum of producer rents and
consumer surpluses occurred, with three-quarters of this percentage decline
being producer rents. The total on-farm value figure of $24 x 109 in Table 1
for eight field crops in five agricultural subregions of the eastern United
States might or might not be a reasonable approximation f the sum of producer
rents and consumer surpluses obtained^ from these crops.- If the 3.01 percent
reduction is applied to the $24 x 10 gross on-farm. value, a loss of $720 x
10, results. In 1978 rather than 1976 dollars, this would be about $828 x
,_6 , ,
10 , a figure that is to be taken no more seriously than the credence one is
willing to give the analogies and assumptions from which the figure is
derived. If one were to include various fruit crops such as apples, oranges,
and peaches, legumes and tubers such as peanuts and potatoes, and ornamental
27
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in the calculations (in 1977, the ^J.S. on-farm value of the productio^i of
these crops was more than $4.0 x 10 ), the figure might reach $1.0 x 10 .
Forestry Effects
Of all the potential effects of acid precipitation, the effects upon
forest ecosystems "seem to be least understood. General qualitative descrip-
tions of what might happen abound, however, e.g., Abrahamsen and Dollard
(1978) , Cowling (1978) , Dochinger and Seliga (1976), and Tamm (1976) . As with
agricultural systems, the health of forest ecosystems can be affected directly
and indirectly by acid precipitation. Moreover, the health states can be
aided as well as hindered [Tveite (1980)].
Detrimental direct effects upon the physiological and metabolic processes
of forests are likely to occur when foliage intercepts acid precipitation.
Reductions in leaf areas, excessive leaching of organic materials, cuticular
erosion, necrosis, and reductions in photosynthesis and the cycling of nut-
rients to other system components are all regarded as likely events. However,
Abrahamsen and Skeffington (1979, p.D.2.1) note that carefully documented
field cases relating necrosis to acid precipitation do not exist. Our search
of the literature has not turned up field demonstrations of the other effects,
although thev all have^een found for one or more tree species in controlled
experimental settings.— All of these studies of particular types of effects
fail to make clear how the observed effect is related to tree growth. There
nevertheless appears to be a consensus that the physiologically most active
developing tissues are the most sensitive [Knabe (1976)1.
Neither the field nor the experimental studies of the effects of acid
precipitation on tree growth have yielded consistent findings. In fact,
findings of no effects or positive effects of acid precipitation upon tree
growth dominate the literature. The results reported in a recent paper by Lee
and Weber (1979) are typical. These authors subjected the seeds of eleven
tree species, including Douglas fir, eastern white pine, yellow birch, sugar
maple, sumac and hickory, to an artificial rain containing enough dilute H SO
to lower rainfall pH levels to 4.0, 3.5, and 3.0. The plants were expos® to4
these rains for three hours for each of three days a week over 1.5 years. In
general, acid precipitation had either no effect or a positive effect upon the
proportion of seeds that germinated and upon the top dry weight and root dry
weight of the germinated seeds. The soil solutions in which the seeds were
placed had high buffering capacities, causing the authors to infer that
whatever effects were observed were direct. In particular, they did find some
negative effects upon foliage but they also frequently found enhanced rates of
growth. The latter they attributed to fertilization of the soil solution by
sulfur, nutrients leached from the plant surfaces, and increased plant uptake
of soil nutrients. For Tee and Weber (1979), the "stimulator" effects of
28
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acid precipitation over the 3.0 - 4.0 pH interval nearly always dominated or
negated the "inhibitory" effects. The results of these authors thus support
Abrahamsen's and Dollard's (197 9, p. 8) statement that: "Statistically
significant effects [in laboratory settings] have been observed only when
applying 'rain' with pH 3 or lower."
Elsewhere, Abrahamsen and Skeffington (1979, p.D.2.4) indicate that they
and their discussants "... could think of no evidence to indicate yield
reductions under treatment with acid rain in laboratory conditions at
realistic levels of acidity (i.e., pH^A). Later on, they state that " — no
artifical acidification experiment has produced a growth reduction at pHs
equivalent to those commonly observed in rain, and some have produced a
stimulation." These stimulator effects of acid precipitation (or acidifying
deposition) have recently been broadcast in several widely read periodicals,
e.g., Maugh (1979). The implicit position would then seem to be that some
limited amount of acid precipitation in excess of that which is natural has a
positive impact upon plant growth, probably as an amendment to sulfur and
nitrogen deficient soils. Given that the time interval over which these
positive amendment effects would occur is typically unspecified, one is left
to presume they would continue at least as long as the amendments continue.
Forest ecosystem acidification leads to reduced nutrient cycling rates.
Not only can nutrients become complexed at low pH levels, as for phosphates,
but decomposition of organic material is slowed. Many potential decomposes
are less active or inactive at pH levels much below 5.0, and protozoa and
earthworms are very rare in soils having pH levels below about 4.0 (Abrahamsen
et al. 1976). Lohm (1980) observed that acidification decreased decomposition
rates for both needles and litter as well, as decreasing fungal lengths,
bacterial numbers and cell sizes. The results of Francis et al. (1980) also
suggests that acidification of forest soils may cause significant reductions
in leaf litter decomposition and reduce nutrient recycling rates in forest
ecosystems by slowing ammonification, vitrification and denitrification. Tamm
et al. (1976) found that even moderate additions of sulfuric acid to soils
produce obvious effects on nitrogen turnover rates.
Besides affecting nutrients through reduced decomposition rates,
depressed environmental pH levels depress nitrogen fixation. Denisen et al.
(1976) found that lowered pH levels caused both the nitrogen fixing bacteria
Azotobacter and nitrogen fixing blue-green algae to disappear from the soil.
The net consequence for terrestrial ecosystems of decreased nutrient
cycling and increased nutrient leaching caused by acidification is reduced
productivity [Abrahamsen et al., (1976); Glass and Loucks (1980); Leivestad
et al., (1976)]. Such responses have been termed "self-accelerating oligo-
trophication" by Grahn et al. (1974). Acidification could reduce or remove
29
-------
nutrient pools, constraining the redevelopment of previous biomass levels
[Glass, (1978)].
Using nitrogen as his example nutrient, Tamm (1976, p. 237) presents a
flow diagram which places all of the preceding results in a most meaningful
perspective. We reproduce with minor adaptations his diagram as Figure 1.
Tamm (1976) states'that the diagram is meant to be ?. hypothetical represent-
ation of the effects of increased strong acid in a system where much of the
nitrogen supply comes "... from decomposition in an orqanic A horizon with a
high carbon/nitrogen ratio (>15)." This suggested structure is consistent
with experimental, observations in which simulated acid precipitation contrib-
utes positively to growth, even though it is expected that, in the long-term,
growth would decline once the buffering capacity of the soil is exhausted.
Tamm (1976, p. 338) also notes that the structure could account for the
frequently observed experimental failure of lime to enhance growth rates: by
immobilizing the nitrogen in organic matter, the availability of nitrogen to
the trees is reduced.
The only available estimate of the long-term effects of acidifying
deposition upon pH levels and base saturation appears to be McFee, et al.
(1976) . These authors estimated that for a "typical" midwestern soil, precip-
itation with a strong and disassociated acidity of pH = 4.0 at 100cm annually
for 100 years would reduce soil base saturation by 19 percent and lower soil
pH by 0.6; at pH 3.7 (a doubling of acidity) and PH 3.0, 50 and 10 years would
be respectively required to bring about the same changes. If the soil
initially has a fairly high pH level, effects of this magnitude would probably
not be noticeable in terms of plant growth results; however, if the soil
already has low pH, it is generally thought [McFee (1978, p. 66)] that leach-
ing would rapidly ^increase. Generally, therefore, it is thought that
d" (Leaching)/d(pH) > 0, implying that the rate of loss of soil nutrients
would get progressively worse as time passes. It thus seems that insofar as
forest soils are concerned, acid precipitation has all the attributes of
acquiring possible short-term gains in forest growth at the cost of probable
long-term losses in forest soil fertility. For both biological and economic
reasons, it seems unlikely that liming can counter the fertility decline. In
addition to the previously mentioned biogeochemical argument of Tamm C1976),
Tisdale and Nelson (1976, p. 428) note that "... particulate of limestone
cannot move in the soil, and consequently they must be placed where they are
needed." Tilling lime into extensive ar|p of forest soils would seem both a
technical and an economic impossibility.- In anything other than geological
time, accelerated soil acidification, therefore, appears irreversible.
Unfortunately, it is quantitatively unclear how the above reductions in
soil fertility will ultimately affect forest yields or the properties of other
forest ecosystem components (water storage, game animal populations,
30
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J
aesthetics, etc.) that humans directly value. We were unable to discover any
information whatsoever that related acid precipitation to the latter compon-
ents.— rJonsson and Sundberg (1972) , in a frequently cited paper, suggest 2
to 7 percent declines due to acid precipitation in the annual growth rates of
forests in southern Sweden during the 1950-1965 period relative to 1896-1949.
However, Cogbill, .(.1976), in a simple time trend study of comparative tree
ring growth in areas of eastern North America subject to and free of acid
precipitation, could find no differences attributable to acid precipitation.
The trends he observed started no later than 1890, and continued until 1.972-
73. However, the credibility of Cogbill's (1976") results must be tempered by
questions about the comparability of sites at which precipitation pH has been
measured [Perhac (1979)] ; the errors inherent in much of the field instrument-
ation traditionally employed to measure pH [Galloway, et al. (1979)]; and one
study TFrinks and Voight (1976)] which gives cause to believe that, at least
in one area of Connecticut, the pH of precipitation has been rather low and
unchanged since the early 1900's.
Given the empirical, confusion that exists with respect to the ultimate
impacts of acidifying deposition on rates of forest growth, we choose to adopt
Jonsson's (1976, p. 842) position that there is "... no good reason for
attributing the reduction in growth to any cause other than acidification."
We adopt this position because it is consistent with existing knowledge of the
biogeochemistry of forest ecosystems [e.g., Likens, et al. (1977)] as wellas
the economic law of variable proportions.
One's willingness to accept estimates, made using current price and
production data, of substantial positive benefits from reducing forest expo-
sures to acid precipitation or acidifying deposition must be tempered by
evidence that the current elasticity of substitution between land and
intensive forestry is very high. Clawson (1976) , for example, argues that the
following outputs of the national forest system can all be economically and
simultaneously increased as follows: net annual growth can be twice as great;
designated wilderness areas can be four times greater; outdoor recreation can
be doubled; and wildlife stocks and water storage can be modestly increased.
Miller (1978), while considering endangered animal species, also emphasizes
that improved management techniques have great potential for maintaining
existing wildlife stocks now suffering from environmental stresses. Hair,
et al. (1980, pp. 514-519) note that if all opportunities offering at least a
four percent net annual return on all forest land, in the South were to be
exploited, the region's 1976 net annual timber growth would have increased by
86 percent. In the Northeast and North Central regions, the corresponding
increase offering a similar minimum return would have been 25 percent. Berk' s
(1979) recent finding that private forest owners act as if they faced a real
before-tax interest rate of only five percent is consistent with management
behavior which fails to exploit the opportunities that Hair, et al. (1980)
31
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think to exist.
In Minnesota and the states east of the Mississippi River, th ^re were,
according the the U.S. Forest Service (1978, pp. 1, 97), 229.8 x 10 acres of
commercial and productive reserved forest land that had a ^iet annual 1977
growth of 6.12 x 10 cubic feet of softwoods and 7.51 x 10 cubic feet of
hardwoods. Lerner*C1978, p. 735) indicates that 1977 stumpage prices in 1978
dollars for the softwoods averaged about $1.3 0 per cubic foot, while for
hardwoods they were about 50 cents per cubic foot. Jonnsson and Sundberg
(1972) and Panel on Nitrates (1978, p. 577) judge that a reduction of five
percent in net annual growth falls within the interval of reduced growth one
might reasonably expect from the acid precipitation now falling upon Scan-
dinavia and eastern North America. If the precipitation in Minnesota and the
states east of the Mississippi River were pristine CpHs5.65), a five percent
ingrease in 1977 net annual growth of softwoods would have amounted to 310 x
10 cubic feet. Hardwood net annual growth would have increased by 375 x 103
cubic feet. Assuming these increases would not have appreciably affected
stumpage prices, the 1978 market value of the additional softwood would have
been $4046x 106. The hardwood increase would have had a 1978 market value of
$188 x 10 . In 1978 dollars, the 1977 market value of the increase for both
softwoods and hardwoods would, therefore, have been $592 x 10 .
The valued outputs of lands devoted to forests are by no means limited to
timber. These lands provide outdoor recreation, aesthetic satisfaction, water
storage, wildlife habitats, and a variety of other services. Unfortunately,
representative estimates of the value of the sum of these services are rare.
The sole immediately and easily useful estimate we have been able to find is
the study of Calish, et al. (1978). These authors, in a rather nonrigorous
but nevertheless extremely clever and interesting paper, estimated that the
1978 annual non-timber value (in terms of harvestable game animals and fish,
water flow, nongame wildlife diversity, visual aesthetics, and prevention of
mass soil movement) of a representative Douglas fir forest in the Pacific
Northwest was $87 per acre. Assume that this same value per acre can be
applied to eastern forests; and further assume that current levels of acid
precipitation reduce these non-timber values in the same proportions as was
assumed for the timber values, i.e. , by about five percent. Calish, et al.
(1978) attribute about 11 percent of the $87 per acre to the production of
harvestable fish, implying that $77 per acre consists of non-timber values for
which we have not otherwise accounted. Five percent of this $77 is $3.85.
Thu s , if pristine precipitation were to replace acid precipitation in
Minnesota and east of the Mississippi River, these procedures imply that 1978
non-timber values in this area would have annually increased by ($3.85 per
acre) (299.8 x 106) = $1.15 x 109. Adding the ^imber and non-timber value
increases yields an annual benefit of $1.75 x 10 in 1978 dollars. Assuming a
15 percent discount rate and that this increase could be sustained
32
-------
indefinitely, a discounted value of $11.66 x 10 results.
Aquatic Ecosystem Effects
Contrary to the forest and forest soil effects of acidification, a sub-
stantial amount of economically useful quantitative information is available
about the aquatic fe'coSystem effects of acidification. McFee C1976) conject-
ures that some soils in Scandinavia and eastern North America have been
subjected to acid precipitation for approximately a century. Only within the
last decade or two, however, are the soils thought to have become sufficiently
acidified to influence the pH levels of inflows to fresh water bodies.
Because of this relative immediacy, changes in the biota of these water bodies
have been observed rather than being considered as historically preordained.
In addition, there has for several decades been an historical record of the
impact of acid mine drainage upon the biota in the streams of the Appalachian
region. Barton, (1978, p. 314) states that in the United States 10,000 miles
of streams and 29,000 surface acres of impoundments and reservoirs ".. . are
seriously affected by mine drainage."
Declines to about 6.0 in the pH levels of fresh water bodies reduce
primary production. Since primary production is reduced, detritus derived
from the decay of plankton tends to disappear. As a consequence, water
transparency increases, detrital material decreases, and there are increases
in soluble alumina, irons, magnesia, and trace metals such as cadmium and
mercury. The phytoplankton and zooplankton species which survive are
obviously acid-tolerant, perhaps because they are resistant to heavy metals.
However, they also concentrate these metals which, in turn, may make them
toxic to many fish and bottom-dwelling (benthic) organisms. Although fish and
insect kills occurring during heavy rains and spring snowmelts have been
frequently observed [e.g., Gjessing, et al. (1976, p. 65)1, the major effects
upon fish and insects are thought to stem from reproductive and recruitment
failures caused by calcium metabolism difficulties, the accumulation of heavy
metals in parents, and the exposure of those young that are produced to these
metals [Fromm (1980)]. Schofield (1976, p. 229) indicates that increased
salinity tends to make fish more acid-tolerant, apparently, according to
Packer and Dunson (1970), because it enables fish to replace the body sodium
losses that low Pi causes. The reproduction failures can result in extinction
of the species in acidified water bodies. Aimer, et al. (1978, pp. 303-307)
cite several cases where surviving individuals of some game fish species grew
more rapidly and were of larger size than were similar individuals in less
acidified water bodies. They attributed this to the lessened competition for
the available food stock.
Both Aimer, et al. (1978, pp. 308-309) and Gorham (1978, pp. 41-42)
remark upon the possible implications of altered (generally reduced) diversity
33
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and biological productivity of aquatic flora and fauna for organisms such as
amphibians, birds, and mammals who spend important parts of their life cycles
in and around aquatic environments or who are dependent upon these
environments for some or all of their food supplies. Aimer, et al. (1978),
tell of fish- eating birds such as loons who have migrated from acidified
lakes in Sweden to sites with more ample food supplies. Gorham (1978)
expresses concern for the impact upon moose populations and distributions if
production of the aquatic plants forming parts of their diets is inhibited.
Birds of prey, such as eagles and osprey, and game birds, such as mallards and
wood ducks, could be subjected to altered populations and distributions from
reductions in their aquatic food sources. Little seems to be known, however,
about the ease with which these animals could substitute nonaquatic food
sources.
In the following pages several attempts will be made to develop rough
economic values for the aforementioned aquatic ecosystem effects. Each
attempt is made in order to exploit a particuar type of natural and/or
economic information. The measures developed are not additive. Most
important, as is the case throughout this report, all the measures are and
very sensitive to minor perturbations in assumptions.
Although the criteria he uses for determining whait is and is not "fish-
able" are unclear, Todd (1970, p. 303) shows 19.14 x 10 acres of fishable
fresh-water streams and lakes in Minnesota and the states east of the Missis-
sippi River. This excludes the Great Lakes which have an area of 38.OCT x 10
acres. Adams, et al. (1973, p. 43) indicate that about 23 percent of the
approximately 168 x 10 people twelve years or older then living in this area
passed an average of 7 days fishing in the summer quarter of 1972. This
6 , , , ,
represents 270 x 10 fishing activity days. No reliable information could be
formed giving the seasonal distribution or the fresh-salt water distribution
of fishing activity days. We, therefore, assume that 85 percent of this
fresh-water fishing occurs during the summer quarter. Upon making the adjust-
. - 6 _,
ments called for by these assumptions, we are left with 287 x 10 fishing
activity days in Minnesota and the states east of the Mississippi in 1972. We
assume that the number of activity days in 1978 was 300 x TO more-or- less.
A number of studies of varying degrees of sophistication are available
which purport to give the representative willingness-to-pay for an additional
fresh-water fishing activity day. These estimates are distributed over a
range from 10 to 30 mid-1970's dollars. The S20.72 uncompensated consumer
surplus estimate obtained in 1972 by Gordon, et al. (1973) is adopted here.
Assuming that increases in real income, in the value of time, and changes in
relative fishing costs have not altered this figure, this amounts to $32.30 in
1978 dollars. If the marginal value of a fishing activity day is a constant
regardless of the availability of opportunities to catch fish and if no
34
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fishing occurs in the absence of fish, the extinction of fresh-water fish life
in Minnesota and the states eas^ of the Mississippi River would have resulted
in economic losses of (300 x 10 activity days) ($32.30) = $9.69 x 109in 1978.
Assuming the number of fishing days is linearly and inversely related to the
acres of fresh-water having fish populations, and if Tables 1 and 2 from
Chapter III are to-be-believed, well over half this loss would occur before
all fresh-water in the aforementioned area reached a uniform pH level of 6.0.
If large regions in the general area retained pH levels for fresh- water at
6.5 - 8.0, even though the average pH over the entire region was 6.0 or less,
the economic losses would be a great deal less. This is because fishermen
would readily be able to substitute away from an acidified to nonacidified
bodies of water.
The recreational value of the fresh-water resource in Minnesota and the
states east of the Mississippi is clearly rot limited to fishing activities.
One major additional use is for hunting, particularly waterfowl hunting.
According to Todd, (1970, p. 303), there exist in this area 48.83 x 106acres
of natural wetlands "... of significant value to fish, and wildlife." In 1980,
the U.S. Water Resources Council (1968) projected that the number of
water-related hunting activity days in the area would be 220 x 10 . This was
projected from the 162 x 10 days taking place in the same area in 1960. On
the other hand, the U.S. Fish and Wildlife Service (1972, p. 31) estimated the
number of 1970 waterfowl hunting activity days by people 12 or more years old
to be 17.58 x 10 . Since, relative to fishing activity days, this seems more
plausible, we employ it here. Hammack and Brown (1974, p. 29), in their study
of the value of waterfowl, found that the average waterfowl hunter passed 9.7
days each season engaged in the activity, and acquired a consumer surplus of
$247 (= $462 in 1978 dollars) from the right to hunt during the 1968 season.
Even if fresh-water pH levels were universally to drop to 4.0 or less
throughout the region east of the Mississippi, it cannot be assumed that all
waterfowl in the region would disappear. Some invertebrates that constitute
part of the diet of waterfowl would survive. More important perhaps, there
are land-based food items (such as agricultural grains) that waterfowl might
employ as a substitute food source. Nevertheless, it should be noted that
several very important hunted species of waterfowl currently get 50 percent or
more of their food supplies from aquatic sources. Martin, et al. (1961)
state, for example, that 50 to 70 percent of the diets of the mallard, the
black, and the common goldeneye ducks consist of aquatic insects, crustaceans,
and mollusks. Moreover, the habitats of these birds, especially the mallard,
tend to be the ponds and shallow lakes thought to be more susceptible to acid
precipitation. Of the waterfowl hunters in the Hammack and Brown (1974, p.
39) sample, 47 percent stated that mallards were their first preference in
waterfowl hunting.
35
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Given the almost total lack of information on the impact of fresh-water
acidification upon the population and distributions of waterfowl, we choose to
make some quite arbitrary assumptions. In particular, we assume that a
representative member of a representative species currently obtains half its
food supply from fresh-water aquatic environments. It, therefore, has some
ability to substitute food from terrestrial or marine environments for the
fresh-water source'without having to alter its location in any given season.
Without guidance from any source, we assume that the destruction by acid-
ification of the acid-intolerant portion of the fresh-water food supply for
waterfowl will result in a reduction of 20 percent in the waterfowl population
during the hunting season in Minnesota and the states east of the Mississippi
River. Further assume that the elasticity of waterfowl hunting activity days
with respect to waterfowl populations is 0.5. If the number of waterfowl
hunting activity days in the region of interest was approximately "JO x'llj in
1978, the assumed elasticity and reduction in waterfowl population implies a
drop in 1978 activity days to 28.5 x TO" . If the marginal value of an
activity day is a constant, the Hammack and Brown (1974) estimate of the
consumer surplus obtained from the right to hunt waterfowl implies an activity
day valuation of $462.00/9.7 = $47.63. The ten million day reduction in
waterfowl hunting activity days, therefore, yields a 1978 economic loss of
$71.45 x 10 . Given our long chain of arbitrary assumptions, we conclude that
an estimate of 70 million dollars is reasonable. It is important to note,
however, that Hammack and Brown (1974, p. 63) found that waterfowl hunters
could annually shoot 76 percent of the waterfowl in the Pacific flyway without
reducing the breeding population. It seems unlikely that fresh-water acidifi-
cation would have an effect upon recruitment of this magnitude. One might,
therefore, conclude that fresh-water acidification will cause no changes in
waterfowl populations and distributions and thus no economic losses will be
incurred. In cases where waterfowl and fish have been competing for the same
aquatic insects, it may be that acidification by reducing fish populations
will reduce competition for the aquatic insect food source and thereby enhance
waterfowl populations.
If the food supplies of waterfowl are harmed, by fresh-water
acidification, it follows that the food supplies of birds that are not legally
hunted will also be harmed. The diet of the osprey consists entirely of fish,
while bald eagles-are mostly dependent upon fish for food. Cranes, including
the sandhill crane, utilize a variety of aquatic vertebrates and invertebrates
for food sources. In spite of the possibility that these and other birds will
suffer population declines from fresh-water acidification, we have no basis
whatsoever on which to formulate a guess at the economic losses a population
decline might entail. Not only do we lack any quantitative information on
population responses to acidification, we also lack any information about the
values people place upon encounters with these birds.
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A somewhat similar problem exists for mammals dependent upon aquatic
ecosystems for part of their food or even for their everyday habitats. These
would include, for example, racoon, mink, muskrat, marten, beaver, river
otter, and even moose and black bear. No readily available information exists
on the population responses of these animals to acidification-induced
perturbations in their aquatic food sources or habitat. Nor does any economic
information exist on the value of an encounter with these animals. Economic
information does exist, however, on their market value when they are killed
for their furs. The U.S. Water Resources Council reports according to Todd
(1970, p. 270) that in 1966, 7.0 x 10 "fresh-water dependent" fur-bearing
animals were captured in Minnesota and the states east of the ^ississippi.
These animals, in 1978 dollars, had a market value of $26.7 x 10 , or
approximately $3.80 per animal, assuming the resources employed in their
capture had no valuable alternative uses. Measured solely then in terms of
the worth of their fur when captured, the economic impact of a fresh-water
acidification- induced population reduction will be minor. Again, however,
this disregards the animals' value in terms of simple observations during
encounters as well as the value they contribute to hunting recreational
activities.
Boating and swimming are additional recreational activities that con-
ceivably could be affected by reductions in the pH of fresh-water. However,
in a study of the acid mine drainage problem in the Appalachian region,
Robert R. Nathan Associates (1969) was unable to find any variation in boating
and/or swimming activity days with respect to different levels of pH. This is
not too surprising since it is generally recognized that boaters and swimmers
respond negatively to increased turbidity. Kramer (1978, p. 354) notes that
there is an approximate doubling in transparency, measured as Secchi depth,
for each unit decrease in pH over the 6.5 - 4.5 pH interval. He attributes
this "... to the dissolution of iron and manganese colloids and the decrease
in organic detritus with decreasing pH due to decreasing photosynthesis" (p.
354) .
Added to all the above results must be the commercial value of captured
fresh-water fish. In 1965, Todd (1979, p. 270), uging data from the U.S.
Water Resources Council, estimated that 2801.6 x 10 pounds of "fresh-water-
dependent" fish were caugh£ in our region of interest. The market value of
these fish was $196.2 x 10 (=$404.2 x 106in 1978 dollars). Sixteen percent
of this catch, was either fresh-water or anadromous species. Assuming the
resources employed to catch this sixteen percent had no valuable alternative
uses, if these fresh-water or androinous species were to be extinguished, the
annual loss would amount to 65 x 10 1978 dollars. This includes the extinc-
tion of the catch from the Great Lakes.
When all the preceding effects of acid precipitation upon fresh-water
37
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ecosystems in Minnesota and the states east of the Mississippi River are
summed, one obtains 1978 annual benefits for preventing pH levels falling
below 4.5 - 5.0 for all fishable fresh-water bodies in this area of $10 to $11
billion. Nearly all the benefits are attributed to the maintenance of
recreational fishing opportunities. It must nevertheless be emphasized that
the economic, and biological analyses on which these estimates are based have
weak, analytical foundations. Given those limits, somewhat more creditability
might be achieved by adopting a different approach to assessing the benefits
of acid precipitation control.
