&EPA
United States
Environmental Protection
Agency
Municipal Environmental Research
Laboratory
Cincinnati OH 45268
EPA 600 5 78-008
1978
Research and Development
Planning Water
Supply: Cost-Rate
Differentials and
Plumbing Permits
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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 SOCIOECONOMIC ENVIRONMENTAL
STUDIES series. This series includes research on environmental management,
economic analysis, ecological impacts, comprehensive planning and fore-
casting, and analysis methodologies. Included are tools for determining varying
impacts of alternative policies; analyses of environmental planning techniques
at the regional, state, and local levels; and approaches to measuring environ-
mental quality perceptions, as well as analysis of ecological and economic im-
pacts of environmental protection measures. Such topics as urban form, industrial
rqix, growth policies, control, and organizational structure are discussed in terms
of optimal environmental performance. These interdisciplinary studies and sys-
tems analyses are presented in forms varying from quantitative relational analyses
to management and policy-oriented reports.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/5-78-008
May 1978
PLANNING WATER SUPPLY: COST-RATE DIFFERENTIALS
AND PLUMBING PERMITS
by
Haynes C. Goddard, Richard G. Stevie and Gregory D. Trygg
Department of Economics
University of Cincinnati
Cincinnati, Ohio 45221
R-803596-01
Project Officer
Robert M. Clark
Water Supply 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 Environ-
mental Research Laboratory, U.S. Environmental Protection
Agency, and approved for publication. Approval does not signify
that the contents necessarily reflect the views and policies of
the U.S. Environmental Protection Agency, nor does mention of
trade names or commercial products constitute endorsement of
recommendations for use.
11
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FOREWORD
The Environmental Protection Agency was created because of
increasing public and government concern about the dangers of
pollution to the health and welfare of the American people.
Noxious air, foul water, and spoiled land are tragic testimony
to the deterioration of our natural environment. The complexity
of that environment and the interplay between its components
require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in
problem solution and it involves defining the problem, measuring
its impact, and searching for solutions. The Municipal Environ-
mental Research Laboratory develops new and improved technology
and systems for the prevention, treatment, and management of
wastewater and solid and hazardous waste pollutant discharges
from municipal and community sources, for the preservation and
treatment of public drinking water supplies, and to minimize the
adverse economic, social, health, and aesthetic effects of pollu-
tion. This publication is one of the products of that research;
a most vital communications link between the researcher and the
user community.
In this report the authors have sought a better understand-
ing of how water supply costs are related to the spatial
features of the physical environment and how the costs of
delivering water to water consumers compare with the revenues
collected from them.
Francis T. Mayo, Director
Municipal Environmental
Research Laboratory
111
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PREFACE
The continuing concern over the quality of the environ-
ment and the consequent search for ways to prevent further
degredation as well as improve it inexorably leads to a closer
examination of all human systems which affect and are affected
by environmental quality. This report considers the case of
urban water supply, a public service over which considerable
concern has been raised about potential negative health effects
resulting from waste discharges.
An examination of such issues inevitably raises questions
about the incurred and opportunity costs of meeting water supply
objectives. This in turn raises the question of alternative
methods to reach the objectives, and of financing them. If the
affected communities believe that the drinking water quality
objectives are too costly to attain, they may reject the
objectives. However, if the affected communities drinking
water systems are not efficiently operated, i.e., at least cost,
then policies designed to make explicit the cost of improved
water to them may lead to unwarranted rejection of the drinking
water standards. The inefficiency may make the cost of deliver-
ing improved drinking water higher than it needs to be.
Because of these kinds of considerations, studies of methods
to improve environmental quality lead to an examination of the
entire set of relevant sub-systems in order to find the least
cost approach to the sought after improvements. This study is
concerned with similar questions, and is focused on two basic
propositions.
°It examines the intra-areal variations in the net revenues
of water use in terms of cost-water rate differentials
across an urban area.
°It seeks to explore how existing data collection activities
at the local governmental level may be utilized by water
system planners to predict water use, specifically plumb-
ing permit data.
IV
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ABSTRACT
This study is concerned with the measurement cost of water
supply, the measurement of net revenue differences among cust-
omers by class, and location, and the analysis of future water
demand as revealed by plumbing permit application data.
Specifically, water supply functions are disaggregated
respectively into (a) acquisition and treatment, and (b) trans-
mission and distribution. From this, the cost of delivering
water to various customers (by classes and specific users) are
calculated as a function of distance, altitude and time of year
(peak vs off-peak) for the Cincinnati, Ohio Water Works supply
area. These costs are then compared with the revenues collected
from the various consumers, and the net-revenues for each are
computed, with the resulting variations displayed through
computer mapping techniques.
Also examined is the hypothesis that future water use in the
same supply area can be predicted through the use of plumbing
permit records. It was concluded that the evidence from
Cincinnati does not support the hypothesis.
This report was submitted in fulfillment of Grant
No. R-803596-01 by the University of Cincinnati under the
sponsorship of the U.S. Environmental Protection Agency. The
work was completed as of January 15, 1977.
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CONTENTS
Foreword ................... . .............. . ............... ill
Preface [[[ iv
Abstract .................................................. v
Figures .................................................. viii
Tables ................. . ......... . ........................ x
Acknowledgment .................................. . ......... xli
I Introduction to Cost Rate Differentials ............ 1
II Conclusions and Recommendations Concerning
Cost Rate Differentials ............................ 5
III Literature Review on the Cost of Water Supply ...... 7
IV Methodologies ...................................... 57
V Empirical Results .................................. 95
VI Introduction to Plumbing Permits and Water Use.... 131
VII Methodology, Empirical Results and
Recommendations ................................... 133
Appendices
A. Supplement to Section IV, Part A ................... 141
B. Residential Water Demand: A Literature Review
C. Commercial Water Demand: A Literature Review ....... 171
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FIGURES
Number Page
1 Vertical summation of demand curves 1A
2 Horizontal summation of demand curves 15
3 Median total costs of treatment 24
4 Step cost functions 29
5 System friction curve ^2
6 System head curve ......... ^^
7 Head loss for a system head curve '
8 Cincinnati Water Works service area 78
9 Service area and zones of the Cincinnati Water
Works 79
10 Schematic diagram of Cincinnati Water Works System. 80
11 Relationship of distance cost of typical average
cost curve *
12 Relationship of altitude cost to typical average
cost curve 8^
13 Monthly indices based on water pumpage for 1965-
1975 90
14 Spatial mapping of off-peak period costs for all
classes combined 115
15 Spatial mapping of peak period costs for all classes
combined 116
16 Water main routes with indicated mile points. ... 117
17 Peak/off-peak cost differentials 119
viii
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Number Page
18 Water rates per CCF minus off-peak delivered
costs 120
19 Water rates per CCF minus peak delivered costs . . 121
20 Net revenues for off peak residential water use. . 122
21 Net revenues for peak period residential water
use 123
22 Net revenues for peak commerical water use .... 124
23 Net revenues for off-peak commerical water use . . 125
24 Net revenues for peak industrial water use .... 126
25 Net revenues for off-peak industrial water use . . 127
26 Distribution of initial water use 134
27 Declining weights for plumbing permits 135
IX
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TABLES
Number Page
1 Summary of selected Mines' statistical cost
regressions 31
2 Summary of Ford-Warford's statistical cost „
regressions
•ZQ
3 Summary of Andrews' statistical cost equations. . . J*
4 Number of data points stratified by service zone
and user classification 89
5 Cincinnati Water Works water rates 93
6 Impacts of quantity on total cost of delivered
water 97
7 Impacts of altitude and distance on average costs
of delivered water 10°
8 Peak and off-peak cost elasticities 1°5
9 Residential and industrial samples 104
10 Average cost elasticity estimates arrayed by
distance
11 Industrial average cost elasticities 106
12 Peak and off-peak average cost elasticities .... 107
13 9596 confidence limits for distance cost
elasticities 107
14 Mean water use by customer class no
15 Residential net revenues. 112
16 Commercial net revenues 113
17 Industrial net revenues 114
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Number Pa^e
18 Residential users, route C1 129
19 Residential users, route C2 130
20 Lag time in days by user group 137
21 Total water consumption and plumbing permits;
analysis of Pascal lags 139
B Water consumption by type of dwelling unit 166
C Industrial water user categories 186
XI
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ACKNOWLEDGEMENTS
We acknowledge our indebtedness to the many individuals who
were of great assistance at many points in this work. Prominent
among these are Charles M. Bolton, Superintendent of the
Cincinnati Water Works (retired), Robert Heheman, Supervisor of
Central Services for the City of Cincinnati, and Lisa Gaker,
student intern from Wittenburg University. Dr. Robert M. Clark,
project officer at EPA provided much useful advice during the
course of the project. Cindy Brown, Susan Burns and Valeria
Wright contributed many hours of typing all through the project.
Xll
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SECTION 1
INTRODUCTION TO
COST RATE DIFFERENTIALS
BACKGROUND
The metering and pricing of municipal water supplies is a
wiedespread practice in the United States, with some important
exceptions. There is also now widespread recognition of the
impact that charging for water use has on the demand for water,
both in residential and commercial-industrial uses. As a result,
then, pricing can have a substantial impact on the requisite
capital investment in acquisition, treatment and distribution
facilities, especially if water pricing alternates peak demands.
For those water systems which do charge for their water, it
is appropriate to ask which are the appropriate rate structures,
especially with respect to delivering water under varying cost
circumstances, as determined by distance, topography, and peak
conditions. An inappropriate rate structure, while financing
the system, can lead customers to utilize water in such a way so
as to increase the quantity demanded, and thus create a "need"
for more investment in expanding the system, thus making total
and average costs unnecessarily higher, unless offset by scale
economies.
It is, of course, necessary to have a definition of what
constitutes an "appropriate" rate structure. The usual definit-
ion employed in cost-benefit analysis is to choose a rate
structure (and thereby the quantity of delivered water given
supply and demand conditions) that generates the maximum net
benefits associated with water use. The usual first approxima-
tion this is to equate price (.rate) to the incremental cost of
delivery, or marginal benefit equals marginal cost.* Of course,
this first approximation may be changed depending on the kinds
of constraints added to the problem, such as the need to be self
financing, even in the presence of scale economies.
*See for example, A. Maass, et al., Design of Water Re-
source Systems. Harvard, 1962, Chapter 2.
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For operational purposes, a water pricing policy which
equates the rate (price) to the appropriately defined marginal
cost of delivering water to a customer is the rate structure
which will lead to maximum net benefits. This is generally
termed "marginal cost pricing".*
The implications of this concept for our purposes is that
if the rate is set less than marginal cost for some uses of
water, then this water will be overused, in the sense that its
value to the users will be less than its cost. The resulting
increased demands, if not completely offset, will signal water
supply officials that the water supply system needs to be ex-
panded. An expanded system, however, would in fact be unwarrant-
ed.
Similarly, if rates are less than marginal cost for some
customer classes and greater for others, it might seem that the
effects would cancel out, with no net effect on the system.
However, some users, particularly industry, are in better positions
to economize on water use than others, as through water reuse,
especially for process cooling and washing, such that the net
effect would not be zero. Again, this can result in a system
which is too large, and thus unnecessarily expensive.
This extra expense can take a number of forms, among which
are:
1. excessive investment in all phases of water supply:
acquisition, treatment, and transmission and distribution.
2. Operating costs, especially in treatment and distribution
will be higher. A new element has also entered the picture:
the discovery that surface waters contain potentially
hazardous levels of carcinogens, of which removal is quite
expensive (and the technologies are unproven). Excessive
water use will mean excessive and expensive water treatment.
3. More water throughput means more sewage treatment, which is
an expensive proposition for secondary and teritiary treat-
ment. Policies which permit costs to be higher than they
need to be (because of excessive water use) means that the
public will demand less environmental quality, and be more
accepting of lower water quality.
In addition to these cost considerations, there is the
problem of equity. If water rates are less than the average
cost (and the marginal cost) of supply for some water customers,
*See e.g. Hirschleifer, deHaven and Millsman, Water Supply:
Economics, Technology and Policy. University of Chicago Press,
1969, Ch. 5.
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this means that internal cross-subsidies among customer classes
will be established. Such transfers can take a variety of forms:
(1) there can be transfers between peak and off-peak users; (2)
among customer classes (residential, commercial and industrial;)
(3) between those near and those distant from the treatment
facilities; and (4) between those at high altitudes and those
lower. Such transfers violate common perceptions of economic
Justice or fairness, and may mean that the poorer members of a
community subsidize the wealthier members. The evidence develop-
ed in this study on these questions will be presented below.
PURPOSE OF RESEARCH
The specific outputs of this research include the following:
1. Estimates of the costs of delivering finished water to
customers in the Cincinnati Water Works (CWW) area, prin-
cipally in terms of the main user classes (residential,
industrial and commercial). Also, some evidence is pre-
sented for particular (unidentified) customers. Distance
and altitude are analyzed explicitly as factors which
determine costs.
2. Evidence on the nature and extent of cost-rate differentials,
or subsidies along the dimensions mentioned above.
Three chapters follow:
1. An extensive review of the literature on the cost of water
supply;
2. Methodologies used to compute the cost estimates developed
in this study;
3. Empirical results, including estimates of costs and revenues,
and the associated spatial distributions in the CWW system.
4. Conclusions and recommendations for future research.
The principal limitations of this study include:
1. An inability at the current level of analysis to detail
more precisely the impact of distance on the cost of water
supply. These impacts were measured for the average cost
of supply, but not for total cost, as there are some
statistical problems to be surmounted. As a result, this
analysis needs more refinement in order to be able to
separate out the implications for regionalizations of water
supply systems.
3
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2. Excluded from the analysis are the explicit impacts of
provision of water for fire protection on the measured
costs. It is included implicitly, however, through the
cost allocations.
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SECTION II
CONCLUSIONS AND RECOMMENDATIONS CONCERNING
COST-RATE DIFFERENTIALS
In Section m we formulated six hypotheses concerning the
relationships which were examined subsequently. We restate the
hypotheses and summarize the empirical findings pertinent to
them.
Hypothesis 1; Total water supply costs vary positively
with distance and altitude. Statistical problems prevented a
direct examination of the relationship between total cost,
altitude and distance at this stage, but examination of the
relationship between average cost, altitude and distance reveal
positive effects. By implication, then, TC does vary positively
with altitude and distance. Actual measurement of this effect
requires more refined analysis.
Hypothesis 2; Peak period total costs exceed off-peak
total costs.The results with respect to this hypothesis both
support and do not support it, depending on the customer class,
the region examined, and the variables included. Once the
spatial aspects of costs are treated separately, it is quite
possible for off-peak costs to be higher, as they are not off-
set by scale economics in acquisition and treatment (A&T). At
the present level of understanding, it is not possible to
determine whether there is a consistency among the pattern of
results for peak and off-peak results.
Hypothesis 3: Scale economies in transmission and distri-
bution CTSDj~aremainly determined by industrial water demands,
as opposed to commercial or residential demands. While the
results obtained should not be regarded as conclusive, the
findings in Table 14 suggest greater economies in residential
supply as opposed to commercial or industrial supply.
