Socioeconomic Environmental Studies Series
A Cost Evaluation of Alternative
Air Quality Control Strategies
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Washington Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D. C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the SOCIOECONOMIC
ENVIRONMENTAL STUDIES series. This series
describes research on the socioeconomic impact of
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other recovery operations with emphasis on
monetary incentives. The non-scientific realms of
legal systems, cultural values, and business
systems are also involved. Because of their
interdisciplinary scope, system evaluations and
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this series.
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EPA-600/5-74-003
January 1974
A COST EVALUATION OF ALTERNATIVE
AIR QUALITY CONTROL STRATEGIES
By
Scott E. Atkinson
and
Donald H. Lewis
Washington Environmental Research Center
Environmental Protection Agency
Washington, B.C. 20460
Program Element No. 1HA091
Prepared for
WASHINGTON ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 • Price $1.05
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ABSTRACT
A computer simulation is employed to evaluate three alternative
particulate air pollution control strategies utilizing St. Louis as a
model region with the following objectives:
(i) Quantification of the cost savings of two least-cost
strategies based on alternative linear programming (LP) formulations —
an air pollutant emissions least-cost (ELC) strategy and an ambient air
quality least-cost (ALC) strategy, and comparison of these minimum cost
strategies with a third strategy suggested in the State Implementation
Plan (SIP) Guidelines (typical of the strategies included in the plans
submitted to EPA by the states).
(ii) Evaluation of the relative importance of two important
characteristics of the regional air pollution problem — the variation
in marginal control costs from source-to-source and the variation in the
impact a source may have as a function of location, stack height, etc.
(iii) Evaluation of the impact on total regional costs of
increasingly stringent ambient air quality standards, with ambient
quality levels ranging approximately from the primary to the secondary
standard.
(iv) Derivation of the costs of alternative emissions tax
strategies, based on the ELC and ALC solutions, which achieve the
primary and secondary standards.
(v) Comparison of marginal costs and benefits of control at
the primary standard.
The ELC strategy assumes a linear relationship between air quality
and total regional emissions (i.e., that a given percentage reduction
ii
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in total regional emissions will give the same percentage improvement in
air quality) and allocates the control burden on the basis of marginal
control costs only. This assumption leads to the least-cost method of
attaining a given reduction in total regional emissions. The ALC
strategy produces the least-cost method of attaining prescribed regional
air quality by considering individual source-receptor transfer
coefficients (i.e., geographical location), as well as marginal control
costs. These two degrees-of-freedom are found to be of roughly equal
importance in determining least-cost solutions. That is, the ELC
strategy captures only one-half of the total potential savings achieved
by ALC in attaining a given air quality standard. In addition, the ALG
strategy requires as little as one-tenth the expenditure of the SIP
strategy which ignores both degrees-of-freedom. A policy which employs
a single emissions tax based on mass emissions, rather than implementing
the ALC solution to attain a desired air quality, sacrifices substantial
savings since the emissions tax strategy can be no cheaper than the
ELC solution. The inclusion of area sources and costs of standards
enforcement may erode some advantage of the least-cost strategies over
the SIP strategy, and of the ALC over the ELC approach.
A comparison of marginal costs and preliminary marginal benefit
figures for health and welfare at the primary standard indicates that
stricter control is economically justified. Marginal control costs for
the entire region at the level of the secondary ambient air quality
standard are found to be four times the marginal costs at the level of
the primary standard.
111
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CONTENTS
Page
Abstract i:L
List of Figures v
List of Tables vi
Acknowledgments viii
Sections
I Conclusions *-
II Recommendations ^
III Introduction ^
IV Review of the Literature 9
V Problem Formulation 13
VI Discussion of Results 28
VII References 48
VIII Appendices 50
iv
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FIGURES
No.
1 MAP OF RECEPTORS AND SOURCES
FOR ST. LOUIS REGION 18
HYPOTHETICAL EXAMPLE OF TOTAL COST AS
FUNCTION OF TONS REMOVED FOR GIVEN
SOURCE AND APPLICABLE CONTROL DEVICES 25
TOTAL REGIONAL CONTROL COSTS PER YEAR
AS A FUNCTION OF AIR QUALITY 30
4 TOTAL REGIONAL TONS REMOVED PER DAY AS
A FUNCTION OF AIR QUALITY 33
REGIONAL AIR QUALITY AS A FUNCTION
OF LOCATION 34
TOTAL REGIONAL CONTROL COSTS PER YEAR
AS A FUNCTION OF TONS REMOVED 36
7 MARGINAL TAX VS. MARGINAL CONTROL COST
FOR A TYPICAL SOURCE 39
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TABLES
No.
1 INPUT DATA FOR SOURCES CONTROLLED UNDER
ALL STRATEGIES 17
ALC EMISSIONS TAX — $/TON 41
vi
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ACKNOWLEDGMENTS
Thanks go to William Watson, Lowell Orren, and other members of
the Implementation Research Division for their helpful comments.
VII
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SECTION I
CONCLUSIONS
Particulate air pollution control strategies of the type included
in the State Implementation Plan (SIP) Guidelines are six to ten times
as costly in achieving a given level of air quality as an ambient least-
cost (ALC) strategy which allocates the control burden on the basis of
both individual source marginal control costs and source-receptor trans-
fer coefficients (derived from dispersion parameters such as location,
stack height, and other meteorological parameters). The ALC strategy,
based on a linear programming (LP) solution, is the least-costly method
of attaining ambient air quality standards.
A second LP solution, an emissions least-cost (ELC) strategy,
allocates the control burden only on the basis of marginal control costs
without considering the impact of variations in transfer coefficients,
realizing approximately half of the cost savings of the ALC strategy.
The ELC method produces the required reduction in regional emissions (as
computed assuming ambient quality and total regional emissions are
linearly related) at minimum cost, but only in the trivial case yields
the minimum cost to achieve the corresponding ambient air quality stand-
ard. The cost of a single emissions tax based on mass emissions would
approach that of the ELC strategy. Consideration of area source control
costs, which make up 20% of the regional emissions, and strategy enforce-
ment costs may reduce the advantage of the least-cost strategies over the
SIP strategy and of ALC over ELC.
Comparison of marginal costs and preliminary marginal benefit figures
for health and welfare at the primary standard indicate that stricter
levels of control are economically defensible. Moving from the primary
to the secondary standard, total regional control costs increase by a
factor of four.
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The problem-solving technique used in this analysis could be improved
in several ways. An ideal formulation would be one which meets technical
feasibility requirements and resource constraints, while including the
intermedia and multipollutant impacts of control devices, i.e., marginal
control costs, transfer coefficients, and several discrete control
alternatives for each pollutant and source would ideally be included in
a mixed-integer optimization program. However, the large number of
source-device combinations would require years of computer effort if
conventional techniques (e.g., branch-and-bound) were used. A heuristic
approach could be adopted with the caveat that the solution is only an
approximation (though hopefully a close one) to the optimum.
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SECTION II
RECOMMENDATIONS
A number of recommendations can be made for future work in develop-
ing least-cost air pollution control strategies so that cost-benefit
accounting will be more complete:
(1) Considerable reduction in the total cost of control can be
achieved by utilizing the assimilative capacity of the ambient air.
(2) More research attention should be given to estimating the
appropriate level for the secondary standard, since marginal benefits
to health and welfare appear to exceed marginal costs at the primary
standard, i.e., it appears that a cost-benefit analysis would support a
more stringent standard. In particular, this will require more infor-
mation on the costs of fine-particulate control and the resulting
benefits.
(3) Because some control measures generate significant multiple-
pollutant effects, least-cost solutions should be developed which simul-
taneously meet air quality standards for the five primary pollutants.
(4) The other-media effects of air pollution control, especially
water quality degradation, may also be important and should be introduced.
(5) Techniques for including area source control costs should be
incorporated into the least-cost solution. This will be especially
important as mobile sources of pollution (represented as area sources)
are included in the analysis.
(6) The informational requirements as well as administrative and
enforcement costs (transaction costs) associated with the implementation
-------
of least-cost solutions should be investigated. Because each source has
a unique emission level in a least-cost strategy, transaction costs will
almost certainly be higher than they are for the SIP strategies and will
partially offset the cost advantages of the least-cost strategies.
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SECTION III
INTRODUCTION
In accordance with the Clean Air Act of 1970, each state has
submitted to the Federal Government a State Implementation Plan (SIP),
which describes their basic air pollution control strategy for achieving
the Federally set ambient air quality standards. This strategy has
essentially the same structure for all states, usually consisting of a
set of three emission standards, each of which defines the allowable
emission rate for all point sources in a broadly defined category.
Typically, plant size is the only variable in the function describing
allowable emissions within each category. Larger plants are allowed
greater emissions in all cases, even though some standards require a
decrease in emissions per unit of plant input or output as plant size
increases. Allowable emissions for each SIP control strategy are deter-
mined by adjusting the level of the standard, e.g., the number of pounds
of particulates allowed per million BTU heat input, until the resulting
air quality, predicted by a meteorological model or rollback calculation,
is equal to or less than the Federal standard. The rollback calculation,
which assumes that air quality is improved by the same percentage that
emissions are reduced, is explained below in greater detail. (See also [2l].)