If the acidification of fresh-water does negatively influence ecosystem
attributes that human beings value, one would expect these negative influences
to be capitalized into land that offers ready access to these valued attrib-
utes. In particular, economic theory predicts that land prices will be
consistent with the values people attach to the differences in these advan-
tages of access. Freeman (1979) outlines the circumstances in which these
prices will reflect the variations in consumer surplus generated by the
differences in access advantages.
Adams, et al. (1973, p. 111-110) present estimates by farming region of
differences in the 1972 per-acre value of recreation land with and without
water. For the states east of the Mississippi River, the median difference by
region appears to be about $1,250 per acre. Recreation land without water is
generally about 33 to 50 percent the value of land with water. If the values
of both types of recreational land behaved as did farm real estate values
between 1972 and 1978, their values approximately doubled [Economic Research
Service (1978)], implying that the $1,250 per acre difference in 1972 had
increased to a $2,500 per acre difference by 1978.
Excluding the Great Lakes, Todd (1-970, p. 301) finds that there exist
...
21.86 x 10 acres of inland water available for recreation m Minnesota and
the states east of the Mississippi. This is somewhat greater than the 19.14 x
1.0 acres that he ^considers to be "fishable" (p. 303)6Of this "fishable"
acreage, 3.83 x 10 is in streams, leaving 15.31 x 10 acres in natural and
man-made lakes, exclusive of the Great Lakes. Assume that each surface acre
of fishable freshwater lakes, excepting the Great Lakes, is associated with
one riparian acre. This one acre figure is a judgment formed by using a table
in Todd (1970, pp. 126-127) of the surface acreages and shoreline lengths of
the largest lakes in each state of the United States. Man-made lakes tend to
have shoreline mileages about 10 times as great as the square mileages of
their surface areas, while the shoreline mileages of natural lakes tend to be
about half as great as the square mileages of their surface areas. We
estimate then, that of the nearly one billion acres of the surface of the
globe contained within ^he boundaries of Minnesota and the states east of the
Mississippi, 15.31 x 10 (or 1.6 percent) of them are riparian to lakes and
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ponds.
Added to the lake and pond riparian acreage must be the acreage that is
riparian to rivers and streams. Minnesota and the states east of the Missis-
sippi contain about 36 percent of the 260,000 stream miles in the 50 U.S.
states, meaning that they have about 94,000 stream miles. Assuming 50.66
riparian acres pef'sfream mile, these 94,000 stream miles yield 4.76 x 10
riparian stream acres. By way of contrast, this means that we estimate 1.24
of riparian acres per acre of stream surface water, as opposed to the one
riparian acre estimated for each acre of lake and pond surface water. upon
summing the estimated stream and lake and pond riparian acreages for Minnesota
and the states east of the Mississippi River, we obtain 16.55 x 10 acres.
Now let us consider under some extremely strong assumptions what the
_ _ - - 6
extinction of fish life on these 16.55 x 10 acres might mean for their
values. According to Unger, et al. (1976, pp. B.6 - B.8), there were 1.70 x
10 fresh-water rel ^ed recreation activity days in 1970 in the United States,
of which 0.63 x 10 days, or 37 percent, were devoted in some part to
fresh-water fishing. Of the estimated $2,500 per acre difference in 1978
between the values of recreational land with and without ready access to
water, we presume that exactly 37 percent, or a $925 premium is attributable
to the fishing access the former offers. If the game fish in all of the
waters to which the above mentioned acreages are riparian were simultaneously
to disappear forever, the total value of these acreages would then decline by
($92.5) (16.55 x 1"0 ') ^$15.32 x 109 .
Earlier, using recreational data on fishing activity days and the
consumer surpluses associated with them, we estimated that the disappearance
of all game fish would have generated annual losses of $9.69 x 10"in 1.978.
If these losses were to continue in perpetuity, and if they were all to be
capitalized into the values of riparian acreages, a discount rate in excess of
200 percent^wg^-d have to be applied in order to yield a present value of only
$15.32 x 10 This hardly seems realistic. When a more reasonable discount
rate of 15 percent is applied to this presumed present value for riparian
property losses of $15.32 x 109, one obtains annual losses of $2.0 x 109.
Lower discount rates imply still lower annual losses. For example, a discount
rate of 5 percent, implies annual losses of only $0.73 x 10 . On the other
hand, if one applies a 15 percent discount rate to the earlier estimate of
$9.69 x 10 in annua losses, one obtains a present value for this stream of
losses of $74.29 x 10' , a considerable amount of wealth indeed.
Before rejecting the previous $9.69 x 109 annual loss estimate in favor
of an annual loss estimate derived from an equally limited treatment of the
annual losses implied by reductions in riparian property values, it is
important to keep in mind that these latter losses are related only to the
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losses in consumer surplus suffered by the riparian property owners plus the
fees they might collect from present and future fisherman who wish to gain
access to fresh-water bodies over present owners' riparian lands. in the
great majority of cases, these fees are not collectable because of the costs
of policing access. One can thus make a strong argument that the impact of
acidification upon"riparian property values, even if the structural conditions
outlined by Freeman (1979) are fulfilled , must be a substantial underestimate
because of the failure to register the surpluses accruing to fisherman who
have free access over the land.
The preceding accounting, in addition to its rather severe limitations in
terms of economic analysis, fails to consider the actions private and public
bodies might undertake to ameliorate the effects of acid precipitation. In
particular, one might lime and/or restock acidified fresh-water bodies. The
ecological evidence for the likely restorative successes that can be achieved
by liming is mixed. As for restocking, if one is willing to devote the
requisite resources, it is perhaps a feasible technical alternative. whatever
the technical and financial feasibility of either or both of these restorative
procedures, it must be recognized that some set of decisionmaking bodies must
be formed and maintained to implement the restorative procedures. Given the
common property attributes of that which is to be restored and the public good
nature of the restorative and restocking actions, one might reasonably have
serious doubts about whether effective massive restoration and restocking
programs can be formulated and implemented.
In principle, the liming of fresh-water bodies will simultaneously serve
to raise the pH values of the water and to make the heavy metals abundant at
low pH substantially less available biologically. Hagerhall (1979) estimated
that in 1973 it would cost $45-70 x 10 to acquire and apply one million tons
of CaCO in Sweden. Assuming similar costs in the United States, this amounts
to $66-1 03 per ton per year in^.1978. He also states that apparently a one-
time application of 30-50 x l'O" tons of CaCO (p. 10) would suffice to return
22.24-27 x 10 acres of Swedish lakes to the fr pH states at the beginning of
the 20th century, if acid precipitation were to cease. Simply to counter the
current yearly increment in acidification over this lake area would, according
to Hagerhall (197,9, p. 10), require the annual application of one million
tons of CaCO Thus restoration by liming in 1978 to pH levels of the earrjy
2 0th century would require a one-time outlay fg om (30 x 10 tons/27 x 10
acres)($66) = $73.33, to (50 x 10" tons/22 x 10 acres) ($103) = $234.09 per
acre. The mid-range of this interval is $150 per acre. Thus, always remem-
6
bering the limits of the analysis, if all the 19.14 x 10 acres of fishable
fresh-water bodies in Minnesota and the states east of the Mississippi River
were to become acidified in a fashion similar to the aforementioned Swedish
lakes, a one-time 1978 outlay for liming of $2.87 x 10 would be required to
return them to pH levels in excess of 6.0. However, if the number of
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acidified fresh-water acres is extended to the natural, wetlands . of
significant value to fish and wildlife" [Todd (1970, p 3031, this estimate
increases to ! (48.83 x 10" acres) + (19.14 x 10 acres)] $150 = $10.20 x 109.
On an annualized basis, using a 15 percent rate of discount, these one-time
outlays are respectively equivalent to $430 x 10 and $1.53 x 10 .
Assuming the $150 per ton cost figure for the purchase and application of
CaCO^ to be reasonable, a rough check on the above estimates can be obtained
by exploiting a statement of Holden's (1979, p. 11").
"An alkalinity equivalent to ^.5 ugl calcium carbonate requires
the solution of 2.5 g. metre . A lake of 10 ha with a mean depth of 2 m
(a small lake), requires 500 kg of dissolved calcium carbonate, and
probably ten times this amount of ^the-, s°lid to obtain sufficient in
solution. A stream flowing at 1 m s-'" would require about 80 tonnes
year in solution. These quantities must be maintained each year. .."
Assume that the lake Holder. (1979) describes is representative of most
lakes in Minnesota and the states east of the Mississippi River. Further,
assume that, because of the greater ability of streams to dilute materials,
that representative streams annually require the injection of twice as much
CaCO as do the representative lakes. Given that "sufficient" solution of
CaCO requires the injection from all sources of ten times as much Caflf^ in
soliaform, this is stating that each acre of our representative lake annually
requires the introduction of about 450 pounds of CaCO . Streams, therefore,
by our assumption, reci^ ire 900 pounds of CaC03 for earn acre of their surfacg
areas. The 15.31 * 10 acres of fishable freshwater lakes and the 3.83" x 10
acres of fishable fresh-water streams in Minnesota and the states east of thg
Mississippi River, therefore, require the annual introduction of (^.5.31 x 10
acres) (450 pounds) + (3.83 x 10 acres) (900 pounds) = 5.17 x 10 tons of
CaC03 or equivalent. If all this CaCO^ had to be introduced by man, and if
each ton of CaCO cost $^50 to acquire and inject, the total annual cost in
1978 would be $7?76 x 10 . This figure is much greater than even the one-time
cost earlier obtained using the data of Hagerhall (1979). Note, however, that
the estimate from Holden (1979) assumes that all CaCO entering these
fresh-water bodies is somehow to be supplied by man. If, for example, half
the CaC03 necessary to raise the pH leve] of a fresh-water body is naturally
supplied from the catchment area, the $7.76 x 1? cost estimate would have to
be reduced accordingly. However, if the 48.83 acres of wetlands "... of
significant value to fish and wildlife" are taken into account, and if one
assumes that the residence time of water in these wetlands is twice as long as
in Holden's (1979) representative lake (implying that only half as much CaOg^
is required as in the representative lake), then an additional (48.83 x 10
ac^es)(225 pounds) = 5.49 x 10 tons at an additional total cost of $8.24 x
10 would be required annually. Thu s , at least in terms of the sets of
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assumptions employed here, the use of Holden's figures on liming requirements
leads to an estimate of the annual cost of liming more-or-less similar to the
value of the fishery that would be lost if fresh-water acidification were
allowed to proceed unhindered.
The literature occasionally mentions two other alternatives to amelio-
rating the effects of extant pH. For example, Swarts, et al. (1978) and
Leivestad, et al. (1976) find differences within fish of the same age and
species with respect to their ability to tolerate low pH. This raises hopes
for natural selection processes serving as a means to maintain natural
populations, given, of course, that the rate of toxic acidification does not
outstrip the rate of natural genetic improvement in tolerance.
Alternatively, the awareness of differences in acid tolerance among
species raises the prospect, [e.g., Schofield (1976, p. 230)] for the selec-
tive breeding or genetic engineering of acid-tolerant individuals. These
individuals would then be used to restock acidified waters. However, if
acidification also has a major impact upon the populations of other fresh-
water organisms, it is unclear what the restocked fish would eat other then
their peers. A similar comment applies to all restocking programs, whether or
not with acid-tolerant individuals. Aimer (1978, p. 307) nevertheless
mentions several species in acidified waters which have substituted surviving
invertebrates for their usual food which consists of other fish. It thus
seems worthwhile to make some estimates, even if exceedingly rough, of the
cost of restocking fish populations.
Bennett (1971, p. 89) presents a table showing average standing crops cf
various species of fish per acre of fresh-water. The species range from trout
and channel catfish to suckers and carp. The table was constructed to show
the relative masses of the 19 species listed, given that some species are
usually seen in combination with other species. The average of the mean
pounds per acre for the 19 species is approximately 36. If there are 19.14 x
10 acres of fresh-water lakes and streams in Minnesota and6the states east of
the Mississippi River, this implies that there are 689 x 10 pounds of fish in
these waters. Recording to Lerner (1974, Table 332) the Federal government
spent $298 x 10 in 1973 for the maintenance of fish and wildlife populations.
Part of this money was spent to propogate and distrribut;, , according to the
U.S. Fish and Wildlife Service (1974, p. 27), 303 x 10 fish eggs. Jf, on
average, 5 percent of these eggs survive to one pound adults, and if all the
above $298 x 10 1973 Federal expenditures were for fish, then each pound of
adult fish cost the Federal government $19.67 (= $28.91 in 1978 dollars). For
obvious reasons, this is an overestimate. Nevertheless, even if the survival
rate is increased and/or the cost per adult fish is reduced, a substantial
annual outlay remains. Given the extreme crudeness of the calculation, the
difference from the $10-11 x 10 estimated annual value of a loss of the
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entire game fishery in the region of interest does not seem sufficent to
conclude, tentatively or otherwise, that the annual value of the impact of
acid precipitation upon aquatic ecosystems is the cost of restocking game fish
populations.
Health Effects ' • •
The Safe Drinking Water Committee (1977, p. 439) defines "hard" water as
that containing 75 mg/liter or more of calcium carbonate or the equivalent.
Increased hardness is indirectly associated with elevated pH. Although the
Committee does not adopt an unequivocal position, it does state that the body
of evidence for "soft" water being a causal agent in cardiovascular disease
"... is sufficiently compelling so that "the water story'is plausible .
(p. 447). Soft water has a relative lack of inorganic solute health-support-
ing agents such as calcium, magnesium, and manganese, and a relative abundance
of health-degrading metal agents such as cadmium, lead, copper, and zinc. In
addition, the effectiveness of several standard methods (chlorination,
filtration and sorption, etc.) for reducing concentrations of bacteria,
viruses, and protozoa in water intended for human internal consumption some-
times varies directly with pH.
Our brief review of the available evidence makes us reluctant to map
disease incidence into the PH levels of drinking water. Nevertheless, it is
worth noting that quite small incidence due to the inorganic and organic
solutes and the microbiological agents whose human health-degrading potentials
are activated by low pH levels can result in large economic losses. For
example, about half of the two million annual deaths in the United States are
attributed to the various cardiovascular diseases. Jf only one percent of
these one million deaths were indirectly attributed to low pH drinking water
supplies, a toll of 10,000 deaths would result. In this context, it is worth
noting that the Safe Drinking Water Committee (1977, p. 447) states: "On the
assumption that water factors are causally implicated, it is estimated that
optimal conditioning of drinking water could reduce this annual cardiovascular
disease mortality rate by as much as 15% in the United States." Recent
economic research [e.g., Thaler and Rosen (1975)] indicates the value of
safety from death, to be about $500, 000 - $1,000,000 in 1978 dollars. Using
the lowest point in this range along with the one percent mortality
assumption, would then result in annual economic benefits of $5 x 10 . This
figure would be increased substantially if one were to account for the losses
in life- cycle earnings (and implicitly in labor productivity) due to
cardiovascular diseases that do not now and perhaps never will result in
death. Bartel and Taubman (1978) , while working with a panel of 40-50 year
old male twins, found that those with cardiovascular diseases had their annual
earnings reduced by 20 - 30 percent relative to their healthy peers.
According to the National Center for Health Statistics, 15.7 percent of the
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1976 U.S. population suffered from cardiovascular diseases [Lerner (1978, p.
120) ] .
The preceding makes it appear that the health impacts and consequent
economic effects of reduced pH in water used for internal human consumption
could readily be v
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marginal costs, the total cost of providing lime treatment for 264,175 gallons
of raw water would be $2.05. Given our previous assumptions about the
distribution of the U.S. population and water withdrawals for rural domestic
and municipal uses, this implies that the daily cost of lime treatments for
raw water supplies east of the Mississippi River would be about $148, ()00.
This amounts to an"'annual cost of $54 x 10 1976 dollars or $62.1 x 10 for
1978. Of course, given the existence of acid mine drainage in important
watercourses of the region as well as natural acidification due to soil
leaching, much of this cost burden would have to be borne independently of any
acid precipitation problem. Thu s , the external costs (the environmental costs
of increased mining activity for CaCO^ and its equivalents and the negative
health effects) of increased liming of raw water supplies would have to be
extremely large (at least as much as the value of the negative health impacts
of increased acidity) to justify a refusal to ameliorate the health impacts of
acid deposition by the liming of raw water intended for internal human
consumption.
Household, Commercial, and Industrial Water Supply System Effects
Reductions in the pH levels of water supplies may cause corrosion in
household, commercial, and industrial water conveyance systems and water-
using appliances, thereby shortening their useful lifes and reducing the flow
of their services while in use. In the absence of ameliorative measures, the
potential economic losses from this corrosion could be severe. On the other
hand excessively high pH levels can have similar effects due mainly to mineral
deposits forming on the interior surfaces of the systems and appliances.
Several studies are available that assess the impact of increased levels
of total-dissolved-solids (TDS) and/or water hardness upon the economic life-
times of household and commercial water supply and use systems. Using an
eight percent discount rate, d'Arge and Eubanks (1976) estimate 1975 economic
lose? for a typical Los Angeles household to range from $620 to $1,010 in
present value terms for an increase in total dissolved solids from 200 to 700
mg/1. This estimate is three to four times higher than estimates developed by
Tihansky (1973) for a similar TDS range throughout the United States. In an
appendix to their, study, d'Arge and Eubanks (1976, pp. 274-275) used data from
Black and Veatch (1967) to explore the extent to which the ratio of TDS to
total hardness was important to the useful lifetimes of household conveyance
systems and water-using appliances. They found that increases in the ratio
made a statistically significant positive contribution to the lifetime of
garbage grinders and a statistically significant negative contribution to the
lifetime of wastewater pipes. Total hardness, when entered as a separate
explanatory variable in a multiple regression, was negatively associated with
the useful lifetime of faucets but the association was not statistically
significant. It thus appears that the acidification of water supplies, to the
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extent that it "softens" water in areas with "hard" raw water, could have
economically beneficial effects upon water conveyance systems and water-using
appliances. Nevertheless, if the effects of excessive "softness," as induced
by low pH, upon useful life are more-or-less symmetrical to those of excessive
hardness, the economic impacts upon households, and commercial establishments
could be considerable.. Since the ferro-alloys, copper alloys, and brasses
used in household and commercial water supplv systems and water-using appli-
ances are also found in industrial systems and equipment, substantial economic
impacts could also be expected in these sectors.
In spite of the potentially large economic impacts of low pH water upon
household, commercial, and industrial, water supply systems and water-using
appliances and equipment, it does not appear useful to try to calculate the
magnitude of these impacts. The reason is that inexpensive neutralization
techniques using hydrated or calcined limes are readily available.
In the health effects section, we have calculated the cost of liming
rural domestic and municipal water supplies. According to Todd (1970, p.
312), the "optimal" pH levels for domestic water supplies are about neutral
(pH = 7.0), although (p.320) the median for the 100 largest U.S. cities in
1962 was pH = 7.5. Thus, given that all rural domestic and municipal water
supplies are treated as if intended for internal human consumption, acidifica-
tion of raw water will have no extraordinary effects upon household and
commercial conveyance systems and appliances.
Many industries supply and treat their own process water. The USDA
Economic Research Service (1974, p.37) estimates that self-supplied industrial
water withdrawals (excluding steam-electric power) from fresh surface and
ground sources in the U.S. in 1.970 were 45.87 X 109gal./day. According to
Todd (1970, pp. 329330) , most industrial processes require or are indifferent
to water with pH in the 6.0 to 9.0 range. In 1968 [Todd (1970, p. 221)],
about 72 percent or 33.03 X 10 gals./day of these withdrawals occurred in the
states east of the Mississippi River and in Minnesota.
Assume that all of the self-supplied industrial fresh water east of the
Mississippi and Minnesota has been acidified to the 4.0-4.5 pH range prior to
withdrawal. Further assume that in order for it to be used as a process water
its pH must be raised to an average 7.5-8.0 across industries, and that it
would otherwise require no treatment prior to use. Thus , excluding the
possibility of tying into municipal systems, each plant will have to construct
and operate its own treatment facility. Our presumed necessary increase in pH
happens to correspond to the pH increases experienced with several acid mine
water treatment plants. For example, Bituminous Coal Research, Inc. (1971,
pp. 133-134) reports total 1970 capital and operating costs of 97.3, 35.3, and
26.5 cents/1,000 gals, with a plant respectively processing 0.1, 1.0, and 7.0
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million gallons/day. They also report on another plant which experienced 1970
total capital and operating cost of 13.6 cents/1,000 gallons for treating an
average of 4.0 million gallons/day. In each case, the pH of the acid mine
water was raised from about 4.5 to more than 7.0. Barton (1978, pp. 351-354)
summarizes the experiences of one mine where water were raised from 4.0 or
less to more, than ^7.5.. The commercial operation with 12,800 tons of lime,
processed 3.4 X 10 gallons of water with an original pH of 4.0 and a finished
pH of 7.9 at 20 cents/1,000 gals.
Using a very fine and therefore more costly limestone slurry, the pilot
plant raised a mine discharge of 2.8 pH to 7.4 pH at estimated 1970 capital
costs of $55,000 to $766,000 for 100 X 1$ to 600 X 10 gals/"day operating
capacities. Estimated 1970 operating costs, including amortization, were
respectively 44 cents to 2 cents/1,000 gals. In the words of Barton (1978, p
352) :
"Limestone could be the preferable choice for treating nearly all
but the most severly loaded discharges. It has the advantages of avail-
ability, lower cost, reduced hazards, ease of application, simplicity of
plant design, impossibility of water overtreatment, ease of storage, and
higher solids concentration of the precipitated sludge."
A review of Todd (1970, pp. 246-274) makes it appear that the median
water-using industrial establishment withdraws about 1.0 million gals./day.
We therefore estimate, on the basis of the material presented in the preceding
paragraph, that, including amortization of capital facilities, a
representative 1970 total cost of raising 4.0 pH fresh water to 7.5 pH would
be 50 cents/1,000 gals./day. On a yearly basis, therefore, the 1970 total
annual cost of treating the 33.03 X"10 gals./day of self-applied industrial
water withdrawn east of the Mississippi could be $5.66 X 10 '(="$"9 .'51 ~X "10 for
1978) . Even though it is fair to presume that the unit cost of lime and
treatment plants might increase with an increase in demand of the magnitude
posited here, it should also be recognized that the posited increase in demand
is also probably vastly exaggerated. Not all fresh water east of the
Mississippi is likely to suffer a reduction in pH to 4.0 or even 5.0. Many
industries are fairly indifferent to quite low PH. For example, in a survey
of the impact of acid mine water upon patterns of industrial water use in the
Appalachian region, Whitman, et al. (1969) found that the most impacted
industry, primary metals, saw fit to raise the pH level of its cooling water
only to 5.0. This was accomplished at minor cost by integrating lime
treatments with otherwise existing water treatment facilities. Todd (1970, p.
345) makes it appear that possibly half the industries in the United States in
1959 had their own treatment facilities. Finally, we have-not considered
possible substitutions from fresh to saline water sources. - "The stated
estimate might therefore readily be exaggerated by more than an order of
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magnitude. One can be quite sure that it is not biased downward. Given the
industrial treatment facilities already in place, we prefer to treat as
trivial the additional costs of treatment attributable to acid precipitation.
Materials Effects
Several 'studio's df the economic impact of air pollution upon the useful
lifes of materials have been published, e.g., Gillette (1975), Commission on
Natural Resources (197 , pp. 616-619, 695-699) , Kucera (1976) , and Salmon
(1972) . Nriagu (1978) presents an extremely thorough review of the physical
science literature on the effects of sulfur pollution on materials. A brief
review of the material effects of nitrate aerosols is available in Panel on
Nitrates (1978, pp. 417-418).
Acid precipitation (or acidifying deposition) accelerates the decay rates
of a wide variety of materials mainly because the presence of acids upon the
material surfaces increases the flow across the surfaces of the electric
currents that cause corrosion, discoloration, and embrittlement. Among the
metals, ferro-alloys, copper, and some galvanized metals are known to be
particularly susceptible. In some cases (e.g. zinc), the dissolution of the
metal surface by acid precipitation is thought to increase the pll level of the
product, thus resulting in an even more corrosive surface film. Carbonaceous
building materials, such as limestone and cement, are more rapidly weathered,
roughened, eroded, and stained. Paints are bleached and crystallized, and
their drying and hardening times are increased. The tensile strength of
textiles is degraded and textile dyes can suffer from fading. Losses of
tensile strength also occur in paper, as does discoloration. Other cellulose
products, such as wood, suffer similarly. Leather products deteriorate because
the acids break down their fibrous structure. As Nraigu (1978) emphasizes,
these processes are further intensified for those materials, such as cement,
concrete, and some metals, often used in subaqueous and/or high temperature
environments.
The recent economic impact studies of air pollution upon materials have
yielded estimates for the entire United States of losses ranging from the $904
x 10 Gillette (1975) attributed to sulfur oxides in 1968, to the $3.8 x Iff
Salmon (1972) attributed to all air pollution in 1970. None of these studies
provides any substantial basis for attributing a portion of their estimated
losses to acid precipitation, although the decline in sulfur dioxide levels
throughout most of the eastern United States during the 1970's implies that an -
increased portion of whatever materials damages are occurring is attributable
to acid precipitation. Most important, since all these studies basically do
little more than inventory some existing materials, attach a market price to
them, and then use physical science estimates of increases in replacement
frequency to obtain a total loss estimate, they are susceptible to all the
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criticisms that can be directed toward most of the estimates In this chapter.
As Glass (1978, p. 34) correctly points out, many extremely resistant
materials, such as aluminum clad steels, have been widely adopted in the last
decade; most estimates relate to uncoated rather than coated galvanized
steels; the economic lives of many materials are so short (e.g., paper) that
air pollution does not have time to affect them in a noticeable fashion; and,
that when a substitute material, is adopted, the cost differential often cannot
be assigned entirely to pollution since the substitute may have features that
reduce cost dimensions other than useful life. In addition to these factors,
the available studies sometimes have failed to discount the stream of costs
properly. Moreover, all the studies have failed to consider that individuals
may choose simply to bear a reduced stream of services from a material rather
than purchasing a replacement, may alter behavior patterns so as to compensate
for the stress that acid precipitation imposes upon the material, and may
adopt materials more resistant to the ravages of acid precipitation. Finally,
entire categories of useful materials such as limestone and concrete
structures, including dams and pipes, and automobiles have had no economic
attention devoted to them. Given the lack of economically useful physical
science information and the lack of sound economic information, it is tempting
to plead .an absence of any basis whatsoever to make a judgment about either
the fact or the potential for the economic impact of materials damages from
acid precipitation and acidifying deposition. This is particularly so because
many of the factors for which information is lacking can have either a
positive or a negative economic impact. Of those factors that are most likely
positive, or most likely negative, it is impossible to tell which will
dominate. One is thus unable to state whether any estimate of the total (or
marginal) impact represents an upper or a lower bound.
In spite of the preceding, it should be recognized that the costs of acid
precipitation-induced materials decay could indeed be very substantial. The
Commission on Natural Resources (1975, p. 696) refers to studies which
estimated 1970 damages in Sweden to painted steels from all corrosion of
$25.00 per capita (= $41.98 in 1978 dollars) . From the same source, the
Commission (197 ) quotes $23.00 per capita (= $38.64 in 1978 dollars) as being
the total annual cost of deterioration of painted woodwork associated with all
sources of deterioration. The studies from which these figures come appear to
have at least as -complete a physical science basis as any available, and no
worse an economic basis than any of the extant studies.