Hypothesis 4: The Cincinnati Water Works earns revenue
surpluses on customers close to the A&T facility, and incurs
deficits on those farther away. For making statements about the
questions of equity, it is best to use AC information to abstract
from quantity variation. For the two routes examined, C^ and C,
it was found that (l) for residential users, the surplus tended
in fact to be higher for the more distant users (Table 22) and
(2) for commercial and industrial users, the reverse pattern of
what was hypothesized (Tables 2? and 24).
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Hypothesis 3; The CWW incurs revenue deficits on industrial
and commercial water supply, and surplus on residential supply.
Again, for comparisons on a unit basis, the findings in Tables
22, 23 and 24 tend to support this hypothesis.
Hypothesis 6; Peak period water users are subsidized by off-
peak users.The findings in Tables 22, 23 and 24 do not support
this hypothesis.
In general, the pricing structure chosen by the CWV does not
fare too badly with respect to the analysis of a major variable,
distance, in terms of the hypothesis that city residents ( who
tend to have lower incomes than the regional average) do not sub-
sidize suburban residents (whose incomes tend to be above the
regional average). However, the correspondence between rates and
average delivered cost is weak, as measured by the methodologies
developed here, although the system is self financing. Thus,
there are cross-subsidies within the system. A realignment of
rates would improve equity, if by equity we mean each customer
paying his costs.
Suggested Research
The cost methodologies developed and utilized for this study
are new, and considering that the level of effort v/as relatively
modest, there are some refinements and improvements that need to
be undertaken to improve the reliability, and the specificity of
the technique. Additionally, although the resulting estimates
do seem plausible and reasonable, it is desirable to develop
methods of checking their accuracy. Thus, while the tools util-
ized do hold promise, the following should be done:
1. Closer investigation of the appropriate functional form
for the estimates of the cost elasticities. While we chose
our specifications based on the normality of various variable
transformations, other criteria, such as R , should be explored
for the implications and impacts on the elasticities.
2. Population density is a factor which affects water
supply costs, as has been found in other studies, and it should
be introduced into this analysis.
3. In order to give more precision to the technique as a
tool for rate setting purposes, more spatial detail or spec-
ificity needs to be introduced into the analyses in order to
obtain a clearer picture of the spatial distribution of the
cross-subsidies. This conclusion applies to peak and off-peak
period analysis as well.
4. For the purpose of determining the economic boundaries
to water supply systems, it is necessary to have a better under-
standing of its quantitative impact. It was not possible to
determine the separate effect^of distance on total, cost within
the framework of this study, but the data are useable for this
analysis.
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SECTION III
LITERATURE REVIEW ON THE COST OF WATER SUPPLY
INTRODUCTION
The costs of providing a safe and potable water supply for
a regional and metropolitan area is becoming an increasingly
important factor for water supply utilities. Expansion of the
capacity to satisfy demand, as occurred in the 1940's, 1950's,
and 1960's, may not be warranted due to excessive investment
cost. In the 1970's and 1980's, future expansion must be
carefully analyzed in terms of efficiency of resource use and
the effect on total water supply costs, as well as adequacy of
supply.
Increased costs are a major problem in the water supply
industry. In 1965, capital requirements exceeded two billion
dollars and were estimated to be about three billion in 1975-a
Operating costs continue to increase as inflation persists."
Comprehensive analyses of costs are necessary to improve decision
making. Without such research, decision on capital expansion
and replacement, level and structuer of utility rates, and
general operating procedure will be hampered. Adequate supply
to meet water demand is an important factor, but knowledge of
the costs to meet that demand are crucial.
PRINCIPAL COST COMPONENTS
In general, a water supply system's costs can be broken
down into five major categories: acquisition, treatment, trans-
mission, distribution,0 and overhead. A brief synopsis of each
follows.
aAmerican Water Works Association - Staff Report. "The
Water Utility Industry in the United States". Journal of the
American Water Works Association, 58 (July, 1966), p. 781.
bln 1974, chemical costs at the Cincinnati Water Works
increased over 100%.
°American Water Works Association - Staff Report, "The
Water Utility Industry in the United States", p. 767.
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The cost of acquisition involves the collection of raw
water from a surface water source (lake or stream) or ground
water source (well or spring). Pumping and plant facility cost,
labor, and energy are the major portions of acquisition cost.
Treatment to produce a safe and palatable water supply can
be very complicated or straight-forward, depending upon the in-
put quality of the raw water and the output quality desired.
Treatment generally comprises the following steps: settling,
mixing of chemicals, flocculation, and filtration. Use of other
processes for softening or removing iron or manganese are de-
pendent on local management decisions. The costs of treatment
are chemicals, sand, power, and depreciation on the physical
plant.
Transmission pipelines are the major trunk lines used to
transport large volumes of water. They connect the treatment
plant to the pumping station, if gravity tunnels are not used,
and the distribution system. Pumping stations, pipelines, and
energy comprise the major costs of transmission.
Distribution works include the meters, pipelines, and
storage facilities (water tanks) necessary to convey the water
from the transmission system to the customer. A pumping station
might also be involved if ground-storage exists. Therefore,
distribution systems include the cost of pipelines, water towers,
pumping stations, and energy.
The final category is overhead. Administration, interest
on the debt, meter reading, billing, revenue collection, and
the equipment involved are the major elements in this category.
This is a highly labor intensive operation even though computers
may be employed to speed work flow. The above five components
represent a general breakdown of water supply costs.
In the following sections, two major issue areas are
covered: methods of cost allocation, and water supply cost
analyses.
METHODS OF COST ALLOCATION
This section reviews the issues surrounding the problem of
cost allocation. Familiarity with this method provides a better
understanding of the types of costs involved in water supply
public utilities, and how they are related.
8
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The basic principle of an allocated cost method is the
"equitable" distribution5 of costs to specific functions and
customer classes. The American Water Works Association suggests
two methods of allocating cost in their manual of water rates.b
One is the commodity-demand method; the other is the base extra-
capacity method.
Under the commodity-demand method, costs are divided into
three functions0 — demand costs, commodity costs, and customer
costs. Demand costs are directly related to the cost of pro-
viding system capacity to meet peak demands (i.e. maximum day,
peak hour, or maximum week). This includes plant as well as
operating expenses. Fire protection costs may also be covered
here. Commodity costs vary directly with the quantity of water
produced and sold. This involves the costs of power, chemicals,
and other operating and maintenance expenses connected to the
amount of water supplied. Customer costs consist of expenditures
on meter readings, billing, accounting and collecting, meters,
and maintenance of customer related equipment (billing machines
and meters). Those costs vary with the number of customer
accounts, but are independent of the water produced or the
demand rate.
The commodity-demand method is one approach to the alloca-
tion of utility costs to specific functions. The other prominent
method is the base extra-capacity method. R.L. Greene notes
that this breakdown "is the one generally accepted in the
field."d All costs are again divided into three components:6
aEquity here is not similar to an economic concept of
equity, where income distribution becomes important. Rather, it
refers to economic efficiency where the price paid approximates
the cost incurred.
American Water Works Association. Water Rates Manual.
(New York: American Water Works Association, 1972.Second
Edition).
°The three components of the commodity-demand method are
easily classified into fixed or variable costs, traditional
economic cost concepts. Demand costs represent fixed costs,
while commodity and customer costs comprise variable costs.
Customer costs are variable, since they cease if output stops.
R.L. Greene. The Economics of Municipal Water Rates.
Unpublished Ph.D. dissertation, University of Florida,1968.
eln the base-extra capacity method, the three components
are not easily classified as fixed or variable. Customer costs
remain variable as before, but base and extra-capacity costs
both contain fixed and variable elements. This results from the
use of average daily demand as the demarcation between base and
extra-capacity.
9
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customer, base, and extra-capacity. The definition of customer
costs is the same as for the commodity-demand method. Base
water costs are the costs associated with the quantity of water
demanded and the operation, maintenance, and capital costs of
servicing the average daily demand on the system. The average
daily demand is identified as a 100% load. In this component,
operating costs are joined with capital costs, while only
operating costs comprised the commodity component above. Extra
capacity costs consist of the costs to meet use requirements
above the average 100% load. It includes capital and operating
costs for additional system capacity beyond the average, such
as the maximum hour or day.a
Once costs have been allocated to the correct functions,
the proper appointments to customer classes remain to be deter-
mined. Briefly, allocation of capacity or demand costs to
customer classes" are decided primarily on the basis of ratios
of peak demands to average demand. Commodity or base costs are
distributed according to the volume of water used. Customer
cost allocation, though, depends on the number of customers or
meters. The AWWA theorizes that equity is approximated if a
rate structure attempts to recover costs allocated in this
procedure.
Linaweaver and Geyerc, in a study on residential water use,
appear to promote the base extra-capacity method. They discuss
how part of the John Hopkins University Water Research Project
is attempting to gather data on peak use by customer class which
may prove useful in the allocation of extra-capacity costs.
But, they do question one point in this type of allocation,
namely, the use of average annual consumption in determining
the proportion of plant investment to be allocated to base
capacity.d Average daily use fluctuates around average annual
use. During the winter, average daily use is lower than the
average annual; but it is higher during the summer. Rather,
Linaweaver and Geyer suggest the use of domestic water require-
ments, average daily winter demand, to determine base costs.
aFire protection costs may also be included.
bThe major customer classes are residential, commercial,
and industrial users. Sometimes, special cases are considered
as hospitals, schools, government buildings, and welfare cases,
but they are ignored here.
CF.P. Linaweaver and John Geyer. "Use of Peak Demands in
Determination of Residential Rates". Journal of the American
Water Works Association. 56 (April, 195^;, p. 403.
dlbid, p. 405.
10
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Also, sprinkling demand can be identified and used for the extra-
capacity cost allocation. As far as residential water demand
is concerned, that seems more equitable than use of average
annual demand for cost allocation.
Another proponent of the base extra-capacity cost method
is W.L. Patterson.3 His article on water rates in 1962 is widely
quoted as the major article in this field. Patterson provides
an extensive example of cost allocation, using the base extra-
capacity method to allocate system costs and noncoincidental
extra capacity method to distribute peak use costs to customer
class.
A noncoincidental method implies that the peak character-
istic (ratio of maximum use to average annual use) of each class
be examined. The term, noncoincidental, signifies that the
ratio of peak to average is not related to the time of the
.system peak. If a certain customer class did not consume during
the system peak time, but was characterized by a high ratio of
peak to average use at another time, then part of the system
capacity costs would be allocated to that customer class.
Patterson notes that:
"this method of allocation most equitably distributes
costs among customer classes whose individual maximum
demands would not. necessarily occur simulatneously or
at the time of the system peak."b
The actual degree of equity in this and other forms of peak load-
cost allocation is an issue that has received, much attention in
the literature.
Davidson, in his bock on price discrimination, devotes a
full chapterc to all the proposed methods of capacity cost
allocation. In brief, he demonstrates that all twenty or more
methods, including the noncoincidental method, possess varying
degrees of discrimination. One or another group of customers
can force a reallocation of costs from themselves to others
by_adjusting their demand losds, even though their load con-
tributes to the system peak. As a result, the nonceincidental
method is shown to increase discrimination among users if rates
are based on such a cost allocation.
Q
W.L. Patterson. "Practical Water Rate Determination".
Journal of the American Water Works Association. 54 (Aug., 1962),
p. y04-12.
blbid, p. 909.
Q
Ralph K. Davidson, Price Discrimination in Selling Gas
.and Electricity. (Baltimore: John Hopkins University Press,
Chapter 8.
11
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Davidson applies the commodity-demand method in his
analysis, but adds one important point: the relevant costs.
The relevant cost concept
"is not the expost accounting record of costs incurred
in producing, distributing, and selling the (commodity)
purchased by the consumers in a period just past. All
attempts to ascertain unambiguously total costs, or
average costs per unit of output from ex post accounting
records encounter insuperable difficulties in the alloca-
tion of fixed costs, common costs, and joint costs; these
costs are arbitrarily allocated, if they are allocated at
all. This particular problem of allocation of fixed,
common, or joint costs is not encountered in finding
marginal or incremental costs, but it is also true that
marginal or incremental costs cannot be determined from
usual accounting records. The usual accounting records
are records of the past and the relationship with which
economists are concerned are the expected or anticipated
relationships—a matter of the future."a
Marginal or incremental costs, if possible to determine, are the
relevant costs. Davidson theorized that the important elements
to be defined are the additional costs incurred if another unit
of output is sold, the incremental cost of an additional unit
of capacity for peak load demand, and the marginal cost of
another customer served by the system. Employment of these
definitions of costs would improve resource allocation and avoid
some of the problems of a strict cost allocation.
Davidson also mentions the problem of allocation under
conditions of joint and common cost. Though not directly dis-
cussed by Davidson, other articles have elaborated on it.
Greenet* criticizes Patterson's work and discusses the problem
of joint cost. He argues that the ratio (noncoincidental)
method of cost allocation used by Patterson favors large
quantity users more than other users, since the larger ones have
a higher average hourly use than the smaller customers. It
also tends to penalize users, with or without a peaking character-
istic, who do not take water during the system peak. A cost
allocation based on Patterson's method would distribute cost on
the basis of differences in demand characteristics rather than
differences in costs imposed by the various user classes. This
does not lead to an equitable allocation if rate differentials
are based on this allocation.
aDavidson, Price Discrimination in Selling Gas and
Electricity, (Baltimore:John wopkins University Press, 1955),
p. 69.
^Greene, The Economics of Municipal Water Rates, p. 110.
12
-------
According to Greene, the cost allocation methods were
derived because of the joint cost conditions between peak and
off-peak conditions. Capacity costs are joint costs if the cost
of producing the services (joint products) is rendered at
different periods of time.a Time jointness is the correct term.
Capacity which is used to meet a peak demand, is also available
for off-peak use. Services produced at those different times
are true joint products because capacity cannot be adjusted.
Greene points out that the utility solution to joint cost
conditions (Patterson approach) implies that the distinct
customer class demands are summed vertically, (Figures 1 and 2),
to determine the distribution of costs to each consumer group
on the basis of relative demand strengths. The vertical
summation requires that each class be allocated a different per
unit cost of capacity, depending upon the relative heights of
their demand curve, even if the customer classes were to consume
identical quantities of the commodity in the same time period.
If the demands were summed horizontally, as in Figure 2, the
same per unit charge could be allocated to each customer class,
but the total cost allocated would vary because the quantity
consumed by each group in the same time period is not the same.
aJames C. Bonbright, Principles of Public Utility Rates.
(New York: Columbia University Press, 1969), p. 35^. iMote
that the Quarterly Journal of Economics published a number of
articles by Pigou and Taussig on the issue of joint costs: A.C.
Pigou, "Railway Rates and Joint Costs", Quarterly Journal of
Economics, 27 (May, 1913 and August, 1913); F.W. Taussig, "Rail-
way Rates and Joint Costs Once More", Quarterly Journal of
Economics. 27 (February, 1913); and F.W. Taussig (Untitled re-
buttal to A.C. Pigou). Quarterly Journal of Economics. 27 (May,
1913 and August, 1913). The issue centered upon the separ-
ability of certain costs of production when joint products were
produced. Wool and mutton is a classic example of joint products
with unallocable costs. Cost, therefore, was allocated on the
basis of relative forces of demand. Taussig believed that
principles of joint product pricing were applicable to railroad
rate setting, while Pigou opposed such an adoption.