In determining the allowable emissions for each SIP strategy, two
important variables are omitted:
(1) transfer coefficients — some sources degrade air quality more
than others because of different location, stack height, average mixing
height, stack exit conditions, stability wind rose (speed, direction,
and stability class) and pollutant decay rates -- factors referred to
as dispersion parameters throughout this paper. Transfer coefficients
are derived from dispersion parameters and are employed to transform
individual source emissions into ambient air quality at specific receptors.
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(2) control costs — marginal control costs not only rise rapidly
with increasing abatement, they also vary considerably from one source
to the next.
The work described in this report is a first step in attempting to
quantify the typical penalty in economic efficiency associated with the
current SIP air pollution control strategies, i.e., to identify the least-
cost solutions, and to investigate ways of modifying the SIP strategies
to move them closer to the least-cost solutions. One of these solutions,
the emissions least-cost (ELC) strategy, is the least-cost method of
achieving a regional mass emissions standard and utilizes only the
information in (2) above. The other, the ambient least-cost (ALC)
strategy, employs both (1) and (2) and is the least-cost method of
achieving a specified ambient air quality standard. However, the ALC
solutions as developed in this paper will not quite be the true least-
cost solutions, since area source control costs and strategy enforcement
costs are not included in the analysis.
Since the ALC program makes use of more information than the ELC
routine in minimizing costs, the latter must be at least as expensive as
the former in achieving a specified air quality. To make clearer the
importance of optimization subject to constraints employing transfer
coefficients, consider the case of a large modern suburban power plant
which incurs lower marginal control costs than a smaller antiquated city
plant. In the ELC solution the suburban plant would probably be controlled
more than the central city source, since the latter has older, less
efficient abatement equipment. Levels of control will differ, however,
in the ALC solution, if the large suburban source contributes less to
degradation of ambient air quality measured at monitoring sites (generally
located in or near the urban core) than does the central-city source.
The greatest abatement would be required of the source which achieves
the largest improvement in ambient air quality per dollar spent on
particulate control. The ELC-based level of emission control for the
suburban source might be unnecessarily costly. The use of additional
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information relating individual emissions to ambient air quality will
reduce ALC total cost below the ELC level or leave cost unchanged in the
unlikely case that all individual transfer coefficients are identical.
The thrust of this paper is that the omission of both variables
produces SIP control strategies that are more expensive than necessary
to achieve a given level of air quality. If the view is taken that the
assimilative capacity of the atmosphere is a scarce resource which can
be rationed by standards and that environmental goals should be achieved
at minimum cost, both of these variables must be considered.
This study utilized emissions data based on the 27 largest point
sources of particulate emissions in the St. Louis Air Quality Control
Region (AQCR), plus an added constant to account for natural (i.e.,
uncontrollable) background groundlevel concentration. However, the
model should give realistic results, since the 27 sources account for
approximately 80% of the particulate emissions in the St. Louis AQCR.
This analysis included the following steps:
(1) Development of the ALC and ELC linear programming (LP) strategies
and the SIP strategy for achieving particulate air quality standards,
using the same meteorological model, emissions data, and cost coefficients
to predict the impact of each strategy; (2) Determination of the loss in
economic efficiency associated with the SIP strategy as a function of
ambient air quality for the AQCR by comparing the SIP strategy costs with
those of the two least-cost solutions; (3) Comparison of the costs of
an emission tax strategy to the costs of the ALC and ELC solutions;
(4) Comparison of marginal benefit and cost figures at the primary
standard; and (5) Analysis of alternative problem formulations used by
various investigators in the field, making recommendations for future
research.
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In this last effort, interest was focused on alternative ways of
defining the objective function and independent variables in the LP
algorithm used to find the least-cost solutions. Alternative problem
formulations were judged by their solutions' engineering feasibility
and the handling of synergistic effects of multiple-pollutant control
measures, both within and between media. Ultimately, it is hoped that
it will be possible to compare cost data with highly refined benefit
numbers to determine the appropriate standard.
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SECTION IV
REVIEW OF THE LITERATURE
Many least-cost models have been formulated in which direct regional
control costs are minimized subject to ambient air quality constraints.
Kohn [6, 7, 8] employs an LP model for the St. Louis region to minimize
control costs while satisfying certain production and consumption
constraints and ambient air quality standards for five pollutants. His
decision variables are levels of control activities, and he assumes a
linear relationship between total regional emissions of each pollutant
and regional air quality. This linear mapping means that only source-
to-source variations in marginal control costs are used to structure the
LP solution, i.e., the effects of individual source transfer coefficients
are ignored. This approach is defined above as the ELC strategy and is
usually considerably more costly than the ALC strategy, as demonstrated
below.
The engineering feasibility of Kohn's work comes into question when
divisibility is considered. A solution may call for the use of two or
more design efficiencies whose joint utilization might be incompatible.
In addition, Kohn's decision variables are defined so that marginal costs
are constant at all activity levels, regardless of the control measure
throughout. More is said on the importance of these assumptions later.
The approach of Seinfield and Kyan [16] will not guarantee attain-
ment of ambient air quality goals at minimum cost since they also employ
an ELC program. Individual transfer coefficients are omitted during the
least-cost solution of the Seinfield-Kyan program, and are only employed
to map mass emissions into regional ambient air quality after the cost-
minimization problem has been solved.
In an approach similar to Kohn's, Teller [17, 18] minimizes the
total cost of low- and high-sulfur fuel for all sources subject to ambient
9
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air quality constraints for SO . He finds that the ALC solution is
X
considerably cheaper than the ELC, and that abatement only when pollution
episodes are forecast is much less costly than constant abatement.
Teller utilizes Turner's somewhat rudimentary diffusion model and allows
only fuel substitution as a control measure. Despite this, he avoids
the shortcomings of Kohn's ELC solutions (which optimize subject to mass
emission constraints).
Norsworthy and Teller [13] extend Teller's analysis [17, 18] by
suggesting an LP approach in which the benefits as well as costs of
pollution abatement are directly evaluated in the objective function.
They suggest a separable programming approach to handle the non-linear-
ities in total benefit and cost functions. The objective function is
defined as net social benefits, i.e., the difference between total
pollution control costs (including regional impacts) and total savings
from reduced mortality, morbidity, and structural damage. Although not
quantitatively estimable because benefit functions are poorly developed,
the solution to this formulation would be socially optimal.
Burton and Sanjour [l] and the Consad Corporation [2j employ integer
programming to compare three strategies for SO and particulate control
for the Kansas City area. Individual source transfer coefficients are
employed in the constraint equations. The integer program first ranks
the alternative control methods for each source according to annualized
cost. The algorithm then examines an initial case involving the least-
costly control methods for each source and-heuristically searches through
the other source-control combinations for a least-costly solution that
satisfies the air quality constraints. The solution converges toward
the global optimum (assuming it avoids local optima) but rarely reaches
it, in contrast to linear and separable programming. However, an advan-
tage of heuristic integer programming is that solutions are in terms of
discrete control levels with no more than one device per source. Certain
problems of device incompatibility and interpretation (explained in more
10
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detail below) are avoided. Comparison of the three Kansas City strategies,
a strategy of maximum control for each source, equiproportional particulate
emission rollback of at least 20% for all sources, and the ALC least-
cost solution, indicate savings from the latter strategy are quite
substantial. Total costs are $26, $16, and $7.5 million, respectively,
3
to achieve an air quality of about 85 )ig/m particulate matter and
.025 ppm SO . The maximum-control strategy requires substantial abate-
ment of many large sources which degrade air quality very little (because
of suburban location) and other exptinsive-to-control plants. Thus, an
equiproportional strategy should be less expensive than maximum control
in meeting given ambient standards but not as cheap as the ALC least-
cost method.
Russell and Spofford [15] employ an LP model to maximize social
welfare subject to constraints on levels of production and,consumption
as well as requirements for transport, treatment, and discharge of
residuals, rather than ambient air and water quality standards. The
quantities of generated residuals are input to diffusion models which
determine ambient concentrations. These in turn are input to damage
functions, whose cost figures enter the objective function on successive
iterations as shadow values. Standards (with their implicit cost-
benefit comparisons) are not required in the LP model, since damage
functions are explicitly introduced into the objective function.
Plotkin and Lewis [l4] have followed an approach similar to that of
Teller [17, 18] in utilizing an LP routine with transfer coefficients in
the constraints to determine least-cost emissions consistent with given
particulate air quality goals. The authors employ data for twenty-seven
point sources and nine receptors using St. Louis as a model region.
They employ the cost model of the Implementation Planning Program (IPP)
[19] to determine piecewise linear cost functions for particulate control.
A Gaussian plume-rise diffusion model developed by Martin and Tikvart [l2j
is also utilized. The ALC particulate control strategy is compared to
two alternative emission control programs: an ELC strategy and an SIP
11
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strategy representative of those currently being implemented by the
states. The latter two strategies are found to be two to five times as
expensive as the ALC approach in achieving one particular air quality
goal.