Other than the direct and indirect products of chemical weathering,
soiling is the major source of reductions in the usefulness of materials.
Some of what passes for soiling (e.g., staining of the exterior stone surfaces
of buildings) may, in fact, be chemically-induced discoloration. We thus
presume that, in economic terms, soiling is relatively minor as opposed to
chemical weathering. Some enhanced chemical weathering occurs to materials
49
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located near marine environments. This, however, is probably not an important
source except for those materials frequently exposed to sea breezes and/or
salt sprays. Some chemical weathering would naturally occur in humid areas
since pristine precipitation is somewhat acidic (pH = 5.65). All these
factors suggest that the aforementioned annual per capita costs in Sweden of
the weathering from all sources of painted steels and painted woodwork are
exaggerations of the "losses caused by the impacts of acid precipitation upon
these materials. However, as we previously emphasized, these materials
constitute only a portion (though not a small portion) of the economically
significant materials susceptible to acid precipitation-induced decay.
To generate a number for the materials damages caused by acid precipita-
tion, we assume that the current per capita exposures of the great bulk of the
Swedish population is very similar to the per capita exposures of the popula-
tion in the eastern part of the United States. We further assume that the per
capita mixes and magnitudes of painted steels and woodwork used by United
States residents residing in Minnesota and east of the Mississippi River are
similar to those of the Swedes. A simple multiplication of the sum of $41.98,
for painted steels, and $38.64, for the painted woodwork, by the approximately
170 x 10 people residing in Minnesota and the states east of the Mississippi
River in 1978, yields a calculated annual loss from materials damages of
$13.71 x 10 . It should be noted that this figure is an order of magnitude
higher than previous estimates of all air pollution-induced materials damages
over the entire United States. However, given both the physical science,
economic, and inventory accounting limitations of the previous estimates (and
this estimate), it seems as likely to be an underestimate and an overestimate.
Nevertheless, given the difficulty and trivial gains to us in trying to
justify the discrepancy between the above weak estimate for materials damages
and those obtained by previous investigators, we do not deem this exercise to
be a good forum for a display of intellectual stubbornness. We, therefore,
state that materials damages are likely to be the largest category of the
types of acid precipitation-induced damages we have surveyed, but we have no
wish to assign to acid precipitation all materials damages that previous
investigators have attributed to air pollution. We, therefore, set the 1978
materials damages caused by acid precipitation at $2 x Iff , while recognizing
that the figure could plausibly be much larger.
Summary and Conclusions
Although most of the analysis has been rather primitive, the economic
benefits likely to accrue to a variety of life and property forms from the
control of acid precipitation have been surveyed. It must be recognized,
given the robust techniques available for doing economic assessments of the
effects of acid precipitation, that the estimated magnitudes presented in this
chapter cannot be justified indefinitely.
50
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On the basis of our survey and synthesis of a fairly large volume of
biological literature and stock, price, and output information, we conclude
that if sufferers are viewed as either having to accept it or to take actions
at their own expense to negate its effects, it is very unlikely that the
current annual benefits of controlling acid precipitation for existing
economic activities exceed $5 X 10 1978 dollars in Minnesota and the
states east of the'Mississippi River. Our best estimates are that $2 x 109
is^in materials benefits, $1.75 X 109is in forest9ecosystem benefits, $1 X
10 is in direct agricultural benefits, $0.25 X 10 is in aquatic ecosystem
benefits, and $0.10 X 1.0 is in other benefits, including health and water
supply systems. The rationales supporting each of these sector estimates are
presented in the chapter text. With the exception of a few instances where
analogies could be drawn with the results of other studies using more robust
estimation techniques, all these estimates disregard acid
precipitation-induced price, activity, and location changes. We therefore
have substantially more confidence in the rank-ordering by sector of the
current annual benefits than we do in our estimates of the absolute magnitudes
of these benefits.
If acid precipitation events continue to worsen, certain sectors could
readily climb in the above ranking. For example, aquatic ecosystems currently
have a relatively low position only because the geographical scope and
severity of the aquatic acidification problem does not yet seem to be large
enough to reduce substitution possibilities greatly across fresh-water fishing
and hunting sites. Because of the water and soil treatment facilities already
in place that can readily be adapted to handle liming procedures, the acid
precipitation control benefits accruing due to the prevention of human health
effects, indirect agricultural effects, and household, commercial and
industrial water supply system effects are now and are likely to continue to
be insignificant compared to the other classes of effects. Large-scale liming
of aquatic and forest ecosystems appears to be neither technically or
economically feasible.
The preceding conclusions are not the major conclusions we wish to draw
from our survey and synthesis of the acid precipitation literature. We are
unconvinced that either the above ordering or the above absolute magnitude
estimates of the- current annual benefits of control (even if correct)
constitute the really important issues to consider when evaluating the acid
precipitation problem. Indeed, we are unable to reject the discomforting
notion that the effects for which one may feel secure using these simple or
the much more sophisticated but still conventional methods of economic
analysis reviewed in Chapter I are those having the least long-term economic
significance. Instead, we suspect that these important issues relate to the
impact of acid precipitation upon the stock and the assortment of natural
resources. The next two chapters consider the implications of some of these
51
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issues regarding resource stocks and assortments for assessments of the
benefits of controlling acid precipitation.
52
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REFERENCES
— It should be noted that there may be some exceptions to acid precipitation
acting as a sort of negative fertilizer. For example, Maugh (1979) reports on
a TVA-sponsored study which found that if the sulfur emitted by coal- burning
power plants in the Tennessee Valley region were removed, and not replaced by
another sulfur source, crop production, especially cotton, would decline by at
least 10 percent. Tisdale and Nelson (1976, p. 411) point out that raising
soil pH in the Deep South to more than 6.0 may actually be harmful to yields.
2/
See Freeman (1.979) for a presentation of the conditions under which it
would be a good approximation. For the Adams, et al. (1979) study, the on-
farm value of the 14 crops was 16 percent less than the estimated sum of
producer rents and consumer surpluses. When cotton was excluded the non- farm
value of the 13 remaining crops was 20 percent less than the estimated sum of
the producer and consumer surpluses.
3/
— In a news item, Rich (1979) reports that field studies m southern Poland
have attributed drops of 13 to 18 percent in the photosynthetic activity of
pine needles subjected to wet and dry sulfur deposition. Dennis Knight of the
Department of Botany at the University of Wyoming informs us that the Polish
investigators believe that this reduction is due to SO entering the leaf
through the stomata and then being converted to ^SO^ ¦W-J-J'-h-i-11 the leaf. This
perspective may be contrasted with the bulk of the published literature which
emphasizes the growth reducing properties of cuticular erosion and nutrient
leaching from leaves and soil. Apparently, the Polish studies have not yet
been widely distributed.
4/ . . . ...
— In principle, the spreading of sufficient lime on top of forest soils
might raise pH before precipitation moves down the soil column. Other than a
vague statement by Rich (1979) on aerial lime spraying in Poland, we have
found no commentaries on either the technical or the economic feasibility of
this practice.
5/ .....
— If the forest growth effects of acid precipitation are viewed as analogous
to a selective cutting policy, one could draw upon the technical forestry
literature relating the effects of this type of cutting upon these com-
ponents. We have not exploited the analogy here because of the likely wide
53
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variations in responses of the components to tree species mixes, topographical
attributes, and other factors.
— Let V be the present value ^15 .32 x 109) of the stream of losses, let A
be the annual losses ($9.69 x 10 ) , and let r be the rate of discount. Then:
1+r —
V = A C )[l - (1+r) ].
r
The term in brackets can obviously be disregarded when one is dealing with an
infinite future.
According to the Economic Research Service (1.974, p. 37), 1970 self-
supplied industrial water from saline sources in the United States was 10.07 x
10 gallons/day. It is unclear, however, how this use is distributed over
ocean, estuary, and saline groundwater sources. The pH of any saline source
could obviously differ greatly according to the extent to which the acidic
fresh-water had been diluted by the saline water.
8/ . .
~ In Hick's (1973) terms, the qualifying "if..." phrase indicates that an
equivalent, as opposed to a compensating, measure of value is being em-
ployed. In effect, it is assumed that those who cause acid precipitation,
rather than those who suffer from it, have the de facto property rights to the
air resource. Moreover, since all our crude assessments are in willing-
ness-to-pay terms, they will be less than if the assessment had been made in
willingness-to-accept compensation terms TRandall and Stoll, (1980)].
54
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y • • »
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Ill, DECISION PROBLEMS IN THE CONTROL OF ACID PRECIPITATION:
NONCONVEXITTES AND IRREVERSIBILITIES
Acid Precipitation Dose-Response Functions
The sole recurring theme of the previous two chapters is that empirical
application of economic methods for assessing the benefits of acid precipita-
tion control generally requires prior knowledge of the response of biological
and material entities to variations in acid precipitation exposures, Increas-
ing pollution has been treated as leading to progressive deterioration in the
size of the resource stock and the flow of material and life support services
issuing from it. Moreover, this deterioration could be reversed and, by-
reducing the level of pollution, recovery could occur along the same path as
did deterioration. This behavior is a standard representation in the environ-
mental economics literature. It leads to results in which some immediate
environmental damages are borne in order to obtain some of the immediate
benefits that a productive but polluting activity confers. Assuming the
pollutant to be acid precipitation, Figure 1 introduces the costs of control-
ling the acid precursors in a comparative static version of the standard
representation. Unit prices of the elements of the resource stock and of
pollution control equipment are assumed constant.
The economically efficient pH level in Figure 1 will, be at A, where the
marginal benefits of reduced acidity are equated to the marginal costs of
controlling acidity. The marginal benefit of reduced acidity is the marginal
damage that is avoided by having less acidity. That a point such as A is
optimal can be seen from the following simple argument. Suppose that the
benefits are measured by the size of the fish population denoted Pop. The Pop
is an increasing function of the pH level as is the cost of control, C. The
net benefit of a given pH level is
it = PopCpH)-C(pH) (1)
This expression is maximized when its first derivative is set equal to zero,
that is:
d(PoP) = dC
d (pH) d(pH) .
65
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Figure 3.1
The Standard Representation
d(Control Costs)
d (pH)
d(Damages)
d (pH)
PH ^ ^ A . „. A
Greater Acidity —
66
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The left hand side is the marginal benefit (or marginal damage avoided) and
the right hand side is the marginal control cost. In terms of Figure 1, for
states to the left of A, the additional costs of control exceed the additional
benefits of reduced damage; to the right of A, the opposite is true. A
decisionmaker who wishes to maximize net economic benefits will, therefore, be
striving for .a point such as A. If instead the vertical axis represents the
present value of a stream of expected damages and control costs, he will also
strive for A, given independent damages and control costs across periods. Tn
short, whether observed or inferred by benefit-cost analysis, the "prices" of
additional damages or additional controls given to the decisionmaker in the
neighborhood of an initial acidity state will always be a signal to move
toward that state maximizing the net benefits of control.
There exist at least two reasons why the form of the underlying ecosystem
dose-response function in the preceding figure may be inaccurate insofar as
acid precipitation is concerned. The nature of the inaccuracies implies that
the rationales usually offered for compromising between the benefits of
pollution-generating activities and the prevention of ecosystem damages mav
not always be applicable to acid precipitation issues.
The All.-or-Nothing Feature: Nonconvexities
The preceding analysis has presumed that, within any one period, the
increments to ecosystem damages are monotonj.tally increasing with respect to
ecosystem acidity. At least insofar as fish and some other aquatic organisms
are concerned, this presumption is contrary to some published evidence [Raddum
(1978)]. Consider, for example, the following two tables constructed from
data appearing in the study of Butler, et al. (1973) on the impac^f acid
mine drainage upon fish and other organisms in Pennsylvania streams.— For
varying sustained pH levels, Table 1 shows the number of stream sections that
had fish populations out of 25 sampled sections in different streams; while
Table 2 shows, of the 116 fish species known to exist in Pennsylvania as of
1957, the variation with respect of pH of the number of species in these
stream sections. Table 2 also indicates the pH levels at which assorted game
and food fish disappeared due to lethal effects and/or recruitment failures.
Both tables exhibit very rapid declines in fish populations once pH drops
below 6.5. However, this decline itself rapidly decreases
2 2
K9 Population/aPH )>0l as PH levels reach and drop below 6.4. Assuming that
the implicit unit price of remaining fish and species 1S a constant, Figure 2
is a sketch of Tables 1 and 2.
Returning temporarily to Figure 1, in order that A be a maximum' rather
than a minimum, it is necessary that,
67
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Table 3.1-Sections with Fish at Various PH Levels for a Sample of Pennslyvania
Streams Suffering from Acid Mine Drainage
Stream Sections
with Fish
24
12
6
3 .
1
0
From: Butler, et a I., (1973, P. 112)
Table 3.2-Variation of Number of Fish Species with Respect to pH Levels for
a Sample of Pennslyvania Streams Suffering from Acid Mine Drainage
Number of
No Longer
EJ±
Species Present
Present
> 6.5
116
6. k < pH < 6.5
48
Catfish, smelt
6.2 < pH < 6.^
41
Redfin pickerel
6.1 < pH < 6.2
36
6.0 < pH < 6.1
34
Smal1 mouth Bass
5.9 < pH < 6.0
18
Brown Trout
5.6 < pH < 5-9
12
5.5 < pH < 5-6
10
Yellow perch
5.2 < ph < 5-5
9
5.0 < pH <5.2 ""
8
Brook Trout
k. 7 < pH < 5 • 0
7
Largemouth Bass
^. 6 < pH < I*. 7
5
Chain pickerel
"
0
From:
Butler, et a 1 . , (1973, Pp-
96 99, 1 1 4)
6.4
6.3
5.9
5-3
4.6
4.5
68
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Figure 3.2
The Nonconvexity Problem
d(Control Costs)
d (pH)
d(Damages)
7.0
pH
6.0
4.0
5.0
Greater Acidity —^
69
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d2 (Pop)
d(pH)2
d2C
d(pH)2
(3)
and sufficient that
d2(Pop) d2C < Q
d(pH)2 d(pH)2
(4)
A further sufficient condition is
d (Pod)
< o, and
> 0,
(5)
2
2
d(PH)
d (pH)
as Figure 1 presumes.
2 2
The data in Table 2 shows that d (Pop)/d(pH) > 0. Hence the sufficient
conditions may not^e satisfied at a point where marginal benefits are equated
to marginal costs.— The second order necessary condition could be violated
turning such a point into a local minimum rather than a maximum. This is what
happens at point C in Figure 2. The observed or inferred current prices
existing at and to the right of C provide unreliable signals about whether the
decisionmaker is at a maximum, or minimum and the direction in which he must
move in order to obtain an increase in net benefits.
It is also evident in Figure 2 that if the environment were already
highly acidified, a large cost burden with relatively few benefits would have
to be borne prior to reacquiring the benefits of a relatively nonacidified
state. Thus , given limited restoration resources, it may no longer appear
worthwhile to restore the nonacidified state. As a result, decisions to
control acid precipitation may have strong "all-or-nothing" elements: inter-
mediate control measures can lead to burdensome control costs while generating
few environmental benefits. Literal interpretations of prices applying to
initial states lying at and to the right of C in Figure 2 would guarantee high
levels of acidification: the ecosystem destruction wrought has been so great
that the benefits from reduced acidification appear minor. To use an extreme
example, the benefits from increasing fish recruitment cannot appear large
when there are no fish around who can reproduce. Only by undertaking the far
more arduous and complex task of empirically accounting for the ecosystem and
economic adjustments and consequent changes in price structure resulting from
70
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Figure 3.3
Possible Time Path of Acid Precipitation Effects
PH = 5.65
Time
'1
0
71
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a large move from an initial state at or to the right of C to a state in the
vicinity of B could the benefits of reduced acidification be captured. —
The Now-or-Never Feature: Irreversibilities
Tn the abovewe-have remarked on the distorted picture of reality that
market or market-like price signals can introduce when the incremental damages
of acidification within a period are declining. It is argued that if a state
of high acidification is reached, the decisionmaker must expand the scope of
his vision and analysis to include discrete rather than marginal alterations
in existing states. Given this scope, we have presumed that he is able to
reverse the current and future consequences of current and past acidification
so that acidification levels henceforth remain in the vicinity of B. In
short, we have presumed that the marginal damage function in Figure 2 is
invariant with respect to both the status quo point and the direction of
movement. The presumption appears to be incorrect for the effects of acid
precipitation upon many components of forest and aquatic ecosystems.
Figure 3 is consistent with findings which attribute via soil amendments
stimulator [Lee and Webber (1979); and Maugh (1979)] and debilitating
[Jonnsson and Sundberg (1972); Tamm (1976)] effects upon plant growth to acid
precipitation. In Figure 3, it is assumed that over some decade-or-longer
period, a forested region is annually subjected to precipitation averaging pH
"3.5. The line labelled V5.65 refers to a "no acid precipitation regime. It
decays slowly because of the natural tendency over millennia of soils in humid
regions to become acidified. Under an acid precipitation regime, where forest
management practices and influential factors other than acid precipitation are
assumed invariant, the line labelled pH = 3.5 becomes relevant. Acid
precipitation thus accelerates the natural tendency over time of soils to
become acidified, as McFee, et al. (1976) and Peterson (1980) emphasize.
Over the t - t interval, the acid precipitation (or acidifying
deposition) is neutral with respect to or contributes positively to forest
yields. The sulfur and nitrogen compounds in the precipitation can directly
and indirectly enhance the nutrient content of the forest soils. After t ,
however, the atmospheric inputs of positively charged hydrogen ions are
greater than the ability of the forest soils to neutralize them. Organic and
mineral nutrients are then leached from the forest soils at a rate more rapid
than they can be replaced from atmospheric, decomposition, weathering, and
microbial sources [Likens (1977)]. Simultaneously, phytotoxic metals, such as
soluble inorganic aluminum and iron, are made more available and organic
matter accumulates to seal the upper layers of the soil column while
permitting various phytotoxins to be formed from the matter [Brady (1974,
Chap. 14)]. As time passes, with the frequency and intensity of acid
precipitation invariant, the rate of nutrient leaching and phytotoxin
72
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formation accelerates [McFee (1978, p. 66)]. In turn, this is expected to
cause forest yields to decline at an increasing rate. Moreover, since water
bodies serve as catchment basins for land areas, they too are expected to
experience increases in hydrogen ion concentrations and heavy metals.
Once levels of- forest soil (and water body) acidification beyond t^ are
widespread, there is no evidence that large-scale reverses are economically
for even technically) feasible in anything other than geologic time. The
addition of lime to acidified soils and water bodies is the only widely
considered technical remedy. It is, of course, a commonly used remedy in
agriculture. However, as Tisdale and Nelson (1976, p. 428) note, limestone
particles cannot move in the soil and must therefore be placed where they are
needed in the soil column. Rorison (1980, p. 206) remarks that isolated
additions of lime to acid sulfate soils are of no lasting value. Tilling lime
into extensive areas of forest soils with striding trees would seem an
economic, if not a technical, impossibility. - Moreover, Tamm (1976, p. 338)
adds that when lime has been added to forest soils in small-scale experiments,
tree growth rates have typically not been enhanced. He attributes this to the
tendency of the lime to immobilize the nitrogen in organic matter and thereby
reduce its availability to trees. Abrahamsen, et al. (1980, p. 357) found
that soil animal populations nearly always failed to increase when soil
acidity was reduced by liming.
The practicality of large-scale liming to resolve the problems life forms
have in acidified water bodies appears to be no better than for forest soils.
As Holden (1979, p. 11) emphasizes, the effective use of lime to raise the pH
of natural water bodies requires a great deal of information about the hydro-
logical and chemical properties of each body of water. He notes that most of
the added lime is flushed out, fails to dissolve, or remains in the sediment.
Reactivity of the lime will vary with its purity, particle-size, hardness,
magnesium content, chemical constituents and stratifications of the water bodv
by season, and a host of other factors.
Finally, according to Dickson (1978, p. 58) and Bengtsson (1980), care
must be taken when raising aquatic pH levels to ensure that they are not
allowed to persist in the 4.5-6.0 range. Heavy metals, particularly the
inorganic aluminum that acidified waters contain in abundance, becomes espec-
ially toxic to ol-der fish. Thus liming must be calibrated for the state of
the fish aswell as for the state of the water. This toxicity is dramatically
illustrated in Bengtsson's (1980) report on the successes of Swedish lake
liming experiments. His data indicate that the perch in one lake before liming
were all large and mature individuals. After liming, the number of perch
increased by a factor of 100 but the size of the representative individual had
declined by a factor of 10. Liming redresses the balance of harm by
destroying the older and larger fish surviving the original acidification. As
Bengtsson (1980, p.35) states, "when liming an acid lake the organisms suffer
73
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a transition period before the metals have been precipitated . . . liming has
even killed salmon and trout when the aim was to save the fish." This problem
is further substantiated by Professor Harold Harvey a zoologist at the
University of Toronto. In a July 15 article on the "Acid Lakes" in the
Toronto Globe and Mail, Professor Harvey is quoted as saying, "Noone knows to
what degree -of certainty what liming will do." He adds that indiscriminate
liming "may improve the pH and end up killing all the fish" by setting off a
chemical reaction involving lime and heavy metals in the lake. if continuing
acidification requires intermittent liming, Bengtsson's (1980) data are
therefore consistent with an inability to retrace the damage function relevant
to declining pH.—
This litany of complexities in deciding how much lime an acidified water
body requires and when this lime is required by no means suggests that wide-
spread and large-scale intermittent or continuing liming is likely to be
economically attractive. At best, the litany suggests that a subtraction of
the expected costs of successful liming from the marginal damage (marginal
benefit) curve of Figure 3 will drastically lower the curve when the status
quo point is less than pH = 6.0. Thus for given marginal costs of reducing
actual emissions, even though pH may vary over the same interval, the net
benefits of recovering the pH at the high end of the interval will be less
than the net benefits of preventing a decline of pH to the low end of the
interval.: the marginal benefits of ranging pH are less than the marginal
benefits of preventing declines in pH.—
As is true for nonconvexities, the irreversible features of acid precip-
itation-induced ecosystem deterioration can mean that current prices will
provide misleading signals about the most valuable corrective steps to take.
Standard economic representations of the efficient depletion of environ-
mental or other assets require that the present value of the gains from
further depletion in any period be equal to the sum of the depletion losses
and interest charges. When property rights to the resource are secure, this
implies, as Scott (1973) has shown, that the present value of the marginal
unit of depletion in each period must be the same in all periods; otherwise,
gains could be obtained by shifting units of depletion from periods where
their present value is lower to those where it is higher. Delays avoid the
costs of engaging in the activity that causes the depletion, but they also
require an increased waft for the benefits the activity yields. Given a
positive discount rate, if the present value of marginal depletion units is to
be the same across all periods, the current undiscounted value of the marginal
unit in each subsequent period must be greater by the rate of interest than
the current value of the marginal unit in the immediately proceding period.
In short, the rate of increase in the va
7
tend to approach the rate of interest. -
lie of the resource that remains will
74
-------
The above result explicitly weighs the impact of current depletion
activities upon the opportunities for depletion that remain in future periods.
This result can be contrasted with a situation where the depletion is
reversible. Consider, for example, the agriculturist who acidifies his soils
by the use of ammonia fertilizer amendments. He will simply allow
acidification to continue until the current period net gain from further
acidification no longer exceeds the current period net gain from, restoration
accomplished by liming. Since his soil acidity can easily be reduced by liming
at any time he wishes, there is no reason for him to weigh the impact of his
current fertilization practices upon his future opportunities for growing
corps. There are no future opportunity losses for him to count as a cost: he
will therefore base his decisions only upon current market prices.
Acid precipitation accelerates the rates of depletion of the buffering
capacities of forest soils and water bodies in addition to reducing the
current flows of material goods and amenity and life support services from
these resources. Any control plan which accounts only for the value of the
reduction in current flows, as registered in actual or inferred current market
prices, will thus underestimate the damages acid precipitation is causing.
Stated in an alternative manner, even though the current net benefits of
continuing acid precursor emissions may still be positive, it may be optimal
to cease emitting. Some immediate losses must be borne in order to avoid the
possibility of even greater losses later on that the current precursor
emissions can readily cause.
If the benefits of acidification decline over time relative to the bene-
fits of natural environments, the irreversible effects of acidification, when
combined with a positive discount rate, lend the acidification issue a now-or-
never character. This is most easily seen by assuming perfect foresight and
by disregarding anv short-term fertilization benefits. In particular with a
positive discount rate, any delay in causing above-background acidification
will only make it look progressively less attractive. Not only are the
relative benefits of acidification declining over time by assumption, but the
positive discount rate causes the present value of acidification benefits to
be reduced with every delay. In the meantime, since the unacidified
ecosystems already exist, the material goods and life support and amenity
services they produce continue unabated. Therefore, cet. par., the net gains
from ecosystem acidification will never be greater than they now are.
The presence of declining relative benefits of acidification (or increas-
ing relative benefits for preserving natural environments) is a necessary
condition for the above conclusion. As set forth by Smith (1974) and others,
two key propositions lead to a prediction of increasing relative benefits for
natural environments. First, environments that have remained unsullied by
man's activities and artifacts are superior goods. That is, as real incomes
75
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increase, the willingness-to-pay for natural environments increases at an even
greater rate. Man-made substitutes become progressively less attractive.
Second, because of the imperfect reproducibility of natural phenomena, techno-
logical change tends to reduce the supply prices for man-made goods relative
to the supply prices for natural environments. The obvious general conclusion
is that both the relative cost of supplying and the willingness-to-pay for
natural environments are going to increase progressively over time. Both of
these countervailing supplv and demand forces imply that the citizenry will
attach increasing values to natural environments relative to fabricated goods.
When combined with the fact that at present very little is known about
many of the social, environmental, and financial consequences of ecosystem
acidification, the irreversibility phenomenon introduces yet another basis for
expecting declines over time in the relative benefits of acidification. As
Arrow and Fisher (1974) have demonstrated, the possibility that current
actions might burden and constrain (deplete) future opportunities must be
counted as a cost against the current action. In short, the irredeemable
nature of current acidification may foreclose valuable future options, whether
due to currently unknown technologies, price structures, or changing tastes.
Since new information can be exploited only if irreversible consequences have
been avoided, the consequences of a decision to acidify cannot be undone even
if the new information suggests that the decision was mistaken. Thus if
acidification is ultimately discovered to have only trivial irreversible and
undesired consequences, a delay in the decision to acidify can only mean that
the present value of its ultimate benefits is reduced. On the other hand, if
these undesirable consequences will actually be present, delay serves to
enhance the probability they will be discovered, thus making a decision to
acidify appear less attractive than it now does. Of course, the chances of
discovering nontrivial adverse consequences of acidification might reasonably
be directly related to the completeness of the existing state-of-knowledge
about these^consequences and the prospects for rapid advances in this
knowledge. — If this relation is direct, it follows that the expected
decline in the relative benefits of acidification will be less than otherwise:
delays in the acidification decision are then made to appear more favorable.
Summarv and Conclusions
We have discussed two decision problems in the optimal control of acid
precipitation. The first problem concerns the shape of the dose-response
function while the second concerns a possible ratchet-effect associated with
movements along a given dose-response function.
