&EPA
United States
Environmental Protection
Agency
Municipal Environmental Research
Laboratory
Cincinnati OH 45268
Research and Development
Treated Water
Demand and the
Economics of
Regionalization
Volume 1
The Residential
Demand for
Treated Water
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3 Ecological Research
4. Environmental Monitoring
5, Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series. This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution. This work
provides the new or improved technology required for the control and treatment
of pollution-sources to meet environmental quality standards,
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-80-162
August 1980
TREATED WATER DEMAND AND THE
ECONOMICS OF REGIONALIZATION
Volume 1. The Residential Demand
For Treated Water
by
Billy P. Helms and J. F. Vallery
University of Alabama
University, Alabama 35486
Grant No. R805617
Project Officer
Robert M. Clark
Drinking Water 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 Municipal Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publica-
tion. Approval does not signify that the contents necessarily reflect the
views and policies of the U.S. Environmental Protection Agency, nor does
mention of trade names or commercial products constitute endorsement or
recommendation for use.
ii
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FOREWORD
The U.S. 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 testimonies to the deterioration of our natural
environment. The complexity of that environment and the interplay of its
components require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem
solution; it involves defining the problem, measuring its impact, and
searching for solutions. The Municipal Environmental Research Laboratory
develops new and improved technology and systems to prevent, treat, and
manage wastewater and solid and hazardous waste pollutant discharges from
municipal and community sources, to preserve and treat public drinking
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 and provides a most vital communications link between the
researcher and the user community.
This report presents a data base and methodology for estimating the
determinants of residential demands for treated water.
Suggestions are also made regarding methodologies useful for future
research into the nature of water system costs by drawing upon the literature
on the electric power industry.
Francis T. Mayo, Director
Municipal Environmental
Research Laboratory
ill
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ABSTRACT
This two-volume report examines the present and future demands and costs
for residential water in view of the new requirements for water quality
standards under the Safe Drinking Water Act of 1974 (PL 92-523). Volume 1
investigates the determinants of residential water demand (including water
price, family income, and appliance ownership) and develops a methodology by
which utilities can determine future customer demand. A data base has been
developed, and results of the analysis are given. These data can be used to
test many hypotheses other than those examined in this study, and they could
be a valuable tool for further research into the household demand for water.
Methods are discussed sufficiently to provide a point of departure for water
utilities that may wish to analyze their own demand.
Volume 2 investigates consolidation in the electric power supply
industry as an example of a possible method of offsetting the increased costs
of water treatment that will be incurred under the new Federal regulations.
The structure of the power industry is examined and the history, advantages,
and cost benefits of coordination are evaluated. Several alternatives to the
present system are considered, including consolidation of existing systems,
encouragement of competitive markets, and public ownership of generation and
transmission facilities.
This report was submitted in fulfillment of Contract No. R805617-01-1 by
The University of Alabama under the sponsorship of the U.S. Environmental
Protection Agency. The report covers the period 4-1-78 to 12-31-79 and work
was completed as of 12-31-79.
iv
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CONTENTS
Foreword ................................
Abstract ................................ iv
Figures ................................ vi
Tables ................................. vii
Acknowledgments ............................ *x
1. Introduction .......................... 1
2. Conclusions .......................... 2
3. Sources and Organization of Data ................ 4
4. Effects of Price and Income on Water Demand .......... 8
5. Appliances and Other Determinants of Water Demand ....... 44
References ............. .................. 61
Bibliography .............................. 62
Appendices
A. Estimates of consumption associated with the ownership
of appliances ......................... 63
B. Local Study Questionnaire ................... 70
C. Statewide Survey Questionnaire ................. 78
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FIGURES
Number Page
1 Demand for Brand A toothpaste 10
2 Declining Block Rates, Schedule A 14
3 Declining Block Rates, Schedule B 16
4 Increasing block rates 18
5 Ex ante price variables calculated from the rate schedule of
Figure 2(a) 26
vi
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TABLES
Number Page
1 Correlation Coefficients Between Household Water Bills at
Various Consumption Levels, Rate Schedules of 78 Water
Utilities in Alabama 22
2 Regression Coefficients Explaining Water Consumption with
a Single Price Variable 31
3 Regression Coefficients Explaining Water Consumption with
Rate Schedules Defined by Two Variables 32
4 Comparison of Elasticity Estimates for Annual, Summer and
Winter Water Use Using Multiplicative and Additive Forms
of the Estimating Equation 36
5 Profile of Water Use Differential Under Various Rate Structures . 39
6 Average Monthly Water Use Per Household (gal/month) 41
7 Water Consumption According to Income Category 42
8 Average (Mean) Water Use of Customers in Alabama by Number
of Household Occupants 47
9 Profiles of Water Customers in Alabama by Economic Status and
of Household Occupants 48
10 Average Water Use of Customers in Alabama by Family Income ... 49
11 Profiles of Water Customers in Alabama by Household
Characteristics and Family Income 52
12 Water Use Profiles of Alabama Water Customers by Lawn Sprinkling
Habits and Appliance Ownership 53
13 Water Use Estimated Derived From Regression Analyses Using
Appliance Ownership and Demographic Variables 55
14 Regression Analysis of Demand for Lawn Irrigation Water,
Tuscaloosa, Alabama 58
vii
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TABLES (continued)
Number Page
A-l Regression Analysis of Annual Water Demand for Lawn
Irrigation and Selected Appliances 64
A-2 Regression Analysis of Water Demand for Lawn Irrigation 66
viii
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ACKNOWLEDGMENTS
The authors gratefully acknowledge the helpful suggestions and assis-
tance of Robert M. Clark and Richard Stevie. Research assistance was provided
by Edward R. Bruning, Marillyn A. Hewson and Antonio J. Rodriquez; editorial
assistance was provided by Anne Hamilton and typing was provided by Sharon K.
Carnes, Linda D. Hill, Mamie F. Jeffcoat, Jean B. Lewis, Martha C. Oneal,
Karen Roberts and Sherry A. Vyatt. Special thanks is due to Mary Ann Albright
for the coordination of the final preparation of the report.
ix
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SECTION 1
INTRODUCTION
The object of this two-volume study is to examine the determinants of
residential water demand, to develop a method for determining future customer
demand, and to investigate the possible benefits of regional consolidation as
a method of offsetting the increased costs that will be incurred with the new
Federal regulations under the Safe Drinking Water Act of 1974 (PL 92-523).
This first volume accomplishes two main tasks. First, it examines the
determinants of residential water demand with regard to water price, family
income, and the number of water-using appliances in the home. Second, Volume
1 develops a methodology by which utilities can determine future customer
demand.
To accomplish the first task of examining residential demand, a data
base was developed and analyzed. These data can be used to test many hy-
potheses in addition to those examined in this study, and they could be a
valuable tool for further research into the household demand for water.
A detailed description of the data base is given in Section 3, and the
methods are discussed sufficiently to provide a point of departure for water
utilities that may wish to analyze their own demand.
The estimation of price and income effects on water consumption is
discussed in Section 4 along with a consideration of many of the technical
problems associated with estimating demand equations when price to the con-
sumer is determined by a block rate structure. Aside from the conclusion
that the price elasticity of water is very low, the chapter will be of pri-
mary interest to those concerned with the econometrics of the study. Section
5 discusses the relationship of appliance ownership to the demand for water
and the usefulness of descriptive statistics in analyzing water demand. The
chapter should be of particular interest to. those concerned with pricing and
conservation policy and forecasting.
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SECTION 2
CONCLUSIONS
The data base in this study is unusual when compared to others used to
estimate residential water demand. It provides an unusually sound basis for
the study of price and income effects when the cost of the,goods to the con-
sumer is determined by a block rate structure. Even this data base has cer-
tain limitations, however, including the implicit assumption that individuals
in different cities have the same reactions to price changes. The ideal
study would impose different rate structures on individuals in the same loca-
tion and then determine the effects of these different rate structures.
These data are useful for presenting a general understanding of price
elasticity relationships. But to make specific policy decisions, a similar
study should be conducted by the affected utility. The techniques developed
as a result of this study indicate that such a data collection effort is
feasible at reasonable cost.
The primary conclusions drawn from the data base analysis are as
follows:
1. The number of persons in the home and family income are
the most important determinants of water consumption.
2. Price affects consumption, but much less than has been
indicated in most previous studies. The findings of
this study indicate a price elasticity of -0.2 as op-
posed to estimates of approximately -0.6 in recent
studies. The policy implications of this are far
reaching, since a utility that needs a 5 percent in-
crease in revenue would have to raise rates only 6.35
percent if price elasticity is 0.2, and 16.67 percent
if price elasticity is 0.6. Thus environmental regu-
lations that increase revenue requirements may not
create as many problems for the utilities as had
been expected under previous elasticity estimates.
3. The presence of various water-using appliances affects
the use of water, but the presence of household appli-
ances is generally a reflection of income, and there-
fore information on appliances may be redundant if
accurate income data are available.
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4. The presence of a lawn sprinkler provides little indica-
tion of water use for irrigation. The percent of cus-
tomers irrigating (which averages 20 percent over all
income groups) increases with income; but heavy waterers
are found scattered throughout the mo derate-to-high income
levels, and they are in the minority at all income levels.
5. The use of water for lawn irrigation is an important source
of residential water demand during the summer months. The
price elasticity of water used for irrigation is not rad-
ically different from that for other uses.
6. Completely eliminating lawn irrigation cannot greatly
curtail the need for new water supplies, since irri-
gation water accounts for only about 3.5 percent of total
use. Controlling lawn irrigation use is useful in solving
peak load problems, however.
7. Significant water conservation is unlikely to be achieved
through the use of rational rate increases. Future re-
ductions in water demand will more than likely come from
technological changes in the household water-consuming
appliances. Some of these changes (for example, the use
of bottle dames in toilet tanks) can be implemented
quickly with the shock effect of high-penalty water rates.
Other techniques (such as building codes requiring water-
efficient appliances) would take years to produce a mean-
ingful change in the average use per household.
8. If the peak load is 10 to 20 percent above normal levels,
there is no economic justification for declining block
rate structures that encourage (or fail to discourage)
the increased demands of irrigaters. A declining block
rate structure is socially and economically justifiable
up to a usage level representing the average monthly use
for a large family. For above-average use, or for higher
summer use within a household, however, the most justi-
fiable structure might be an increasing block rate
structure.
9. An increasing block rate structure may be feasible only
in systems with computerized billing systems, and it
would induce only limited conservation with relatively
high, widely publicized rates.* The primary advantage
would be that the revenue would be collected from those
primarily responsible for the peak load.
*A fair billing system for conservation would require that the number
of household occupants be considered in determining the point at which the
increasing block rate would take "e'ffect and/or when a given customer con-
sumed greater than his usual average.
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SECTION 3
SOURCES AND ORGANIZATION OF DATA
The data used in the study were obtained from several sources and
organized into two data sets. This chapter describes the data sets and
their sources, quality, and limitations. A section on survey methods and
applications also provides suggestions for use by other utilities who nay
want to forecast demand. Copies of questionnaires (which may be useful In
future studies) are reproduced in the appendices.
HOUSEHOLD INFORMATION AND SURVEYS USED
The two data sets used were based on separate surveys of utility cus-
tomers. The first and larger sample of more than 700 is referred to as the
statewide set, and it serves as the basis for the elasticity estimates
developed in Section 4. A second, smaller sample (188) was drawn from a
single water utility and is referred to as the local sample. The local set
is used primarily as a supplement to the statewide set, first in defining
price (Section 4), and later in the analysis of detailed characteristics of
water consumption (Section 5).
STATEWIDE DATA SET
The first survey was conducted by a utility serving a large part of the
State of Alabama in early 1977 as part of a (usually) biannual series. (The
exact data source must remain confidential.) Information on household occu-
pants, income, appliance ownership, and housing characteristics was obtained
from interviews conducted in the customers' homes. The authors were per-
mitted to add some key water questions to the survey in anticipation of this
study, and to participate in field testing and other aspects of the survey.
Overall emphasis was on determining appliance saturation and conservation
practices of electric utility customers. The same type of demographic and
appliance information is needed for a water survey. Thus various utilities
interested in making such surveys should consider conducting them as a joint
effort.
The statewide survey Included 3,000 interviews with customers from the
service area. Interviewers were chosen from 3,000 pairs of names randomly
drawn from all customers. Each pair consisted of two consecutive customers
in a meter-reading route, and a prime and an alternate was designated for
each. Alternates were interviewed only if the prime could not be contacted
after several attempts over a period of time.
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More than 60 water utilities serving the geographical area of the
original interviews participated in an effort that successfully matched more
than 1,200 interviewees with the names and addresses of water customers. The
largest loss stemmed from the failure of one large metropolitan area to
participate (because of legal advice) and the inability or unwillingness of
several smaller water systems to participate. In addition no water records
were available for many interviewers because water is often furnished in
rental units and the service area of the interviewing utility included areas
with no water service. The data set was further reduced to 1,008 records by
eliminating the records from systems that were not on a monthly billing cycle.
The remaining records were compiled by statistical distributions and compared
with similar statistics from the original 3,000 records. The comparison
indicated that the sample reduction was essentially random. For example, the
average number of occupants is 3.0 in the recorded sample versus 2.9 in the
full set; average family income is $12,500 versus $11,500, etc. The direc-
tion of change is consistent with the loss of samples that occurred because
of furnished water (about half of the apartments and mobile homes) and
because of rural residents without water service. Thus the sample of 1,008
seems to represent about the same population as does the sample of 3,000.
The sample of 1,008 was used in a number of descriptive statistical tabula-
tions and serves as the basis for part of the analysis in Section 5. The
regression analysis in Section 4 is based on a sample size of 773. This
further reduction was necessary so that identical billing months could be
used for samples and so that samples with large leaks or other questionable
content could be rejected.
Regressions were also run on subsamples from three cities (i.e., three
separate water systems). One contained 153 samples, another had 97 samples,
and the last had 55. These subsets were used for a limited comparison of
variations in water consumption patterns among the water systems.
LOCAL DATA SET
The second survey was conducted under the direction of the authors
during the summer of 1978 as part of a continuing study of residential energy
demand and as a means of obtaining specific information on water use not
included in the statewide survey. Utility customers drawn from a sample in
one city were interviewed by telephone. A major objective was to determine
how well customers understood the price under block rate structures and
which component of price influenced their consumption. The problem of the
appropriate price specification is common to all utility demand studies. A
second purpose of the local survey was to add questions about the ownership
and use of water sprinklers, the frequency of car washing, and the presence
of swimming pools, water-cooled air conditioners, or other large water-using
appliances. Finally, the survey was used to test some innovations in inter-
view techniques.
A random sample of 250 customers was drawn for the local data set.
Because of several changes in the questionnaire (primarily in the effort to
pinpoint sprinkler use) and a number of unsuccessful attempts to contact some
of the samples drawn, only 188 usable samples were obtained. The customers
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interviewed are slightly biased toward older heads-of-households and higher
incomes.
USE OF SURVEYS AND SURVEY METHODS
Gas and electric utilities have a long history of surveying the appli-
ance ownership of their customer. The earliest surveys of the utility pro-
viding the statewide data set for this study were concerned with determining
saturation rates for ranges and water heaters. The major question was wheth-
er these appliances had been accepted rather than the type of fuel used,
thereby establishing whether there was a market for selling such appliances.
Later, more appliances were added to the surveys, and the emphasis shifted to
market shares and competitive positions, as virtually all customers owned
ranges and water heaters of some type. The saturation of appliances is also
of increasing importance to gas and electric utilities in forecasting both
peak system demand and long-range sales. These data have also been used,
with limited success, in estimating bills during a month when the meter was
not read and in experimentation with monthly billings and quarterly meter
readings.
We are not aware of surveys by water utilities similar to those by gas
and electric utilities in the United States, arid only Batchelor [1975] (in
England) has made use of such surveys in readily available water research
literature. Our speculation is that water system management would have re-
ceived only marginal benefits from such data in the past; however, as trends
toward higher cost and increasing scarcity continue, relatively simple survey
techniques and analyses will be of increasing value in pricing and other
measures to alleviate the peak load problem (if any) and encourage conser-
vation.
For most managerial questions, including rather simple evaluations of
elasticities within a particular water system, we believe that a simple data
set could be collected by much less elaborate survey methods than used here.
However, the usefulness of survey data could be greatly enhanced by
(1) tracking a sample of customers over time for an evaluation of water use
changes for those customers remaining at the same place, (2) following cus-
tomers in the sample that move elsewhere in the system, and (3) tracking the
water use in the original housing unit as occupants change. More sophisti-
cated studies of elasticities and how they may differ with location, density,
or other characteristics would also benefit from survey designs incorporating
the longitudinal observations suggested above. Thus the inclusion of ques-
tionnaires in the appendices and the following description of key survey
techniques are offered only as suggestions, not as a package for replication.
The differences in interview methods should be of interest to those
planning surveys. The statewide survey interviews were conducted in the
customers' homes, and emphasis was placed on the accurate recording of exact
responses. Only questions with definitive and objective answers were used in
order to avoid bias or error by the interviewer. In some questions, however,
the interviewer was allowed to help with factual questions such as the number
of square feet of heated space. In the local survey interview, emphasis was
placed on the skill of the interviewer in avoiding bias or error in a
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tradeoff for additional objectives. The first objective was to cut the
average time per interview by asking open-ended questions, such as "how much
water do you use outside the house?" Most responses, as anticipated, in-
cluded the details sought with minimum need for follow-up questions. A
second objective was to obtain the interviewee's perception of prices and a
description of how key appliances were used. To obtain such information
from questions in a simple yes or not format would have required much longer,
with no assurance of greater accuracy.