The study presented in this paper utilizes the work of Plotkin
and Lewis as a starting point and is similar to their work in that:
(1) The ALC and ELC strategies are compared to a strategy repre-
sentative of those currently employed in the SIP's;
(2) The cost of each strategy is related to the achievement of
ambient air quality standards.
However, the present paper differs from previous studies in that:
(1) The costs of all strategies are compared over a range of
ambient air quality standards;
(2) The implications of an emissions tax are considered and prelim-
inary comparisons of marginal control costs and damages to health and
welfare are made at the primary standard.
12
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SECTION V
PROBLEM FORMULATION
DIFFUSION MODEL AND COST DATA
This section describes the general data requirements for the
derivation of the control costs and transfer coefficients employed
in this paper. These requirements are discussed in greater detail
in the Operator's Manual for the IPP Model [19],
Transfer coefficients, employed in the constraint equations, are
derived using a Gaussian diffusion model developed by Martin and
Tikvart [12]. The meteorological input data required for the model
are referred to in Section III as dispersion parameters.* The output
consists of a matrix which gives the contribution of each of m sources
to the predicted annual arithmetic average pollutant ground level
concentrations at each of n receptors. Transfer coefficients, with units
of micrograms per cubic meter per ton per day are obtained by dividing
the concentration at the i receptor due to the j source by the
number of tons emitted by the j source (usually written as a matrix
a.., i = 1, ..., n; j = 1, ..., m).
To determine costs three basic types of data are required: source
information, regional information, and control cost data. The first
category includes sources identified by Standard Industrial Classification
code and source type. Source data describes the important point and area
sources, although the latter were excluded from the present analysis.
Point sources include major stationary fuel combustion plants (primarily
industrial and steam-electric power plant boilers), industrial process
*For a more complete discussion see [19],
13
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sources, and solid waste disposal sources (incineration and open
burning). The twenty-seven largest point sources were included in the
present analysis and they accounted for 80% of total particulate emissions
in the St. Louis area. All mobile sources and any other sources too
small or too numerous to categorize as point sources were treated as
part of the background.
Additional required source input data includes temperature and
volume of the effluent gas stream, type and efficiency of existing
pollution controls (since new ones must be compatible with them), plant
operating schedules (for use in deriving device operating costs), fuel
usage requirements (to determine the applicability and effectiveness of
fuel substitution), and the maximum process rate (to again determine
device applicability).
Regional information consists of data on wage and interest rates,
the availability, costs, and ash content of fuel, and utility costs.
To develop control cost data, the applicability of control measures
to each source was considered. A number of devices were examined: wet
scrubbers (low, medium, and high efficiency); mechanical collectors
(gravity and centrifugal with low, medium, and high efficiency); electro-
static precipitators (low, medium, and high efficiency); mist eliminators
(low and high velocity); fabric filters (low, medium, and high temperature);
afterburners (catalytic and direct flame, both with and without heat
exchanger); and fuel substitution (elimination of coal, use of low sulfur
coal and fuel oil, or a change of all fuel to natural gas).
The compatibility of control devices for each point source within
a region was then determined. A number of restrictions on device usage
are built into the IPP, e.g., gravity collectors are too ineffective to
be employed, cyclone collectors are not applicable for control of fuel
combustion sources burning fuel oil or gas, electrostatic precipitators
must be high efficiency with oil or gas fuel sources, and only one of
14
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the three alternative baghouses may be applied to each source and cannot
be used in conjunction with wet scrubbers. Other particulate control
devices can be utilized with few restrictions.
The expected pollutant reduction efficiency is calculated for each
device. Corrections for reduction in pollutant-collection efficiency
over time have also been incorporated.
The costs of each device are obtained from the Control Technique
Documents prepared by EPA [22], The total annual cost of a control device
includes annualized capital and installation cost (based on a rate of
interest and rated life of the device) as well as annual operating and
maintenance costs. Capital costs are principally a function of the source's
size, with installation costs assumed to be a given percentage of capital
costs. Operating and maintenance costs are based on the quantity of
power, labor, and fuel used by the control device, and the cost or credit
from disposal of the collected pollutant. Once computed, the same
control cost figures were employed in all control strategies examined
in this paper.
A number of costs were ignored, however. These included the
administrative costs of enforcing the three control strategies and any
dislocation of workers or alteration of output caused by the purchase of
control devices, as well as any dynamic adjustment in costs. The usage
of "cost of control" and "least-cost" must be understood in this restricted
sense.
AIR QUALITY CONTROL STRATEGIES
The control strategy portion of an SIP consists of a listing of
emission regulations, sufficient to cover all stationary sources of air
pollution in the given region, as well as a demonstration that the allow-
able emission levels included in these regulations will achieve the Federal
ambient air quality standards. The similarity of these plans from
15
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state-to-state is surprising and is probably due to the fact that emission
regulations developed by a few of the more progressive states were used
as models by the others. Virtually every control strategy is based on
a grouping of all stationary air pollution sources into fuel combustion,
industrial process, and solid waste categories, with an emissions
regulation for each category.
For purposes of this study, a representative set of emission regulations
suggested in 'the SIP Guidelines [2l] has been selected to form the
SIP control strategy. The particulate standards include a heat input
standard for fuel combustion sources (.30 pounds particulate matter per
million BTU), a process weight standard for industrial process sources
(46.72 Ibs/hr of particulates per million Ibs/hr process weight), and a
refuse-charged emission standard for solid waste disposal sources (.20
pounds particulate per 100 pounds of refuse charged).
The total cost of applying the SIP strategy to the St. Louis area
was determined from the cost of control data by reducing particulate
emissions to the SIP strategy levels for all twenty-seven sources.
Emissions remaining from the controlled sources were then run through a
diffusion model which predicted ambient particulate ground-level concen-
trations, termed "achieved" air quality, at nine receptors.
For each of the twenty-seven particulate sources, the source type,
pre-control emissions level, and control cost data are listed in Table 1,
and their approximate location relative to the major features of the
St. Louis region is depicted in Figure 1. The locations of the nine
receptors for which air quality predictions are made are also indicated
in Figure 1. This source-receptor pattern was used for all computations.
Simulation of the ambient air quality resulting from the SIP strategy
gives a single point on the curve relating regional air quality to total
control cost. Each point on this curve is the maximum of the predicted
ground-level concentrations for the nine receptors. In order to generate
16
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Table 1. INPUT DATA FOR SOURCES
CONTROLLED UNDER ALL STRATEGIES
Source
No.
L
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2010;
2041;
2041;
2041;
2041;
2046;
2082;
2082;
2600;
2800;
2816;
2819;
2819;
2911;
2911;
2952;
3241;
3241;
4911;
4911;
4911;
4911;
4911;
4911;
4911;
4911;
4911;
Standard Industrial
Classification
Meat Packing, Boiler
Feed and Grain Mill
Feed and Grain Mill
Feed and Grain Mill
Feed and Grain Mill
Wet Corn Milling, Boiler
Brewer, Boiler
Brewery, Boiler
Paper Products, Boiler
Chemical PH., Boiler
Inorg. Pigments, Boiler
Inorg. Ind. Chem Plant
Inorg. Ind. Chem Pit., Boiler
Petro, Refinery
Petro.. Refinery
Asphalt Batch. , Boiler
Cement Plant, Dry Process
Cement Plant, Dry Process
Powerplant
Powerplant
Powerplant
Powerplant
Powerplant
Powerplant
Powerplant
Powerplant
Powerplant
Pre-control
Site Emission
No. Rate (T/D)
001
001
009
010
012
001
001
002
002
002
002
003
007
001
002
001
001
003
001
002
003
004
005
006
008
009
010
6.25
5.70
11.37
17.15
5.09
4.21
2.95
2.67
21.22
3.42
7.30
6.00
10.70
6.00
4.72
2.90
3.28
3.68
3.72
7.60
5.00
5.10
11.90
80.00
6.90
32.50
5.60
First
Control
Node
Cost Data
Second Node
Cost, Emission Cost, Emission
$/Ton Reduction $/Ton Reduction
16.
16.
11.
15.
341.
19.
13.
600.
4.
34.
63.
32.
4.
128.
58.
15.
2.
118.
214.
251.
86.
909.
75.
5.
104.
39.
240.
75.
80.
75.
75.
52.
75.
75.
76.
75.
75.
52.
68.
75.
75.
52.
75.
75.
97.
93.
63.
66.
74.
81.
75.
75.
75.
93.
73.75
57.68
184.25
279.0
1830.2
97.38
41.88
2114.02
20.5
1172.5
79.85
111.84
32.88
1064.38
72.75
321.77
10.25
464.5
1138.0
311.5
173.0
3138.65
201.5
17.38
4469.77
96.75
1312.5
99.
99.
99.
99.
99.
99.
99.
95.
99.
99.
99.
99.
99.
99.
99.
99.7
99.
99.
99.
99.
99.
92.4
99.
99.
89.2
99.
99.