The shape of the dose-response function determines the shape of the
marginal damage (benefit) function associated with varying levels of acidity.
Studies of the impact of acidity on fish species suggest that the relevant
76
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marginal damage curves are nonmonotonic functions of the acid level. As a
result there may exist more than one level of acidity and associated price
structure which balances the marginal benefits and marginal costs of reducing
acidity. Not all of these levels and price structures will be welfare max-
imizing, some may be welfare minimizing in the sense that small deviations in
either direction may improve welfare.
The analysis presented with respect to the shape of the dose-response
function did not explicitly consider the dynamic costs of adjustment. If an
ecosystem becomes highly acidified as a result of having made decisions based
upon prices in the neighborhood of a minimum point, then it may become optimal
to forget about attempts to control. This result occurs because the possibly
large short-run costs of control dominate the benefits of the action. This
result was obtained, by Forster (1975) in a study of water pollution control.
For sufficiently high levels of pollution, it is economically optimal to allow
a waterway to become biologically dead. This result depends upon a high rate
of discount. As the discount rate approaches zero, the result evaporates,
This is not surprising since the adjustment costs loom large in the short-run
while the discount rate shrinks the present value of future benefits. We will
not enter into a debate over the appropriate discount rate--but its importance
should be noted.
The ratchet-effect of the dose-response function refers to the possible
irreversibility of the environmental disruption caused by increased acidity. A
given increase in acidity reduces natural resources by an amount AR determined
by the dose-response function. Subsequent equivalent reductions in acidity
may not increase natural resources by as much as AR or may not increase them
at all. As long as this relationship is known and understood by all, then
market price signals should correctly reflect the net benefits of the
situation. If the relationships are not known, however, then current market
prices will not reflect the future costs of current actions and acidification
will proceed too far.
These decision problems suggest certain research and policy strategies
for acid precipitation. The potential irreversibilities dictate that systems
which are on the verge of acidification be subjected to immediate research to
ascertain the properties of their dose-response functions. Fisher and
Krutilla (1974) have argued that uncertainty regarding any irreversible
destruction that might be caused by an activity may be sufficient reason to
justify postponing the activity until the relevant information has been
collected. In the case of disruption due to acid precipitation, the activity
is now occurring and may intensify even while the information gathering is
taking place.
The discussion regarding the shape of the dose-response function suggests
77
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a possible poli Cy strategy for control in aquatic ecosystems. It suggests
that systems may be classified into two groups according to their current
acidity levels. The first group consists of those systems whose pH levels are
sufficiently high (to the left of B in Figure 2) to make them worth saving.
costs dominate potential benefits. - this negative prescription mav be put
in a more positive light. Much work needs to be done quickly to keep more
systems from moving from the first group to the second. At the same time, the
frequency with which this nonconvexity issue occurs in the responses of eco-
systems must be more completely identified. Table 2 raises the possibility
that it could be a creature of ecosystem diversity. It is to the problem of
valuing this diversity that we turn in the next chapter.
The second group
worth saving--the adjustment
78
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REFERENCES
— Although waters that are acidified from mine drainage perhaps contain
more iron compounds than waters derived from acid precipitation, mine drainage
otherwise seems to have a chemistry generally similar to that of
precipitation-derived water. The high concentrations of iron hydroxides
present in acid mine drainage are known to intensify the harmful effects of pH
<. 6.5.
The situation in lakes may be different than in streams. Streams may be
more capable of flushing themselves than lakes. Also the ability of fish to
migrate in order to avoid high levels of acidity may be greater in steams than
in lakes.
Fromm (1980) warns that "Data relating to the specific effect of low pH
on growth of freshwater fishes are ambiguous." It is significant for the
purposes of the present paper which seeks to point out potential difficulties
in the control of acid rain to fird one example of the type presented.
However, the frequency with which this nonconvexity issue occurs in the
responses of ecosystems must be more completely identified.
?¦/ . ....
Arthur Okun has an interesting comment on economic optimization:
"The wise economist knows, however, that merely finding a marginal- that
is not sufficient for an evaluation. A rigidly incrementalist approach
can lose sight of major opportunities. Locating the least soggy spot in
a swamp is not optimizing if high ground is accessible outside the
swamp."
The Political Economy of Prosperity (Brookings Institution, 1970), p. 4.
3/
— There is some evidence that there may be nonconvexities present m the
benefit function for improved forest aesthetics. For example, in a
psychological study of individuals' responses to insect and damaged southern
pine forests, Buhyoff and Leuschner (1978) found that "visual preference"
dropped rapidly as damages increased to 10 percent of the forested area but
that preference declines were minor thereafter.
4/
— In principle, the spreading of lime on top of forest soils might raise
precipitation pH before it moves down the soil column. We are unaware of any
commentaries on either the technical or the economic feasibility of this
79
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practice.
— The tone of Bengtsson (1980) is optimistic with respect to the
practicality of large-scale liming to restore acidified water bodies. He
tends, however, to abstract from details that might compromise the optimistic
tone. Barnes (1979,.. p. 1.232) speaks approvingly of the prospects for
neutralizing to be obtained by placing a lime column in a river bank.
Andersson (1980, p. 6) reports that six-fold higher neutralization effects
have been acquired using sodium hydroxide rather than lime- in laboratory
experiments.
6/ .....
— Houck (1977) provides a technique for specifying and estimating
nonreversible functions.
7/ . ...
— Let the extraction of the marginal depletion unit be delayed frnm to
t . This delay would cause the undiscounted net return i_n t to be (p^-pt c),
where the dot indicates the time derivative of price. Assuming c=0, if"
instead the depletion unit is extracted in t and the net returns (p0c)
o ,
invested m some other asset, the value of the investment in t would be (Pq~
c)d+rk"), where k is the time interval between t, and t , and r is the rate of
• 1 o
interest. Upon equating (p^-pt^-c) and (pQc)(1+rk), and simplifying, we are
left with p = r(p c), which*says that in a regime of secure property rights in
the resource, its market price increases at the rate of interest over time.
8 /
— With the possible exception of limnology, where experimental means have
been extensively used to study the behavior of ecosystem functions such as
productivity and decomposition. TVervelde and Ringelberg (1977)], many
ecologists view the prospects for rapid accumulation of new information as
unfavorable. Most of the relevant ecological disciplines lack a corpus of
empirically testable propositions derived from a broadly encompassing
analytical structure as well as quantitative bits of information that have
been related to or associated with each other [Clark, Jones, and Helling
(1979)] . Resort, therefore, has been either to simulation models or to the
real-time tracking of the behavior of a system under stress.
9/
~ Allen Kneese has reminded us that the West Germans approximate this
policy in their assignment of separate rivers and streams to pristine and
highly polluting uses. Note also that the PSD program of the 1977 Clean Air
Act Amendments in the United States is consistent with this policy approach.
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BIBLIOGRAPHY
Abrahamsen, G., et al. , "Effects of Artificial. Acid Rain and Liming on
Soil Organisms and the Decomposition of Organic Matter," in T.C.
Hutchinson and M. Havas, eds. , Effects of Acid precipitation on
Terrestrial Ecosystems, New York; Plenum Press (1980), 341-362.
Andersson, F., Swedish Research on the Effects of Acid Deposition on Forests
and Waters, A paper presented at the International Conference on the
Ecological Impact of Acid Precipitation, Oslo, Norway (March 11-14, 1980).
Arrow, K.J., and A.C. Fisher, "Environmental Preservation, Uncertainty, and
Irreversibility," Quarterly Journal of Economics 88(May 1974), 302-319.
Barnes, R.A., "The Long Range Transport of Air Pollution: A Review
of European Experience," Journal of the Air Pollution Control
Association 29(December 1979), 1219-1235.
Bengtsson, B., "Liming Acid Lakes in Sweden," Ambio 9(1980), 34-36.
Brady, N.C., Nature and Properties of Soils, New York: Macmillan and Company
(1974) .
Buhyoff, G.J., and W.A. Leuschner, "Estimating Psychological Disutility from
Damaged Forest Stands," Forest Science 24 (June 1978), 231-246.
Butler, R.L., et al., Fish and Food Organisms in Acid Mine Waters of Pennsylvania
USEPA Ecological Research Series EPA-R3-73-032, Washington, D.C.: USGPO
(Feb. 1973).
Clark, W.C., D.D. Jones, and C.S. Hell.ing, "Reasons for Ecological Policy Design:
A Case Study of Ecosystem Management," Ecological Modelling 7(1979),
1-53.
Dickson, W., "Liming," in G. Hendry, cd., Limnologlcal Aspects of Acid
Precipitation, Upton, N.J.: Brookhaven National Laboratory, BNL51074
(Sept. 1978), 57-58.
Fisher, A.C., and J.V. Krutilla, "Valuing Long Run. Ecological Consequences and
Irreversibilities," Journal of Environmental Economics and Management 1
(.Tune 1974), 96-108.
Forster, B.A., "Optimal Pollution Control with a Non-Constant Exponential
Decay Rate," Journal of Environmental Economics and Management 2(Sept.
1975) 186-194.
Galloway, J.N., et al., "Acid Precipitation: Measurement of pH and Acidity,"
Limnology and Oceanography 2(1979), 1161-1165.
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Glass, N.R., cd., Environmental Effects of Increased Coal Utilization:
Ecological Effects of Gaseous Emissions from Coal Combustion,
Corvallis, Oregon: USEPA-600/7-78-108 (June 1978) .
Holden, A.V., "Surface Waters," in M.J. Wood, cd., Ecological Effects of Acid
Precipitation, A Report of a Workshop held at Gatehouse-of-Fleet, United
Kingdom; Sept'.'4-7, 1978, Surrey: United Kingdom: Central Electricity
Research Laboratories (July 1979) .
Houck, J.P., "An Approach to Specifying and Estimating Nonreversible Functions,"
American Journal of Agricultural Economics 59(August 1977), 570-572.
Jonsson, B., and R. Sundberg, Has the Acidification by Atmospheric pollution
Caused a Growth Reduction in Swedish Forests? Research Note No. 20~,
Department of Forest Yie.1.d Research, Royal College of Forestry, Stockholm,
Sweden (1972) .
Lee, J.L., and D.F,. Weber, "The Effect of Simulated Acid Rain on Seedling
Emergence and Growth of Eleven Woody Species," Forest Science 25
(Sept. 1979), 393-398.
Likens, G.E., Biogeochemistry of a Forested Ecosystem, New York: Springer-
Verlag (1977) .
Maugh, T.H., "Sulfur Pollution May be Good for Plants," Science 205(July 25,
1979), 383.
McFee, W.W., et al. , Acid Precipitation Effects on Soil pH and Base Saturation
of Exchange Sites, U.S. Forest Service Technical Report NE-23, Washington,
D.C. : USGPO (1976) .
McFee, W.W., "Effects of Acid Precipitation and Atmospheric Deposition on
Soils," In J.N. Galloway, et al,, A National Program for Assessing the
Problem of Atmospheric Deposition (Acid Rain), A Report to the President's
Council on Environmental Ouality by the National Atmospheric Deposition
Program, Fort Collins, Colo.: Natural Resource Ecology Laboratory,
Colorado State University (Dec. 1.978), 64-73.
Perhac, R.M., Transcript of testimony before the National Commission on Air
Quality, Washington, D.C. (Oct. 5, 1979).
Peterson, L., "Podzolization: Mechanism and Possible Effects of Acid Precipitation,"
in T.C. Hutchinson and M. Havas, eds. , Effects of Acid Precipitation
on Terrestrial Ecosystems, New York: Plenum Press (1980), 21-42.
Raddum, G., "Invertebrates: Quality and Quantity as Fish Food," in G.
Hendry, cd., Limnological Aspects of Acid Precipitation, Upton, N.Y. :
Brookhaven National Laboratory, BNL 51074 (Sept. 1978), 21-42.
Rorison, I.H., "The Effects of Soil Acidity on Nutrient Availability and
Plant Response," in T.C. Hutchinson and M. Havas, eds., Effects of
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Acid Precipitation on Terrestrial Ecosystems, New York: Plenum Press
(1980), 223-237.
Scott, A., Natural Resources: The Economics of Conservation, Ottawa, Ontario:
McClelland and Stewart (1973) .
Smith, V. K."Intertemporal Production Externalities, Technical Change, and
Public Expenditure Analysis," Journal of Environmental Economics and
Management l(Aug. 1974) 120-131..
Tamm, C.O., "Biological Effects in Soil and on Forest Vegetation," Ambio
5(1976), 235-238.
Tisdale, S.L., and W.L. Nelson, Soil Fertility and Fertilizers, New York:
Academic Press (1976) .
83
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IV. VALUING ECOSYSTEM FUNCTIONS: THE EFFECTS OF ACIDIFICATION
Iv.production
Population growth and human territorial expansion are placing unprec-
edented burdens on ecosystems. Farmlands are being converted to suburbs,
while forests are being converted to farmlands. The Amazon forest, earth's
richest biological region, is losing to development each year an area half the
size of Great Britian [Prance, (1977)]. Pollution is now recognized as a
global problem with particular emphasis on acid precipitation and the
greenhouse effect. Estimates of species lost to extinction worldwide are as
high as 1000 per year [Myers (1979)] .
But what values are reflected by this and similar data on our dwindling
natural environment? Part of the answer can come from a study of ecological
systems placed in an economic framework. Ecological systems must be reduced
to tractable analytical, frameworks which can then be incorporated into
economic models that are able to ascertain benefits and costs. For example,
in environmental economics, studies have estimated the willingness to pay for
trout fishing along a particular stream. These studies could then be used to
estimate the value of the effect of acid precipitation on trout populations.
Trout have value to people, and if the trout were to vanish so would the
benefits of the fishing. But trout are only one species in a complex
ecosystem. By removing other species, say certain insects that may appear to
be of no value, the trout may also vanish. Thus, a proper valuation of an
ecosvstem entails not just the valuation of end products like trout, but a
recognition of the interactions between trout and other species so that the
value of these other species can be established. By doing this, better
estimates can then be made of the uncompensated costs associated with
population growth and industrial expansion which affect the sources of
pleasure and life support services that ecosystems provide.
Ecosystems are incredibly complex. They may be composed of thousands of
species interacting in diverse ways. Each species fills a niche in the
overall system, and depends on one or more of the other species for survival.
But complex systems are not foreign to economists who have the difficult task
of sorting out complex economies. Notions such as short-run and long-run
equilibriums, steady states, and exogenous shocks appear to be applicable to
both ecosystems and economies. In addition, the same type of questions arise
84
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in either system. For an economy, the economist uses models to determine the
effect a tax in one sector has on other economic sectors. For an ecosystem,
the ecologist (and the economist} may need to know the effect a particular
pollutant that harms one insect species will have on all other species.
The parallels1 ¦ between ecosystems and economics suggest that similar
models may be used for each. Moreover, if this can be accomplished, then
linking ecosystems with economies may be possible. Such a linkage would
permit not only detailed descriptions of how a pollutant will effect an
ecosystem, but how the changes brought about in the ecosystem will effect the
economy and, in turn, how these changes in the economy will influence the
ecosystem.
Ecologists attempt to answer such questions by using energy as a unit of
value. By measuring the flow of energy through an ecosystem, one can
determine how an exogenous shock might affect that energy flow [Grodzinski
(1975)]. The effect is then evaluated using some pecuniary value placed on an
energy unit. Some support for this approach once was found among economists.
The English economist, J.A. Hobson (1929) has remarked that:
"... all serviceable organic activities consume tissue and expend energy,
the biological costs of the services they render. Though this economy
may not correspond in close quantitative fashion to a pleasure and pain
economy or to any conscious valuation, it must be taken as the groundwork
for that conscious valuation. For most economic purposes we are well-
-advised to prefer the organic test to any other test of welfare, bearing
in mind that many organic costs do not register themselves easily or
adequately in terms of conscious pain or disutility, while organic gains
are not always interpretable in conscious enjoyment." (p. xxi)
According to one's perspective, Hobson1s statement can be taken as
support for an energetic basis of value, and as a plea for economists to
devote more attention to the workings of the biological world and its
implications for human welfare, both as a source of pleasure and as a
life-support system. Hobson's first point has been received warmly by
ecologists such as H.T. Odum (1971), to the point where it has been enshrined
alongside cost-benefit analysis as a means of evaluating proposed energy
technologies [Energy Research and Development Agency (1975)]. However, it has
been coldly received by modern economists. Georgescu-Roegan (1979) neatly
expresses the economists' source of difficulty with energy as the unit of
value for the satisfaction of human wants:
"The entropic nature of the economic process notwithstanding, it would be
a great mistake to think that it mav be represented bv a vast system of
85
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J
thermodynamic equations .... The entropic process moves through an
intricate web of anthropomorphic categories, of utility and labor above
all. Its true product is not a physical flow of dissipated matter and
energy, but the enjoyment of life. . ..pleasure is not related by a
definite quantitative law to the low entropy consumed." (p. 1042)
/ -»
Thus the value of energy varies with its use. The correct approach is there-
fore to include the ecosystem in the economy where the uses of the ecosystem
can be evaluated relative to all other goods.
Hobson's second point, that economics should give deeper consideration to
the role of biosphere in human affairs, has suffered from neglect. With the
exception of the work inspired by Boulding (1966) and Krutilla (1967), the
economics discipline continues to be notable for its inability to capture many
of the concerns of biological scientists, particularly ecologists, about the
impacts of human activities upon ecosystems and, via these ecosystem impacts,
ultimately upon human welfare. Perhaps economists have dismissed these themes
simply because the economics discipline has lacked a means of fitting them
into the framework of economic analysis.
The purpose of this paper is to develop a link between ecosystem and
economy that will allow an economic evaluation of ecosystem structure. We try
to broaden traditional approaches to environmental economic problems by
encompassing bioenergetics, but without resorting to the use of energy as the
unit of value used by humans. There are two main phases of the development.
First, an ecosystem model is described using the notions of production
functions, optimization, and equilibria. Humans are absent from this phase.
All energy input into the model derives from the sun. In the second phase,
humans are introduced under the familiar guise of utility maximizer. This
I.cads to behavior that interferes with the ecosystem through changes in the
sources and uses of energy.
The second section develops a model of the optimizing behavior of a
single organism in an ecosystem. The third section extends this idea to
multiple organisms and to ecosystem equilibrium. In the fourth section,
common ecological- themes are discussed as they relate to the model. Human
perspectives of the ecosystem enter in the fifth section. The sixth section
uses the developments of previous sections to address questions about the
value of pollution impacts upon ecosystem structure. The seventh section is a
simple general-equilibrium model incorporating the concepts of previous
sections.
Optimization by Individual Organisms
86
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Initially, we develop a model of an ecosystem where humans have no
influence. The model can be considered a depiction of prehistoric times or of
very remote areas in modern times. In this world, all energy is derived from
the sun.— Organisms may use this energy directly, in the case of plants, or
indirectly, in the case of herbivores and carnivores. Each organism is a
member of a particular trophic level, where a trophic level is defined as
". ..a collection of species which feed from the same set of sources and which
do not produce for each other" [Harmon, (1976, p. 260)]. In |ssence, each
trophic level can be thought of as a stratem in a food pyramid.— The
objective is to link mathematically the trophic levels. This will provide a
framework for discussing equilibria in the ecosystem.
Before deriving the links, however, the actions of the individual
organisms must be described. In a general equilibrium model, of an economy,
individual consumers and firms are usually described as maximizers. But in an
ecosystem, do nonhuman organisms maximize? Most people do not credit a weasel
with thoughtful preference revelation when it raids the chicken coop instead
of ferreting out a mouse or two. " . ..men consciously optimize, animals do not
- they survive by adopting successful strategies 'as if' conscious
optimization takes place" [Hirschleifer (1977, p. 4)] . This "as if"
assumption is sufficient to capture much of the behavior of nonhuman
organisms, and, thereby, establish a fruitful model: if one always remembers
that these organisms are not human, it can be worthwhile to treat them as
solving human-like problems.
Various suggestions have been made as to what it is that nonhuman
organisms maximize, or behave as if they are maximizing. Lotka (1925)
developed a model where the maximand is the rate of increase of the species.
This rate is a function of food capture, shelter, and other physical needs.
Obtaining these needs requires energy expenditure. If a species is to be
successful, then the energy expended on the needs must be less than or equal
to the energy acquired. Lotka characterizes a maximum in this system with a
set of equations where the marginal productivity (i.e. , an increase in the
species) of an energy expenditure equals the marginal loss (i.e., a decrease
in the species) of that energy expenditure.— Modern work has emphasized the
role of energy more directly in the search for a maximand. Odum (1971, p. 90)
points out that life requires power and "... the maximum and most economical
collection, transmission, and utilization of power must be one of the
principal selective criteria. .." Finally, Hannon (1976) develops a model
using stored energy as the maximand. Stored energy is simply the energy
squired by the organism less the energy needed to maintain itself. Hannon
argues for the reasonableness of this objective based on general observation,
and on the increased organism stability it provides during periods of
fluctuating inputs.
87
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The stored energy approach is used here. It does not seem to differ
significantly from Lotka's approach, particularly since he viewed organisms as
energy transformers. As indicated in the next section, if organisms of a
species are successful in storing energy, this is interpreted as leading to an
increase in the species. Hence, the stored energy approach appears acceptable
to modern ecologists,.and consistent with the pioneering work of Lotka.
For specificity, suppose the organism is a fox which, as an energy
transformer, gathers all its energy from food, and then assimilates this
energy for various purposes. All input energy must be accounted for as output
energy in the form of waste heat, metabolism, growth, reproduction, losses to
predators, detritus, mechanical activities, and storage. Let x. and e',
,n, be the mass flow from the ith source to the organism and the energy
content per unit of mass i respectively. The x. may be various species of
small mammals preyed upon by the fox. Total input energy is then:
n
I! e'.x. CI)
11
i= 1
Let e" be the energy spent to obtain a unit of x., so that the net input of
enerqy from a unit of x, is E.'E' E". Therefore, net input energv is:
1111
n
i= 1
E X
i i
(2)
The energy outputs are given bv x , k = n+1 ,.. . ,m and the energy content per
unit of x^ is For example, x^ may be the activity of searching for a den,
and e, is the energy spent per unit of searching. For some inputs such as
heat foss, Xt is measured in energy and e^_ = 1; however, no loss of generality
results from using Total energy output is:
K
m
k=n+l
e x (3)
k k
Stored energy is the difference between input and output. It represents
energy in excess of what is needed for viability. Let r be this energy.
Then, using (2) and (3):
n m
r= > e x. - y , , <4>
*!-• x i . Lt 1 kxk
i= 1 k=n+ 1
For convenience, all inputs and outputs will henceforth be denoted x ,
j
88
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j=l, ...,m+n, where x. _> 0 for inputs and x. <_ 0 for outputs. Each e x is
interpreted now as a net input of energy. ^Thus, if index j is heat l^s^, the
net energy input from heat loss is -e x . Expression (4) can be rewritten as
3 j
m+n
r= y - e.x. (5)
. . 3 3
3= 1
The objective of the fox is to maximize expression (5) .
A bundle of net inputs for the organism is represented by the m+n real
numbers x=(x^,. . . , .x+ ) . Not all bundles are feasible for the organism. The
fox cannot continually catch squirrels without ever losing^heat energy. The
set of feasible bundles will be called the physiology set.— In essence, this
set places constraints on what is achievable for the organism by describing
the physiological processes which convert inputs to outputs. For example, as
a general rule of ecology, in order for the organism to use ingested material,
it must oxidize the organic molecules in the material it ingests. [See
Morawitz (1968, Chap. 5)] . This creates useful energy, but some formerly
useful energy is also lost as heat. The physiology set also will depend on
ambient temperature, time of year, and other environmental conditions. Human
activities may influence this feasible set. Acid precipitation is a good
example of a human activity that interacts with an ecosystem via alterations
in physiology sets.
A simple diagram illustrates these notions. Suppose for the fox there is
only one input, squirrels, and one output, mechanical activity. Figure 1
shows the physiology set as the shaded region. The set is entirely within the
second quadrant where squirrels are consumed in positive quantities and
mechanical activity is a loss or a negative quantity. With mechanical
activity of x the fox can attain a quantity of squirrels x, a quantity or
any amount between x and the horizontal axis. Bundle x repesents the greatest
amount of squirrels attainable for & For this reason, x is labelled a.n
efficient point of the physiology set; and all points along the heavy curved
border of the set are referred to as the physiologically efficient points.
Definition: "A bundle x = (x ,x ) in the physiology set X is
-1 - n+m
physiologically efficient if there does not exist an alternative bundlex
= (x,, . ,.x ) inx such that X > x., j "1,. ..,m+n, and x > x, for at
, n+m .1 3 3
least one ].
Thus , a physiologically efficient bundle is one where greater amounts of
energy cannot be attained without even greater losses of energy. Note that
points along the nonheavy border in Figure 1 are, therefore, not
89
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physiologically efficent.
The dependence of the physiological set on environmental conditions is
depicted in Figure 2. The upper cross-hatched area may represent the
physiological set of a lake trout prior to the occurrence of acid
precipitation, while the lower cross-hatched region represents the trout's set
subsequent to the acid precipitation. This change clearly indicates a
detrimental effect from the pollution.
The fox behaving as a stored energy maximizer can be illustrated in the
simple diagram as well. With one input and one output, the fox maximizes the
expression from (5)
r ~ eiXl+ 12X2 ^
For a fixed level of stored energy, r, (6) can be plotted as the line in
Figure 3 labelled r. A higher level of stored energy is shown by the line
r. The vertical and horizontal intercepts indicate the stored energy
attainable, and the further the line from the origin in the first quadrant,
the greater the stored energy. Given a particular point, say x, and energies
and the stored energy is given by r. The slope of the line is the
ratio -e /, or the rate at which squirrels can be transformed into
mechanica~T.ee.argy in the ecosystem. Thus , the e ' s are the energy prices the
fox faces.
The fox is assumed to take and as given.; that is, he has no control
over these values. Thev are parameters in his maximization problem. The
point of maximum stored energy will be given by that stored energy line that
is furthest above the origin, but still having at least one point in common
with the physiology set. Obviously, this point will be one that is
physiologically efficient. Figure 4 illustrates maximums of f for values
and e0, and r for values e, and e . The maximizing solution depends on the
shape^of the physiological^set and the values of e1 and e . At x, greater
levels of mechanical activity and squirrels prevail, because squirrels have
more energy content > ep and/or mechanical activity results in less
90
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Figure 4.1
The Physiology Set
squirrels
Mechanical activity
Figure 4.2
Effect of Environmental Conditions
output
Input
91
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Figure 4.3
Attainable Stored Energy
r/e
"£2/e
r/e
r/e
r/e
Figure 4.4
The Maximizing Solution
xi
»/e
l
f 1
\
I-/E,
"X2
92
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energy loss
< e^)» For values £L and_ f_ the fox would not move beyond point x. To
do so would mean more memaariicaTactivity and more squirrels, but the energy-
gained would be less than the energv lost. Moving from x to x would mean a
drop in stored energy from r to r.
¦4 • • .