In a more recent article, R.L. Weil, Jr., "Allocating Joint
Costs", American Economic Review. 58 (December, 1968), p.
A5, a mathematical model which allocates joint costs is pre-
sented. His allocation is based on the idea that joint cost
allocations equal marginal revenues and are determined in part
by conditions of demand.
13
-------
PC
PI
PR
R + C + I
Q*
Q
Q*
P*
R
C
I
PR
PC
PI
= plant capacity.
= weighted average of PC + PR + P|.
= residential demand curve.
= commercial demand curve.
= industrial demand curve.
= residential price.
= commercial price.
= industrial price.
Figure 1. Vertical summation of demand curves.
-------
R + C+ I
QC Q|
Q*
Q
Q* = plant capacity
P* = price per unit
QR= residential demand at price P
Q£= commercial demand at price
Q| = industrial demand at price P*
Figure 2, Horizontal summation of demand curves
-------
It would depend on the demand curve of each separate class.
This is a more realistic description of the peak-load situation
when characteristics of consumer classes are considered.
The principle foundation to Greene's argument is the
distinction between joint and common costs. Greene states,
"there is no justification for charging different users,
in the same time period different rates for the same
quantity of service, since the costs are common costs
and not joint costs.
. . . Any difference is discrimination based on criteria
other than economic efficiency criteria."3
Wallace presents, in a rather lengthy discussion, the
distinction between joint and overhead costs (common costs).
Briefly, he argues that in the case of joint supply, productive
capacity available is fixed in proportion to the demands of
different customer groups. An entrepreneur cannot increase or
decrease his output capacity in one market without affecting
the capacity available in another market.b This is similar to
the situation of a water works. Capacity available to handle
peak-load operation is available for off-peak periods.
But, if capacity may vary in relation to the demands of
different customer groups, cost is common. For services pro-
duced with common cost, no element of jointness, uniformity in
rates is appropriate. This may occur in a water utility when
many consumers demand at the same point in time. As a result,
under condition of common cost, allocation to consumer groups
csnnot be made, because cost is not related proportionally to
the different groups. For correct analytical results, Wallace
promotes long-run marginal cost as the relevant dimension to
study.
The basic issue of joint costs revolves around the time
period in v/hich output is consumed. Time jointness refers to
the fact that capacity cannot be adjusted to meet changing
demand. Peak demand is responsible for the amount of capacity
available. Off-peak demand is serviced with excess capacity.
Therefore, cost should be allocated differently between these
periods. An off-peak unit, consumed by a residential customer,
aGreene, The Economics of Municipal Water Rates, p. 114.
Donald H. Wallace, "Joint Supply and Overhead Costs and
Railway Rate Policy," Quarterly Journal of Economics. 48
(August, 1934), pgs. 584-586.
16
-------
costs differently than a peak unit.a As a result, cost alloca-
tion, according to Greene, Wallace, and Bonbright, should depend
on the time jointness of the costs. Changes in demand rates
require different cost allocations between peak and off-peak
regardless of the relative strengths of demand at a given point
in time by each customer class. Once the peak has been reached,
the capacity cost per unit of output is the same whether a
residential, commercial, or industrial user consumes the service.
The issue of cost allocation still remains. Bonbright
notes that the main reason for difficulty with the full-cost
apportionment method:
"lies in the special character of the only costs that
can be allocated, on a cost causation basis, to specific
quantities of specific types of service."'3
The costs that are allocable are of necessity the differential,
incremental, or marginal costs. Bonbright also points out that
only rarely would these costs sum up to total operating and
capital costs.c other cost allocation deficiencies discussed
by Bonbrightd are the inability to define fair value of capital6,
investment for peak load allocations, the failure of the cost
analyst to allocate all costs to three or four categories, and
the poor handling of joint cost issues by the cost analyst.
aThese are the same results implied but not as explicitly
stated in articles by Steiner, hirshleifer, and Williamson, on
peak load pricing where the peak user alone pays for capacity
costs and common costs are not allocated by customer class-
ification. See: Peter 0. Steiner, "Peak loads and efficient
pricing", Quarterly Journal of Economics. 71 (November, 1957),
585-610; Jack Hirshleifer,"Peak loads and efficient pricing:
comment", Quarterly Journal of Economics, 72 (August, 1958),
451-62; and Oliver E. Williamson, "Peak-load pricing and optimal
capacity under Indivisibility Constraint", American Economic
Review, 56 (September, 1966) 810-27.
bJames C. Bonbright, "Fully Distributed Costs in Utility
Rate Making", American Economic Review. 51 (May, 1961), p. 307.
°This occurs because of the existence of returns to scale.
Bonbright, Principles of Public Utility Rates, p. 367.
eThis refers to the discussion over the use of historical
or reproduction costs or the fair value of capital.
17
-------
Like Wallace and Davidson above, Bonbright favors an
estimation of the long run marginal costs to service different
classes and a formula apportionment among the classes for all
unallocable residues of total cost. This could free the analyst
from pressure to divide up all the costs, even though there
would still be problems in finding a rational method to apportion
the unallocable residual costs. Bonbright concludes that,
"the really important analyses are not those which attempt
to apportion total capital and operating costs among the
different classes or units of service. Instead, they are
the analyses designed to disclose differential, incremental,
or marginal, or escapable costs—costs which are not
ordinarily derivable from total costs and which cannot
be added together so as to equal this total."a
In their excellent book on water supply, Hirshleifer,
DeHaven, and Milliman also discuss the issues involved with a
cost allocation method. They argue that because of the existence
of joint costs, there is no unique way to segregate total costs
into three components: customer, commodity, and capacity.
"This is logically equivalent to the impossible task of
dividing sheep costs into wool costs, mutton costs, and
hide costs. A new reservoir, for example, may at one
stroke increase system capacity, permit connection of a
new class of consumers, and lower unit costs of deliver-
ing the commodity.""
With regard to capacity allocation, Hirshleifer, DeHaven, and
Milliman, believe that capital costs cannot be correctly divided
between the various service dimensions represented by capacity
and commodity. Any attempt to do so, as exemplified by the
Water Rates Committee of the AWWA, is defective in theory and
inconsistent in application.0 This also applies to the general
classification of costs under the commodity-demand method.
Their alternative is identical to that offered by Davidson,
Wallace, and Bonbright. The relevant dimension to examine costs
is the marginal cost: the cost of adding another customer with
albid, p. 363.
Jack Hirshleifer, James C. Detiaven, and Jerome W. Milliman,
Water Supply: Economics. Technology, and Policy. (Chicago:
University of Chicago Press, 1960), p. 98.
°Ibid, p. 99. Note: Some arbitrariness may be required.
It is not easy to classify what is incorrect, if no correct way
exists.
18
-------
capacity and commodity elements constant; the cost of adding a
unit of capacity with customer and commodity elements constant;
and the cost of increasing output by one unit with customer and
capacity elements constant. Those costs are measurable and more
relevant for rate purposes. In another article, Milliman points
out that,
"Pricing according to incremental costs, water rates
that reflect true economic scarcities, must become
the order of the day if we hope to deal with the
problem of water supply in the future."3
In general, this discussion on allocation of costs has
attempted to outline some of the problems associated with current
practices in use and the correct way to examine costs. Though
there has been no final solution to the issue, the present state
of the literature appears to favor the Davidson, Bonbright,
Wallace, hirshleifer, DeHaven, and Milliman analysis of costs to
the AWWA or Patterson approach because of the latter1s misin-
terpretation of the joint vs. common cost issues.
WATER SUPPLY COST
This section reviews existing literature on water supply
cost functions and analyses. In estimating statistical cost
relationships, two different approaches stand out as the most
significant.13 One is a factor-cost approach; the other is an
explanatory variable approach.
The factor-cost approach develops a statistical relation
between total cost and the price and quantity of the factors
employed. This type of cost function can be defined if the
production relation, quantities of inputs, and prices of inputs
are known. One major difficulty with this method is the
identification and estimation of the production relation. Also,
the cost function developed tends to be more of an accounting
relation than an economic one.
The other method is an explanatory variable approach. This
method attempts to estimate the statistical relationship between
cost and certain key explanatory variables. A general functional
relation is theorized, the specific form of which is determined
by the interdependencies among the variables. A functional cost
relation can be stated as c = f (x) or f: x -» c where c is cost
(total, average, or marginal) and x is a vector of explanatory
aJerome W. Milliman, "Economics and Water Supply", Water
and Sewage Works, 110 (Reference number), p. R-16.
J. Johnston. Statistical Cost Analysis. (New York:
McGraw-Hill, 1960), Chapters 2 and 3.
19
-------
variables and shift parameters. a The form may be linear or non-
linear. The statistical relation does not attempt to examine
cost in actuality for accounting purposes. Rathei , the
explanatory variable approach tries to identify the inter-
relationships that exist to improve predictive and explanatory
capability. This is the direction that this discussion will
follow.
Three major categories exist in the literature on water
supply cost. They are treatment, total cost, and transmission
cost. One brief look at peak-load cost will be included, but
it is not as important because no articles appear to concentrate
on peak-load cost estimation.
Treatment Cost
Two main elements which comprise treatment cost are
analyzed. One is construction or capital cost; the other is
operation - maintenance cost. Orlob and Lindorf0 examined
treatment cost to determine its relationship to the costs of
surface water importation, reclamation of waste waters, ground
water recharge, and any other alternatives available for in-
creasing water supply to California. Their study consists of
a cross-section of 32 treatment facilities as existed in 1956
in California.0 All construction cost data was adjusted by
means of a water treatment plant construction cost index.
Based on the Engineering-News Record Construction Cost Index
and the Marshall and Stevens Equipment Cost Index, they de-
veloped their own index for the Pacific Coast States. The ,
treat plants included were only those with complete treatment.
factor cost approach could be modeled as follows:
C = S r.X, where C = total cost; r. = price per unit of the
1=1
(i)th factor; and X. = amount of the (i)th input purchased.
G.T. Orlob and M.R. Lindorf. "Cost of Water Treatment in
California," Journal of the American Water Works Association, 50
(January, 1958; p. 45-55.
°Since this is a cross-sectional analysis, the long-run
cost curve is generated. See Johnson, Statistical Cost Analysis.
Chapter 5.
dOrlob and Lindorf, "Cost of Water Treatment in California",
defined complete treatment as including "at least flocculation,
sedimentation, rapid-sand filtration, and chlorination.
Aeration or special chemical treatment, such as softening or
taste and odor control were not common to all plants", p. 47.
Use of other processes or technology will affect shape of cost
curve.
20
-------
Construction cost was theorized as a function of the
explanatory variable, design capacity. In general, the form of
the equation would be:
where C = total capital cost of a complete water treatment
facility;
GL = the design capacity of the plant in million
gallons per day (MGD); and
at = intercept
3 = elasticity of total cost with respect to design
capacity.
Estimation of the equation generated this relationship:a
O CJ7
Cc = 257 ^ • The value of 3 = 0.67 implies that economies
of scale may exist in treatment plant construction. If t-
statistics were provided, it would have been possible to test
whether 3 is significantly different from one. Since the
relevant statistics are not available, no conclusion can be made
concerning economies of scale.
Operation and maintenance cost is assumed to be related to
average daily flow in million gallons per day in the same func-
tional form as construction to design capacity above. The
statistical relation estimated by Orlob and Lindorfb is:
Co = 68.4 Qa"°'41
where Co = the cost of operation and maintenance (including
labor, chemicals, power, and plant overhead);
and
Qa = the average daily flow, MGD.
This is an average cost function, not total cost. The dimension
of Co is (S/million gal.)» Converted to total cost,
0 59
C = 68.4 Qa * . Since 0 = .59, economies of scale may also
exist in the operation and maintenance of treatment plants.
a 2
No R or t-statistics were provided. Note: construction
cost expressed as cost per million gallons per day of design
capacity as derived from the estimated total cost equation, is
Cc/Q = 257 Qn~'33.
T^ O
Again, no R or t-statistics were provided.
21
-------
The importance of their work is not the statistical merit,
but the fact that it is one of the first attempts to estimate
the costs of water treatment. The authors ignored discussion
of the issues of economies of scale. Instead, they concentrated
on determining the relation of treatment costs to the production
costs of all plausible alternatives for water supply expansion.
As a result, important economic issues were not examined.
In a more recent article, L. Koeniga further investigates
the area of water treatment cost estimation, he attempts to
provide a detailed analysis of the physical characteristics,
operating data, and costs of a water treatment plant. Once the
information is presented in a standardized form, comparisons may
be made between plants.
The general objective of Koenig's study was to identify
the relevant costs of water treatment and their proportional
contribution to total cost. The purpose was to provide data
and information to decision-makers, such as utility managers,
engineers, planners, and economists, and to aid in cost-benefit
analyses.
This study is based on the cost engineering audits of 30
water treatment plants as of 1965. The sample data is a re-
presentative cross-section of water purification plants.b The
methodology employed is similar to that used by Orlob and
Lindorf in that a cost index was used to adjust investment
expenditures to one common year. But Koenig expanded his study
to examine in detail specific treatment costs such as: chemical,
filter, energy, heating, and manpower costs as well as capital
expense. With respect to investment expense, Koenig estimated
an equation similar to the one Orlob and Lindorf used. The
only difference is that Koenig's is an average cost relation.
He finds that:
C = 30.7 Qd~°*^25(with a correlation coefficient = 0.768 and
significant from zero at the .001 level)
aLouis Koenig. "Cost of Water Treatment by Coagulation,
Sedimentation, and Rapid-Sand Filtration", Journal of the
American Water Works Association. 59 (March, 1967), p. 290-336,
bThe class of water treatment plants studied by Koenig
differs from those examined by Orlob and Lindorf. Koenig in-
cluded those plants having coagulation, sedimentation, and
rapid-sand filtration. Orlob and Lindorf include the chlorina-
tion process in their plant description.
22
-------
wher*e Q^ = design capacity; and
C = cost, 0/gpd.
Orlob and Lindorf found the total capital cost relationship:
o Av
Cc = 257 On * which upon conversion to an average cost function
became 7?c = 257 On"0'3-5. The value of the exponent of Q is
nearly equal in both. Koenig continued his analysis by adding
Orlob and Lindorffs data to his. The combined regression
provided a correlation coefficient of 0.57 and a line flatter
and below the line estimated from Koenig's data alone. The
difference, according to Koenig, is the several small plants
with exceptionally low investment costs which were included in
the Orlob-Lindorf study. As a result, their data was dropped in
Koenig1s subsequent analyses.
Instead of estimating an operation-maintenance cost
equation, Koenig estimated average total cost for complete
treatment for different utilization ratios. A utilization ratio,
lJ, was defined as the ratio of average raw water intake in MDG,
"3, to the design capability for raw water in MGD, Q,. Total
costs were computed for each plant at U = 0.2, 0.5 and 1.0, the
Q, lines in Figure 3. A statistical regression was then per-
fornied relating ^ and unit total costs at each U value to derive
the TJ lines in Figure 3. All showed high correlation coeffici-
ents, but unfortunately, Koenig did not provide the parameter
estimates or the specific form of the regression. He did in-
clude a graph of the function, Figure 3,a From this, one can
roughly estimate the total treatment costs of various size
plants and average daily flows.
