&EPA
United States
Environmental Protection
Agency
Municipal Environmental Research EPA-600,'£-78-013
Laboratory August 1978
Cincinnati OH 45268
Solid and Hazardous Waste
Economics of
Municipal Solid
Waste Management
The Chicago Case
EP 600/S
78-013
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RESEARCH REPORTING SERIES
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EPA-600/8-78-013
August 1978
ECONOMICS OF MUNICIPAL SOLID WASTE MANAGEMENT:
THE CHICAGO CASE
by
G. S. Tolley
V. S. Hastings
G. Rudzitis
University of Chicago
Chicago, Illinois 60637
Purchase Order No. CA-6-99-3381-A
Project Officer
Oscar W. Albrecht
Solid and Hazardous Waste Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
This report has been reviewed by the Office of Research and Development,
U.S. Environmental Protection Agency, and approved for publication. Mention
of trade names or commercial products does not constitute endorsement or rec-
ommendation for use.
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FOREWORD
The Environmental Protection Agency was created because of increasing
public and government concern about the dangers of pollution to the health
and welfare of the American people. Noxious air, foul water, and spoiled land
are tragic testimony to the deterioration of our natural environment. The
complexity of that environment and the interplay between its components re-
quire a concentrated and integrated attack on the proolem.
Research and development is that necessary first step in problem solution
and it involves defining the problem, measuring its impact, and searching for
solutions. The Municipal Environmental Research Laboratory develops new and
improved technology and systems for the prevention, treatment, and management
of wastewater and solid and hazardous waste pollutant discharges from munici-
pal and community sources, for the preservation and treatment of public drink-
ing water supplies, and to minimize the adverse economic, social, health, and
aesthetic effects of pollution. This publication is one of the products of
that research; a most vital communications link between the researcher and the
user community.
This report provides an extensive discussion of the theory of demand
for household solid waste collection and disposal services, and concepts for
measurement of the quantity and level of services demanded. An investigation
of relationships between several socio-economic characteristics and quantity
of household solid waste, conducted in an earlier study for the Chicago area,
is repeated to determine to what extent the earlier hypotheses are supported
by use of more current data. It is hoped that the results of this study will
provide policymakers and solid waste managers with additional information on
the structure of demand and implications for managing the increasing quanti-
ties of household solid waste.
Francis T. Mayo, Director
Municipal Environmental Research
Laboratory
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ABSTRACT
This study is a result of a request by the U.S. Environmental Protec-
tion Agency (EPA) to undertake and extend certain economic studies related
to municipal solid waste collection/disposal services. The EPA requested
that four tasks be undertaken: 1) an extension of the theory of demand
with particular attention to methods of financing, factors affecting demand
shifts, and price elasticity, 2) a review and critique of prior studies of
demand for residential solid waste collection/disposal service, with par-
ticular emphasis on empirical results related to price and income elastici-
ties, 3) statistical regression analysis to update the analysis in the
1971 Sheaffer and Tolley study on solid wastes collection in Chicago, and
to compare results with related studies, including but not limited to a
number of studies specified, and 4) the identification of areas of needed
research on the economics of solid and hazardous waste management and the
recommendation of procedures and methodology. Each task comprises a
separate section.
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CONTENTS
Foreword i i i
Abstract iy
Figures vi
Tables yii
Acknowledgement viii
I. Extension of the Theory of Demand for Municipal Solid Waste
Collection/Disposal Services 1
Introduction 1
Extension of the theory of demand - private economic
utilities only 4
Extension of the theory of demand for residential solid
waste collection disposal to include public good
considerations (environmental externalities) 42
II. Review and Critique of Prior Studies of Demand for Residential
Collection/Disposal Services 45
Price effects 45
Income effects and income elasticity of demand estimates. ... 48
Other effects 49
Environmental effects 50
III. Factors Affecting Residential Solid Wastes in Chicago 51
Purpose 51
Solid waste distribution in Chicago 51
Explanatory variables 55
Model specification 61
Regression results 66
Summary of Results, comparison with 1971 study and with
other results in the literature, and conclusions 85
IV. Areas of Needed Research and Recommendations for Research
Procedures and Methodology 98
Research needs 98
Recommendations for research procedures and methodology . . . 103
References 105
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FIGURES
1 Cost functions for waste collection and disposal services .... 9
2 Location of collection point as supply shifter ......... '. n
3 Cost functions for waste collection and disposal services
for different types of waste ................. 13
4a Willingness to pay for back-door services on pay-as-you-go
basis ............................. 25
4b Willingness to pay per collection for back-door service . . . . . 25
5 Marginal willingness to pay for percent back-door services as
a function of number of containers per week .......... 27
6a Willingness to pay for frequency of collection showing
summer winter differences ................... 31
6b Willingness to pay for frequency of service showing
critical prices for shifting frequency ............ 31
7 Supply and demand functions for cleanliness/spaciousness .... 35
8 Shift in cleanliness/spaciousness supply function with
change in collection frequency ................ 36
9 Shift in demand for quantity of service when collection
frequency is increased .................... 37
10 Ward map of Chicago ...................... ' 52
11 Average pounds of solid waste collection per dwelling unit
by^weeks, 1969 and 1970-1971 ................. 53
12 Relationship between ward median family income and percentage
of dwelling units served by municipal waste collection .... 60
13 Income elasticity of the demand for solid waste disposal .... 73
14 Per capita waste volume elasticities with respect to family
income for simple and multiple regressions for 9 weeks
tested ............................ 87
15 Per capita waste volume elasticities with respect to income,
1968, 1969, and 1970-1971 .................. 94
VI
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TABLES
Number Page
1 Cost functions for solid wastes collection services 17
2 Weekly solid waste collection in pounds per dwelling unit,
by political ward 54
3 Rank order of weekly waste collection in pounds per dwelling
unit, by political ward 56
4 Estimates of median family income by ward, 1970 58
5 Median family income rank, by ward 59
6 Family income variances by 50 political wards 62
7 Ward populations, 1970 63
8 Household size and percent blacks by ward, Chicago, 1970 ... 64
9 Ratio between municipal and total collection of household
solid wastes, by political ward 67
10 Results of weighted and unweighted regressions, week 32
(8/6/71) 68
11 The typical relationship between alternative specifications
(week 32, 1971) 70
12 Solid waste - income relationship, 1970-1971 71
13 Solid waste - income relationship, 1969 72
14 Solid waste - variance relationship 75
15 Solid waste - income, variance relationship 76
16 Solid waste - household size relationship 78
17 Solid waste - income, household size relationship 79
18 Solid waste - race, income relationship 82
19 Best specifications for income and race, 1969 83
20 Solid waste - income, race, variance relationship 84
21 Per capita waste volume elasticities with respect to
family income from simple and multiple regressions for
9 weeks tested 86
22 Per capita waste volume elasticities with respect to
income variance from simple and multiple regresssions
for 9 weeks tested 91
23 Per capita waste volume elasticities with respect to
percent black from multiple regressions for 9 weeks
tested 92
24 Per capita waste volume elasticities with respect to
income and R
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ACKNOWLEDGMENT
Various officials of the City of Chicago cooperated in providing the
necessary information for this study. Mr. Oscar W. Albrecht of the Solid &
Hazardous Waste Research Division, Municipal Environmental Research Labora-
tory, Cincinnati, Ohio served as the EPA's project officer, and he and Dr.
Haynes C. Goddard, Associate Professor of Economics, University of Cincinnati,
provided valuable comments on a draft of this study. Dr. Yi Wang assisted in
data collection and analysis of previous work and provided valuable comments.
vm
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SECTION I
EXTENSION OF THE THEORY OF DEMAND FOR
MUNICIPAL SOLID WASTE COLLECTION/DISPOSAL SERVICES
INTRODUCTION
General
As pointed out in the 1971 Sheaffer-Tolley solid wastes study, one way
of projecting future demand for waste collection and disposal services would
be to simply extrapolate past trends. However, one might be caught by sur-
prise in so doing, as new trends may become predominant that were not appar-
ent in global figures, but would have been detected upon more careful analy-
sis and systematic analysis of the data. The trend approach would leave
unutilized the more specific information that is in fact available. In
introducing the subject of applying economic analysis, the Sheaffer-Tolley
study emphasized that the elements that enter into the economic analysis of
the quantity of services demanded over time are becoming important topics to
economic theory, even without the obvious need for projecting the future
volume of household wastes. These elements include 1) costs (which, with
external environmental costs included, are increasing at a rapid rate) and
2) the demand functions for waste services. They are important because
they bear on effective and efficient ways of achieving private and social
objectives related to collection and disposal of solid wastes.
The Sheaffer-Tolley report extended the conceptual basis of the demand
for residential and municipal solid waste collection/disposal services
further than it had been carried previously, and further extensions have
since appeared in the literature. There have been some notable extensions
since the Sheaffer-Tolley report. (These extensions, as well as empirical
findings contained in the literature, will be discussed in Section II of
this study, A Review and Critique of Prior Studies of Demand for Residential
Solid Waste Collection Disposal Service. In addition, at various points in
this first section, significant contributions by others in extending the
theory will be cited and referenced.) Nevertheless, there is room for still
further extension. The EPA request for further work suggests some of the
areas in which extensions are needed. A major area is on the specific
effects of price. The empirical part of the Sheaffer-Tolley study, because
of lack of data, was void of price considerations, as is this study for the
same reason. Review of the literature reveals that little has been done
in this area. Another area is that of analysis at the disaggregated level
for particular kinds of service such as more or less frequent service or
different service for different types of solid wastes. Still another area
in which the need for extension is emphasized is the effect of financing
1
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methods on the quantity of services demanded. Little has been done on this,
again largely because of the lack of specific data needed to conduct the
analysis.
The Role of Public and Private Economic Utilities
in the Extension of the Theory of Demand
Demand for residential solid waste collection and disposal services is
based on the consumer utility that a household derives from these services.
The services are thus inputs to consumer production functions producing
such utilities. In the Sheaffer-Tolley report, Tolley, who was the author
of the economics sections of the report, begins with the consumption deci-
sion, adding to it the related waste decision in producing consumer utili-
ties. In this framework, wastes are an output of the general utility pro-
duction process. Economists have for long treated this output as having a
zero price, but in fact, at least in a social sense, this output has a
negative price, i.e., there is a demand for, and it costs something for,
getting rid of the wastes.
Overall utility is maximized not only by taking action to get rid of
the wastes, based on utility derived from that action per se, but also by
undertaking consumption actions that produce the wastes, based on the
utilities derived from consumption. Since the consumption decisions neces-
sarily involve some waste production, the cost of waste disposal bears on
the consumption decisions and the overall maximization of consumer utilities.
The utility derived from waste collection and disposal is based on the
desire to get wastes out of the way and to provide a clean, orderly,
healthy, and safe environment. The interest applies not only to wastes gen-
erated in one's own household, but to those generated at the residences of
others, in the streets, public areas, and in the off-the-beaten-track areas
of the community. Leaving a picnic area littered or depositing wastes in
open dumps, in abandoned quarries or in a marshy area behind the woods are
no longer acceptable disposal methods. Cleaner methods produce greater
utilities.
It is this public interest in a pollution-free environment that
justifies public intervention in the solid waste area. The individual is
willing to pay not only for collection of his own household wastes, but
also, through a public agency, some amount to induce or require others to
have wastes collected and disposed of in a non-polluting way. Indeed, he
himself may require some inducement to act in the way he desires others to
act, because, if he does not so act, the main adverse effect of his action
alone is on others, not himself. In other words, self interest alone may
not produce optimum waste collection and disposal. Incentives, educational
programs, enforcement programs with penalties, and the like may be required.
There is, of course, a fundamental interest on every individual's part
in obtaining and inducing others to obtain waste collection and disposal
services to maximize his utilities derived from them. Maximizing individual
utilities in this way will produce the socially optimum waste services.
This involves finding the least cost way of obtaining utilities and "buying",
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either directly (for service to one's own residence) or indirectly through
a public agency, an incremental utility when and only when it costs no more
than it is worth, taking into account in the solution all benefits and costs
including the environmental.
The solution would be relatively simple if the interest were in fact
solely in the collection and disposal of one's own wastes, or if others in
the community, through no special inducement, always acted in a non-polluting
non-littering way. In such a situation, while there would still be an
interest in a clean community, there would be no need for concern, nor need
to provide inducements to (or impose penalties on) others to achieve it.
In fact, in some communities, something very close to this situation
may apply. With increasing awareness of the advantages of a clean environ-
ment, this may include an increasing number of communities. In such communi-
ties, sanitary land-fill operations are required by law. Even if incremental
user charges are imposed for collection and disposal services, and these are
based on the higher costs of non-polluting collection and disposal opera-
tions, households do not avoid these costs by disposing in alternative ways
that litter or pollute. This may be basically because of altruistic public
interest, but partially because there are real as well as psychological costs
attached to the alternatives. Litter baskets are provided and are used in
public places, with costs financed by taxes or through fees for use of public
parks, and refuse containers are kept in cars and the contents disposed of
at home. Finally, with incremental user charges for the various services
provided, households generate and dispose optimum amounts of refuse based
on these costs. Thus, there is no reason for concern with respect to non-
optimum use of resources.
In such a situation, the essential role of government would be reduced
to minimum surveillance and enforcement needed to ensure continued success-
ful operation of the system. There would still be private reasons for con-
tinued local government involvement based on tax and subsidy considerations,
but there would not be valid social reasons. These points will be discussed.
The specific Federal concern, however, would be reduced to general interest
in surveillance and general interest in the economic use of the nation's
resources.
As pointed out earlier, the major governmental concern would be where
pollution externalities are involved. However, from the standpoint of
developing the framework of demand for services, it will be convenient to
start with the relatively simple case of non-concern with pollution extern-
alities. The demand and optimum resource allocation framework will then
represent a building block to which the analysis of externalities can be
added. In addition, starting with this will give a basis for gauging the
relative importance of factors that may affect externalities.
The organization of this section will thus be to first look at exten-
sion of the theory of demand where only private economic utilities are in-
volved or are of concern. What is needed is an economic model that can be
used both to explain and predict the amounts and kinds of services that are
and will be demanded, and in a way that maximizes the individual utilities
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from such services. It was pointed out in the 1971 study that a comprehen-
sive economic analysis of waste demands can be organized using a three-part
framework consisting of demand, supply, and price. This basic procedure will
be followed here. First, what-is-demanded and supplied will be listed, dis-
aggregating the separate kinds of services provided from a demand standpoint.
Again, as earlier pointed out, analysis can proceed at the aggregate level,
but a comprehensive extension requires disaggregation. Measurement of what-
is-demanded will be discussed. The what-is-demanded listing and discussion
will be followed by development of cost or supply concepts, and this by the
development of demand concepts. Then price will be discussed as the inte-
grating factor between supply and demand. However, this will not be the
first introduction of price, since price is intimately and directly involved
in the concepts of supply and demand themselves. Finally, the concepts of
environmental externalities will be added.
In developing these theories, it will be convenient to assume, at a
first level of analysis, that the costs of administering a price system,
that is of measuring and charging for services based on quantity, are zero.
The effect of the assumption of costless billing and how these costs would
actually be charged and passed on to households will be discussed in the
price section.
EXTENSION OF THE THEORY OF DEMAND -
PRIVATE ECONOMIC UTILITIES ONLY INVOLVED
Disaggregated Municipal Solid Waste Collection/Disposal Services
Identifying and Listing the Services
Ernst (1975), in a section on "supply of solid waste management ser-
vices," provides one possible categorization of the solid waste collection
and disposal services that are demanded and supplied. He divides the basic
solid waste management (SWM) services into two broad categories: 1) collec-
tion and transportation (C&T) and 2} processing and disposal (P&D). He
then adds to this a third, which he terms ancillary services. Under this
heading, he includes "management of the system, with its implications for
institutional and financial arrangements, and the enforcement of ordinances
and regulations against improper waste disposal methods."
For purposes of analysis in this paper, the focus will be on the ser-
vices demanded, rather than supplied. This will at least serve the purpose
of keeping things in order, since it is the demands for the various services
that bring forth the supply of these services. Looked at this way, many of
the services discussed by Ernst are not really services directly demanded
by households, but, rather, are inputs to the production function for pro-
ducing the services that are in fact demanded by households. (They are,
rather, services demanded by the suppliers of services to households.)
Transportation is a good example. This is an input, the need for which
varies from place to place and possibly from time to time. Nevertheless,
it is an input for providing collection and non-polluting disposal services
which are demanded by households.
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In addition, although households do demand non-polluting disposal of
their wastes, in this section the disposal services per se, along with pro-
cessing, will be treated as a production function input for providing
"collection/disposal" services. This point is worth at least a paragraph
of discussion here, and is also covered, along with the need for treating
and analyzing disposal as a subject of demand analysis, in Section IV of
this paper, Identifying Areas of Needed Research on the Economics of Solid
and Hazardous Haste Management.
In this section, it will be taken as given that society accepts the air
quality, water quality, and sanitary land fill standards that are associated
with solid wastes processing and disposal, and that are imposed by various
Federal, state, and local jurisdictions. Thus, the transportation/processing/
disposal requirements to achieve these standards are treated as necessary
inputs for following through with collection services. They will not be
treated as services demanded that may vary with their cost independently of
the amount or types of wastes collected. No consideration will be given to
pricing them separately. Nor will they be treated as subject to independent
variation with income or other household means or characteristics. There
are basically three reasons for treating these standards as given and accep-
ted. First, the question of what standards to set for maximizing social
welfare, or alternatively how to determine the amount of pollution control
that society should "buy", is in itself a large subject. If it can be
feasibly isolated for independent analysis without reducing the relevance
of the analysis, and this is in fact the case, it makes the analysis more
manageable. Second, the analysis methodologies required are quite different,
as Ernst points out, with the determination of the optimum amount of pollu-
tion control over the processing/disposal of community collected solid wastes
involving the estimation of social environmental-damage functions. Third,
while there has been some progress along these lines of environmental analy-
sis, the analysis is largely undeveloped in any application to the solid
wastes field. Thus, it is more appropriately treated under needs for new
research than under extending the theory and reviewing the existing litera-
ture on theory of demand for solid wastes collection/disposal.
Given the focus on waste collection/disposal services from the house-
hold demand viewpoint, which is at the collection end, the list of important
services demanded and provided is limited. The important services, as iden-
tified in the literature, include frequency of collection and location of
pickup. Services can be measured by the frequency of collection and loca-
tion of pickup, and by the amount of pickup and the kind or character of
wastes picked up. This latter is included for two reasons. First, there
may be a different demand function for different type wastes. One may want
to get rid of the garbage quickly, but not be so concerned with newspapers.
One may have a relatively low cost means of disposing of newspapers (giving
them to Boy Scouts) but not lawn clippings. Second, the household may be
faced with different supply functions (prices for collection) of different
type wastes if differentiations are made with respect to salvage value or
difficulty of handling different type wastes.
Amount and frequency of collection are in one sense merely measurements
of the quantity of the basic service demanded and provided, which is
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collection/disposal. Location of collection (curb, back door) is merely a
description of the bundle of collection/disposal services provided. And kind
of service is merely a description of what is collected. Nevertheless, there
is a separable demand, as well as supply, for each. Thus, in this paper,
they will be treated as separate services. Recapitulating, the services are:
1. frequency of collection
2. amount of collection
3. location of collection (curb, back door)
4. kind or character of wastes collected.
There may, of course, be other demands for services associated with
waste collection. For example, there may be an interest in which day of
the week the service is provided—Monday may be preferred because it follows
weekend lawn, yard, and home clean-up activities. Noiseless refuse trucks,
as well as collectors, or trucks that come only during waking hours, may be
preferred. However, it is believed that the four services listed above
represent the main ones, and that they provide a sufficient coverage of dis-
aggregated demands for realistically developing the supply, demand, and
price concepts.
Measuring the Services
Before proceeding to the development of these concepts, however, it
will be useful to discuss measurement of the quantities involved. Ernst
again introduces this as a supply side problem. He states that the major
supply side questions are 1) How can solid waste management outputs be
adequately measured? and 2) What are the cost functions associated with
these outputs? Of course, measurement of services is as much a demand side
question as a supply side question.
With respect to frequency of service, the usual measure is the number
of collections per week, a very unambiguous quantitative measure. There is
both conceptual and empirical support that both costs on the supply side and
utilities on the demand side are directly associated with this variable.*
As for location of collection, the usual place is either the curb (or
alley), or back door, and the usual quantitative measure assigned in analy-
sis is a zero for curb (or alley) service, this representing no special
service, or a one for backdoor service. Again, there is both conceptual and
empirical support that both costs on the supply side and utilities on the
demand side are directly associated with these variables. There is, of
course, the fact that some back doors are farther from the street than
others. The distance also is a clear quantitative measure that may directly
The point is sometimes made that the demand is really for reducing the
interval between pickups rather than for frequency, since it is the length
of the interval that causes space and nuisance problems. Regardless,
except for the fact that 7 days does not divide easily into equal parts,
service tends to be spread into equal intervals, and frequency, that is
collections or collection visits per week, is thus a measure of interval.
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affect both cost (supply) and willingness to pay for the service (demand).
The major demand problem, as discussed in the literature, is with the
measure of the quantity of wastes collected. The quantity has two important
dimensions, volume and weight. Both dimensions may affect costs (supply
functions), and both may affect demand. Taking the supply side first, space
or volume required for ultimate disposal (sanitary land fill) is an important
cost component. To hold down these costs, wastes are compacted and some-
times reduced (incinerated or composted). For compacting, collection trucks
with compactors are now frequently employed. These trucks compact wastes
as collected and thereby also hold down the collection and transportation
costs that are associated with uncompacted volume (as well as ultimate dis-
posal costs). The compacting costs are relatively low cost compared to the
costs of weight-associated haul to disposal sites and ultimate disposal;
thus the main supply side costs are associated with compacted volumes, for
which weight of the collected refuse is believed to be a better proxy measure
than uncompacted volume. Thus, if incremental user charges are to be insti-
tuted, and if to reduce complications one measure must be chosen over the
other, it should be weight. Households would then pay attention to weight,
but ignore as inconsequential any volume effects of their waste generation,
except to the extent that volume might affect household costs other than
those imposed by the user charges (the costs of storing greater volumes in
the between collection intervals). In buying, households would tend to
shift to lighter weight packaging, ignoring volume (to the extent such dis-
criminations may be possible.)
However, these considerations are probably inconsequential compared to
the problems and costs that would be involved in measuring individual house-
hold quantities on a weight basis. Accounting for the number of containers
(cans or bags), on the other hand, is relatively low cost, and, in fact,
volume by container is the measure used where user charges are imposed
(Ernst, 1975, p42). Unless or until a practical way of weighing and re-
cording weight by individual household collections is found, volume will
probably have to do as a proxy for weight, that is for the main system cost-
causing factor.