The results with open-ended questions were highly satisfactory in more
respects than the closed questions. After a little experience, the inter-
viewers found that most information sought could be quickly obtained. They
also suspected (and the results confirmed) that the attempt to quantify
sprinkling in terms of frequency and intensity was unsuccessful. Some re-
spondents who claimed to water lawns "frequently" used considerably less
water than those who thought they sprinkled just enough to keep the grass
from dying—primarily a difference in viewpoint between moderate- and high-
income customers. (Similar attempts to obtain information on the intensity
and frequency of use of energy-using appliances were much more successful.)
The statewide and local interviews were also different in emphasis. Of
major concern in the statewide survey was obtaining results representative
of the population, and a large and random sample was important. The local
survey interview was designed to fill gaps in statewide data sets and to
develop estimated ranges of water amounts used by irrigators as opposed to
the total or average amount of water used for irrigation.* For such ques-
tions, accuracy in a limited and non-random number of observations is more
important than the usual considerations to avoid bias.
*Data on lawn watering practices were used to develop a technique for
identifying customers with high irrigation demand in the primary data set.
The technique is further discussed in Section 5.
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SECTION A
EFFECTS OF PRICE AND INCOME ON WATER DEMAND
Interest in the price elasticity of water is associated with policy
measures to encourage conservation and with forecasts of system loads. Ear-
lier studies have focused on the amount of conservation caused by metering,
and they have stimulated interest in estimating the elasticity of water de-
mand (Howe and Lineweaver, 1967; Clark and Goddard, 1977; Batchelor, 1975).
Initially, conservation appeared to be synonymous with restricting the de-
mand for sprinkling, but later studies suggest possible reductions of in-
house usage as great as 30 percent (Howe and Vaughn, 1972). More recently,
a greater public interest in both price and non-price control measures has
been created by environmental objections to reservoirs, the high cost of
upgrading water and sewer treatment facilities, and forecasts of critical
water problems in many areas (Consumer Reports, 1978).
Published estimates of price elasticities range from zero to above
unity, and there is little evidence of consensus as to the actual magnitude
(see Goddard et al. (1977) for a detailed literature review on residential
water demand). In spite of evidence that the elasticities in humid areas
are probably difference from those in arid areas, and that different usage
patterns may exist in urban and rural areas or in cities of different sizes,
it is unlikely that these differences could account for the wide range in
elasticity estimates. Limited experimentation with pricing to induce
conservation suggests that the demand for water is quite inelastic, however.
In one case cited by Consumer Reports (1978), an affluent suburban water
system accomplished a 65 percent temporary reduction and (apparently) a
45 percent permanent reduction in residential water use, partially by pro-
hibiting outside use, but mostly through a temporary inverted rate structure.
Rates were doubled for consumption up to a targeted high conservation quota
per household; they were increased eightfold for consumption up to twice
the quota; and they were raised fortyfold beyond that level.
We contend that the higher estimates of price elasticity stem from
misspecification of price variables. After a review of the controversy,
we tested this hypothesis by recreating the errors found in previous stud-
ies and comparing the results with estimates from more plausible price
specifications. The findings explain the wide range of estimates previ-
ously reported and point out the type of improvement needed in future
studies. Tentative estimates of the water demand elasticities in our study
area are then evaluated on the basis of suitability for pricing policy and
forecasting.
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In this section, the concept used for estimating elasticity is related
to the empirical calculations. Examples are generally drawn from the data,
analyses, and definitions used in subsequent sections. In addition, key
definitions are given for ex post and ex ante prices as applied to the aver-
age and marginal prices used in the study, and two additional prices are
introduced that have been developed in the theoretical literature but not
extensively in empirical work—the intramarginal price and the lum sum.
These four price variables are tested and compared in various combinations is
various combinations in several estimating equations. The best combination
of price variables and estimating equation is used to develop elasticity
estimates for the study. This section also illustrates some policy applica-
tions of demand, analysis.
METHODOLOGY FOR ESTIMATING PRICE ELASTICITY
This subsection outlines the concept of elasticity and the generally
accepted methodology for estimating it. First, it is essential to understand
two basic types of pricing—ex ante and ex pos t. When a conventional good is
priced by the seller ex ante, the price per unit is given before the amount
purchased is decided. There are no discounts for large purchases or penal-
ties for small purchases. Ex post, or after the fact, pricing is used to
determine water bills under block rate schedules.
The following discussion of estimating conventional ex ante elasticity
identifies several alternative methods of price specification that have been
used in estimating the price elasticity of utility services. The comparison
shows how the ex post block rate pricing system used by utilities has created
unique problems in the proper specification of price.
Concept and Calculations
The law of demand states that the price of a good determines the quantity
taken, all else equal. Price elasticity is a measure of the inverse rela-
tionship between price and quantity hypothesized by the law of demand. Or,
stated more simply, elasticity is a measure of the relative influence of
price on the quantity taken. Conceptually:
„ percent change in quantity taken
e * percent change in price
The standard method of calculating price elasticity is illustrated in
Figure l(a), in which a drug chain has set up a controlled experiment to de-
termine the price elasticity for their brand of toothpaste. In one store,
they have priced Brand A at $1 per tube and find that 100 boxes of 20 tubes
each are sold per month. In a second store, located in another shopping
center with essentially identical characteristics (customer traffic, neigh-
borhood income, etc.) sales of 110 boxes are obtained at the lower price of
$0.90. The demand curve illustrated is fit to the data and extrapolated.
The conceptual formula must be modified to obtain logically consistent
results. The can be seen from a literal interpretation of the conceptual
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o-
100 11O
es sou*
a
2
o.
o-
.75.-
50 100 ISO
5O 100 ISO
of
Figure 1. Demand for Brand A. toothpaste.
10
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formula. Assuming a drop in the price to $0.90, elasticity would be:
+10/100 _ 10% _ 10
-.10/1.00 -10%
or, if we assume a price increase;
e - -10/110 -9% _Q a
•K10/.90 11% ^'8
Actual estimates are obtained by the empirical definition:
change in quantity/average of the initial and final quantities
e * change in price/average of the initial and final price
. 10/105 - 9.5% . 0 Q
.10/.95 10.5%
It is understood that a price elasticity coefficient is negative, so elas-
ticities are sometimes referred to without making the sign explicit. The use
of percentages insures that the calculations would be identical if price had
been stated in cents rather than dollars, or if quantity had been stated in
tubes rather than boxes.
The nature of an elasticity estimate is further clarified by assuming
that a third store in the controlled experiment recorded sales of 90 boxes
at a price of $1.10. If elasticity is calculated for the arc of the demand
curve between $1 and $1.10 (as opposed to the arc between $1 and $0.90 as in
the paragraph above):
.10/1.05
The elasticity may differ depending on which range of the demand curve is
chosen in making the calculation in this example.
A major point to be made by the above examples is that an elasticity
estimate is only an approximation of the price-quantity relationship. In
general use, most economists would refer to either the 0.9 or the 1.1 esti-
mate as "about unitary," meaning that the change in sales to be expected
from a change in price would be about in proportion to the price change.
Similarly, elasticities of 0.4 or 0.5 would Indicate that the product was
relatively price inelastic, or that sales were not very responsive to the
price.
Since controlled experiments are rare, Figure l(b) offers a more real-
istic picture of a typical data base used in elasticity estimates. Here,
price-quantity observations for Brand A during a given time period are plot-
ted for several outlets of the hypothetical chain of drugstores.* The scatter
occurs partly because the outlets of the chain are in neighborhoods of vari-
ious income levels and different population densities. .To estimate the price
elasticity, the independent variable, sales, is explained by price (P),
11
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income (I), population (POP), and any other relevant factors in a multiple
regression demand equation:
Q - br + b2 P + b3 I + bn POP + . . .
The coefficient b2 is used to obtain an estimate of the price elasticity.
Similarly, b3 provides the estimate needed to calculate an income elasticity.
Income elasticity is a measure of the relative influence of income on the
quantity taken; the calculation is similar to those illustrated above, except
that income is substituted for price. The population variable is included,
along with other factors, to hold all else equal.
The concept of quantity being partially determined by price and partial-
ly determined by income is further illustrated in Figure l(c). The demand
curve to the left represents purchases in response to price differential by
purchasers with incomes up to $12,000 per year. On the right, the demand
curve represents the influence of price for purchasers with incomes over
$12,000 per year. These estimates would be obtained by splitting the data
deck at the approximate median income and explaining the quantity taken in
each data subset. As illustrated, the higher-income groups purchase more at
any given price, and their demand is less price elastic than the demand of
the lower income groups.
Linear and Curvalinear Shapes of the Demand Curve
Instead of hypothesizing a straight-line relationship between quantity
taken and the determinant variables, as in Figure 1, a curvalinear relation-
ship could be used in other specifications of the estimating equation. A
common alternative to the specification above is to specify all variables in
natural logarithms. Log-linear estimates of the demand equation have the
special characteristic of explaining the percentage change in quantity taken
by a percentage change in price or income. The coefficients thus become
direct estimates of the elasticities. A second characteristic of the log
specification is that in this form of the demand equation, one assumes that
the elasticity is the same at any point on the demand curve.
In estimating the demand function, both log and non-log specifications
and other variations are frequently used to determine the shape of the de-
mand curve and thus determine the extent of its variations at different price
levels.
Block Rates and the Simultaneous Determination of Price and Quantity
The simultaneous determination of price and quantity for products such
as water and electricity creates a problem in the specification of the price
per unit of these products. A utility typically prices its products under a
block rate schedule so that customers pay different prices for various units.
The problem is illustrated by a typical rate schedule for water. As usage
increases, each additional gallon is priced at the same or at a lower price.
An example of a declining block rate would be a charge of $6 for part or all
of the first 4,000 gal, $1 per 1,000 gal for the next 4,000 gal, and $0.80
12
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for each additional 1,000 gal. The various possible bills calculated from
this schedule are shown in Figure 2(a).
Figure 2(b) shows a graph of the marginal price, which is the price per
unit (1,000 gal in this case) for the last unit purchased. The first block
is a fixed cost; therefore the marginal price is zero until the quantity
consumed is greater than 4,000 gal.
Marginal price is frequently selected as the price variable in elastic-
ity estimates. This practice is justified on the assumption that additional
use (or conservation) is based on the price for the additional unit only.*
A clear example is seen in the special case of a single block where water is
priced at a flat monthly rate. The marginal price is zero, and the customer
has no incentive to conserve. In the example in Figure 2(b), a customer
contemplating the cost of filling a swimming pool might consider only the
additional cost of $0.80 per 1,000 gal.
In other elasticity studies, average price per unit has been used as the
price variable. One justification for using this variable is based on the
assumption that most utility customers react to total charges and do not
know the marginal block rates anyway.t A more important justification is
based on theoretical considerations introduced at a later point. In addi-
tion to the counter argument that marginal price is more appropriate, crit-
icism of the use of average price is based on an upward bias introduced in-
to the price elasticity estimates.t The bias is illustrated by the behav-
ior of average price in Figure 2(c). In a declining block rate schedule,
the average price declines as the quantity consumed increases. Regression
estimates of price elasticities are based on the assumption that price de-
creases would cause increases in consumption. To the extent that the re-
gression results reflect the effect of the level of consumption on the price
(as opposed to the effect of price on the level of consumption) the rela-
tionship is meaningless as an elasticity.
*Gibbs (1978) justifies the use of marginal price on the basis of a
comparison of results from using it and the average price in two otherwise
identical equations. The comparisons, however, establish nothing other than
the fact that the two variables yield different results. The a priori ar-
gument of Howe and Lineweaver (1967) and his own supporting assertions as
summarized here remain the basis for the use of this price specification.
tWilder and Willenborg (1975) present this argument, but following
Halvorsen (1975), they also argue erroneously that use of the average price
will give the same results as the use of the marginal price. (See earlier
reference to Gibbs, 1978.) it can be shown that Halvorsen 's mathematical
proof is a special case.
possible bias is recognized by Howe and Lineweaver (1967) and
Halvorsen (1975) among others. Taylor (1975) provides the most detailed
theoretical treatment of the problem, and he is generally followed below.
Our exceptions to Taylor's specification of price are detailed later in this
chapter under Intramarginal Price and the Lump Sum.
13
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(a.)
(b)
Figure 2. Declining Block Rates, Schedule A.
14
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The problem of simulteneously determining price and quantity also
applies to marginal price. Consider, for example, Figure 2(b). Apartment
dwellers would tend to cluster in groups of customers consuming relatively
small quantities of water—perhaps 4,000 to 8,000 gal. Thus regression re-
sults using the marginal price actually paid by a typical population would
show a strong association between price and quantity, and the elasticity
would tend to be overestimated. To the extent that a large number of cus-
tomers might be consuming in the initial block with zero marginal price, how-
ever, the data base would contain the lowest price for the lowest users, and
elasticity estimates could be biased downward or even estimated with the
wrong sign.
Price as a Measure of Relative Charges Among Schedules
One solution to the simultaneity problem is to specify price directly
from rate schedules. The average price in previous studies was usually de-
fined as total expenditures divided by quantity consumed—that is, the price
was determined after the consumption level load been established, or ex post.
This caused the bias illustrated in Figure 2(c). To avoid the bias, average
price must define the charges under the schedule, not the price actually paid
by each customer.
One possible way to specify price in the schedule illustrated would be
to select the average consumption of all customers in the data set (6,000
gal, for example,) and to use the bill at this predetermined (ex ante) level
to determine the price variable for each customer under this and other sched-
ules. Thus $8 would serve as a proxy for charges under the schedule illus-
trated, and this price, which represents total expenditure, would be compared
with similar calculations of bills under other schedules. The expenditure
concept is discussed later; here, it is simply the price stated for a unit of
6,000 gal. As an alternative, the ex ante average price, which would pro-
duce the same regression results as the expenditure price, is $1.33 per 1,000
gal, as illustrated for the 6,000 gal consumption level in Figure 2(c).
A similar approach for defining a marginal price that defines the
schedule is considered below. First, we consider the extend to which the
ex ante average price accomplishes the objective of defining the relative
price levels among schedules. The major determinant is the extent to which
the rate structures in the data set are based on similar pricing objectives.
In general, the rate for the first block reflects fixed cost in servicing the
account and paying for capital outlays. Lower marginal rates reflect the
lower cost to the utility for extra water purchased. Each utility's rate
structure is designed to cover total cost, and a low-cost system, represented
by Figure 3, will typically have lower charges for each block relative to the
high-cost system as shown in Figure 2 on page 14. In Figure 3, the rate
schedule is Illustrated based on charges of $4 for the first 4,000 gal or
less, $0.80 per 1,000 gal for the next 4,000 gal, and $0.60 per 1,000 gal for
everything over 8,000 gal.
Figure 2(c) and 3(c) provide a number of possible price comparisons at
ex ante or predetermined consumption levels. All reflect the fact that cus-
tomers pay less under the schedule used in Figure 3 than do the customers
15
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e
2..00
V._L>
Figure 3. Declining Block Rates, Schedule B.
16
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facing the charges illustrated in Figure 2. By selecting price according to
our predetermined criteria, we find the 6,000 gal ex ante average prices of
$1.33 and $0.93 for the two schedules. With the empirical definition of the
percentage differential described on page 11, the $0.40 difference in average
prices under the two schedules is 35 percent. (Note that the sane percent
differential would have been calculated from the two bills at 6,000 gal.)
The ex ante average price selection is arbitrary in the sense that some
other bench mark would produce a different measured differential between the
two schedules. For example, there is a 40-percent differential in average
prices at the 4,000 gal use level and only a 32-percent differential at the
12,000 gal use level. This limitation, however, is inherent in block rate
schedules, because no single price variable can reflect the exact price dif-
ferential for all of the possible levels of consumption. Nevertheless, any
ex ante average price based on any selected consumption level within the
range of typical use would provide a measure of the relative level of charges
under various schedules to the extent that the marginal price is typically
higher in schedules with higher first-block charges.
Whether the average and marginal prices are positively correlated with a
roughly proportional allocation of fixed and variable cost to the rate sched-
ules (as in the examples above) for a given data set is an empirical question
that will be discussed in the following subsection. The possible case of a
random mix of schedules (some with high initial charges and low marginal
rates, and others with marginal rates about as high as the average cost in
the initial block) would make the ex ante average price either inappropriate
or incomplete in comparisons of charges among schedules. The extreme case of
a nonproportional mix is illustrated by comparing the inverted block rate
structure in Figure 4 with the schedules discussed above.
Figure 4 illustrates an inverted block rate based on charges of $4 for
the first 4,000 gal, $1.50 per 1,000 gal for the next 4,000 gal, and $2 per
1,000 gal for each additional 1,000 gal. Increasing blocks are advocated by
conservationists as a way to induce consumers to reduce their consumption of
water or energy. The average price behaves quite differently for this sched-
ule than for those in Figures 2 and 3. After an initial decline for use up
to the minimum charge, average price increases with higher use. The ex ante
average price would not be used as a measure of the relative cost of water in
this schedule as compared with the other two schedules. The unambiguously
higher marginal prices of Figure 4 are the basis for assuming that the
inverted schedule would induce conservation.