-------
Figure 1. MAP OF RECEPTORS AND
SOURCES FOR ST. LOUIS REGION
Mississippi River
Receptors
Approximate Location
of worst air quality
NOTE:
Numbered points indicate
location of sources listed
in Table 1.
18
-------
a functional relationship between total regional control costs and various
air quality levels, a number of SIP strategies were developed by scaling
up and down the levels of the suggested SIP emission regulations.
As indicated above, the guidelines issued by EPA for the preparation
of implementation plans allow the states to use either a diffusion model
or a simple proportional model to demonstrate that their proposed emission
standards would achieve the Federal ambient air quality standards. Most
of the states elect to use the proportional model, which is based on a
linear relationship between regional emissions and air quality. In effect,
a given percentage improvement in air quality is assumed to require the
same percentage reduction in emissions. This approach, known widely as
the "rollback" technique, requires calculation of the percentage improve-
ment in air quality required to meet the ambient standard at the receptor
with the worst air quality. This percentage improvement in air quality
or reduction in emissions for the i pollutant, R., is defined as:
X ,.x - X
max(i) back(i)
where: max(i) = existing concentration of the i pollutant
at the location having the highest measured
or estimated concentration in the region,
std(i) = air quality standard for the i pollutant,
back(i) = background concentration for the i pollutant.
The actual ambient air quality impact of a given reduction in
regional emissions will depend upon the exact pattern of individual
source controls. Since the level of emission reduction dictated by the
SIP's for an individual plant is generally determined by its source
category in conjunction with plant size, required regional emission
reductions may be achieved by heavy control of rural sources, such as
19
-------
outlying power plants. In this case, ambient air quality in the urban
core where concentrations were initially highest may not be improved
the same percentage as regional emissions are reduced. Consequently,
the rollback approach will not necessarily achieve the desired air
quality in the core area. (See [24] for a more complete discussion.)
The SIP strategy does not take advantage of marginal control costs
or transfer coefficients. Rather, it places prime importance on equity
which is to be achieved when all sources of a particular type and size
are treated equally, regardless of cost and transfer coefficients.
The complete functional relationship between total regional costs
and ambient air quality was generated for the ELC and ALC as well as
SIP strategies. Since the ALC strategy includes the appropriate source-
receptor relationships (i.e., transfer coefficients) in the constraints,
output from each run of the ALC strategy directly provides a point on
the function relating air quality to regional control costs. Because
the constraints in the ELC approach guarantee only that a given emission
reduction has been reached, derivation of this air quality vs. cost
function for the ELC strategy requires the additional step of mapping
the post-control ELC pattern of regional emissions into ambient air
quality using a diffusion model. As shown below, the rollback technique
is an integral part of the ELC strategy, and leads to the required air
quality only under the most fortuitous of circumstances.
The ELC strategy minimizes the total cost of control for all sources
subject to a set of equations which include only one constraint repre-
senting the emissions reduction required as computed by applying the
rollback assumption to the receptor with the poorest air quality.* The
reduction in regional emissions required to meet the ambient standard
*The other constraints are bookkeeping equations for the separable
variables (see Appendix B).
20
-------
at the eight other receptors must be less than that for the receptor
with the greatest required improvement in air quality. (See Appendix A
for a proof of this assertion.) The constraint is generally stated in
terms of air quality improvement, which, for ELC, is simply a constant
times the emission improvement (reduction) required.
The ELC problem may be stated mathematically as:
T
minimize c x
subject to: a x S b ,
^>
where x — 0.
b = scalar equal to the greatest reduction
3
in particulate concentration (ug/m )
needed to achieve the standard among
the i receptors (i=l, ..., 9),
x = (27x1) vector whose element, x.,
(j=l, ..., 27) is tons of particulate
matter required to be removed per day
,- , .th
from the j source,
c = (27x1) vector whose element, c.,
(j=l, ..., 27) is the cost of removal
of one ton per day of particulate matter
th
by the j source,
a = (27x1) vector whose elements, a , are
equal to the coefficient (in this model,
.1214) which relates total regional
emissions to air quality, computed using
the rollback technique.
21
-------
The ELC constraint, a x f^ b , embodies the rollback calculation,
which determines the required percentage reduction in emissions as:
X - X fc ,
max std .
X - X, ,
max back
This is easily proven. The transfer coefficient a is defined in
terms of pg/m /tons/day as:
X - X, .
max back
RE
where RE is regional emissions/day. The term b is the maximum required
3
improvement in ambient air quality (MIA) measured in jug/m and is defined
as X - X ,. Since 2_iX. is the ampunt of regional emissions which
max std j
must be removed (RER) to satisfy the ELC constraint, and since a is a
constant, it can be factored out of the constraint, so that a 2_
-------
emissions into ambient air quality.* An important assumption of the ALC
solution is that the contribution of each source's emissions to air
quality degradation is independent of the contributions from other
sources and additive in effect, at each receptor.
The separable ALC model can be expressed algebraically as follows:
T
minimize c x
subject to: Ax — b,
-o,
where b = (9x1) vector whose element, b., (i=l, ..., 9)
represents the required ambient air quality
improvement for particulate matter at the i
receptor.
x — (27x1) vector whose element, x., (j=l, •••, 27)
is the number of tons of particulate matter
required to be removed per day by the j
source.
c = (27x1) vector whose element, c , (j=l, ..., 27)
is the cost of removal of one ton per day by
the j source. The c
that of the ELC model.
the j source. The c vector is identical to
A = (9x27) matrix of coefficients whose element,
a , (i=l, ..., 9; j=l, ..., 27) is the
transfer coefficient relating tons of pollutant
to be removed from the j source to the
incremental improvement of air quality at
the i receptor.
*With all three strategies, the assumption that the worst air quality
is actually measured is critical to the validity of the solutions.
23
-------
Rapidly increasing costs for each additional unit of control (i.e.,
increasing marginal cost) is a significant characteristic of pollution
abatement, and it is important that this characteristic be adequately
represented in both the ELC and ALC solutions. In fact, total cost
curves may approach a vertical asymptote, reflecting infinite costs
for 100% pollutant removal. These convex cost functions are represented
by a series of piecewise linear segments and, based on a set of special
assumptions, separable convex programming is employed. The interpretation
of solutions obtained using this technique is discussed in the next
section.
INTERPRETATION OF THE PIECEWISE OBJECTIVE FUNCTION
AND ALTERNATIVE FORMULATIONS
Twenty-seven piecewise linear cost curves, one for each source, are
used to compute the objective function.* Each curve traces out an
approximation to the lower bound of points representing the total cost
of the particulate control devices technologically applicable to each
source; there may be a dozen or more control measures contained in this
set of points. Each curve is convex to the origin and consists of two
straight-line segments. These curves were drawn such that the break-
points (nodes) in the straight-line segments represent physically
realizable control measures (e.g., a high voltage precipitator). Since
all the constraints are linear, a local optimum will be global.
If the solution calls for a level of control (in terms of tons of
particulate removed per day) at a node point (in Figure 2, either 0, A,
or C), the control device to be employed, the number of tons to be
removed, and the total cost can easily be determined.
If the solution for the source is at point 0, the source is
completely uncontrolled. If the solution is A, 20 tons per day are
*For more details on the formulation of the separable program see
Appendix B.
24
-------
Figure 2. HYPOTHETICAL EXAMPLE OF TOTAL COST
AS FUNCTION OF TONS REMOVED FOR GIVEN
SOURCE AND APPLICABLE CONTROL DEVICES
TOTAL COST
$200
$150
•=$10/TON
$100
TONS REMOVED
20
25 30
25
-------
removed at a total cost of $100. The control method employed and its
removal efficiency are represented by point A. Removal efficiency of
this device (operated at full power) is calculated as the ratio of tons
removed to uncontrolled tons emitted by the source times 100. Point C
has a similar interpretation.
Solution points between 0 and A and between A and C require a
different interpretation. Since decision variables are in terms of tons
removed per source at a specified cost, they must be translated into a
corresponding optimal control device or combination of devices. However,
since there are only a discrete number of applicable control devices, a
unique corresponding device may not exist. In this case the closest
device, or a convex combination of two devices which bound the theoretically
optimal (but nonexistent) device, will have to be chosen. Any point B
is a convex combination of devices A and C if B = aA + (l-a)C, O^Ta —1.
In addition, B can be expressed as a convex combination of any devices
which bound B and lie between A and C. Such convex combinations would
be optimal, i.e., they would correspond to the solution point called for
by the LP algorithm. Although these convex combinations can be inter-
preted as requiring that the gas stream be split and routed through the
nodal devices in the proportions a and (1-a) (in the case of point B,
50% of the gas stream would pass through device A and 507» would pass
through device C), this is not likely to be a practical engineering
solution. Thus, the greater the number of non-nodal solutions, the less
the engineering feasibility of the result.
The LP algorithm selects solution points along the segments OA and
AC on the basis of the marginal control costs for the devices which lie
on these segments. For any device between points 0 and A, the marginal
control cost is simply the slope of a ray from the origin to point A.