In addition to volume not being a perfect proxy for weight, there is an
additional problem. Households can avoid charges by doing their own com-
pacting. To overcome this, there could be one charge, that is one price per
container, for uncompacted wastes, another, higher price per container, for
household-compacted wastes. Possibly on a weight basis, the compacted waste
price could be slightly lower since the waste is already compacted, thus
saving the collection agency a slight amount on compacting. This would
slightly reduce the overall collection costs. The household could decide
whether the storage space savings the household would obtain from compacting,
along with possible collection cost savings, would justify compacting.
Another way to overcome the problem might be to outlaw household compactors.
However, this would deny households the opportunity of'reducing their storage
costs, and in fact some households own and use compactors for this or other
reasons even without user charges.
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In any event, these possible solutions appear impractical, and are in
fact not used, and in the presentation of concepts below, number of contain-
ers is used as the measure of quantity. This is done despite the fact that
all empirical analysis to date has been in weight terms. It has all been in
terms of weight collected by community, community subsection, or collection
route, either on a total or average per household or per capita basis. This
makes sense since it is easier to determine the net weight of a truckload
than to count the number of containers emptied into it. There has, in fact,
been no empirical analysis uncovered in this study based on the measurement
of individual household amounts. This is also true of the one analysis un-
covered of the effect of imposing or not imposing user charges (Wertz, 1976).
This study, using San Francisco area data, compared average pounds collected
per capita between areas where charges are on a container basis and all areas,
where flat charges predominate. Indeed, for more sophisticated and detailed
analysis of the effect of incremental user charges, weight rather than volume
would probably be used for two main reasons. First, individual responses are
not interesting; it is the average that is of concern. Second, it would be
impractical to measure and record gross amounts on a volume basis. For
example, "truckloads" might tend to measure what the truck contained at the
end of a route, rather than a more or less definite number of containers.
Thus, another measurement error may, of practical necessity, be introduced by
turning the measure back to weight for analysis, even though charges are in
fact made on a volume basis.
Finally, the measure by type of waste presents no particular additional
problem. The identification of different, at least grossly different, types
is relatively easy. Newspapers are newspapers, and the same is true of gar-
bage, metals, and bottles. For separation of wastes, the problem of measure-
ment for some types might be eliminated. There would be no measuring of
quantities needed if, for certain wastes such as metals, the unit salvage
values just offset the unit collection costs. For the usual case, however,
the same problems in measurement would apply.
Having discussed these preliminary matters of the measures of the ser-
vices involved, development of supply, demand, and price concepts can now
proceed. Again, it is emphasized that social costs from alternative dis-
posal, such as littering, are not included in this development of basic
concepts. In this development of basic concepts, the previous work by Ernst
(1975) and others is drawn upon. Goddard's (1975) work is also drawn upon,
but mainly in carrying the work forward to include littering and the like.
Cost or Supply Concepts
The first step is to develop the concepts of cost or supply for the
services. The costs would be those to the entity supplying the collection
services. Under marginal cost pricing, these would also be the costs to
the consumer. The costs of three of the four services—frequency, amount,
and location-- are relatively easy to visualize, and it should not be diffi-
cult to obtain data on them. The marginal costs would be the costs added
to the total costs of a particular service by more of that service.
Figure 1 is a hypothetical depiction of total costs for different levels
8
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A. Frequency of collection
Cost per
customer
per week
($)
B. Amount of collection
Cost per
customer
per col-
lection
($)
• Service to rural area
• Service to suburban area
. t Service to dense urban area
I
4 Frequency of collection--
times per week
A Service where disposal sites
are high cost at long
distance
•• Service where disposal sites
are low cost at short
i distance
Location of collection
Cost per
customer
per col-
lection
($)
Amount and number of
containers per collection
.2 containers per collection
1 container per collection
Curb
Backdoor
Location of collection-
distance from curb
Figure 1. Cost functions for waste collection and
disposal services.
-------
of these three services. Note that in the depiction, it is the total cost
of the particular service only that is depicted. For example, the cost of
location-of-collection is taken as zero at the curb. This is not, of course,
the total cost of collection service at the curb. Also, in the depiction,
marginal costs (the slopes of the total cost functions shown) are shown as
constant. However, this is for purposes of simplifying the presentation
only. It should be emphasized that this might not necessarily be the case.
However, this would not affect the conceptualization. Also shown is an
indication of how total costs would tend to vary with other things. Some-
times this may be a strict cost factor, sometimes a level-of-service factor
imposing added costs. For example, the cost of a collection should be higher
the more sparsely populated the area of service because of the greater travel
distances from one residence to the next. The term supply shifters is used
below to refer to such changes in cost relationships due to other things.
The location-of-collection costs, shown as separate functions in Figure
1, can be treated as supply shifters of the frequency-of-collection and
amount-of-collection cost functions. This is shown in Figure 2. The most
obvious shifter is with respect to the cost of collection. Each time an
additional collection per week is added, another trip to the back door is
added, regardless of the amount of collection. However, an additional amount
of time and thus cost may be required for each container. There may, in
fact, be something like a break point between 2 and 3 containers per collec-
tion. Three containers may require an extra trip to the back door, but
carrying 2 containers or the waste from 2 containers from the back door to
the curb may require no more time than carrying one. Thus, for other than
developing basic concepts, a linear assumption would be unrealistic.
The cost function for waste collection and disposal services for differ-
ent types or character of wastes cannot be depicted as a single function in
the same way as the above three services, since there is no continuum;
different costs are associated with different waste types. Nevertheless,
the elements of the relationships between characteristics and costs can be
described and these can be treated as supply shifters, as will be indicated.
There are basically two different types of wastes, those that cost less than
the average to service, which are basically those with a salvage value, and
those that cost more, which are basically those that are hard to handle.
Each basic type is discussed separately below.
Providing collection and disposal services for wastes with a higher
scrap or salvage value will tend to cost less for two reasons. Salvage
values may be obtained, and there is less waste to dispose of as a waste
when materials are salvaged. Salvage or recycling values may be obtained
in two ways: 1) by the collecting agency or enterprise separating and
selling salvageable materials (these may include glass, metals, paper, and
animal-edible garbage for their material value, or burnables for their fuel
value and 2) the collecting agency or enterprise may be able to obtain
labor at a lower cost if there are valuable items such as old furniture,
appliances, and clothes that collectors may salvage and sell for supple-
menting their incomes.
The salvageable content of refuse may vary from place to place and time
10
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A. Frequency of collection
Cost per
customer
per week
($)
• Service at back door
•Service at curb
Frequency of collection
times per week
B. Amount of collection
Cost per
customer
per
collection
($)
•
-*-
* Service at back door
,-.-Service at curb
Amount of collection -
number of containers
per collection
Figure 2. Location of collection point as supply shifter.
11
-------
to time for various reasons, including the consumption habits of the waste
generators (buying returnable or non-returnable bottles, wearing old clothes
out and making a patchwork quilt with them after they do) and their own
salvaging activities (finding a market for the old appliances rather than
scrapping them). The actual value itself will also vary from place to place
and time to time based upon costs of salvage operations and prices for sal-
vaged items and materials.
Pre-separation by the waste generators will tend to further reduce
costs; indeed, in some areas, this may make salvage and recycling viable
where it would otherwise not be. (It is not necessary that the same enter-
prise collect the salvageable and non-salvageable materials.)
Certain characteristics of waste would tend to increase costs of waste
collection/disposal. Bulky items with no salvage value would tend to cost
more to handle than general wastes, the inclusion of hazardous materials in
the waste requiring special handling would increase costs, as would any other
materials that might be difficult to handle for various reasons. As with
salvageable materials, separation of these items from the general wastes
would tend to change the cost functions, in this case decreasing average
costs for the total waste.
The depiction of the characteristics of wastes as supply shifters, as
previously suggested, is shown in Figure 3. Costs for collecting and dis-
posing refuse containing relatively large proportions of salvageable materi-
als are shown as less than costs for handling normal refuse. Costs for
collecting separated wastes may be positive, as is depicted for separated
glass, although less than for average refuse because of salvage value, or
negative--that is, a positive price paid for that separated "refuse"--as is
depicted for separated metals, such as aluminum. In other words, the most
economically separable item as represented here is separated metals. (Note
again that all of the cost functions have a zero intercept because costs
apply only to the service of quantity collected.)
These cost relationships can be generalized in mathematical form as
follows. Again, it is emphasized that the linear form adopted for presenta-
tion purposes is not meant to imply that the relationships are necessarily
linear. Indeed, empirical evidence is available to indicate non-linearity
in a number of cases.
The cost per customer per week is the sum of the cost for collections
(number of visits) per week and the amount of collection per week, or
Cw - Cf + Cq (F) (1)
The cost for collection visits, without considering shifters, is a
function of the frequency of collection, or
Cf = S/ (2)
When shifters are considered, the cost function is
12
-------
Cost per
customer
per week
Hard to handle,
hazardous materials
Hard to handle
wastes such as
bulk items
Refuse containing
little if any
salvageable material*
Normal or average
refuse
Refuse containing
high proportion
salvageable material
Separated glass
Amount of collection
pounds per week
Separated metal
(aluminim, ferrous,
others)
* May contain little salvageable material because of pre-separation
or merely due to the general waste characteristics of a particular area.
Figure 3. Cost functions for waste collection and disposal
services for different types of waste.
13
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Cf
Specifically, for those shifters discussed, we have cq, the urban density
shift factor, and 0.2 the location-of-collection shift factor. The marginal
cost or supply price, for visits is the derivative of the function, or
dCf
= P
dF 'fs pl ' ul T a2
Stated another way, this is the added cost of each collection visit.
The cost for quantity collected, again without considering shifters, is
a function of the amount collected, or
Cq = 32 (Q) = B2f (F) (5)
When shifters are considered,
cq = (B2 + YI —+Yn) Q (6)
Again, for those shifters specifically discussed, there is YI» the shifter
for haul distance, Y2» the shifter for location of collection, and Y3, the
shifter for type of waste. The marginal cost, of supply price, for number
of containers collected is again the derivative of the function, or
= P__ = ft+V+V+V /7\
qs p? M '? >•} \'i
• C_ J. &. \J
If prices are set to customers according to these marginal cost factors,
that is the a's, B's, and y's in Equation (4) and (7), there can be optimum
(conceptually optimum) provision of waste collection and disposal services.
The conceptually optimum billing, B, would be at least a two-part tariff:
B = Cf + CqF
= (Bj + dij + a2)F + (B2 + YI + Y2 + Y3)QF
Conceptually optimum here means optimum before taking into account measure-
ment and billing costs that may make marginal cost pricing not optimum in
fact.
If back-door service were fully optional, and two separated types of
wastes, Qi and Q2, were involved, the back-door service and each waste should
be charged for separately, based on the quantities of each involved. The
billing would become quite complex. While a computer could handle the
computations, explaining the billing and its interrelationships would be
-14
-------
quite difficult. (Separate count must be kept of each back-door service and
of the quantities of each type waste collected at the curb and at the back
door. Also, the cost of back-door service depends both on the number of
collection visits to the back door and the quantity carried from the back
door.) The billing computation for a weekly period would be:
B = (31 + a1 + a2)m + (BJ + oj) (F-m)
+ (B21 + YU + Y21 + Y31)n + (B21 + YU + Y31) (FQrn)
+ (B22 + Y12 + Y22 + Y32)P + (322 + Y12 + Y32) (FQ2-P)
where m = the number of collections per week at the back door out of F total
for the week
n = the number of containers with type Qi waste carried from back door
out of QI total containers for the week
and p = the number of containers with type Q2 waste carried from back door
out of Q2 total containers for the week.
(The B's and y's may be different for different type wastes because the
handling requirements may be different. Thus, they are designated with
different subscripts, 1 for type Qlt 2 for type Q2.)
While a charge based on frequency of service alone, that is a flat
charge of a given amount per week for a given frequency of service, might
come close to the conceptually optimum, it would only be the actual optimum
if the added cost per container were small, and not worth the trouble and
cost of setting up the charge system on the full marginal cost basis.
For the case where this latter might be true, a cost function can be
derived. Given the various demand factors, for each location, frequency,
and type (waste type) of service, and with no charge on a container basis,
a certain number of containers per collection will be "generated" (the free-
service amount). Then the cost per week is the sum of the cost for collec-
tion visits (what visits cost per se) and the cost related to the specific
amount collected on visits. Then
the cost per week, GW = Cf + C J, (8)
and the cost per collection visit, Psd = Cf/F + C d (9)
where the subscript d indicates that costs and prices are demand as well as
supply determined.
To complete the discussion of the various ways of charging, just as a
charge based on number of collections, or a flat weekly charge, would be non-
15
-------
optimum, so would a charge based on quantity alone. This might be termed a
flat quantity charge. A cost function can be set up on such a flat quantity
basis, made up of the variable cost for quantity and a charge, distributed
on a quantity basis, for service, as follows:
Cf
r I-P \ - r +
LQdd ( Kqsdd' Lq QddF
Note again that the Q, in this case Q^, and thus the cost per unit or
"supply price," is demand determined. Also note that marginal cost pricing
based on quantity alone would not cover costs.*
Table 1 presents these various cost and conceptual optimum billing
functions, along with units of measurements, in a single table, and in the
order presented above.
Before proceeding, it will be useful to discuss alternative means of
financing, and ways in which the alternative means may affect supply func-
tions, and thus prices or charges that households face and their resulting
demand for services. If services are paid for through local taxes but not
explicitly paid for, there may be a savings to households because the pay-
ments are deductible on Federal and State income taxes, and because the
base for Federal revenue-sharing is enlarged. This is true whether or not
the local government actually operates the collection/disposal service.
The work could be contracted out. In addition, local government operations,
as opposed to business-run operations, may qualify for research and demon-
stration grants that may help reduce costs to households, even though direct
reduction in costs may not be the purpose of the grants. From a community
standpoint, although not from an overall social (national) viewpoint, there
is apparent reason for members of a community to consider taking advantage of
these cost savings, particularly those related to taxes and revenue-sharing
which are automatic and do not depend on any action such as applying for a
grant or becoming involved in a grant program. In fact, results of surveys
indicate that most communities do finance service from general revenue,
that is from taxes (Wertz, 1976, p 264). The question might be, why don't
they all? The answer is not that private firms are favored by some communi-
ties, because this is not the issue; the work can be contracted to private
firms. Nor would the fact that private firms are already set up in a com-
munity be a convincing answer. If this were the case, payment of bills to
Ernst, in his 1975 study, reached the same conclusion, but apparently con-
fused this with true marginal cost pricing. Ernst assumed that a choice
must be made between either a flat charge or a quantity charge. He related
all costs to quantity. This led him to attribute certain empirical
findings to "scale" factors related to population size, whereas in fact
there are other much more plausible and reasonable explanations, based
on true cost relationships. Ernst's cost relationships would result in
no costs for traveling a route or going to the back door to look when
no wastes were collected. His conclusions concerning the efficacy of
quantity and marginal cost pricing are subject to similar comments.
16
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TABLE 1. COST FUNCTIONS FOR SOLID WASTES COLLECTION SERVICES
1. Basic Number-of-Collection Cost Functions
Total cost of a collection service
Without shifters
cost of collection f cost of collection , collection}
per customer per week per customer per collection per week
With shifters (Shifters specified are urban density, ai, and back-door service, 02.
Back-door service is subject to individual choice, and o£ is a function
of distance, street to back door.)
cost of collection
per customer per week
"(per cu
LPj T a- T i
cost of collection density ccst shifter + b«c>-door serv
customer per collection per collectionper collect
'ce costl. collection
TonJ per week
where
back-door service cost , back-door service cost . distance
per collectionper unit of distance per collection
Marginal cost of a collection service (added cost per visit, since the basic cost, as shifted
oy density, applies tor the visit, not whether or not an actual collection is made.)
dCF
HT
fs
°1
cost of collection m 'baste' cost of collection + density cost shifter [pack-door servli
*r customer per collection per customer per collection per collection [per uck-door c
1ce cost . beet-door collection!
',1 lection visit J
(p » 0 if back-door collection not made; p = 1 if back-door collection is made)
(continued)
-------
00
TABLE 1 (continued)
2. Basic Quantity-of-Hastes-Collected Cost Functions
Total cost of quantity-of-wastes-collected
Without shifters
cq e2 x Q
cost of the Quantity collected . cost of Quantity collected , quantity collected (containers)
ptr cusUMer per collection per unit of Quantity collected (contil-ers) per custorer per collection
Cq(F) = B2 X Q X F
cost of the Quantity collected . r X collection!
per custowr per neck l/^ per week
With shifters (Shifters specified are haul distance, yi» location of collection, ^2>
and type of waste, Y3- Again, back-door service is subject to individual
choice, and ^2 is a function of distance, street to back door.)
q !
of the qmntlty collected .Ibislc cott of Quantity c
cvstaoer per collection ^ P*r container
cost of the Quantity collected .[basic cost of quantity collected t h»ul distance cost shifter + back-Coor service cott
per cvstooer per collectionL P*r container per container per container
Y3] X Q
type of xaste cost shifter] » containers
per container per customer per collectton
. back *or u
Marginal cost of quantity of wastes collected.
(continued)
-------
TABLE 1 (continued)
3. Optimum Cost (Billing) Functions
With back-yard service on an either/or basis, and one type waste
B = Cf + Cq(F)
' PfsF 4 Pqs QF
= (&! + oj + a2)F + (62 + YJ + Y2 + Y3) QF
With back door/curb service optional at each collection visit and two type wastes, Q1 and
B = (B! + aj + a2)m + (BJ + OjKF-m) + (B21 + Yn + Y21 + Y31)n
+ (62 + Yn + f3iHFQi-n) + (*22 + yl2 * Y22 + Y32)p + (322 + Y12 +
(See text for definition of symbols)
4. Combined Number-of-Collections and Quantity-of-Wastes-Collected Cost (Billing) Functions
on a Flat Meekly BaTTs ~~~
Basic combination, regardless of basis for charge
Without shifters
C
(cost
With shifters
Cw * &l + °1 + *Z$ (F) +C62 + Yl + ^2 + Y3^ Q(F)
(continued)
-------
TABLE 1 (continued)
Combined charge with rates for all services on a weekly basis
[the charge on a weekly basis only with no incremental quantity charge):
The quantity, Q = Qd
and the cost per unit of quantity, C = C .
where the subscript d denotes the quantity, or cost for the quantity, at a zero quantity charge.
Then, Cw=Cf+CqdF
The cost per collection:
dC
« _ n — / /» _i_
dF
Where the back-door/curb service is optional on an either/or basis and separately charged:
Psd
= (ij + Uj + (a2 M ) + [^2 + ^1 ^ ^2 M ) + Y3 J Qd
(The case where back-door/curb service is optional for each visit is much more complex to
express on a weekly charge basis, and is not given.)
(continued)
-------
TABLE 1 (continued)
5. Combined Number-of-Collections and Quantity-of-Wastes-Collected Cost (Billing) Functions,
on a Flat Quantity Basis ~~~~
CQd ' Cq +
tost for 111 ttrvlcn _ cost for ouantm terylce Jcost for collection >erv
-------
the private firm could be shifted from individuals to the local government
with taxes raised to cover the costs. Three possible answers are, first,
that there may be institutional barriers. This would require investigation.
Second, if private firms charge on an incremental quantity basis, financing
from general tax revenues would eliminate the effect of such pricing on
amounts of waste to be handled, and might increase costs, thus offsetting
the tax advantages. However, for the most part, private firms do not charge
on an incremental quantity basis. Third, the advantages of deductions from
income taxes may be more apparent than real.
Despite this latter consideration, it appears that the tax savings for
homeowners can be substantial. At a 25-percent marginal Federal and State
tax rate, the savings on these taxes alone would be an equivalent 25 per-
cent on waste collection service. This would not include revenue-sharing
benefits. Nor would it include possible savings on separate billing for
services that would be avoided. Wertz (1976) concludes that, "From a local
perspective the value of transfers foregone by pricing (to individual house-
holds on a quantity basis) may exceed the value of resources conserved in
the public treatment of less refuse."
However, since conceptual optimum billing is composed of two parts,
Cf and CgF, the Cf portion, which is not quantity based, could be covered
out of general revenue without loss of system efficiency (not merely a loss
from a local perspective). If this Cf portion were a major part of the
total billing (that is of total costs), which may well be the case, a
change to financing only the Cf portion out of general revenues would
involve a loss of only a minor part of the tax and revenue sharing savings
that may be available to households. Retaining general revenue financing
of the Cf portion would, of course, reduce the potential for conserving
through the public treatment of less refuse, as this might be impacted
by fully quantity-based pricing. However, there would be no loss in over-
all system efficiency, that is, overall savings.
Demand Concepts
Demand for a service depends on its price and on various demand shifters
such as prices of other related goods and services, including both substi-
tutes and complements (cross-price effects), income, other characteristics
of the household, and demographic variables. Own-price relationships can
be looked on as the households' willingness to pay for different types and
levels of services or as the response on the part of households in terms of
types and levels of services taken to changes in price. The willingness
to pay, or price-quantity relationship, may be shifted by various factors.
The first step in developing the demand concepts below will be to consider
price effects on each of the services. Both own-price and cross-price
effects will be considered. First, some general points concerning these
effects, and the role of substitutes and complements, will be made. Then
the various price effects on the collection/disposal services will be con-
sidered one service at a time, beginning with the location of collection
and ending with the quantity of different type wastes. This will be
followed by consideration of the effects of income and other demand shifters.
22
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Price Effects
In actual practice the price facing a household is frequently either
zero, or, in effect, infinity. The household can get additional amounts
collected at no added charge, and can get back door or a second weekly col-
lection without added charge where those services are provided (that is,
there is no credit for taking the refuse to the curb or setting it out only
once a week where these services are provided). Or, the household can get
only curb or once-a-week service, and cannot, at least from the regular
community service, get back-door or twice-a-week service. Nevertheless,
the relationships between price and what households would take still exist,
and the relationships would apply to finite, non-zero prices as well as to
the actual prices. (Of course, by definition, none of an infinitely-priced
service would be taken.)
Price- and cross-price effects--0wn-price changes will affect the
quantity of a service demanded in two ways, through income effects and
through substitution effects, the latter being the more quantitatively im-
portant. A price change will effect general substitution between the par-
ticular service and all other goods and services, but the main effects will
be with close substitutes. There will also be major cross-price effects
from changes in the prices of substitutes themselves. Finally, another
cross-price effect, a change in the price of complementary goods and ser-
vices, will affect the quantity of a service demanded by directly changing
the cost of its use relative to the price of other goods and services,
particularly close substitutes.
Consumer non-durables (as opposed to durables and services) and waste
disposal are complements. Thus, an increase in the price of non-durables
will tend to decrease the quantity of waste disposal services demanded
(with, of course, all prices being in real terms, and changes being relative
to other prices). Alternative or own disposal, such as by sink disposals
or returning bottles, is a substitute for community collection/disposal.
For avoiding the odors and nuisances of stored wastes, more frequent service,
better containers (e.g., with screw-on lids), and alternative disposal, such
as by sink disposals, are substitutes. For reducing space requirements for
between-collection storage, frequency of service, alternative disposal, and
home trash compactors are substitutes. For carrying wastes to the curb (or
paying for this service if it is charged for on an incremental basis),
alternative disposal, lighter containers (paper or plastic bags) are substi-
tutes. Given these relationships, frequency of service, back-door service,
and community collection/disposal are complements. That is, if the price
of any one decreases, the use of all three will increase.