Relative Marginal Prices—The Problem of Random Block Sizes
The rate schedules of Figures 2, 3, and 4 also serve as a basis for
considering the marginal price that applies to the schedule as opposed to the
marginal rate a given customer might pay. If all schedules in a data set
were based on rate changes at 4,000 and 8,000 gal, as illustrated, the
specification of the marginal rate at the mean consumption level of 6,000 gal
would provide a simple solution. From Figures 2, 3, and 4, the ex ante
marginal rates would be $1, $0.80, and $1.50, respectively.
17
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\.'2,5
(\JKfcs)
Figure 4. Increasing Block Rates.
18
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There are, however, two problems with a predetermined use level as the
basis for Identifying marginal prices that would be comparable among several
schedules. First, the extra use (which may be associated with a low marginal
rate) for many customers Is the seasonal demand for lawn sprinkling, which
may fall In more than one block. An example Is the customer whose average
winter use Is 6,000 gal and whose average use In hot, dry months Is 10,000
gal. Under the schedules Illustrated, and If It Is assumed that this pattern
of use as opposed to a single consumption level Is taken as the ex ante bench
mark, the appropriate marginal rate for each schedule might be the average of
the two marginal rates within each schedule—$0.90, $0.70, and $1.75, respec-
tively, in Figures 2, 3, and 4.
The second and more serious problem is that breaks in the blocks among
schedules are randomly scattered. Consider the rate-maker's decision in the
(typical) schedules represented by Figures 2 or 3. His objective is to col-
lect some target total revenue per customer, with the constraint that the
schedule must take some equitable distribution of fixed and variable produc-
tion cost among customers.. Blocks might have been selected at 2,000-gal
intervals up to 10,000 gal, or all of the fixed charges might have been col-
lected in an initial block of 6,000 gal with a single additional block beyond
that amount. The problem is specifying a marginal price that is comparable
among schedules is to avoid variations based on the arbitrary decisions in
rate-making.
The solution is to select a uniform basis for calculating ex ante
marginal prices. This part of the charge should be obtained by calculating
the rate over a typical range of extra use, rather than selecting some point
within the range, since a point is less likely to be uniform among schedules.
An example of the type of calculation required is provided by Figure 2(a),
where the marginal charge can be calculated directly for the block between
6,000 and 10,000 gal. The difference between the two bills ($11.60 - $8.00)
divided by the interval (4,000 gal) is equal to $0.90 per 1,000 gal. This
marginal price will be comparable to marginal prices in other rate schedules
to the extent that other schedules are based on comparable allocations of
fixed and variable cost to the rate schedules. (Recall that ex ante average
prices are comparable in Figures 2 and 3, but not in Figure 4.)
Non-Uniform Allocation of Costs in Rate Structures
Although the inverted schedule of Figure 4 serves as an example of a
case In which a single variable could not be considered as a proxy for the
entire schedule of prices among the three schedules illustrated, a more
important constraint for empirical elasticity estimates is found in a similar
discrepancy among the ways utilities choose to allocate their costs to rate
schedules. The problem is most notably present when the water bill includes
all or part of a sewer charge. In the pricing policy adopted by a utility,
there is almost equal logic (sometimes influenced by political consideration)
for either (1) adding an additional flat charge because it is assumed that
the sewer system is virtually all a fixed expense, or (2) using a separate
declining rate for the sewer based on the assumption that the household load
on the sewer is in proportion to the household use of water. These two cases
can be considered with further reference to Figure 2.
19
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First, assume that approximately $4 per sewer customer is required to
cover the cost of providing the service. The charge could be made by adding
$4 to the first block, or by adding a 50-percent surcharge on to the water
bill. In either case, the ex ante combined average price to the sewer custo-
mer would be 50 percent higher than it would be to the customer in the same
system with no sewer charge. (In the first case, the minimum bill increases
from $6 to $10; in the second case, the average price of $8 at 6,000 gal is
multiplied by 1.5.) The difference between these two pricing decisions (and
implicitly, an important difference in water rates, depending on how the total
charge is allocated to the minimum and variable components of the rate) is
reflected in the marginal rate relative to the average price.
Because utility rate schedules are not uniform in their concepts and
treatment of the fixed and variable components of charges, a single price
variable cannot be depended on to define the differentials in charges among
schedules. Theory predicts that the customer with the increase in the mini-
mum charge will react somewhat differently from the customer faced with the
surcharge.
Income and Substitution Effects
An increase in the fixed charge would tend to reduce consumption even
though there was no change in the marginal rates. Theoretically, a reduc-
tion in water consumption would be predicted because of the income component
of the price effect. At higher prices, the household will cut back on water
and all other goods to stay within the budget.
The same is true for the 50-percent surcharge, because the higher total
charge will induce a reduction in water and/or other goods consumed. A
higher price of any good and a fixed budget will require economies somewhere,
and thus cause an income effect. With the surcharge, however, the household
would be expected to cut back on water expenditures to a greater extent than
it would with the fixed-charge increase, even though the total bill will have
increased the same amount for both households and the income effect would be
the same for both. In the second case, the marginal price is 50-percent
higher than in the first. We predict that the second household will also
make fewer purchases at the margin. Such behavior is known as the substi-
tution component of the price effect. The two separate effects of income and
substitution are additives in the total price effect.
Summary and Conclusions
Thus theory predicts that water consumption will decrease both with
(a) an increase in average price an no change in marginal prices, and (b) an
increase in marginal price and no change in average prices. A theoretically
appropriate price specification will therefore require that both average and
marginal rates be considered. One possibility is to specify both variables
in an estimating equation. The example here, however, illustrates the ob-
jective common to all possible specifications. Two variables should be used
to define (or serve as proxy for) the level and slope of the function
representing the total bill.
20
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The need for two variables in the price specification stems from the two
components—income and substitution effects—that make up the total price
effect. For utility products priced under a block rate schedule, the average
and marginal components of price will produce differing income and substi-
tutional effects. In this respect, the price for a utility product is
uniquely different from the prices of typical goods such as toothpaste, where
the average and marginal prices are identical and any price impact includes
both income and substitution components.
Use of ex post price will result in different prices being paid by dif-
ferent customers under identical rate schedules, and use of an ex ante price
will result in different prices only if the customers are subject to differ-
ent rate schedules. Ex post prices have been used in most previous studies,
and the major disagreement on methodology has been over whether the marginal
or average price was the appropriate variable. Taylor (1975) in his theoret-
ical critique, which still applies to errors in more recently published elas-
ticity estimates, places emphasis on correctly defining variables—ex ante as
opposed to ex post—and using more than one variable to define a rate struc-
ture.
Though emphasis has been limited in this subsection to the ex post and
ex ante definitions of marginal and average prices, two additional price
variables are considered later under Intramarginal Price and Lump Sum. They
are conceptual variations of and alternatives to the use of average price for
defining price level.
DATA SET AND DEFINITIONS USED IN THIS STUDY
Examples in the previous subsection, with the exception of the inverted
rate structure, are consistent with our statewide sample, which contained
about 60 rate schedules (some for water only and some for the combined water
and sewer) provided by more than 40 utilities. All schedules have a fixed
charge for a minimum purchase. Initial blocks were between 2,000 and 5,250
gal, and the number of blocks ranged from two to seven. Sever rates were
mixed between schedules with declining blocks similar to the water rates and
schedules with all or most of the sewer charge in the initial block.
More than 700 observations of household water consumption showed month-
ly use to average about 6,000 gal annually and 5,000 gal during the winter
months. Extra use in the hottest months averages about 4,000 gal in samples
with seasonal variations in usage patterns. These observations served as the
basic justification for using the ex ante bench marks of (1) 6,000 gal for
calculating the average price or total expenditure variable, and (2) 6,000
to 10,000 gal as the range for calculating marginal price.
An analysis of the validity of the ex ante bench marks is provided later
in this chapter under Elasticities of Water Demand. Preliminary indications
of validity were obtained from an analysis of possible ex ante specifications.
Table 1 provides an example of one of the factors considered.
Table 1 shows the correlation coefficients obtained by comparisons of
ex ante prices for various consumption levels. The correlation of .994
21
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TABLE 1. CORRELATION COEFFICIENTS BETWEEN HOUSEHOLD WATER BILLS
AT VARIOUS CONSUMPTION LEVELS, RATE SCHEDULES OF 78 WATER
UTILITIES IN ALABAMA
Consumption
level
(gal)
4,000
5,000
6,000
7,000
8,000
9,000
10,000
11,000
Consumption level (gal)
5,000 6,000 7,000 8,000 9,000 10,000
0.928 0.918 0.880 0.842 0.804 0.769
0.987 0.972 0.952 0.930 0.907
0.994 0.986 0.963 0.944
0.996 0.987 0.974
0.998 0.990
0.998
11,000
0.736
0.883
0.924
0.959
0.979
0.992
0.998
12,000
0.705
0.860
0.903
0-943
0.967
0.984
0.993
0.999
22
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between prices at 6,000 and 7,000 gal, for example, would indicate that the
ex ante price based on 6,000 will be an almost perfect proxy for the price
actually paid by all customers actually using 7,000 gal—that is, the ex ante
price will measure the price differential among schedules. Thus the table
indicates that a bench mark level of 4,000 gal would not serve as a very
accurate indicator of level of charges faced by customers consuming 10,000
gal per month (correlation of less than .8, obtained by reading across the
top row). Conversely, the high correlations among expenditures in the 5,000-
to 8,000-gal range indicated why there was virtually no difference in the
results expected (and later actually obtained) from any of the bench marks in
this range. The lower correlations for 4,000 gal in comparison with bills
for 5,000 and above stem mostly from minimum charges based on 5,250 gal in
a number of samples and from variation in the proportion of fixed-to-variable
charges among rate schedules.
A similar correlation matrix (not shown) was used to verify the fact
that the bench mark selected for specifying the ex ante marginal price was as
good or better than alternative bench marks. Correlation between the mar-
ginal price calculated from the 6,000 to 10,000 gal range and other ranges
were generally greater than .94.
INTRAMARGINAL PRICE AND THE LUMP SUM
The arguments for the use of two prices to define a rate schedule were
drawn primarily from Taylor (1975) in his theoretical critique of price vari-
ables. In this section, we consider his concept of the distinction between
the intramarginal and marginal components of price. Our primary concern is
with bridging the gap between this reasonably clear concept of price and how
the concept can be converted into empirical specifications.
The Concept and Taylor's Specifications
The distinction between intramarginal and marginal price can be seen in
Taylor's instructions for specifying the variables. Refer to the rate sched-
ule in Figure 2 and assume that a customer is using 6,000 gal of water per
month. The intramarginal price is defined by Taylor as the initial expendi-
ture or amount paid up to but not including the block of actual consumption.
In this case, the intramarginal price is the bill associated with the first
block, $6. Taylor also noted that the intramarginal price could be stated
as the average price per unit within the initial block or blocks and that the
two specifications would produce identical results in regressions—it makes
no difference whether price is stated at $1.50 per 1,000 gal or $6 per 4,000
gal. Marginal price is that within the block of consumption, or $1 per 1,000
gal.
Taylor's Intramarginal price represents the sunk cost in the customer's
bill, or the reduction in his household budget that will limit his expendi-
tures on water and other goods. Taylor believed that this price variable
would measure the income effect discussed earlier. He associated the mar-
ginal price with the substitution component of the price effect. Although
it is demonstrated below that the intramarginal price would cause only part
of the Income effect (i.e., the marginal price would cause some income
23
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effect), it is clearly desirable to find the extent to which the two compo-
nents of price (intramarginal and marginal) affect consumption differently.
In short, it would be helpful to know if a 50-percent increase in marginal
price would have a greater effect on conservation than would an equivalent
increase in the first block, as discussed in the example on sewer charges.
Nordin's Lump Sum Specification
Nordin (1976) proposed a modification to Taylor's specification of the
intramarginal price; he identified the sunk cost part of the rate as a lump
sum. He defined the lump sum as Taylor's initial expenditure less the prod-
uct of the marginal rate times the quantity taken up to the last block. The
lump sum for a customer consuming 6,000 gal under the rate schedule of Figure
2 would be $2: A,000 gal at the marginal rate of $1 per gal is subtracted
from the initial expenditure of $6.
The lump sum specification adds clarity to the concepts, since it is
closer to real-world pricing practice and is especially similar to a new
trend in rate structures now gaining in popularity among energy utilities.
Utilities charge for making their service available; in residential rates,
the usual practice is to cover most of the fixed investment and administra-
tive cost in the minimum charge. Some but not all rate structures now spread
the fixed cost over several blocks. A trend toward a flat customer charge
on energy use makes the rate-making process more explicit. The lump sum cal-
culated under a rate structure with a customer charge would simply identify
the customer charge. Under most water schedules, the lump sum will be an
estimate of the fixed load in price schedule.
From a theoretical standpoint, Nordin claims that the lump sum is supe-
rior to the intramarginal price on a technical basis, but he assumes that
Taylor is correct in the belief that income and substitution effects can be
separated. Since we do not believe these components of price effects can be
segmented, our primary interest in the lump sum is that it appears to be a
logical conceptual specification for separating the marginal and intramar-
ginal price effects. Technical differences in the two specifications will
be further discussed after modifications are made in the way the variables
are specified.
A Common Ex Post Error
Both Taylor and Nordin would obtain the price variables for each cus-
tomer directly from the rate schedules on the basis of each customer's use
level. In spite of Taylor's emphasis on this pitfall, such a step would lead
to the simultaneity bias, as can be seen in comparisons of Taylor's intra-
marginal prices for different customers under the rate schedule of Figure 2.
A customer using 10,000 gal per month would have an initial expenditure of
$10 (the bill for 8,000 gal for the blocks up to the block of consumption).
This amount is equivalent to an initial price of $1.25 per 1,000 gal. In
the example above, in which a customer was using 6,000 gal, the initial
expenditure was $6 and the average price of the initial expenditure was $1.50
($6^4,000 gal). Regression using the initial expenditure to explain demand
would produce a positive correlation between price and quantity, those using
24
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the average intramarginal price would produce a negative correlation, and
both correlations would reflect the effect of quantity on price instead of
vice versa. The bias in Nordin's lump sum or the marginal price variables
could be demonstrated with similar comparisons.
The Correct Conceptual Specifications and Empirical Ambiguities
The error in the literal interpretation of the instructions of Taylor
(1975) for specifying variables appears to be an oversight on his part. The
initial expenditure and average price in the initial blocks are statistically
equivalent (a condition emphasized by Taylor) if and only if: (1) there is
only one intramarginal price and one marginal price per schedule and (2) the
initial block or blocks in each schedule are for an identical quantity.
Given the random distribution of breaks and the size of blocks in various
rate schedules, the conditions will obtain only under ex ante specifications
of the initial block. Similarly, the range of use on which the marginal
price will be specified must be determined ex ante.
An empirical ex ante definition of the initial block could be based on
the average size of all initial blocks as defined by Taylor, which would be
about 4,000 gal in our data set. As noted in the previous subsection, how-
ever, there is essentially no difference in the regression results expected
if the initial block is defined as 5,000 or 6,000 gal instead of 4,000 gal.
We have therefore elected to define the initial block as 6,000 gal and there-
by emphasize that the conceptual distinction between Taylor's initial expen-
diture and the traditional notion of the average price (derived from the
average expenditure) cannot be extended to an empirical distinction for our
rather typical data set.
The 6,000 gal consumption level is also used to calculate the ex ante
lump sum. In specifying (i.e., estimating) the fixed load of a given rate
schedule, calculations based on the average use level are at least as sound
as those based on an initial expenditure. The reason is that the initial
block or blocks are arbitrarily selected by the rate maker. The random se-
lections in rate decisions will tend to understate the lump sum for any rate
structure which spreads the fixed charge over a higher level of use, such as
5,000 gal, relative to one with the entire load in an initial bldck of
2,000 gal.
The ex ante consumption range of 6,000 to 10,000 gal for defining the
marginal price is also retained from our previous definition. There are no
significant conceptual or empirical differences in marginal price, regard-
less of the conceptual model used for empirical estimates.
Figure 5 shows the original rate schedule of Figure 2(a) in dashed lines
and how the schedule is restructured in the calculation of the ex ante
variables. The major purpose of the figure is to summarize the conceptual
differences among the average price, the intramarginal price, and the lump
sum, and to clarify the nature of the empirical ambiguities of these
variables.
25
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Figure 5. Ex ante price variables calculated from the rate schedule of
Figure 2(a). Note: Charges under the schedule are $6 for all or
part of the first 4,000 gal, $1 for each additional 1,000 gal up
to 8,000 gal, and $0.80 for each additional 1,000 gal. To compare
prices under this schedule with dissimilar blocks in other sched-
ules, the initial block is defined as 6,000 gal, and the marginal
price is calculated directly for the 6,000 and 10,000 gal in all
schedules.
26
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The solid line in Figure 5(a) illustrates the ex ante average price
conceptualized as the slope of the average expenditure function. The average
bill of $8 for 6,000 gal converts into a price of $1.33 per 1,000 gal so the
function is drawn through the origin with a slope of 1.33. The price illus-
trated contain both marginal and intramarginal components of the rate sched-
ule and is the correctly specified equivalent of the average price used in
previous studies that assumed (1) that a schedule can be quantified in a
single variable and (2) that the average price as opposed to the marginal
price is the one that influences consumption.