To evaluate the impact of bringing devices on segment AC into the
solution, the LP algorithm again uses the marginal cost, which is no
longer the slope of a ray through the origin, but is rather the slope
of the segment from A to C. For points on segment AC, the slope of rays
26
-------
from the origin represent average, rather than marginal, costs. The
marginal cost is $5/TON between 0 and A, $10/TON between A and C, while
the average cost is $5/TON on segment OA and $6 2/3/TON on AC.
Two alternative formulations would eliminate the need to consider
convex combinations. The first alternative would define variables in
terms of tons removed by a specific control device or units of consumption
and production activities (e.g., tons of high grade steel produced with
1.6% sulfur coal or kilowatts of electricity produced in a steam-electric
powerplant with a wet scrubber installed). This approach is utilized by
Kohn [6],
The second alternative is integer programming, with explicit consid-
eration given to each discrete control measure alternative. However, this
would require consideration of the marginal cost of each control device
within the set bounded by segments OA and AC, at considerably greater
programming and computational costs. It ten devices were included for
27
each of twenty-seven sources, 10 possible combinations of control devices
would have to be considered. The machine time required for a typical,
say, branch-and-bound, solution would be measured in years, although a
heuristic integer program could be employed to approach an optimum
(usually very closely) at a much lower cost. In contrast, the separable
programming formulation actually attains an optimum. However, an integer
program could consider the synergistic and multi-media effects of control
devices much more easily than the present approach.
On the other hand, the present formulation allows consideration of
a number of control alternatives for each source, yet is much simpler to
program and cheaper to run than approaches which use activity levels as
independent variables or are based on integer programming techniques.
Only two node points and the slopes of lines between them are input data
for each source in the present approach. In addition, control variables
are formulated directly in terms of tons removed, an advantage in computing
regional aggregates and possibly in enforcing control strategies.
27
-------
SECTION VI
DISCUSSION OF RESULTS
CAVEATS
In reviewing the results presented in this section, the following
assumptions and conditions must be kept in mind:
1) Annual concentrations are in terms of arithmetic rather than
geometric averages.
2) Only the cost of particulate control is considered. Synergistic
effects of particulate and SO control and multi-media effects are ignored.
X
3) Area source control costs, dynamic adjustments to control costs,
and externalities are not measured or considered.
4) Since the ALC strategy considers only a few sources and receptors,
it is probably not the true optimal solution for the St. Louis AQCR. The
use of a different or larger source-receptor set would most likely alter
the solutions for the three strategies considered, although differences
should be small.
5) The control cost segments must be carefully interpreted as
explained above. Problems of technological feasibility may be encountered
and marginal control costs may vary at different utilization rates.
6) Constraints on production activities are omitted from the
problem. Such constraints insure that the region considered consumes
only the available supply of resources and generates no surpluses. A
short supply of eastern low-sulfur coal, for example, is an important
limitation to SO control efforts. Resource constraints were omitted
X
28
-------
from this paper since particulate control would not impinge on scarce
resources to a significant degree. If control of other pollutants were
considered, resource constraints would probably be required.
GENERAL COST ANALYSIS
Figure 3, which contains the principal results of this study,
presents total regional control costs for three control strategies as
a function of air quality.* The functions for the SIP and ALC strategies
relate costs to "achieved" air quality as explained above. Two ELC
curves are presented — one for "achieved", and one for "predicted"
ambient quality. The predicted level is that which is employed in the
ELC constraint equation (representing the greatest improvement required
in ambient quality). The achieved level is obtained by feeding the
controlled emission levels from all sources into the diffusion model and
selecting the highest receptor concentration.
The control costs for the SIP strategy in Figure 3 are seen to be
as much as one order-of-magnitude larger than those for the ALC strategy.
3
Over the range of interest, 60 to 40 ug/m , in this figure, the ratio
never drops below six, indicating a very substantial penalty for using
the SIP strategy.
The range of interest was determined by assuming that controlled
area sources and remaining point sources, which account for 20% of
regional emissions, contribute approximately 25 pg/m to the maximum
receptor. The Federal ambient air quality standards for particulates
3
are stated as geometric averages (75 and 60 ug/m ), while the results of
this paper are stated in terms of annual arithmetic averages. Given a
standard geometric deviation for the region, it is possible to relate
these two quantities, but they may vary considerably. Assuming a moderate
*Total costs, as explained above, only include control costs.
29
-------
Figure 3. TOTAL REGIONAL CONTROL COSTS
PER YEAR AS A FUNCTION OF AIR QUALITY
AIR QUALITY LEVEL
Equivalent to:
Primary Standard
Secondary Standard -
10 i-
ALC STRATEGY APR QUALITY ACHIEVED
PARTICULATE CONCENTRATION,/Ug/m
30
-------
standard geometric deviation, the Federal standards become 85 and 65
3
ug/m annual arithmetic average (primary and secondary, respectively).*
3
The 60 and 40 jug/m concentrations in Figure 3 correspond roughly to
these primary and secondary ambient particulate standards when the
3
25 jug/m increment for omitted sources is added.
The difference between the cost functions for ALC and ELC quantifies
the importance of the location variable (i.e., transfer functions), since
ALC includes this variable plus variations in marginal costs, while ELC
3
considers only marginal costs. Over the 60 to 40 ug/m range, ELC
requires at least twice the expenditure required by ALC in achieving the
same ambient quality level. This result is not surprising in view of
the fact that source-to-source variations in the magnitudes of the
transfer coefficients and marginal costs are about the source (each
varies by as much as a factor of 100), i.e., these two variables are of
roughly equal importance. Note that the emphasis in the ALC/ELC comparison
above is on achieved air quality, and that, because of use of the roll-
back calculation, ELC performance falls short of predicted levels for
3
air quality better than 50 ug/m .
Despite the considerable cost savings of the ALC strategy over ELC,
the latter still possesses a substantial cost advantage over the SIP
strategy. The ratio of SIP to ELC control costs is as high as six to
3
one at 60 jug/m , but drops to about eight to six at the secondary stand-
ard. Regardless, a substantial cost differential exists for a wide
range of air quality.
An alternative way of looking at control strategy efficiency is to
consider air quality as a function of tons of pollutant removed as in
3
*Based on Larsen [ll], the annual geometric average of 75 ug/m translates
into an annual arithmetic average of 77 or 96 ;ug/m , depending upon whether
the standard geometric deviation for the region has a very low or a very
high value. Annual geometric standards of 75 and 60 jug/m , assuming a
moderate standard geometric deviation of 1.50, correspond to arithmetic
standards of 85 and 65 ug/m , respectively.
31
-------
Figure 4. Here the assimilative capacities of landfill sites as well as
the atmosphere are regarded as scarce resources; the more efficient the
allocation, the smaller the number of tons which must be removed to
achieve a given level of ambient air quality. The ALC strategy not
only achieves air quality goals at minimum cost, but minimizes the tons
of particulate matter to be disposed of in land-fill or on-site locations.
This strategy, therefore, poses the fewest inter-media pollutant-transfer
problems. From Figure 4, the ALC strategy achieves an ambient quality of
3
50 jug/m by removing 100 tons/day of particulate matter, while both the
SIP and ELC strategies must remove almost twice this amount to achieve
the same result.
However, by removing far more tons per day than the ALC strategy,
ELC does buy cleaner air. That is, the air quality under ELC not only
meets the standard at the worst receptor but is substantially cleaner
at most other receptors than ALC, which tends to improve air quality to
the minimum extent required. The same improvement in air quality is
produced by the SIP strategy vis-a-vis ELC and ALC. These relationships
are illustrated in Figure 5.
The cross sectional profiles of regional air quality shown in this
figure are, of course, illustrative only. The upper curve shows existing
(uncontrolled) air quality, with the receptor recording the maximum
particulate concentration located in the Central Business District (CBD).
Implementation of the SIP strategy brings the air quality at this receptor
down to the level of the standard, and at the same time, improves air
quality at all other receptors in the region (bottom curve, labeled "SIP").
The ALC strategy also meets the standard, but, because maximum use is
made of atmospheric assimilative capacity, air quality is improved only
as much as it needs to be, generating the "plateau" appearance shown in
Figure 5 (dotted line labeled "ALC"). The ELC strategy lies midway between
the ALC and SIP — note that it has been assumed that this ELC strategy
achieves the air quality standard. The cross hatched areas illustrate the
increments of clean air associated with the higher cost ELC and SIP strategies,
32
-------
Figure 4. TOTAL REGIONAL TONS REMOVED
PER DAY AS A FUNCTION OF AIR QUALITY
275
a
K.
UJ
Q.
c
UJ
O
S
UJ
cc
cc
200
u
H
cc
<
D-
U-
o
C/)
O
100
Air quality actually
achieved is plotted
for all strategies.
_L
JL
70
60 50
PARTICULATE CONCENTRATION
40
35
33
-------
Figure 5i REGIONAL AIR QUALITY AS A FUNCTION
OF LOCATION — CROSS SECTIONAL VIEW
o
ec
K
Z
O ?