An interesting factor that Koenig fails to point out is
the existence of economies of scale. His regression line of
investment costs and the functions estimated, as shown in Figure
3, both point to the existence of positive economies of scale
in treatment plant investment and operation-maintenance, he
discusses methods of cost reduction and the contributions to
cost of key inputs as manpower, but appears to have ignored
any discussion of economies of scale. This probably can be
attributed to the fact that Koenig's objective was to improve
data acquisition and estimation of treatment costs and not to
investigate for economies of scale.
Qd lines _in Figure 3 resemble short-run average total
cost lines and the U lines resemble long-run average total cost
lines. The graph is from Koenig, "Cost of Water Treatment by
Coagulation, Sedimentation, and Rapid-Sand Filtration", p. 327.
23
-------
loon
(0
3
o
Q
Z
W
3
O
10
,-1
u
.2
.5
1.0
i i i i i i i i
1.0 10'
AVERAGE PRODUCTION (Q)- MGD.
10'
icr're 3. Median total cost of treatment
-------
One other article examines treatment cost. Hinomoto
estimated unit and total cost functions for water treatment
based on Koenig's data. A formula is developed to estimate the
total annual cost of surface water treatment incurred by the
plant of a given capacity operated at a given use rate. This
formula is derived from seven regression equations on the major
factors of water treatment: capital investments, chemicals,
pumping energy, heating energy, manpower, maintenance and re-
pair, and miscellaneous. Non-linear functional forms of the
type C = aK (total cost) or C/K = alv " (average cost) are
specified for all seven equations. A logarithmic transformation
was performed to permit linear estimation of the regression
relationship. The estimated unit cost functions obtained are:
Capital Investment = U~1(81.9SK~°*325)
Chemicals =1.20 K~'236
Pumping Energy =2.78 K~'282
heating Energy = U~1(.307K~*519)
~1
Manpower = U
Maintenance and Repair =
Miscellaneous = U~1(.102K**07)
aHirohide Hinomoto, "Unit and Total Cost Functions for
Water Treatment Based on Koenig's Data", Water Resources
Research. 7 (October, 1971) p. 1064-69.
25
-------
where U = the daily use ratea, output divided by design capacity;
S = the annual amortization factor (fraction of plant to
be depreciated); and
K = design capacity.
Hinomoto combines all seven equations to define a total per unit
cost equation for a treatment plant. Therefore, given a K, S,
and U, the total unit cost can be obtained.
Again, no mention of economies of scale is made. Also,
Hinomoto points out that he obtained results very close to
Koenig's which is not surprising since he used Koenig's data
and methodology. The merit to Hinomoto's analysis rests upon
his rigorous use of the U variable.
aHinomoto estimated the relationship C/K = o/K for all
seven equations. But, certain of the variables (capital, heat-
ing, manpower, maintenance, and miscellaneous) are indirectly
related to U, while chemicals and energy vary directly. The
assumption is that capital, heating, manpower, and miscellaneous
are fixed costs. Therefore, as U increases, C/Q would decrease,
C/K = K^1
since
U = Q/K
where Q = quantity of output
produced. Maintenance expense was assumed by Koenig and Hinomoto
to vary indirectly with U because maintenance and repairs
presumably contain fixed and variable elements of cost. Choice
of .5 is arbitrary.
Finally, the equations for chemical and energy do not con-
tain U since cost increases in direct proportion to an increase
in output.
The use of U by tiinomoto is unusual in that it is incor-
porated into the equation after the empirical relationship is
determined. It actually appears as a constant. One explanation
for the approach may be attributed to the formula-type results
generated. Hinomoto has attempted to develop a formula for the
estimation of the cost of water treatment. Given a U and K,
C/Q can be derived. That is a different way of establishing a
relation than statistically estimating the relation of all the
variables.
26
-------
In general, treatment cost studies have concentrated on
estimating the relationship of cost to design capacity and
improving the generation of data for better decision making.
The Orlob-Lindorf study began the analysis of treatment cost
with a simple relationship. Koenig improved the structure of
the analysis by incorporating the utilization factor. Hinomoto
extended the use of the U in his set of statistical equations.
The next step to be taken in this field appears to be the
estimation of costs on a process oriented basis. Instead of
estimating the costs of each input, estimate a relationship
between cost of flocculation or filtration with respect to a key
explanatory variable.a
Total Cost
This section reviews the existing literature on total costs
of water supply. Total cost of water supply suggests two major
divisions: treatment and transmission/distribution. Briefly,
treatment involves purification of water; and transmission/
distribution consists of finished product transportation to
the consumer.
The difficulty of analysis on total cost arises in
correctly identifying variables that are related or explain the
variation in costs. Coase, in his article on uniform pricing
systems, examines the shape of the supply and cost curves when
the same price is charged for a product or service over a given
area, even though the cost of supply may vary from one part of
the area to another.c if a public utility is to be self-
supporting, and a uniform price is adopted, then if
"the additional costs of supplying certain groups of
consumers exceed the receipts obtained from those
consumers, the difference will have to be made up
by additional payments from other groups of
consumers."^
Peak costs of treatment is another aspect for further re-
search. Treatment plants may be designed for the average day or
maximum day depending upon the local demand characteristics. In
either event, a peak-load can exist in the treatment process.
Analysis of this peak cost is needed to improve the basis for a
rate structure.
R.h. Coase, "The Economics of Uniform Pricing Systems",
Manchester School of Economics and Social Studies. 15 (May, 1947)
p. 139-56.
°See also: Robert H. Nelson, "Economies of Scale and Market
Size", Land Economics ^8 (August, 1972), p. 297-300.
Coase, "The Economics of Uniform Pricing Systems", p. 140.
27
-------
In his discussion, Coase assumes that the marginal costs of
supply to each consumer rise with an increase in distance from
the plant and that the marginal costs of supply to each in-
dividual consumer are constant at a given distance from the
production source. As a result, the shape of the cost curve
depends upon the quantity consumed by individuals at various
distances from the plant. This is exemplified in Figure 4.a
Line (1) would be obtained if consumer demand at each cost/
distance level is relatively large compared to that in line (2)
or line (3). Total cost can be dependent upon many factors.
Coase points out two: quantity supplied and distance. Even
though the price charged appears to affect the shape of the cost
curve, it is the marginal costs at each demand level, not price,
that are important. Other explanatory variables are used in
several empirical studies.
L. Hines attempts to estimate a long-run cost function
based on a cross-section sample of Wisconsin community water
supply systems.0 Since a long-run cost function is estimated,
certain issues must be handled. Equipment and operating costs
must be converted to the same price level using a cost index.
The adjusted capital expenditures have to then be depreciated at
a rate reflecting the remaining capital value. Estimates of
capacity are necessary to make comparisons among different in-
stallations, because one plant operating near capacity may have
lower per unit costs than one producing lesser capacity. A
competent measure of scale is very difficult to obtain.
Hines estimates the relationship of cost to per cent
capacity utilization (% Cu) and adjusted plant investment (API)
for three production classes: surface water supply, ground
water supply, and ground water supply with partial treatment.
Two cases in each class are specified with respect to adjusted
plant investment: API1 = historical plant cost adjusted to the
albid, p. 142. An implied assumption is that a utility
sells more, the further it extends it service area, which is not
an unrealistic assumption.
Lawrence G. Hines, "The Long-Run Cost Function of Water
Production for Selected Wisconsin Communities", Land Economics,
45 (February, 1969) p. 133-140. ~"
cZvi Grilieches, "Cost Allocation in Railroad Regulation",
Bell Journal of Economics and Management Science. 3 (Spring,
1972), P. 30.According to Lrriliches, a cross-section is
preferred to a time-series, since the latter is affected strongly
by short-run and irrelevant fluctuations.
28
-------
TOTAL COST
(3)
(2)
(1)
Q
Figure 4. Step cost functions
29
-------
1957 price level; and API2 = historical plant cost less power
and pumping plant adjusted to the 1957 price level. Mines
justifies this demarcation because:
"there is more nearly continuous capital addition to
the transmission and distribution part of the system
than that of power and pumping equipment, and the
capital change in the former is more directly related
to the number of customers served by the water facility."a
The results obtained using API^ were not significant at the .05
level. However, when API2 is used, the hypothesis of constant
costs must be rejected because the coefficients are significant
at the .05 level for surface and underground water supply class-
es. The statistical results developed are presented in Table 1.
For those two classes, the inverse relationships between cost
and size are very evident.
The capacity utilization variable was only measurable for
surface water supply. It appears to be more closely related
to AFC than to AVC since it is not significant with respect to
AVC. Wo relationship was demonstrated between cost and % CU or
API1f when power and pumping expenditures were included, except
between AFC and API, for underground water supply.
Hines concludes that though the constant cost hypothesis
can be rejected, no statement about the capacity range of
economies of scale can be made because there is no orderly
change in API2 in relation to capacity utilization. Also, the
specification by nines of the regression equation is linear in
relation to API and ?6CU. As a result, economies of scale would
be difficult to analyze. Hines should have more clearly specifi-
ed the functional relationship of the variables before setting
up the reduced form regression equations. Also, Hines is not
specific in explaining why power and pumping costs are dropped.
He even admits that it may be an imperfect adjustment. Power
and pumping is a legitimate major expense of water supply.
In his cost distribution between fixed and variable
expenditures, Hines allocates administrative costs to the
variable cost category. Usually, administrative costs are
considered part of overhead and not variable with respect to
output. Finally, the ^CU variable is not adequately defined in
the text of his analysis.
aHines, "The Long-Run Cost Function of Water Production
for Selected Wisconsin Communities", p. 137.
30
-------
TABLE 1.
SUMMARY OF SELECTED HINES' STATISTICAL COST REGRESSIONS.
A. Surface Water using APIp
(9 cases; 6 d.f.: 0.05 = 2.45)
i.) Average Fixed Cost = 132.5927 - 1.320(9/aCU) - . 000004373 ($API,)
0000
.062)
(AFC) s.d. (.30755) (.000001428)
(4.293) (3.
ii.) Average Variable Cost -209-7173 - 1. 4672 (%CU)-. 00001092 ($API0)
(AVC) s.d. (1.0125) (.000004849) 2
t (1.450) (2.252)
iii.) Average Total Cost = 342.3376 - 2.7880(#CU)- .000015 30 ($AP.I0)
(ATC) s.d. (1.0268) (.00004917) ^
t (2.715) (3.111)
B. Underground Water using
(25 cases; 23 d.f.: 0.05 = 2.07)
i.) Average Fixed Cost = 77.9359 - .000004178
(AFC) s.d. (.000001787)
t (2.337)
ii.) Average Variable Cost = 106.2546 - .000006971($API.
(AVC) s.d. (.0000033664) '
t (2.071)
iii.)Average Total Cost = 184.1822 - .00001114 ($API0)
s.d. (.00000'
t (2.294)
where ATC = AVC + AFC;
AFC = API2/output; and
AVC = total operating costs less power and pumping
operating costs/ output.
-------
In general, Hines attempts to estimate the relationship
between cost and 5oCU and between cost and API for surface and
ground water supply. The statistical work is acceptable, a but
the methodology employed leaves something to be desired.
A more detailed and precise attempt to estimate v/ater
supply costs was made by Ford and Warford." Their work tries to
explain unit costs in the water supply industry. On the basis
of a cross-section sample for a given year, Ford and Warford
want to estimate the long-run average total cost curve of the
envelope category. Costs are defined as the sum of expenditures
on sources of supply, transmission of water, and treatment of
water.
The functional forms employed and used as regression
equations are linear, quadratic, and exponential with a log-
arithmic or semi-logarithmic transformation.0 The key explan-
atory variables chosen for estimation of the cost function are
Q (daily supply in thousands of gallons), AREA (area in square
miles), and Q/AERA. The results found are listed in Table 2.&
Notice that equations 3, 6, 7, 8 and 9 provide the best results.
In all five, the estimates of the coefficients are significant,
they have the expected signs, the Von Neumann ratio is satis-
P
factory, and the R s are highly significant.
These results can be obtained from the equations:
1). From equations 3, 6, 8, as Q/AREA increases, cost decreases;
this signifies the existence of economies of scale in water
supply.
2). From equation 7, holding Q constant, as AREA increases,
costs rise, but at a decreasing rate.
3). Also, from equation 7, holding AREA constant as Q rises,
average cost falls, but at a decreasing rate.
aNo R s were presented.
J.L. Ford and J.J. Warford, "Cost Functions for the Water
Industry", Journal of Industrial Economics. 18 (November, 1969)
p. 53-63.
cThe general forms are:
C = a+bx; C = aQ2 -»• bQ + d;
C - aQ , or C = In a + b In Q, or
InC = In a + b In Q; and C = ae or InC = In a + b(Q).
Ford and Warford, "Cost Functions for the Water Industry"
60. J '
32
-------
TABLE 2. SUMMARY OF FORD-WARFORD STATISTICAL COST REGRESSIONS.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
C = 31.17* - .140* x 10~3 + .36Q2 x 10~10
C = 26.8* + .12Area - .13Area2 x 10~5
C = 33.3* - .035 (Q/Area)* + .49 (Q/Area)2
x 10~5
log C = 3.76* - .05* log Q
log C = 2.91* + .83 log Area
log C = 3.84* - .13 log (Q/Area)
log C = 3.78* + .133 log Area - .124 log Q*
C = 46.58* - 4.23* log (Q/Area)
C = 53.37* + 3.92 log Area - 4.82 log Q
C = 52.8* - 2.63* log Q
C = 19.75 + 1.99 log Area*
log C = 3.3* + .140 x 10~7
log C = 3.23* +.00034 Area*
log C = 3.32* - .67 (Q/Area) x 10~4
log C = 3.23* + .00034 Area - .43Q x 10~7
C = 29.49* + .11Q x 10~5
C = 27.31* + .084 Area
C = 29.8* + .0022 (Q/Area)
R2
.018
.024
.116*
.020
.094
.219*
.214*
.206
.21
.058
.045
.00
.057
.004
.052
.000
.028
.004
d
2.12
2.10
2.09
2.07
1.62
2.06
2.06
2.09
2.10
2.10
1.4V
2.11
2.14
2.11
2.14
2.11
1.55
2.11
-------
19. C = 27.3* + .0086 Area - .180 x 10~5 .024 2.11.
Notes: d 15 Von Neumann ratio
* significant at 90% or better
a not significant at 5%
34
-------
Thus, use of Q, Q/AREA, and AREA give some indication of the
relation between area serviced and cost incurred. The cost of
transmission is obscured because cost is examined in total and
not disaggregated into major components. Therefore, the degree
of existence of economies of scale as estimated may be mislead-
ing. Also, a cross-sectional study can indicate economies of
scale at one point in time; but, there may be vast differences
in the operating method or management of a utility in the sample
which could bias the measure of return to scale.
In general, the article was methodologically correct and
>•)
statistically significant in terms of results. But, the R
values were not very high, .219 for equation (6). Ford and
Warford offer two conclusions on this subject:
"either (a) we should break down costs into the
production costs of the textbooks and seek to
explain these by using our independent variables;
or (b) the technological and natural differences
that do exist between the various water under-
takings in the industry-the unquantifiable variables-
must be such as to rule out the existence of a so-
called long-run cost curve for the industry; such
technological differences between areas must swamp
the independent variables we have used."3
Their latter conclusion may not be too important because the
level of technology employed in the water supply industry is
fairly equal at one point in time except where extreme age
differences exist or where ground water vs. surface water
differences exist which are net embodied in the model.