These relationships will be more fully developed in the following
sections.
Demand for back-door col lection--In this section, demand with respect
to location of collection is considered. There would be some willingness to
23
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pay for back door as opposed to curb or alley collection because back-door
service would substitute for own labor.* Conceptually, the service could be
provided in one of three ways: 1) if it is provided at all, every household
receives the service, 2) on an either/or basis, that is, the service would
be optional to each household, but taken either on a regular continuing
basis, or not at all, or 3) on a pay-as-you-take-it basis, optional to
each household and at each collection.**
If the choice were optional at each collection, the total willingness
to pay would increase at a decreasing rate, as shown in Figure 4a. The mar-
ginal willingness to pay (demand for services) would be the first derivative
of this function, a declining function. The explanation of these decreasing
rates and declining relationships is the usual one of declining marginal
utility of a good or service as more is taken. Specifically, on some days
there would be a high cost to the household to set refuse out on the curb
(due to sickness or incapacitation, foul weather, or other pressing uses of
time), and on others, low cost. Household utility would be maximized by
receiving services on this basis, with back door collection service being
taken by the household only when the households' utility cost of not re-
ceiving the service exceeded the cost of providing the service. (It should
again be emphasized that in the final analysis, this cost should also in-
clude the cost of recording and billing for the service.)
For either/or service, the willingness to pay for service would be a
fixed amount per collection, as shown in Figure 4b. Also shown is the
effect on willingness to pay of having more or less refuse per collection.
Obviously, the willingness to pay would tend to be greater the greater the
average number of containers per collection. (This would also shift the
curves of Figure 4a, as is discussed below.) (Figure 4b is also shown with
an x axis representing distance to back door, comparable to the x axis for
the supply function of back-door service previously discussed. This is
further discussed below.)
The willingness to pay of Figure 4b can be derived from the parameters
of Figure 4a. The willingness to pay in Figure 4a for 100 percent back-
door collection service is the integrated sum of the households' marginal
utility (marginal willingness to pay) for back door collection, or the area
under the demand (marginal willingness to pay) curve, which is the total
willingness to pay at 100 percent service. This divided by the number of
collections per year is the willingness-to-pay per collection for either/
or service shown in Figure 4b.
Figure 4b shows willingness to pay as a function of distance to back
According to the U.S. EPA (1976), approximately 60 percent of collections
in the United States are curbside and alley, 40 percent backyard.
**Again, according to the U.S. EPA (1976), some communities provide a choice
of curb or backyard service and charge a different rate for each. While
not indicated, it might be assumed that most or all of this is on an
either/or basis.
24
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Willingness
to pay
Total willingness
to pay for back-door
service
Marginal willingness
to pay for back-door
collection
100%
Percent of services per
year at back door
Figure 4a. Willingness to pay for back-door services on a
pay-as-you-go basis.
Willingness
to pay ($)
, • Two containers per collection
t One container per collection
Curb
Back door
Location of collection
Figure 4b. Willingness to pay per collection for
back-door service (on an either/or basis).
25
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door. This is portrayed in this way mainly to make the relationship compara-
ble to the cost function portrayed in Figure Ic. The cost relationship in
that figure is shown as linear and proportional to distance, a reasonable
assumption since it is time that is involved in cost, which is directly pro-
portional to distance. However, for willingness to pay, there is probably
a large fixed cost involved in going out and moving the refuse to the curb,
unrelated to distance, as is indicated by the location of the functions in
Figure 4b. Of course, variation in distance from back door to curb would
shift the curves of Figure 4a, with total willingness to pay at 100 percent
service equal to the willingness to pay at the actual back door distance if
different from that indicated.
Before proceeding to the relationship between price and frequency of
collection, the next service to be discussed, and between price and the
amount of collection, which will follow, some preliminary discussion of
possible relationships between location and amount of collection in the
context of prices should be presented. Wertz (1976) states that a shift to
curbside collection from collection at the permanent place of outdoor con-
tainers, usually in the backyard, decreases the marginal utility of commodi-
ties in proportion to their unit refuse weight and induces a decrease in
refuse production because households must transport refuse to the curb on
collection days and then return the containers to their permanent place.
Thus, he states, a shift to curbside collection can reduce a municipality's
outlays for refuse service not only because collectors spend less time
transporting refuse but also because they collect less of it. On the first
point, he cites Hirsch (1965) who, using St. Louis area data, found a sig-
nificant positive relationship between backyard service and collection costs,
While Wertz makes a valid specific point, he fails to cover the more
general point. The point is that where there is a marginal cost, however
imposed, that is based on the volume of waste to be transported from the
backyard to the curb (to the collection truck), there will be an inducement
to produce less waste. This may be either where a household member trans-
ports the refuse himself, or when the service is provided if charges are
based on marginal costs for the service according to the volumes transported.
Referring back to Figure 4b, a greater willingness to pay for two con-
tainers per pickup is shown than for one. However, the marginal willingness
to pay, as suggested by the position of the curves, is seen to be decreasing.
(That is, the willingness to pay for two containers per pickup is less than
twice that for one, or equivalently, the willingness to pay for the second
container is less than for the first.) This can be depicted as the percent
of services per year at back door as shown in Figure 5.
The extent to which this marginal willingness to pay is a declining
function depends on the alternatives open to the household, such as reducing
the amounts of wastes generated, and alternative disposal options, such as
garbage disposals. It would, of course, also depend on frequency of service.
This point will be discussed later.
The relationship can be put in general mathematical form. First, the
total willingness to pay for back-door service can be represented as
26
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Willingness
to pay ($)
Two containers
per week
One container
per week
Two containers
One container
Total
willingness
to pay for
back-door
service
Marginal
willingness
to pay for
back-door
service
100%
Percent of services per
year at back door
Figure 5. Marginal willingness to pay for percent back-door services
as a function of number of containers per week.
27
-------
WT =
-------
Then ,, _ v NT
Wc - 1 WciT
n
I
and w'c = £ fii - Z eiT
It has also been indicated that, for any given T, WC1 > WC2> •" WCn.
Demand for frequency of collection—Consider next the demand for fre-
quency of collection, or, stated alternatively, the interval between collec-
tions. The usual frequency of service that is provided appears to be once-
a-week, with twice-a-week services a close runner up.*
Again, as with curb service, there would be some willingness to pay for
more frequent service. More frequent service, by reducing the interval
between collections, would reduce the buildup of odors, the breeding and
hatching of insects,** the attraction to rodents, exposure to scattering by
animals, and the pressure on space and facilities required for between-
collection storage.
Again, the service could be provided (taken) on an either/or basis or
on an optional-at-each-collection-offered basis. With respect to the latter,
for example, if 3 times a week curb service were offered on Mondays, Wednes-
days, and Fridays, one could choose not to set the refuse out on the curb
on Wednesdays and in fact receive twice-a-week service. Or, if back-door
service were provided, one could notify the agency not to collect on Wednes-
days. In addition, there would also be some positive willingness to pay up
to continuous, taking-the-wastes-away-as-produced services. However, if the
nth weekly service were not offered, its price would in effect be infinity,
and no one would choose to take it on an individual basis. Nevertheless,
the individual household willingnesses to pay, which are based on the
utility the households derive from more frequent service, would provide a
guide to the agency or firm providing service with respect to what frequency
should be provided.
* According to the U.S. EPA (1976), approximately 50 percent of urban sys-
tems provide weekly service, about 45 percent (mainly in the South, par-
ticularly Southeast) twice weekly, and about 5 percent more frequent
service.
** One source states that at least twice weekly service is needed to break
the fly-breeding-hatching cycle. Thus, it is reasonable that more fre-
quent service would be in higher demand in the South compared to the
North. This should also be true for summer compared to winter.
29
-------
Willingness to pay for frequency of service is shown in Figure 6a. The
figure also shows that there may be a significant difference between summer
and winter demands, with summer demands greater than winter. In summer,
decomposition of wastes occur, whereas in winter there is an icebox effect.
Flies and other insects breed in the summer, garden and yard waste add to
waste storage problems in the summer, and the alternative of burning papers
in the fireplace is not attractive in the summer (although outside burning
is, if not prohibited by laws against open burning).
Figure 6 shows a declining marginal willingness to pay for collections
per week. This ties in to the demand for services for collecting different
type wastes and the alternatives for disposing of the different types. Thus,
the demand for added frequency of collection also ties into the demand for
quantity of collection.
If service were relatively infrequent, say once a week, there would be
considerable inducement to dispose of wastes in alternative ways. Whether
the alternative is easy or difficult, high cost or low cost, quickly adopta-
ble or not, depends on the type waste. Buying and using sink disposals to
dispose of garbage (and thus avoiding the fly and other insect-breeding
problems, animal attraction, and odors), would be relatively more attractive
with infrequent service. Buying returnable bottles, having Boy Scout news-
paper and aluminum can collections, and buying compactors would become
relatively more attractive with infrequent service to reduce storage needs.
Back-yard composting, depositing of old clothes in the church rummage-sale
bin, or finding a taker for old things would all become relatively more
attractive. If, going to an extreme, regular collection were only once
every 6 months, most households would in fact find such alternative "outlets"
for almost all of their wastes. The point of the declining marginal-
will ingness-to-pay curve is that as frequency increases to the 2, 3, and
more times a week rates, there is likely to be increasingly less avoiding
of alternative outlets as these alternative options are dropped.
Now how can these functions be used to guide what services should be
provided? Consider a waste collection agency providing twice-a-week ser-
vice studying whether it should stay with this or go to once- or three-times-
a-week service. (Again, it should be emphasized that it is assumed that
households do not adopt polluting alternatives, such as littering, even
though this is a definite alternative that would almost certainly be adopted
when faced by extremes such as a 6-month collection frequency, particularly
lower income groups that would find non-polluting alternatives taking a very
substantial fraction of their budget.) Refer to Figure 6b, which is a
detail of Figure 6a for service. If every individual along the route had
the demand shown, the solution would be easy. If the average cost per house-
hold of service were greater than a, as shown on Figure 6b, but equal to or
less than b, the agency should shift from twice- to once-a-week service.
If the average cost were c or less, at least 3-times-a-week service should
be provided. If greater than b, less than once-a-week service should be
provided. Costs could be recovered by charging the average cost per custo-
mer, and since this average would not exceed marginal willingness to pay,
costs would be covered. However, if different households have different
demand functions, a complication arises. In this case, the costs cannot be
30
-------
Willingness
to pay
$/week
Total
willingness
to
Summer
Winter
Marginal
willingness
to pay
6 7
Collections/week
Figure 6a.
Willingness to pay for frequency of collections
showing summer winter difference.
Willingness
to pay
$/week
i
b
a
c
Customer minimum
total willingness
to pay for
collection
Demand (marginal
willingness to
pay)
Collections/week
Figure 6b. Willingness to pay for frequency of service
showing critical prices for shifting frequency.
31
-------
recovered by charging the average cost if individual households have the
option of not taking the full number of services per week and thereby
avoiding the charge for added services.
This can be overcome in one of two basic ways. One is to make no
charges for frequency of service directly to users, but to fund from taxes.
Another is to charge the average cost to each household, but not give the
option of avoiding charges for frequency of service. A non-setting-out of
refuse on any of the added days of the week would be treated as a zero
quantity on that day, not as a case of not receiving the third weekly ser-
vice. (Or, if back yard service were provided, a notification by an indi-
vidual not to collect on a particular day would be treated as a zero quanti-
ty, not as a case of not receiving back yard service on that day, that is,
not as a case of not receiving the 3rd weekly service.)
Considering this latter case, if the only option for avoiding charges
were to not receive waste collection service at all, the question would
be whether everyone is better off with than without the service. For 3
weekly collections, as long as i, the total value to the household to whom
services are worth the least, is equal to the total cost for the 3 collec-
tions per week (average cost for 1st, 2nd, and 3rd), then every household
is better off. This is likely to be the case for all practical purposes.
Neither taxing or charging as suggested violates marginal conditions
for maximizing household utilities. This is true because no non-optimum
action is induced by such charges. "Taking" or "not taking" the third
weekly service does not affect efforts or costs. The third service is
there, once it has been decided upon, whether "taken" or "not taken" by the
individual.*
Another question that might be asked is whether a denial of the third
weekly service to those who might have a high marginal willingness to pay
does not somehow impose an artificial, non-optimum restriction. If just
a few along the route have high enough marginal functions, high enough so
that the sum equals cost of the added collection cost, the service would
be provided. At the extreme, this few could be one, but this would be a
high cost service indeed if, also in the extreme, no others along the route
found any marginal utility in the added service.
There is considerable support in the literature for frequency of ser-
vice affecting quantity of wastes set out for collection. Probably the
main empirical support for this comes from Quon et al (1968), who state
that "the information on refuse quantity (from wards in the City of Chicago)
when categorized with respect to collection interval, clearly reveals an
increase in refuse production with greater frequency of service." Ernst
(1975) supports the possibility of such a relationship in a footnote.
*There could be a small incremental charge for the cost of a stop and start
when refuse is set out for collection, avoidable when not set out. However,
this would almost certainly be smaller than administrative cost of such
a discrimination.
32
-------
In his text, Ernst states that "it is unlikely that either of these com-
ponents (collection location and frequency) is functionally related to the
amount of waste collected," but in a footnote to this statement, he allows
that "It is possible, though, that higher collection frequency increases the
total amount of solid waste collected by providing fewer incentives to
reduce waste generation." Obviously, Ernsts' thinking was for some reason
narrowed on this point, not only because he made the point as a footnote,
and as a "possible" exception, but because he failed to recognize the main
ways in which this could occur. He places considerable emphasis in his
report on distinguishing between amounts of waste collected and amounts
generated. According to his definitions, wastes generated include, in
addition to wastes collected, wastes disposed of by alternative means. It
is thus surprising that he fails to consider the effect of frequency of
service on the proportions of wastes generated that are collected and dis-
posed of by other means. On this point, it is interesting to note that
Quon et al suggest both reduced generation (less spring cleaning) and alter-
native means of disposal (outside burning) as possible explanations for
reduced quantities collected where there is reduced frequency of service.
Wertz (1976) also supports the point that increased frequency of service
leads to increased wastes. He cites Quon et al for empirical evidence.
Wertz, unlike Ernst, does indicate that alternative disposal may be im-
portant. He states, "That more (frequency of service) is preferred to less
is evidenced by households' expenditure for sink disposals and trash com-
pactors, devices that also reduce on-site accumulations of refuse or their
undesirable properties." By the word "also", Wertz clearly means that
frequency of service and various alternative disposal devices are substi-
tutes for achieving the ends indicated. Wertz follows this discussion of
the relationship between frequency of service and amounts collected through
substitution of alternative disposal for greater frequency of service with
a paragraph on the mathematics involved in the inducement to generate more
wastes or to adopt fewer substitutes for disposing of wastes (garbage dis-
posals) with more frequent service.
The mathematics of the demand for frequency of service can now be
presented. The total willingness to pay for frequency of service is
Wf = 6F - %\ F2
and marginal willingness to pay per service per week is
W'f = e - A F
where W^ = total willigness to pay
w'f - marginal willingness to pay, and
F = frequency of service per week.
e and A are parameters of the relationship.
The willingness to pay for more frequent service is related to demand
for quantity of service through the demand for cleanliness/spaciousness,
33
-------
as suggested by Wertz.
Now, there exists a demand function for cleanliness/spaciousness,
which can be visualized as beginning at some low-level-of-cleanliness/
spaciousness point where the marginal willingness to pay is very high, and
as crossing the axis at a point near perfect cleanliness/spaciousness where
the marginal value is zero.
In addition, there exists a production function which represents the
technical means using various combinations of inputs (substitutes) for
producing cleanliness/spaciousness. For any given level of cleanliness/
spaciousness, and for any given set of prices of the inputs for producing
it, there exists a least-cost combination of inputs. These costs over the
range of outputs represent the cost function. The household willingness to
pay/cost functions are shown in Figure 7.
While there is a cost attached to each input option, there is (under
the arguments presented above) no marginal cost to the individual household
for providing or receiving an additional collection per week if offered.
Marginal costs of obtaining various degrees of cleanliness/spaciousness
to the individual would, however, shift with a change in collection fre-
quency, for example, downward and to the right in going from 2 to 3 collec-
tions per week, as shown in Figure 8. Of course, the slope of the total
cost function will decrease. However, if average costs of the firm pro-
viding the collection services, which will increase in going from 2 to 3
collections, are charged to the household, the level of the total cost
function will rise, but not necessarily above the level for 2 collections
per week, as shown in Figure 8.
There will be a consumer surplus associated with going from 2 to 3
collections a week. This should equal the marginal utilities previously
discussed, and, if this area is greater than the increase in total costs
to households (increment a on Figure 8), shifting from 2 to 3 collections
per week would be justified (assuming the household depicted is the average.)
By depicting the demand and supply in the above way, it can be more
clearly seen what the utilities are that the households receive in going
from 2 to 3 collections per week. First, the households get more cleanli-
ness/spaciousness. Second, they may avoid higher-cost means of disposing
wastes, such as by use of disposals, or of providing space, such as by
use of trash compactors, or for cleanliness by use of better containers
(for example with screw-on lids)--all of which are alternatives for fre-
quency of service. In addition, they may shift their buying to a higher-
utility producing more waste intensive buying pattern.
Figure 9 shows that this tendency to avoid alternative means of dis-
posal and shift buying to more waste intensive goods will, when going from
2 to 3 collections/week, shift the demand for quantity of service upwards
and to the right. Here again, a consumer surplus is shown, representing
the marginal value of the shift (the difference in total value between 3
and 2 collections per week). This, too, should equal the marginal utilities
and consumer surplus discussed above. Note that if price b is charged per
34
-------
Willingness
to pay/unit
Total cost to
household
Marginal cost
to household
Marginal willingness
to pay (demand)
Low level
Perfect
Figure 7. Supply and demand functions for cleanliness/spaciousness,
35
-------
Willingness
to pay/cost,
$/week
Total cost to households:
2 collections per week
00
01
3 collections per week:
to agency and to individual household if charged
to individual household if no added charge
Marginal cost to individual households:
2 collections/week
3 collections/week
Marginal willingness to pay
Low level
Perfect
Figure 8. Shift in cleanliness/spaciousness supply function with change
in collection frequency.
-------
Willingness
to pay,
$/container
Total willingness
to pay
three collections per week
two collections per week
two collection
per week
Marginal willingness to pay for:
three collections per week
Quantity of service/containers per week
Figure 9. Shift in demand for quantity of service when collection
frequency is increased.
-------
container the consumer surplus is the slashed area, but if there is no
incremental user charge, it includes the cross-hatched area. Under con-
ceptual optimum pricing, price b should be charged, and all incremental
utilities or surpluses in going from 2 to 3 collections per week would be
net of the added cost for added containers. If not, however, this cost
would have to be included in the total (and average) cost of the added
collection.
Demand for quantity collected—The willingness to pay for quantity
collected for two different frequencies of service is depicted in Figure 9.
The demand for the service is the marginal willingness to pay, a declining
function. The number of containers at zero marginal willingness to pay
would be the quantity of service demanded under the usual flat charge (no
incremental quantity charge) system.
In equation form, total willingness to pay,
Wq = v. Q - httf ,
and marginal willingness to pay,
W'q = v - ?Q
The relationships among location, frequency, and quantity are symmetrical
when viewed from the standpoint of one or the other, and since the relation-
ships have been viewed from the standpoint of location and frequency, they
need not be repeated here.
Demand for collection of different type wastes—As has been previously
indicated, there are two reasons for considering the demand for collection
of different type wastes. One is based on a supply side factor. Different
type wastes may involve different handling costs or provide different
salvage values and households may face different supply price functions for
separated wastes. If wastes are separated, advantage can be taken of these
differences. The second reason is that households may have different demands
for the collection/disposal of different type wastes, based either on differ-
ences in storage/nuisance problems avoided or alternative disposal options
open for the different type wastes. The two reasons may go together for a
particular type waste.
The willingness to pay on the part of a household for collection/
disposal by the community collection agency of two separated wastes would
be less than the demand for unseparated disposal because of the cost to
the household of separation. To otherwise make separation worthwhile,
there would have to be a positive value to the household, such as nuisance
avoidance, from the act of separation and separate storage. This does not
seem likely. Thus, the sum of the supply prices for separated wastes must
be lower by enough to offset the decrease in separated-waste demand prices
(the cost of separation to households.) This would depend on the extent of
reduced handling cost/increased net salvage values, as seen by the collec-
tor, for separated wastes as opposed to combined wastes.
38
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Where one part of the wastes is disposed by alternative means (own
disposal), and the residual is deposited for collection and collected by the
community collection service, the reason is likely to be a positive value
of separated wastes and alternative disposal resulting in the avoidance of
space/nuisance problems. Here, the algebraic sum of the decrease in the
supply price for residuals collection/disposal compared to total-wastes
collection/disposal (if there is in fact any change, one way or the other)
and the space/nuisance avoidance values achieved must offset the costs of
separation and alternative disposal of the separated wastes.
Income Effects
The effects of income levels on the quantity of goods and services
demanded, and the application of these theories to demand for services in
the solid wastes collection/disposal field, have been fairly well developed
and presented in both words and equation form, as well as supported through
empirical analysis, both in the original Sheaffer-Tolley study and in sub-
sequent studies. It is believed that little needs to be added in this ex-
tension. The main extension here, which is new empirical analysis using
more recent data, is reported in Section III of this report. That extension
supports earlier conclusions concerning the likely direction and range of
income effects. Both conceptual and empirical extensions by others are
reported in Section II, where studies by others are reviewed and critiqued.
Nevertheless, a brief restatement of the theory of income effects and
their application in the solid wastes field, along with a few added or re-
phrased theoretical points, is in order.
Because prices attach to various goods and services that produce
utilities, income restricts the total size of the bundle of priced goods and
services that can be purchased. Optimum allocation of income among priced
goods and services requires that marginal utilities (incremental utilities
per incremental dollar of income) be equal among all allocations. For goods
and services that are not priced, amounts are taken to the point where their
marginal utilities are zero.* This also places a limit on the amount of ser-
vices, in this case of free services, that will be taken. Since, in the
usual case, and in the Chicago area of study reported here and in the 1971
Sheaffer-Tolley study in particular, prices (incremental-quantity user
charges) do not apply, it is this zero marginal utility amount which is the
usual limiting amount.
This limit comes about in one way because of complementary relation-
ships (in the household-utilities production function) between the quantity
of community waste collection services and the quantity taken by households
of other goods and services that are limited by income. In particular,
the quantities of goods purchased, particularly consumer non-durables, or
* In general, goods and services are taken to the point where their marginal
utilities equal their marginal costs. For priced goods and services, this
is the marginal opportunity cost of other goods and service (their marginal
utilities), and for non-priced goods and services, zero.