The difference between block rates and conventional prices is easily
seen in the illustration. The single price for a conventional good such as
toothpaste selling at $1.33 per tube would also be illustrated by the solid
line in Figure 5(a). For toothpaste, however, the single price is both the
average and the marginal price. The basic problem in defining the rate
structure in a single variable is to match the slope of the actual rate
schedule with a straight line through the origin.
Figure 5(b) is one possible conceptualization of the two-variable spec-
ification of the rate structure proposed by Taylor (1975). Here, the intra-
marginal price is illustrated as the initial expenditure of $8 for a range
of consumption in which the marginal price is zero, i.e., the slope of the
function is zero. Beyond 6,000 gal, the marginal price of $0.90 (calculated
as the average of marginal prices between 6,000 and 10,000 gal) is repre-
sented by the slope of the solid line. The use of the intercept and slope
more closely approximates the actual rate schedule.
The modification proposed by Nordin (1976) is illustrated in Figure 5(c).
The solid line here is the same marginal price of $0.90 extended to the ver-
tical axis. The intercept at $2.60 is the lump sum. Conceptually, the total
bill is separated into two distinct components—the variable charge and the
fixed charge. In effect, Nordin's specification eliminates the double-
counting in Taylor's intramarginal price. The price function is more pre-
cisely defined by the intercept and the slope of a straight line.
The segmentation of price into fixed and variable components (the inter-
cept and slope) is not unambiguous when considered in the context of a mul-
tiple regression. Figure 5(d) shows each of the variables as either slopes
or intercepts to illustrate this point. The intramarginal price, or inter-
cept in Figure 5(b) is identical to the average price function in Figure 5(a).
In a regression, the percent differential among bills is the same as among
prices per gal. The marginal price in Figure 5(d) is the same as in Figure
5(b) and (c) except it is now drawn through the origin. As indicated in the
diagram, the marginal price is equivalent to $5.40 of the average bill
(6 x $0.90 • $5.40). The lump sum is converted to the average amount of
fixed charge per 1,000 gal ($2.60 + 6 - $0.43) and drawn as a slope rather
than an intercept. Each variable is independent; any or all of the variables
could be included in a regression along with other unrelated and independent
variables to test the extent of their influence on water consumption.
27
-------
Figure 5(d) also shows the relationship among the various price vari-
ables. The lump sum plus marginal price is equal to the average price when
these variables are considered as parts of the total bill (the intercepts) or
as fixed and variable components of the price per unit (the slopes). The
intramarginal price and average price are identical here by definition; how-
ever, any redefinition of the intramarginal consumption block to more closely
approximate the block of up to but not including the block of actual consump-
tion would not alter its equality to the lump sum plus marginal price. Both
the intramarginal and average price concepts are to measure the difference
in the overall level of charges among schedules.
Finally, Nordin's refinement which equates the parts to the whole is
based upon the notion that the income component of the price effect can be
and should be isolated. This in turn, is based on the notion that only the
substitution effects are relevant in the elasticity measurement. If this is
not the case, then the older issue of whether the average price or the mar-
ginal price is the appropriate price variable in elasticity estimates is more
relevant than Nordin's lump sum-marginal price dichotomy. A major contribu-
tion of the Taylor price specification is that both the marginal and average
prices are theoretically relevant in the consumption decision.
Figure 5(d) provides a useful insight on the relationship between the
average price and the marginal price in a block rate structure. The marginal
price is the average price less the built-in fixed charges; to the extent
that this price is relevant to all or part of a customer's decision on the
amount of water to consume, the price effect would contain both income and
substitution effects as in the price of a conventional good. Any influence
on consumption exerted by the lump sum would be an income effect; however,
this effect would be in addition to, not instead of, other price impacts.
Moreover, the income effect of a utility's change in the fixed charge would
still be a price impact and should be included in the price elasticity.
The questions raised above as to which variables are relevant to the
consumption decision are subject to empirical testing. Since the intramar-
ginal and average prices are identical, a test of Taylor's model is a test of
the original and ongoing controversy over the appropriate specification of
price—marginal or average. If both prices are included as regressors along
with other independent variables such as income and occupants in explaining
water demand, the results should shed light on both the relative importance
of the variable and what they actually measure.
The question of what a variable measures (as opposed to the hypothesis
of what it should measure) is illustrated by the lump sum. As conceptual
defined, we would anticipate a reduction in water consumption as the fixed
charge increases, all else equal. As illustrated in Figure 5(c), there is a
single price of $0.90 per 1,000 gal plus this differential charge for having
the service available. An alternative interpetation is offered in Figure
5(d), however. We could interpert this schedule to have a basic (average)
price of $1.33 per 1,000 gal with a discount of $0.43 per 1,000 gal on addi-
tional use. Since the lump sum enters the regression equation as an inde-
pendent variable, it is not clear whether it will measure the negative impact
of a penalty charge or the positive iiapact of a quantity discount.
28
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Summary and Conclusions
Neither the intramarginal price nor the lump sum can screen out the
income effects of a price schedule because the marginal price gives rise to
both income and substitution effects. Also, the specificaiton of the rate
schedules with two variables is still essential because the fixed and vari-
able components should, 11 priori, cause different amounts of price impact.
In addition, this anlysis reinforces an earlier point—that the general con-
cept of elasticity is to measure the total price effect without regard to
whether it comes from the income of the substitution components of the price
effect.
No sound a_ priori grounds appear for declaring either the marginal or
the average price in a rate schedule as a price equivalent to MP = AP in
unit-priced goods, as has been done in most published studies. There are
also conceptual and even more formidable empirical barriers to specifying two
price variables that define a schedule of prices and at the same time clearly
distinguish between what is the marginal component of the rate and what is
not. These limitations, however, should not obscure the real issue, which is
to answer elasticity questions such as whether and how much an increase in
the fixed charge will effect consumption, as opposed to a comparable increase
in variable charges.
EMPIRICAL RESULTS—COMPARISONS OF ALTERNATIVE MODEL SPECIFICATIONS
This subsection addresses the central issues through a comparative anal-
ysis of several specifications of estimating equations using the alternative
price specifications developed to this point. With other determinants held
constant, price impacts are estimated in the following models:
(1) Q = f (AP)
(2) Q - f (MP)
(3) Q = f (AP, MP) = f (IP, MP)
(4) Q = f (LS, MP)
(5) Q = f (AP, LS)
The empirical ambiguities noted earlier are resolved by interpretation
of the results within the context of each model.
Since ex post definitions are used for comparison with the correctly
specified ex ante variables, the data set was reduced to observations of
household customers with average monthly use in excess of the minimum charge,
thus eliminating samples with MP = 0.
All estimating equations are in the general form:
InQ = B0 + Bj InAP + B2 InMP + B3 InINC + B^ InPEO
where Q is the average monthly consumption (which is explained for five win-
ter months and five summer months as well as on an annual basis), coeffi-
cients of the price variables are' direct estimates of the elasticities, B3 is
29
-------
an estimate of the income elasticity (ING is on household income from all
sources), and PEO is the number of household occupants.
Table 2 reports results from model specifications based on the assump-
tion that one variable is sufficient to define the price under a schedule.
The ex post specifications are based on the prices actually paid by each
customer in the sample. The elasticity associated with the average price is
in the range of -0.4 to -0.8 and is consistent with estimates reported in
previous studies that we consider invalid because of the simultaneity bias.
Elasticities based on the marginal rates in the range of actual consumption
indicate no significant relationship between this price and the quantity
taken in winter. Even the significant coefficients for annual and summer use
indicate that the marginal price could have little influence on consumption.
Conversely, considering the bias, the level of use has little influence on
the marginal rate in this data set.
In contrast to the biased estimates, the ex ante average price specifi-
cations indicate a price elasticity of about -0.2, and the marginal price has
no influence on consumption levels. A comparison of the ex post and ex ante
specifications Indicate the extent of the bias from the misspecification of
price.
Other effects of misspecification can be seen in comparisons of coeffi-
cients for the income and occupant variables. In particular, the estimate of
the income elasticity has a downward bias as a result of the misspecified
average price. In addition, the coefficients of determination (R s) are
inflated as a result of the quantity taken, which explains the average price
rather than vice versa.
Finally, a comparison of the R2 between ex ante specification for
average and marginal price for each season indicates that even though average
price is significant, the variable adds very little to the explanatory power
of the entire equation.
Table 3 presents results obtained by defining the rate schedules with
two variables. The ejc post specifications in the upper part of the table
have no validity in explaining consumption, but they are of interest as a
basis for comparisons with ex ante specifications. They are also similar to
results obtained (but not shown) from the literal or ex post specification
of Taylor's average price in the initial expenditure. Regressions specified
with Taylor's optional intramarginal price (the ex post initial expenditure)
in combination with marginal price changed both the magnitude and signs of
the price coefficients but were otherwise similar. In all three combina-
tions of two misspecified variables, the typical effect was to increase the
R2 in comparison with results from the ex^ post average price specification
in Table 2. Opposite signs on the price variables are attributed to an
interdependence between the price variables in all three combinations.
The results in the second three regressions in Table 3 can be viewed as
either a test of Taylor's conceptual model with intramarginal and marginal
price, or as a test to determine whether average or marginal price, neither,
or both influence the customer's behavior. (The IP in this case is either
30
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TABLE 2. REGRESSION COEFFICIENTS EXPLAINING WATER CONSUMPTION
WITH A SINGLE PRICE VARIABLE
Specification of prices Period
Ex post Annual
Summer
Winter
Annual
Summer
Winter
Price
AP
-0.55
-0.40
-0.76
elasticity
MP
-0.13
-0.16
-0.05*
Income
0.16
0.20
0.11
0.24
0.26
0.20
No. of
household
occupants
0.34
0.43
0.34
0.48
0.48
0.50
R2
0.51
0.44
0.62
0.34
0.33
0.32
Ex ante Annual
Summer
Winter
Annual
Summer
Winter
-0.18
-0.19
-0.17
__.
— -
"•"•«
— _
-0.05*
-0.01*
-0.02*
0.23
0.26
0.19
0.24
0.26
0.20
0.48
0.49
0.50
0.48
0.48
0.50
0.34
0.33
0.33
0.34
0.32
0.32
*Not significant at 0.025 level.
31
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TABLE 3. REGRESSION COEFFICIENTS EXPLAINING WATER CONSUMPTION WITH
RATE SCHEDULES DEFINED BY TWO VARIABLES
u>
Price elasticity
and variable
Specification of price Period
Ex post Annual
Summer
Winter
Ex ante Annual
Summer
Winter
Annual
Annual
Variable
No. 1
-0.60 AP
-0.40 AP
-0.91 AP
-0.31 AP/IP
-0.31 AP/IP
-0.32 AP/IP
-0.02*LS
-0.18 AP
Variable
No. 2
+0.19 MP
-0.05*MP
+0.41 MP
+0.19 MP
+0.17 MP
+0.21 MP
+0.04*MP
-0.01*LS
Income
0.16
0.20
0.09
0.23
0.25
0.19
0.24
0.23
No. of
household
occupants
0.39
0.43
0.29
0.47
0.47
0.49
0.74
0.48
R2
0.52
0.44
0.67
0.35
0.33
0.33
0.34
0.34
*Not significant at 0.025 level.
-------
the initial expenditure or average price in the initial expenditure.) The
fact that the coefficients are all significant appears to support Taylor's
analysis indicating that both intramarginal and marginal elements of price
contribute to the consumption decision. The opposite signs and inter-
dependence between the price proxies are inconsistent with a clear division
of the rate into two components, as envisioned by Taylor. Interdependence or
multicollinearity will tend to create opposite signs on marginal and average
prices in the regression results. There is no indication that either initial
or total expenditures will measure an income effect.
The opposite signs on the two price variables preclude a straightforward
interpretation of the results. It is apparent from a comparison of R^'s
among the various equations specified (with either or both ejx ante average
and marginal price) that marginal price contributes very little to the
estimating power of the various models. It therefore appears that average
price specified alone provides an adequate specification of relative charges
under various price schedules in this particular data set.
A sample of results using the lump sum as one of two variables used to
define rate schedules is reported in Table 3. Results obtained from ex £Qg_t
specifications (not shown) were similar in the respect that the lump sum was
small and insignificant regardless of the way the model was specified.
When the lump sum is specified with the marginal price, as suggested by
the conceptualization of Nordin (1976), there is no evidence of an income
effect associated with the fixed charge in the rate schedule. This could be
because the fixed component is unimportant, as is the marginal price in
isolation; or the results may stem from the fact that both variables proxy
the same thing (that is, how the discount or lower rate differs from the
overall level of charges). In either case, the variables in combination
provide no information on the overall level of consumption. On the other
hand, if the lump sum is specified with average price and interpreted as a
discount for quantity purchases, we are lead to the conclusion that the
overall charge influences consumption, but that the mix or fixed and variable
charges is insignificant for this particular data set.* These results are
consistent with the interpretation above based on various combinations of the
average and marginal price.
*More important, perhaps, is that these results are-not inconsistent with
the use of the lump sum or some other variable in other data sets to obtain
usable estimates of how the mix of fixed and variable charges influences
consumption differently from the overall level of charges as indicated by
the LS, by accident rather than design, is a measure of the mix of fixed and
variable charges in the rate structures of this data set. Two more explicit
mixed variables, lump sum/expenditure ($2.60/$8.00 in Figure 5(c)) and 1.0
dummy variables, which identified samples with the highest or lowest propor-
tion of fixed charges in the mix, as indicated by ratios from the variable
lump sum/expenditure, were specified and tested in several equations similar
to those reported. No evidence was found that the mix had any influence on
consumption independent of the consumption explained by average price.
33
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Conclusions
In summary, the comparative analysis of results from various price
specifications indicates that the use of ex ante average prices alone should
provide reasonably accurate estimates of elasticities in this data set.
This conclusion is based on tests indicating that average price explains the
price-associated variations in consumption so well that several proxies
identifying variation in the mix of the fixed and variable components of the
rates make no sifnificant contribution to explaining demand.
The single-variable determination is not consistent with ji priori
expectations and may reflect a special case where the marginal price as
opposed to average price is simply an insignificant influence in the
customers' decisions. The marginal rate cannot be written off as unimpor-
that, however, because average price contains both intramarginal and marginal
components of the rate. The interrelationship between average and marginal
price suggests that the variables are not statistically independent and that
either could explain part or all of the impact of the other. Results from
previous elasticity studies that assume a single price is a sufficient
measure of price differential among schedules and assert that either the
average or marginal price is the appropriate measure are subject to errors
that could substantially understate the true elasticity, even when sufficient
precautions are taken to avoid mlsspecification of the variables. The
inadvertant misspecificatlon of price variables remains a pitfall even when
the problem is clearly recognized. Misspecifications lead to substantial
overstatements of price elasticity and distort the estimates of income
elasticity and the impacts of other determinants.
The conceptual foundation for the use of two price variables provided
by Taylor (1975) and the modification suggested by Nordin (1976) are major
steps toward correcting the possible errors in previous work. Neither
approach, however, provides a clear division of price into the intramarginal
and marginal components. An alternative approach is to specify price as
(1) one variable (such as average price) that will explain the consumer's
behavior relative to the purchase of goods with a single unit price, and
(2) another variable (such as the lump sum) that specifies the difference
between a unit price and the scheduled price. The objective is to uncover
any unexplained difference in consumption explained by the difference between
average and marginal price.
USE OF PRICE ELASTICITIES IN MAKING POLICY AND MANAGEMENT DECISIONS
The validity of results obtained earlier from jx ante average prices
alone are given further consideration here in the context of using price
elasticities to make policy and management decisions. Since the end use of
the price proxy is in the price elasticity estimate, we move directly to
improvements in the final estimates. Results are reported from subsets of
the data that (1) illustrate findings more useful than the elasticity
estimates per se, and (2) provide independent evidence that the estimates are
reasonably accurate.
34
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Price Elasticity Results
Customers with zero ex post marginal prices were deleted from the sample
in the previous estimates because of the possible distortion to results
obtained with ex post marginal price. Since marginal price is dropped from
consideration in this section (and, in any event, would have been derived
from the schedule), these samples were replaced in the data set and equations
were estimated again. Results comparable to the ex ante average price
specification in the previous subsection are presented in the first three
equations of Table 4. These variables are specified in logarithms, so the
coefficients of the price and income variables constitute one set of elasti-
city estimates. Results from the second three equations were obtained from
the same variables, with the estimating equation specified in additive (as
opposed to the multiplicative) form. Elasticities were calculated from these
coefficients at the mean use, price, and income.*
An interpretive evaluation of the results from each form of the model
suggest that the price elasticity is about -0.2, with no difference between
summer and winter. The income elasticity is almost +0.3, and it is
significantly higher in summer than winter. From the t-values and other
tests reviewed below, it appears that the multiplicative form provides a
better fit and superior estimates of the price and occupant coefficients.
The additive form is somewhat better for Income.
Further modification of the variables or the estimating equation could
possibly produce a better fit of the data, but it is not likely that the
interpretation could be made more definitive. Furthermore, the accuracy of
these estimates is sufficient for any plausible applications. A reasonable
expectation for elasticity estimates derived from several market areas is
that they provide a general description of the response to be expected from
consumers as a result of changes in income or rate schedules. They are no
more than a point of departure for a specific decision on rates or a fore-
cast for a specific utility.