A maximum will exist provided certain restrictions are placed on the
physiology set. In particular, the set must be bounded and include its
boundaries. These restrictions do not seem unrealistic. Figure 5 illustrates
a set that is not bounded. For positive e and £ maximum stored energy is
infinite. The shape of the set must be leitt to experiments, observations, and
statistical analysis, and it can be expected to vary significantly among
organisms. Research into these shapes is necessary to apply the theory
presented here.
Further insight into the maximization model can be gained by returning to
the general case with n+m variables. To do this, the concept of a physiology
function is introduced using the physiology set. For arv set of values of all
but one of the net flows, x , there is only one value of x_ that is compatable
with physiological efficiency. This is obvious for the two variable case from
the figures above. For n+m variables, efrat ^x =- fx ,...,x x_ ,.. . ,x ),
then there is a one-to-one correspondence between th^ fn+tn-"l
x - and the scalar x . In functional form,
x. = fCx
or equivalently
.1
F (x) = x.-f(x ~1) = o (7)
3
The function F(x) is the physiology function, and, by construction, it
embodies physiological efficiency. That is, x is physiologically efficient if
and and only if F(£) = 0. In two dimensions, F(x) = 0 implies that x is on
the border of the physiology set.
The maximization problem can be restated as
m+n
max r = ) ex
3=1 J ^ (8)
subject to F(x) =0
where FCx) is assumed to be twice differentiable and the physiology set is
93
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Figure 4.5
An Unbounded Physiology Set
94
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assumed to be strictly convex. Strict convexity assures that the second-order
sufficiency conditions of the maximization problem are satisfied, and that
there is a unique maximum. The Lagrangian for problem (8) is:
m+n
L(x,'X) ¦•=
5" E x + AF(x)
j 1 1 j
(9)
and the first-order conditions for a maximum are
3F(x)
x. : E , + X =o j = 1,... ,m+n (10)
li
ax
j
g: F(x) = 0 (11)
Dividing any two conditions in (10) by each other yields
3F(x)/3x. e.
l = _i
3F(x)/3xj ei
(12)
so that for a maximum, the ratio of partial derivatives of F(x) must be equal
to the ratio of energy prices. Using (7),
F(xr . . • (x""') >xj+1>» 'Vn} = 0
and differentiation with respect to x. , i yields
** J.
it, -"K 3F(x)/3x,
3f (x ) 1
ax, " 3F(x)/3x. (13)
i 3
Thus , the left-hand-side of (12) can be interpreted as the rate at which x.
must be substituted for x. while all other values are held constant. Or, f^r
the fox's predatory behavior, (12) states that the rate at which he can trade
squirrels for rabbits while maintaining stored energy must equal the rate^at
which he can exchange squirrel energy for rabbit energy in the ecosystem.-
Alternatively, (12) and (13) can be used to obtain
3e . f(x ^)
= 1
(14)
3e
i i
The left-hand-side of (14) is the rate at which energy from source j must be
traded for energy from source i in order to remain physiologically efficient.
95
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Or, substituting squirrels for rabbits must lower the input of rabbit energy
at the same rate squirrel energy is increased.
The conditions for a maximum given by (12) can. be related to the earlier
figures. Condition (12) for the one input-one output case is shown by the
tangency in 'Figure1 4-; The left-hand-side of (12) is the slope of the
physiology set border, and the right-hand-side of (12) is the slope of the
stored energy line.
The first-order maximum conditions given by (10) and (11) constitute
m+n+1 eauations which can be solved for the optimum values of the x, and X as
functions of the energy prices. A solution is guaranteed by the assumption of
a convex physiology set. Thus , there exist the functions:
x. " .(e) j = 1». ..,m+n (15a)
3 3
X _ * (e) (15b)
, . th , , th
The function 6.(e) indicates the amount of the j input acquired or ] out-
put spent, givtn the energy prices of all inputs and outputs. Substituting
these amounts back into the objective function gives the maximum stored
energy,
m+n
¦ I
.1-1
£.<)>. (e)
3 3
(16)
If j represents rabbits, .(e), can be thought of as the fox's demand for
rabbits at prices e. J
Finally, the <)>. (e) terms can be substituted into (10) and (11), and
derivatives can be 4:aken with respect to the e . This yields the system of
J'
equations:
m+n 9F(x) 8(j) (e) 3 (e) 3F(x)
1+7" cf> e — + — = 0 (10')
% - 3x.3x, 3e. 3e. 3x. '
k=l 3 k j 2 3
j »k = 1,.. . ,m+n
96
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i
m+n
v 3F(x) 3 (e) _
2j ax k ~ 0 J - 1». .. ,m+n
k= 1 k 9e
]
This system can bemused to solve for the 9^ (e )/&£ , values,
second-order conditions, K J
3 . C e)
.j >0 j = 1,. ... m+n (17)
The interpretation of (17) is that an increase in the energy price of a net
input results in an increase in the use of that input. If the net energy the
fox could obtain from a rabbit were to increase while the net energy obtained
from a squirrel remained the same, the fox would chase more rabbits and fewer
squirrels. A similar interpretation holds on the output side.
Before closing this section, a brief comparison between this model and
economic models is worthwhile. The energy storage maximizing organism is
analogous to the profit maximizing firm. The firm uses inputs (capital,
labor, etc.) to produce outputs (guns, butter, etc.). The firm's technology
set consists of net outputs, so that inputs are negative and outputs positive.
This is opposite to the organism whose physiology set is made up of net
inputs. Moreover, the firm pays money to buy inputs, and collects money in
selling outputs. This also is opposite, since the organism collects energy
from inputs, and pays energy for outputs. Inequality (11) is, however, the
same for the firm and the organism since the two opposites cancel..
Multiple Organisms
An ecosystem, comprises manv stored energy maximizers which must be linked
to provide a. complete picture. Each organism belongs to a species, and sets
of species form trophic levels. The trophic levels are links in a food chain
or levels in a hierarchy. Each species feeds on species in lower trophic
levels, and in turn provides food for species in higher trophic levels. Some
hierarchies may be considerably more complex than others in that some species
may interact with other species from, many different trophic levels. Thus the
inputs and outputs of the previous section represent inputs from other
organisms and outputs to other organisms.
At the bottom of the hierarchy are the simplest plants who derive all
their input energy from the sun. In fact, in an ultimate sense, the sun
supplies all the energy consumed by the ecosystem. This provides one equation
in the ecosystem model: total output energy in the form of heat which is lost
(11*)
and, by the
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in the ecosystem equals total input energy from the sun.
By responding to energy prices, e, each organism behaves as the stored
energy maximizer of the previous section. We assume each organism to be
inconsequential with regards to its effect on the ecosystem, since there are
so many other organisms. From this we infer that each organism has no control
over the energv prices. This is consistent with the maximization process
discussed above. However, the relative energy prices are determined by the
activities of the organisms in the ecosystem. The fox's energy price for
acquiring rabbits will depend on the availability of rabbits. If an
exogenous shock were to reduce the number of rabbits drastically, we would
expect the energy price to increase for the fox, causing a decrease in the
fox's stored energy.
The existence of an equilibrium ecosystem, given the number of interact-
ing maximizers, and given a set of initial conditions or initial numbers of
organisms and environmental surroundings, requires a set of energy prices such
that all organisms are maximizing stored energy while at the same time inputs
are consistent with outputs and total energy is conserved. Existence will
depend on the forms of the physiology sets and on any threshold conditions
that may prevail. For instance, too few individuals of a certain species may
lead to a total collapse of the species. There is also the possibility of
multiple equilibria. That is, equilibrium, if it exists, may not be unique.
Different equilibria may consist of a variety of configurations of species
numbers.
In accordance with Hannon (1976), stored energy is zero for all organisms
in the equilibrium ecosystem. Recall that stored energy is energy above and
beyond what is needed to survive. This is analogous to all firms making zero
profit in a perfectly competitive economy. To see why this is, suppose an
equilibrium exists and all species have zero stored energy; then consider an
exogenous change that causes foxes to have positive stored energy. The foxes
are healthy, vigorous, and increasing in numbers. But this means that each
fox will now face greater competion in his search for energy inputs. Numb ers
of rabbits will decline, and the energy price of rabbit inputs will increase.
This increase will cause a decrease in the foxs' stored energv, until zero is
again attained. A new equilibrium is established, although it mav be one with
more foxs and fewer rabbits than before. The same type of scenario can be
used to show how the system responds to negative stored energies.
Setting up a mathematical model to study this ecosystem equilibrium is
similar to the problem of setting up a general equilibrium, competitive model
of an economy. The mathematics of existence can be complex, and will not be
pursued here. However, efforts along these lines should be rewarding.
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Insights could be had regarding: 1) whether the stored energy behavior
concept is consistent with observed equilibria; 2) those restrictions on the
physiology sets consistent with equilibria and with field and experimental
observations; and 3) the effects exogenous shocks, such as human induced,
acid precipitation, have on these equilibria.
Common Ecological Themes
Watt (1973, p. 34) sets forth the following as a fundamental principle of
ecological science: the diversitv of any ecosystem is directly proportional
to its biomass divided by its productivity. That is:
g
D = k(-) , (18)
where D is a diversity measure directly related (Pielou, 1977, Chap. 19) to
the number^of species in a given habitat and the relative abundances of each
species; ~ B is the total weight or standing biomass of living organisms in a
habitat; P is the amount of new living tissue produced per unit time; and k is
a constant differing from one habitat to another. Thus, for a given biomass,
system diversity and system productivity are inversely related.
Within a given habitat, d(B/P)/dt > 0, implying that in the early life of
an ecosystem, the production of new tissue is very large compared to the
amount of biomass. This high relative productivity is the source of biomass
growth. It is achieved by introducing into an abiotic or stressed environment
a small number of pioneer species (e.g., weeds) with rapid growth rates, short
and simple life cycles, arid high rates of reproduction. In the mature stages
of an ecosystem, a wider variety of organisms that grow more slowly and have
longer life spans is present. Net production or "yield" is lower in a mature
system because most energy is invested in maintenance of the standing biomass.
Thus, whereas energy in the pioneer stage is used to increase biomass, so that
a relatively empty habitat can be filled, all the captured energy coming into
a fully mature system is employed to maintain and operate the existing
biomass, which already occupies all the habitat territory available.
Ecosystems that must live under intermittent or continued severe stress
exhibit the attributes of immature systems: they have relatively low
diversity and biomass but high throughput of energy and thus high yields.
Ecologists traditionally prefer ecosystems with large biomass and
diversity. This preference for mature ecosystems appears to rest on two
positions: the maximization of system energy capture; and the maximization of
system stability. In the first case, more energy is captured per unit biomass
in a mature system because less energy has to be "wasted" in growth and
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reproduction activities. The distinction is similar to Boulding's (1966)
description of the "cowboy economy" and "the spaceship economy", where the
former maximizes throughput and therefore energy diffusion, while the latter
maximizes incoming energy concentration and fixation. According to Margalef
(1968), the immature or stressed system expends more energy per unit biomass
in reproduction in,order to make up for its more frequent loss of individuals.
In addition, because of its relatively small energy recycling capacity and its
relative inability to alter and to renew its environment in ways favorable to
its sustenance, it must expend relatively more energy per unit biomass in food
gathering activities. The immature system thus expends relatively more energy
in producing new tissue to replace that which has disappeared (depreciated).
In contrast, the mature system expends most of its incoming energy in keeping
what it has already developed: it is durable. Because it sustains a greater
biomass per unit energy, the mature system is frequently said to be more
"efficient" (B.P. Odom, 1971, p. 76).
Although exceptions appear to exist [May (1971), Jorgensen and Meier,
(1..979)], the greater efficiency of mature ecosystems is associated in
ecological thought with greater stability, where stability is variously
interpreted to mean system resiliency to exogenous shocks or infrequent
fluctuations in standing stock. This stability is thought to originate in a
set of homeostatic controls present in greater number and variety in mature
systems, thus providing a greater number of avenues through which the system
can recover from damages to one or more of its components. The greater
simplicity of the immature system is thought to increase the likelihood that
if anything goes wrong, everything goes wrong. Thus monoculture, which are
by definition the simplest and least diverse of ecosystems, are susceptible to
being wiped out by any single pest or event to which they are sensitive.
Incoming energy flows only through one or a small number of pathways; when
this pathway is degraded, no means to capture energy remains. The system
therefore collapses unless energy subsidies (e.g., fertilizers) are provided
from outside. These subsidies are of course a further source of the low
biomass supported per unit incoming energy that is characteristic of immature
ecosystems.
The human dilemma posed by the ecologists then involves a tradeoff
between high yield but risky immature systems with undifferentiated
components, and low yield, reasonably secure systems with a variety of
components. Even if the requisite energy subsidies were usually available, an
earth covered with cornfields would be dangerous. Moreover, given, as
Scitovsky (1976) convincingly argues, the human taste for variety and novelty,
a world of cornfields would be exceedingly dull. Nevertheless, flowers and
butterflies nourish only the human psyche; they provide little relief to an
empty stomach. Human activities increase biological yields by accelerating
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energy flows through ecosystems. In terms of the model of the previous two
sections, these activities increase overall energy prices. To accomplish
this, they simplify ecosystem structures, either by keeping them in a
perpetual state of immaturity or by impoverishing the energy flows their
habitats can produce.
In the context of the above perspective, pollution, such as acid precip-
itation, harms human welfare by reducing yields of the material scaffold of
wood, fish, and corn and by increasing ecosystem simplicity: yields are
reduced and monotony is increased. Woodwell (1970) notes that by elimination
of sensitive species,. SO^ air pollution around the Sudbury smelter in Ontario
first resulted in a reduction in the diversity and biomass of the surrounding
forest. Finally the canopy was eliminated with only resistant shrubs and
herbs surviving the assault. He also notes that chronic pollution reduces
plant photosynthesis without having much effect upon respiration requirements.
As a result, large plants, which have high respiration requirements, are
placed at a disadvantage relative to small plants. In a vivid image, he
posits the replacement of the great variety of phvtoplankton of the open ocean
by the algae of the sewage plants that are insensitive to just about any
stress.
Valuing Diversity and Yield
In accordance with the treatments of Hannon (1979), Mauersberger (1979),
and sections two and three of this chapter, the ecosystems refered to in the
following development are long-run equilibria sustainable with various
combinations of energy from solar, biogeochemical, and subsidy sources.
Contrary to much of the ecological literature, day-to-day transient states in
the relative abundances of various species are disregarded. This permits us
to concentrate upon a small number of key expressions and basic principles,
thereby avoiding the bewildering black-box flow diagrams often used by
ecologists. We wish to gain insight into two questions. First, what is the
economic value of the quantity of each species that a location is producing?
For our purposes, a location is simply a set of map coordinates. Second, what
is the economic value of the assortment or bundle of species that the location
is producing? That is, what is the value of a particular ecosystem design?
For a particular species assortment, the first question is usually answerable,
given that market (not energy) prices of each species unit are readily
8 /
observed or inferred.— However, the second question, whether treated singly
or in combination with the first, has not yet been grappled with insofar as
ecological questions are concerned. We adapt a model, of Lancaster's (1.975) to
deal simultaneously with the two questions.
To analyze these two questions, we need a model permitting us to trace
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through the impact upon the economic benefits derived from ecosystems of
changes in specie quantities and assortments caused by changes in energy
II10WS. The first step in doing this is to define an ecosystem, e., as a set
of species, where these species are in fixed proportions to one another.
Expression (19) identifies ecosystem i with n species and
' - i i i
e. = (r ,r ,. .. ,r ) (19)
1 1 2 n
i
where r4 is the quantity of species j. Biomass is used to normalize the
measureJof different species. An ecosystem thus contains different species in
a particular proportion at a single location. Ecosystems that contain species
in different proportions are considered to be different ecosystems. Given the
linearity of (19) , the species content of x units of an ecosystem is simply x
times the content of each species in an ecosystem unit.
Allow some time interval sufficiently long to permit each feasible eco-
system to attain a long-run equilibrium defined in accordance with the model
of sections two and three. Assume that a given amount of energy, E, from
solar, biogeochemical, and subsidy sources is available for this time interval
at the location in question. Included in the biogeochemical energy source is
the energy currently stored in the standing biomass. With E, a variety of
ecosystems can be established, the range of the variety being determined by
the physiology sets of each species and the ways in which the species interact
with each other.
Note that our notion of long-run equilibrium need not be a climax bio-
logical equilibrium; that is, it includes other sustainable states as well.
In particular, by including energy subsidies and biogeochemical energy in
available energy, we allow immature ecosystems to be formed and sustained.
For example, an energy subsidy is being provided a vegetable garden when it is
weeded and when it is harvested. The weeding prevents the garden from
"reverting" to field, woods or prairie; the harvesting prevents the standing
stock of vegetable plants from suffering the effects of congestion. This
standing stock will produce, period after period, a unique sustainable flow of
new biomass or yield as long as the requisite biogeochemical energy and energy
subsidies are provided. Similarly, with enough of an energy subsidy (as with
a greenhouse) in Wyoming, one can sustain a banana-mango ecosystem with its
associated flow of bananas and mangoes. We assume, whether reference is to an
entire ecosystem or to a particular species within that system, that the
sustainable yield measure is an order preserving transformation of the
standing stock measure.
For a particular quantity of incoming energy, there will b^^ome maximum
amount of each ecosystem that a particular location can produce.— Let the
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minimum energy requirements for producing an ecosystem be given by:
E = E(e(r)) " (r)
will be called a diversity possibilities function. It shows the maximum
quantities of various species combinations that a location can sustain with
given available energy each period. We assume that <(>(r) is homothetic and
convex, and that > 0. For a given energy flow at a particular location.
Figure 6 illustrates a diversity possibilities function for grass and corn.
In Figure 6, four ecosystems are depicted, one of which, e , contains
only grass, and another of which e , contains only cows. Two ecosystems, e^,
and a containing grass and cows in different combinations, are also
depicted. If enough alternative ecosystems are possible, a continuous
diversity possibilities frontier, E, can be formed, as we assumed in (20) .
For given energy availability, each point on the frontier, E, represents the
maximum quantity of one species that can be produced with a particular
quantity of the other species being produced. Since cows probably use
relatively less, if any, solar radiation directly, a progressively greater
proportion of biogeochemical energy and energy subsidies will be included in E
as one moves from the vertical axis to the horizontal axis.
The convexity of the frontier follows from an ecological version of the
economic law of diminishing returns known as Mitscherlich's law [Watt (1973,
p. 21)]. As progressively more energy is diverted from grass production to
cow production at the location in question, the increment to the latter will
decline. Similarly, the diversion of energy from cows to grass will result in
declining increments to grass production. Since in Figure 6, the cows could
feed upon the grass, the convexity of the feasible region is also attributable
to the less biologically efficient use of the given available energy by cows
than by grass. As a food chain lengthens, the amount of original, energy used
for production by species distant from the original energy input tends to
decrease at an increasing rate (E.P. Odom, 1971, Chap. 3). Of course, as
Tullock (1971) recognizes, the croppings and droppings of the cows may recycle
some of the energy originally embodied in the grass and cause both grass and
yields to increase over some portion of the frontier. However, as grass
becomes scarce, the cows must expend progressively more energy in search for
it, if it is to remain a part of their food supply. Finally any cow grazing
whatsoever might be so harmful to grass that the frontier bows inward, causing
a nonconvexity problem for applications of economic optimization techniques.
The assumptions of homotheticity and <)>' > 0 for (20) imply that: $ (A, r) "
F(X)cj>(r) for all X, r > 0. In terms of Figure 6, these assumptions mean that
103
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Figure 4.6
A Diversity Possibilities Frontier
Cows(r.)
Figure 4.7
The Compensating Function
Cows
104
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there could exist a series of similar diversity possibility frontiers, one for
each level of energy availability. The greater the level of energy
availability, the farther would be the associated frontier from the origin.
Therefore the biomass of any species obtained in a particular ecosystem to
which greater quantities of energy are made available will increase but not
necessarily on a one-to-one basis with the increase in available energy.
To make different ecosystems comparable, we define the solar radiation to
which the location in question is exposed per period as the unit amount of
energy, E . Each of the ecosystems that can be produced by this unit energy
are therefore comparable in terms of the biomasses of each species embodied in
them. We shall call them unit ecosystems. Keeping in mind that an ecosystem
is defined as embodying species in fixed proportions, an altered quantity of
an ecosystem is a simple multiple of the quantity of any species appearing to
some positive degree in the unit ecosystem.
To complete the most fundamental parts of our analytical apparatus, we
introduce a well-behaved utility function, U(r), for a representative person.
Assuming others, energy subsidies to the relevant location to be
predetermined, the Lagrangian of this individual's decision problem then can
be stated as:
L = U(r) + u(E - 4>(r)). (21)
The first-order necessary conditions for a maximum of (21) are,
3U 3d> (22)
~Z~ ~ U =0
3r 9r
and the constraint expressing the available energy. Expression (22) states
that the individual will equate the marginal utility he obtains from an addi-
tional unit of a species to the marginal cost of expending the energy to
acquire that additional unit. Figure 7 is a diagrammatic representation of
(22) for two types of ecosystems, e and e , and two indifference curves U,
r ..... . ... r
r, E, tthe
and U .With available energy, E, tthe individual's utility-maximizing choice
is clearly at A, which corresponds to (22) . We shall therefore call any eco-
system which conforms to (22) the ideal ecosystem. This is the ecosystem
having that species assortment most preferred by the individual.
Assume that our representative individual, perhaps because he is unable
to exercise enough influence over land use, cannot have the e^ ecosystem.
Instead, he must face the -fjvstem, a system containing substantially more
cows and less grass. The latter system may be considered to be less "natural"
since its maintenance likely requires substantial man-supplied energy
105
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subsidies. With the available energy, E, the individual will be worse off
with the e system since the highest utility level he will be able to reach is
U at C. If he were to be as well off with the e system as he would be with
tne ideal system at A, he would have to be at B. The attainment of B,
however, requires more input energy as indicated by the diversity
possibilities frontier, E*. Since OA and OC both require E units of energy,
while OB requires ft* "energy units, the energy auantity required to compensate
the individual for the fact of the e^ system is E* - E along the e^-rav. The
compensating ratio, OB/OC _> 1, is then the quantity of the existing system
relative to the quantity of the ideal, system that keeps the individual at the
original utility level. Since OB and OC are each defined in energy units, the
compensating ratio is a pure number. A glance at Figure 7 makes it obvious
that this compensating ratio will be greater, the less substitutable the two
systems are for one another, the steeper the slopes of the diversity
possibility frontiers, and the wider the difference between the ideal
ecosystem and the actual ecosystem. In addition to depending upon underlying
preferences and production conditions, this ratio is obviously a function
h(e, e*), where e* is the species ratio in the ideal ecosystem and e is the
species ratio in the existing system. Lancaster (1975, p. 57) describes the
properties of this compensating function, which must be convex.
If all existing ecosystems are not to be ideal ecosystems, the preceding
framework implies that in the real world there are some ecosystems produced
under conditions of increasing returns-to-scale. If decreasing returns-to-
scale were universal, less energy would be used by producing fewer units of a
greater variety of ecosystems. In the extreme, each individual would have his
ideal ecosystem available to him. Similarly, under constant returns-to-
scale, the quantity of energy used to produce a quantity of an ecosystem is
directly proportional. Thus , with decreasing or constant returns-to-scale,
any individual, who does not have his ideal ecosystem available is using more
input energy to attain a particular utility level than would be required with
his ideal ecosystem. Casual observation suggests that everyone is not happv
with the ecosystems they have available. One plausible reason for this is ^the
presence of increasing returns-to-scale in the production of ecosystems.—
That is, the presence of increasing returns-to-scale for some ecosystems may
force the individual to choose between an ideal diversity of ecosystem
components and reduced energy consumption per unit of production for some
smaller set of these components.
Let us momentarily return to (20), which gives the amount of input energy
required to produce some amount of a particular ecosystem. Because of our use
of energy to bring the unit quantities of different ecosystems to the same
measure, and because of the properties we have assigned to the diversity
possibilities frontier, if 0 , and Q2 represent quantities of different
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ecosystems, e and e , then ^(Q..) = f„(Q0) 0 =Q . allows
J I _ 1 2. J. x hpn 1 9 xhiq x c x
perform the analysis in terms of a singtl® input riincriion:
E = f(0) (23)
The energy required to produce quantity Q„ of e and quantity 0 of e is
1 l 2 2
given by the sum of the two input functions:
E = f1(Q]_) + f2(Q2), (24)
and not the sum of the quantities of (Q^ + Q^). If + f CQ \ =
f(Q^ + Q^), then constant returns-to-scale would exist. As usua'l , we assume
f(Q) > 0, and f' (Q) >0, but we need not assume that all incoming energy
results in additional biomass, nor need we attach any sign to f"(0).
Now define a degree of economies-of-scale parameter, 0(Q), which is the
ratio of the average energy input requirement to the marginal energy input
requirement. This is simply the inverse of the elasticity of (23), or:
, . ffO) f .
8(Q1 " " o f 1251
If 0 is a constant, fCO) will then have the form:
1/0
E = E Q , (26)
o
the inverse of which is
0
0 = aE (27)
This last expression is immediately recongizable as a homogeneous function of
degree 0. If 0 > 1, there are increasing returns-to-scale; if 6 = 1, there
are constant returns-to-scale, and if 0 < 1, there are decreasing
returns-to-scale.
In expressions (21) - (22), we derived the representative individual's
ideal diversity of ecosystem components, assuming that he faced no tradeoffs
between this ideal and lowered unit energy costs of ecosystem production. We
are now prepared to consider this question of the optimal deviation of the
actual ecosystem available to the individual from the individual's ideal
ecosystem.
Assume we wish to enable the individual to re.,some predetermined
arbitrary utility level with minimum use of energy. " Let Q* be the
quantity of an. ideal ecosystem, e*, that is required for the individual to
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reach this predetermined utility level. If the available ecosystem, e, is
nonideal, the individual will have to be compensated by being provided more
than Q* of the available system. According to our previous definition of the
compensating function, h(e, e*) , the amount of the available eco-system
required to bring the individual up to the predetermined utility level will be
Q*h(e, e*) . Since the input function (23) is independent of the species
ratios (by the assumed homotheticity of production and the definition of unit
quantities), the optimal ecosystem is that which minimizes the quantity, Q,
required to reach the predetermined utility level. That is, we wish to
minimize:
0 = C/*h(e, e*) (28)
This minimum is given by:
Q* — = 0 (29)
3e
which obviously corresponds to (22). This result is relatively trivial but it
does serve as a necessary prelude to determination of the optimal deviation of
the available ecosystem from the ideal ecosystem.
Suppose there are n-1 less-than-ideal feasible ecosystems, the deviation
of each less-than-ideal system from the ideal system being given by x. = e* -
e, . Then the quantity of the ith ecosystem required to reach tfte
predetermined utility level is given by: Q. " 0*h(x ). The total energy
inputs required to reach this utility level ^or all systems, whether ideal or
not, are then:
E = frq*hCx )] , (30)
i
where the x, are the variables of the problem. From (30) is obtained:
iE = 0A df dh = Q*f.h. <"31a)
dx ' dh dx
1 i
or
Q*h' = j, (31b)
for a minimum expenditure of energy.