39
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size of lawns kept, which produce wastes, are limited by income/price, thus
limiting the demand for community waste collection services. (Households
do not fill their garbage cans with sand merely to take greater advantage
of a free service. This costs something, that is, has a negative marginal
utility.)
The phenomenon of less wastes at lower incomes through lower consump-
tion appears to be a complex one. Lower consumption at lower incomes is
reasonable. However, just what the effects of lower income on collected
wastes are are not clear. Studies by Richardson and Havlicek (1976, 1975,
1974) and Saleh and Havlicek (1975), reported in Section III, have indicated
that yard wastes and newspaper wastes do increase with income, but not food
or clothing wastes.
The simple explanation of lower income persons not producing more
food and clothing wastes could be that they do not really (to any extent)
eat or wear less. However, as earlier pointed out, lower income families
may tend to eat more leftovers, use scraps to feed the dog rather than buy
dogfood, wear clothes out more and make patchwork quilts, and otherwise
"save string" and "mine" wastes. They may do so because the alternative
value of their labor, used in mining and converting wastes to reusable
products, is lower, and because this may represent their best alternative
for increasing their incomes. At higher incomes, more goods are purchased,
and, not violating the law of conservation of matter, more wastes should
be produced from these goods at a faster rate. Or, as Tolley has stated it,
to maintain a desirable quality of life commensurate with income, consumers
have incentives to scrap earlier and buy a new item as incomes increase.
Thus, lower income families may generate less food and clothing wastes.
However, as Havlicek and his coauthors have pointed out, the effects of
such higher scrapping rates on quantities of collected wastes may be offset
by greater use of alternative disposal at higher income, such as use of
sink disposals and finding takers for old clothes.
The extension of the theory in this paper suggests that there are
other complementary relationships that may limit the quantities of waste
collection services demanded. One is moving-the-waste-to-the-curb, which
involves either an own cost for moving the containers to the curb, or pur-
chased back-door service. To the extent that income restricts the amount
of back-door service purchased (in a broader sense, also, to the extent that
the availability of own household labor, which is a form of income,
restricts this "service"), less of the complementary quantity-of-wastes-
for-community-collection will be taken. Also, to the extent that income
restricts the frequency of collection service taken, less of the comple-
mentary quantity of service will be taken.
Ernst (1975) further suggested that at lower incomes, the general
quality of waste collection service taken (provided) may be lower, and
thus less attractive for use. This is the same point, extended beyond
location/frequency attributes.
Marginal utilities of various goods and services, including those of
non-priced goods and services, may change as income and total spending
40
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change. Thus, the same proportions of added income, compared to base income,
may not be spent on the various goods and services. The 1971 Sheaffer-Tolley
study revealed a positive income elasticity of demand for community waste
collection (indicating that the service was not an "inferior good")* but one
of less than 1.0, specifically between 0.3 and 0.7, indicating that less
than a proportional amount of waste collection is demanded as incomes rise.
This is reasonable, as Ernst confirms, on at least two grounds. First, the
marginal propensity to consume with respect to income is less than 1.0. This
is certainly true with respect to transitory income, and the data used in-
clude transitory elements. Second, the proportion of added income spent on
non-durables tends to decrease as income increases. Thus, proportionally
less wastes would be produced as incomes rise.
Other Effects on Demand
In addition to price and income, there are a number of factors that
may affect quantity of services demanded. These may include, but are not
limited to, population density and lot size, season of the year, working
and eating-away-from-home status of members of the household, race, age
structure and education levels of household members, region of the country
(climate), ownership of alternative disposal facilities (sink disposals) or
means-of-saving-leftovers facilities (home freezers). Laws on bottle
return, use of sink disposal practices, and customs in certain areas may
affect quantity. Population or number of households will affect total
quantities for a community, and household size may affect both per-household
and per-capita amounts. The theory of these relationships is more or less
obvious. The extent of the effects can be determined by regression analysis.
Additionally, some information might be obtained from production function
analysis.
Integration of Supply and Demand Through Price
Price is the integrating factor between supply and demand. This role
has been largely covered in discussing supply and demand themselves. The
economic efficiency role of price is to avoid social losses from under- or
over-pricing. Without considering the costs of administering a pricing
system or of externalities, this means marginal cost pricing based on quan-
tities of services provided.
Where solid waste services are not quantity-priced, the price for
more or less of the services to the household is zero. To the extent that
the use of service is responsive to price, more of the services are used
than would be used if prices were set to reflect the costs of more or less
services. This is true because the services are worth less than their cost.
The net social loss from zero pricing (flat charging) is measured by the
cost of services provided they cost more than they are worth, less the
value of these services. Marginal cost pricing would avoid this net social
loss.
* Less is not taken (to keep its marginal utility equal to its marginal
cost) as incomes rise.
41
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However, there are administrative costs involved in quantity pricing.
First, the quantity must be measured, and second, billing becomes more
complex. (There may, of, course, be offsets from better record keeping.)
In addition, as has been discussed, there may be external costs, such as
littering, resulting from pricing, and, from an individual community
point of view, loss of tax and revenue-sharing advantages. Thus, the total
net benefits of pricing may not be positive. Whether or not incremental
charge systems based on marginal costs should be instituted would depend
on whether or not the net total benefits are positive in each particular
case. This involves a benefit-cost analysis. Apparently no empirical
studies of such benefits and costs have been undertaken (see Section II).
EXTENSION OF THE THEORY OF DEMAND FOR RESIDENTIAL SOLID WASTE COLLECTION/
DISPOSAL TO INCLUDE PUBLIC GOOD CONSIDERATIONS (ENVIRONMENTAL EXTERNALITIES)
Community cleanliness, which involves sanitation, health, and safety
and a sense of neatness and orderliness, is a public good. A principal
input for achieving the desired level of community cleanliness is the non-
polluting collection/disposal of all community solid wastes. Where indi-
viduals do not "automatically" use non-polluting services for collection/
disposal of their solid wastes, the public-good aspects of solid waste
collection/disposal must be considered in developing the theory of demand.
Non-polluting collection/disposal involves, first, the community
having a regular collection/disposal service; second, rules for its use,
particularly rules prohibiting alternative polluting disposal, such as
littering, open burning, and dumping; and third, observation of the rules
by members of the community.
There are certain economic aspects of this community waste collection/
disposal input for achieving community cleanliness. These include the
demand for cleanliness, mainly litter control, the alternatives for achieving
it, and optimum solutions. Goddard (1975) has developed a comprehensive
"complete pricing model" for taking these considerations into account in
pricing solid waste collection/disposal pricing. This model is discussed
in Section II of this study. Others have also presented and discussed
models, including McFarland's empirical model (1972), and Ernst (1975).
Rather than repeat what Goddard and others have already done, these economic
aspects are taken up in a series of numbered discussion points that are
presented below.
1. If the rules for use of collection/disposal service are fully
observed by households and others (and if the collection/disposal
service itself meets certain standards for preventing scattering
of wastes along routes and for proper disposal), essentially 100
percent control of solid wastes effects on community cleanliness
will be maintained.
2. With respect to this 100-percent control, it is almost univerally
assumed that the marginal public benefits, in terms of community
cleanliness, of observation of the rules (and certainly public
plus private benefits) are greater than the marginal private costs
42
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of observation up to the full observation of the rules. Thus,
if there could be full observation of the rules at essentially
no public cost, there would be no question of the optimum level
of control of solid wastes effects on community cleanliness.
It would be 100 percent.
3. While costs probably do tend to rise (for example, it requires
more effort to not-litter while in a public place the farther the
litter basket) and while benefits may tend to decline as 100-per-
cent control is approached, there appears to be little if any
reason, either on judgmental or empirical grounds, to substantially
question the above assumption. (This does not necessarily apply
to disposal itself according to standards. Standards for sanitary-
land-fill and other disposal methods, for both typical residential
wastes and those including hazardous elements, are included as
an area for needed research in Section IV.)
4. On private grounds alone, there may be reason for less than 100-
percent observation of rules. Littering and dumping or other
own-disposal that pollutes may be privately less costly than use
of the community service for certain wastes, at certain times,
or in certain places. There are, it is emphasized, two aspects
of this, the private costs of the community service and the private
costs of the alternatives.
5. Because there are these two sides, there are two approaches to
reducing or eliminating the littering and dumping itself, one
is that of encouraging the use of the community service, which
means lowering its cost to the user, and the second that of dis-
couraging use of alternatives, which means raising the cost of
alternatives to the user.
6. The costs that are subject to modification are not limited to
monetary costs, although price and monetary considerations may
play an important role and may be directly involved in non-
monetary considerations.
a. On the side of encouraging greater use there are first, of
course, price considerations. The marginal charge for
collection/disposal could be less than cost by any amount
to encourage use. Flat charges, that is zero marginal
charges, are typical, probably because these avoid any
accounting and have tax advantages, not strictly because
zero (flat) charges are the optimum price. Better, more
frequent service with back-yard collection would in effect
also reduce costs of use, as would providing free containers.
All of these approaches may involve encouraging greater
generation of wastes in addition to greater relative use
of community collection facilities to reduce or eliminate
littering. This is a price paid for encouraging use of
community facilities, which must be compared to the bene-
fits achieved.
43
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b. On the side of discouraging alternatives, one cost may
be the conscience cost—knowledge that in littering and
dumping, one is breaking the golden rule and stealing
environmental quality from one's neighbors, and where there
are laws, that one is breaking laws. For those without,
or with insufficient, conscience, there is the cost attached
to the probability of getting caught and paying a fine.
Again, there may be a cost associated with promoting greater
observation of the golden rule and the laws, and with
enforcement of the law, which costs must be compared with
benefits achieved by such promotions and enforcement, as
indicated below.
7. In addition to reducing littering and dumping itself, the effects
of littering and dumping on community cleanliness can also be
reduced by increased community litter collection and general
street and public place cleaning.
8. Where the rules for use of solid waste collection/disposal are
not observed 100 percent, there js^ the question of how much
community cleanliness is wanted. The marginal benefits of
different levels of cleanliness, and thus demand for cleanliness,
would vary with community income and other characteristics.
9. The actual degree of cleanliness demanded will also depend on
the marginal costs of achieving cleanliness through the various
approaches, that is, the cost for added units of cleanliness,
as measured by some index, in the various approaches—subsidizing
use of the community system; advertising, education, promoting
and enforcing greater observation of rules and laws; and cleanup.
10. The optimum program for "cleanliness management" would, of
course, be one that equated the marginal costs in each of the
approaches to obtaining cleanliness to the marginal benefits of
cleanliness.
44
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SECTION II
REVIEW AND CRITIQUE OF PRIOR STUDIES OF DEMAND FOR RESIDENTIAL
SOLID WASTE COLLECTION/DISPOSAL SERVICE
In this section, prior studies of demand for residential solid waste
collection/disposal service are reviewed and critiqued, with particular
emphasis on empirical results related to price and income elasticities, as
called for in the EPA request. The section is organized into four parts.
The first three cover effects of various factors on the quantity of solid
waste collection/disposal services, first price, second income, and third
other factors as reported in the literature. The fourth section discusses
studies dealing with environmental effects. Because of this organization
around topics rather than around studies, particular studies may be dis-
cussed in more than one part.
PRICE EFFECTS
Effects of Price on Quantity of Service Demanded
and Price Elasticity of Demand Estimates
Effects on Quantity Collected
No regression analysis has been uncovered in the literature of the
effect of price on quantity of solid wastes collected, and only one empiri-
cal estimate of any kind has been discovered, an estimate by Wertz (1976).
Wertz, averring that "there is one place among the largest American cities
to find a clue about the predicted decline (in quantity of waste collection
as price increases), San Francisco," compared pounds per capita collected
in those sections of the San Francisco area where prices were charged on a
per container basis (699 pounds per capita in 1970) with pounds per capita
collected in all San Francisco urban areas, where general revenue financing
predominated (937 pounds per capita). Wertz, after estimating the price
per pound from given price per container, estimated "an arc-elasticity of
-0.15," but stated that this "does not exactly represent the independent
effect of price of service upon refuse quantities—because of variations in
income, frequency of service, weather conditions, etc.—" In general,
these points are certainly correct (although it is not clear why weather
variation within a single metropolitan area should be important). Regression
analysis, covering all important variables, and using cross-section, time-
series, or combined analysis appears definitely called for to extend this
analysis. Furthermore, although Wertz seems to suggest that the search
should be limited to large American cities, it is not clear why. A number
of smaller American communities, including but not limited to suburbs of
larger cities, employ incremental-quantity charges. The quantities in these
45
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communities could be compared with the quantities in nearby areas where flat
charges are employed to give insights into price effects just as well as in
large American cities. The need for such extensions is covered in Section IV
on areas of needed research.
McFarland et al (1972), using a "price proxy," ran a regression analysis
for estimating the "effect" of this price proxy and per capita income and
population density on per capita pounds of wastes collected. However, as
Ernst (1975) suggests, this proxy variable, which was average revenue per
household, was not a price variable in the true sense "since no solid waste
management in the analysis used pricing (on a quantity basis)." Even so,
McFarland et al obtained significant and negative correlation coefficients
between pounds per capita of wastes collected and average revenue per house-
hold, the result that would be expected if average revenue were a true price
proxy. Ernst provides some interesting speculation concerning other-than-
price effects that may have brought about the relationship. As Ernst
suggests, price effects if any should be extremely small under flat charge
systems which relate charges to average community rather than individual
actions. In any event, the findings in the McFarland study cannot be taken
as estimates of price effects.
In addition to empirical studies, other studies have focused on develop-
ing concepts and models of pricing. Goddard (1975) develops a model for user
charges. The model includes submodels for 1) demand and supply in collection
and disposal, 2) demand and supply of litter control: individual preferences,
3) demand and supply of litter control: collective preferences, and 4) pro-
duction conditions: litter control. Goddard's focus is thus on pricing in a
context where litter control or externalities are a primary concern. Goddard's
model specifies in equation form the various considerations for pricing and
for determining associated quantities. Ernst (1975) also presents models for
pricing taking externalities into consideration.
Effects of Back-Door Service and Frequency of Collection
Stevens (1977) found the frequency of service demanded was significantly
and negatively related to the price for frequency of service, and significant-
ly and positively related to the quantity of pickup, measured either in tons
or cubic yards. She found that frequency was also significantly related to
pickup location (with quantity measured in tons) but not significantly related
to income. She found that backyard pickup service was significantly and nega-
tively related to price for backyard service, and significantly and positively
related to the frequency of service, household income, and number of persons
in the household. Savas (1977) concluded that the frequency and mode of pick-
up were not associated with the form of payment for collection services, tax,
flat, or quantity variable.
Effect of Pricing (Methods of Financing) on Costs of Service
There is a need for analysis of how incremental pricing, or other
methods of financing, affect costs as well as quantities demanded. Incre-
mental pricing can affect costs in different ways. It can reduce quantities
taken, thereby reducing costs. It can be administratively more expensive,
thereby increasing costs. It can also reduce costs indirectly through
46
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improvement in management, for example, improved record keeping through
increased cost consciousness, improved technology, etc. These effects need
to be analyzed separately under various circumstances. One analysis, in
which multiple regression techniques were used, has been discovered in the
literature on the subject of the effect on costs of type of financing. Clark
et al (1971), using Ohio data, regressed average annual budgeted cost of
residential refuse collection per pickup unit against a number of potential
cost factors. They found collection frequency, collection location, and
nature of financing arrangement to be significant. For financing arrange-
ment, a zero-one variable was used, zero when a user charge is assessed,
one for other method of payment. It was not stated whether the user charge
was defined as an incremental charge or merely a direct charge to user as
opposed, for example, to taxes. User charges added $8.17 to annual budgeted
costs per pickup unit (customer).
Because of failure to report the definition of user charges, and because
of limited information and analysis in general, it is impossible to draw any
conclusions from this result. It should certainly not be taken to mean that
administrative costs of pricing more than offset cost savings due to quantity
reductions.
The need for further analysis along these lines is recommended in
Section IV.
Effects of Costs on Price and Quantity of Service Demanded
Where prices are charged for individual waste collection/disposal
services based on costs, the quantity of the services demanded will ulti-
mately be a function of their individual costs. There is a considerable
literature on the costs of the various services and of the various technolo-
gies and management approaches in providing these services. Two in particu-
lar have been previously cited (Clark, 1971; and Hirsch, 1965). Unfortunate-
ly, most such studies are not oriented toward supply/demand/price analysis,
and their number is too great for individual review and critique in this
paper. The U.S. Environmental Protection Agency (Larsen, 1976) has prepared
a bibliography of studies and reports in the solid wastes field, and this
bibliography cites a number of such studies.
In addition, rate information is available in the literature. Rates
tend to reflect costs, and descriptions of the services and the basis for
charge will indicate whether prices or flat rates are charged. As an
example, a 1965 University of Oregon study, prepared in cooperation with the
League of Oregon Cities, Refuse Collection and Disposal - A Survey of
Practices in 164 Oregon Cities, provides information on the character of
service and rate schedules for residential and commercial service. Among
the data supplied are city population, normal residential charge per month,
type of disposal, distance to disposal site, and rate schedule information
for residential and commercial collection by amount and frequency of service,
and other information on cost factors for particular cities.
As examples of the information provided, Portland and Corvallis offered
once-a-week service, with charges per month based on number of cans per week.
47
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For Portland, the charge was $1.75 for 1, $3.00 for 2, and $4.00 for 3 30-
gallon cans. For Corvallis, it was $1.50 for 1, $2.25 for 2, and $3.00 for
3 35-gallon cans. Eugene offered either once- or twice-a-week service, for
once a week $1.50 for 1, $2.25 for 2, and $3.00 for 3 32-gallon cans per
week. The twice-a-week pickup charge was just twice as much per can, except
for 3 cans where the charge was slightly less on a per-can basis. Spring-
field added extra charges for its per-can pickup rate in less-developed
areas and in areas farther from the dump. Hillsboro added an extra charge
if the 30-gallon cans' weight exceeded 100 pounds. Empire had one rate for
cans under 30 gallons (using a standard 27-gallon can), a higher rate for
cans 30 gallons or over ($1.50 for one can under 30 gallons, $1.75 for one
can over 30 gallons). Redmond had no limit on the number of cans. It
offered a standard $1.45-a-week fee for once-a-week collection, as long as
the cans contained household refuse. Port Oxford had a standard fee for
cans at the curb, a higher fee for cans "on lot." This report provides a
good example of the kinds of services provided and the pricing practices
employed, as well as some indication of costs based on charges.
INCOME EFFECTS, AND INCOME ELASTICITY OF DEMAND ESTIMATES
Studies providing estimates of income effects are more numerous than
price, though still only a very few. In addition to the 1971 Sheaffer-
Tolley study and the updated analysis reported in Section III of this report,
these studies include Wertz (1976); Downing (1975); results from studies
covering two areas in Indiana, one for Indianapolis reported in Richardson
and Havlicek (1976, 1975, and 1974) and one for Lafayette reported in Saleh
and Havlicek (1975); and McFarland et al (1972).
As has been previously indicated, the 1971 Sheaffer-Tolley study re-
vealed income elasticities of demand between 0.3 and 0.7. In the McFarland
et al (1972) study, no significant effect of income was found, a result
Ernst found surprising in the light of the Sheaffer-Tolley Chicago findings.
More recent studies, as cited above, tend for the most part to support the
existence of significant positive effects of income, with elasticities less
than 1.0.
Wertz, using cross-section analysis and data from 10 Detroit suburbs,
found an implied income elasticity of 0.279. In a second analysis, using
data from 6 different Detroit-area communities, he found an elasticity of
0.272. Both studies produced significant estimates. He compared these
results with an income elasticity estimate by Downing, 0.39, based on obser-
vations made in Riverside, California.
Saleh and Havlicek (1975), in a study of food consumption and the food
wastes components (garbage and food and beverage containers) of solid wastes
in the Lafayette/West Lafayette, Indiana metropolitan area, found a signifi-
cant positive effect of income on the value of food consumed at home. Their
estimated elasticity was 0.19. However, income did not have a significant
effect on the total food component of solid waste. As an implied explana-
tion, based on higher income households owning garbage disposals, it was
reported that the availability of a garbage disposal unit channeled 3.337
48
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"Ib./household/week into the sewage system, out of an average 4.626 Ibs./
household/week of garbage (primarily food wastes), and out of 11.337 Ibs./
household/week total food-waste components (the difference being food-and-
beverage containers).
Richardson and Havlicek, in studies of the components and seasonality
of solid wastes in the Indianapolis area, found a significant positive linear
relationship between total annual wastes collected and income. They found
this relationship both when using income alone and income and income squared
as independent variables. They did not find a significant relationship between
income squared and either total annual collections or collections for any of
the 13 four-week periods of the year analyzed. The authors explain that they
may not have had sufficient observations at the higher-income levels to obtain
significant results. Regressions were not run in double-log or semi-log forms,
and no test was made of whether income elasticity varied with income.
In their analysis of income effects on the quantities of different type
wastes, Richardson and Havlicek found both positive and significant relation-
ships for 4 of 11 components. Grass was the most responsive to income.
Other solid waste components with positive significant relationships were
newspapers, green glass, and aluminum. Significant negative relationships
were found for textiles, plastics, and garbage-and-other (food wastes, dirt,
ashes, and miscellaneous). Regarding textiles, Richardson-Havlicek specula-
ted that higher income houses may dispose of clothing through goodwill insti-
tutions, and regarding garbage-and-other, that higher income households may
have garbage disposal units. Significant seasonal effects on quantities were
found, with lowest amounts in the winter. Income was found to have a sig-
nificant positive effect on quantities in all of 13 four-week periods in the
year except one, a mid-winter period. This was the case where the income
squared term was retained in the regression. Where it was not, collections
for 3 additional winter periods and one fall period, a total of 5 of 13
periods, showed insignificant relationships with income (unsquared).
OTHER EFFECTS
Estimates of the effect of a few factors other than price and income on
residential solid wastes quantities collected have been reported in the prior
literature. These include effects of season and of household size, race,
and age distribution, reported by Richardson and Havlicek (1976, 1975, and
1974); population density, reported by McFarland et al (1972); and for the
food component of solid wastes, sex and age of family head (neither found
significant), housewife's education, and ownership of a garbage disposal,
reported by Saleh and Havlicek (1975).
Richardson and Havlicek found that total solid waste amounts collected
were significantly related to household size. All components were also
positively related and at a significant level for 7 of 11 components of
waste. Each added household member added 8.8 pounds per week to total solid
wastes. For race, percent black was used. A negative, but not significant,
effect was found for total wastes, but significant negative race effects were
49
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found for three components, paper other than newspapers, plastics, and brown
glass. Percent of household members 18 to 61 was found to have a significant
positive effect, each percent adding almost one pound per week to household
solid wastes. As previously reported, Richardson and Havlicek found a sig-
nificant seasonal effect.
McFarland et al found that population density had a significant negative
effect. This could be due to less yard and garden wastes at higher popula-
tion densities. It might also be speculated that population density was
negatively correlated with income and that population density was partially
picking up an income effect. This could be an explanation of the fact, re-
ported above, that McFarland et al found no significant income effect on
solid waste collection amounts.