The next few articles reviewed here deal explicitly with
the issue of economies of scale and total cost functions. The
issue has been previously mentioned, but not directly discussed.
Returns to scale can be increasing, decreasing, or constant
depending on whether the elasticity of cost to an explanatory
variable as output is less than one, greater than one, or equal
to one. Griliche" calls this the percent variable. It equals
the ratio of marginal cost to average cost. McElroy,c in a
comment on returns to scale, points out that one cannot make
inferences about economies of scale at levels of output
albid., p. 61.
Griliche, "Cost Allocation in Railroad Regulation", p. 27.
CF. McElroy, "Returns to Scale and Cost Curves: Comment,"
Southern Economic Journal 37 (October, 1972) p. 228.
35
-------
arbitrarily distant from the point estimated just on the basis
of the sign of the slope of the average cost curve. McElroy
adds that Bassetta criticized the use of point or arc elasticity
to measure returns to scale because of either's inability to
estimate correctly outside an c - neighborhood. McSlroy attempts
to clear up the confusion by arguing that this is true of any
approximating tangent line to a non-linear function:
"It would seem, however, no more reasonable to conclude
from it (Bassett's statement) that the slope in question
provides no useful information about returns to scale,
than it would be to argue that knowledge of the slope
of the average cost curve at X provides no useful infor-
mation about changes in average cost, on the grounds
that it is an insufficient basis for determining whether
average cost at X is higher or lower than average cost
at outputs at arbitrarily large distances from X."D
Scarato,c in his article on urban water systems, briefly
discusses economies of scale. Costs are divided into treatment
and distribution, each consisting of capital and operatio-
maintenance components. Capital costs for both treatment and
distribution are theorized as exponentially related to capacity:
C = K (X)*
where C = total cost
X = capacity; and
a = constant, the cost elasticity with respect to capacity
and a measure of economies of scale.
Scarato mentions the Orlob-Lindorf and Koenig studies on capital
treatment expenditures as the foundation for his cost functions.
In both articles, a was estimated as 0.6?d thus exemplifying the
existence of economies of scale. With respect to operation-
maintenance expenses, the Orlob-Lindorf and Koenig studies are
again given as basis for his analysis. Instead of capacity,
aLowell Bassett, "Returns to Scale and Cost Curves",
Southern Economic Journal. 34 (October, 1969), p. 189-190.
McElroy, "Returns to Scale and Cost Curves: Comment",
p. 228.
Q
R.F. Scarato, "Time Capacity Expansion of Urban Water
Systems", Water Resources Research 5 (October, 1969), p. 929-36.
See the Orlob-Lindorf and Koenig studies noted above.
36
-------
though, average daily flow is used as the explanatory variable.
Scarato argues that the operation-maintenance cost curve is a
decreasing function over a capacity range becoming proportional
to capacity and demonstrating economies of scale up to an out-
put of 20 MGD.
Scarato only theorized the relationship of capacity to
cost. In another article, F.T. Moorea reviewed some statistical
and engineering analyses of economies of scale. He found that
the statistical evidence in previous studies was incomplete.
Moore discusses some facts and relationships concerning
economies of scale. The vehicle for analyzing the degree and
existence of returns to scale is the envelope or long-run cost
curve. Engineers have noticed that the cost of an item is
frequently related to its surface area, while the capacity of
the item increases in accordance with its volume. Moore refers
to this as the .6 factor rule where the increase in cost is
given by the increase in capacity raised to the .6 power. A
form of this is:
c2 = c^y^/x,,)'6
where CL, Cp = cos"ts °^ two pieces of equipment; and
X,j, X2 = their respective capacities.
The general expression is: E = aC
where E = capital expenditure;
C = capacity; and
a,b = parameters, b < 1 implies economies in capital costs.
Moore argues that returns to scale are best estimated if
these three conditions hold for the industry in question: (1)
the industry is not specified by a batch-operation, but a
continuous process; (2) the industry is capital intensive; and
(3) the industry produces a homogeneous product. Those con-
ditions appear to fit the water supply industry in general.
Of 33 industries analyzed, the average value of b was
found to equal .68, but the relationships were not significant
(besides, a t-statistic on b was not presented). Therefore, the
importance of the results remain unknown. Moore concludes that
aF.T. Moore, "Economies of Scale: Some Statistical
Evidence", Quarterly Journal of Economics. 73 (May, 1959),
p. 232-45.
37
-------
there are no scale factors which adequately test the hypothesis
of constant returns. But, use of a curvilinear logarithm
relation and more homogeneous data may improve the results.
One other article examines the existence of economies of
scale in relation to size of water utilities and communities.
In this analysis, Andrews3 attempts to investigate the total
and per unit costs of providing water as these costs relate to
the quantity of water produced and the size of the community in
New Hampshire and New England. The general model specified has
the form:
Y = aXibi or LnY = In a + bilnXi
Y = a log-identified dependent variable
where a = constant term;
XA = a log-identified independent variable;
and b^ = elasticity or coefficient of log X.
The data employed was obtained from the American Directory of
Water Utilities (1968-69). It included information on annual
total production of water, annual revenue, population served,
and number of services. Andrews attempts to evaluate b, the
cost elasticity and measure of returns to scale, using a log-log
regression equation.
Total and average cost functions were estimated for two
categories. One related cost to output and number of customer
accounts; the other related cost to population and number of
services. The statistical results are presented in Table 3.
Andrews found, in equations 1-3, meager economies of size for
New England and significant economies of size for partially or
not metered utilities in New Hampshire. Metered utilities were
not found to possess economies of size. Also, a *\% increase in
water treated, holding the number of services fixed, resulted
in a .1 to .3% cost increase as shown in equations 4-6. That
implies that a very small cost increase occurs when water use
per customer rises. The costly part for increased water pro-
duction is the number of services or customers. Unit cost
equations, equations 7-12, estimated by Andrews provided the
same conclusions as the total cost equations.
aR. Andrews, "Economies Associated with Size of Water
Utilities and Communities Served in New Hampshire and New
England," Water Resources Bulletin, 7 (October, 1971) p. 905-12.
-------
TABLE 3. SUMMARY OF ANDREW'S STATISTICAL COST EQUATIONS.
Equation
Number
1-6 Total
(D
(2)
w
(4)
(5)
^l
(7)
(8)
(9)
(10)
(11)
(12)
Area+
Type
Cost; 7-12
New Hampshire
Metered
Partially or
not metered-
New England
New Hampshire
Metered
Partially or
not metered-
New England
New Hampshire
Metered
Partially or
not metered-
New England
New Hampshire
Metered
Partially or
not metered^
New England
Constant
Term
Ave. Cos
5.4113
6.7012
4.7122
.7783
.2805
.4875
.5510
.6682
.4620
.0743
.0280
.0584
13-18 Total Cost
(13)
(14)
(15)
(16)
(17)
(18)
New Hampshire
Metered
Partially or
not metered,.
New England
New Hampshire
Metered
Partially or
not metered1
New England
1 . 3446
.6294
.7563
.3451
.1804
.2549
Elasticity:
Total gallons
produced,b>j,
(standard
error)
.9312(.0483)
.7774(.0480)
.9166(.0088)
.3094(.1635)
.1261(.0864]
.2283C.0257;
•.0721 (.0486.
,2217(.0480
.0766(.0086
.71471.1624
-.8726(.0864)
-.7042(.0265)
Elasticity:
Population
b.(standard
error)
1.0040(.0486)
1.0989C.0533)
1.0661(.0084)
Elasticity
Number of
services,b2,
(standard
error)
.9184
.7801
.9193
.7227(.1842) .9449
.9694(.1176) .8861
.8226(.0296) .9354
.0623
.7469(.1829)
.9686(.1178)
.7501(.0306)
Elasticity:
Number of
Services
b (standard
^ error)
.2239
.0764
.3825
.5972
.4345
.9283
1 Excluding New Hampshire
.8516
.9438
1.0605(.0472) .9387
1.1266(.0477) .8827
1.0776(.0079) .9517
39
-------
Andrews drops gallons produced and adds population as shown
in equations 13-18. The cost elasticity coefficients indicate
that total cost increases about the same rate or faster than
increases in population or number of services.
One problem, though, is the use of demand variables such as
population and number of customer accounts to estimate cost. As
a result, the structural form is estimated. Simultaneous equa-
tion analysis of demand and cost curves may allow the derivation
of reduced forms and the estimation of simultaneously related
parameters.
In general, the regressions demonstrate that if per capita
water consumption would increase, holding the number of customers
fixed, substantial economies of scale would be achieved.a
Economies associated with community size were not as great as
those found within the utility. As the population rose, there
was a tendency for the larger communities to use more water per
capita per day. Andrews suggests that larger communities
apparently produce more public services that require water and
also service a larger commercial base than smaller communities.
Of course, other demand factors as increased incomes can con-
tribute to such a rise in water use.
This discussion on total costs has attempted to present the
relevant analysis to date on statistical cost estimation and
existence of economies of scale for water supply systems. Most
studies estimated cost as a function of design capacity or
average daily flow. Other analyses added different explanatory
variables, as area, population, and number of customers. Re-
lationships between cost and those variables give indications
of the degree of economies of scale with respect to market area.
Existing empirical studies do not adequately deal with this issue.
That economies of scale are achieved in treatment and total cost
is generally accepted. But, further analysis should attempt to
delve into the demarcation between treatment and distribution
costs in relation to economies of scale.
Transmission Costs
The cost of water transmission consists of capital expen-
ditures for pipeline, pumping stations, and storage facilities;
and operation-maintenance expenses of which energy cost is a
major element. Before reviewing the transmission cost studies,
a short description of engineering hydraulic factors involved in
water transmission will be presented.
aJ.F. Sleeman, "Economies of Water Supply," Scottish
Journal of Political Economy. II (1955) p. 231-45. Sleeman
found a similar relation in London, p. 241.
40
-------
PHYSICAL FACTORS AFFECTING COSTS
Total dynamic head is the major element involved in water
transmission engineering. It consists of three major elements:
static head, velocity head, and friction head. The importance
of total dynamic head rests upon the fact that power or energy
consumption per unit of water is directly related to the degree
of head existing in the system. Head can be defined as the
pressure in pounds per square inch or as the number of feet of
liquid which would exert an equal pressure on the horizontal
surface at the bottom of a pipe. The height of the column of
liquid producing the pressure is known as the head on the
surface.
The height of a column of liquid is often termed the static
head on the inlet or outlet of a pipe. It is the difference in
elevation and is expressed as a certain number of feet. Total
static head equals the vertical difference, in feet, between the
supply level and the discharge level.
Velocity head refers to the kinetic energy possessed as the
liquid moves through a pipe at any velocity. It is the distance
through which the liquid must fall to acquire a given velocity
a ?
and is found from hv = V /2g where
hv = velocity head, feet of liquid;
V = liquid velocity, feet per second; and
g = accleration due to gravity, 52.2 ft.
2
per sec.
Friction head is also measured in feet. It is the equivalent
head required to overcome the resistance of the pipe, valves,
and fittings in the pumping system. Friction head is related
to the liquid flow rate, pipe size, type of pipe, viscosity of
fluid, and interior condition of the pipe. Friction head loss
varies roughly with the square of the flow for a turbulent
system and directly for laminar systems.*3 Once the particular
aTyler, Hicks, P.E. and T.W. Edwards, P.S., Pump Application
Engineering (London: McGraw-Hill, 1971), Chapter 4.
Ibid, p. 132. "The flow of a liquid is said to be laminar
or turbulent, depending on the liquid velocity, pipe diameter,
liquid viscosity, and density. For any given liquid and pipe,
these four factors are expressed, in terms of a dimensionless
number called the Reynolds number, R." The following ranges
apply: R < 2000, flow is laminar
2000 < R < 4000, flow is assumed turbulent, but could be
laminar; and R > 4000, flow is turbulent.
-------
head (ft.)
System Friction
Curve
Capacity
Figure 5. System friction curve
Capacity
Figure 6. System head curve.
-------
friction characteristics are determined, a system friction curve
can be derived which plots head vs. capacity, Figure 5. The
combination of static head, the system friction curve, and any
pressure differences creates a system head curve, Figure 6. The
system head curve can be used for examination of design
characteristics in the transmission works. One issue that has
received a lot of attention in the literature is the measurement
of head loss and the key variables associated with it. Many
approaches to the head loss measurement problem have been
offered.a
Hicks and Edwards discuss one method in their book on pump
application: h = fLV /2gD or the Darcy-Weisbach formula where
h » friction head loss, feet of liquid pumped;
f * a friction factor
V = average velocity in pipe, feet per second;
D = internal diameter of pipe, feet; and
g « 32.17 feet per second squared
L » length of pipe in feet.
This is an engineering relationship. Given D, L, V, and a b
calculated f, h (friction head loss) can be determined. Suess
presents the same equation, but substitutes for V. Since,
O fy
Q = (Ti/4)D V, where Q = quantity or flow capacity; V =
(16Q2/TT2D4). Therefore, h = f(l6L/2gn2D5)Q2. Letting
K - f (l6L/2gTT2D5), h m KQ2. This derivation is useful for
simplifying the analysis. Many articles use a variation of this,
aThe studies of this issue are voluminous. A few
relevant approaches are presented.
nMichael J. Suess, "Adoption of Equations for Analysis of
Hydraulic Flow Systems by General Purpose Analog Computers",
Water and Sewage Works. 114 (1967), p. R-41.
43
-------
McPherson and Prasada set up a functional relationship similar
in nature to Suess: Eh = Qdm « cp(Qp/Qd)n where
h » head loss, feet;
Q, » demand rate;
GL « pumping rate;
Qg = GL - Qd, the storage rate; and cp, m, n = constants.
The author developed this framework to define generalized net-
work characteristics under proportional loading conditions, cp
and n are determined by the data for a given m value. A sim-
ulation technique was used to estimate the optimal network
conditions.
In another article, Singh calculates head loss with:
Ho = 984.8 f Vo2/D x 1.05 where
Ho = head, feet of water;
f a Darcy-Weisbach friction factor;
Vo * average velocity of flow in the pipeline, feet per
second;
D * inside diameter of pipeline, inches; and
1.05 = factor allowing for losses in the valves, bends,
etc., in the pipeline.
This is a variation of the Darcy-Weisbach formula above. Singh
computes f by using the Colebrook-White equation:
(e/D)/3.7 + 2.51/Nr/F
aM.B. McPherson and R. Prasad, "Power Consumption for
Equalizing Storage Operating Options," Journal of the American
Water Works Association. 58 (January, 1966;, p. 67-90.See
also:M.B. McPherson and M. Heidari, "Power Consumption with
Elevated Storage compared to Direct and Booster Pumping",
Journal of the American Water Works Association. 58 (December,
^966) p. 1585-9V and M.B. McPherson and R. Brasod, A Study of
Distribution System Equalizing Storage Hydraulics (Urbana: The
Department of Civil Engineering, University of Illinois, 1965).
TCrishan Singh, "Economic Design of Central Water Supply
Systems for Medium Sized Towers", Water Resources Bulletin, 7
(February, 1971), p. 84.