The finding that price elasticity is -0.2 instead of -0.6 indicates that
price affects consumption much less than has been indicated in other studies.
A utility facing a need for an increase in revenue of 5 percent would have to
raise rates only 6.35 percent if price elasticity were -0.2, and 16.16
*The mean annual, summer, and winter use is 6,061, 6,571 and 5,346
gal, respectively. Average price per 1,000 gal is $1.32, and average
family income is $12,300.
35
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TABLE 4. COMPARISON OF ELASTICITY ESTIMATES FOR ANNUAL, SUMMER
AND WINTER WATER USE USING MULTIPLICATIVE AND
ADDITIVE FORMS OF THE ESTIMATING EQUATION
Model
Multiplicative
Multiplicative
^ Multiplicative
Additive
Additive
Additive
Dependent
variable
Average annual use
Monthly summer use
Monthly winter use
Average annual use
Monthly summer use
Monthly winter use
Average
Constant price
5.92 -0.20
(-3.43)*
5.78 - .22
(-3.55)
5.17 - .19
(-3.09
2729 -659
(-2.24)
(( -.14))*
2747 -650
(-1.89)
(( -.13))
2703 -644
(-2.60)
(( -.16))
Income
0.24
(9.14)
.27
(7.32)
.20
(7.32)
139
(10.38)
(( .28))
170
(10.69)
(( .32))
95
( 8.33)
(( .22))
No. of "house-
hold occupants
0.47
(13.95)
.46
(12.70)
.49
(13.94)
848
(12.16)
888
(10.71)
794
(13.30)
R2
0.34
.33
.32
.30
.28
.29
*The t-values are in single parentheses, and elasticity estimates calculated for the additive
model are in double parentheses.
-------
percent if price elasticity were -O.6.* Thus a utility may have more lati-
tude in increasing their rates than some recent studies have indicated.
Most policy issues require a less general description of consumer
response t^an the one provided by elasticity estimates. A utility may wish
to know whether there is some threshold price level at which higher prices
become a significant deterrent to consumption, or how higher rates can be
expected to influence revenue from low-income sectors of their service area.
Such information is only partially available from a single elasticity
estimate. More relevant inputs are available from a direct examination of
the issues.
*This calculation is based on the assumption that price elasticity
remains constant throughout the entire range of the price increase. The
equation is derived as follows:
R = current revenue
Q » current quantity consumed
P - current price
e - absolute value of price elasticity
g - required percentage increase in revenue
b - percentage increase in price
Current revenue is equal to current quantity consumed multiplied by current
price.
R - Q.P
If there is a need to increase revenue requirement by g, then the new
revenue will be (1 + g) R. The new price will be P (1 + b), and consumption
will drop to Q (1 - be). Thus the following equation holds:
(1 + g) R - Q (1 - be) R (1 + b)
and
(1 + g) R - Q.P (1 - be) (1 + b)
since R - Q-P
(1 + g) - (1 - be) (1 + b)
solving for b
1 - e + / (e - I)2 - 4 eg
D ™ ————________
2 e
37
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Applications of Demand Analysis to Policy Issues
A direct approach to the threshold question Is to estimate the shape of
the demand function rather than an elasticity coefficient. The extent to
which groups of customers behave differently under different rate structures
is obtained by substituting rate structure dummy variables for the price
variable:
Q = f(Dr D2, .... D6, INC, PEG)
where D^ is given a value of 1 if the customer faces a rate schedule that
charges a monthly rate between $5.51 and $6.50 for 6,000 gal, otherwise D^
is 0. D2 through Dg similarly represent schedules charging $6.51 through
$7.50, $7.51 through $8.50, etc. up to charges over $10.50 for 6,000 gal.
Customers under schedules charging $5.50 or less (for which there is no
dummy) thus become the bench mark for comparisons. The model is specified
in additive form so that coefficients may be read in gallons and compared
directly with prices. The results are presented in Table 5.
These results can be converted into a demand curve by calculating the
consumption at each price level, as follows:
(coefficient for annual use per person x average number of occupants)
+(coefficient for income x average income) + the constant = total consumption
For example, at $5 (the approximate average bill for the lowest price
schedules):
(850 x 3) + (137 x 12.3) + 2802 = 7,065 gal
At the average price of $6, all else equal, the customer consumes 6,352 gal
(since 731 fewer gallons are consumed at rates between $5.51 and $6.50).
Another drop in quantity taken is observed at the next higher price range,
but the expected price-quantity relationship does not hold for the higher
prices.
The null hypothesis that the coefficients of variables D^ through Dg
are all equal to a common value is not rejected. The common value, however,
is significantly less than zero, which implies that additional water is
consumed at the lowest prices. Further confirmation came from splitting the
data into households with rates above $8 per 6,000 gal and those below. In
the low price group, regressions similar to those in Table 4 produced price
elasticity estimates from -0.27 to -0.47. No significant price elasticities
could be obtained in the higher price range.
The analysis provides insights into the nature of price impacts that
might be anticipated in response to rate increases. At very low rates, some
customers behave as if faced by a flat rate schedule, and at higher rates,
conservation probably stems from the general recognition that the bill will
be less if less water Is used. The amount of the price differential does not
appear to be important.
38
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TABLE 5. PROFILE OF WATER USE DIFFERENTIAL
UNDER VARIOUS RATE STRUCTURES
Dependent
Variable
No.
occupants
per
$5.50 to $6.51 to $7.51 to $8.51 to $9.51 to Over house- Income 2
$6.00 $7.50 $8.50 $9.50 $10.50 $10.50 hold ($1,000) Constant R
Average annual
w use -7.13 -1296
* (-1.73) (-2.75)
Monthly summer
use -544 -1347
(-1.11) (-2.40)
Monthly winter
use -948 -1225
(-2.70) (-3.04)
-1054 -1123 -1715 - 898 850 137 2802 0.31
(-2.14) (-2.77) (-3.19) (-1.94) (12.15) (10.10)
- 928 -1246 -1703 - 769 895 168 2276 .28
(-1.58) (-2.58) (-2.67) (-1.40) (10.76) (10.39)
-1230 -952 -1731 -1079 788 95 2839 .30
(-2.92) (-2.75) (-3.77) (-2.78) (3.19) (8.16)
-------
Validity of the Elasticity Estimates
The emphasis of the analysis above is on policy application; the results
also show that the price elasticity estimate of -0.2 is reasonably accurate
and, conversely, that estimates of -0.4 to -0.8 are too high.
To check the validity of the formal estimates in Table 4, independently
of the technical considerations in defining variables or regression models,
simply observe the relatively large percentage differences in rates relative
to the small differences in consumption levels.
Consider, for example, the difference in use between the customer with
the highest and lowest rates, derived from dividing the data set for the
analysis above. Averages for monthly use per household for the three periods
are shown in Table 6. These data tend to confirm the low price elasticity
estimates and clearly show the upward bias of estimates made with misspeci-
fied price variables.
Income Elasticity and Other Determinants of Water Consumption
The details of how income influences consumption, which underlie the
general description provided by the elasticity estimate of +0.3, are also of
interest for policy decisions. Dummy specifications for income groups were
used to estimate the income consumption relationship, with occupants and
prices constant. Regression results are shown in Table 7, where the
differences in consumption among income groups are representative of results
obtained with alternative dummy specifications. A nearly linear increase in
consumption is shown up to middle incomes, where increases level off for the
upper-middle group and become exponential in the highest income range. Few
customers fall in the exponential range of the curve, however.
These estimates are consistent with conventional elasticity estimates
for customers with incomes over $20,000, where the income elasticity was
found to be in the range 0.4 to 0.6 and no significant price elasticities
were obtained. For incomes below $20,000, however, price and income
elasticities of -0.2 and +0.2 were highly significant.
Similar use was made of dummy variables to test for significant differ-
ences in water consumption associated with urban-rural, metropolitan-suburban,
climatic, and other factors. The study area offers some variation in
moisture conditions (arid versus humid), but no influence on total water
consumption could be attributed to the difference between subtropical and
semimountainous areas. There were some differences in the use patterns by
months, however. Some density variables were significant, but the differen-
tials in use that were indicated by these tests were negligible. Urban use
was not significantly different from suburban or rural use in comparable
housing units.
40
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TABLE 6. AVERAGE MONTHLY WATER USE PER
HOUSEHOLD (GAL/MONTH)
Period
Annual
Summer
Winter
Above $8/6
(N = 399)
Mean
5,929
6,395
5,276
,000 gal
Std. Dev.
of Mean
198
235
162
Below $8/6
(N = 369)
,000 gal
Std. Dev.
Mean
6,201
6,745
5,426
of Mean
175
200
156
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TABLE 7. WATER CONSUMPTION ACCORDING TO INCOME CATEGORY
Income category
Dependent $6,000+ to
Variable $10,000
Average annual
use
gallons 787
t- value* (2.40)
.e-
NJ
Monthly summer
use
gallons 923
t-value (2.37)
Monthly winter
use
gallons 596
t-value (2.13)
$10,000 to
$20,000
1409
(4.72)
1686
(4.76)
1022
(4.01)
$20,000 to
$30,000
2934
(7.98)
3537
(8.10)
2090
(6.64)
$30,000 to
$40,000
3092
(3.82)
3645
(3.79)
2319
(3.35)
$40,000
or more
6316
(7.10)
7999
(7.57)
3958
(5.20)
No. of
occupants
in
household
854
(12.06)
896
(10.66)
795
(13.13)
Average
cost of
6,000
gal
- 587
(-2.35)
- 705
(-2.03)
- 661
(-2.65)
2
Constant R
3203 . 30
3359 .28
2983 .29
*The t-value indicates the level of significance of the variables.
-------
CONCLUSIONS
Estimates of the price elasticity for water in the study area indicate
that water consumption is relatively insensitive to the price except for
conservation induced by the knowledge that a price must be paid. Most
previous studies have apparently overestimated the elasticity by misspeci-
fying the price variable. Some have apparently underestimated the elasticity
by failing ta identify the appropriate price variable. These possible errors
have been verified by comparisons of models and variables deliberately
misspecified with our corrected models and variables. Our results are
strongly supported by direct comparisons of subsets of the data that indicate
price/quantity relationships independent of the specification technicalities
of the econometric estimates.
The limitations of the price specifications used are inherent in the
nature of block rates and are not necessarily more severe than limitations
in income measurements or general shortcomings of most data sets. Elasti-
cities suitable for forecasts of high accuracy would require system-specific
data; our estimate of a price elasticity of about -0.2 is no more than a
descriptive indicator of what might be found in a specific market area.
Within the overall range of price elasticity, the price effect is
greater at lower prices and lower incomes. There is no evidence that the
price elasticity of water for sprinkling is greater than that of water for
other uses, but summer demand is more sensitive to income.
Some policy implications of these findings are that higher price would
not be an effective approach to short-run conservation, or, conversely, that
increased rates to finance the upgrading of water of sewer systems would only
slightly reduce consumption and not interfere with collecting adequate
revenues. The analysis raises doubts that stricter Federal regulations of
water quality would necessarily have to be offset with Federal grants. In
addition, low elasticities imply that water fees might be used as a source
of additional municipal revenues.
43
-------
SECTION 5
APPLIANCES AND OTHER DETERMINANTS
OF WATER DEMAND
This section adds descriptive details to the demand determinants dis-
cussed in Section 4 and considers the policy implications of these findings.
Given the conclusion that the price elasticity for water is quite low and the
deduction that demand for irrigation use is no more elastic than the demand
for other uses, it appears that pricing policy should be based primarily on
revenue considerations and that conservation policies will require maximum-
use targets and incentives to stay within the limits established.* Descrip-
tive patterns of residential water use can serve as a basis for establishing
targets consistent with the conservation desired.
The following discussion tabulates water usage and selected family
characteristics for subgroups of the population based on the most important
determinants of consumption—the number of occupants and income. A similar
set of profiles based on ownership of water-using appliances is also
developed for an analysis of outside summer use for irrigation and other
needs.
CUSTOMER AND WATER USE PROFILES
Tables 8 through 11 reveal the interrelationships of the number of house-
hold occupants and income in determining the demand for water. They also
introduce other factors (such as irrigation practices), that contribute to
demand. The patterns of water use, but not necessarily the amounts, are
probably typical of those that would be found in any water system. Table 8
shows a descriptive tabulation such as might be undertaken by even a small
utility conducting a background study for policy decisions.
Several points are apparent from these tabulations. A dominant factor
in determining water consumption is the number of occupants per unit. With-
in the profiles, it can be seen that average monthly water consumption in the
summer is more than 20 percent greater than that for the average winter
months and that the peak load for monthly water use is some 50 percent higher
*Actual policies for ongoing as well as temporary conservation
measures might well be patterned after the California experiment
described in Consumer Reports (1978). The results reported in this
chapter suggest how targets might be established and which conservation
practices would contribute most to meeting the targets.
44
-------
than that during low-use months. The peak load for a hot, dry week is
probably considerably higher in most systems.
In more detailed breakdowns not shown in this chapter, a wide range was
found between the first and third quartiles, such as those illustrated in
Table 8. The gap increased slightly when customers were grouped by income as
opposed to the number of household occupants. But even comparisons of con-
sumption by groups with similar incomes and the same number of occupants do
not change the pattern of dispersion. The findings give support to conclu-
sions in previous studies that water-efficient appliances could be used to
achieve conservation with little or no reduction in the function served by
water use.
Table 9 supplies a breakdown of the economic characteristics of customers
grouped by number of household occupants. One-person households consist
largely of retired individuals with low to moderate incomes. Age and income
and number of occupants are the major factors which explain consumption.
Within the two lower income categories, a distinction is made between retired
homeowners and others, since the nominal retirement income tends to under-
state the real income of the retired. Income increases with the number of
occupants up to four and drops for households with more than five occupants.
The drop occurs primarily because the percentage of poor increases with
family size, but they replace middle rather than high-income families.
In Table 10, the sample is disaggregated by income groups. Monthly and
seasonal averages and the extra use per category are calculated as in Table 8.
In addition, Table 10 includes the percent of customers in each group with
extra summer consumption over 10,000 gal. This measure was used as a proxy
for households with moderately high to heavy irrigation demand. (The proxy
was tested in the local data set and found to be an accurate indicator of the
use of water for irrigation purposes. The amount of extra, however, includes
all extra summer use and is considerably higher than the amount for irriga-
tion alone.)
Comparisons of high- and low-use months, winter and summer use levels,
and the amount of extra use show a clear relationship between incomes and
extra use. The percent of households with high lawn irrigation demand also
increases. Of equal interest, however, is that winter use also increases
with income; furthermore, a large percentage of higher-income units do not
use great amounts of water for lawn irrigation, and a fairly large number of
lower-income groups do irrigate substantially. The importance of these
patterns are further discussed below, but the reasons are partially apparent
in Table 11, where additional characteristics of each groups are presented.
The relatively low use of retired homeowners compared with others of
similar income but fewer assets (Table 10) is partly explained by the lower
average number of occupants per household (Table 11). The effect of greater
assets is partially evident in the size of dwelling and appliance ownership,
but regression analysis shows that any increase in water consumption as a
result of high income is offset by reduced consumption at retirement age.
Finally, the percent of customers with moderate to heavy lawn irrigation
demands (Table 10) is influenced almost as much by type'of dwelling (Table 11)
45
-------
TABLE 8. AVERAGE (MEAN) WATER USE OF CUSTOMERS IN ALABAMA
BY NUMBER OF HOUSEHOLD OCCUPANTS
Number of household occupants
o\
iype or water use
Monthly water use (gal):
July 77
Aug. 77
Sept. 77
Oct. 77
Nov. 77
Dec. 77
Jan. 78
Feb. 78
March 78
April 78
May 78
June 78
Total
Average monthly water use (gal) :
Annual
Winter
Summer
Extra water use during the
summer season (gal)*:
1
4692
3305
3670
3551
2996
3161
3563
3510
2933
3873
4069
3797
42823
3569
3173
3851
4747
2
6255
5680
5942
4893
4609
4560
5474
4751
4493
5787
5175
6078
63707
5309
4779
5687
6359
3
7179
7424
7330
5945
5758
5708
6191
4515
5476
6619
6241
7051
76537
6378
5750
6827
7537
4
10130
8228
9013
7483
7079
6926
6939
6678
6654
8558
8127
8994
95805
7983
7055
8647
11145
5
10732
9519
10141
7801
7600
7541
9092
7791
7029
9253
8457
10576
105528
8794
7811
9492
11796
6
12736
9614
10411
9640
9018
8569
9255
8831
8131
10206
8994
10788
116193
9683
8761
10341
11061
(continued)
-------
TABLE 8 (continued)
Type of water use
Number of household occupants
Daily water use (gal/person) :
Winter months:
Mean
Median
1st quartile
3rd quartile
Annual:
1st quartile
Median
3rd quartile
105
84
58
115
70
97
140
77
65
45
94
52
77
113
62
61
45
80
48
70
84
57
53
39
71
43
61
81
50
44
35
63
39
55
73
41
41
30
57
31
58
92
*Extra is the difference between annual use and twelve times the winter monthly average.