Saleh and Havlicek found that housewives' education had a significant
positive effect on total-food solid waste, with an elasticity of 0.56 for
average weekly pounds with respect to years of schooling. They found a
significant negative relationship with respect to ownership of a garbage
disposal, with a unit, as previously indicated, reducing collection by 3.337
pounds per household per week.
ENVIRONMENTAL EFFECTS
Goddard (1975) cites Gueron's (1972) conclusion "that collection should
not be sold; an efficient price is a zero marginal price." Gueron based
this conclusion on assumptions of "an increase in litter, burning, etc., and
not a reduction in waste generation" with pricing, and "that the social cost
of any unrestricted own disposal exceeds the direct cost of collective hand-
ling." However, as Goddard points out, the conclusions cannot be reached
on a priori grounds, and Goddard further states that the two assumptions
are most likely not valid. McFarland (1972) includes street sweeping costs
with collection costs in her 1972 analysis. She found that such costs are
higher in communities with positive marginal waste collection charges,
$14.05 per person annually compared to $9.15. The inference was that pricing
leads to increased littering. As Goddard (1972) points out, "because of
several shortcomings to this empirical analysis—it is not possible to
reach such conclusions within a reasonable margin of doubt." Goddard dis-
cusses various reasons for this, including the fact that street sweepings
are only partially litter and that "the sample includes cities in both
northern and southern California, with the possible result that the presence
of deciduous vegetation in the former has biased the estimates." In addi-
tion, Goddard discusses lack of control of income, race, and other socio-
economic factors. No other empirical studies of the environmental effects of
pricing have been discovered.
50
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SECTION 11,1
FACTORS AFFECTING RESIDENTIAL SOLID WASTES IN CHICAGO
PURPOSE
The purpose of this section is to update the findings of the Sheaffer-
Tolley (1971) study dealing with the demand for solid wastes in the City of
Chicago. That study specified and tested various econometric models in
the course of investigating the nature of the relationship between the demand
for solid waste collection and various socioeconomic factors. The same
regression models are now tested using more recent and more satisfactory
data. In this manner, the reliability of the previous econometric models,
as well as the earlier findings, are evaluated. The results are also com-
pared with results from other studies reported in the literature.
SOLID WASTES DISTRIBUTION IN CHICAGO
This study is based, as was the earlier study, on data collected by
the Bureau of Sanitation of the City of Chicago. The data collected provide,
on a weekly basis and by fifty political wards, the pounds of solid wastes
collected by municipal trucks. The Department of Streets and Sanitation
collects refuse only from residential buildings with four dwelling units
or less, and it does so free of charge. Approximately one half of all solid
wastes accruing in the City of Chicago are covered by these services. The
fifty political wards are shown in Figure 10.
The earlier study used 1968-1969 solid waste collection data. The data
used in this study cover the period 1970-1971. Only a fraction of the data
was available for 1970, with the majority of the weekly data used covering
the 1971 period. Where weekly data for 1971 were missing, 1970 data were
used to obtain representative data for each period.
In Figure 11, weekly pounds of solid waste collection, on a per dwelling
unit basis, are shown for both 1968-1969 and 1970-1971. In the 1970-1971
period, the average weekly pounds per dwelling unit is higher than in 1968-
1969. Otherwise, the data show similar patterns. In both time periods,
a seasonal pattern is evident. The demand for solid waste collection ser-
vices was comparatively low in the first few months of the year. It reached
a peak in April, and fluctuated around a high level until around Labor Day
weekend, after which time it began a decline to relatively low levels.
In both 1968-1969 and 1970-1971, solid waste collection in pounds per
dwelling unit varied substantially from ward to ward. Table 2 shows the
1970-1971 waste collection in pounds per dwelling unit for the 50 political
51
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Lok« Michigan
WANO BOUNDARIES
Mild
Figure 10. Ward map of Chicago.
52
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en
GO
Pounds/
Dwelling Unit
75
70
65
60
55
50
45
40-
35
1970-1971
10
15
20
25
30
35
40
45
Meek
Figure 11.
Average pounds of solid waste collection per dwelling unit by weeks,
1969 and 1970-1971.
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TABLE 2. SOLID WASTE COLLECTION IN POUNDS PER
DWELLING UNIT, BY POLITICAL WARD
Ward
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
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Week 21
(1971)
43.
25
44
42
49
41
60
52
49
43
48
43
44
49.8
39.8
54.0
37.9
38.6
42.6
42.8
27.3
37.7
45.6
53.8
81
40
40
32
38
26
30.0
40.0
93.
52.
57.6
41.2
24.6
58.3
54.0
69
58
77
83
66
82
61
60.8
70.9
72.4
78.4
74.1
33.2
75.6
63.6
86.2
67.4
82.7
72.0
69.
66.
64.0
66.7
56.2
66.8
55.0
87.0
59.8
71.5
62.4
70.6
43.0
50.9
87.7
72.6
108.2
53.0
71.9
41.1
50.0
33.3
40.0
50.4
Week 32
(1971)
106.5
49.9
68.8
49.8
19.
58.
54.
64.
57.4
70,
88.
63.
81.
57.
55.0
68
73
68
65
35.8
76.6
63.1
78.2
71.6
85.6
69.6
73.0
61.9
74
58
58
66
54
85
54
61
59
65
37
48.0
73.3
74.9
101.8
49.5
60.2
38.0
52.6
33.0
37.0
48.8
52.5
54
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wards in selected weeks, 7, 21, and 32 of 197! and 50 of 1970. The medians
are 45.2 pounds in week 7, 42.7 in week 21, 66.0 in week 32, and 62.5 in
week 50. As an example of the difference between wards, in week 32, for
Ward 5, the pickup was 19.7 pounds per dwelling ui.it, in Ward 1, 106.5
pounds.
As was the case in 1968-1969, for the 1970-1971 period the relative
positions that the various wards held within the distribution shifted drama-
tically over the year. For 1970-1971, this can be seen by an examination
of Table 3, which shows the ranking of the fifty political wards according
to their solid waste yield for the 4 selected weeks. Certain wards kept a
relatively stable position within the waste distribution (Wards 5, 7, 43,
and 48). Others shifted dramatically in rank (Wards 8, 18, and 45). Some
wards such as the 8th and 16th ranked high in the winter, while others
ranked low in the winter (llth, 24th, 35th). An indication of the changes
in ranks throughout the distribution can be obtained by examining the
Spearman correlation values between weeks:
Spearman Correlation Coefficients
Week 7 0.88 0.93 0.65
Week 21 0.93 0.71
Week 32 0.63
Week 21 Week 32 Week 50
The correlation between Week 7 (beginning 2/13/71) and Week 21 (beginning
5/21/71) is 0.88 and between Week 7 and Week 32 (beginning 8/6/71) is 0.93,
both high. The correlation between the two winter weeks, 7 and 50 (begin-
ning 12/11/70) is relatively low, 0.65. The correlation between the two
spring-summer weeks (21 and 32) is quite high (0.93). The spring-summer
weeks 21 and 32 have a rank order correlation with winter week 50 of 0.71
and 0.63 respectively. From this, it can be concluded that seasonal factors
do have a substantial effect on the relative positions the wards hold,
just as was revealed to be the case in the 1971 study.
EXPLANATORY VARIABLES
The earlier study used intercensal estimates for the explanatory varia-
bles. The explanatory variables in the present study were either obtained
directly from or derived from the 1970 U.S. Census. Thus, the explanatory
variables for this study were measured close in time to the dependent varia-
ble, waste collection in 1970-1971. Also, because these were either direct-
ly taken or derived from those in the Census, they are relatively free of
estimation error. Derivation of the explanatory variables for the present
study is described below. Estimates of the explanatory variables are pre-
sented and these estimates are compared with estimates in the earlier
study.
Median Income
The median income for each ward for this study was obtained by
55
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TABLE 3. RANK ORDER OF WEEKLY WASTE COLLECTION IN
POUNDS PER DWELLING UNIT, BY POLITICAL WARDS
Ward
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
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Week 7
(2/13/71)
2
44
22
45
50
36
39
18
42
16
4
31
5
28
30
13
15
19
23
49
17
27
11
29
3
8
10
21
12
24
20
9
35
6
40
37
26
25
47
41
14
7
1
33
32
43
38
48
46
34
Week 21
(5/21/71)
2
40
35
45
50
33
38
21
34
10
6
26
7
30
31
18
14
9
12
49
11
28
5
22
8
15
20
25
27
24
36
23
37
4
32
17
29
19
44
41
3
13
1
39
16
46
43
48
47
42
Week 32
(8/6/71)
1
40
17
41
50
32
38
23
34
15
3
24
6
33
35
18
11
19
22
48
8
25
7
14
4
16
13
26
10
30
31
20
37
5
36
27
29
21
46
44
12
9
2
42
28
45
39
49
47
43
Week 50
(12/11/70)
4
23
47
48
50
39
41
10
18
13
15
29
3
36
42
11
22
7
8
37
2
34
5
43
6
30
33
16
20
45
28
26
24
21
40
31
38
14
46
35
9
27
1
25
17
12
32
49
44
19
56
-------
averaging the median 1970 family income of all census tracts that fall
within a given ward. The median family income estimates for each ward are
shown in Table 4. (No estimates of income by season were made.)
Table 5 shows for each ward the relative median family income rank
from the earlier study and for the present study. A comparison of rankings
reveals that while many wards did not shift very much in rank, others did,
some quite dramatically. For instance, Wards 5, 34, 39, and 40 moved up
significantly in the rankings. On the other hand, Wards 7, 15, 18, 37, and
38 moved down in rank. The change in rankings between wards is further
demonstrated by the Spearman correlation coefficient which is 0.83. While
there is still a high correlation between the ward rankings, the impacts
of movements up and down the ranking order on the correlation are reflected
in the Spearman correlation coefficient.
In Figure 12, median ward income is plotted against the percentage of
residential dwelling units served by municipal waste collection in the
various wards. A positive relationship between income and percent served
can be seen by inspection of this figure. This is the same relationship
revealed in the earlier study. As was indicated in the earlier study, this
finding indicates that the higher income groups receive the greater advan-
tage of a municipal service free of charge.
Variance of Income
One of the findings of the earlier study was that, using regression
analysis, median income explained the main impact of incomes on the volume
of solid wastes, but not all. Income variance explained some of the impact.
To elaborate on this point, suppose that families in a ward with extremely
low or high incomes produce more or less solid wastes than the average family
produces, based on the income-waste relationship. Then, for a given median
family income, a ward will produce more or less solid wastes the higher the
variance of the income distribution. Consequently, in a multiple regression
analysis, the variance may have a positive or negative coefficient. There-
fore, when significant coefficients for the variance (a2) are found in a
cross section analysis, the indication is that the response of households
to income is different for households with extremely high or low incomes
from that of households with incomes closer to the center of the income
distri bution.
There is one income distribution for each political ward. Let it be
lognormal with parameters y and a2. Median income (i.e., the geometric
mean income of the population, y, is then given by y = e^. The parameter
o2 represents the variance, or the inequality of the income distribution.
The estimate of the income distribution for each ward was obtained
following Aitchison and Brown (1957). Aitchison and Brown pointed out
that, if the income distribution is lognormal, then the fractions of house-
holds with an income of more than y-j form a straight line when plotted on
lognormal probability paper against log y-j. Using the fact that quartiles
of order 16 percent and 50 percent are given by
57
-------
TABLE 4. ESTIMATES OF MEDIAN FAMILY INCOME BY WARD, 1970
Ward
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
Median Family
Income ($)
8,794
7,689
6,090
7,138
12,046
8,407
10,261
12,181
8,821
11,450
9,042
11,078
12,532
10,297
10,497
7,947
9,378
12,058
14,763
7,343
11
9
130
468
12,522
6,681
7,941
Ward
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Median Family
Income ($)
8,315
6,015
7,384
8,415
10,863
8,490
8,936
10,003
11,821
11,216
11,762
11,013
12,144
12,804
12,334
13,577
11,553
10,971
9,963
12,308
9,717
10,554
10,227
11,549
13,983
58
-------
TABLE 5. MEDIAN FAMILY INCOME RANK, BY WARD
Rank, Rank, Rank,
Ward 1971 Study Present Study Ward 1971 Study
1 46 37 26 41
2 49 44 27 50
3 48 49 28 37
4 45 47 29 40
5 42 12 30 21
6 36 40 31 28
7 7 27 32 35
8 11 9 33 25
9 22 36 34 26
10 16 17 35 18
11 33 34 36 19
12 23 20 37 13
13 9 5 38 5
14 29 26 39 8
15 14 25 40 15
16 34 42 41 2
17 39 33 42 43
18 4 11 43 30
19 1 1 44 24
20 44 46 45 6
21 20 19 46 27
22 32 32 47 17
23 10 6 48 31
24 47 48 49 12
25 38 43 50 3
Rank,
Present Study
41
50
45
39
23
38
35
29
13
18
14
21
10
4
7
3
15
22
30
8
31
24
28
16
2
59
-------
Ol
01 >
C S_
•i- QJ
O)
2
-o
100
— 80
QJ tO
o +-»
S- •!-
O> C.
a. 3
60
40
20
5,000
10,000
15.000
Median income ($)
Figure 12. Relationship between ward median family income and percentage of dwelling units
served by municipal waste collection.
-------
C 16% - e^ + °
s SOX = e^
\i and a were determined by graphical means. This method was shown in the
earlier study to be a close approximation to estimates derived using more
sophisticated techniques. The estimates derived using this method are shown
in Table 6 along with estimates from the previous study. It can be seen
that in certain wards the variance increased from those in the earlier study
(Wards 1, 20, 28, and 48), in some it decreased (Wards 19, 23, 27, and 41),
and in others it remained fairly stable (Wards 9, 11, 16, 22, 32, and 33).
The average variance for the 50 weeks did not change much, being 0.59 in
the earlier study and 0.63 in the present study.
Population. Household Size, and Percentage Blacks
The remaining explanatory variables used in the previous study, which
were also used in this study, were population, household size, and percen-
tage black (non-white). Population was used to calculate solid wastes per
capita. The population figures in the previous study were based on adjust-
ments to update them from 1960 whereas the current study used directly the
close-in-time Census figures. The 1970 figures are presented in Table 7.
Household size was included as an explanatory variable when using waste
collections per household as the dependent variable because larger house-
holds are expected to produce more pounds of waste per household than
smaller ones by virtue of the fact that more people live in them. The
percentage black was used because consumption habits could differ between
black and other families with equal incomes. The household size and per-
cent black figures in the earlier study were also updated from 1960 Census
figures. The ones used here are from the close-in-time 1970 Census. The
data for household size and percent black are shown in Table 8.
MODEL SPECIFICATION
The econometric analysis of waste collection was carried out using two
alternative dependent variables. The first dependent variable, D-j, was
the pounds of solid waste collected per dwelling unit per week in the i^"1
ward. The second dependent variable, C-j, was the pounds of solid wastes
collected per capita per week.
The explanatory variables, as discussed earlier, were:
Yj = the median family income of the i^h ward
B-j = the ratio of blacks to the total population in the itn ward
Sj = average household size of the i'th ward
V.j = variance of the income distribution in the itn ward.
As indicated above, the average household size, S-j, was used only when
D-j was the dependent variable.
61
-------
TABLE 6. FAMILY INCOME VARIANCES BY 50 POLITICAL WARDS
Ward
Estimates
from
1971 Report
Estimates
Derived from
1970 Census
Ward
Estimates
from
1971 Report
Estimates
Derived from
1970 Census
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
0.68
0.78
0.74
0.75
0.77
0.63
0.60
0.54
0.57
0.53
0.56
0.50
0.45
0.51
0.50
0.61
0.69
0.46
0.56
0.69
0.54
0.56
0.44
0.73
0.60
1.18
0.76
0.86
0.86
1.00
0.79
0.67
0.41
0.55
0.41
0.55
0.67
0.25
0.67
0.67
0.59
0.98
0.25
0.25
1.19
0.44
0.55
0.24
0.86
0.79
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.64
0.75
0.63
0.64
0.55
0.51
0.53
0.51
0.49
0.48
0.50
0.53
0.49
0.52
0.55
0.47
0.95
0.72
0.63
0.50
0.66
0.50
0.68
0.59
0.57
0.79
0.59
1.19
0.79
0.67
0.55
0.55
0.55
0.42
0.67
0.42
0.67
0.42
0.42
0.42
0.14
0.98
0.67
1.02
0.42
0.55
0.67
1.02
0.42
0.25
62
-------
TABLE 7. WARD POPULATIONS, 1970
Ward Population Ward Population
1 68,932 26 68,555
2 75,506 27 67,795
3 68,979 28 69,274
4 68,528 29 67,004
5 66,906 30 65,752
6 67,695 31 66,854
7 68,036 32 67,692
8 65,971 33 68,503
9 66,925 34 67,944
10 67,072 35 65,418
11 66,535 36 68,086
12 66,382 37 66,970
13 56,759 38 64,060
14 66,630 39 68,747
15 67,495 40 65,531
16 65,872 41 66,923
17 68,504 42 69,336
18 67,717 43 69,159
19 66,875 44 66,558
20 69,486 45 67,071
21 67,167 46 65,222
22 68,267 47 68,264
23 66,424 48 67,979
24 67,359 49 68,531
25 66,122 50 66,997
63
-------
TABLE 8. HOUSEHOLD SIZE AND PERCENT BLACKS BY WARD, CHICAGO, 1970
Persons Per
Household Percent
Hard Unit Black
1 2.3 35.76
2 2.5 91.88
3 3.2 98.99
4 2.5 91.04
5 2.6 57.78
6 2.7 97.73
7 2.4 26.91
8 2.9 77.84
9 2.9 28.32
10 3.0 9.16
11 3.0 11.26
12 2.6 5.31
13 2.8 0.02
14 2.6 6.20
15 2.6 8.26
16 3.6 95.31
17 3.5 97.63
18 3.1 28.23
19 2.8 2.18
20 2.3 97.45
21 3.1 86.44
22 2.6 0.01
23 3.1 98.59
24 3.8 36.25
25 3.0 4.71
Persons Per
Household
Ward Unit
26 2.6
27 2.7
28 3.2
29 3.6
30 2.4
31 3.0
32 2.5
33 2.4
34 3.2
35 2.3
36 2.4
37 2.4
38 2.6
39 2.4
40 2.3
41 2.7
42 2.1
43 1.9
44 2.1
45 2.4
46 1.9
47 2.3
48 1.9
49 2.0
50 2.4
Percent
Black
8.98
83.35
83.35
88.60
0.11
1.
3.
.42
.85
0.30
66.30
0.01
0.02
12.49
0.51
0.65
0.14
0.01
39.17
4.93
0.75
0.02
2.63
0.08
2.72
1.20
0.17
64
-------
The regression analyses were run using three functional forms. The
first form specified a linear relationship between the dependent and inde-
pendent variables. The second form specified a semi-log relationship. In
this relationship, natural logarithms are taken of the independent variables
only. Finally, a double-log form was specified. In this relationship,
natural logarithms are taken of both the dependent and independent variables,
To bring out the implications of these different specifications,
consider a two-variable model describing pounds of wastes per dwelling unit,
D, as a function of the median income, Y. Disregarding the disturbance
term, the linear specification is then:
(1) D = a + 3 1
dD Y _ „ Y _ p Y _ 1
(2)
dY D p D a + BY 1 + a/3Y
Some of the characteristics of this form are that the income elasticity is
positive and less than unity when a and 3 are both positive, approaching
unity as _Y_ increases. That is, income elasticity is less for low-income
households than it is for well-to-do households, but always less than unity
for finite incomes. For a negative a, income elasticity is greater than
unity but likewise approaches unity as _Y_ increases.
If Y_ were to increase exponentially with rate g in a time series con-
text, then the income elasticity would follow a logistic curve.
dD . Y _ 1
The semi-log form is:
(4) D = a + 3 log Y
dD Y _ 3 _ 3 _ 1
dY D D a + 3 log Y log Y + a/3
The income elasticity is thus positive if both a and 3 are positive.
In this case, it is not necessarily less than unity but decreases as D
increases; in fact, it approaches zero as D goes to infinity. As income
increases, the same is true. In other words, the income elasticity is
higher for low-income households than it is for well-to-do families, but
instead of approaching unity as in the linear specification, it approaches
zero as income rises.
The double-log specification is:
(6) log D = a + 3 log Y
(7) D = ea YB
65
-------
ea 3 Y8" v ea
Y
dY D D ea Y3 "
The income elasticity is thus equal to 3 and is constant as income increases.
In other words, the same income elasticity applies to all households regard-
less of the level of their actual income.
REGRESSION RESULTS
Weighted vs Unweighted Regressions
The regression analyses were run both with unweighted and with weighted
observations. Weighting was undertaken to reflect the fact that the solid
waste data do not cover wastes from the entire population of a political
ward. The City of Chicago collects solid wastes only from housing units
containing 4 households or less. However, the explanatory variables cover
the total population of each ward. The question arises, How to control for
the differences? One way, as discussed in the earlier study, was to in-
clude only those wards in which some minimum percentage of the total popula-
tion was served. However, any such method would be arbitrary in terms of
what the minimum fraction should be. In the earlier study, weighted regres-
sions were used. If a high fraction of the ward were served by municipal
collection, then that particular ward entered the regression with a high
weight. If the fraction were low, the observation was given a small weight.
The squared fraction of household units receiving municipal service was
used in the earlier study. As explained, squaring had the effect of further
accentuating wards for which the values of explanatory variables were highly
representative. The same weighting scheme was used in this study for two
reasons. First, it makes the two studies comparable on this point. Second,
the weighting scheme still appeared to be reasonable, based on comparison of
alternative schemes, as discussed below. The basic weighting figures are
shown in Table 9.
The earlier study found that the use of regressions weighted by the
squared fraction of residential dwelling units municipally served was best
by the R^ criterion. The present study also carried out the regression
analysis (a) unweighted, (b) weighted by the fraction of residential dwel-
ling units municipally served, F-j , and (c) weighted by (Fi)2.
o
The results verified that (c) was uniformly best by the R criterion.
For illustrative purposes, Table 10 shows the results for Week 32 (beginning
August 6, 1971). The results are shown using the two dependent variables
(D-j,C-j)» and the three functional forms. In each case, both the R^ and the
F values are highest when the (F^)^ weights are used. Furthermore, the para-
meter estimates also become sharper as indicated by the smaller standard
errors, and hence the increasing significance levels of the parameters. The
results shown in the rest of the text are those of type (c).