2 '5
o 8
O |
uj c
U
p
cc
<
o.
RECEPTOR WITH MAXIMUM
PARTICIPATE CONCENTRATION
EXISTING AIR QUALITY
I
Distance from CBD
CENTRAL
BUSINESS
DISTRICT
(CBD)
ALC STRATEGY
ELC STRATEGY
SIP STRATEGY
Distance from CBD
34
-------
Area A shows the air quality improvement gained in going from ALG to ELC
and Area B shows that gained in going from ELC to SIP. As shown above,
each of these jumps (from ALC to ELC, and from ELC to SIP) may increase
costs by a factor of 2 or more.
The substantial cost differences between the three strategies is
again demonstrated in Figure 6, where cost is a function of tons removed.
The ELC strategy removes the required 200 tons/day at only one-fourth
the cost incurred by the SIP strategy, for example. Figure 6 also clearly
illustrates that the ELC strategy minimizes costs to achieve a given
emission reduction, not a given ambient air quality.
Although the foregoing analysis indicates what to expect as the
primary standard is attained and the states begin to move toward the
secondary standard, the impact of area source control costs must be
included before a definitive result can be obtained. However, it is
highly probable that the cost ratios among strategies will basically
remain unaltered.
EQUITY, TAX STRATEGIES, AND EFFICIENCY
A number of alternatives exist to the discriminatory emission regula-
tions described above. These alternatives involve imposing taxes, either
uniform or discriminatory: a set of positive and negative tax payments
to equalize the net control costs to each firm while enforcing the ALC
solution; a discriminatory emissions tax to obtain the ALC solution; a
single emissions tax to obtain the ELC solution; and a single emissions
tax derived from the ELC solution with a tax on remaining emissions.
Least-cost solutions of the ALC type are often criticized on grounds
that they require unequal and therefore inequitable expenditure on control
as well as lead to non-optimal solutions over time. Sources in a given
process and size category which operate different vintage control devices
and have different control costs would be required to remove different
35
-------
Figure 6. TOTAL REGIONAL CONTROL COSTS
PER YEAR AS A FUNCTION OF TONS REMOVED
cc
2j 10
oc
8
o
cc
o
o
1
2
cc
I
SIP STRATEGY
ELC STRATEGY
20
40
60
80
100
120
TONS REMOVED, 103 PER YEAR
36
-------
percentages of emissions, even if there were no variation in dispersion
parameters. In a dynamic context, the ALC strategy may create disincen-
tives to improving emission control technology. For example, a new sewage
treatment plant may be required to bear a larger control burden than an
older plant of equal size but with higher marginal control costs. This
penalizes the use of more efficient devices, retards technological
development, and may adversely affect plant location and expansion.
Equality of inter-plant control costs could be achieved without
abandoning the ALC solution of differential emission control. After
calculating this solution and enforcing the computed levels of control,
positive and negative taxes could be levied against all plants in a
given size and process classification so that the control costs for each
plant are the same. This would reduce some of the disincentive to utilize
newer control technology while still minimizing the cost of control summed
over all firms to achieve ambient standards. Credit could even be given
for implementation of more cost-effective control devices in order to
stimulate technological development. The sum of this expense and the
total cost of ALC would still probably be less than the total cost of the
ELC or SIP strategy.
However, equal payment for unequal environmental degradation may not
be any fairer than differential payment based on the ALC solution. With
the latter, polluters pay in relation to environmental degradation.
Thus, in keeping with the concept of marginal cost pricing and as
an alternative to directly controlling emissions based on the ALC
solution, the shadow values of the ALC solution (one for each receptor)
can be employed to determine tax rates which will reproduce the emissions,
ambient quality, and total cost of this strategy. Since shadow values
are the marginal costs of degrading air quality at each receptor, sources
can then be left to decide on the least-costly course for themselves —
whether to abate or pay a pollution tax (which will likely be unique for
each source). The tax for the j source would equal the sum over the
37
-------
i receptors of the shadow value of each receptor, s., times the transfer
l~ Vi
coefficient, a. ., which is the degradation of air quality at the i
1-1 th
receptor per ton emitted by the j source.Q For this source, the
pollution tax per ton emitted would equal )
i=l
a. .s..
An emissions tax based on the ALC solution requires that the agency
levying the tax know the levels of control required under this solution
and announce either the appropriate tax rate or number of tons which
must be removed. A tax would be announced simply to motivate firms to
undertake the required level of control, and once the ALC solution is
attained, remaining emissions would not be taxed.
The minimization problem for the ALC solution as defined above is:
. . T
minimize c x,
subject to: Ax ^ b,
The dual problem is:
• • Tu
maximize s b,
T
subject to: A s— c,
s * 0.
The dual maximizes the value of air quality subject to j constraints
which require that the total marginal tax paid by the j source £ a. .s.,
i i- J -i-
must be less than or equal to the marginal cost of control for the
j source.* Any source which is required to control emissions must
*In the separable programming algorithm, this marginal cost is one of
two possible values which is applicable for the level of control deter-
mined in the primal problem.
38
-------
abate until the total marginal tax equals the marginal cost. For a
typical source, this level is represented by point A in Figure 7. To
control to a lower level would mean paying more per ton in taxes than
the marginal cost of control, violating the constraint. Control beyond
A would imply £_, a. .s.< c., which requires that x. = 0. That is, the
J J J
source need not abate at all.
Figure 7. MARGINAL TAX VS. MARGINAL
CONTROL COST FOR A TYPICAL SOURCE*
Marginal Control Cost
Total Marginal
Tax per ton
Tons particulate removed
In terms of Figure 7, the tax is announced to inform firms of the
appropriate marginal tax rate. Once they know this, they will control
to point A, where the total marginal tax rate equals the marginal control
cost, under threat of having to pay the more expensive total marginal
tax. To reiterate, a tax need only be collected when firms are uncooper-
ative; normally no tax needs to be collected beyond the optimal level
(point A). Rather than risk miscalculation by firms, the control agency
*The marginal cost of control curve for the separable program would
consist of two discontinuous horizontal segments. A smooth upward-
sloping curve is employed here for simplicity.
39
-------
may prefer to simply announce the level of control required by each source.
With perfect knowledge, the result would be the same with either method.
Analysis for the ELC strategy is analogous and is not presented here.
One major difference is that the ELC strategy involves only one meaning-
ful shadow value, which means a uniform marginal tax rate for all sources.
Table 2 contains the emissions tax specified for each source as calculated
from the ALC solution based on the air quality level represented by the
3 3
63 jag/m concentrations (approximately the primary standard) and 40 jag/m
(approximately the secondary standard) in Figure 3. For the former, the
range is from $4.21 to $643.21 and for the latter from $.11 to $51.03 per
ton of particulate matter. The single emissions tax for the 63 and
3
40 Jig/m predicted concentrations calcule
$16.00 and $239.99 per ton, respectively.
3
40 Jig/m predicted concentrations calculated from the ELC solution are
The foregoing analysis produces important implications about a
pollution control strategy based solely on a uniform emissions tax not
calculated from individual cost and transfer coefficient data, as were
the ALC- and ELC-based emission tax strategies. Such a uniform tax
will probably be revised in an iterative fashion as air quality improves,
and is fittingly termed an iterative emissions tax (IET). An IET such
as a sulfur tax, based on the rollback calculation, will probably result
in far more costly control to meet a given ambient standard than the
ALC tax strategy, but would approach the cost of the ELC-based tax as a
lower bound as the variation among individual cost coefficients approaches
zero. Since the IET ignores individual source transfer coefficients and
costs of control, which produce different tax rates per ton for each
source in the ALC solution, an IET must be more costly than an ALC-based
strategy. The difference should be very large, based on the cost savings
attainable with the ALC strategy.
If the agency administering the IET first calculated the ELC
solution (for an achieved air quality) and announced its single shadow
value as the uniform tax per ton, the IET and ELC solutions would coincide,
40
-------
Table 2. ALC EMISSIONS TAX - $/TON
SOURCE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
ALC SOLUTION
3
40 jug/m
261.08
517.54
184.29
84.54
73.03
249.73
136.16
600.04
66.08
465.55
189.00
177.92
579.39
133.48
31.41
643.21
156.62
6.51
14.26
6.75
86.00
90.73
25.90
25.82
23.26
25.89
4.21
63 ;ag/m
4.33
18.38
2.26
1.06
.87
3.04
3.27
51.03
1.20
11.85
13.08
5.57
32.87
2.92
.55
15.00
6.54
.25
.48
.20
1.28
3.25
.29
.45
.41
.46
.11
41
-------
Otherwise, the agency must rely on its ingenuity or successive iterations
of air quality monitoring and tax revision. However, since legislating
an IET would be difficult, efforts to revise it would probably be even
harder.
Those who propose the IET strategy quickly point toward modification
of a strict emission-based tax to overcome its shortcomings. One suggestion
involves the use of geographical zones to help determine differential
IET rates, since suburban sources will probably degrade ambient quality
less than urban ones. But since location is only one dispersion parameter,
a method for handling the other parameters must be devised. For example,
a strategy for dealing with two sources with greatly unequal stack height
must be devised. In addition, problems of equity, enforceability, and
prevention of collusion — if emission rights purchased with taxes are
transferrable — cannot be lightly dismissed.