The interpretation of (31b) in economic terms is quite easy. The l.h.s.
of the expression shows the increase in the quantity of the ith ecosystem
required to maintain the predetermined utility level if there is a one unit
biomass increase in the deviation of the available ecosystem from the ideal
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ecosystem. The denominator of the term on the r.h.s. shows the increase in.
the available quantity of the ith ecosystem to be obtained with a one unit
increase in input energy. Thus (31b) says that the optimal deviation of the
available ecosystem from the ideal ecosystem occurs when the change in the
compensating ratio is equal to the reciprocal, of the additional energy
required to produce more of the ith ecosystem. As the available ecosystem
deviates less from'the ideal system, the compensating ratio decreases. if the
energy inputs required to reach the predetermined utility level also decrease,
then the ideal system would clearly be optimal. However, if the compensating
ratio increases and, due perhaps to eccmomies-of-scale in production with
simplified ecosystems, energy inputs per unit of yield decrease, then the
achievement of an optimum requires that the tradeoff between the two be
recognized.
The optimum condition (31b) can be clarified when stated in elasticity
terms. Upon defining the elasticity of compensating function as n = xh' /h
h
and substituting this and the elasticity, (23), of the input function into
(31b), we have
A Q*e
"h x f ' (32)
which if f, h, and 0 are fixed is simply
n (x) = 9 • (32b)
h
Thus the optimal deviation of the available ecosystem from the ideal ecosystem
occurs where the elasticity of the compensating function, D fx) , is equal to
the degree, 0, of economics of scale in production. If x were such that ^.(x)
> 0, a one percent decrease in deviation of the available ecosystem would
require n percent less in ecosystem quantity (remembering that all ecosystems
h
are measured m the same units because they are defined relative to a unit
ecosystem) and require .tj (x)/0 > 1 percent less energy resources, so that
energy inputs would be made smaller by reducing the extent Of deviation from
the ideal system. However, if n (x)/0 <1, an increase in the extent of
deviation would reduce energv inputs. Thus when ^(x) = 6, the deviation, is
optimal. The welfare loss from an increase in the deviation of the available
ecosystem from the ideal ecosystem is balanced by the increased ecosystem
quantity obtained for a given energy input.
The Impact of Pollution
In the previous section, we have presumed that over some interval of the
input function, (23), there exists increasing returns-to-scale: that is, as
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more energy is devoted to the production of a particular ecosystem, the
ecosystem yield per unit of energy is increasing. When there are feasible
monocultural ecosystems that yield an output (e.g. beef) highly valued for
consumptive purposes, or as an input (e.g., sawtimber) for a fabricated good,
and if these ecosystems exhibit increasing returns-to-scale, then some
deviation of the available ecosystem from the ideal ecosystem may be optimal.
The condition for optimality is 0*h'=(f') " or, in elasticity terms, n, (x) = 0
It is thus apparent that the extent of optimal deviation will vary with the
parameters that influence the above conditions. The elasticity, n , is
determined by the properties of the compensating function, h. The eco-
nomies-of-scale parameter, 0, is either an exogenous parameter (with homo-
genous production) or is a function of yield, and thus of the compensating
function.
Consider a pollutant, a, which might, in principle, effect h' , f' , or
both. For example, a pollutant stresses ecosystems, making them immature, and
thus less diverse. In addition, for at least some of the ecosystems remaining
viable after the introduction of a pollutant, their yields are less than they
would be without the presence of the pollutant, i.e. , the level of ecosystem
yield obtainable with any given provision of energy is reduced. Thus, in
terms of Figure 7, the diversity reduction would be reflected in a rotation of
the available ecosystem toward one or the other axes, while the reduction of
yield of whatever ecosystem was ultimately available would register in a shift
of the diversity possibility frontiers toward the origin. If the ideal
ecosystem is unchanged, and if the reduction in diversity represents a
movement away from this ideal system, then the individual will require
additional compensation if he is to remain at the original utility level. A
similar result occurs if f' (the additional energy input required to obtain an
additional unit of an ecosystem) increases. In both cases, an increase in the
deviation of the optimal from the ideal ecosystem occurs. The effect of a
variation in a on the optimal deviation is easily found by differentiating
either (31b) or (32b) .
Upon differentiating (32b) with respect to a, we get:
dx (d0/da) - (dn, /da) (33)
h
da (dri, /dx) - (d0h/dQ)
n
Given the convexity of the indifference curves, the dn /dx term in the denom-
inator must be positive. If the degree of economies-of-scale is fixed or
declines with increases in the level of output, the d0/dQ term in the denomin-
ator must be negative. Thus the denominator in (33) will be unambiguously
positive. The sign for (33) will therefore depend solely upon the terms of
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the numerator. If the ideal ecosystem has high diversity, the sign of dn/da
. . . . , . . . h.
will be positive since the convexity of the indifference curve requires that
reduced ecosystem simplification imply increased responsiveness of the
necessary compensation to further simplification.
The sign of d0/da in (33) is less easily determined. Remembering that 0
= (f)f/(Q)» it is plausible that increases in a would increase only f',
implying that d0/da would be positive, but leaving the sign of the numerator
in (33) dependent on the relative magnitudes of d9/da and dn /da . It is of
course possible that pollution would reduce the yields obtainable for every
ecosystem for all output levels. This event would be reflected in a reduction
in f, implying that d0/da < 0, for a given f' and Q. In this case, the
increase ir pollution would reduce rather than increase the optimal deviation
of the available ecosystem from the ideal ecosystem!
These results obviously imply that economic analyses which concentrate
only on the ecosystem yield effects of pollution can be seriously misleading.
In cases where pollution reduces both yields and diversity, the analyses will
tend to underestimate the economic losses from the effects. Similarly, if
there exist cases where diversity is decreased while yields are increased, the
usual analyses might not perceive any losses. However, in some cases, the
usual analyses will exaggerate the severity of the losses. Harkov and Brennan
(1979 pp. 157-158) conclude, for example, "... that slower growing trees, which
often typify late successional communities, are less susceptible to oxidant
damage than rapid-growing tree species, which are commonly early successional
species." Assuming that the ideal ecosystem is more diverse than was the
available ecosystem before the increase in pollution, the increase in
pollution could reduce f',6, or both. In either circumstance, more incoming
energy would be required than before to obtain a given yield with the immature
ecosystem. The pollution may therefore reduce the optimal deviation of the
available ecosystem from the ideal system. In short, pollution can enhance
rather than hinder the willingness of individuals to live with mature
biological communities! Obviously, in this case, any economic analysis which
neglected the increase in diversity would overestimate the economic damages
attributable to the pollution.
A Simple General Equilibrium Model.
A simple general equilibrium model of an economy and ecosystem will now
be presented that in some respects captures more dimensions of our basic
concerns than do preceding sections, but which does so at the cost of neglect-
ing some dimensions that the preceding sections feature. The ecosvstem will
be represented by the single stored energy variable r. Of course, this masks
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many interesting questions (e.g. diversity vs. scale economies) due to the
level of aggregation taking place. Nevertheless, the ecosystem solves the
one-input problem
max r = e x -ex
1.1 2 2
St . x = gfx ; E^) (34)
where E is a parameter indicating the amount of human supplied energy into
the ecosvstem. T.n the second section, we saw that E = o. The solution to
r
the problem is characterized by the first-order condition,
h. 3S(X1;V (35)
ax
ll 1
This is the analogue of (12.) ¦ If the ecosystem is in equilibrium, with no
human interaction (i.e., E - 0), r = 0.
r
In order to capture a general equilibrium setting, we now introduce a
Hicksian composite good, z, into the individual's utility function. Thus
human preferences are given by:
U(z,r) (36)
The term r appears in the utility function to indicate the human preference
for a natural environment. Ideally, that environment should be pollution free
with little trace of intervention. In other words, for some z value, zero is
an optimum value of r. As intervention increases through increased E , r
r
increases and utility decreases for fixed z. Consumer preferences are shown
by the indifference curves of Figure 8. The arrow shows the direction of
preference.
The production of z is given by the function
z = f (E ,r) (37)
z
where E is the energy used in the production of z. Stored energy enters z
since it represents that part of the ecosystem which is cropped to provide
goods in the economy.
The human problem is to maximize (36), subject to (35), (37), and the
resource constraint on total available energy.
E + e • E (38)
r z
112
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Figure 4.8
Consumer Preferences
z
Figure 4.9
A Natural State Optimum
r
z*
z
Figure 4.10
An Interventionist Optimum
z
113
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The solution is shown graphically by the two possibility curves in Figures 9
and 10. In Figure 9, curve P* is the production possibility frontier. As we
move from z*, incoming energy is being diverted from the production of z to r,
and, therefore, more r is produced. Greater r means more natural environment
is available for producing z. However, the shape of P* indicates that the
increase in r does not make up for the decrease in E in the production of z.
The optimum 'is z* where the ecosystem is in a natural state.
The second possibility is curve P** in Figure 10. Again, energy is being
diverted to r. But now in producing z, the increase in. r more than makes up
for the loss of energy E as shown bv the shape of P**. The optimum is now
r**; z** where intervention in the ecosystem is justified. Examples of these
possibilities may be forest harvesting since most would agree that harvesting
forests for lumber is a worthwhile task. The first case may be harvesting
baby harp seals, since many argue that the goods made from the seals can be
made inexpensively using synthetics.
While this is a very simple example, it is a useful means of displaying
the potential for describing the links between economies and ecosystems.
Questions of optimum exploitation and extinction can be inferred from sophis-
ticated versions of the analyses in Figures 8 through 10. But research is
needed to determine the shape of the possibility frontiers, which means that
research into physiology sets of ecosystems and the technology sets of
economies will be required.
Summa ry and Conclusions
We have tried to demonstrate how the application of economic analysis to
bioenergetics, a framework with some degree of acceptance in ecology, can be
used to describe the behavior of ecosystems. Moreover, we have indicated how
the descriptions thereby obtained can be made an integral part of a model
adapted from Lancaster (1975) that, in principle, can be used to value both
the yield and the diversity impacts of stresses upon ecosystems. We are by no
means the first to express the thought that the human-induced ecosystem
effects for which one may feel secure using the conventional methods of
benefit-cost analysis may be those having the least long-term economic
significance. The conventional analysis disregards mayflies because their
contribution to the food supply of trout has been untraceable. We believe
further attempts to combine bioenergetics and economic analysis might make
this neglect untenable. Neglect of the life support services that mayflies
and their peers provide for trout may mean that the ultimate effects of
pollution on trout, via mayflies, may go unrecognized and therefore
unaccounted.
114
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Just as the conventional analysis disregards the life support services
provided by soil microbes, dung beetles, and caddisflies, it focuses upon an
(incomplete) item-by-item listing of organisms in the ecosystem while failing
to consider how the proportions in which these organisms are present might be
sources of human pleasure. The ecologist, even though he has lacked an
acceptable means to value ecosystem diversity, seems to have been more
sensitive t6 this "source of welfare than has the benefit-cost analyst.
Economic efficiency, narrowly interpreted as minimizing the inferred or
observed cost of producing a given quantity of ecosystem yields (and thereby
taking advantage of all scale economies), need not result in maximum human
welfare if there exists diversity in tastes among individuals for types of
ecosystems or if ecosystem components are not valued independently of the
environmental state from which they come. We speculate that traditional
benefit-cost analysis, to the extent that the information it generates has
been used for decision purposes, may occasionally have fostered Pareto- losses
rather than Pareto-improvements. At a minimum, it has probably brought about
wealth transfers from those who value ecosystem diversity and variety to those
who possess the machinery for producing and maintaining ecosystem homogeneity.
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REFERENCES
This ignores other possibilities like geothermal systems or tides.
* ¦
This is somewhat simplified in that it ignores more complex chains.
Lotka likens the development of this model to the work of Jevans and the
marginalist school of economists. He recognizes that this maximal is not
appropriate for humans. Borrowing from Pareto, he describes humans as
maximizers of pleasure. This is consistent with maximizing species
growth only if the marginal pleasures (i.e., marginal utilities) are
proportional to the marginal productivities of the physical needs. Thus ,
Lotka essentially denies the validity of an energy theory of value which,
as pointed out earlier, has been propounded by many modern day
ecologists.
The physiology set is analogous to the firm's technology set often used
in economics. The development of the model presented here closely
parallels the development of the economic model in Russell and Wilkinson
(1979, Chapter 7).
This is paraphrased for Russell and Wilkinson's (1979, p. 129) definition
of technologically efficient bundles.
Condition (12) is analogous to the geometric solutions of Rapport (1971)
where he determines the optimum selection of two different preys. His
indifference curves represent two net inputs and one net output in. the
model used here.
The numbers of a particular species are capable of interbreeding.
See Freeman (1979) for a thorough survey of available techniques
for answering this question.
The work of Bigelow and his colleagues (1977) is a detailed account
of the ecosystem possibilities in a Dutch estuary. Odom (1971) and
other ecology texts are replete with other examples.
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Other plausible reasons exist. For example, a process through
which the individual can register his ecosystem preferences may be
lacking.
11/ The envelope theorem (Shephard's lemma) assures us that the solution
to this problem -is equivalent to the solution of the utility maximization
problem.
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BIBLIOGRAPHY
Bigelow, J.H., C. Dzitzer, and J.C.H. Peters, Protecting an Estuary From
Floods - A Policy Analysis of the Oosterschelde, Vol. Ill, R-121/3-Neth,
Santa Monica, CA: The Rand Corporation (April 1977) .
Boulding, K.E., "The Economics of the Coming Spaceship Earth," in H. Jarrett,
ed. , Environmental Quality in a Growing Economy, Baltimore, md. : The
John Hopkins Press (1966), pp. 81-92.
Coleman, D.C., et al. "Energy Flow and Partitioning in Selected Man-Managed
and Natural Ecosystems," Agro-Ecosystems, 3(1976), pp. 45-54.
Energy Research and Development Agency, A National Plan For Energy Research,
Development, and Demonstration: Creating Energy Sources For The Future,
Washington, D.C.: US Government Printing Office, (1975).
Freeman, A.M. Ill, The Benefits of Environmental Improvement, Baltimore, md:
The John Hopkins University Press (1979) .
Georgescu-Roegen, N., "Energy Analysis and Economic Valuation," Southern
Economic Journal 45(April, 1979), 1023-1058.
Grodzinski, W., R.Z. Klekowski, and A. Duncan, Methods for Biological Energetic
Oxford, U.K.: Blackwell Scientific Publications (1975).
Hannon, B., "Marginal Product Pricing in the Ecosystem," Journal of
Theroetical Biology, 56,(1976), 253-267.
Hannon, B., "Total Energy Costs in Ecosystems," Journal of Theoretical
Biology, 80(1979), pp. 271-293.
Harkov, R., and E. Brennan, "An Ecophysiological Analysis of the Response of
Trees to Oxidant Pollution," Journal of the Air Pollution Control Asso-
ciation 29(February 1979), 157-161.
Hirshleifer, J., "Economics from a Biological Standpoint," The Journal of Law
and Economics, 20(April 1977), 1-52.
Hobson, J.A., Economics and Ethics, Boston: D.C. Heath and Company, (1929).
Jorgensen, S.E. , and H. Mejer, "A Holistic Approach to Ecological Modeling,"
Ecological Modeling, 7(1979), pp. 169-189.
Kormondy, E.J., Concepts of Ecology, Englewood Cliffs, N.J.: Prentice Hall,
Inc. , (1969) .
Krutilla, J.V., "Conservation Reconsidered," The American Economic Review,
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57(December, 1967).
Lancaster, K.J., "Socially Optimal Product Differentiation," The American
Economic Review, 65(December, 1975), pp. 567-585.
Lotka, A.J., Elements of Physical Biology, Williams and Wilkins, Baltimore,
MD: (1925).
Margalef, R., Perspectives in Ecological Theory, Chicago: University of
Chicago Press, (1968) .
Mauersberger, P., "On the Role of Entropy in Water Quality Modeling,"
Ecological Modelling, 7(1979), pp. 191-199.
May, R.M., "Stability in Multipspecies community Models," Mathematical
Biosciences 12(1971), 59-79.
Myers, Norman, The Sinking Ark, Permanan press, Ltd., oxford England, 1979.
Odom, E.P., Fundamentals of Ecology, Philadelphia: W.B. Sanders Company, 1971.
Odom, H.T., Environment, Power and Society, New York: John Wiley and Sons,
Inc. , (1971) .
Pielou, E.C., Mathematical Ecology, New York: John Wiley and Sons, 1977.
Prance, G.T., "Floristic Inventory of the Tropics: Where D.W. Stand?" Annuals
of the Missouri Botanical Garden, 64(1977), 659-684.
Rapport, David J. "An Optimization Model of Food Selection," The American
Naturalist, 105(Nov.- Dec. 1971), 946-952.
Russell, R. Robert and Maurice Wilkanson, Macroeconomics, New York: John Wiley
and Sons, (1979).
Scitovsky, T., The Joyless Economy, New York: Oxford University Press (1976).
Tullock, G., "Biological Externalities," Journal of Theoretical Biology , 33
(1971), 565-576.
Watt, K.E.F., Principles of Environmental Science, New York: McGraw-Hill
Book Company (1973).
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Woodwell, G.M., "Effects of Pollution on the Structure and Physiology of
Ecosystems," Science, 168(April, 1970), 429-433.
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v. NATURAL SCIENCE RESEARCH USEFUL TO THE ECONOMIST
Introduction
Throughout the preceding chapters, we have emphasized the necessity of
knowing the influence of various physical and biological factors upon some
ecosystem variable of interest if economic methods foj assessing the benefits
of controlling acid precipitation are to be applied.— At the same time, we
have formulated several analytical and empirical characterizations of the acid
precipitation problem intended to be helpful in deciding which of these
relations are likely to be worthy of more immediate research attention. For
example, our discussion of nonconvexities and irreversibilities in Chapter 111
leads to the conclusion that the very early stages of ecosystem acidification
often have the greatest economic consequences. The devotion of research
resources to understandings of the behaviors of already highly acidified
systems may, therefore, yield little information that is economically
important. However, before abandoning or greatly reducing research on already
highly acidified systems, it is obviously important to establish accurately
the temporal and spatial frequencies of the nonconvexity and irreversibility
issues. If these issues appear with considerable frequency, then an
allocation of research resources that accords with the ordering of current
annual sectoral control benefits estimated in the "first exercise" of Chapter
II might well be mistaken. The economic import of a unit of information on
indirect ecosystem effects could presently be much higher than would more
information on materials damages or direct agricultural effects.
The treatment in Chapter IV is intended to reinforce the theme that the
(relatively) easily observed current direct economic effects of acid precipi-
tation could readily have the least long-term economic significance. By
providing a skeleton for combining economic analysis with ecological
energetic that is built upon resource allocation processes, we have tried to
establish a basis for valuing the possible effects of acid precipitation upon
the life support services and human pleasures that ecosystems supply.
Traditional economic assessment methods, as set forth in Chapter I, disregard
these services except insofar as they are valued independently of the
environmental states that produced them. Any empirical implementation of the
skeleton set forth in Chapter IV that captures at least some features of the
values of these life support services will clearly require substantial
contributions from that part of ecology which describes the combinations and
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quantities of ecosystem components resulting from various quantities of
available energy.
Although knowledge of the response of some result to various mixes and
magnitudes of inputs is central to the concerns of previous chapters, we have
as yet discussed few criteria for deciding when a particular response, given
limited research resources, is worthy of attention. in succeeding sections of
this last chapter, we present some qualitative criteria for deciding when
attention is warranted. We also shall point to some factors that might
determine the relative benefits and costs of alternative research efforts into
particular ecosystem responses to acid precipitation. In economic language,
the concern of this chapter is with the value of research into the effects of
acid precipitation upon ecosystem production functions or response surfaces.
Because the economist's concept of the production function often differs in
subtle but economically important ways from the natural scientist's idea of a
dose- response function, we take a brief respite in the next section from the
central purpose of the chapter to present a brief overview of concepts in
production theory particularly relevant to later discussion.
The Production Function
All results or outputs require at least two kinds of causative agents or
inputs. Usually many more than two inputs are required. In general:
Y = f(xn ,x0, . . .,X ), a)
X i. II
where Y is the quantity in similar units of an output rather than the number
of possibly dissimilar individuals in some biological, population, the X,(i =
are input quantities which may themselves be an output of some other
production process, and Y, X^>_0. without exception. It is usually^ but ^eed
not be, assumed that (1) is twice differentiable, with 8Y/8X, > 0, a-y/ax,
< 0, and £(X^/Y)C9Y/9X.) < 1. Negative inputs such as acid precipitation can
be defined so that redactions in their levels constitute positive inputs. The
first two assumptions are typically referred to respectively as positive but
diminishing marginal products, while the third assumption represents
decreasing returns-to-scale. The expression (1) is typically viewed as being
perfectly reversible, where reversibility is defined as the absence of
asymmetrical changes with respect to the status quo point and the direction, of
movement. Rarely are anv restrictions placed upon the sign of 8 Y/3X 3X. for
i + j • J
Expression (1) implies that all the x are variable and of relevance for
determining the value of Y. However, there are many instances where the in-
fluence of an X upon a Y is trivial or nonexistent either because the X is
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fixed or has so little influence that it can be disregarded. Thus if n-m
inputs are fixed or considered to be trivial, (1) can be written as:
Y = f(X..,. . .X ; X . . ,,x) , (2)
1 m m+ 1 n
with the X's to the right of the semicolon being treated as irrelevant for the
problem at hand. "
Neither (1) nor (2) are necessarily concerned with growth in terms of the
number of individuals in some biological population. Temporal considerations
may nevertheless be introduced by treating time as one of the inputs or by
treating the inputs themselves as functions of time. However, most economic
treatments treat the time interval as fixed and emphasize various relations
between and among the biophysical and human inputs and between these inputs
and the outputs. These latter relations, rather than population dynamics
considerations, tend to be emphasized because they are the key to most
applications of the economic assessment methodologies outlined in Chapter I.
For a particular level of output, Y, rates of substitution, dX^/dX^,
between any pair of inraitq. X and X2, can be determined by total implicit
differentiation of Y = ffX^X^). Thu S , since X fCX^.Y), we have:
dX
9Y 1 + 9Y = 0
3X^ dX^
and therefore:
dX 9Y/8X2 (3)
dX 3Y/3X
2 1
where, as before, the numerator and the denominator on the right-hand-side are
the marginal products of the respective inputs. If the marginal products are
positive, (3) means that the level curve or isoquant depicting dX /dX^ for a
particular Y must have a negative slope as in Figure 1. The isoquant, Y, in
Figure 1. does not represent the rate of substitution of X for X^ in any basic
biochemical, or physiological process or production technique. It merely
displays the fact that within limits the same quantity of output can be
obtained from various combinations of possibly very diverse inputs. For
example, there are probably numerous combinations of reductions in acid
precipitation and liming of forest soils which will result in identical
standing stocks of timber. "The underlying physiological processes are of
interest only insofar as they contribute to comprehension of the effects of
input mixes and magnitudes upon an output or result that has economic
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relevance.
Given that there are positive marginal products for all inputs, there
will exist a series of isoquants like those depicted in Figure 1. Levels of
output are increasing as one moves away from the origin. The set of all such
isoquants is a response surface. If all inputs but one are fixed, say at X?in
Figure 1, then the' response of Y to various applications of is a response
function.
If the marginal £>rodu£ts of each input are someplace positive but dimin-
ishing OY/9X. > 0, 3 Y/9X. < 0), then some portion of a level curve or
isoquant , .1 . dX /dX2^or a particular Y will have a convex shape as in
Figure I — -imp, ies that as one moves up (down) the isoquant, it becomes
progressively more difficult to substitute X2^) for xl(x2)'" that is, a
larger and larger quantity of X2(XJ is required "to replace the loss of a unit
of X|(Xo) if the level of output is to remain, unchanged. There is, of course,
no reason whv the isoquant could not be depicted as in Figure 2, where the
concave interval ABCD implies either that the marginal product of one or the
other inputs has become negative (the intervals AB and DC), or that the
marginal products of both inputs are negative (the interval BC). Whether
reference is to human decisions or to the behavior of a nonhuman organism, if
the d.soquant were everywhere concave, only one input would ever be used since
the marginal benefits of use of the first input would decrease the more of the
other input was used. The use of only one input does not usually accord with
experience in either the human or natural worlds, thus implying convexity of
the level curves. Production objectives would be ill-served by operating in
the concave portion of the isoquant (the interval ABCD): the same level of
output could obtained by^ysing less of both inputs or less of one input and
no more of the other input.—
In Figure 2, we see that the concave portion (the interval ABCD) of an
isoquant need not be described in any detail because these portions ill-serve
any organism that acts "as if" it wishes to minimize the resources that must
be expended to reach a given level of an objective. For example, a human
might wish to minimize the costly resources he must use to achieve a given
goal, and a nonhuman organism might behave so as to minimize the available
energy it must expend to acquire a particular amount of nutrition. If only
those portions of the response surface are studied where all inputs have
positive marginal products, one may rest assured that concave portions are
being avoided.
Economic analysis can be employed to delimit further the portions of the
response surface that are worthy of description if organisms behave as if they
minimize the resources that must be expended to reach a given level of an
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Figure 5.1
A Response Surface
x
Figure 5.2
Convexity and Concavity
B
D
124
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objective, or, equivalently, as if they maximize subject to available
resources the level of attainment of some objective, whatever this objective
might be. Reconsider the fox in Chapter IV who obtained his nourishment from
various combinations of rabbits and squirrels. The combinations that he chose
and therefore the only steady-state or long-run equilibrium combinations that
would be observed in nature would conform to a condition where any reduction
in the net input of energy obtained from rabbits (squirrels) would be matched
by an increase in the net input of energy obtained from squirrels (rabbits).
Thus , if one were trying to describe the effect of pollution upon the feeding
habits of foxes with respect to rabbits and squirrels, only those combinations
of rabbits and squirrels on the convex portion of each fox isoquant that
conformed to the condition under various pollution levels would be of
interest. Of course, these combinations mav themselves constitute the object
of any research effort. Nevertheless , it is likely that an accumulation of
research knowledge would ultimately indicate that some rabbit and squirrel
combinations on the convex protions of the isoquants are clearly inconsistent
with the condition, meaning that their impact upon the well-being of the fox
need not be candidates for description. They would certainly be of no concern
to the fox, and if the only research object is to describe naturally occurring
states, information about them would be of no value to humans. Alternatively,
if it is initially thought that any one of the combinations on the convex
portion of a particular isoquant could ultimately prove to conform to the
condition, information on the state of the fox's well-being under each of
these combinations would have some positive value. In short, the researcher,
if he is interested in describing naturally occurring states must dismiss
consideration of input combinations known to be inconsistent with the behavior
of the organism that is the subject of the research. Economic analyses of
research allocation processes, as set forth in this and the previous two
chapters, can contribute to identifying the aforementioned combinations.
Those who refuse to let the behavior of organisms direct their research would
apparently perceive no qualitative difference between studying the effect of
feeding corn to a beached whale and studying the impact of SO^ fumigations
upon a laboratory plant that is supplied with more nutrients than it could or
would acquire in its natural or agricultural state.