Functional Form and Best Dependent Variable
Table 10 indicates that for both dependent variables, D^ and C-, the
66
-------
TABLE 9. RATIO BETWEEN MUNCIPAL AND TOTAL COLLECTION OF
HOUSEHOLD SOLID WASTES, BY POLITICAL WARD
Ward
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
Fraction of Household
Refuse Collected by
City of Chicago Ward
0.661 26
0.414 27
0.348 28
0.241 29
0.230 30
0.654 31
0.632 32
0.817 33
0.953 34
0.936 35
0.683 36
0.943 37
0.957 38
0.850 39
0.919 40
0.870 41
0.652 42
0.908 43
0.963 44
0.461 45
0.955 46
0.848 47
0.976 48
0.546 49
0.736 50
Fraction of Household
Refuse Collected by
City of Chicago
0.657
0.593
0.674
0.663
0.806
0.791
0.762
0.852
0.815
0.854
0.943
0.743
0.956
0.845
0.772
0.973
0.336
0.564
0.566
0.940
0.487
0.670
0.285
0.397
0.702
67
-------
TABLE 10. RESULTS OF WEIGHTED AND UNWEIGHTED REGRESSIONS WEEK 32 (8/6/71)
Weights
Used
_ _
Fi
r\
(Fi)2
—
Fi
o
(Fi)2
--
Fi
i.ii
--
Fi
(Fi )2
--
Fi
o
(Fi)2
--
Fi
(Fi)2
Dependent
Variable a
Di 70.039
(12.05)
Di 54.278
(6.08)
Di 56.404
(4.51)
Di 130.20
(103.17)
Di -11.525
(41.51)
Di 10.491
(22.75)
log Di 5.516
(1.85)
log Di 2.394
(0.731)
log Di 2.908
(0.395)
Ci 55.687
(8.94)
Ci 4.0735
(1.31)
Ci 7.080
(0.929)
Ci -67.272
(32.97)
Ci -65.020
(8.81)
Ci -32.424
(4.38)
log Ci -2.878
(3.23)
log Ci -4.784
(0.873)
log Ci -1.895
(0.415)
3
-0.000730
(0.0012)
0.001102
(0.000746)
0.00103
(0.00065)
-7.342
(11.20)
8.401
(4.70)
6.179
(2.68)
-0.1541
(0.201)
0.1930
(0.083)
0.1410
(0.047)
0.000172
(0.000857)
0.00139
(0.000161)
0.00125
(0.000133)
8.88
(3.58)
9.022
(0.997)
5.574
(0.517)
0.5911
(0.351)
0.8334
(0.099)
0.5295
(0.049)
Explanatory
Variable
Y.
Yi
Yi
log Yi
log Yi
log Yi
log Yi
log Yi
log Yi
Yi
V
w
log Yi
log Yi
log Yi
log Yi
log Yi
log Yi
R2
0.0082
0.0434
0.0503
0.0089
0.0624
0.0993
0.0121
0.1019
0.1600
0.0008
0.6079
0.6474
0.1138
0.6303
0.7074
0.0559
0.5968
0.7082
F
0.399
2.18
2.54
0.430
3.20
5.29
0.588
5.44
9.14
0.040
74.40
88.14
6.16
81.84
116.07
2.84
71.05
116.50
— indicates unweighted.
68
-------
double-log, or constant elasticity, specification was usually best by the
R2 and F criteria, and the semi-log specification between the linear and
double-log specification. This is more clearly shown in Table 11, showing
typical relationships between alternative forms taken from Table 10. (Ci in
the example shown, the double-log formulation was only slightly preferable
to the semi-log formulation based on the R2 as well as F criteria.)
As for dependent variable, the per capita model performs significantly
better than the dwelling unit model. This was a tendency that, as will be
seen, was found in most of the regression models used in this study. In the
discussion that follows, emphasis is given to R2 values in comparing results.
However, in all cases, where R2 values were highest F values were also highest.
Income
In Table 12, the empirical solid waste income relationship is given for
nine weeks studied. For both dependent variables, R2 and F statistics are
reproduced. (Standard errors are given in parentheses.) For comparison
purposes, the linear version for the dwelling unit approach is given, even
though it is never the best specification by either the R2 or F criterion.
The double-log specification turns out to be best on a dwelling unit
basis for all of the weeks studied. On a per capita basis, the double-log
specification is best in six weeks, and the semi-log form is best in three
weeks. Thus, in both cases, the double-log form is the dominant one. The
semi-log form is slightly better on a per capita basis in Weeks 26 (in June)
and 36 and 37 (in September). (Compare R2 values for the semi-log form in
Table 12 with R2 values for the double-log form in Table 21.) Consequently,
in those weeks the income elasticity is higher for low income as opposed to
higher income persons. In all cases, the income variable has a positive sign,
and the per capita formulation dominates the per dwelling unit specification.
How do these results compare with those from the earlier study? An
indication can be obtained by comparing the results shown in Table 12 with
comparable results from the earlier study, shown in Table 13. In both cases,
the income variable had a significantly positive sign. The differences which
have emerged are in terms of which specification is best. Whereas the double-
log form was the dominant one in the current study, generally the linear
specification was best on a dwelling unit basis and the double-log form
was best on a per capita basis in the previous study. Additionally, as
shown in Table 13, in the earlier study the linear per dwelling unit speci-
fication dominated the per capita formulation while, as shown by Table 12,
the per capita formulation was better than the per unit specification in
the present study. In comparing the amount of explained variation, the
results from the earlier study, shown in Table 13, have higher R2 on a per
unit basis than on a per capita basis, whereas the opposite is true for the
present study. In 1970, the R2's for the per capita double-log formulation
were much higher than for alternative formulations, as shown in Table 12,
with at least 70 percent of the variation being explained by income.
Income elasticity may have followed a slight seasonal pattern in 1970.
Figure 13 shows the nine per capita double-log formulation coefficients. The
69
-------
TABLE 11. THE TYPICAL RELATIONSHIP BETWEEN ALTERNATIVE
SPECIFICATIONS (WEEK 32, 1971)
Dependent
Variable a
Di 56.40
(4.51)
Di 10.49
(22.75)
log Di 2.91
(0.39)
Ci 7.08
(0.93)
Ci -32.42
(4.38)
log Ci -1.90
(0.42)
3
0.00103
(0.00065)
6.18
(2.68)
0.1410
(0.05)
0.00125
(0.00013)
5.57
(0.52)
0.5295
(0.05)
Explanatory
Variable
Yi
log Yi
log Yi
YT
log Yi
log Yi
R2
0.0503
0.0993
0.1600
0.6474
0.7074
0.7082
2.54
5.29
9.14
88.14
116.07
116.50
70
-------
TABLE 12. SOLID WASTE - INCOME RELATIONSHIP, 1970-1971
19
21
26
32
36
37
43
50
Dependent
Variable
log Di
log Ci
Q.
log Di
log Cf
Ol
log DI
log Ci
Ol
log Dj
Ci
"1
log DI
log Cj
0
log Di
Ci
01
log Oi
Ci
Oi
log Di
log Ci
Oi
log Oi
log Cf
Ol
f
a
2.75
(0.360)
-2.05
(0.363)
41.34
(3.15)
2.98
(0.369)
-1.82
(0.386)
55.90
(4.34)
2.50
(0.340)
-2.30
(0.355)
52.12
(4.12)
2.76
(0.374)
-37.99
(4.45)
58.49
(4.76)
2.91
(0.395)
-1.89
(0.415)
56.40
(4.51)
2.80
(0.418)
-34.31
(4.41)
58.26
(5.03)
2.86
(0.388)
Tl.87
(25.47)
63.68
(5.11)
1.90
(0.392)
-2.90
(0.314)
43.49
(4.66)
1.81
(0.41)
-3.00
(0.31)
37.93
(3.84)
,
B
0.1172
(0.042)
0.5056
(0.428)
0.000345
(0.00045)
0.12%
(0.043)
0.5180
(0.045)
0.000851
(0.00062)
0.1922
(0.040)
0.5806
(0.042)
0.00202
(0.00059)
0.1675
(0.044)
6.386
(0.526)
0.00153
(0.00068)
0.1410
(0.047)
0.5295
(0.049)
0.00103
(0.00065)
0.1574
(0.049)
5.861
(0.522)
0.00111
(0.00072)
0.1643
(0.046)
8.884
(3.01)
0.00156
(0.000732)
0.2523
(0.046)
0.6408
(0.037)
0.00265
(0.00067)
0.2414
(0.049)
0.6300
(0.037)
0.00189
(0.00055)
Explanatory
Variable
log Yi
log Yf
YJ
log Yi
log YI
Yi
log Y{
log YJ
Y.J
log Yi
log Yi
Yj
log Yi
log Yi
r
log Yi
•
log Yi
YJ
log Yt
log Yi
Y t
log Yi
log Yi
Yi
log Yi
log Y,
Y j
R^
0.1369
0.7439
0.0120
0.1558
0.7294
0.0375
0.3231
0.7999
0.1966
0.2301
0.7544
0.0956
0.1600
0.7082
0.0503
0.1748
0.7245
0.047-3
0.2110
0.7359
0.0862
0.3821
0.8617
0.2471
0.3389
0.8582
0.1972
F
7.61
139.43
0.584
8.86
129.37
1.87
22.91
191.88
11.75
14.35
147.46
5.07
9.14
116.50
2.54
10.17
126.23
2.38
12.84
133.77
4.53
29.69
299.03
15.75
24.61
290.56
11.79
71
-------
TABLE 13. SOLID WASTE - INCOME RELATIONSHIP, 1969
Meek
19
21
32
36
37
50
Dependent
Variable
log D,
i
log C..
I
o.
i
log C.,
1
log D,
1
0.
^
log C.
1
log D.
1
0.
1-
log C.
i
log D,
i
o.
1
log C.
I
log D.
i
D.
1
log C.
1
log 0.
1
D.
1
log Ci
1
log D,
i
^
a
0.763
(0.811)
-0.879
(1.10)
35.98
(7.15)
-1.312
(1.06)
0.330
(1.01)
31.94
(6.50)
-1.40
(1.06)
0.200
(0.988)
36.71
(6.95)
-0.93
(1.06)
0.72
(1.02)
29.56
(6.53)
-2.156
(1.022)
-0.513
(0.936)
25.05
(6.15)
-1.940
(1.12)
-0.297
(1.04)
-121.24
(33.75)
-1.714
(1.10)
-0.071
(0.797)
^
8
0.320
(0.090)
0.376
(0.121)
0.00352
(0.00082)
0.4822
(0.117)
0.426
(0.112)
0.0034
(0.0007)
0.483
(0.117)
0.432
(0.109)
0.00295
(0.00080)
0.432
(0.117)
0.376
(0.113)
0.00436
(0.00075)
0.5768
(0.1130)
0.5204
(0.1034)
0.00340
(0.00070)
0.5293
(0.123)
0.473
(0.115)
18.61
(3.73)
0.4889
(0.122)
0.433
(0.088)
Explanatory
Variable
log Y.
1
log Y.
i
Y.
1
log Yi
1
log Y.
1
Y.
l
log Y,
1
log Y.
]
Y.
i
log Y.
i
log Y.
1
Y,
log Y.
1
log Y.
1
Y.
log Y.
1
log Y.
1
log Y.
1
log Y.
1
log Y.
I
(•»
R2
0.2100
0.1674
0.2792
0.2514
0.2312
0.3068
0.2613
0.2458
0.2238
0.2219
0.1873
0.4150
0.3516
0.3453
0.3279
0.2770
0.2603
0.3412
0.2509
0.3345
72
-------
Income
elasticity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
7 19 21 26 32 36 37 43 50
Week
Figure 13. Income elasticity of the demand for solid waste.
73
-------
elasticities were about average in the summer months when the volume of
solid wastes collected was relatively high (Figure 11), was highest in the
fall and early winter months when the volume of solid wastes collected was
moderately low, and low in mid-winter when volumes collected were lowest.
However, since in the summer and early fall the semi-log specification was
dominant, in those months the income elasticity was higher for the lower in-
come groups. If there is a basic volume of solid waste that is generated
throughout the year, and in the summer months there is an additional waste
component arising from increased consumption of soft drinks, beer, fruits,
etc., then this component is more sensitive to income of those in lower than
higher income brackets. During the hottest part of the summer (August), this
consumption is relatively less sensitive to income. Seasonal variation in
income, with high earnings in mid-summer among low income groups, could also
cause this seasonal variation. (However, as previously indicated, no esti-
mates of seasonal income were made.) While based on relatively sparse infor-
mation, if there is such seasonal variation in income elasticities, there is
a possible policy implication: pricing can be used to dampen seasonal vari-
ation in solid waste amounts. Summer would remain a problem, for which
additional incentives for reducing amounts, such as greater incentives for
using returnable beer and soft drink bottles, might be required.
The Variance of the Income Distribution
The variance of the income distribution was significant in all cases
with the double-log formulation, and the double-log formulation was best
both on a dwelling unit and per capita basis. In no case was the linear or
semi-log form better. The results for the double-log specification on both
a per household and per capita basis are shown in Table 14. A positive re-
lationship was found between the amount of solid waste generated and the
amount of variance in the income distribution. That is, the greater the
inequalities in income in a ward, the greater the solid wastes in that ward.
This finding was different from that of the previous study where a negative
sign was found with respect to the income variance variable. Variance as an
explanatory variable does better than income in explaining solid waste vari-
ation on a dwelling unit basis, while income does better on a per capita basis.
The combined effects of income and the variance of the income distri-
bution are shown in Table 15. The per capita model always does better in
terms of the explained variance with the R2 ranging from 0.574 to 0.8698.
The income and variance variables, when they are significant, both have a
positive sign. On a per dwelling unit basis, in no single week are the
income and variance variables both significant. The income variable is
significant in Weeks 21, 43, and 50 whereas the variance is significant in
Weeks 7, 19, 36, and 37. However, on a per capita basis, both variables
are significant with the exception of Weeks 43 and 50 when the variance,
though positive, is insignificant. In the other seven weeks, both income
and variance are positive and highly significant. Thus, on a per capita
basis, as incomes and the variance of the income distribution increases,
the total amount of solid waste generated also increases. In the earlier
study, this was not generally true since the variance became insignificant
when income and variance are both included as independent variables.
74
-------
TABLE 14. SOLID WASTE - VARIANCE RELATIONSHIP, 1970-1971
Week
7
19
21
26
32
36
37
43
50
Dependent
Variable
log Di
log Ci
log Di
log Ci
log Di
log Ci
log Di
log Ci
log Di
log Ci
log Di
log Ci
log Di
log C,
log Di
log Ci
log Di
log Ci
a
4.00
(0.084)
3.02
(0.115)
4.36
(0.086)
3.38
(0.120)
4.44
(0.086)
3.47
(0.132)
4.50
(0.089)
3.53
(0.129)
4.40
(0.092)
3.42
(0.126)
4.47
(0.098)
3.49
(0.127)
4.60
(0.089)
3.63
4.36
(0.108)
3.39
(0.147)
4.17
(0.111)
3.19
(0.144)
6
0.1960
(0.051)
0.6117
(0.078)
0.2114
(0.056)
0.6270
(0.082)
0.2395
(0.058)
0.6552
(0.090)
0.2415
(0.061)
0.6571
(0.088)
0.2259
(0.063)
0.6416
(0.086)
0.2566
(0.066)
0.6723
(0.085)
0.2641
(0.061)
0.6797
0.2509
(0.074)
0.6666
(0.100)
0.244
(0.076)
0.6601
(0.098)
Expl anatory
Variable
log Vi
log Vi
log V{
log Vi
log Vi
log Vj
log V,
log Vi
log Vi
log V,
log V,
log V,
log Vi
log Vi
log Vi
log Vi
log Vi
log Vi
R2
0.1970
0.5601
0.2133
0.5500
0.2582
0.5240
0.2462
0.5370
0.2111
0.5349
0.2392
0.5572
0.2805
0.5608
0.1944
0.4797
0.1787
0.4849
F
11.77
61.11
13.02
58.64
16.71
52.84
15.67
55.68
12.84
55.21
15.09
60.39
18.71
61.29
11.58
44.26
10.44
45.19
75
-------
TABLE 15. SOLID WASTE - INCOME, VARIANCE RELATIONSHIP, 1970-1971
Week
7
19
21
26
32
36
37
43
50
Dependent
Variable
log Di
log Ci
log D{
log Ci
log Di
log Ci
log D{
log Ci
log Di
log Ci
log D-j
log Ci
log Di
log Ci
log D-j
log Ci
log Di
log Ci
a
3.60
(0.546)
-0.7019
(0.514)
3.87
(0.559)
-0.4305
(0.551)
0.309
(0.527)
-1.21
(0.523)
3.60
(0.572)
-0.7050
(0.573)
3.83
(0.601)
-0.4688
(0.600)
3.88
(0.630)
-0.4229
(0.598)
3.95
(0.580)
-0.3490
(0.594)
2.04
(0.621)
-2.26
(0.482)
1.98
(0.652)
-2.32
(0.479)
Explanatory
Log Y
0.0410
(0.056)
0.3848
(0.052)
0.0501
(0.057)
0.3938
(0.056)
0.1400
(0.054)
0.4837
(0.053)
0.0992
(0.053)
0.4366
(0.055)
0.0583
(0.061)
0.4020
(0.061)
0.0697
(0.063)
0.4047
(0.061)
0.0670
(0.051)
0.4107
(0.060)
0.2402
(0.063)
0.5840
(0.049)
0.2260
(0.066)
0.5697
(0.049)
Variables
Log V
0.1574
(0.078)
0.2498
(0.073)
0.1643
(0.079)
0.2567
(0.078)
0.1079
(0.075)
0.2003
(0.074)
0.1541
(0.081)
0.2465
(0.081)
0.1711
(0.085)
0.2635
(0.085)
0.1993
(0.090)
0.2917
(0.085)
0.2011
(0.082)
0.2935
(0.084)
0.0250
(0.088)
0.1174
(0.069)
0.0319
(0.093)
0.1243
(0.068)
R2
0.2061
0.7948
0.2260
0.7796
0.3516
0.8266
0.2845
0.7882
0.2260
0.7574
0.2534
0.7710
0.2996
0.7777
0.3832
0.8698
0.3406
0.8676
F
6.10
91.04
6.86
83.13
12.74
112.01
9.36
87.46
6.86
73.36
7.98
79.13
10.05
82.21
14.60
156.98
12.14
153.98
76
-------
Household Size
Household size was included in the analysis where the dependent variable
was on a dwelling unit basis. The expectation was that the larger the
average family size in a ward, the more solid wastes per households would be
generated, thus the greater would be the volume of solid waste collection per
household. However, the results of the earlier study did not bear this out.
In that study, household size alone turned out to be insignificant in all
weeks except Week 32. However, the results of the current analysis indicate
that household size is indeed positively related to the volume of solid
wastes collected. Table 16 shows the results in double-log form, which was
again best by the R2 criterion.
The impact of controlling for income is shown in Table 17. The double-
log specification is shown since it was the best, as was the case where
household size was used as a single explanatory variable. In every case,
where the income variable was significant, so was household size. This was
the case for the summer and early fall months (Weeks 19, 32, 36, and 37). In
these months, the income variable had a negative sign while household size
had a positive sign. Consequently, when controlling for household size as
income increases, the amount of solid waste generated decreases. (See, how-
ever, the last paragraph of this section in which it is concluded that the
positive effect of income on waste volume is confirmed.) Additionally, in
three weeks (7, 21 and 26), income was insignificant whereas household size
had a positive sign. During those weeks, household size was a better predic-
tor than income of the amounts of solid waste generated. For two weeks, (43
and 50) both income and household size were insignificant. This may give
more credence to the notion that during the winter months there is a basic
volume of solid waste that is generated that is fairly insensitive to both
income and household size. In the earlier study, household size was also
insignificant, but income was significant, as well as positive. For Week 50,
in December 1968, the relationship was:
D. = 29.57 + 0.00152 Y,- + 1.07 S, R2 = 0.1462
1 (8.44) (0.00054 (2.15) F = 4.02
However, comparing 1970 results with 1968 results, from Table 17 it is evi-
dent that for Week 50 in 1970, both explanatory variables were insignificant.
The linear formulation for that week gave:
D- = 34.46 - 0.000347 Yj + 11.11 Sn- R2 = 0.2631
(4.08) (0.000121) (5.42) F = 8.39
Thus, when the linear specification was used, it appears from the current
analysis results that household size was a relatively more important factor
in the winter. This again suggests that there is a basic amount of solid
waste which is tied more to the number of persons in a family than to their
i ncome.
The results of the regressions using solid wastes collected per house-
hold as the independent variable and household size and income as the depen-
dent variables must be compared with the results using solid wastes collec-
ted per capita as the dependent variable and income as the independent
variable. As can be seen by comparing Table 17 with Tables 12 and 15, the
77
-------
TABLE 16. SOLID WASTE - HOUSEHOLD SIZE RELATIONSHIP, 1970-1971
Week
7
19
21
26
32
36
37
43
50
Dependent
Variable
log D-J
log DI
log D-J
log Di
log Di
log Dj
log Di
log D-J
log D-J
/\
a
3.71
(0.352)
4.04
(0.035)
4.08
(0.032)
4.13
(0.035)
4.06
(0.037)
4.09
(0.039)
4.21
(0.036)
3.98
(0.039)
3.79
(0.041)
^
6
0.1503
(0.043)
0.1795
(0.042)
0.2296
(0.039)
0.2183
(0.042)
0.1972
(0.045)
0.2180
(0.047)
0.2248
(0.043)
0.2729
(0.047)
0.2659
(0.049)
Explanatory
Variable
log Si
log Si
log Si
log Si
log Si
log Si
log Si
log Si
log Si
R2
0.2057
0.2734
0.4217
0.3577
0.2859
0.3067
0.3613
0.4086
0.3757
F
12.43
18.06
35.00
26.73
19.21
21.23
27.16
33.16
28.89
78
-------
TABLE 17. SOLID WASTE - INCOME, HOUSEHOLD SIZE RELATIONSHIP, 1970-1971
Week
7
19
21
26
32
36
37
43
50
Dependent
Variable
log Di
log Di
log D-J
log DJ
log Di
log Di
log Di
log Di
log Di
Explanatory Variables
a
4.77
(0.930)
5.98
(0.891)
4.88
(0.851)
5.87
(0.900)
6.27
(0.942)
6.44
(0.989)
6.51
(0.894)
3.41
(1.04)
3.52
Log Y
-0.1293
(0.1127)
-0.2350
(0.108)
-0.0970
(0.103)
-0.2099
(0.109)
-0.2680
(0.114)
-0.2850
(0.120)
-0.2789
(0.108)
0.0690
(0.127)
0.0333
(0.132)
Log S
0.2764
(0.112)
0.4088
(0.113)
0,3242
(0.108)
0.4230
(0.114)
0.4587
(0.119)
0.4961
(0.125)
0.4969
(0.113)
0.2056
(0.132)
0.2334
(0.138)
R2
0.2273
0.3401
0.4324
0.4046
0.3609
0.3812
0.4403
0.4123
0.3766
F
6.91
12.11
17.90
15.97
13.27
14.47
18.50
16.48
14.19
79
-------
per capita formulation is far superior based on the R2 criterion. The R2
values range from 0.2273 to 0.4403 in Table 17, and from 0.7082 to 0.8617
in Table 12. This even more strongly confirms that waste volume is heavily
tied to the number of persons. However, in the per capita results, the im-
portance of family income as an explanatory variable is confirmed. It appears
that household size is strongly correlated with family income, and, in the per
capita formulation, could be used as a proxy for income. However, this was
not tested.