Winter is November through March. Summer is defined here as April through October; but for a
specific system, the irrigation season may differ.
-------
TABLE 9. PROFILES OF WATER CUSTOMERS IN ALABAMA BY
ECONOMIC STATUS AND OF HOUSEHOLD OCCUPANTS
ca
Economic status
Percent of customers by 1976 income
category :
$0 to $6,000, retired homeowners
$0 to $6,000, other*
$6,000 to $10,000, retired homeowners
$6,000 to $10,000, other*
$10,000 to $20,000
$20,000 to $30,000
$30,000 to $40,000
Over $40,000
No answer
Average income
Percent of customers by 1976 employment
status:
Head of household employed
Head of household unemployed
Head of household retired
Spouse employed full time
Spouse employed part time
Homemaker — not employed
Other adults employed full time
Other adults employed part time
Other adults employed
Other adults retired
Number of household occupants
1
35.2
22.1
14.8
13.1
9.0
3.3
0.0
0.0
4.9
$6,795
36.9
9.0
54.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2
14.2
10.9
11.3
12.4
29.1
12.0
2.9
1.5
6.5
$12,281
56.4
5.5
38.2
23.6
4.4
56.4
3.6
1.5
2.5
4.0
3
3.7
10.6
3.7
19.3
32.9
14.3
2.5
0.6
17.4
$13,298
80.1
8.1
11.8
34.2
3.1
46.6
9.9
0.6
9.9
5.6
4
1.3
10.5
2.0
10.5
39.5
20.4
2.0
2.0
12.5
$16,041
85.5
6.6
7.9
23.7
5.9
60.5
4.6
1.3
3.9
2.0
5
3.8
19.2
0.0
11.5
44.2
13.5
3.8
1.9
1.9
$13,173
80.8
9.6
9.6
25.0
3.8
63.5
5.8
1.9
7.7
1.9
6H-
0.0
21.5
0.0
20.0
30.8
10.8
6.2
1.5
1.5
$13,858
84.6
15.4
0.0
26.2
4.6
55.4
15.4
4.6
23.1
6.2
As per-
cent of
total
11.1
13.9
7.0
14.0
29.8
12.7
2.5
1.2
9.8
$12,514
67.1
7.7
25.0
22.5
3.7
47.2
5.6
1.3
5.8
3.5
*0ther than a retired homeowner. The retired homeowner is presumed to have wealth that may
influence consumption.
-------
TABLE 10. AVERAGE WATER USE OF CUSTOMERS IN ALABAMA BY FAMILY INCOME
js
vo
Type of water use
Monthly water use (gal):
July 77
Aug. 77
Sept. 77
Oct. 77
Nov. 77
Dec. 77
Jan. 78
Feb. 78
March 78
April 78
May 78
June 78
Total
Average monthly water use (gal):
Annual
Winter
Summer
Extra water use during the summer
season (gal):
Daily winter water use (gal/person):
Percent of units with extra summer use:
Greater than 20,000 gal
10,000 to 20,000 gal
Income Category
Other*
($0 to $6,000)
5975
4995
5719
4965
4700
4858
5685
5286
4446
4848
4774
5452
61703
5142
4995
5247
1763
53
2.6
14.8
Retired
homeowner
($0 to $6,000)
4344
3822
4027
3561
3316
3323
3695
3407
3389
3800
3891
4005
44580
3715
3426
3921
3468
66
4.3
15.2
Other*
($6,000 to
$10,000)
7423
6569
7201
5922
4377
5426
6145
5429
5285
6527
6636
6986
74926
6244
5532
6752
8542
58
12.9
16.4
Retired
homeowner
($6,000 to
$10,000)
4759
4667
4379
3726
3765
4190
4648
4185
3735
4256
3854
4325
50499
4208
4105
4282
1239
68
3.4
19.0
(continued)
-------
TABLE 10 (continued)
ui
O
Type of water use
Monthly water use (gal):
July 77
Aug. 77
Sept. 77
Oct. 77
Nov. 77
Dec. 77
Jan. 78
Feb. 78
March 78
April 78
May 78
June 78
Total
Average monthly water use (gal) :
Annual
Winter
Summer
Extra water use udring the summer
season (gal) :
Daily winter water use (gal/person) :
Percent of units with extra summer use:
Greater than 20,000 gal
10,000 to 20,000 gal
$10,000 to
$20,000
7863
7276
7302
6489
6001
5930
6736
5963
5346
7279
6568
7815
80968
6749
6075
7227
8068
58
15.1
18.0
Income
$20,000 to
$30,000
10902
8776
10004
7430
7362
6835
7736
6778
6469
9205
7798
9431
98726
8227
7036
9078
14294
70
25.4
25.4
category
$30,000 to
$40,000
11491
10335
9347
7323
6439
6708
8108
6499
6780
10666
8660
11462
103818
8652
6907
9898
20934
62
47.6
19.0
$40,000+
20922
11683
12260
10986
10201
8890
11795
10118
8917
13546
16270
14735
150323
12257
9984
14343
30515
95
50.0
18.7
tion.
*Other than a retired homeowner, who is assumed to lease assets that may influence consump-
-------
and home ownership (Table 11) as by income. For example, single family home-
owners in the lowest income/asset category would have about the same percent
of moderately heavy waterers as the middle-income group.
An assessment of how appliance ownership and lawn irrigation contribute
to the system load is begun with data provided by profiles in Table 12.
Before evaluating the content of the table, however, it is useful to review
what cannot be found from these data. The approach used in Table 12 was
proposed and tested by Batchelor (1975). This investigator first ranked
water-using appliances in order, from the most frequently owned to the least
frequently owned. He then grouped households by ownership of appliances—all
appliances, all but the least frequently owned, all but the two least fre-
quently owned, etc. Batchelor then subtracted the average consumption of the
second group from that of the first group to estimate the water used by the
appliance least frequently owned. For example, if in the first two columns
of Table 12, annual water use of about 110,000 gal for households with dish-
washers and washers is subtracted from the annual use of about 138,000 gal
for households with garbage disposals as well, the resulting 28,000 gal is
the theoretical annual estimate of water used by a garbage disposal. (An
estimate of 19,000 gal is produced by using the same procedure for the fourth
and fifth columns.)
Batchelor found his method of estimating appliance use unsuccessful,
however, because the hierarchy of appliances tends to measure income and
therefore overstates the water use of the less frequently owned appliances.
The average incomes shown in Table 12 and the estimates of water use by
garbage disposals above confirm the limitation noted by Batchelor, but they
also suggest that the appliances owned reflect characteristics other than
income that contribute to water consumption. Greater water consumption is
associated with the user's lifestyle (as reflected in the greater mobility
and newer housing of heavy water users) and life cycle (as reflected in the
fewer occupants and greater ages of those using less water).
Table 12 contains an important modification of Batchelor's approach,
since the ownership of lawn sprinklers (or more precisely, their use) is
removed from the hierarchy of appliances owned. As noted above, a greater
percentage of lawn sprinklers is found at higher incomes, but they are
scattered over the population, whether ranked by occupant's income or other
characteristics such as age of occupants or type of housing unit. Thus the
income bias associated with the use of lawn sprinklers is reduced (although
not entirely eliminated) when comparing the water use of customers who do
moderate to heavy sprinkling with that of customers who do little to no
sprinkling. Comparisons of annual water use therefore provide rough indi-
cators of the maximum amounts of water use for lawn irrigation. The esti-
mates range from 35,000 to 48,000 gal per year for heavy lawn waterers.
-The upward bias of these estimates is revealed by the calculation of
extra summer use shown in each column... These indicators show that moderate
to heavy lawn waterers probably use no more than 26,000 to 34,000 gal for all
extra summer needs. In addition, comparison of monthly use levels in winter
months show that the heavy irrigators also use considerably more water than
the non-sprinklers for other purposes. We thus conclude that the value of
51
-------
TABLE 11. PROFILES OF WATER CUSTOMERS IS ALABAMA BY
HOUSEHOLD CHARACTERISTICS AM) FAMILY INCOME
ro
Household characteristic
Average occupants per household
Average square footage of home
Percent of units with:
Dishwasher
Food disposal
Clothes washer
Water heater
Type of dwelling (percent):
Single faulty
Duplex
Apartnent
Mobile home
Homeowners (percent)
Employment status (percent):
Head of household employed
Head of household uneaployed
Head of household retired
Spouse employed full tine
Spouse employed part tine
Honenakers — not employed
Other adults employed full time
Other adults employed part time
Other adults uneaployed
Other adults retired
Retired
homeowners
($0 to $6,000)
1.71
1157
7.6
0.0
77.2
93.2
95.7
1.1
1.1
2.2
100.0
0.0
10.9
89.1
1.1
1.1
33.7
3.3
2.2
5.4
8.7
Other*
($0 to $6.000)
3.04
995
3.5
0.9
50.4
92.2
70.4
14.8
9.6
5.2
40.9
50.4
30.4
18.3
8.7
0.9
K35.7
5.2
2.6
10.4
3.5
Incora
Retired
homeowners
($6,000 to
$10,000)
1.90
1501
29.3
5.2
86.2
98.3
98.3
0.0
0.0
1.7
100.0
0.0
3.4
96.7
6.9
0.0
56.9
8.6
1.7
1.7
3.4
e category
Other*
($6,000 to
$10,000)
3.06
1131
13.8
4.3
80.2
98.3
83.6
4.3
8.6
3.4
67.2
92.2
6.0
1.7
23.3
4.3
46.6
6.0
1.7
7.8
2.6
$10,000
to
$20,000
3.88
1542
44.4
11.6
92.2
99.6
93.7
1.4
2.5
2.5
88.0
85.6
3.2
11.3
31.0
4.9
51.1
4.6
0.7
4.9
3.5
$20,000
to
$30,000
3.29
1964
81.7
34.1
98.4
100.0
98.4
0.0
0.8
0.8
97.6
92.1
0.8
7.1
39.7
7.1
46.8
5.6
0.8
4.8
1.6
$30,000
to
$40,000
3.52
2431
90.5
57.1
95.2
100.0
95.2
0.0
4.8
0.0
90.5
95.2
0.0
4.8
19.0
4.8
76.2
14.3
0.0
4.8
1.6
$40,000+
3.44
2900
87.5
56.2
100.0
100.0
100.0
0.0
0.0
0.0
100.0
75.0
0.0
25.0
12.5
0.0
75.0
12.5
0.0
0.0
0.0
*0ther than a retired homeowner, who is assumed to have assets that may Influence consumption.
-------
TABLE 12. WATER USE PROFILES OF ALABAMA WATER CUSTOMERS BY LAWN SPRINKLING
HABITS AND APPLIANCE OWNERSHIP
in
U>
Customers practicing
moderate to heavy springling
Customer
characteristics
Age of head of household
Tear moved In
tear home built
Square footage of home
.Number of residents per household
Average 1976 income
Water use (gal):
July 1977
August 1977
September 1977
October 1977
November 1977
December 1977
January 1978
February 1978
March 1978
April 1978
May 1978
June 1978
Annual water use (gal)
Monthly average winter use (gal)
Monthly average summer use (gal)
Extra use, summer season (gal)
Dally winter use (gal/person)
Daily summer use (gal/person)
Difference (gal/person)
Percent of customers
With
disposal, With
dishwasher, dishwasher
and washer
47
1970
1965
2,355
3.64
$24,576
17,655
12,427
13,074
9,373
8,865
8,268
10,026
8,091
8,015
14,316
12,910
15,193
138,213
8,653
13,564
34,377
79
124
45
5.1
and washer
48
1968
1958
1,968
2.76
$20,245
14,112
11,488
11,326
8,364
7,088
6,957
7,766
6,566
6,629
9,812
8,974
11,168
110,250
7,001
10,749
26,236
85
»• 130
, 45
7.0
With
washer
52
1964
1951
1,373
3.39
$11,500
12,301
9,863
10,939
7,349
5,986
5,780
5,993
5,413
6,000
9,118
9,762
11,063
99,567
5,834
10,056
29,554
57
99
42
7.4
Customers practfcing
little or no sprinkling
With
disposal,
dishwasher,
and washer
48
1967
1958
2,088
3.23
$21,008
9,236
7,379
8,124
7,450
7,645
7,154
8,383
7,642
6,952
8,073
6,783
7,326
90,149
7,555
7,767
1,484
78
80
2
6.4
With
dishwasher
and washer
49
1964
1955
1,703
3.09
$15,879
6,123
6,018
6,567
5,661
5,570
5,581
6,346
5,637
5,198
6,465
5,667
6,101
71,254
5,666
6,131
3,255
61
66
5
17.0
With
With
washer no washer
52
1963
1951
1,282
2.94
$ 9,306
6,123
5,591
5,677
5,212
5,006
5,093
5,836
5,231
4,835
5,441
5,103
5,661
64,811
5,200
5,544
2,401
59
63
4
40.7
55
1964
1943
985
2.53
$ 4,870
4,674
4,034
4,576
4,094
3,782
3,893
4,674
4,213
3,837
4,336
3,944
4,575
50,632
4,079
4,319
1,673
54
57
3
13.6
-------
Batchelor's appliance grouping lies in the identification of more or less
homogeneous groups of customers rather than in providing a methodology for
estimating water use by appliance.*
USE OF REGRESSION ANALYSIS TO ESTIMATE WATER USE BY APPLIANCE
An alternative method for estimating the water used by various appli-
ances is to specify the appliances and independent variables in a regression
analysis explaining water consumption. Ideally, every use of water would be
associated with an appliance such as a sprinkler or toilet. As a practical
matter, the number of occupants serves as a proxy for the group of appliances
such as toilets present in almost all housing units. Income is used as the
regressor to explain the intensity of appliance use in general. Though the
general limitations of this alternative method of estimating the amount of
water consumed by specific appliances are almost as severe as the limitations
of the profile method used above, they are different and the two methods are
complimentary.
Table 13 gives the results of regression equations using appliances and
demographic variables to explain monthly water use for summer and winter, and
average annual water use. The coefficient for each of the independent vari-
ables is the amount of use per month that can be attributed to the particular
characteristic described by the independent variable. The R2 for the first
equation indicates that the age and number of children in the household plus
the types of water-using appliances explain about 35 percent of the total
variation is use. The dishwasher variable is the only variable that is not
significant, which indicates that the presence of a dishwasher gives no addi-
tional information about the water-use characteristics of the home. The
regression indicates that 643 gal per month can be attributed to an automatic
washing machine and 776 gal can be attributed to a garbage disposal. The
fact that a customer employs heavy sprinkling in summer indicates an addi-
tional 976 gal of use even in the winter.
Equations explaining appliance use in the summer and annually have simi-
lar interpretations. As in the profile analysis, the 787 gal per month of
annual use associated with a garbage disposal must reflect the surrogate
relationship of this variable to income and lifestyle. For our purposes,
however, we note that whatever the proxy relationship may be, it explains a
constant factor over the year (the difference in summer and winter-use
amounts to only 17 gal), so we presume that the presence of garbage disposals
does not identify lawn waterers. The use associated with clothes washers and
dishwashers is at least in a comparable range with studies that have esti-
mated water use by functions. But over all, these estimates of water use by
*The concept is nevertheless a substantial contribution to utility
demand analysis. Unfortunately, the major water-using appliances are toilets,
tubs or showers, and sinks, which cannot be included in the analysis because
they are present in virtually all residences served by water systems. In the
analysis of energy demand, the most important appliances can be segmented
into customer groupings, and the hierarchy problem can be more successfully
avoided.
54
-------
TABIE 13. WATER USE ESTIMATED DERIVED FROM REGRESSION ANALYSES USING
in
01
Independent variable
Dependent
variable
Monthly winter use:
gallons
t value*
Monthly sinner use:
gallons
t' value
Average annual use:
gallons
t value
No. of persons /household
Pre-school or teen-
eleaentary children agers
269
(2.50)*
312
(2.34)
294
(2.50)
1102
(9.90)
1141
(8.27)
1125
(9.24)
Adults
other than
head of
household
813
(5.57)
906
(5.01)
867
(5.44)
Appliance ownership
Automatic
clother
washer
643
(2.59)
424
(1.38)
516
(1.89)
Garbage
disposal
776
(2.39)
793
(1.97)
787
(2.21)
Dish-
washer
200
(.83)
120
(.40)
153
(.58)
(continued)
-------
TABLE 13. (continued)
in
Independent Variable
Dependent
variable
Monthly winter use:
gallons
t value"!"
Monthly summer use:
gallons
t value
Average annual use:
gallons
t value
Moderate
to heavy
sprinkling
976
(4.05)
4651
(15.59)
3120
(11.35)
Age of head
of household
55 62
to to
61 64
-698 -1006
(-2.40) (-2.44)
-1033 -1346
(-2.87) (-2.63)
-894 -1204
(-2.81) (-2.67)
65
and
over
-831
(-3.15)
-936
(-2.86)
-892
(-3.90)
Total
family
income
($1000)
41
(2.86)
75
(4.25)
60
(3.90)
Constant R^
2905 0.35
3160 0.47
3054 0.44
•Derived by checking whether the customer used more than 5,000 gal more than the average winter use during any
single summer month and more than 10,000 gal extra during the entire summer
tThe t value indicates the level of significance of the variable
-------
appliance (other than the sprinkler, which is discussed below) contribute
little to an understanding of water consumption, because 70 to 80 percent of
water use occurs in the bathroom (see Kim and McCune, 1977).