The Value of Information and of Alternative Models
Returning momentarily to (1), there are several levels of completeness of
knowledge that one might acquire about the effect of pollution on a given
production or response surface. Completeness would involve knowledge of the
coefficients attached to each of the input variables on the right-hand-side of
(1) and of its functional form. In the absence of knowing the values of the
coefficients knowledge of whether each input variable has a "strong" or a
"weak" influence on the output would be nearly as useful. If this knowledge
l.?5
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is not directly available, knowlege of the functional form of (1) can allow
deductions to be made about the relative levels of influence of particular
input variables, given that one has some _a priori idea about the plausible
bounds for the values of some coefficients. Moreover, knowledge of functional
form assists in directing research to those input variables likely to be most
influential in determining output magnitudes. However, a priori knowledge of
the functional form of (1) is very frequently beyond the analytical powers of
the relevant disciplines to obtain. Most often, the specification of
functional form must wait for the gradual accretion of empirical experience.
Usually well before this empirical experience has been fully accumulated,
deductive or empirical insight is acquired into the signs of 3X./3X,, 3Y/3X ,,
a Y/axi, and a Y/3X.3X.. As the bodies of theory in many disciplines, 1
including macroeconomics! and ecology, attest, knowlege of these signs can be
most helpful. in drawing inferences about the underlying structure of the
natural or social system being investigated. Having acquired these structural
insights, bounds can often be imposed upon functional forms, the relative
influences of variable pairs, etc. If knowlege of the signs attached to the
preceding derivatives cannot be obtained, decisions founded on particular
production or response surfaces must resort to simple listings of all or some
of the variables thought to enter the right-hand-side of (1). However, unless
these listings can ultimately be molded into a theoretical structure, they can
contribute little to ultimate knowledge of the production or response surface.
Only by sustained and substantial efforts to accumulate empirical experience
can this knowledge be acquired. Even then, it must remain, unknown whether the
accumulated empirical knowledge is generalizable to as vet unobserved events
or whether different results obtained from seemingly similar settings are
reconcilable.
There exist, as is clear from the preceding remarks, two mutually rein-
forcing yet partially substitutable fundamental ways in which knowlege about
response surfaces can be acquired. Two legs, the theoretical and the
empirical, are required to walk well, but for some tasks, one leg can
accomplish more than the other. The question nevertheless remains as to how
far toward complete specification of the form of the response surface
investigation, whether theoretical and/or empirical, must proceed. This
question can best be understood within the context of the economics of
information. Two concepts, the value of information and the value of
alternative models, are central to any research effort into the effects of
acid precipitation upon the response surfaces of various ecosystems
components.
The results of this research are intended to be of direct use to persons
who must make decisions about the control of acid precipitation or to serve as
inputs into other research efforts providing results useful to decisionmakers.
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Research designed only to reveal a greater understanding of basic biochemical
or physiological processes must be evaluated on some basis other than that
developed here. In order to establish a framework for evaluating research
into the effects of acid precipitation upon the response surfaces of ecosystem
components, one must consider together the decision which is at issue and the
decisionmaker. As.Crocker (1975, p. 342.) remarks, "the choice of a particular
research effort or information system implies the use of a particular class of
decision models since certain tvpes of information are relevant to some models
and not relevant to others. Converselv, the choice of a decision model
implies the use of a particular class of information systems yielding the
parameters of the model. — decision variable of interest here is the
amount of acid precipitation to which an ecosystem component is to be
subjected. The payoff from the decision is the net benefits of controlling
the acid precipitation, defined as the economic value of the ecosystem
component damages prevented less the cost of controlling the acid
precipitation. The payoff is related to the decision through some imperfectly
understood response surface.
As earlier noted, the arguments of the response surface include a great
many other variables in addition to acid precipitation. The imperfectly
understood response surface is approximated by some expression such as (1),
where some X's might represent a taxonomic system (e.g., soil classes)
originally established for an entirely different purpose, other X's might be
measures set up specifically for the study of acid precipitation effects upon
the ecosystem component of interest, and still other X's are inputs which can
be measured but not predicted. Finally at least one X in fl) must represent a
residual or error term intended to capture unknown, unacknowledged, and purely
stochastic influences on the response surface.
The payoff, it is approximately related to the decision variable as:
II = p f(-) - CXA (4)
where p is the observed or inferred unit price of the ecosystem component of
interest, c is the cost of reducing acid precipitation by one unit., and X . is
A
the number of units of acid precipitation. Since there exist unknown,
unacknowledged, and purely stochastic influences upon f(*)> and since the
values of some other variables cannot be predicted prior to the control
decision, for any given level of acid precipitation, the payoff is a random
variable.
Whether performed by economists or noneconomists, the standard way to
account for the randomness in expressions such as (4) has been to use range
sensitivity tests. Waddell (1974) , for example, includes upper and lower
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bounds and "best guesses" for various air pollution damage categories. A
similar procedure is adopted in most of the ambitious work in d'Arge, et al.
(1975) on the economic impact of climatic change as well as in Fisher's,
et al. (1979) work on air pollution, damages in the State of California. An
alternative but unfortunately rarely used procedure is to generate probability
distributions for the random variables or the right-hand-side of (4) , and then
to aggregate these distributions to produce a probability distribution for the
payoff measure.
Two readily un.derstandable examples of this approach, where the Weibull
(1951) family of distributions is employed, are Pouliqueri (1.970) and Mercer
and Morgan (1975) . These studies demonstrate that the valuable information
made available to the decisionmaker and the researcher can be considerably
enhanced: not only is he provided with the range of possible outcomes and
payoffs but he is also presented with various common summary statistics
allowing him to assign a probability statement to each outcome. These state-
ments can be subjective rather than objective. Accumulated wisdom and
intuition can be incorporated in an explicit and communicable fashion.
Although many would object to the inclusion of subjective information, the
question of real importance is not whether a particular probability assessment
is subjective or objective but whether it has important consequences for the
decision problem. Rather than fulminating over variables in some particular
algebraic specification that fail to have coefficients significantly different
from zero, most concern should be displayed about whether the formulation in
question predicts better than the next best alternative. Errors of omission
would seem no less worthy of critical scrutiny than errors of commission.
Another major advantage of the probability approach is that it does not
throw away useful information. For example, in a poorly coordinated group
research effort attempting to assess direct acid precipitation damages to
commercial crops, the biochemist or agronomist might specify a response
function relating some attribute of the crop to acid precipitation. This
function, which the economist will employ to perform his assessment tasks,
will likely be what the natural scientist considers to be the "best" of a set
of several alternatives. In the absence of a thoroughly coordinated research
effort in which the economist specifies the variables, units of measure, and
sampling procedures the natural scientist is to use, it is likely that the
natural scientist's conception of "best" does not coincide with the
economist' s.
It is then up to the economist, who usually is only semi-literate in the
relevant natural science, to translate the natural scientist's results into
something useful for purposes of economic analysis. Moreover, by being asked
to present a "best" function, a great deal of the natural scientist's unique
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knowledge is being thrown away. Finally, the failure to report the full set
of probable outcomes to the economist and thereby the decisionmaker means that
yet another decision problem has been introduced: the natural scientist must
assess which of the alternative formulations the decisionmaker will find most
useful. By requiring that probabilities be assigned to the various plausible
outcomes, the force of this decision problem is greatly ameliorated.
Any specification of a reponse surface will, except by chance, always be
wrong. The suggested probability approach to the study of acid precipitation-
induced response surfaces captures this fact. The implications of this for
planning research into these response surfaces can be perceived by considering
the investigator who must begin with very little information about the surface
to be investigated. Guided by the principle that information should be
acquired only as long as its value exceeds the cost of obtaining it, he can
search for a finite number of kinds of information in varying quantities.
Paraphrasing Marschak and Radner (1971), the value of additional information
is the difference between the decisionmaker's current expectations of: (a)
the payoff value that will occur if he chooses his act as well as he can
without the information; and (b) the payoff value that will occur if he were
to obtain the information and then choose his act as well as he can. In
short, the value of the information is the increment in expected payoff that
can be realized by having the information contribute to the decision.
When additional information is defined as a finer partitioning of some
natural state, it may consist of both observations and experiments on a
greater number of variables or on a particular variable, and a more
discriminating model of the surface, i.e., a model that is better able to
distinguish among alternative outcomes. The researcher must decide whether
the reduced uncertainty and systematic broadening of identifiable alternatives
that more information offers outweighs the costs of acquiring the information.
The number of distinctions drawn can be no greater than the number of
measurable consequences, if differences in payoffs are distinguishable only
insofar as they generate measurably different results. In the next section,
we take note of some of the more important aspects from the economist's
perspective of this problem.
Issues in Designing Studies of Response Surfaces
Anyone who proposes to engage in estimation of, as opposed to expatiation
about, response surfaces must give pragmatic consideration to several
practical and interrelated issues. All these issues require compromises with
the abstract analytical frameworks of the applicable disciplines. A
reasonably complete listing with particular relevance to the study of acid
precipitation-ecosystem component response surfaces might be as follows: the
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design of response surface experiments; the estimation of these surfaces; the
choice of a model to represent the surface; and the sources of discrepancies
between response surfaces estimated in controlled or experimental conditions
and observed in field conditions. We shall deal with each of these issues in
sequence, trying to highlight those features of the issue that seem
particularly relevent to studies of the impact of acid precipitation upon
response surfaces.
Experimental Design: In situations where an experiment is the
biologically appropriate way in which to generate and to test hypotheses about
response surfaces, it is highly important that the economically relevant
region (as defined in a previous section) of the surface be purposively and
systematically covered. The great majority of biological research into
response surface questions is of minimal use to the economist because it does
no more than use analysis of variance techniques to establish only whether
there exist statistically significant differences in the output obtained from
a few levels of a single input. Rather than trying to design a systematic
coverage of the economically relevant portion of the surface, the traditional
emphasis has been and continues to be on replication, as if arbitrarily
selected levels of statistical significance could impart structural
understanding of system behaviour. Not only is the replication intended to
improve the analysis of variance but to measure the variance as well. When
the objective is to estimate a response surface, replication is much less
essential. Primary concern should be with developing a model that predicts
real world outcomes better than the next best alternative rather than testing
whether the results of some particular model have statistically significant
differences. Predictions are made so that something can be done: they are
not first objects of contemplation. The proper object is informed
manipulation of the system.
Changes in input mixes and magnitudes can substitute for replications of
a particular input mix and magnitude since both types of observati.ons are
intended to locate the response surface more accurately. For a given outlay
of research resources, the information provided by more observations on output
responses to an assortment of economically relevant input, mixes and magnitudes
will usually be more valuable than will the information garnered from
additional replications using a particular input mix and magnitude. Moreover,
if alternative models have similar a priori plausibility as descriptors of a
response surface, empirical discrimination among models will obviously be
assisted more by increasing the breadth and the density of the sampling
coverage of the surface rather than by replication of experiments directed at
only one point on the surface. A near-infinity of models is consistent with a
single point.
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Bluntly put, the traditional experimental designs of biologists inv-
estigating response surfaces have been motivated by the maximization of disci-
plinary integrity. Designs have been structured via the mechanical
application of purely statistical criteria so as to minimize the probability
of accepting a false hypothesis. The result has been an excessive emphasis
upon replication, if the purpose of the research is taken to be the provision
of useful information to economists and to decisionmakers. To pose the point
in an extreme fashion, given that it is well-known that acid precipitation
harms fish, it is ridiculous even to advance for testing purposes the null
hypothesis that fish are unaffected by acid precipitation. Neither the
economist nor the decisionmaker cares whether there is a five per cent or less
chance that a fish-acid precipitation response surface exists. Their problem
is to know the value of the fish that are lost due to acid precipitation.
Thus, if disciplinary custom dictates the supplication of significance tests,
logic, rather than custom, requires instead that their application to the
value-related quantities derived from the response surface be stressed. This
stress would be consistent with our remarks in the previous section about the
desirability of having probability distributions for the payoff measure.
Put in yet another way, because of the reasonable desire of each
specialist to maximize his disciplinary integrity, a tension exists between
the biologist and the economist with respect to the design of response surface
research. The biologist will obtain less approval from his peers if he does
not replicate in accordance with traditional standards. The economist will
obtain less approval from his peers if he tries to draw inferences from a
small undense and narrow sample of the response surface. For the latter
individual, the cost of knowing nothing about large portions of the response
surface will typically greatly outweigh the costs of small errors in estimates
of a single point on that same surface. In design language, the economist is
interested in the magnitudes of differences in treatment effects rather than
in the existence of these differences.
Having pointed out a source of conflict in the desires of biologists and
economists with respect to the design of response surface experiments
conducted with limited research resources, we would like to provide some
specific criteria a neutral observer could use to weigh the tradeoff between
replication and density of coverage. Anderson and Dillon (1968) provide a
detailed treatment of the efficiency conditions for this choice. Conlisk
(1973) , Conlisk and Watts (1979), and Morris (1979) extend earlier treatments
of optimal experimental designs to cases where the form of the response
function is unknown and both the research budget and the number of
experimental units are limited. In the absence of a specification of a
particular design problem, the three universal implications of these
conditions for response surface experimental design are rather simple and
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4/ ...
apparent. First, the greater the sensitivity of the system being
investigated to variations in exogenous parameters, the greater the
desirability of additional replication. Second, the greater the number of
factors thought to impinge in nontrivial ways upon system behavior, the more
desirable :s increased density and breadth of coverage of the economically
relevant regions of the response surface. Third, since it is along these
portions that outputs are sensitive to input mixes and magnitudes, research
resources should be aimed at denser coverage and greater replication along the
steeper parts of the economically relevant portions of the response surface,
i.e., along those portions where 3 Y/8X &i YY/3X. 3X. , 3X./9X., and
Z (X./Y) (9Y/9X.) are substantial in absolute value. Th^se pa"rts have the
11....
greatest economic significance.
The preceding remarks with respect to the tradeoff between increased
density of coverage of the response surfaces versus increased accuracy of
estimation of a point on that surface apply with equal force to spatial and
temporal influences. For example, those who determine the allocation of
research resources into the ecosystem effects of acid precipitation will be
faced with choices about whether it is preferable to study one or a very few
locations in depth or to distribute limited research resources over a wide
variety of locations. To the extent that the economically relevant portions
of response surfaces are susceptible to spatially and temporally distributed
factors, it is important to account for them. A one time period, one location
experiment will provide little useful information for analysis. Some insight
on how response experiments might best be located over space and time so as
appraise variability is provided by Anderson (1.973).
Tn general, the essential fact of which the allocator of research
resources must be aware is that there likely exist positive but declining
marginal payoffs to additional observations drawn from any particular system
or for any variable or particular combination of variables in that system
thought to influence the response surface: that is, each additional
observation adds something to the expected payoff, but these additions get
progressively smaller as the number of observations increases. If the cost of
research is a monotone increasing function of the number of observations, one
obtains the familiar optimality condition determined by the equation of
marginal costs and marginal payoffs.
Evenson and Kislev (1975) have made use of this condition to distinguish
between basic and applied research. They describe the latter as involving
drawings from a given probability distribution of the research payoff, while
basic research shifts the first moment of the distribution or discovers new
distributions from which to draw. A similar distinction might be made between
acid precipitation response research which proposes to concentrate on one or a
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few locations, and thereby proposes to draw observations from only a very
limited number of payoff probability distributions, and response research
intended to draw from a variety of distributions by spreading out its
available resources over a substantial number of locations. Research bound to
one location will, by definition, have to concentrate its observations around
one payoff value. 4There is thus very little chance of discovering different
payoffs because the system responses that might yield these payoffs remain
unobserved. Consideration of a larger number of spatial and/or temporal
settings would bring about a large increase in the sample variance, partly
because more natural experiments are likely to appear and partly because a
wider range of system input combinations would come under investigation. In
many areas of scientific research (e.g. , plant breeding) this wider range of
natural experiments and system input combinations has ultimately led to the
development of techniques to affect the distributions from which the drawings
are taken, and thus to allow the acquisition of information outside the range
of historical experience as well as enabling the researchers to limit drawings
to those response surfaces of greatest concern. In effect, the ability of
decisionmakers who use research results to predict the outcomes of alternative
programs is enhanced. Or, equivalently, the range of alternative programs
available to the decisionmaker will be systematically narrowed as his inform-
ation structure loses its ability to discriminate among different real
outcomes. Unlike programs may appear to be similar in terms of their measured
results and may thus be mistakenly treated as identical. Given the apparent
sensitivity of the ecosystem impacts of acid precipitation to a large number
of alternative combinations of biological and geochemical factors, we feel
secure in adopting the position that a deaf ear should be turned to scientific
counsel that urges the concentration of acid precipitation response surface
research to a very limited number of locations. There appears to be
insufficient understanding at present of acid precipitation response surfaces
to permit the easy transfer of a surface established at one location to other
locations.
Estimation of Response Surfaces: Setting aside the issue of the unthinking
application of significance tests, the circumstances in which the statistical
techniques available for estimating response surfaces in well-controlled
experimental settings are appropriate are well understood. Apart from
analysis of variance techniques, any good econometrics text such as Kmenta
(1971) will provide a detailed and thorough treatment of the subtle issues of
estimation that arise in a wide variety of commonly faced contexts, i~.eluding
joint outputs, nonlinearities in the parameters, observations which vary
cross- sectionally and temporally, systems of equations, non-normality of
error terms across experiments on the same response surface, truncated
dependent variables, and other matters. Econometrics appears to have little to
offer biometrics with respect to useful and correct applications of these
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techniques.
However, when the natural scientist uses field data rather than or along
with experimental data to arrive at response surfaces, the perspective of the
econometrician does have something valuable to offer. In particular, the
econometrician will be sensitive to the implications for estimation of the
fact that organisms' make or behave "as if" they are making choices. Accurate
estimation of the response surface parameters thus requires data on the
factors that influence these choices. Moreover, an explicit representation of
the organism's choice problem must be built into the structure to be
estimated. As was argued in Chapter TV, the choice paradigm is potentially as
powerful a means of explaining the behavior of monhuman organisms as it has
been for human organisms. The importance of accounting for its influence even
in a supposedly pure natural science exercise in estimating response surfaces
is easily illustrated.
Earlier, we have indicated that if response surface research is to be
most helpful to the economist, then it should be limited to what has been
defined as the economically relevant portions of the surface. Identification
of these relevant portions would likely be enhanced if an economist were to be
included in the initial stages of research design. Research resources would
be conserved. In the following illustration, inclusion in the original
research design of inputs from someone who thinks like an economist is not
only desirable. It is imperative if unbiased estimates of response surface
parameters are to be obtained.
To make the illustration fully plausible, assume the research problem to
be the estimation, through a combination of field and experimental data , of
the response of trout populations to acid precipitation. In implicit form,
a good approximation of the expression the natural scientist might apply to
the field data collected over a given time interval is:
Y = f(X,W,Z,E,£) (5)
where Y is the stock of trout, x is a vector of aquatic ecosystem character-
istics, W is a vector of weather characteristics during the period of
analysis, Z is a. measure of the fishing pressures imposed by humans upon the
trout stock, F, is a measure of trout stock exposures to acid precipitation,
and e is a stochastic error. The a priori information that experimental
regimens have provided might be used to determine the functional form and the
listing of variables on the right-hand-side of (5) , to restrict the signs
and/or the magnitudes of the coefficients of these variables, and/or to
specify the properties of the error term. For simplicity, assume that (5) is
linear in the original variables. The coefficient attached to the acid
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precipitation variable is then the reduction in trout stocks due to a one unit
increase in acid precipitation. Would it then be reasonable to infer a
dose-response association from the coefficient of this variable?
The aforementioned inference would be correct if and only if it is
possible to alter £he, acid precipitation exposure without altering the value
of any other explanatory variable in the expression. It is easy to show that
this cannot be done unless the structure of the response surface is presumed
to consist of no more than one relationship. More than one relationship is
present in (5) ; it contains a variable, Z, the levels of which have been and
continue to be subject to control by fishermen. That is, during the period
over which it is thought acid precipitation effects can occur, the fisherman
can influence by his voluntary choices the fishing pressures applied to the
trout stock. For example, the reduction in trout stocks due to exposures to
acid precipitation might be dependent on the number of mature fish capable of
reproduction that fisherman have caught. In order to explain the trout stock
outcome, the researcher must do more than simply enter the amount of fishing
pressure: he must also explain the structure underlying the choice of the
degree of fishing effort applied. One element in this choice will be the size
of the trout stock. The following simple example shows one way in which trout
stocks and fishing pressures might be jointly determined.
If both the acid precipitation-trout, stock response function and the
fishing activity demand function can be linearly approximated, they can be
written as:
Y = + a^E + a^X + a^Z + a^W + C6)
Z"61 + B2Y * V * B4P & 65P i G2 171
Expression (7) states that the quantity of effort the fishermen choose to
expend is related respectively to the trout stock, fishermen income, an index
of the unit prices of substitute recreational activities, and the unit price
of fishing effort.
Solving (6) and (7) for Y, we have:
a + 8 a a a 8 a aee
Y = 1 a 4 1 + 2E+ 3 X + 4 3 I + 5w+421
(o)
1 - a 8 1-a 8 I.-a 3 1-a 6 1-a 3 1-a B
42 42 42 42 42 4 2
Consider the coefficient attached to E in (8) . If E is acid precipitation,
(8) shows that an estimate of (6) will not yield the response of trout stocks
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to acid precipitation, even though, the dose-response function is "adjusted"
for aquatic ecosystem characteristics, weather, and fishing effort. Instead
the coefficient for E in (8) will be an amalgam of stock effects due to acid
precipitation, fishing effort, and the effects of trout stocks on fishing
effort. The product of the coefficients for the latter two effects would have
to approach zero in order for the response of trout stocks to acid
precipitation alonfe' t'6 be obtained. For this to occur, trout stocks could
have no effect upon the amount of fishing effort and/or fishing effort could
have no effect on trout stocks. Both assertions are equally implausible. In
fact, in the absence of further information, the sign that would be obtained
for E when (6) is estimated alone is ambiguous since
lone, that one would find that acid precipitation enhances trout
stocks. In any case, because the product of a and B is negative in sign,
the effect of acid precipitation on trout stocks wil^L be underestimated.
However, this negative bias in the response estimate is not predestined.
Given (7), a slightly different specification of (6) could readily introduce a
negative bias.
It might be reasoned that the difficulty with the preceding example could
be removed if the ability of fisherman to influence trout stocks were removed.
Expression (6) would not then have anv human decision variables in it and
would therefore seem amenable to the customary ministrations. These customary
ministrations might, however, continue to be incorrect, for the trout, while
acting "as if" they maximize net energy storage, are able to alter their food
gathering behavior in response to a change in the competition for food. Thus
the trout stock and some of the aquatic ecosystem characteristics, X, in (6)
are jointly determined: the trout stock helps to determine the competition
for food, and the competition for food helps to determine the trout stock.
Arguments similar to those above can readily be constructed for forests,
agriculture, materials, and most items and systems thought to be impacted by
acid precipitation. For example, productivity of a forest is influenced by
the management practices selected by the forest owners, who are reciprocally
influenced by the forest's chosen response to the selected practice. The
selections of the forest owners are not based upon physical parameters alone
but also on the economic factors that influence the benefits and costs of
management alternatives. Similarly, the estimated response to acid precipit-
ation of the salmonid species in an aquatic ecosystem is determined not only
by the acid precipitation and the fishing pressures applied but also by the
price of access for fishermen and the factors that determine the avoidance
behavior of the fish.
To attempt to account for the additional factors thought to influence an
and 3
>_ 0. It is entirely conceivable, if one were to
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organism's response to acid precipitation by simply stringing out variables in
a single expression must clearly often be incorrect. During the period in
which the response is supposed to occur, organisms can behave so as to
influence the magnitudes assumed by certain of these variables. Each variable
susceptible to this influence must be explained by an expression of its own if
the purpose of the^research is to explain the response of the organism to acid
precipitation rather than simply to predict its response. Unless
circumstances are identical across space and time, predictions based on some
version of (8) will err for reasons no one will be able to identify until the
response structure is comprehended. Because some human decision variables
both influence and are influenced by the response, economic analysis is
frequently necessary to impart an interpretable form to response expressions.
Purely biological constructs will therefore often be insufficient tools with
which to establish acid precipitation response surfaces. Moreover, even when
human decision variables have no role to play, the constructs of economic
analysis can assist, as was argued in Chapter IV, in explaining the behavioral
adjustments that organisms make to changes in acid precipitation exposures.
The above remarks need not lead to the conclusion that research on
complex basic biochemical and physiological processes is required for the
estimation of response surfaces. Jointly determined variables need be of
interest only insofar as they contribute to understanding to the manner in
which input mixes and magnitudes act upon outputs and results having economic
relevance. Nevertheless, the fact of joint determination does complicate
modeling and estimation procedures, occasionally beyond the ability of
available analytical and estimation procedures to grasp. For this reason,
there is information to be gained by establishing baseline descriptive
measurements for a variety of ecosystems and locations thought to be
susceptible to acid precipitation-induced effects. These effects can be
economically valued even if there is no more that an association between
changes in input mixes and magnitudes and changes in levels of the
economically relevant outputs. The latter change can be valued whether or not
the reasons for the change are comprehended. A demonstration that the
economic value of the change, whatever caused it, is great can serve to
stimulate research into the causes that might otherwise have been neglected.
However, if acid precipitation-induced changes are to be recognized, baselines
must be established against which the change can be estimated. These baseline
measures must, of course, document seasonal, variances.
Although the economic value of a change in an ecosystem can be
established even though there is no more than an association between outputs
and inputs, it is important to recognize that the units of analysis must be
defined in terms that contribute to the informed manipulation of the system.
In particular the research designer must be wary of employing measures which
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may be good predictors but which effectively deny the existance of certain
substitution possibilities of interest to human and/or nonhuman
decisionmakers. These denials are most likely to occur when the researcher
aggregates or groups variables. If the aggregate is, for example, a weighted
sum of a collection of inputs, there is an infinite number of combinations of
the inputs consistent with anv given magnitude of the aggregate. The
economically" relevant' substitution possibilities are then impossible to
discover. Furthermore, if spatial or temporal comparisons are being made
among ecosystems, unregistered changes in input mixes and magnitudes could
readily occur. The increases and reductions in the input components could
cancel each other out so that no change in the aggregate would take place. In
general, therefore, researchers should be extremely reluctant to employ
aggregated or grouped input variables when there exist grounds for suspecting
that ecosystem components have more than one way available to adjust to the
presence of acid precipitation.
Choice of Models: The comparative assessment of alternative models to
explain the bahavior of identical phenomena is among the most engaging
activities of any discipline. The usual criteria applied in models of
ecological systems appear to be an amalgam of statistical measures of goodness
of fit and significance, a priori considerations relating to the biology and
chemistry of the process in question, subjective judgement, and computational
tractability. Generalizations about the desirable properties of ecological
models, whether of the axiomatic or simulation types, relative to these
criteria are very scarce. This is perhaps because model appraisals based on
these criteria are bound to be misdirected.
The criteria for choosing among alternative models or theories of
ecosystem behavior when stressed by acid precipitation should relate to the
value of information they provide. If two models have the same costs in terms
of data requirements and application, the preferred model should be that which
provides the greatest expected payoff. If the models differ in their costs,
this difference should also be allowed for in the payoff appraisal. In
general, the important question is not whether any particular type of model is
biologically or statistically better than its alternatives, but whether it can
better serve the objectives of decisionmakers.