Race
When the fraction of blacks was used as a single explanatory variable,
the general results were insignificant both on a per dwelling unit and per
capita basis. The F values for the overall equation were insignificant. This
was true for the linear, semi-log, and log-log formulations. In this case,
the double-log specification did not do significantly better. However, there
were three exceptions to the general results. All of the exceptions were
found using a linear specification with the dependent variable defined on a
dwelling unit basis. The three weeks are shown below.
Week 37/1971: D. = 68.87 + 0.3126 B- R2 = 0.0964
(3.19 (0.138) ] F = 5.12
Week 43/1971: D, = 55.37 + 0.3005 B. R2 = 0.0884
(3.22) (0.139) n F = 4.65
Week 50/1971: D. = 45.75 + 0.2627 B. R2 = 0.1060
1 (2.54) (0.110) 1 F = 5.69
The three weeks were all in the fall or winter months. The relationship was
a positive one indicating that for these three weeks, the higher the percen-
tage of blacks, the higher the total amount of solid wastes. The dominance
of the linear formulation for the three weeks indicated that the elasticity
of waste yields with respect to the percentage of blacks was higher, the
greater the percentage of blacks in a ward in those weeks. In the previous
study, race by itself was a better predictor than in this study, being sig-
nificant in most cases. However, the relationship there was a negative one.
When both income and the percentage of blacks were used to explain the
solid waste yield by ward, then the influence of the percentage of blacks in
a ward became apparent in the double-log specification. The double-log form-
ulation again yielded the highest R2 values in all cases. In the linear
specification, the percentage of blacks was insignificant in most cases.
Income, however, was generally statistically significant. In the semi-log
formulation on a dwelling unit basis, the percentage black was generally
insignificant during the fall and winter months but significant during the
remainder of the year. This could seem to indicate that race is not a very
important factor during the winter months whereas it is during the rest of
the year. In the semi-log form, income was significant in all cases irres-
pective of whether the dependent variable was defined on a dwelling unit or
per capita basis.
80
-------
Table 18 shows the results for the double-log formulation. The explana-
tory power of the model was found to be much higher on a per capita basis
than on a per dwelling unit basis. On a per capita basis, the average R2
was 0.79, compared to 0.31 on a dwelling unit basis. The income variable
was positive and significant in all cases. The percentage of blacks varia-
ble was also positive and generally significant. The exceptions were Weeks
7 (in February) and 43 (end of October) when race was insignificant.
In analysis of the effects of income and race in the earlier 1971 study,
the linear formulation was generally better than logarithmic versions, and
the dwelling unit approach was better than the per capita approach. Both the
percentage of blacks and income variables had a positive sign. The best
results for comparable weeks from the earlier study are shown in Table 19.
The dwelling unit basis was best in all cases. Furthermore, in all but two
weeks (7 and 50) the linear formulation was best. Additionally, these were
the weeks in which the race variable was insignificant. As in the present
study, race was an insignificant factor during winter months in terms of the
amounts of solid waste generated. During the rest of the year, race was
significant in determining the volume of solid wastes generated, especially
during the summer months. Thus, both the 1971 and current studies provide
support for the differentiation of solid wastes into a "basic" and "excess"
component.
If the results of the previous and current analysis are compared in
terms of the amount of variance explained, the current study does better.
In the earlier study, the R2 values of the best specification were generally
around 0.40 as compared to around 0.80 in the present study. A significant
portion of this may be due to the availability of more current data which
has minimized the need for ad hoc estimation procedures.
Income, Income Variance, and Race Combined
It has been pointed out that one of the differences between the results
of this study and the earlier 1971 study was the effect of the income vari-
ance variable. In the earlier study, the variance was generally insignifi-
cant when income was also included in the equation, whereas it was signifi--
cant with a positive sign in the current analysis.
A set of regressions was run with income, income variance, and the
percentage of blacks as the independent variables. The results on a per
capita basis using a log-log specification are shown in Table 20. Both
income and variance were significant in all cases. However, the race vari-
able, although still positive in each week tested, was not significant in
any week. It is probable that, in the analyses with just two variables,
income and income variance and income and race, the income variance variable
was in part picking up the influence of race in the former and the race vari-
able in part picking up the variance effect of the latter. The correlation
between percent black and the income variance was 0.47 indicating that the
higher the percentage of blacks in a ward, the higher the income variance.
81
-------
TABLE 18. SOLID WASTE - RACE, INCOME RELATIONSHIP, 1970-1971
19
21
26
32
36
37
43
50
Dependent
Variable
log Di
log C{
log D{
log Ci
log Di
log Ci
log Di
log Ci
log Di
log Ci
log Di
log Ci
log Di
log C,
log Di
log C{
log Di
log Ci
a
2.57
(0.368)
-2.21
(0.373)
2.73
(0.366)
-2.06
(0.388)
2.31
(0.344)
-2.48
(0.362)
2.50
(0.370)
-2.28
(0.397)
2.63
(0.3919)
-2.15
(0.417)
-2.49
(0.411)
-2.29
(0.419)
2.55
(0.376)
-2.24
(0.416)
1.71
(0.401)
-3.07
(0.318)
1.57
(0.417)
-3.22
(0.309)
Explanatory
Log Bi
0.02290
(0.013)
0.0208
(0.013)
0.0325
(0.013)
0.0304
(0.014)
0.0253
(0.012)
0.0231
(0.013)
0.0338
(0.013)
0.0316
(0.014)
0.0350
(0.014)
0.0329
(0.015)
0.0397
(0.015)
0.0376
(0.015)
0.0404
(0.014)
0.03826
(0.015)
0.0244
(0.014)
0.0223
(0.012)
0.0305
(0.015)
0.0284
(0.011)
Variables
Log Yi
0.1366
(0.043)
0.5232
(0.044)
0.1571
(0.043)
0.5437
(0.045)
0.2135
(0.043)
0.6002
(0.042)
0.1960
(0.043)
0.5826
(0.046)
0.1707
(0.046)
0.5573
(0.049)
0.1910
(0.048)
0.5776
(0.049)
0.1984
(0.044)
0.5851
(0.049)
0.2730
(0.047)
0.6596
(0.037)
0.2673
(0.049)
0.6539
(0.036)
R2
0.1876
0.7561
0.2511
0.7538
0.3773
0.8122
0.3209
0.7705
0.2558
0.7348
0.2830
0.7467
0.3348
0.7542
0.4168
0.8718
0.3916
0.8752
F
5.43
72.85
7.88
71.94
14.24
101.65
11.10
78.90
8.08
65.10
9.27
69.29
11.83
72.12
16.80
159.78
15.12
164.77
82
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TABLE 19. BEST SPECIFICATIONS FOR INCOME AND RACE, 1969
Pounds of
Waste Per
Linear (L), Household
Semi-log (SL) or (D) or Per
Week Double-Log (DL)
7
19
21
24
32
37
43
50
DL
L
L
L
L
L
L
SL
Capita (
D
D
D
D
D
D
D
D
C)
0.048
(0.957)
14.95
(9.09)
11.56
(8.14)
12.74
(8.95)
13.20
(8.58)
14.28
(8.40)
-10.27
(7.67)
-145.62
(40.11)
Bi Y
0.404
(0.108)
0.0056
(0.00097)
0.0054
(0.0009)
0.00563
(0.00095)
0.00596
(0.00091)
0.00446
(0.00089)
0.00816
(0.00082)
21.47
(4.52)
&? B
0.014
(0.010)
17.98
(5.44)
17.42
(4.87)
14.47
(5.35)
13.99
(5.13)
9.20
(5.02)
11.88
(4.58)
-4.86
(0.435)
R*
0.2405
0.4153
0.4554
0.4392
0.4950
0.3728
0.7256
0.3583
F
7.44
16.69
19.65
18.41
23.04
13.97
62.13
13.12
83
-------
TABLE 20. SOLID WASTE - INCOME, RACE, VARIANCE RELATIONSHIP, 1970-1971
6
Explanatory Variables
Week
7
19
21
26
32
36
.37
43
50
Dependent
Variable
log Ci
log Ci
log Ci
log C.j
log Ci
log Ci
log q
log Ci
log Ci
a
-0.7321
(0.611)
-0.7222
-1.42
(0.619)
-1.06
(0.673)
-0.8174
(0.706)
-0.8426
(0.701)
-0.7836
(0.695)
-2.640
(0.563)
-2.859
(0.549)
Log Y
0.3877
(0.061)
0.4218
(0.065)
0.5039
(0.062)
0.4702
(0.068)
0.4354
(0.071)
0.4450
(0.070)
0.4524
(0.070)
0.6200
(0.056)
0.6212
(0.055)
Log 8
0.00134
(0.014)
0.0129
(0.015)
0.00933
(0.014)
0.0155
(0.016)
0.0154
(0.016)
0.0186
(0.016)
0.0192
(0.016)
0.0166
(0.013)
0.0237
(0.018)
Log V
0.2462
(0.085)
0.2214
(0.089)
0.1748
(0.085)
0.2011
(0.092)
0.2213
(0.096)
0.2409
(0.096)
0.2409
(0.095)
0.0721
(0.077)
0.0594
(0.075)
R2
0.7949
0.7331
0.8282
0.7926
0.7620
0.7773
0.7843
0.8742
0.8759
F
59.41
55.34
73.89
58.61
49.08
53.52
55.76
106.53
109.18
84
-------
The correlation between income and income variance was -0.64. The higher
the income in a ward, the lower the income variance. The three-independent-
variable analysis suggests that the much more significant variable is income
variance, and probably not race per se. The lower income fraction of the
families in a ward contribute more wastes than are indicated by the_income
relationship based on median ward incomes. This fraction is predominantly
black, but it is income variance that has the greatest explanatory power.
SUMMARY OF RESULTS, COMPARISON WITH 1971 STUDY AND WITH
OTHER RESULTS IN THE LITERATURE, AND CONCLUSIONS
In this subsection, the results of this study are first summarized.
The results are then compared with results from the 1971 Sheaffer-Tolley
study and with results from other solid waste socioeconomic studies that
have appeared in the literature. Finally, conclusions are summarized.
Summary of Findings
In general, the findings of the current study are that solid waste
volume can be best explained on a per capita basis using a double-log
formulation for regression equations. The per capita double-log formulation
is generally best by both R2 and F statistics criteria. The double-log
formulation implies a constant elasticity with respect to explanatory vari-
ables. Income has a strong positive effect, as does income variance. However,
percent black has no significant effect when income, income variance, and
percent black are considered together. In the 3 explanatory variable re-
gressions, income elasticities range between about 0.4 and 0.6 and income
variance elasticities between about 0.06 and 0.24 for the 9 weeks tested.
R2 value, the percent of solid waste collection variance explained, ranges
from 0.76 to 0.88.
The results in somewhat more specific detail are as follows:
1. Solid waste volume collected by the City of Chicago is best
explained on a per capita basis. In all cases, this was superior
to explanation on a per household basis, even with household size
included as an explanatory variable.
2. In most cases, waste volume is best explained using a double-log
formulation for regressions. This formulation implies a constant
waste volume elasticity with respect to esplanatory variables
over their range of variation.
3. On a per capita basis, significant positive relationships were
always found between waste volume and ward median family income.
The results, for both simple income regressions and for multiple
regressions, with income variance and percent black as the other
explanatory variables, are presented in Table 21, and are shown
in Figure 14. Elasticities range between 0.38 and 0.66. Since
these elasticities are based on cross-sectional data, they tend to
be long-run elasticities. The range thus does not cover short-run
elasticities, which would probably tend to be lower.
85
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TABLE 21
PER CAPITA WASTE VOLUME ELASTICITIES WITH RESPECT TO
FAMILY INCOME, B(log Y), FROM SIMPLE AND MULTIPLE REGRESSIONS
9 WEEKS TESTED
Week
7
19
21
26
32
36
37
43
50
Income
3(log Y)
0.5056
0.5180
0.5806
0.5559
0.5295
0.5458
0.5527
0.6408
0.6300
Only
R2
0.7439
0.7294
0.7470
0.7139
0.7207
0.7245
0.7359
0.8617
0.8582
Income &
Variance
3(log Y)
0.3848
0.3938
0.4837
0.4366
0.4020
0.4047
0.4107
0.5840
0.5697
R2
0.7948
0.7796
0.8266
0.7882
0.7574
0.7710
0.7777
0.8698
0.8676
Income
& Race
3(log Y)
0.5232
0.5437
0.6002
0.5826
0.5573
0.5776
0.5851
0.6596
0.6539
R2
0.7561
0.7538
0.8122
0.7705
0.7348
0.7467
0.7542
0.8718
0.8752
Income, Variance
& Race
3(log Y)
0.3877
0.4218
0.5039
0.4702
0.4354
0.4450
0.4524
0.6200
0.6212
R2
0.7949
0.7831
0.8282
0.7926
0.7620
0.7773
0.7843
0.8742
0.8769
86
-------
Income
elasticity
0.7 f
Code Independent variables
0.6 »
0.5 ,
0.4
0.3
o
x
*
Income only
Income, variance
Income, percent black
Income, variance, percent black
*
o
1
f
*
B * .* »
*
0
0
<
1
1
p
0 0
0
0
r
i
i
i
r
i
>
1
r )
i
4
I
f
7 19 21 26 32 36 37 43 50
Week
Figure 14. Per capita waste volume elasticities with respect
to family income from simple and multiple regres-
ions for 9 weeks tested.
87
-------
a. When regressing solid waste volume on income only, on a per
capita basis the double-log formulation was best in 6 of 9
weeks analyzed, and the semi-log formulation was best in 3.
R^ values, measures of the proportion of variation explained,
range from 0.71 to 0.86 and income elasticities from 0.48 to 0.64.
b. When regressing per capita volume on income and income vari-
ance, the double-log formulation was best in all weeks. R2
values ranged from 0.76 to 0.87 and income elasticities from
0.38 to 0.58.
c. When regressing per capita volume on income and race, the
double-log formulation was always best in terms of R2, with
the R2 values ranging from 0.73 to 0.88 and income elasticities
from 0.52 to 0.66.
d. When regressing per capita volume on all three variables, income,
income variance, and percent black, the same pattern emerged.
R2 values for the double-log formulation ranged from 0.76 to
0.88, and income elasticities ranged from 0.39 to 0.62.
On a per household basis, the double-log formulation explained best
in all of the 9 weeks tested, both when regressing per household
volume on income only and when regressing per household volume on
income and household size. However, income had a positive effect
only in the simple regression, and the R2 values were consistently
lower than in regressions on a per capita basis.
a. When regressing per household volume on income only, a signifi-
cant positive income effect was found in each week, but R* values
ranged from 0.14 to 0.38 compared to 0.71 to 0.86 for the re-
gression of per capita volume on income only.
b. When regressing per household volume on income and household
size, in 7 of the 9 weeks, including the 4 weeks when the income
effect was significant, the income effect was negative. However,
it was concluded that this was a spurious result, probably due
to correlation between the independent variables income and house-
hold size. The R2 values in these household regressions were
considerably lower than in the per capita volume against income
regressions, where income had a highly significant positive effect.
The R2 values ranged from 0.71 to 0.86 for the per capita regres-
sions, compared to 0.23 to 0.44 for these household regressions.
On a per capita basis, income elasticities were highest in the fall
and late fall/early winter (October and mid-December), low in mid-
winter (February), and lower in the summer than in the spring and
fall. It appears that this may represent a seasonality in income
elasticities, particularly since this tends to repeat a pattern ap-
pearing in the 1968-1969 results, to be discussed in the next sub-
section in which results are compared. The low mid-winter volume may
suggest that there is a basic, year-round volume of wastes, represen-
ted by the mid-winter volume, that is relatively less sensitive to
88
-------
income than "excess" volumes in other parts of the year, except
possibly mid-summer.
6. Both on a per capita and per household basis, significant, positive
relationships were always found between waste volume by ward and
ward income variance. Also, the double-log formulation was always
best in terms of explanatory power. These results were obtained
when regressing waste volume on income variance only, and when
regressing waste volume on income and other variables. The elastic-
ities with respect to income variance for both simple and multiple
regressions are reproduced in Table 22.
a. When regressing volume on income variance only R2 values
for the per capita, double-log formulation ranged between
0.48 and 0.56. The elasticity of volume with respect to
income variance ranged between 0.61 and 0.68.
b. When regressing volume on income variance and income, R2
values, as reported under 3b above, ranged between 0.76 and
0.87, but the income variance elasticities were reduced
considerably, ranging between 0.12 and 0.29.
c. When regressing volume on all three variables, R2 values,
as reported under 3d above, ranged between 0.76 and 0.88,
and the income variance elasticities ranged between 0.06
and 0.25.
7. When it alone was the explanatory variable, percent black was a
significant explanatory variable in only 3 of 9 weeks. In these
weeks, it showed a positive effect on per household waste volume
in the linear formulation. It became significant in 7 of 9 weeks
for explaining per capita volume when both income and percent
black were used as the explanatory variables in the double-log
formulation, with a positive effect on both per capita and per
household volume in all weeks. However, percent blacks, though
still positive in its effect, was not a significant variable in
any week when income variance, which was positively correlated
with percent black, was added to the regression equations. The
per capita elasticities for the two multiple regressions in the
double-log form are reproduced in Table 23.
Comparison with 1971 and Other Study Results
The current study confirms the 1971 Sheaffer-Tolley study in at least
one major respect. Income has a major effect on per capita waste volume.
Much higher R2 values were obtained for the simple relationship between
income and per capita waste volume in 1970-1971 than in 1968-1969, ranging
from 0.71 to 0.86 for the weeks tested in 1970-1971 compared to 0.12 to 0.57
for the weeks tested in 1968-1969. The median income elasticity was about
0.5 in the earlier study, about 0.55 in this study. The comparative results
are provided in Table 24 and are shown graphically in Figure 15.
The higher R2 values are attributed to having better socioeconomic data,
89
-------
TABLE 22
PER CAPITA WASTE VOLUME ELASTICITIES WITH RESPECT TO
INCOME VARIANCE, 3(log V), FROM SIMPLE AND MULTIPLE
REGRESSIONS FOR 9 WEEKS TESTED
Variance, Income,
Variance Only Variance & Income & Percent Black
Week
7
19
21
26
32
36
37
43
50
3(log V)
0.6117
0.6270
0.6552
0.6571
0.6416
0.6723
0.6797
0.6666
0.6601
R2
0.5601
0.5500
0.5240
0.5370
0.5349
0.5572
0.5608
0.4797
0.4849
3(log V)
0.2498
0.2567
0.2003
0.2465
0.2635
0.2917
0.2935
0.1174
0.1243
R2
0.7948
0.7796
0.8266
0.7882
0.7574
0.7710
0.7777
0.8698
0.8676
3(log V)
0.2462
0.2214
0.1748
0.2041
0.2213
0.2409
0.2409
0.0721
0.0594
R2
0.7949
0.7831
0.8282
0.7926
0.7620
0.7773
0.7843
0.8742
0.8769
90
-------
TABLE 23
PER CAPITA WASTE VOLUME ELASTICITIES
WITH RESPECT TO PERCENT BLACK, 3(log B),
FROM MULTIPLE REGRESSIONS FOR 9 WEEKS
Percent Black
Income
Percent Black, Income,
Variance
Week
7
19
21
26
32
36
37
43
50
0(log B)
0.0208
0.0304
0.0231
0.0316
0.0329
0.0376
0.03826
0.0223
0.0284
R2
0.7561
0.7538
0.8122
0.7705
0.7348
0.7467
0.7542
0.8718
0.8752
B(log B)
0.00134
0.0129
0.00933
0.0155
0.0154
0.0186
0.0192
0.0166
0.0237
R2
0.7949
0.7831
0.8282
0.7926
0.7620
0.7773
0.7843
0.8742
0.8769
91
-------
TABLE 24
PER CAPITA WASTE VOLUME ELASTICITIES WITH RESPECT TO
INCOME, $(1og Y), AND R2 VALUES, SIMPLE REGRESSION RELATIONSHIPS
1968
Week
7
19
21
24
26
32
36
37
43
46
50
edog Y)
0.6977
0.6723
0.2911
0.5213
0.4712
0.7278
0.3367
R2
0.4369
0.3789
0.1229
0.3383
0.2298
0.4281
0.1246
1969
B(log Y)
0.376
0.4822
0.483
0.542
0.432
0.5768
0.5293
0.9840
0.4889
R2
0.1674
0.2614
0.2613
0.3222
0.2219
0.3516
0.2770
0.5745
0.2509
1970-1971
edog Y)
0.5056
0.5180
0.5806
0.5559
0.5295
0.5458
0.5527
0.6408
0.6300
R2
0.7439
0.7294
0.7999
0.7544
0.7082
0.7245
0.7359
0.8617
0.8582
92
-------
Income elasticity
(Ci)
CO
1 . U
0.8
0.6
0.4
0.2
0-
R2
1.0,
0.8
0.6
0.4
0.2
Q
•
^
1
iB 20 3t)
I
\
I
<
I
I
1
1
I
i
1
I
1
1
t
1
1
'
1
1
I
. i
1
4b 56
1968
'
4
'
I
1
|
1 |
1 .1
1
T
1
i
1
1
1
'
'
1
I . .
1 !
| |
1
'
1
1
I
1
it) 2fo 3b 4fo 5
i
t
1
t
1
'
,
b ib 2"6 3B 40 5
!)
1969 1970-1971 Week
Figure 15. Per capita waste volume elasticities with respect to income and R2, 1968, 1969, and 1970-1971,
-------
that of the close-in 1970 Census, for the analysis using 1970-1971 waste
volume. However, while the 1970 socioeconomic data were better, the data for
the two studies revealed similar general characteristics with respect to ward
population, percent of households served, family income, income variance, and
percent black, with some shifting among wards. (Percent black, the race vari-
able reported in the 1970 Census, rather than percent non-white as reported
in the 1960 Census, was used in this study. The difference is taken to be
negligible in comparing results.)
In addition, the waste volume data, while showing somewhat higher col-
lection rates per capita in 1970-1971 than in 1968-1969 (to be expected with
increasing incomes given the strong income-waste volume relationship), reveal-
ed similar patterns in the two periods, generally high collection volumes in
the summer, low in the winter.
The 1970-1971 study also tends to confirm a seasonality in income elas-
ticities, with waste volume more sensitive to income in the spring and fall,
and less sensitive in mid-winter and mid-summer. This tends to confirm an
hypothesis put forth in the 1971 study that there is a basic year-round
volume of wastes, represented by the mid-winter volume, that is, less sensitive
to income than is "excess" wastes, except possibly in mid-summer. The season-
al pattern can be seen in Figure 15.
There were, however, some major differences between this study and the
1971 study results. There were differences in signs, statistical significance,
and seasonal patterns of effects, and in the unit basis (per capita or per
household) and form (log-log, semi-log, or linear) of the relationships that
best explained the variance in waste collection. The differences are describ-
ed and possible reasons for the different results are discussed below.