44
-------
where e * the pipe roughne3s height, 0.005 inch for the useful
life of 50 years of a cement-lined pipe; and
Nr = the Reynolds number.
The Colebrook-White equation is extremely complex. Solution
requires computer analysis, or trial-by-error because of the
logarithm term which hampers its degree of adaptability and use
by water supply utilities.
An alternative to the Darcy-Weisbach type of head-loss
equation is the Hazen-Williams formulation. In its original
form, it is written: V = .000-T'04 CR°*63 S'54, where V »
average velocity in feet per second;
R = hydraulic radius of the pipe, feet;
S = L/H, a pure number in feet per foot;
L » length of pipe, feet;
H = headloss in pipe line, feet; and
C = a roughness coefficient.
Since S * L/H, R = D/4, and V « Q/j-D2 where D is the internal
diameter of pipe in feet, and Q is capacity; the equation can be
written as: "rf^ = .0001-04 C(£)°'63 (i)'54 or
Q/(TrD2/4) = .0001"*04 C(D/4)'63 (L/h)'54
H = 4.72688 (T1'8518 L/D4'870 Q1'8518
Letting K = 4.72688 c"1'8518 L/D4'870, H = KQ1'8518. That is a
more simple expression as altered by Suess.8 A variation of the
Hazen-Williams equation was employed by Karmeli, Gadish, and
Meyers^ in their article on cost minimization of water dis-
tribution networks using linear programming. Their formulation
is:
aSuess, "Adoption of Equations for Analysis of Hydraulic
Flow Systems by General Purpose Analog Computers", p. R-4?.
David Karmeli, Y. Gadish, and S. Meyers, "Design of
Optimal Water Distribution Networks", Journal of the Pipeline
Division. Proceedings of the A.S.C?E. 94 tPL1), ^October,
T968;, p. 1-16.
45
-------
J-1.13X1012
where
J » friction loss in meters per kilometer, in %;
Q = discharge, cubic meters per hour;
D = pipe diameter, millimeters; and
C = a friction coefficient.
Two differences stand out. First, the Hazen-Williams equation
was converted to the metric system, and second, the length of
pipe term, L, was apparently dropped. Derivation of the Karmeli,
Gadish, and Meyers formulation was not presented in the article.
But, J could be considered as H/L where H is headless in meters
and L is kilometers of pipe. Reasons for the change were not
apparent.
There are two other interesting formulations to the problem
of headloss measurement. One is by Rishel; the other is by Hey.
Rishela examines headloss by using a system head curve,
Figure 7 as calculated for each part of the system. At Qo, there
is no flow. Q2» H = S + F. Q1 represents any intermediate flow
that might occur in the system. Rishel postulates this relation-
ship for those intermediate flows: H = S + F (Q1/Q2)2.
Obviously, if Q1 = Q2» "the equation reverts to H = S + F.
Rishel's formulation, though, is dependent on the knowledge of
the system head curve and the nature of F. H = S + F appears
to ignore the problem. The theoretical derivation is similar in
concept to the McPherson-Prasad model, but is much more sim-
plistic. Actual computation of the system head curve and the
friction element requires a great deal of information, the
complexity of which is not examined in Rishel's article. Rishel
does include the static head which none of the previous models
included.
aJames B. Rishel, P.E., "Packaged Pumping Stations for
Suburban Water Distributions," Water and Sewage Works. 121
(1974) p. R-131-134.
46
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H
t
Q2
Q = quantity of water pumped.
H = total head required of pump station.
S = static head of system.
F = friction head of system piping, valves, and fittings.
H = S+(Q1/Q2)2.
Figure 7. Head loss for a system head curve
-------
The other formulation os headless measurement is the
Bernoulli equation as presented by Hey.a It is the most complete,
because it includes not only static and friction heads, but also
velocity and pressure differences. Hey expresses it as:
Ep - Zi - ZQ f P^Y - PO/Y + Vi2/2g - Vo2/2g + HLQ-1
where
EL « total dynamic head in feet between points 0 and 1;
Zi = elevation of point i, feet;
P, = pressure at point i, pounds per square foot;
Y = specific weight of water, 62.4 lbs./ft.5;
VA = average velocity at point i, feet per second;
g = gravity constant, 32.2 feet per second squared; and
HL0_1 = headless due to friction between points 0 and 1.
HL is measured by the Darcy-Weisbach or Hazen-Williams equations
for friction head measurement as described previously. The
Bernoulli equation is the most comprehensive and complete model
for analysis of headless. All the relevant factors are incor-
porated. It is complex, but accurate. Use of the Hazen-
Williams charts for estimating the C coefficient has reduced the
difficulty in the use of the .Bernoulli approach. Those charts
can be found in many water supply engineering books.0 In any
event, a competent examination of system head curves, friction
headless, pressure variations, and velocity differentials must
use the factors employed in the Bernoulli equation to develop
the correct results, whether it is an engineer working on
transmission optimization, or an economist analyzing the marginal
cost differences of water transportation.
aD. Hey, A Marginal Cost Basis for Metropolitan Water Supply
Allocation and Qperatio'nlAn unpublished Ph.D. dissertation,
Northwestern University, 1974, p. IV-4.
See also: D. Hey and Robert Gemmell, Metropolitan Water
Supply Allocation and Operation. (Urbana: Department of Civil
Engineering, Water Resources Center, Northwestern University and
University of Illinois, 1974).
bSee: Gordon Fair and John Geyer, Elements of Water Supply
and Waste-Water Disposal. (New York: John Wiley and ions, 1958),
48
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CAPITAL COST
With regard to water transmission cost, two components are
important: capital and operation-maintenance cost. Capital
costs of water transmission consist of the construction cost of
pumping stations and pipelines. Storage facilities are not
included because they are built for peak-load demands. Operation-
maintenance costs include energy and repair costs incurred in the
transmission of water.
Pipeline capital cost was estimated by Ackermann in a
technical letter for the Illinois State Water Survey.a All cost
figures were indexed to the 1964 cost level by means of the
Handy-Whitman Index of Water Utility Construction Costs.
Ackermann estimated an exponential relationship between con-
struction cost and pipe diameter:
Cp - 2.16 D1*2
where
Cp = construction cost for a transmission line in dollars
per mile;
D = pipe diameter, inches.
The results suggest diseconomies in per mile construction costs
as the pipe diameter increases. Linaweaver and Clarkb also
estimated a similar relation between cost and diameter:
K - 1,890 D1'29
where
K « capital cost in dollars per mile; and
D = diameter in inches.
Again, the value of 3 implies diseconomies exist in the per mile
construction costs of pipes as diameter increases.
aWilliam Ackermann, "Water Transmission Costs", Technical
Letter 7, Illinois State Water Survey. 1967.
bF.P. Linaweaver and C. Clark, "Costs of Water Transmission",
Journal of the American Water Works Association. 56 (December,
1964), p. 1552.
49
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Both studies estimate cost per mile in relation to pipeline
diameter and find diseconomies of scale. Scarato", though,
suggests that significant economies of scale exist between
capital cost and pipeline capacity. He suggests a function of
A
the type: C =» f [k (capacity) ] where C = total capital cost;
k (capacity) = function measuring capacity; and s = parameter
which measures the scale effect of capacity on total costs.
Eliassen is mentioned by Scaratoc as having measured a 3 as low
as .56 which would imply economies of scale with respect to
capacity, not diameter. Which is the proper approach, capacity
or diameter, remains an unresolved issue. An alternative that
might prove useful is to estimate the following relation:
C = <*DB1 L02 where
C = total construction costs;
D = diameter of pipe in inches;
L « length of pipeline in feet or miles;
and
01, 82 * cost elasticity parameters
That could provide estimates of the degree of economies of scale
with respect to diameter and length. As length increases, econ-
omies of scale should become prevalent.
Singh presented a complicated approach to pump station
cost estimation in his article on water supply systems. The
capacity installed is assumed related to the headless in the
system. If head » 300 feet, then the capital cost of a pumping
station is:
Cp = 17,000 -f 135 (
Scarato, "Time Capacity Expansion of Urban Water Systems"
p. 933.
Neither article provided R s or t-statistics.
CR. Eliassen, The Economics of Water in the Pulp and Paper
Industry> Engineering Economic Planning Program, Department of
Civil Engineering, Stanford, California, June, 1967.
Singh, "Economic Design of Central Water Supply Systems
for Medium Sized Towns", p. 81.
50
-------
where
Cp = total cost of a pimping station; and
= the installed horsepower necessary to boost the water
pressure 300 feet.
Singh does not present any regression statistics on the co-
efficients, on R , or the derivation of his specific functional
form. The value 1.01 is definitely ambiguous as a measure of
economies of scale. Its relevance to the cost function is not
explained. Also, a relationship between cost and capacity is
not examined.
In general, there does not appear to be any conclusive
evidence for the existence of returns to scale in water trans-
mission capital costs. The articles presented here have in-
vestigated specific factors, but have not analyzed or discussed
all the relevant variables that may be better associated with
capital costs.
OPERATING COST
Operation-maintenance cost is the second component assoc-
iated with transmission costs. The relation between cost and
quantity supplied is similar to that theorized by Coasea, where
the slope of the cost curve depended on the amount consumed at
each distance from the supply curve.
Singh presented some theoretical relations between
operation-maintenance cost and certain key variables. For pipe-
line operation, maintenance, and repair costs:
C = 10D
where
C = cost per mile; and
D = diameter in inches.
That is a simple linear relation which is not unrealistic. Pipe-
line breaks can occur anywhere on old or new pipe. A linear
distribution of costs based on pipe diameter is a close approx-
imation to the actual cost of maintaining transmission lines.
aSee Figure 4.
Singh, "Economic Design of Central Water Supply Systems
for Medium Sized Towns," p. 79-90.
-------
Energy costs are shown to be a function of static and
friction headloss:
C m kQQ (Pf Ho + Ps Hs)
where
C = cost of energy per mile;
k = a relation dependent on the cost per kilowatt-hour and
pump efficiency;
Pf = ratio of actual and constant energy cost spent during
the year for friction headloss;
Qo « average yearly demand in gallons per day;
Ho m total headloss per mile of pipeline for a constant Qo;
Ps » ratio of actual and constant energy cost spent during
the year for static headloss;
and
Hs * static headloss per mile of pipeline.
Singh proceeded through a complex derivation to arrive at the
cost function. The function, though, neglects minor variations
in the friction factor because he uses Qo instead of a Q that
may vary. This could be an important factor in a residential
district with a high peak to average demand ratio.
Singh also sets up a cost relation for pump station opera-
tion, maintenance, and repair cost which is not presented here.
It is based on the P^QQ variable noted above, but, Singh does
not provide the derivation of this cost function.
In the end, Singh combines all the factors of unit con-
veyance cost into one equation:
Cu = 27.38 C/QQ
where
Cu m cents per thousand gallons per mile;
Qo = average yearly demand in gallons per day;
and
C = total annual cost of conveying Qo through a pipeline of
D inches for a distance of one mile.
52
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This suggests that as Qo increases, Cu decreases. That is an
empirical question which has not been adequately analyzed by
Singh, Also, use of Cu hides any relevant marginal cost con-
sideration. Singh does provide a graphical analysis of Cu for
selected values of Qo and pipe diameter. But, his equation is
derived from a set of seven other equations which apparently
are not empirically estimated. It appears that Singh lifted
specific relationships from various articles to derive his cost
functions. Those derivations are not adequately explained.
One final article on water transmission costs by Linaweaver
and Clarina provides a coherent derivation of water conveyance
cost functions. It combines engineering and economic consider-
ations into one equation.
Capital cost of pipe was set up as:
CK - Kf/365 X 103Q(.75)
where
CK » unit capital cost in dollars per thousand gallons per
mile;
f m the capital recovery factor, i(l + i)n/(l + i)n - 1;
b
K = capital cost in dollars per mile
2 « thousands of gallons per ;
millions of gallons per day;
365 X 10*Q « thousands of gallons per year with capacity Q in
and
.75 * the load building factor, proportion of utilized
capacity.
Operation and maintenance costs consisted of the costs of energy
required for pumping plus an added 8 per cent of that cost for
other operation and maintenance expenses, unit energy costs are:
C0 m (sS)P/E
w
S consists of friction loss, Sf, and an average line slope, SL>
is defined as
aLinaweaver and Clark, "Costs of Water Transmission", p.
15^9-1560.
1800D1*2" was estimated as noted above.
-------
"the difference in elevation in feet between the water
level in the intake and discharge basins divided by the
length of line in thousands of feet."a
Since this is constant overtime, a fixed load building factor
of .75 is used. Sf, though, in the Hazen-Williams expression.
1 85
varies approximately as Q . A load building factor of .66?
is incorporated for Sf on the assumption that the average flow,
at a given point over the design life, will be 2/3 of capacity.
Substituting these factors for S in Ce, the following re-
lation is derived:
Ce = 1.66 X 10~2 (.75SL + .667 Sf) P/E. Since, Sf = 103 X
Q1<85/(405 X 10"6CD2*63)1'85, where C is the Hazen-Williams
coefficient and D is the pipe diameter in inches,
Ce = P(1.66 X 10~2) C.75SL + .667(103 X Q1*85/(405 X
1CT6CD2*63)1-85]/E
Therefore, Cm, total unit transmission cost in dollars per
thousand gallons per mile is: CK + 1.08 C . Rewritten:
CT = Kf(274Q X 103) + 1.35 X 10~2PSL/E + 12PQ1*85/E
(405 X 10'6 CD2'63)1*85.
Linaweaver and Clark provided a specific derivation of a general
expression relating the principal factors that influence trans-
mission costs to the cost of transporting water. There are two
points of interest. First, this equation does not include any
consideration of pump station capital cost. And second, the
headloss characteristics incorporated do not allow for changes
in pressure or velocity as done in the Bernoulli equation. If
only short distances are analyzed, the pressure and velocity
differentials can probably be ignored.
Transmission costs consist of capital and operation-
maintenance expenses. This discussion reviewed the existing
literature on measures of headloss and the theoretical and
empirical studies of transmission costs. The empirical analyses
were not rigorous in nature and the theoretical analysis of Singh
was overly complex and unclear. Linaweaver and Clark did provide
a competent approach to water transmission costs, but appear to
overlook pump station capital cost.
aLinaweaver and Clark,"Costs of Water Transmission", p. 1553,
54
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PEAK-LOAD CONSIDERATIONS
Peak-load costs are reflected in the cost of storage tanks,
greater capacity pumping stations, and larger sized pipelines.
The empirical studies that investigated the costs of water
supply ignored peak-load cost considerations. Instead, they
examined average flow cost relations. This is probably due to
the paucity of data on peak-load characteristics. The articles
that do examine peak-load conditions usually analyze the trade-
off between cost of increased pump capacity vs. increased
storage capacity. Schmida points out that
"to produce at a greater pumping rate than the peak-day
average may necessitate larger transmission and distrib-
ution mains and greater investment in booster stations
and controls for limited use over the year. To produce
at a lesser pumping rate than the peak-day average, on
the other hand, requires costly additional storage."
Those considerations are important for future cost studies of
water transmission systems. It is felt that more competent
analysis is necessary in this field.