Adoption of the value of information perspective does allow ^ojpe obvious
generalizations to be made about the value of alternative models. - The
disciplinarian will usually opt for the analytical delights of ever increasing
generality in the specification of the models supporting his empirical
analysis. His ultimate objective would be the ability to predict the results
of every alternative source of system perturbation without having to alter any
of the relations expressed in his model. The generality and realism of the
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ideal model would be so great that there would never be any doubt in the
researcher's mind as to whether an observed change in some variable was random
and thus transitory in nature or whether it was due to changes in the values
of fundamental model parameters. However, the greater the progress of the
researcher toward this intellectually captivating state, the greater are
likely to be the number of variables for which he must make observations,
collect and organize data, and establish parameter values. Furthermore, the
complexity of relations among these model variables may be so great that
estimating techniques are either extremely costly or perhaps even nonexistent.
In effect, the elaboration and required detail of the model may be so great
relative to the availability of research resources that only superficial
attempts can be made to ascertain the true value of anv one parameter. The
problem in this case is not with a model that involves dangerous
simplification of reality but with a model which, given available research
resources, is alarmingly complex. The model is insufficiently artificial.
Just as one fails to capture the truth when he fails to comprehend the
complete structure of a system, he also fails when he is unable to measure
with some fair degree of accuracy the parameters of any given comprehension of
the structure.
On the other hand, the ideal of many applied scientists is to design an
experiment or research effort such that the scientist does not have to think
about what the results mean: the answer the experiment gives is unequivocal.
Attainment of this state requires that measurement be free from bias. That
is, it must be clear that the deviation of the result of any single
measurement effort from the mean of the results of repeated applications of
measurement effort under the least constrained conditions is purely random.
The measurement errors which occur when this condition is not fulfilled can be
reduced by devoting more resources to constructing measurement devices, and
techniques, by allowing more time for measuremen.ts to be made, and by better
training of measurement personnel. But measurement resources are expensive.
Paratt (1961, pp. 109-118) offers the following expression as a device
for weighing increased detail of model elaboration against reductions in the
error with which model parameters are measured. Let u be a derived property
related to the directly measured properties, x , . , x , by IT y(x^,. ..x ).
For example, u might be a measure of the economic benefits of acid
precipitation control. Given that the x's are not independent of each
other--they might, for example, be the parameters of a model for estimating
the effect of acid precipitation upon soil nutrient content, fresh water pH,
and fish populations-- the error in u due to the accumulation of errors in the
seperate estimates of the x's is given by:
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3f
e = Z I a
u I 3x
\ I
2,3e V2 _ (3f) (3f) (3e) (3e)
+ EE ~—„ ~—. ——r tz.—r r
3x1 Ox.) Ox.) Ox ) Ox.) ij (9)
if ... 1 i i t v '
if]
where e is the error in the estimate of u and r. . is the correlation between
iandj U The presence of the corrleation coefficient in the above expression
makes apparent at least one thing to avoid in the construction and use of
complex axiomatic or simulation models in ecology (and economics): do not
employ variables in the same model that are highly correlated with one
another. Generally, the greater the number of attributes introduced into a
model in the form of properties that must be directly measured, the more
likely are some pairs of these properties to be highly correlated. Relatively
simple models, by definition, require fewer directly measured properties for
their solution. in addition, with repeated model applications, a low value of
r means that overestimates of the payoff are likely to be compensated by
ii
underestimates, implying that the average of the expected payoffs will be
close to the true average.
Further inspection of (9) readily suggests two more bases for evaluating
the tradeoff between model elaboration and errors in measurement. First, the
presence of the partial derivatives, 3f/3x. and 3f/3x , indicates that
measurement resources are more likely to be allocated efficiently if they are
assigned to those directly measurable properties thought to have a really
significant influence upon the derived property. Since the variables that
have a significant influence upon e. derived property will frequently be the
same in both complex and simple models, the use of the simple model is to be
preferred if avoidance of substantial error in the estimate of the derived
property is of high priority.
Second, given the presence in (9) of the measurement errors associated
with the directly measured properties, it pays to devote resources to reducing
the larger of these measurement errors, including those interactive properties
(i's and j's) whose products in (9) are greatest. Since in simple models
there are fewer estimates of directly measured properties to be obtained, it
follows that, to a greater extent than in a complex model, a given stock of
measurement resources can be used to reduce the error associated with any one
property. Thus, given the cumulative nature of measurement error in models
where measured properties are tied together in long chains of reasoning, this
rule along with the previous two implies that simple models can be highly
advantageous in esitmating ecosystem responses to acid precipitation. The
advantages exist apart from the fact that simple models are relatively easy to
use and, in spite of the interesting scientific detail they may neglect, they
will usually give quick answers to questions.
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The preceding statements about the advantages of using simple models to
describe response surfaces have not been made in the absence of empirical
supporting evidence. For example, Perrin (1976), while studying the responses
of various Brazilian crops to fertilizer applications, has contrasted the
value to farmers of the information obtaine^ from a simple structure based on
Liebig's (1855) "1 aw" of limiting factors — to the information acquired from
a multi-input, nonlinear (quadratic) representation commonly favored in much
controlled fertilizer response research. Using a set of 28 experiments
conducted at various Brazilian sites over a three year period, he compared
farmers' implied ex post net revenues from the two distinct models. If soil
characteristics were accounted for, the simple one input, linear model based
upon Liebig performed equally as well as the nonlinear model.
Empirical, evidence similar to Perrin (1976) is now beginning to appear
for the connected black box simulation models so widely favored in much
applied ecological research. Stehfest (1978) has compared the payoffs from a
simple Streeter-Phelps model of dissolved oxygen and a complex ecological
optimal control simulation model with six state variables. Both models were
built to provide information on the costs of meeting a water quality standard
in a stretch of a West German river. The pavoff was defined in terms of cost
minimization. The total annual costs of meeting the standard when the water
treatments suggested by the simple model were implemented were 8 per cent
lower than would have been the treatments recommended by the more complex
model. Of course, the costs of establishing what constituted the recommended
treatments were also lower for the simple model. Additional reviews of the
performances relative to some objective of simple versus complex models are
available in Beck (1978), Griliches (1977), and Young (1978) . Outside the
econometric literature [Judge, et al. (1980), Chapters 2 and 11], few, if any,
implementable rules, other than those of Paratt (1961) already remarked upon,
issue forth from these discussions. There is, however, general agreement that
although it is naive to view simplicity per se as desirable, the research
administrator should place the burden of proof that valuable information will
be produced onto the proponents of proposals to build ever more complex
ecological and economic models.
Whatever the virtues of model simplicity, it must be admitted that
increases in model complexity are worthy attempts, in the absence of
information acquisition costs, to improve model robustness, where robustness
can be defined as the domain of circumstances where the model can be applied
without undergoing structural revision. However, as an alternative to the
devotion of more and more research resources to molding, measuring, and
manipulating an ever-lengthening string of variables someone reasons or feels
may influence what Young (1978) terms a "badly defined system," axiomatic
methods can be used. These methods, for which an example building upon
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bioenergetics is presented in Chapter IV, permit inferences to be drawn about
difficult-to-measure variables by deriving relationships between them and more
readily observed variables. In addition, these axiomatic methods, prior to
any attempt at measurement, allow discrimination between important and trivial
contributors to system behavior. Suggestions for adoption of holistic methods
[e.g. Levins (1974), Jorgensen and Mejer (1979)] that recurrently appear in
the biological literature are in the spirit of the axiomatic means of
introducing information. More broadly yet, the bioenergetics research of
Bigelow, et al. , (1977), Hannon (1979), and others urges both a holistic,
axiomatic approach and a movement away from near-exclusive emphases upon
short-run, transient population movements in one or a few species to a
concentration upon long-run equilibria for entire systems. The bioenergetics
framework, when considered in a long-run equilibrium context, has appeal to
the economist because it closely accords as a method of reasoning with his
approach to the economy, a system perhaps equally as complicated as any
ecosystem. In ecological contexts, the system complexity to which ecologists
constantly refer is usually imcocipatable with "ideal" scientific experiments
that remove all responsibility for_ex post thinking from the researcher. If
ecosystems are equally or more complicated than are economies, the ecologist
must be prepared to conceptualize a model that explains the data that is to be
and has been observed or generated: he must compose a plausible story having
applicability beyond the immediate circumstances being investigated.
Experimental versus Field Response Surfaces: The methods of most biological
research into response surfaces impede correspondences between surfaces
estimated from experimental data and those estimated from data observed in the
field. Generally, responses under experimental conditions will significantly
exceed in absolute to observed under field
conditions ,2J QbxioMiyf are available and quantitative
relations established between experimentally-derived and field-observed
responses so that suitable adjustments can be made in both experimental
designs and analyses, control decisions based soley on experiment-derived
response surfaces must be less than fully satisfactory. Indeed, these
experimental results might best be viewed as untested hypotheses. They allow
firm generalizations to be made about input configurations not found beyond
the experiment, in a set of exogenous parameters that nature never replicates.
More important perhaps is the fact that the a priori information provided by a
combination of experimentation and field observations will frequently make the
construction of analytical models an effective means of explaining the
discrepancy. The conditions of the experiment and the field observations
reduce and define the domain of circumstances which the model must capture.
When unexpected and/or unexplained differences exist between
experimentally-derived and field-observed outcomes, some worthwhile
generalizations about system behavior can usually be made by searching out the
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sources of the differences.
The reasons for discrepancies between experimentally-derived and field-
observed responses surfaces are probably several. Two come readily to mind.
First, as Anderson and Crocker (1971, pp. 146-1.47) point out, s=o as to remove
confounding source?, of stress, all factors other than air pollution that might
influence behavior in controlled experiments tend to be set at biologically
optimal levels. Given that these biologically optimal levels exceed those
found in everyday environments, it follows that they are less binding,
implying, by the Le Chatelier principle fSilberberg (1978, pp. 293- 298)],
that the contribution of an input to the behavior parameter of interest will
be greater than it otherwise would be.
A second, less obvious reason arises from the role that risk plays in
managed ecosystems, particularly agricultural and forest systems. In strictly
controlled experimental settings, all feasible sources of random variation in
output levels are excised. However, in field conditions, the system manager
must adapt his activities to natural sources of random variation such as
weather, insect infestations, and acidifying depositions. As Adams and
Crocker (1979) and Just and Pope (1979) demonstrate, the input mixes and
magnitudes the system manager selects influence both the level of output in
any one time interval and the variability of these levels over time. Thus ,
for example, if the land area for which a farmer is responsible increases and
he has no more inputs (e.g., lime, fertilizers, labor) than before, the
susceptibility of his crops to any acid Precipitation events which might occur
will also increase. In taking countermeasures to an acid precipitation event,
he has to spread the same inputs over a greater area. The implications of
this as & source of discrepancies between experimentally-derived and
field-observed response surfaces become apparant with the following simple
argument extracted from Adams and Crocker (1979) .
Consider a risk-neutral, net revenue-maximizing farmer who must make all
his input commitments before the start of any single growing season. For
simplicity, further assume that acid precipitation over the growing season is
expected to be either "high" or "low" (g). If acid precipitation is high,
the marginal cost of supplying various crop yields, given the input
commitments already made, will be represented by the (MC|a) curve in Figure 3.
This curve is the highest of the three marginal cost curves in the figure
because the actual occurrence of the a level of acid precipitation will reduce
the marginal products of the preselected mix of inputs, and thereby increase
the marginal cost of producing any particular yield. On the other hand, if
realized acid precipitation levels during the growing season were $, then, in
accordance with the (MC j 6) curve, the marginal, cost of producing various
yields would be reduced. The MC° curve is simply the probability weighted
average of (MC|a) and (MClB).
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v . . Figure 5.3
Effect of Air Pollution Risk Upon Yields
(MC a)
c
S
(MC
marginal
revenue
I
yield (x)
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If, for simplicity, the farmer regards the occurrence of either a or 6
acid precipitation as equally likely, then MC° is the marginal cost curve
associated with the input mix maximizing his expected net revenues. Although
this input mix will, on average, ^yj^eld x", during any one season it will
result in yields of ^either x or x . Thus if acid precipitation is high
during one season, x will result, while if it is low, x will result. In
effect, the variability in levels of acid precipitation causes yields in areas
sometimes subjected to acid precipitation to be more variable than in areas
where acid precipitation never affects yields or where it is always at a high
level. Thus, for given input mixes, the odds of discrepancies between
experimentally-derived response surfaces and field-observed response surfaces
are greater in regions subject to fluctuating levels of acid precipitation.
If maximum acid precipitation levels have been increasing over time, then
one would expect yield variability to increase in those areas where acid
precipitation has been increasing. This is because the lowest level of acid
precipitation (zero) cannot be altered while the highest level has increased,
causing the (MC|a) curve to shift upward. Unless the farmer constantly lives
in the darkest depths of despair about the acid precipitation problem, the MC°
curve, which is a probability weighted average of the other two curves, will
never shift upward as much as the (MC|a) curve. The result will be increasing
yield variability over time. Consequently, discrepancies between
experimentally-derived response surfaces and field-observed surfaces are
likely to be greater where levels of acid precipitation have historically been
increasing.
A Recapitulation
Based or current knowledge, it appears that an ordered, predictable se-
quence of events follows the deposition of acidifying substances on
ecosystems. Acid depositions cause the buffering capacities of ecosystems to
decrease, the rates of decrease depending on the buffering capacity at the
time of deposition. Systems with low buffering capacities will display
relatively rapid decreases, whereas those with high capacities tend to have
slow decreases. Also, systems with low buffering capacities generally show
relatively rapid negative impacts from increasing hydrogen ion concentrations.
Systems with high buffering tend to show initially positive responses from
nutrients entering the system with the acidification and from nutrients
mobilized by increased hydrogen ion concentrations. Over time, however, the
initial positive response to acidifying depositions will reverse as nutrients
leach from the system, mobilized metals reach toxic concentrations, hydrogen
ion concentrations reach toxic levels, and/or nutrient cycling rates are
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reduced as decomposition rates decline.
so and acid particles have harmful direct effects on plants. In
general, when deposited on foliage surfaces, the pollutants enter the plants
through the stomata. Plant seedlings and meristematic tissues are most
sensitive. Therefore, acidification can cause establishment of plant species
to be limited to those most tolerant of acid conditions. Over time, selection
for tolerant species will simplify terrestrial communities and shift
dominance.
Because of their weaker buffering systems, aquatic ecosystems tend to be
more sensitive to acidifying depositions than are terrestrial systems. Within
the aquatic system fish appear to be the most sensitive group of organisms and
the reproductive processes appear to be the sensitive stage of the fish life
cycle. Fromm (1980) ranked various reproductive processes in order of
decreasing sensitivity: egg production > fry survival > fry growth > egg
fertility. With declining environmental pH level, numbers of fish species are
continually reduced. Available data indicates that many of the economically
most valuable fish species are the most sensitive to depressed pH levels and
are the first to be eliminated from the system. Continual depression of pH
levels effects reductions in primary production rates, algal biomasses, and
invertebrate biomasses. In addition, species diversities are reduced as the
most acid tolerant species become dominant. In time, the system can reach a
nearly abiotic state.
Acidifying depositions accelerate the decay rates of a wide variety of
material artifacts mainly because the presence of acids upon the material
surfaces increases the flow across the surfaces of the electric currents that
cause corrosion, discoloration, and embrittlement. These processes are
intensified for those materials, such as cement, concrete, and some metals,
often used in subaqueous and/or high temperature environments.
Because of the water treatment facilities already in place, there is no
substantive evidence at this time that the human health effects of acid
precipitation are worrisome.
In order for the economist to be able to value the aforementioned effects
of acid precipitation upon life and property, the natural scientist must
provide him with information on response surfaces (see footnote 1, however).
A response surface describes the magnitudes of the influences of various
environmental and anthropogenic factors upon something that is valued for its
own sake or for its contribution to something that is so valued. Because it
emphasizes the description of substitution possibilities among the influential
factors, knowledge about the response surface contributes to informed
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manipulation of the system of interest. Thus any natural science exercise
which fails to make explicit the mapping between the influential factors and
the object of value is of no use whatsoever to the economist. A study of the
effect of acid precipitation upon leaf necrosis of apple trees is worthless to
the economist if the relation between leaf necrosis and apple yields is
unknown.
4 • - »
In order for natural science research into response surfaces to be most
useful to the economist, it must always have certain properties.
1) Only those portions of the surface where the marginal products of the
influential factors (reductions in acid precipitation are a positive
input) are positive should be studied. Knowledge about other portions of
the surface is economically irrelevant.
2) Only those response surface input combinations consistent with the
behavior of any organism that is the object of the research is
economically relevant.
3) All economically relevant portions of the surface should be system-
atically sampled. Coverage of these portions should be as dense as
research resources permit. Achieving this broad yet dense coverage will
require that substantially fewer research resources than are traditional
be devoted to replications of experiments at one or a few points on the
surface.
4) Replication should be given greater consideration onlv when the
system being investigated is thought to be extremely sensitive to
variations in exogenous parameters.
5) Increased density and breadth of coverage of the economically
relevant portions of the surface should be striven for whenever there is
a large number of factors thought to impinge in nontrivial ways upon
system behavior.
6) Research resources should be aimed at denser coverage and greater
replication along the steeper parts of the economically relevant portions
of the surface.
7) When the response surface is stochastic, probability distributions
should be stated for the random variables that enter. T^e natural sci-
entist should not leave users of his research with only his "best"
estimate.
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8) The above remarks apply with equal force to temporal and spatial con-
siderations. In particular, research into the effects of acid precip-
itation should neither be devoted only to immediate effects nor concen-
trated only in a small number of locations. Ecological theory cannot
often be depended upon to allow empirical findings at one site and/or
time to be generalized to other sites and/or times.
Even if the above eight factors are consistently adhered to, there remain
factors about which the natural, science researcher must be cautioned if he
wishes to produce results that are useful to the economist.
9) Jointly determined variables plausibly play a large role in ecosystem
response surfaces. Thus attempts to account for the additional factors
thought to influence an organism's response to acid precipitation by
simply stringing out variables in a single expression will often yield
biased estimates. Because some human decision variables both influence
and are influenced by the response, economic analysis must often be
involved in the initial research design.
10) Baseline descriptive measurements of ecosystem states may now be
equally as worthy as research on response surfaces. If researchers are
aware of the fact of change, even though they may be unaware of the
causes of change, the change can, in principle, be assigned an economic
value. Knowledge of the cause of the change is necessary only when one
wishes to manipulate the system and/or assign responsibility for the
change to human agents.
11) Aggregated or grouped variables to which natural science research is
indifferent in terms of informational content may destroy the usefulness
of the research for the economist. In general, natural science research
should structure its units of analysis so that substitution possibilities
are not hidden.
12) The farther is an affected component removed (in the sense of
trophic linkages) from something economically valued for its own sake,
the less research worthy is the component likely to be. This is because
there are more likely to be available substitutes for the component.
We now move from cautionary statements about the performance of natural
science (particularly ecological) research into the effects of acid
precipitation to a set of aggressive statements about how this research might
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be improved to the mutual benefit of the ecologist and the economist.
13) Many ecological models appear to be insufficiently artificial,
perhaps because they stress the short-run dynamics of species
interactions. Their builders compound errors of measurement by
introducing variables that are highly correlated; they seem reluctant to
make prior judgements about the significance or the triviality of a
variable's influence; and they devote inordinate research resources to
reductions in the measurement errors of trivial, variables. These faults
are often evident in the confusing connected black box simulation models
ecologists frequently use.
14) Ecologists often remark on the great complexity of ecosystems. It
is not evident that ecosystems are any more complex than economies.
Economists have fotmd that an axiomatic approach which emphasizes com-
parative static equilibria yields great simplifications of real-world
economies at no apparent cost in robustness. The long-run equilibria are
used as analytical devices rather than as descriptions of reality. There
is recent interest in ecology in viewing ecosystems and their components
as solving a resource allocation problem [Rapport and Turner (1977)],
where energy is the scarce resource. This organizing principle permits
use of the tools of economic analysis as Chapter IV demonstrates. The
contribution these tools can make to understanding the ecological effects
of acid precipitation should be investigated further. Agricultural
systems, because they are immature in ecological terms, and therefore
stressed and unstable, might be a worthwhile place for initial research
efforts. Note that these systems emphasize growth. It is generally
thought that the most active developing tissues in plants are most
sensitive to acidifying depositions.
15) Because strictly controlled experiments on response surfaces often
are poor facsimiles of the real world, their results are best viewed as
untested hypotheses.
Our economic approach to the effects of acid precipitation has yielded
more than a set of generalizations about natural science research into
response surfaces of all sorts. We have gained some insights into particular
economic features of the acid precipitation problem that might be helpful in
planning natural, science research into these problems.
16) The current economic value of the ecosystem effects of acid precip-
itation is very small compared to the value of its direct effects upon
materials and perhaps upon agriculture. However, the existing studies of
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the materials damages caused by pollution are technically weak in
economic terms. New economic approaches to assessing materials damages
must be developed hefore trustworthy results can be obtained.
17) Potentially, the chronic ecosvstem effects of acid precipitation
almost certainlv dominate in economic seriousness the acute effects.
4 • 1 1
Thus natural science research should give greater priority to cumulative
acidity issues rather than to episodic acidic events.
18) Careful inventories of the existing stock of buffering capacities
must be constructed. The frequency with which ecosystem responses to
acid precipitation involve nonconvexities and irreversibilities should be
identified. If, as we suspect, one or both appears with substantial fre-
quency, natural science research should concentrate on those systems that
are about to or just have exhibited the first symptoms of acidification.
This, of course, presumes that good indicators of these first symptoms
are available. If not, these indicators must be identified.
19) Studies of already acidified systems should be limited to attempts
to establish whether natural recovery times, if any, involve less or more
than two or three decades, and whether there exist any human
manipulations that can slow decay rates or accelerate recovery. Because
of the existence of positive discount rates, recoveries occurring more
than two or three decades in the future have little value to the present
generation.
20) The measurement of the changes in long-run equilibrium species
assortments should be a high priority natural sciences research item
because the value that humans attach to the amenities and the life
support services that ecosystems provide is often conditional upon the
species assortments from which they come.
21) Economists are usually unable to value dung beetles, algae, and
assorted other ecosystem components because ecologists have failed to
indicate how their contribution to the directly valued components of
ecosystems varies with acid precipitation levels. The approach suggested
in recommendation (14) might allow these contributions to be specified
and thus valued.
Finally, so as to moderate our commentary about the research efforts of
the natural sciences into the effects of acid precipitation, we direct a few
remarks at our own discipline. have tried to identify those sets of acid
precipitation effects where one may feel resonably secure using the
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conventional analysis. We have also tried to identify some possible special
features of vegetative and ecosystem damages that appear to require^ither
expansions or even complete replacements of the traditional analysis.— In
Chapter IV, we have tried to extend conventional methods to include ecosystem
diversity. Unfortunately, we are unable to reject the discomforting notion
that the effects for which one may feel secure using the conventional methods
are those having the least long-term economic significance. If this is true,
it is important, for both scientific and policy reasons, to set the strengths
and limits of the conventional analysis, and to design valuation methods that
can be extended to phenomena where the analysis either fails or is misleading.
At least insofar as the setting of limits is concerned, it is important for
obvious reasons that the task not be left soley to economists. However,
meaningful participation in this task by noneconcmists means that they must
learn the structure and the requirements of the conventional analysis.
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REFERENCES
* • - >
— As noted in Chapter I, we presume in this report that Shephard's lemma (the
envelope theorem) has limited practical applicability. Nevertheless, the
extent to which applications of the envelope theorem might permit assessors of
the economic benefits of controlling acid precipitation to avoid having to
know these biological and physical influences, awaits some detailed research
attention. To see why, consider the restricted profit function of Diewert
(1974) and Lau (1976) . Let X denote a vector of fixed outputs and inputs,
where the inputs are measured as negative quantities, thus allowing both
inputs and outputs to be stated in terms of net supplies. In addition, allow
p to be a vector of nominal prices of the variable net supplies and let v be a
vector of their rates of production or use. The variable profit is then:
tt = p' i = 1,. . .n (a)
The maximum variable, or restricted, profit is:
IT* = IT(p,x) (b)
Taking the derivatives of it* with respect to the fixed outputs yields of the
negative of the marginal cost. When these derivatives are taken with respect
to the fixed inputs the negatives of the marginal valuations or demand prices
are yielded. Similarly, the derivatives of it* with respect to p vield the
efficient rates of production or uses of the outputs and inputs. These
results are obtained because, under appropriate conditions, every production
possibility set defined with at least one fixed input or output implies a
unique restricted profit function, and, conversely, every restricted profit
function satisfying certain regularity conditions implies a technology. Using
these results, given that nominal prices and quantities of inputs and outputs
can be observed, knowledge of the exact influence of various physical and
biological factors upon ecosystem variables of interest is unnecessary.
However, even if these duality techniques ultimately allow economic analyses
to proceed without prior knowledge of response surfaces, knowledge of
thesurfaces would still prove useful as a means of checking the results
obtained from applications of the duality techniques.
2/
This is not strictly true. For the statement to hold without exception
even for only two inputs, it must also be true that:
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2 2 2
fa Y) 13 Y) _3 Y >
OXL2) OX22) 3Xt3X2
— See Chapter III for further discussion of cancavitv (nonconvexity). The
discussion in that chapter is consistent with activities which operate at
either A or D in Figure 2.
4/
— See also Anderson and Dillon (1970).
— This illustration is an adaptation of a development in Crocker, et al.
(1979, pp. 9-12).
— This and the subsequent three paragraphs draw extensively upon Crocker
(1975) .
—^ The "law," as succintly stated by Swanson C1963), says that yields increase
at a constant rate with respect to applications of each factor unitl some
other factor is limiting.
8/ . ....
— Insofar as acid precipitation is concerned, nonconvexities, as was argued
in Chapter 111, likely constitute an important exception to this statement.
9/
— By no means is our listing exhaustive. For example, benefit-cost analysis
as presently constituted, is less than robust in its treatment of the benefits
and costs of alternative paths of adjustment to an environmental perturbation.
Neither is it very helpful in valuing reduced uncertainty about future
environmental states. Other items could be added to this listing.
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BIBLIOGRAPHY
Adams, R.M. , T.D. Crocker, and N. Thanavibulchai, Yield Variability, Air Pol-
lution, and Producer Risk: An Exploratory Study of Selected Crops in
Southern California, A report to USEPA for Grant # R805059010, Resource
and Environmental Economics Laboratory, University of Wyoming., Laramie
Wyoming, (October, 1979) .
Anderson, J.R., "Sparse Data, Climatic Variability, and Yield Uncertainty
in Response Analysis," American Journal of Agricultural Economics" 55
(March 1973), 77-82.
Anderson, J.R., and J.L. Dillon, "Economic Considerations in Response Research,"
American Journal of Agricultural Economics 50(March 1.968), 130-142.
Anderson, J.R., and J.L. Dillon, "Economics Considerations in Response:
Further Comment," American Journal of Agricultural Economics 52(Sept-
ember 1970), 609-910.
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