Differences in Sign, Significance, and Pattern
The variance of income distribution, taken as a single explanatory
variable, was significant in most cases in the 1971 study, and its effect
on volume was negative. In the current study, its effect was significant
in all cases, but positive. In the 1971 study, the effect of variance became
insignificant in most weeks when both income and variance were taken together
in regressions, though still negative. In this study, when income was added,
the effect of variance was reduced, but its effect remained significant and
positive.
The percent black variable when taken alone in the current study was
usually insignificant, but in 3 weeks in which it showed a significant effect,
this effect was positive. In the 1971 study, on the other hand, the percent
nonwhites taken alone generally showed a negative impact. This was attri-
buted to the relationship between income and race. (Possible reasons for
differences between the studies are discussed below.) Both studies showed
that when income and race were taken together, the effect of race tended to
be positive. Finally, the current study showed the effect of race to be
insignificant in all cases when income, income variance, and race were all
taken together. The earlier study did not proceed to this point. The
earlier study showed, for both 1968 and 1969, a seasonal pattern in income
94
-------
and race sensitivity of weekly waste output. The income and race patterns
were similar. There were low or negative race effects in the winter, high
positive race effects in the rest of the year. These race effect patterns,
however, did not repeat, at least in any clear-cut way, in the current study
results, although, as indicated earlier, this seasonal pattern tended to
repeat with respect to income.
In the current study, household size alone had a significant positive
effect on per household waste collection. In the earlier study, significant
effects, which were positive, were found in only 2 of 16 weeks. In the
current study, when income was added as a variable, the effect of household
size on waste collection remained positive, but was significant in only 4 of
9 weeks. In the 1971 study, the addition of income tended to increase the
significant positive relationship between waste collection and household size.
In the current study, when income was added, its effect on per household waste
collection was negative in 7 of 9 weeks, and negative in the 4 weeks when
significant. In the 1971 study, the effect of income remained positive, and,
indeed, for the weeks reported, showed higher positive effects than when
taken alone.
Differences in Basis and Form
In the current study, solid waste collection variation was always better
explained on a per capita than on a per household basis. In the 1971 study,
explanation was generally better on a per household basis. In the current
study, the log-log formulation explained waste collection variation best in
all cases where per household collection was the independent variable, and
in all multiple regressions and in most simple regressions where per capita
collection was the independent variable. The exceptions were in 3 of 9 weeks
for simple per capita waste-income regressions, when the semi-log formulation
was best, and in 3 weeks when there was a statistically significant relation-
ship between race and per capita waste volume. In the race regressions, it
was the linear form that showed the significant relationships. In the earlier
study, the linear form was generally best.
Possible Reasons for Differences
The fact that solid waste collection volume was always explained better
on a per capita basis in this study, whereas the opposite was generally true
in the 1971 study, and the higher R2 values can be explained by the fact that
better data, particularly on ward population, were available for the current
study. Better data may also be one explanation for the fact that the double
log formulation was almost always better in the current study.
The one striking difference in the effect of independent variables, the
positive rather than negative or insignificant effect of income variance,
could be due to transitory income effects. Variance was highly negatively
correlated with income. It could be that the low incomes were due more to
transitory factors in 1970-1971 than in 1968-1969. This could be due to
business cycle factors or to better data on transitory factors applicable to
the analyzed data. Since waste volume would tend to vary more with permanent
rather than transitory income, a positive relationship between volume and
95
-------
income variance would result when transitory factors were overriding. A
policy implication would be that in forecasting demand, the reasons for any
projected income variance as an explanatory variable would have to be con-
sidered. There is an alternative way of looking at essentially the same
explanation. The current study showed that percent black and income variance
in the current study picked up what appeared as a percent black effect in the
1971 study, and, possibly for the same transitory income reason.
Comparison with Results Reported
Elsewhere in the Literature
As reported in Section II of this paper, Wertz (1976) and Downing (1975)
both found positive effects of income on waste collection, with elasticities
less than 1.0. The elasticities were somewhat lower than found in this study,
0.279, 0.272, and 0.39 compared to a median of a little over 0.5 in the cur-
rent, and about 0.5 in the previous 1971 study of Chicago collection data.
Richardson and Havlicek also (1976, 1975, and 1974) found a positive relation-
ship between income and waste collection. McFarland et al (1972), on the other
hand, found no significant effect of income. Except for this 1972 study, the
finding of a positive income elasticity, generally of less than 1.0, tends
to be confirmed.
Richardson and Havlicek found that waste collection was significantly
related to household size. This confirms the same finding in this study.
They also found that for total wastes, the effect of percent black was in-
significant, the same finding as in this study when controlling for income
and income variance. They further found that income had a less significant
effect on waste volume in the winter than in the rest of the year. This may
tend to confirm the finding of a similar seasonal pattern with respect to
income elasticity in this and the 1971 study, with low elasticities in mid-
winter.
Conclusions
The main conclusion that can be reached from this study is that differ-
ences in median family income can explain most of the variation in per capita
solid waste collection. The added explanatory value of other variables test-
ed were found to be relatively minor. These include income variance and per-
cent black, as well as an alternative mode of explanation, using per house-
hold collection as the dependent variable and income and household size as
explanatory variables. When the three independent variables for explaining
per capita waste collection were taken together, percent black was not a
significant explanatory variable. Income factors, median income and income
variance with the latter relatively minor, were indeed the only significant
explanatory variables.
The income effect on per capita waste volume is best explained using
a constant elasticity formulation. The elasticity is less than 1, ranging
between about 0.4 and 0.6, indicating that waste generation increases less
than proportionally with income.
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There still appears to be a seasonality in income elasticity, with
lower elasticities in mid-winter and mid-summer and higher elasticities
the rest of the year. The low winter values may suggest that there is a basic
year-round volume of waste generation that is less sensitive, except in mid-
summer, to income than are excess volumes generated in the rest of the year.
The low mid-summer elasticity might be explained as a weather effect, with
soft drink, beer, and fruit consumption less affected by income during very
hot weather. Another explanation could be that income varies seasonally,
with earnings among low income groups at a high level in mid-summer.
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SECTION IV
AREAS OF NEEDED RESEARCH AND RECOMMENDATIONS
FOR RESEARCH PROCEDURES AND METHODOLOGY
In this section, areas of needed research in the economics of solid
and hazardous waste management are identified, and recommendations are made
for procedures and methodologies in this research. These needs are des-
cribed, and, in addition, the promotion of programs for improving the
general data base for both research and waste management itself is recom-
mended.
RESEARCH NEEDS
Based on purposes to be served, two kinds of research are needed in
the solid waste management field. One is research of general applicability
to various solid waste management systems, and another is research of
specific applicability to the management and operation of particular systems.
The two are not always distinct in practice, since results of specific
research on specific systems are often needed for generalization, or since
such results can often be generalized. Nevertheless, the discussions and
recommendations in this section will focus on needs for research on the
economics of solid and hazardous waste management of general applicability,
keeping in mind that such research, to be useful, must always be directed
toward ultimate specific applicability. It should provide guidance to
system managers concerning where the payoffs might be, what modifications
should be made in the quantity and quality of services offered and in the
financing of these services, what records should be kept, and the pro-
cedures for specific research to make specific determinations.
Most of the general areas of research needs have been indicated, and
in some cases discussed, in the preceding sections of this paper. This
section largely reorganizes these needs under one heading. However, some
new ideas are introduced.
For the purpose of recommending areas of needed economic research, it
is not enough to merely enumerate the economic questions that solid waste
managers might have or might need to ask and answer. What is needed is a
set of priorities. The priorities depend on what the major questions are,
answers to which would have the highest payoff.
One important question, and a question of major concern, deals with the
rising costs of solid waste collection/disposal. Can there be a payoff in
holding down these costs in ways that take into account the economic con-
siderations of more than a strictly engineering nature in providing solid
wastes management services? The rising costs are largely associated with
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rising input costs, particularly labor, the real cost of which continues to
rise and rising wastes volumes. However, in addition, the costs themselves
are affected by the character of the services rendered, including frequency
of service, which adds to costs both directly and by increasing volumes, and
by demands for a better environment. It is recommended that a high priority
be placed on determining the possible quantitative and other effects of
various economic approaches for reducing these volumes and associated costs,
and to reducing these costs in ways that would increase the net value of
the overall services to the households and to the community served. For
answering these questions, it is recommended that solid-waste-service demand
and supply functions be estimated, relating quantities of service to price
and to other factors that affect demand and supply. In this research, guides
would be developed for application of the research results to research and
to decisions in specific areas. In addition, guides would be provided for
systematically collecting the needed research data.
Volumes of wastes collected and associated waste management services
can only be substantially decreased if there are alternatives to waste
generation and/or alternatives to community collection for waste disposal.
The shape of the demand functions for collection/disposal depend on these
alternatives. These alternatives include using returnable bottles, sink
disposals, and the like. Thus, in addition to research in the area of
demand/supply for waste collection/disposal, it is recommended that research
be conducted in the area of supply functions for these alternatives and
other matters with respect to alternatives. Presently, the supply price for
returnable containers other than returnable soft drink bottles and possibly
a few others (containers for moving vans are returnable) is in effect infini-
ty. The household can't find returnable food jars, returnable other-beverage
or pharmaceutical bottles, or returnable shoe boxes. With rising collection/
disposal costs, would other returnable containers be economic?
A sink disposal decreases not only volume but also frequency-of-service
needs. Households with lower incomes and receiving twice-a-week collection
service might not install sink disposals because they d£ receive twice-a-week
service and thus have a reduced need for sink disposals, and twice-a-week
service may be_ provided because the households do not have disposals. This
cycle might be" broken if the community were to fund the installation of dis-
posals and amortize this investment through savings achieved by being able
to go to once-a-week service where sink disposals are installed. There are
advantages of liquid disposal of wastes, particularly of food wastes, to
the community as well as to individuals, and these advantages could be "used"
to justify partial subsidizing of disposals. These advantages would, of
course, have to be compared with added sewer and sewage treatment system
costs.
Additional areas of research that are recommended for priority consid-
eration include: estimation of demand functions for community cleanliness,
estimation of supply functions for achieving community cleanliness, benefit
cost estimation of a change from flat to other forms of financing, including
full marginal cost pricing, and estimation of the supply functions and demand
functions (environmental damage functions) for various solid wastes disposal
requirements, or stated alternatively, the determination of the benefits and
99
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costs of existing and modified standards. Of particular concern would be
the potential benefits of greater control over possible effects of hazardous
wastes that might be introduced into residential solid wastes, estimated
from hazardous waste damage functions.
In estimation of demand functions for community cleanliness, it might
be possible to develop and assign measures of cleanliness, for example,
using an index ranging from 0 for a continuous mess to 100 for an essentially
litter-free community, and determine by multiple regression analysis if and
to what extent this measure has an effect on land values. Such a land-value
methodology has been used in developing demand functions for air quality.
In estimation of supply functions for achieving community cleanliness, rela-
tionships between an index of cleanliness and various measures of input, such
as expenditures, to achieve and maintain cleanliness might prove rewarding.
The interactions among various inputs in the production function would be
important.
All of the above priority economic research needs can be restated in an
outline of questions requiring research that can be asked by solid wastes
system managers. Since the focus of research should be on ultimate appli-
cability, it is deemed useful to suggest such an outline:
a. What collection services and level of collection services should
be provided?
(1) What frequency of service should be provided? Should this be
decided on a systemwide or individual collection area basis?
(2) Should curb or back-door service be provided? If back door,
should it be optional, and if optional, should it be optional
at each collection?
(3) Should unlimited-quantity service be provided, or should con-
sideration be given to approaches that might limit or reduce
quantities to be collected?
(4) Should combined, same frequency, and location of collection
be offered for all residential solid wastes, or should
separate collection be offered?
b. What degree of community cleanliness, in terms of freedom from
litter and other pollution from solid wastes, is demanded, and
how is this best achieved?
(1) What are the marginal benefits (what is the demand function
for) different degrees of cleanliness?
(2) What are the various means for achieving cleanliness and
what are the marginal cost functions (cost per unit of clean-
liness achieved) of the various means?
(3) What is the optimum level of cleanliness and what are the
100
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optimum levels of input of the various means, given these
demand and cost functions?
c. What disposal services and level of services should be provided?
(1) Should there be processing of wastes prior to ultimate dis-
posal (e.g. incineration)?
(a) What are the benefits of processing in terms of reducing
transportation, ultimate disposal, or other costs?
(b) What are the costs of processing, including economic
costs (net of any energy values obtained) and environ-
mental costs (air pollution)?
(2) What are the options for ultimate disposal? What is the
least-cost alternative, considering environmental costs?
For sanitary land-disposal, are the standards set for this
disposal optimum?
(a) What are the marginal environmental benefits of added
efforts to protect against environmental damages from
the disposal operation? These might include benefits
from:
(i) More frequent covering or burying of wastes.
(ii) More careful site selection, for example, to
find less permeable soils.
(iii) More remote sites, for example, to remove the
site farthur from population centers, or to
remove farther from groundwater sources.
(iv) More care to separate off and neutralize the
possible health and safety effects of potentially
hazardous wastes that might be introduced into
residential solid wastes.
(b) What are the marginal costs associated with achieving
the marginal benefits?
d. How should collection/disposal services be financed?
(1) What are the alternative ways of financing collection/
disposal services? These may include:
(a) Flat charges based on average costs of services
actually rendered over a period of time.
(b) Incremental user charges, based on the incremental costs
of various collection/disposal services rendered.
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(c) Some combination of flat and incremental charges.
(2) What are the advantages/disadvantages (benefits-costs) of
alternative financing methods compared to existing financing
methods, for example incremental compared to flat charge
methods?
(a) What are the estimated changes in the amounts of the
various services in shifting to incremental user charges?
(b) What are the direct benefits (estimated direct cost
savings) from reducing these amounts?
(c) What are the direct costs to households (estimated
loss in benefits) from reducing these amounts?
(d) What are the indirect costs from shifting to incremental
charges?
(i) What are the added (or reduced) costs of
administering such charges?
(ii) What are the added environmental cleanliness
costs?
(iii) What are the tax/revenue sharing costs?
e. How can service requirements be best projected for planning and
decision purposes?
(1) What are the various projection methodologies and how would
they be implemented?
(2) Which projection methodologies are the more reliable in
terms of accuracy? Which in terms of greater flexibility
for different conditions or different modes of operation?
(3) Which projection methodology or methodologies should be used
for the particular system? If more than one, could there
be irreconcilable differences in results, and how would this
be handled?
f. What specific-system research is needed to make all of the above
determinations?
(1) What are the specific questions to be asked and answered?
(2) What are the research procedures?
(3) What are the data needs?
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RECOMMENDATIONS FOR RESEARCH PROCEDURES AND METHODOLOGY ,
There are three basic research approaches that can be used in economic
research. These are analysis of data from existing and operating systems,
controlled experimentation, and simulation analysis (or production function
estimations from cost information). The basic approach in analyzing data
from existing systems is regression analysis.
For reasons given below, regression analysis is recommended as the
generally preferred research approach for determining relationships in the
solid wastes field. Controlled experimentation and simulation analysis can
be used as alternative or supplementary approaches, particularly where insuf-
ficient data are available for obtaining significant regression results.
The analysis of basic relationships would be followed, for some management
questions, with benefit-cost analysis.
Regression analysis and controlled experimentation have the advantage
of equal applicability to demand and cost function estimation. In addition,
they are equally applicable to the estimation of other relationships, such
as between weight and volume as measures of quantities of solid waste. On
the other hand, while simulation analysis can be applied in cost function
estimations, it is severely limited in its applicability to demand estima-
tion. It is applicable where demand for a service is limited by the availa-
bility of alternative means for achieving the same ends. These means can
sometimes be simulated from cost information, and their effects on demand
for the service can thus be estimated. However, this approach cannot fill
the total needs for estimating demand.
With respect to the relative merits of regression analysis and con-
trolled experimentation, where sufficient data are available, regression
analysis has an advantage over controlled experimentation in that the data
needed for analysis are generated from the whole world of actual "experiments".
Generally, a controlled experiment, which is budget and time constrained, can-
not produce the variation in and quantity of data that the "real world" ex-
periments tend to produce. In controlled experiments, there may be a real
problem in obtaining enough variation and quality of data to produce compre-
hensive and significant results. On the other hand, to obtain significant
results from regression analysis, sufficient data must be available.
In the solid wastes field, even where there have been "real world"
experiments, regression analysis tends to face the problem that needed data
generally have not been collected. This has tended to limit the data base
for general research. It also tends to preclude the application of general
research results to particular systems since the particular systems lack
needed data. Therefore, it is strongly recommended that programs for regular
collection of and maintenance of records on quantities and costs be promoted.
Until such general data are available, general research projects will, to a
large extent, have to include specific data collection programs as a part of
the projects.
As for procedures, there are basically three general regression proce-
dures: cross-section analysis, time-series analysis, and combined cross-
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section/time-series analysis. It is recommended that first emphasis be
placed on cross-section analysis. For time-series analysis, a period of
years would be needed in which to collect the data required. The basic
research methodologies to be considered would include ordinary least-squares
multiple regression analysis, particularly for supply/demand analysis. In
determining whether a particular action should be taken, such as shift from
flat charges to incremental charges or the setting of a standard, benefit-
cost analysis would be essential followup to supply/demand analysis.
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REFERENCES
Aitchison, J. and J. A. C. Brown. The Lognormal Distribution, University
of Cambridge, Department of Applied Economics Monography, No. 5.,
Cambridge: University Press, 1957.
Clark, Robert M., Betty L. Grupenhoff, George A. Garland, and Albert J. Klee.
1971. "Cost of Residential Solid Waste Collection," Journal of the
Sanitary Engineering Division, Proceedings of the American Society of
Civil Engineers, 97, SA5, pp 563-568, October 1971.
Department of Development and Planning, Chicago Statistical Abstract,
Part 4, 1970 Ward Summary Tables, Chicago, 1973.
Department of Streets and Sanitation, Unpublished Solid Waste Data by Wards,
Chicago, 1971.
Downing, P. B. 1975. "Intra-Municipal Variations in the Cost of Residential
Refuse Removal." Mimeo. Virginia Polytechnic Institute and State
University, Blacksburg, Virginia.
Ernst, Ulrich. 1975. Evaluation of the Feasibility and Economic Implica-
tions of Pricing Mechanisms in Solid Waste Management. Abt Associates,
Inc., Cambridge, Massachusetts. U.S. Environmental Protection Agency,
January 1975.
Goddard, Haynes C. 1975. Managing Solid Wastes. Praeger Publishers, Inc.
New York.
Gueron, Judith M. 1972. "Economics of Solid Waste Handling." In Public
Prices for Public Products, ed. Selma Mushkin. The Urban Institute,
Washington, D.C.
Hirsch, Werner Z. 1965. "Cost Functions of an Urban Government Service:
Refuse Collection," Review of Economics and Statistics. 47, 87-92,
1965.
Larsen, Julie, L. 1976. Solid Waste Management Available Information,
Materials - Total Listing, January 1966 to June 1976.103 pp.U.S.
Environmental Protection Agency, September 1976.
McFarland, J. M. et al. 1972. Comprehensive Studies of Solid Wastes Manage-
ment. Final Report. Sanitary Engineering Research Laboratory, College
of Engineering and School of Public Health, Report No. 72-3. Berkeley,
University of California, May 1972.
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Quon, Jimraie E., Masaru Tanaka, and Abraham Charnes. 1968. "Refuse Quanti-
ties and Frequency of Service," Journal of the Sanitary Engineering
Division. Proceedings of the American Society of Civil Engineers, 94,
403-420, April 1968.
Richardson, Robert A. and Joseph Havlicek, Jr. 1976. "Economic Analysis of
the Composition of Household Solid Wastes." (In review process for
publication in Journal of Environmental Economics and Management.)
. 1975. An Analysis of the Generation of Household Solid Wastes from
Consumption. Agricultural Experiment Research Bulletin No. 920,
Purdue University, West Lafayette, Indiana. March 1975.
• 1974. "An Analysis of Seasonal Household Waste Generation," Southern
Journal of Agricultural Economics, pp 143-155, December 1974.
Saleh, Abdullah A. and Joseph Havlicek, Jr. 1975. "Household Solid Waste
Associated with Food Consumption Activities," pp 9-18, Southern Journal
of Agricultural Economics, December 1975.
Savas, E. S. 1977. The Organization and Efficiency of Solid Waste Collection.
D. C. Heath & Co., Lexington, Massachusetts.
Sheaffer, John R. and George S. To!ley. 1971. Decision Making and Solid
Waste Disposal, Center for Urban Studies, University of Chicago, April
30, 1971.
• 1973. Socio-Economic Factors Affecting Demand for Municipal Collec-
tion of Household Refuse. A condensation by Battelle, Columbus Labora-
tories of Sheaffer and Tolley (1971), Center for Urban Studies,
University of Chicago, U. S. Environmental Protection Agency, August
1973.
Stevens, Barbara. 1977. Pricing Schemes for Refuse Collection Services:
The Impact on Refuse General ion. Columbia University School of Business
Research Paper 154.
U. S. Census Bureau, Census Tract Data, City of Chicago, Washington, D.C.,
1973.
U. S. Environmental Protection Agency. 1976. Decision-Makers Guide in Solid
Waste Management, second edition.
University of Oregon. 1965. Refuse Collection and Disposal, A Survey of
Practices in 164 Oregon Cities. Bureau of Municipal Research Service
Information Bulletin No. 145, March 1965.
Wertz, Kenneth L. 1976. "Economic Factors Influencing Households' Produc-
tion of Refuse," Journal of Environmental Economics and Management,
2, 263-272, April 1976.
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/8-78-013
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
ECONOMICS OF MUNICIPAL SOLID WASTE MANAGEMENT:
THE CHICAGO CASE
5. REPORT DATE
August 1978 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT
G. S. To!ley, V. S. Hastings, and G. Rudzitis
9. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Chicago
Department of Economics
1126 East 59th Street
Chicago, Illinois 60637
10. PROGRAM ELEMENT NO.
1DC618
11. CONTRACT/GRANT NO.
Purchase Order No.
CA-6-99-3381-A
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Laboratory--Cin.,OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Project Officer: Oscar W. Albrecht (513) 684-7886
16. ABSTRACT
The study provides an extension of the theory of demand, with specific
application to collection and disposal services for household solid waste. The
empirical investigation involving several socioeconomic variables (income, race,
household size) repeated the analysis of an earlier study, using more recent
(1970) Census data. The current findings supported the earlier results indicating
a strong positive effect and a seasonal pattern for waste volume and income
elasticity. There was less evidence of racial influence and household size on the
quantity of solid waste for municipal collection and disposal.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
Decision Making
Waste Disposal
Public Administration
Forecasting
Supply (Economics)
Demand (Economics)
Prices
Economic Analysis
Household Solid Waste
Solid Waste
Prediction
5C
5D
18. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (ThisReport!
Unclassified
21. NO. OF PAGES
115
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (Rev. 4-77)
107
4 U.S. GOVERNMENT PRINTING OFFICE: 1978—7 5 7-140/1384
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