SUMMARY
This literature review has attempted to provide a background
on certain key issues and factors involved in a water supply cost
analysis. The two major areas studied were: methods of cost
allocation and water supply cost.
The proper allocation of costs is the important issue in the
first area. Many methods have been used to distribute costs, two
of which are most frequently used by public utilities. They are
the commodity-demand method and base extra-capacity method.
Most discussion has centered upon the allocation of peak-load
capacity costs to system users. Some authors promoted a
distribution of costs based on a noncoincidental demand method.
As a result, capacity costs are allocated on the basis of demand
characteristics which are the ratios of peak to average use for
each customer class. Therefore, those consumers with a high
ratio, but no consumption at the system peak, could be allocated
a large portion of capacity costs. The proper viewpoint involves
the knowledge of the difference between joint and common costs.
Joint costs exist when the capacity of a water works is available
for use during peak and off-peak periods. Common costs occur if
aGeorge G. Schmid, "Peak Demand Storage", Journal of the
American Water Works Association. 48 (April, 195b), p. 384.
McPherson and Prasad also analyzed the issue of storage vs.
pumping capacity, but do not provide cost relationships.
55
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different customer groups consume at the same time at, for
example, the system peak. As a result, no rate discrimination
among customer classes that consume at the system peak should be
made.
One other point concerns the relevant dimension in which
to analyze cost. Most authors reviewed suggest that marginal
cost is the best concept on which to base decisions. The
problem, though, is proper classification and estimation of
marginal costs of each component analyzed: customer, commodity
or base, and capacity cost.
The section of cost analysis in water supply reviewed
theoretical and empirical studies on treatment, total, and
transmission cost. Most studies consisted of attempts to
empirically relate key explanatory variables to average and
total cost. Capacity and per unit utilization were two major
variables analyzed.
Attempts were made to estimate the degree of economies of
scale in water treatment and the total cost of water supply.
The results may be valid, but few studies supplied the regression
statistics necessary to determine the significance of the
estimated parameters. Also, it is difficult to estimate econ-
omies of scale for total cost of water supply. Because of the
inherent physical andoperational differences between a treatment
plant and a transmission system, separate estimation of the
components would provide better knowledge of the degree of
economies of scale. Combined analysis obscures information
valuable for plant investments and expansion decisions.
Transmission cost empirical studies were not rigorous in
relating key explanatory variables. Also, theoretical deriva-
tions and cost function specifications were inadequate. The
engineering literature is extremely explicit and significant,
but the economic application of engineering relationship needs
further analysis.
Future research in this field should concentrate upon
identification and estimation of peak-load costs and the marginal
costs of each water supply component. Treatment cost has rec-
eived much of attention, but transmission cost considerations
have been largely ignored. Extension of water mains to the
fringes of existing service areas will depend on such analysis.
Only through comprehensive study of the relevant marginal costs
can sound decisions be determined.
-------
SECTION IV
METHODOLOGIES
PART A: COST ESTIMATION METHODOLOGIES
In order to carry out the analysis of cost rate differen-
tials, data is needed on rates, usage or consumption, and the
costs of delivering any amount of water to specific locations in
the CWW (Cincinnati Water Works) service area.
Water rates are published, and data on usage is obtainable
from the account records at the CWW, but costs are another mat-
ter. Part A of this chapter details the specific methodologies
employed to obtain the cost estimates. Part B extends the analy-
sis of Part A to the CWW area specifically, and explains how
the data was gathered and applied to the problem.
Components of Water Supply Costs
To facilitate the analysis, we divide the water supply
system into two major elements: (a) acquisition and treatment
(A&T), and (b) transmission and distribution (T&D). Both ele-
ments, of course, contain capital and operating cost components.
Overhead costs in this analysis will be treated as a constant
and fixed cost per customer account. A&T functions occur within
the framework of a centralized plant, and T&D in effect from the
transportation system (pipelines, pumping stations and storage
facilities) for finished water, and as a consequence, a proper a
economic cost accounting requires separation of these functions.
A&T capital expenditure is determined by the design capacity
of the plant. In a given time period, capacity is fixed and the
marginal capital cost of another unit of output is zero unless
water demand already equals capacity. Once capacity is reached,
the marginal cost of capital for another unit of output must be
included in the cost of production.
However, an important distinction must be made between
capital available for peak vs. off-peak periods. In large
aJarie S. Dojani and Robert S. Gemmell, "Economic Guidelines
for Public Utilities Planning", Journal of the Urban Planning and
Development Division. (September, 1973), p. 171.
57
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scale plants, such as a water works, the base or average winter
load may represent a significant portion of capacity. Therefore
capital consumption (wear and tear on capital equipment) can '
result to a large degree from off-peak use and accordingly that
capital cost must be allocated to the average winter demand
load. This would not be as important for a system with a very
low ratio of off-peak use to plant capacity.a
Operating costs of A&T are directly related to the quantity
of treated water produced. The marginal cost of operating the
plant is not equal to zero regardless of the utilization of
capacity; but it may remain constant over large ranges of output
for a selected plant scale. Operating costs per unit of output
can vary depending upon the economies of operation existing in a
given capacity plant.
The combination of capital and operating costs can be use-
ful in examining the A&T cost of peak-load periods and the de-
gree of existence of scale economies. Analysis of returns to
scale and costs at the system peak facilitate improved cost
allocation.
T&D capital expenditure is determined by the design capa-
city of pipelines, pumping stations, and storage facilities.
Pipeline diameter can be used to relate capital costs to capa-
city, since the volume of water flow possible in a transmission
or distribution main increases as diameter increases. Other
factors such as age and interior condition of the pipe are more
important in their effect on operating costs, not capital costs.
They will be discussed later.
The capacity of a pumping station is measured by the volume
of pumped water it can handle during a given time period. To
increase capacity, a larger facility and greater capital expen-
diture is required. This same relationship holds for storage
tanks, in that the capacity is dependent upon the total avail-
able volume. Storage is utilized mostly during peak-load
periods.
The marginal capital cost of another unit of output is zero
for pipelines and pumping stations up to the point of capacity.
As mentioned before in the section on treatment plant capital
cost, however, off-peak demand may be a significant factor in
capital consumption. Therefore, a proportional amount of capi-
tal cost must be allocated to the off-peak load.
Storage tanks are used only when the pipelines and pumping
stations have reached capacity. Therefore, the marginal cost of
capital for storage tanks is zero until the system peak-load
aRalph Turvey, "Peak-Load Pricing," Journal of Political
Economy. 79, (December, 1968), pp. 101-11^
58
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o
has been reached. This refers to the point in time when the
demand load for a selected service area or the total service
area is greater than or equal to the combined capacity of the
system-pipes, pumping stations, and storage.
Operating costs of T&D, though determined on one main
variable—energy, are very complex. A major portion of operat-
ing expenditures can be attributed to power consumption at pump-
ing stations. Transportation of water over rough terrain and
large distances requires a great amount of energy. Other oper-
ating costs such as manpower and maintenance are incurred, but
they are not as significant or as directly related to output as
energy consumption.
The energy cost of pumping water depends upon the quantity
of water supplied, the distance to a demand point, and the net
altitude between the demand point and supply point. Other
operating expenditures remain relatively fixed with respect to
output.
The marginal cost of operation varies over three dimensions:
quantity, distance, and altitude. Examination of that relation-
ship is a major concern of this study.
Theoretical Considerations
Existing price policies can lead to cross or internal sub-
sidizations for users in all of the service areas: Pricing
inefficiency resulting from inability or refusal to charge con-
sumers on a benefits received basis, may allow substantial intra-
area variation in the difference between rates and costs among
users. Average net subsidy refers to the difference existing
between the price paid and the cost incurred in the supply and
demand for water. Three types of user subsidization may occur
because of the distribution of costs over the service area and
between peak and off-peak periods.
The first is reflected in distance to the customer. A
greater amount of energy is required to pump water a long dis-
tance, for example twenty to thirty miles, than to supply a
customer near to the plant." In a similar manner, this is ap-
plicable to the second factor: topography. Customers served
alt is assumed in this analysis that storage tanks are
erected for peak demand periods. As a result, the total storage
cost can be allocated to the peak period even though tanks may
be utilized during an off-peak period.
Unless, of course, the customer resides at a lower alti-
tude than the plant. Gravity flow can then be utilized. Of
course, T&D capital costs will be higher for the more distant
customer.
59
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at a higher altitude require larger amounts of energy than those
at lower altitudes. The head, (feet), necessary to supply con-
sumers at various altitudes and distances affects energy con-
sumption at the pumping stations. The third factor involves
time of consumption. The cost of water supply varies depending
upon whether demand occurs during the off-peak load or the sys-
tem peak-load. Current water pricing mechanisms do not usually
take account of such cost variations.
Peak vs. Off-Peak
Both distance and topography factors exist during the peak
and off-peak demand periods. Therefore, distinct cost functions
will be developed for the two separate demand loads or periods.
With respect to water supply, the off-peak demand is identified
as average daily water consumption during the winter period.
The assumption here is that for Cincinnati no sprinkling or
other peak-demands occur on an average winter day,a such that
off-peak demand could approach system capacity. Off-peak de-
mand reflects the system's base load which consists of residen-
tial domestic demand and a normal commercial and industrial load,
Peak demand for any user, whether residential, commercial,
or industrial, may occur at any moment. But, peak demand for
the system usually exists at a specific time during the year.
Peak system demand refers to that period of time in which the
daily quantity demanded reaches a maximum for the year. This
may happen more than once a year, but usually occurs during the
late summer when most lawn springling takes place. Average
daily demand during the system peak period is the dimension used
to examine peak costs. The reason for this is two fold. First,
very little storage is required to meat a peak day or a peak
hour, but the peak week (or weeks) usually will strain the capa-
city of most water supply systems. Secondly, data on consump-
tion is gathered either quarterly or monthly. As a result,
average daily demand during the peak period is employed as an
approximation to that of the peak week, which is not unrealistic
since the system peak may last for more than one week.
Cost Function; Off-Peak Period
Two types of cost equations will be considered: peak and
off-peak.
Off-peak costs are related to the base load on the system
or the average daily winter load only. Use of average daily
aAn average winter day generally occurs between December 1
and March 31.
Peak system demand usually occurs between June 1 and
September 30.
60
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annual load would overstate the magnitude of the off-peak load
since peak use is included in the annual totals. The total
cost of supplying the ith consumer in a water service zonea k,
can be estimated for the user's average daily load by adding to-
gether the relevant cost elements of A&T and T&D.
Although A&T cost consists of operating and capital com-
ponents, average operating costs for the off-peak period will be
considered constant for any single customer for mainly the
reason that no single customer is large enough to influence off-
peak operating costs measurably and identifiably. Also, we
shall treat AC for A&T as a constant.
For capital expenditure or cost allocation, there is the
problem of properly allocating costs between peak and off-peak
periods. The capital facilities, though designed for the
maximum day, is available during off-peak periods. Since,
capital costs per unit of capacity vary depending upon the scale
of the plant, and there exist economies of scale, it is diffi-
cult to evaluate off-peak capital costs for A&T. Therefore, the
capital cost of A&T will be indirectly estimated for a hypo-
thetical or simulated off-peak capacity plant to provide an
estimate of the allocation of capacity cost to off-peak users.
This estimation can be derived from equations developed in pre-
vious articles discussed in the literature review.
Once the total capital expenditure relevant for off-peak
production is determined, the capital cost per unit of capacity
may be allocated. This cost is also assumed constant per unit
of acquired and treated water. Therefore, to allocate capacity
costs, each consumer is treated identically and as a result is
apportioned a fixed capacity cost per unit of output. This
represents the proportion of capital expenditure or capacity
required by the consumer to supply his off-peak demand.
The following definitions apply to the analysis presented
below:
aA water service zone is based upon the direction of water
flow and the placement of plumbing stations.
This cost refers to "historical cost". Historical cost
is the actual expenditure for a capital item. Reproduction
cost measures the value of a replacement capital item in the
present period.
61
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Let:
q., is the quantity of water consumed by consumer i in
area r of zone k;D
TCOPikr is the total off-peak treatment cost to supply q ;
Q is the total quantity of metered water produced by the
A&T processes, cubic feet;
KOP is the total capacity required for off-peak loads by
the A&T processes, cubic feet/day;
OT
TC is the total operating cost for A&T;
TCOPKT is the total off-peak capital cost for A&T;
AC = TCOT/Q, average operating cost per unit of output;
and
ACOP1^ « TCOP^/KOP , average off-peak capital cost per
unit of capacity
Therefore, the total cost of A&T during the off-peak
period for consumer i in area r of zone k can be defined as:
(4-1) TCOP*kr = qikr (ACOT) + qikr (ACOP1^) or
TCOPikr = qikr (AC°T + ACOPKT),
where qikr • (AC ) represents total A&T operating cost allo-
KT
cated to consumer i in area r of zone k and Qikr (ACOP )
represents the proportion of total A&T capital cost allocable
to consumer i in zone k. Note that: (q^p/KDP1) (TCOP1^) s
A service zone can encompass a large amount of land.
Therefore, each zone can be subdivided into a number of areas
according to census tracts or other geographic division. Note
also that Qikr represents the quantity of water consumed by i.
The equation developed below can be used to calculate the costs
of supplying water to an individual customer regardless of cus-
tomer class (residential, commercial, or industrial).
62
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KT T
q., (ACOP ) and Q^p/KOP s "the proportion of capacity required
consumer i in area r of zone k.
T&D cost also consists of operating and capital cost com-
ponents. Operating costs are composed of energy and maintenance
of equipment expenses. Capital cost refers to the expenditures
on pipelines and pumping stations.
Since a principal focus of this study is to study explicitly
the spatial aspects of water supply costs, this requires a dee-
per and more detailed examination of the determinants of T&D
costs. The operating cost of T&D is highly complex in nature
since it varies with respect to distance, topography, and out-
put . Maintenance cost is incurred on pipelines and pumping
stations, and in this study are considered constant per foot of
pipeline and per cubic foot of pump capacity, respectively.
Therefore, the operating costs which are variable with output,
refer only to the cost of energy consumption.
The cost per unit of energy is constant in relation to
each consumer in the same service zone. The magnitude of the
cost per unit of output depends upon the heada required to sup-
ply consumer i in zone k. This varies over distance and topo-
graphy.
Mathematically, energy cost per cubic foot for each linear
foot of pipe can be represented by the following expressions.
Let:
TCOPikr is the to'tal T&D operating cost incurred in supplying
to consumer i in area r of zone k;
Qkr is the total metered water supplied to area r of zone
k during the off-peak, cubic feet /time period;
P. is the off-peak cost of energy per kilowatt hour,
K $/kwh;
S& is the static head per foot of pipe, (ft .-lbs./lb.)/
ft.;
Sf is the friction head per foot of pipe,
1 (ft.-lbs./lb.)/ft.;
aHead refers to the amount of energy required to meet
friction, gravity, velocity, and pressure demands.