The pattern of use by age of occupant is of greater interest. Teenagers
account for a greater use than adults or younger children. Water use
declines as the head of the household ages, a trend that slows somewhat in
retirement years. This apparent quirk is explained in the following section.
The moderate to heavy lawn waterer variable provides useful insights
into irrigation demand. The monthly summer use of 4,651 gal is equivalent to
33,000 gal for the season and is consistent with the estimate obtained in
comparing profiles. Since for each winter month these customers use 976 gal
more than the average, we can assume that nonirrigation use during the summer
is at least as high, which would leave an average extra summer demand for
irrigation of no greater than 25,000 gal.
Table 14 gives the results of two of several attempts to pinpoint the
demand for irrigation needs using the local survey data. Conceptually, the
model is specified so that each household is classified by number of occu-
pants and lawn-watering habits (waterers and nonwaterers), according to the
questionnaire response. Thus the first nine variables are dummies for all
customers except the two-occupant households that water a lawn or garden.
(It is necessary to leave out one category when using dummy variables.)
Variables 10 through 13 are dummies for each income class except $10,000 to
$20,000. In step 1 of the regression explaining annual use, subtracting
variable 1 from variable 6 provides the implicit demand of 20,000 gal for
irrigation by the one-occupant household that waters. Similarly, variable 2
indicates that two people who never water use 10,248 gal less per year than
two people who water—an amount represented by the constant. Low t values
and illogical results for three people preclude the use of this estimating
scheme; but some of the general implication of the results from this regres-
sion were supported by other regressions.
The final step, with all the insignificant variables deleted, shows
households with four or more occupants that irrigate and households with
incomes greater than $30,000 as the only groups using significantly more
water than average, and it shows households headed by those past retirement
age as the only group using less water than the average. An alternative
interpretation is that variations in water use among units with three or
fewer occupants are so great for both watering and other uses that identi-
fying the type of use does not increase the predictability of total use. The
picture unfolds as the insignificant income coefficients in step 1 and the
final step of a regression explaining only the extra summer use are consid-
ered.
The fact that variable 10 is positive in the third column implies that
the lowest income groups use more than those with incomes between $10,000 and
$20,000. (Since the $10,000 to $20,000 income group is the dummy variable
left out of the regression equation, all coefficients are relative to use in
the $10,000 to $20,000 income group.) In the final step (summer extra use),
variable 14 is no longer significant, but one-occupant households that are
57
-------
TABLE 14. REGRESSION ANALYSIS OF DEMAND FOR LAWN IRRIGATION WATER,
TUSCALOOSA. ALABAMA*
In
00
Variable no.
and
description
Mean
*Number of samples is 118.
-------
waterers use up to 54,000 extra gal per summer (constant plus the coefficient
for variable 6). The apparent contradictions leave little doubt that one-
occupant households are a diverse group with a wide range of lifestyles and
water consumption characteristics. The group contains a large percentage of
retired individuals, and most of these have minimal demands for water because
of reduced activity or time spent away from home. For some, however, the
yard or garden becomes a recreation, and the amount of water used for irriga-
tion is much greater than for the typical household. Differences within this
group are more extreme, but they are not fundamentally different from the
diverse use patterns resulting from lifestyle variations among households of
other groups.
FURTHER ANALYSES OF WATER USE FACTORS
Through a more detailed examination of profiles and extensive use of
regressions, an effort was made to find factors other than those already
noted that might significantly influence water consumption. In general,
other factors influencing consumption were insignificant, small, or indi-
rectly related to the number and age of occupants or income. For example,
the age and size of the housing unit, lot size, amount of lawn irrigated,
type of neighborhood, and population density were all rejected as independent
determinants of water use. Assessed property values (a variable often used
as a proxy for income) proved to be a better predictor of water use than
income, since it reflects both income and the way it is used. Information on
car washing did not prove to increase significantly the explanatory power of
the model.
The combined analysis of profiles and regressions was also used to add
details to the general outline of demand for irrigation water. The sample
was split into high and low users within each of the appliance categories
(Table 12). From the regression analysis in Table 13, we assume that only
about 80 percent of the extra summer use of heavy irrigators is for lawn
irrigation, swimming pools, water-cooled air conditioners, and other outside
needs. Within the 20 percent of the population assumed to be heavy lawn
waterers, the top half consumes about 10,000 gal for irrigation in a peak
month, and about 45,000 gal for all extra summer needs. The bottom half of
the heavy irrigators averages about 6,500 gal of extra use in a peak month,
but less than 20,000 for irrigation during the entire summer. The extra
summer use within both groups is roughly proportional to their total water
consumption; both groups use about 20 percent of their total consumption for
irrigation, and summer extra use is about 25 percent of the total.
From the local survey, we assume that of the remaining 80 percent of
water customers, about half use more than negligible amounts for Irrigation.
Regression analysis of the statewide sample indicates that the more modest
irrigators average about 5,000 gal per season for irrigation, plus another
1,000 to 3,000 of extra use in the summer for non-irrigation purposes. The
range, especially for occupant-induced consumption, is quite wide and depends
on the ages of children and adults. The last 40 percent includes some large
users with winter peaks and non-irrigators Cor light sprinklers) that have
extra summer needs of only 2 or 3 percent of their total requirements. Over-
all, about 15 percent of the customers account for 60 percent of extra summer
59
-------
use, and half of the customers contribute only negligibly to the need for
excess capacity during the summer.
The overall estimate of lawn irrigation demand shows that such water
accounts for about 9 percent of total use; by contrast, Kim and McCune (1977)
report this figure as 3 percent, and Howe and Lineweaver (1967) estimate
that it accounts for up to 40 percent in metered areas. Given the relative
ease of estimating irrigation demand for specific systems, policies to
encourage conservation of water for outside purposes should be based on local
data and objectives. Our other findings have greater general applicability.
Variations in in-house demand that cannot be traced to occupants, income, or
other factors reflect individual differences to a large extent. Our analysis
suggests, however, that leaks and inefficient appliances must be responsible
for a large amount of the unexplained variations in use among similar house-
holds.
Profiles and regression analyses were also used to further examine the
possibility of a threshold effect. The burden of the water and sewer bill
was calculated as a percent of family income. For the lowest income groups,
the water bill averages slightly over 3 percent of income and ranges from 1
to 4 percent. At median incomes, the burden drops below 1 percent, and at
higher incomes (where demand is more income elastic), the burden averages
less than 0.5 percent. No evidence was found that the impact of the burden
is any greater than the almost negligible price effect. On the contrary,
inconclusive evidence suggested that the incidence and duration of leaks is
most heavy at the lower incomes and that such leaks more than offset the
aggregate conservation induced by price and income for the group as a whole.
CONCLUSIONS
The policy implications of the threshold analysis are that direct regu-
lations such as prohibiting irrigation or setting appliance standards would
be a more effective inducement to conservation than price increases that will
occur from anticipated expansion and improvement of water and sewage facil-
ities. Neither regulations nor normal price increases, however, would be as
effective as the relatively high penalty rates imposed under an inverted
block rate structure. Appliance standards would have only a gradual impact
over an extended period. Bans on irrigation might effectively control tem-
porary peak-load problems, but they would have little effect on the base load
requirements. The sudden shock of a substantial rate increase, combined with
wide distribution of effective and inexpensive conservation techniques, could
be expected to reduce water consumption and sewer loads substantially and
quickly if motivation and cost-effective solutions for conservation were pro-
vided simultaneously.
60
-------
REFERENCES
Batchelor, R.A., 1975. "Household Technology and the Domestic Demand for
Water." Land Economics 51:208-223.
Clark, R.M., and H.C. Goddard, 1977. "Cost and Quality of Water Supply."
Journal of American Water Works Association 69(1).
Consumer Reports, 1978. "Water: Time to Start Saving?" 43(5):294-295.
Gibbs, K.C., 1978. "Price Variable in Residential Water Demand Models."
Water Resources Research 14(1).
Goddard, H.C., R.G. Stevie, and G.D. Trygg, 1977. "Planning Water Supply:
Cost-Rate Differentials and Plumbing Permits." U.S. Environmental
Protection Agency, Cincinnati, Ohio.
Halvorsen, R., 1976. "Demand for Electric Energy in the United States."
Southern Economic Journal 42(4):610-625.
Howe, Charles W., and F,P. Lineweaver, Jr., 1967. "The Impact of Price on
Residential Water Demand and Its Relation to Systems Design and Price
Structure." Water Resources Research 3:13-32.
Howe, Charles W., and William J. Vaughan, 1972. "In-House Water Savings."
Journal of American Water Works Association 64:118-121.
Kim, J.E., and R.H. McCuen, 1977. "The Impact of Demand Modification."
Journal of American Water Works Association 69(2).
Nordin, J.A., 1976. "A Proposed Modification of Taylor's Demand Analysis:
Comment." The Bell Journal of Economics 7:719-721.
Stevie, R.G., 1978. "Water Demand Curve Estimation and Declining Block
Rates." Unpublished paper.
Taylor, L.D., 1975. "The Demand for Electricity: A Survey." The Bell
Journal of Economics 6(1):74-110.
Wilder, R.P., and J.F. Willenborg, 1975. "Residential Demand for Elec-
tricity: A Consumer Panel Approach." Southern Economic Journal
42(2):212-217.
61
-------
BIBLIOGRAPHY
Gottlieb, Manuel, 1963. "Urban Domestic Demand for Water: A Kansas Case
Study." Land Economics 39:204-210.
Halvorsen, R., 1975. "The Demand for Electricity Energy." Review of
Economics and Statistics 57:12-18.
Headley, Charles J., 1963. "The Relation of Family Income and Use of Water
for Residential and Commercial Purposes in the San Francisco-Oakland
Metropolitan Area." Land Economics 39:441-449.
Helms, B.P., E.R. Mansfield, and J.F. Vallery, 1978. "An Estimate of
Residential Energy Conservation." In: Proceedings of the American
Statistical Association, Business and Economics Division, pp. 526-531.
Morgan, W. Douglas, 1973. "Residential Water Demand: The Case From Micro
Data." Water Resources Research 9:1065-1067.
Murray, M.P., R. Spann, L. Pulley, and E. Beauvais, 1978. "The Demand for
Electricity in Virginia." The Review of Economics and Statistics
60:585-600.
North, R.M., 1967. "Consumer Responses to Prices of Residential Water."
In: Proceedings oj^he^ Third^j^nnual American Water Resources
Conference.
Rutledge, E.G., and J.E. Stapleford, 1977. "Residential Demand for
Electricity: A Household Survey Approach." In: Proceedings of the
American Statistical Association, Business and Economic Divisions.
pp. 577-580.
Young, Robert A., 1973. "Price Elasticity of Demand for Municipal Water: A
Case Study of Tucson, Arizona." Water Resources Research 9:1068-1072.
62
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APPENDIX A
ESTIMATES OF CONSUMPTION ASSOCIATED.WITH
THE OWNERSHIP OF APPLIANCES:
A REGRESSION APPROACH
This appendix provides a limited sample of the methodology presented
in the text and summarizes the findings from a number of alternative model
specifications. The data base for these regressions is from the local
survey, and the primary emphasis is on water use for lawn irrigation. In the
local survey, detailed data on lawn irrigation practices were obtained.
Similar data were not available in the statewide survey. By extending a
regression approach tried by Batchelor (1975), an effort was made to
estimate the use of water by sprinklers, washing machines, and other appli-
ances. The analysis supplements data presented in the text, and although it
is of limited success for the intended purpose, it proves valuable in
explaining the interrelationships in life cycles and hetrogeneous lifestyles
that make water consumption difficult to forecast.
Table A-l identifies the importance of irrigation in total water con-
sumption by income groups and the use associated with selected appliances
(variables 14 through 16). Variables 9 through 12 are used to hold constant
the variation accounted for by the number of household occupants. If we
subtract the coefficient for Variable 1 from the coefficient for Variable 5
(14,113-10,745 - 3,368), the difference is an estimate of water associated
with lawn sprinkling in households with incomes up to $10,000. The house-
holds with incomes between $10,000 and $20,000 that sprinkle have been
omitted from the variable list to avoid the multicollinearity problem in the
use of the 1-0 dummy variable. So the coefficient for Variable 2 subtracted
from zero (i.e., changing the sign) (0-(-10,876) - 10,876) becomes the
implicit estimate of irrigation use in this income class. Similarly, the
betas for (Variable 6 - Variable 3), etc., generate an array of irrigation
use estimates for the several income classes considered.
The results are highly distorted, as would be expected from the low t
values of the key irrigation variables; so we skip to Step 8 of our backward
elimination regression program. Here, the coefficients provide a clearer
picture of irrigation use, and the apparent inconsistencies provide insights
into the pattern. Irrigation use is significantly influenced only by incomes
over $30,000, and the influence of household occupants on water use emerges
in the expected patterns. The large and highly significant negative usage
(i.e., deduction from the constant) for households with heads over age 65 is
representative of the results from a number of alternative tests of this
condition.
63
-------
TABLE A-l. REGRESSION ANALYSIS OF ANNUAL WATER DEMAND
FOR LAWN IRRIGATION AND SELECTED APPLIANCES
Variable No.
and brief
description
Nonwaterers :
1. Income; $0-$10,000
2. Income; $10, 000- $20, 000
3. Income; $20,000-$30,000
4. Income; $30,000+
Occasional waterers:
5. Income; $0-$10,000
6. Income; $20,000-$30,000
7. Income; $30, 000- $40, 000
8. Income; $40,000+
9. 1 occupant
10. 2 occupants
11. 4 occupants
12. 5+ occupants
13. Age 65 and over
14 . Disposal
15. No clothes washer
16 . Dishwasher
Mean
%
14.4
11.9
3.4
.8
19.5
12.7
5,9
6.8
11.0
38.1
22.9
14.4
23.7
17.8
11.0
57.6
Step 1
Coefficient
(gal)
14,113
-10,876
-15,706
16,030
10,745
-19,067
42,879
41,875
- 1,274
-18,686
16,506
20,739
-27,435
40,321
-13,320
4,285
t
Value
1.05
- .09
- .73
.39
.91
-1.39
2.48
2.39
- .08
-1.56
1.31
1.41
-2.57
3.68
-1.28
.47
Step 8
Coefficient
(gal)
14,414
-
-
—
14,674
-
52,588
52,324
__
14,160
16,617
24,318
-25,507
9,938
-
-
Without Appliance
t
Value
1.20
-
-
—
1.39
-
3.35
3.36
_
-1.50
1.52
1.86
2.53
3.87
-
-
Coefficient
(gal)
-
-
-
-
-
—
64,552
58,497
_
-11,814
15,952
24,899
-18,036
-
—
-
t
Value
-
—
—
-
-
—
4.07
3.62
—
-1.20
1.40
1.85
-1.92
-
—
-
Constant
79,037
71,299
79,358
.47
.45
.37
-------
The unexpected results indicating that the lowest income groups use
more water than families in the $10,000 to $30,000 range and that waterers
and nonwaterers behave similarly raises several questions as to habits and
lifestyles as well as to the efficacy of the model specification. One
testable hypothesis raised by the regression is that one-person households on
retirement incomes dominate the out-of-line results, with the over-65
variable offsetting the positive low-income variables and the absence of a
negative beta for one person. This possibility is followed in the subsequent
regressions.
A second question is raised by the performance of the household appli-
ance variables. The implied use of over 13,000 gal of water per year by a
washing machine (or in the regression, water not used if there is no washer)
is plausible but not significant. The implied use of over 100 gal per day by
a disposal appears unreasonable and also suggests that this variable may lead
to serious distortions in other results. The matter is resolved by excluding
household appliances from the regressor list in a modified specification of
the model. The coefficients for Step 8 provide the results, and indicate
that the earlier positive coefficient on low income was a distortion.
Table A-2 presents the results of further efforts to trace the patterns
and quantify the amount of water used for lawn irrigation. The new list is
similar to Table A-l in concept and design, but now income is held constant,
and the implicit amount of water used for irrigation is provided by sub-
tracting the coefficient for Variable 1 from the coefficient for Variable 6,
etc. The results, derived from Step 1, are as follows:
Type of Approximate
Household gal/year
1 person 20,000
2 persons 10,000
3 persons 11,000
4 persons 7,000
5+ persons 29,000
The array appears plausible except for the 3-person household. The use
explained by income, (variables 10 through 13 in Table A-2) would also appear
plausible except for the extra 13,000 gal used by the lowest income group.
Although the t values for key variables are small, the results .can be in-
terpreted as a best estimate of the average irrigation use in households with
widely varying irrigation requirements.
Coefficients from the final step, after all insignificant variables are
eliminated, again show that the only dependable forecasting relationship is
extra irrigation needs in households Occupied by four or more persons and
that families with incomes over $30,000 use considerably more water than
lower income groups.