As mentioned above, the ALC- and ELC-based emissions taxes will
create disincentives to develop new control technology. A po'ssible
solution to this problem would involve modification of these strategies
by announcing the tax as previously calculated in either of these
strategies, and then collecting the tax on all uncontrolled emissions.
A dynamic stimulus would be provided to lower the marginal cost curve
over time by introducing more cost-effective devices, even though the
immediate solution would be the sa'me with or without the additional tax.
Under this modified system the sum of control costs and the collected
emissions tax would comprise "total firm costs." For each plant this
will exceed the ALC or ELC strategy costs by the amount of the emissions
3
tax actually paid. At an achieved air quality of 63 ug/m , the total
annual emissions tax is $963,191 and total annual firm costs are
$1,270,050 for the ELC strategy. Again for this strategy, at the
3 3
40 jug/m level of predicted air quality (about 43 jig/m achieved air
quality), the total annual emissions tax is $2,887,806 and total annual
firm costs are $6,733,654. In comparison, the ALC total annual emissions
42
-------
3
tax is $226,354 and total annual firm costs are $292,686 at 63 /ig/m ,
3
while at the 40 ;ag/m level the total emissions tax is $1,625,199 and
the total annual firm costs are $3,534,337. Both strategies, however,
produce total firm costs substantially below total costs of control
for the SIP strategy at both levels of air quality.*
MARGINAL BENEFITS AND COSTS
The optimal level of control occurs where the marginal cost of
control equals the marginal benefit, since total pollution damages
and the costs of pollution control are minimized.** Based on [20],
estimates can be made of nationwide average benefits to health, plant
life, and property obtained by reducing particulate concentration from
the present level to the primary standard.*** Only fuel combustion,
industrial process and solid waste sources are considered. The average
benefit estimates range from a low of $135/ton to a high of $421/ton,
*The above discussion did not consider payments rather than taxes to
induce abatement. The immediate effect on resource allocation from
either scheme should be the same, assuming perfect knowledge of potential
source emissions.
**In all the following analysis, it is assumed that the parties which
suffer damages from particulate matter cannot bargain with the polluters,
If this were not the case, the optimal level of control would be lower.
See [20] for a detailed discussion.
***National benefit figures can be reasonably employed to generate
average and marginal benefit data for the St. Louis area. This region
is large and heterogeneous enough to produce a good approximation to a
random sample of nationwide exposure to pollutants, age distribution,
racial classification, population density, and other variables employed
in the calculation of aggregate benefit figures.
43
-------
with a mid-range estimate of $280/ton in 1967 dollars.* At the level
of the primary standard, most investigators assume that the function
relating total damages to air quality is strictly concave to the origin,
and marginal damages will be less than average damages. However, the
exact shape of the function is unknown. In addition, since total and
average damages are only estimated at one point -- approximately the
primary standard -- marginal damages cannot be directly calculated.
Nonetheless, certain a priori restrictions can be placed on the
relationship between marginal and average damages. Control technology
data indicates that the level of abatement required to achieve the
primary standard principally involves removing large particles, so that
remaining particulate matter must be predominately less than 10 microns.
Health experts feel that these fine particles are most injurious to
human health.
A reasonable assumption, therefore, is that the total benefit
function continues to rise steeply from the primary to the secondary
standard and beyond, so that marginal benefits are not substantially
less than average benefits. That is, some factor k exists such that
average benefits times k equals marginal benefits, 0<=k<=l. Based on
*These figures were obtained by first assuming that 8 million tons of
particulates are miscellaneous, background, or non-urban. Of the 19
million tons remaining, removal of 17 million of them implies about 907o
control of all emissions, and would bring air quality from the present
level to a point very near the primary standard. The low, middle, and
high estimates of total benefits from this reduction are $2.57, $5.11,
and $7.67 billion. However, only the benefits from control of fuel
combustion, industrial process and solid waste sources are desired. The
percentage of total air quality degradation weighted by population
exposure due to these sources (84%) is expressed as a ratio of the total
percentage removed (907»). This ratio is multiplied by each total benefit
figure before dividing by total tons removed to obtain average benefits.
All benefit data is in 1967 dollars so it can be compared with the 1967-
based cost data. Certain factors operate to make these figures both
under- and over-estimates of the true benefits. (See [23] for a complete
discussion.)
44
-------
the above argument, it is reasonable to assume that k is close
to 1.
From Figure 3, marginal control costs can be derived for the SIP,
3
ELC, and ALG strategies. At the 60 .ug/m level (corresponding approx-
imately to the primary standard), marginal costs per jug/m decrease from
$122,500 for the SIP strategy to $55,000 for the ELC strategy and
$15,000 for the ALC strategy. Marginal costs increase rapidly for
all strategies as the secondary standard is approached, rising, e.g.,
3
to about $560,000 per jug/m for the SIP strategy at the secondary
standard.
The cost of control per ton of particulate matter can be obtained
by multiplying the derivative of the cost versus air quality curve
(Figure 3) by the reciprocal of the derivative of the tons versus air
quality curve (Figure 4) and adjusting tons/day to tons/year, or by
simply taking the derivatives in Figure 6 and making the same adjustment
in units. At the primary standard the cost per ton is $5.67, $23.18,
and $64.70 for the ALC, ELC, and SIP strategies, respectively.
A comparison can then be made of average benefits and marginal
costs at the approximate level of the primary standard so the value of
k which equates the product of k times average benefits to marginal
costs can be determined.* At the approximate level of the primary
standard, the marginal cost of $64.70/ton for the SIP strategy is about
one-half the low estimate of average benefits of $135/ton and about
one-seventh the high estimate of $421/ton. If marginal benefits are
more than one-half or one-seventh average benefits, i.e., k is greater
than these values, marginal benefits will exceed marginal costs. These
magnitudes seem very reasonable based on the above reasoning.
*The particulate standard does not specify allowable particle size, so
that at a given ug/m concentration, costs may refer to concentrations
composed of different sized particles than do benefits.
45
-------
For the ELC strategy, the marginal cost of $23.18/ton is about
one-sixth the low estimate of average benefits and about one-eighteenth
the high estimate. For the ALC strategy, the marginal cost of $5.67/ton
is about 1/24 the low estimate of average benefits and about 1/74 the
high estimate. That is, if marginal benefits are at least 1/24 or 1/74
the size of average benefits, then marginal benefits exceed marginal
costs. Ratios of at least this magnitude for the ELC and ADC strategies
seem almost certain.
REFINEMENTS
One of the major objectives of this research was to develop an
understanding of alternative ways of formulating least-cost pollutant
control strategies and to make recommendations for future analysis.
Two alternate ways of defining independent variables have been
utilized in the literature -- the one employed in this paper, where a
single decision Variable represents the controlled emissions at each
source, and the other employed by Kohn [6], where several possible
activity levels for each source describe the quantity of output produced
using various fuel-switching or add-on control measures. In the first
case it is necessary to assume either constant marginal costs, or
represent costs by a convex function and use a separable programming
technique (rather than the normal LP). In the second approach, because
there are several variables per source, the only required assumption is
constant costs per unit of output produced under a given control
alternative. Despite the larger number of independent variables
required by this approach, it is still basically equivalent to the first
One, since special variables have been introduced to define the convex
cost function used with this technique.
Divisibility problems exist with either approach. In the single-
variable-per-source approach, the solution may occur at a point on the
cost-versus-control-efficiency curve where no device exists, requiring
46
-------
a convex combination of two devices, while the solution under the
multiple-variable approach, for example, may call for production of
half of the output using a 99.7% precipitator and half with uncontrolled
emissions. In the real world either of these would mean splitting the
gas stream and running each portion through one or more devices --
something which could be done, but is certainly not common practice.
In addition, devices may be incompatible, e.g., when a solution calls
for production with low sulfur fuel and control with flue gas desulfur-
ization. Despite these criticisms of the multiple-variable approach,
it does satisfy constraints on scarce resources and guarantee required
output.
A mixed-integer program, which would select only one control device
per source, could be employed to avoid these kinds of problems. However,
as discussed above, computational costs rise considerably. The tradeoff
must be carefully weighed.
The fact that this paper has dealt with only one pollutant means
that another important difference between the single and multiple-
variable approach has been ignored. When considering the impact of
simultaneously controlling several pollutants with a single control
measure, the single-variable approach would require a separate cost-
versus-efficiency-of-control function for each pollutant and each source.
The multiple-variable formulation makes the cost of each control device
explicit and allows for much easier tracing of their multi-media impact.
47
-------
SECTION VII
REFERENCES
[l] Burton, Ellison and Sanjour, William. "Multiple Source Analysis
of Air Pollution Abatement Strategies", Federal Accountant,
XVIII (March, 1969), 48-69.
[2] CONSAD Research Corporation, Volume I; The Direct Cost of
Implementation Model. Prepared for the Environmental
Protection Agency, Washington, July, 1972.
[3j Hadley, G., Nonlinear and Dynamic Programming. Reading: Addison
Wesley Publishing Co, Inc., 1964.
[4] IBM, "Mathematical Programming System/360, Version 2, Linear
and Separable Programming", 1968.
[5] Kneese, Allen V. and Bower, Blair T. "Standards, Charges, and
Equity", in Economics of the Environment, Robert Dorfman and
Nancy S. Dorfman, eds., New York: W. W. Norton and Company,
1972, 159-70.
[6j Kohn, Robert E. "Abatement Strategy and Air Quality Standards",
in Development of Air Quality Standards, A. Atkisson and
R. S. Gains, eds. Columbus: Charles E. Merrill Publishing
Co., 1970, 103-22.
[?J Kohn, Robert E. "Application of Linear Programming to a
Controversy on Air Pollution Control", Management Science,
XVII (June, 1971), 609-21.
[8] Kohn, Robert E. "Optimal Air Quality Standards", Econometrica,
XXXIX (November, 1971), 983-995.
[9] Kortanek, K. 0., et al. "On the Numerical Determination of
Optimal Control Strategies for Air Quality Standards and
Regulatory Policy," Carnegie-Mellon University, August, 1971.
[10] Kortanek, K. 0., et al. "Optimal Control Strategies for Air
Quality Standards and Regulatory Policy", Carnegie-Mellon
University, August, 1971.
[llj Larsen, Ralph I. "A Mathematical Model for Relating Air Quality
Measurements to Air Quality Standards", EPA, Office of Air
Programs Publication No. AP-89, November, 1971.
48
-------
[l2J Martin, Delance 0. and Tikvart, Joseph A. "A General Atmospheric
Diffusion Model for Estimating the Effects on Air Quality of
One or More Sources," JAPCA, XVIII (June, 1968), 68-148.
[13] Norsworthy, J. R. and Teller, Azriel. "A Design of a Study to
Estimate the Regional Economic Impact of Air Pollution
Control Policy," Temple University.
[14] Plotkin, S. E. and Lewis, D. H. "Controlling Air Quality:
St. Louis Case Study," TRW Systems Group, June, 1971.
[15] Russell, Clifford S. and Spofford, Walter 0., Jr. "A Quantitative
Framework for Residuals Management Decisions," in Environmental
Quality Analysis, Allen V. Knesse and Blair T. Bower eds.
Baltimore: Johns Hopkins Press, 1972, 115-180.
[l6j Seinfeld, John H. and Kyan, Chwan P. "Determination of Optimal
Air Pollution Control Strategies", Socio-Economic Planning
Science, V. 1971, 173-90.
[17] Teller, Azriel. "Air Pollution Abatement: Economic Rationality
and Reality," Daedalus, LXXXXVI (Fall, 1967), 1082-1098.
[l8j Teller, Azriel. "The Use of Linear Programming to Estimate the
Cost of Some Alternative Air Pollution Abatement Policies",
Proceedings of IBM Scientific Computing Symposium Water and
Air Resource Management, 1968, 345-53.
[19] TRW Systems. "Air Quality Implementation Planning Program,"
Volume 1, Operator's Manual. Washington, November, 1970.
[20] Turvey, Ralph. "On the Divergences Between Social Cost and
Private Cost," Economica, XXX (August, 1963), 309-13.
[2l] U. S. Environmental Protection Agency, "Requirements for Preparation,
Adoption, and Submittal of Implementation Plans", Rules and
Regulations, Federal Register, Vol. 36, No. 158.
[22] U. S. Department of Health, Education, and Welfare. Control
Techniques for Particulate Air Pollutants. January, 1969.
[23j Waddell, T. "The Economic Damages of Air Pollution", Environ-
mental Protection Agency, 1973.
[24] Zimmer, Charles E. and Larsen, Ralph I. "Calculating Air Quality
and its Control", JAPCA, XV (December, 1965), 565-72.
49
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SECTION VIII
APPENDICES
50
A. ELC Constraint Equation 51
B. Separable Linear Program 54
-------
A. ELC CONSTRAINT
The purpose of this appendix is to prove that the use in the ELC
program of only the one constraint whose receptor requires the greatest
improvement in air quality will produce the largest necessary reduction
in regional emissions. This proof will be made for a two-constraint
(two-receptor) case.
Define
CD AE.=ET -ES. 1 = 1, 2
where Z_\ E. is the required reduction in regional emissions
so that the ambient standard is met at receptor i, E is
total regional emissions, and E . is the level of regional
51
emissions which would satisfy the air quality standard at
, .th
the i receptor.
Using a standard formulation (see Kohn [&]) let
(2) q. - b
JL
a.=-—-
where q. is the air quality at the i receptor, b the
background at all receptors, while E is regional emissions.
Then define
(3) qs - b
E . = — i = 1, 2
si a.
51
-------
where q is the air quality standard for the region and
s
a. is defined in (2).
Then from (1) - (3)
A
ET - Esl
ET - Es2
which simplifies to
(4)
" q
q2-b
Assuming that the standard exceeds the background,
(5)
qs -
where C is some positive constant,
substituting (5) into (4) yields
(6)
Thus
A
" -
(q2 - qs) + €
_(qL - qs) +C
(qL - q.)
(q2 - qs)
or
1 +
(7) AE1
1 + f
52
-------
Thtee cases exist for (7):
(a) if q, = q1 , l\ _ 1 _
A P ~ '
A E2
(b) if q > q , A El
AE2
(c) if q «= q , AE1
•L £
Therefore, the constraint with the highest air quality concentration
and therefore the1 greatest requited improvement in air quality will
require the greatest regional emissions reduction.
53
-------
B. SEPARABLE LINEAR PROGRAM
The optimization technique employed is the IBM MPS/360 separable
linear program which employs the "delta method," described in detail
in [4], This algorithm allows approximation of a continuous non-linear
function (e.g., a cost function) of more than one variable provided the
function is separable, i.e., contains no cross-product terms.*
The separable program represents a non-linear objective function
and any non-linear constraints as piecewise approximations defined by
a set of special variables. The use of more linear segments improves
the degree of approximation of the non-linear function. Additional
accuracy is then traded-off against prbgramming and computational
expense.
Let the original non-linear minimization problem be
m
minimize &= 2_i f.(x.),
= l 5 J
(1) subject to:
n
E
1, ..., n.
*Cross-product terms can be separated with a procedure described in
54
-------
The piecewise approximation is then
n j
minimize 2 = 2_, £_,
j=l k=0
(2) subject to:
r
n J
>^ T gk Lk ~ V i = 1, ..., m,
k Ao ku kj x
r.
1 _ 0, for all k, j,
j
Equation set (2) can be written in matrix form as
T
minimize f 1,
(3) subject to:
G 1 ^ b,
1^ 0,
where f and 1 are column vectors of cost coefficients and special
variables, respectively, and G is a matrix containing m + n rows and
2_, r. + n columns. (The delta method actually involves approximating
(1) by the introduction of variables somewhat different from those
employed in (2).)
Each additional j original variable requires one new row and
r + 1 new columns for the G matrix. Additional resolution attained,
j
55
-------
for example, by adding another special variable for one original
variable requires no more rows, but one more column.
The solution to (2) is a global as well as local minimum if the
feasible set is convex and the objective function is convex to the
origin.
56
OU.S. GOVERNMENT PRINTING OFFICE: 1974 546-316/274 1-3
-------
BIBLIOGRAPHIC DATA
SHEET
EPA-600/5-74-003
3.' Uecipirr.:'.; Arcc-ssion .'.
A Cost Evaluation of Alternative Air Quality
Control Strategies
'?. Heport l>.ue
January 1974
6.
Scott E. Atkinson and Donald H. Lewis
8. Performing Organization K
No.
9. l>crtor::;:rit. ' tr^aniza: ion .'-.in.:, .inj AJJrj«ct Task-Work 1.,'n
21ARG 04
11. Contrar'. Grant No.
12. Sponsoring O.-Yani/atK'n Name and Address
Washington Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
13. Type of Report & Petit,J
Covered
Final
14.
15. Supplementary Notes
16. Abstracts
A computer simulation is employed to evaluate three alternative particulate
air pollution control strategies, utilizing St. Louis as a model region, with
the following objectives: (1) quantification of cost savings of two least-cost
strategies based on alternative linear programming formulatibns — an air
pollution emissions least-cost (ELC) strategy and an ambient air quality least-
cost (ALC) strategy, and comparison of these strategies with currently-used
strategies, (2) evaluation of certain variables in the least-cost strategies,
(3) cost impact on region of meeting increasingly Stringent air quality standards,
(4) comparison of marginal costs and benefits of control at the primary standard.
17. Key \Vords and Document Analysis. 17o. Descriptors
Air pollution control; environmental economics; environmental management
17b. Identifiers Open-Ended Terms
17c. COSATI Field/Croup
18. A\ ail.i. ihty Statement
Release Unlimited
19. Sn unty.-lass {'Ihis
20. s^-
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