65
-------
TABLE A-2. REGRESSION ANALYSIS OF WATER DEMAND
FOR LAWN IRRIGATION
Va-r- f aft lo Kfn
VclX-LcLDXc: INU •
and Brief
Description
Nonwaterers :
1. 1 occupant
2. 2 occupants
3. 3 occupants
4. 4 occupants
5. 5+ occupants
Sometimes water with:
6. 1 occupant
7. 3 occupants
8. 4 occupants
9. 5+ occupants
10. Income; $0-10,000
11. Income; $20-30,000
12. Income; $30-40,000
13. Income; $40,000+
14. Age 65 and over
Constant
R2
Step
1
Annual
Mean
%
4.2
11.9
3.4
6.8
4.2
6.8
10.2
16.1
10.2
33.9
16.1
5.9
7.6
23.7
-
_
Coefficient
(gal)
- 6,747
-10,248
17,234
20,230
16,844
13,065
6,158
27,442
45,940
12,684
755
65,475
51,538
-21,489
66,695
t
Value
- .32
- .75
.76
1.21
.83
.75
.43
2.15
2.89
1.14
.06
3.79
3.03
-1.88
.39
Final Step
Annual
t
Coefficient Value
(gal)
-
-
-
-
-
-
-
22,714 2
38,815 2
-
-
60,411 3
51,991 3
-15,756 -1
74,189
-
-
-
-
—
-
-
.09
.72
-
-
.76
.27
.68
.36
Final Step
Summer Extra
t
Coefficient Value
(gal)
-
-
-
-
- —
39,919 2.
-
-
- -
_
s
60,099 3.
80,849 4.
— —
14,247
•
19
10
69
22
-------
The distortions uncovered in Table A-l, that the lowest income group
and one-person households use more water than middle income and two- or
three-person households is generally supported by Step 1 of Table A-2. The
general implication, however, is that a single-occupant household tends to
water much more than the average.* This implication is born out in a modifi-
cation of the regression.
A direct attack on estimating the water used for irrigation is provided
by a regression explaining the extra summer consumption. "Extra" was
defined as the excess use during the summer irrigation period over the base
use as established during the winter months.t Extra use was used as the
dependent variable with an identical list of regressions. The last step of
this model specification is shown in Table A-2. The single-person house-
hold that waters emerges as a highly significant factor, along with higher
income groups; and the age of the head of household is a negligible and
insignificant factor that is dropped out of the variable list.
Taken together, the results in Tables A-l and A-2 supplemented with
similar model specifications leave little doubt that the one-occupant house-
hold is a diverse group with a wide range of lifestyles and water consumption
characteristics. For some, water use may be minimal because of reduced
activity and needs in the retirement years, or because of time spent away
from home. For others, the yard or garden becomes a recreation, and the
proportion of water for irrigation is far greater than for a typical house-
hold. The differences are more extreme, but these are not fundamentally
different from those resulting from lifestyle variations that lead to diverse
use patterns among household that are similar in the most reliable predic-
tors, income and occupants.
These differences among groups similarly defined helps to explain the
relatively low R2's in Tables A-l and A-2. Regardless of the variable in-
cluded or the combinations of variables tried, we were unable to produce an
R2 above 0.50.
*A1though the details of the analysis will not be presented here, the
household with five or more persons is also a special case. Income and
number of household occupants are positively correlated, but households with
five or more occupants tend to be upper-middle to high income or low income.
Since the higher Income families with children nearly all irrigate, and
since those using water for irrigation also use more water for other
purposes, the beta for variable 9 is quite large. But variable 5 is
heavily weighted with low incomes.
tSeveral variations were used to define extra, all with similar results.
Here, the total consumption for October through March bills is subtracted
from the total April through September. This rough approximation is some-
what distorted by vacation periods, Christmas visitors, and leaks from
freezes, but it is less of a problem-in the small pilot survey than in the
primary data set.
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A final factor to be noted in Table A-2 is the constant in the final
step (summer extra) relative to the size of the betas. The average extra
consumption per household being explained is 27,400 gal (this is the mean
of the dependent variable), and the constant implies that 14,247 gal of
extra consumption is the average use for all categories not identified. In
the categories identified as users of the extra, each accounts for several
times the average extra during the summer. The rather large differences
lead to further analyses, which are summarized as follows.
Over 75 percent of the population not identified by the significant
coefficients (income less than $30,000 and households of two or more persons)
are responsible for less than 40 percent of summer extra use. Those who do
water use an average of about 20,000 gal during the summer, and the 30 per-
cent who do not water use an extra 4,000 gal for purposes other than irriga-
tion. In the income-related summer use, the average extra is about 85,000
gal per summer.* Within these averages, one-third to one-half of the
extra summer use is for human use rather than for lawns and gardens. Among
the waterers, the typical household below a $20,000 income (and many of
those above) probably uses far less than 10,000 gal per year for irrigation.
Typical heavy waterers are found randomly over the income ranges and account
for a relatively large amount summer extra use. The use per person, however,
is closely tied to income and is higher in both winter and summer.
The major limitation in the above analysis is the relatively small
sample size and some distortion in responses obtained from an otherwise
random population. The sample is biased toward homeowners and older house-
holds, and the lowest income group of working customers is underrepresented.
However, a number factors were examined other than those reported above.
Those that appear most relevant are summarized as follows.
The use of appliances as regressors, as illustrated by the use of
disposals in Table A-l, will typically act as a proxy for income or life-
style, as found by Batchelor (1975). Though the problem can be circumvented
in some model specifications, the variations in the water consumption of an
appliance according to the number of household occupants makes the procedure
questionable except for a few special analyses.
The use of the assessed value of property as a proxy for family income
can always be expected to produce the desired results. Income partially
determines the housing unit and lifestyle, which in turn determines water
use (along with the other unrelated determinants). The use of assessments
is simply going directly to the primary determinant.
The use of data on lot size and frontage is of little value except as
they indirectly indicate property value. Small frontage usually indicates
lower water use, for example. No relationship was found between the size of
lot and the amount of irrigation, however. The same was true for the size
and type of garden (vegetable or flower).
*[(60,099 + 14,247) + (80,849 + 14,247)] * 2 = 84,721
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Gardeners use more water for irrigation than lawn waterers, on the
average, in both lower and upper income groups. Gardeners are generally
concentrated in the lower to middle income ranges and use less water for
other purposes. "Watering a garden extensively" did not show up as
significant as variable in the list explaining overall water consumption.
The age and size of the housing unit is not significantly related to water
usage except as these variables indirectly reflect value and income.
69
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APPENDIX B
LOCAL STUDY QUESTIONNAIRE
The questionnaire used in the pilot study was part of an energy use
study. Several questions were asked as an aid in a pilot study on water
use in Tuscaloosa County, Alabama.
The questionnaire was constructed so that the interviewer would ask
for general qualitative information and try to qualify the information
or have the interviewee further quantify the information.
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WATER USE QUESTIONNAIRE
Card 1
1. Type of residence:
1. Single Family
2. Duplex
3. Apartment
4. Mobile home
5. Condominium
2. Do you own or rent your home?
1. Own
2. Rent
3. Are utilities included in your rent or are they excluded?
1. Included
2. Excluded
4. What year was your home built?
19 _
5. What year did you move in?
6. Home is served by:
1. Water, sewer, garbage
2. No water
3. Water, no sewer
4. Water, sewer, no garbage
7. Number of rooms (count a combination living room -
dining room as one room unless full size is indicated;
do not count baths) .
8. Square feet (sq. ft. of heated and cooled area)
9. Number of people living in the home.
Total
Children under 25
71
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Appliance Saturation
Which of the following appliances do you own?
10. Range?
0. None
1. Natural gas
2. Electric
3. Bottled fuel
4. Other fuel
11. Dishwasher?
0. No
1. Yes
12. Clothes dryer?
0. None
1. Natural Gas
2. Electric
3. Other fuel
13. Automatic washer?
0. No
1. Yes
14. Freezer?
0. No
1. Yes, one unit
2. Yes, more than one
15. Garbage disposal?
0. No
1. Yes
16. Water heater?
0. None 4. Other fuel
1. Natural gas 5. More than one, using
2. Electric different fuels
3. Bottled fuel
If more than one, specify each use.
17. Do you have a swimming pool, water-cooled air conditioner,
or anything else requiring large amounts of extra water?
0. No
1. Swimming pool
2. Water-cooled air conditioner
3. Other (specify)
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18. Are there any other major energy or water uses besides
the appliances mentioned before?
0. None
1. Shop
2. Rental apartment
3. Other (specify)
4. Swimming pool
5. Pool heater
19. Determine frequency of use, record the impact of
increased use on:
0. None
1. Water
2. Electric
3. Gas
4. Water and gas
5. Water and electricity
6. Gas and electricity
7. All
NOTE: Questions 20-32 were concerned with energy use,
33. How often do you wash your car?
1. Frequently (2 or more times per month)
2. Ocassionally (6-8 times per year)
3. Never (or almost never)
34. Do you water your lawn and shrubs?
0. No
1. Yes
35. If yes, what percent of your lot is watered?
36. Do you water a vegetable or flower garden?
0. No
1. Yes
If yes, what size is it?
1. Very small (10 ft. sq.)
2. Medium size garden (20-30 ft. sq.)
3. Large garden (over 30 ft. sq.)
37. How often do you water?
1. Waters garden frequently (3 times per week)
2. Waters garden occasionally (once a week)
3. Only to keep from dying
4. Never (includes very small amounts and/or almost
never)
73
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38. Have you changed your consumption of water in the
past five years?
0. No change
1. Reduced use, change in lifestyle
2. Increase use, change in lifestyle
3. Reduce use because of increased cost
5. 1 and 3
7. 2 and 3
9. Other
39. Do you know the amount of your water bill? (ask
the amount)
0. Does not know or is vague about
the amount of the bill
1. Knows amount of bill vaguely, not
the difference in high and low
low months
2. Knows the difference between high
and low months
3. Knows the bill runs the same each month
40. Do you know the amounts of your gas and electric bills?
Extra cost during colder or hotter months?
"0. Does not know or is very vague
1. May know, but did not answer
2. Knows amount of bill and
differentials, probably sees price
as both
3. More emphasis on amounts than differentials
4. More emphasis on marginal price
41. Do you know what is included in the bill?
0. Does not know
1. Knows whether bill includes a sewer
or garbage charge
42. Has your water bill changed over the past five years?
0. No change, or has changed by an
Insignificant amount.
1. Increase has been substantial
2. Not applicable (hap only recently
moved to the area, no basis for
comparison, etc.)
43. Has your water bill changed as much as your other
utility bills? (Indicate which of the following
best reflects the customers understanding of water rates.)
0. Understands (correctly) that the rate
increase has been about the same as other
prices in general, less than electric
prices and more than gas prices.
74
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1. Does not know what the relative changes
have been (i.e., has no opinion).
2. Show considerable misunderstanding of
relative prices.
44. If customer volunteers a comment on high electric rates, ask
how much these rates have increased relative to other prices
(i.e., encourage further comment). Record the response which
best reflects customers belief.
0. No comment or no definable position.
1. Understands (correctly) that electric rates have
increased up to 100%, other prices about 50%, and
that rates are up about 25% in real terms, (i.e.,
has general understanding that the relative
Increase is less than the apparent change)
2. Sees electric rates as doubling in,absolute
terms, no concept of relatives,
3. Has no concept of how much but believes the
increase has been unreasonably high.
4. Other (briefly describe).
45. When your hone was first constructed, was it well
insulated with:
1. Attic insulation
2. Wall insulation
3. Storm doors
4. Storm windows
5. All of the above
6. 1 and 2
7. 1 and 3
8. 1 and 4
46. Has there been a regular effort to upgrade efficiency
in your home since it was built?
0. No
1. Yes
If so, what has been done?
47. What have you done in the last three (3) years to conserve
energy in your home?
Card 2
48. What is the age of the head of household?
49. Where does the head of household-work? What does he do?
/5
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(This information will serve only as a basis for
estimating income or verifying the answer given.
Record, as appropriate, from answer given:
0. Head is employed or (apparently)
temporarily unemployed
1. Head is retired
2. Head is disabled or (apparently)
generally unemployed (i.e., just
does odd jobs, etc.)
50. Is the spouse employed outside the home? Where? What
does spouse do?
Record as appropriate
0. Spouse works at least part time most
of the time
1. Has no outside employment
51. What was last year's family income from all
sources?
In case respondent is reluctant to give precise level
of income, use one of the intervals (A, B, or C) below.
Take the mid-point or the chosen interval as the best
estimates.
A
(1) $0-3,000
(2) $3,001-6,000
(3) $6,001-9,000
B
(4) $6,000-10,000
(5) $10,001-15,000
(6) $15,001-20,000
C
(7) $10,000-20,000
(8) $20,001-30,000
(9) $30,001-40,000
(0) over $40,000
52. Questionnaire validity as perceived by interviewer
1. Very reliable
2. Reliable
(continued)
76
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3. Acceptable
4. Somewhat reliable
5. Very unreliable
53. Lot valuation
54. Total valuation
55. Frontage
56. Acreage
77
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APPENDIX C
STATEWIDE SURVEY QUESTIONNAIRE
The questionnaire used in the general household survey was a part of
a statewide energy use study. The questions given are those relating to
water use. All rate structure and consumption data were collected from
the water utility.
78
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HOUSEHOLD QUESTIONNAIRE
I. Appliance Saturation;
1. Has dishwasher:
Yes
No
2. Has food waste disposer:
Yes
No
3. Type of clothes dryer:
Electric—combination washer-dryer
Electric
Natural gas
Bottled gas
None
A. Type of clothes washer:
Wringer
Automatic
None
5. Type of water heater:
Natural gas
Bottle gas
Electric
Other fuel
No water heater
If ELECTRIC, what size water heater?
30 gallon
40 gallon
50 gallon
80 gallon
120 gallon
Don't know
II. Demographic Data;
6. Type of residence:
Single family
Duplex
Apartment
Condominium
Mobile home
79
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7. Type of tenure:
Own residence
Rent residence
8. Year moved into residence:
9. Year home built: Age of home:
10. County code:
11. Location of house:
Metropolitan area
Urban (Incorporated city limits)
Suburb (Unincorporated area close to city)
Rural-proximity of metropolitan area
Nonmetropolitan area
Urban (Incorporated city limits)
Suburb (Unincorporated area close to city)
Rural area
12. Type of neighborhood: (interviewer only)
sub-standard area
(section deteriorating)
Declining neighborhood
(changing to commercial)
Older established area
(age over 15 years - not declining)
Newer residential area
(age—5 to 15 years - developed)
A new subdivision
(in development stage, 5 years or less)
Other;
13. Is home or apartment served by:
Fire hydrants and/or full fire protection
Garbage collection service
Sewer service
Water service
None of these
14. Age of head of household
15. Total number of people living at this residence:
80
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16. Number of children living at this residence:
Preschool
Elementary
Junior high
Senior high
College
(out of school - employed)
(out of school - not working)
None
17. Is head of household:
Employed
Not working
Retired
(a) If married, is spouse employed:
Full-time outside employment
Part-time outside employment
Homemaker—no outside employment
(b) If other adults, are they:
Employed full-time
Employed part-time
Not working
Retired
(c) If employed.
Where is head of household employed
(name of employer):
Type of employment:
1. Title
2. Duties
III. Dwelling Construction and Conservation
18. Number of square feet in home:
19. Have you reduced your energy use (gas or electric) of the
following:
Water heater Yes No
Dishwasher Yes No
81
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20. What is the 1976 Total Household Income (all sources) based on
the following broad categories:
$6,000 or less
$6,001 to $10,000
$10,001 to $20,000
$20,001 to $30,000
$30,001 to $40,000
Over $40,000
Customer would not answer
Interviewer to complete Question
21. Mark the level of income based on your personal judgement:
Estimated Income category:
Low income - $6,000 or less
Lower middle Income - $6,001 to $10,000
Middle income - $10,001 to $20,000
Upper middle income - $20,001 to $40,000
High income - Over $40,000
82
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TECHNICAL REPORT DATA
(Please read Instruction! on the reverse before completing)
1. REPORT NO.
EPA-600/2-80-162
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
TREATED WATER DEMAND AND THE ECONOMICS OF
REGIONALIZATION
Volume 1. The Residential Demand For Treated Water
6. REPORT DATE
August 1980 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S) __
Billy P. Helms and J.F. Vallery
8. PERFORMING ORGANIZATION REPORT NO.
>. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Alabama
University, Alabama 35486
10. PROGRAM ELEMENT NO.
C61C1C SOStfl Task 64
11. CONTRACT/GRANT NO.
R805617
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 Report 4/78 - 12/79
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
See also Volume 2 (EPA-600/2-80-163)
Project Officer: Robert M. Clark (513) 684-7488
16. ABSTRACT
This two-volume report examines the present and future demands and costs for
residential water in view of the new requirements for water quality standards under
the Safe Drinking Water Act of 1974 (PL92-523). Volume I (this volume) investigates
the determinants of residential water demand (including water price, family income,
and appliance ownership) and develops a methodology by which utilities can determine
future customer demand. A data base has been developed, and results of the analysis
are given. These data can be used to test many hypotheses other than those examined
in this study, and then could be a valuable tool for further research into the house-
hold demand for water.
One of the most significant products of this research is the development of a
information collection format that can be used by a water utility to collect
data on household water use.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Conservation
Economic Analysis
Statistical Analysis
Water Consumption
Water Distribution
Water Supply
13B
18. DISTRIBUTION STATEMENT
Release to Public
IB. SECURITY CLASS (ThisReport)
Unclassified
91. NO. OF PAGES
93
20. SECURITY CLASS
22. PRICE
EPA Form 2220-1 (R.». 4-77)
83
U.S. GOVERNMENT PRINTING OFFICE: 1980--657-1S5/0107
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