63
-------
S is the pressure and velocity head per foot of pipe,
p (ft.-lbs/lb.)/ft.;
R is the efficiency of the pumping station in zone k, %;
ACOP. .k is the cost per unit of water in zone k in area r for
1JKr pipe size j per foot of pipe, ($/cu.ft . )/ft . ;
D-k is the diameter of off-peak pipe size j in area r of
J zone k, inches;
K., is the net altitude between the treatment plant or
pumping station and consumer i in area r of zone k,
ft.;
C is the friction coefficient, a measure of roughness
of pipe;
g is the gravity constant, 32.2 feet per second squared;
L., is the length of pipe of diameter size j in area r of
JKr zone k, feet;
Q
PR. is the pressure in zone k, Ibs./inch ;
Q
P is the conversion factor, 2.31 ft ./(Ibs/inch );
c is the conversion factor used to convert
[(ft.-lbs./lb.) x (1/ft.) x (ft/kwh)] to C($/cu.ft.)
x (1/ft.)!;
V is the average velocity, feet per second.
The unit pumping cost of output for pipe size J in area r
of zone k is:
(4-2) ACOP = (Pk/E^) (Sa + Sf + Sp) c.a
Since the dimension of ACOP./? is [(S/cu.ft. ) x (1/ft.)],
while the dimension of (P^/E^CSa + Sf + Sp) is [($/kwh) x
(ft .-Ibs./lbs.) x (1/ft.) ], a conversion factor, c, is required
to establish dimensional homogeneity. Two conversion are
necessary:
s equation is used in the literature by Linaweaver and
Clark, "Costs of Water Transmission," Journal of the American
Water Works Association. 56 (December, 1964) pp. 1549-1560; and
W.C. Ackermann, "Cost of Pumping Water" Technical Letter 9,
Illinois State Water Survey (July, 1968).
6A
-------
(a) (kwh/ft,-lbs.) = 3.77 x 10~7; and
(b) (Ibs./cu.ft.) = 62.37
Therefore, c = 3.77 x 10~7 x 62.37
= 2.3513^9 x 10~5.
The head on a pipe consists of static, friction, pressure,
and velocity elements. For purposes of cost allocation, the
pressure, velocity, and friction coefficients per foot of pipe
can be assumed constant. Thus, variations in cost over distance
and topography can be identified through the relationship de-
rived in equation (6) from the appendix to this chapter. This
equation establishes the following function for a given pipe
size:
Sa + Sf "" SP = Zikr/Lokr + (pRk x p + (4-8256 x 105Q2kr)/
(n2g D4 Jkr))/L.kr + (2.85125 x 105) Q1^518 x C'1'8518
v D -4'87
x Djkr '
The problem remains, though, to calculate the head required to
serve customer i in area r of zone k through an assortment of j
pipe sizes. Water must be transported through some of the r
areas of a zone, and only a few of the k zones. Each area may
contain any combination of j pipe sizes and lengths.
Also, Pk and Ek may vary from zone to zone. Since a zone
is defined by the direction of water flow, the pumping station
serving one zone may use energy differently than another pump
station supplying a different zone. Thus, changes in P, and
are important in the examination of cost variations.
Incorporation of all those factors can be mathematically
represented.
Let:
T).. = 1, if consumer i resides in zone k or water to consumer
Ik
i travels through zone k;
= 0, otherwise;
6. = 1, if consumer i resides in area r or water to consumer
ir
i travels through area r;
0, otherwise; and
65
-------
*. . is the length of pipe size j in area r, feet.
I jr
Therefore,
K R n
(4-3) TCOP £ = q., £ n . E 6 E
ikr ikr ik ir
Y
V^0
o- ' J.J1 »-
x (Zikr/Ljr * PRk x p/Ljr
+ (4.8256 x 105 Q2kr)/(rT2g D4 orLjr)
+ 2.85125 x 105 Qk;8518/C1 •8518D^87/Qkr]
The term in brackets signifies the unit cost of pumping
Qkr per foot of pipe size ^ in area r of zone K' ACOPi^? •
This multiplied by the length of the jth pipe size, Y. . , in
zone r; and added over all pipe sizes to obtain the pumping
cost per cubic foot of water in area r of zone k. Summation
of that unit cost over all r areas generates total energy cost
necessary per unit of output to supply consumer i in area r of
zone k.
There are principally two components to T&D capital ex-
penditures: pipelines and pump stations. Maintenance costs
incurred on pipelines and pump stations can be incorporated
into considerations of capital cost.
As in treatment expenditure, the issue of peak-load cost
allocation appears. Pipelines are designed to handle the peak-
load, but exist during the off-peak also. Therefore, an off-
peak network will be developed on the basis of capacity neces-
sary to serve the average daily winter load.a Per foot cost of
pipe may be calculated by using the amount that the Cincinnati
Water Works actually incurred on pipes of each separate dia-
meter, that is, historical cost."3
Maintenance cost for T&D pipelines is assumed constant
here per foot of pipe per unit of capacity for all diameters.
The reasoning for this rests upon the fact that no relationship
has yet been established between the cost of repair and selected
size mains. As a result, T&D pipelines maintenance cost will
be considered as a fixed cost.
aFire flow is considered part of the off-peak load.
Pipe cost is not related to flow capacity since flow
capacity varies with the age and condition of the pipe, while
depreciation cost per time period still continues.
66
-------
The mathematical description of pipeline cost relationships
appears similar to that for energy cost in general formulations.
Let:
TCOP1? be the total off-peak T&D pipeline capital and
maintenance expenses in area r of zone k, (constant
over all R areas and K zones for a given size j);
K. be the flow capacity for pipeline of size 3; and
9 be the average maintenance cost per foot of pipe.
Therefore ,
(4-4) TCOPL = q. £ H. E 6 E
ir
vJ
The term in brackets represents the average capital and main-
tenance cost per foot of pipe size j, per unit of capacity of
pipe size j, in area r of zone k. The per unit capacity cost
is multiplied by the amount of water supplied to consumer i.
The parameters T], 6, and * are used in the same manner as in
equation (4-3).
The capital and maintenance expenditures for pump stations
depends upon the capacity installed to transport water through
each zone. The design capacity of pump stations is determined
on the basis of peak-load demand, though the capacity in service
is available for off-peak as well as peak-loads. Therefore, an
off-peak capacity pumping system must be developed to correctly
identify the off-peak capital T&D costs for the average daily
winter load just as in the case of treatment and pipeline capi-
tal expenditures .
Capital cost per unit of capacity and maintenance cost per
unit of capacity are assumed fixed in relation to each customer
in the same zone. The proportion of capacity allocated to a
customer depends upon the amount of capacity required by his
average daily winter load. This occurs for each zone through
which water must be transported to reach consumer i in zone k.
A mathematical formulation of pumping station capital and
maintenance cost must incorporate those considerations of
capacity.
Let:
TCOPikr be tne total off-Peak capital expenditures for T&D
pumping stations;
67
-------
K? be the capacity available for the off-peak pumping
station in zone k;
ACOPikr toe the TCOPikr / \ ' avera£e capital cost per unit
of capacity during the off-peak in zone k;
MP
TCvf be the total maintenance cost for the pumping
r station in zone k;
\ s TCikr//Kk ' avera£e maintenance cost per unit of
off-peak pump station capacity in zone k; and
P JCP MP
TCOPikr s TCOPikr * TCikr' total cost of maintenance and
off-peak capacity for pumping stations allocated
to consumer i in zone k.
Therefore,
(4-5)
The term in brackets contains the average capital and mainte-
nance cost per unit of capacity in zone k. This expression is
summed over each zone through which water must be transported
to serve CUT,,, "to consumer i. T|^ is again used to delineate
the pumping stations used to serve consumer i from all available
pumping stations .
The remaining element comprising off-peak water supply
costs is overhead. Revenue collection, billing, meter reading,
accounting, and administration are items unrelated directly to
output or capacity of the system. As such, they may be con-
sidered as fixed overhead necessary for proper management of a
water works. This cost can be allocated to each customer
account on an even basis since every account incurs overhead
costs. a Let A represent the overhead cost per customer for the
peak and off-peak periods.
Off-peak costs may be mathematically defined by combining
all the elements discussed above.
Let:
is a difference between monthly billed and quarterly
billed accounts in that the monthly account requires three meter
readings and billings per quarter. This difference is neglig-
ible for cost allocations presented here.
68
-------
TCOP1k be the total off-peak costs of supplying consumer
i in area r of zone k.
Therefore, from (4-1), (4-3), (4-4), and (4-5),
(4-6) TCOPikr = TCOP^kr + TCOP°°r + TCOP^r + TCOP^kr + A.
Upon substitution into (4-6) for the total cost variables, the
following cost function for the off-peak is generated.
(4-7) TCOP = q. (ACOT +
(Fkc/Efc) x (Z.kr/L.r + PRk x
+ (4.8256 x 105 Q2 kr)/(n2gDSrLjr)
+ (2.85125 x 10V;8518)/(C1'8518 x D^
itr ij^*
K R n
+ fn ^ *r\ ^i C r* ~
^ik L ^ik S ir Z Y^-nr
1K k=1 1K r=1 ir j=1 ar
K
K R n
E Tl Z 6 ir E
k=1 1K r=i j=
K R n
s 5ir E Y x
r=1 ir j»1 ijr
* wk3 + A.
Rewritten:
(4-8) TCOPikr = qikr [ACOT + ACOP1^ + E Hlk (ACOP1^ + WR)
J^^ I
x /L.jr * 4.8256 x 10
* 2.85125 x 105Qkr8518/C1<8318D^;87)]/Qkr * A.
TCOPikr represents the cost incurred in supplying one customer
account in area r of zone k during the off-peak period. It is
69
-------
important to note that this equation does incorporate all the
identifiable elements involved in off-peak water supply. The
next section will discuss the peak-load cost problem.
Cost Function; Peak-Period
Off-peak capital costs reflect the capacity necessary to
supply the base load on the system or the average daily winter
demand. Capital costs required to serve the peak-load are one
component of incremental capacity expenditures existing in a
water supply system. The other is the expenditures needed to
enlarge the whole or part of a system. For the purposes of
this study, these incremental costs can be measured by sub-
tracting the required off-peak capacity from the system capacity
available for peak use.
Capital costs are fixed per unit of peak capacity as for
the off-peak. In general, the peak-load cost function framework
is similar to that for the off-peak except for considerations
on capacity and storage. Total cost is also broken into A&T
and T&D components.
Given the peak capacity A&T operating and capital costs
remain fixed for each customer as in the off-peak period. Peak-
load capital costs for treatment and acquisition consist of the
expenditures on marginal plant capacity constructed to handle
the maximum day.
Let:
q., be the quantity of water consumed by customer i in
licr area r of zone k;
^. be the total peak-load treatment cost to supply q
to consumer i in area r of zone k; 1Kr
OT
AC be the average operating cost per unit of output;
KT
TCO be the total capital cost for A&T, or total peak-load
capital cost for A&T;
be the total A&T plan
capacity available for A&T; and
KP be the total A&T plant capacity or total peak-load
ACpKT = rpcpKT^pT^ average peak-load capital cost per unit
of capacity.
Therefore,
70
-------
(4-15)a TCP*kr = qikr (AC°T + ACPKT), where qikr (ACPKT)
equals the proportion of total treatment peak-load capital cost
allocable to consumer i in zone k and q.,,_ (ACP ) = (q., /KP )
rrm 1Kr 1Kr
TCPKT
T&D cost contains operating and. capital cost elements.
Operating cost consists of energy consumed in pumpage of water
into the service areas. The cost of energy may be formulated in
the same fashion as in the section covering off-peak costs. The
only change is reflected in the variable D. , diameter of the
3^
pipe. For the off-peak period, the pipe diameter is smaller
reflecting lower capacity requirements to meet demand. For the
peak demand, though, the pipeline diameter must be larger to
handle a greater flow. This change in diameter affects the
friction and velocity heads in the transmission system and there-
fore the cost per unit .
Let:
PP, be the peak-price of power in zone k, $/kwh;
TCPikr be the "total operating cost in T&D incurred in supply-
ing consumer i in area r of zone k;
D. be the diameter of pipe 3 in area r for the peak-load
^ period;
QP. be the total metered water supplied to area r of zone
k during the peak-period, cu. ft. /time period;
OC
and ACP,^ be the cost per unit of qik_ in zone k in area r for
pipe size 3 per foot of pipe during the peak-period,
($/cu.ft.)/ft.
Therefore, from (6) in the appendix, total head loss per foot
of pipe may be adjusted to:
(4-9) Sa + Sf + Sp = Zikr/Lkr * (PRk x P + (4.8256 x 105
+ 2.85125 x 10
p
5
Combining the changes in (4-9) with equation (4-3) provides the
aEquation number advanced from later in text.
71
-------
peak-load total operating cost in supplying consumer i in area
r of zone k.
(4-10) TCP°°r . q^ ^ 6.r *ijf C(PPk/(Ek)
PRk x p /I"'r * 4-8256 x 105
x (QP2/"2gD4..L.) + 2.85125 x 105
kr".jr.Jr.
Use of peak D. may lower energy cost per foot of pipe since
J-^
peak D., is larger than the off-peak D. used because of
greater load requirements. The total effect, though, depends
upon the volume of metered water pumped as well as the pipe
diameter.
T&D capital and maintenance cost for pipelines and pumping
stations remains to be discussed. A large capacity exists for
supplying customers during peak-load periods. Capital and
maintenance cost per foot of pipe per unit of capacity for all
consumers for a given pipe size. Also, capital and maintenance
cost per foot of pipe size 3 per unit of capacity does not
change between the peak and off-peak periods for a given pipe
size, but the cost to consumer i varies. The reasoning behind
this rests on the fact that the pipe sizes used to serve
customer i changes, which affects the capacity available in the
T&D system.
Let:
KD
TCPvrr be the total peak T&D pipeline capital and main-
tenance expense in area r of zone k;
KD
A<""iikr be the avera£e capital cost per foot of pipe size
J in area r of zone k (constant over all R areas and
K zones for a given size);
? be the average maintenance cost per foot of pipe;
D and
KP. be the flow capacity of pipe size j for pipelines
J used during the peak-load.
Therefore, total pipeline cost to consumer i for the peak-load
period may be mathematically represented by the following
equation.
72
-------
(4-11)
.
J
This equation is very similar to (4-4) in the off-peak cost
section. The only differences are in the pipe flow capacity
variable, KFr, and the values of AC. ., . Since larger pipe
j ijKr
sizes are used during the peak period, KFT changes for a
KD
selected customer and AC. ., correspondingly varies with the
pipe diameter as KFr changes. Peak-load capital and mainte-
nance costs only reflect changes in pipe diameter and capacity
since the capital and maintenance cost for a foot of pipe is
the same regardless of whether that pipe size is used in the
peak or off-peak periods.
Pumping station capital and maintenance cost for peak-load
periods reflect the capacity necessary to serve greater demand
rates. Capital and maintenance cost per unit of capacity is
constant for each customer, but varies between peak and off-peak
periods because different design capacities are required to meet
the two types of demands. Capital facilities are constructed in
relation to a specific capacity. The cost of capital per unit
of capacity, therefore, depends upon the design volume of the
plant and the degree of economies of scale existing in construc-
tion of capacity. As a result, capital cost per unit of plant
capacity may vary between periods. Maintenance cost per unit
of capacity is constant within a demand period, but can change
between the off-peak period because capacity available for T&D
is increased for the peak-load.
Let:
p
TCP-k be the total cost of maintenance and peak-load
capacity for pumping station allocated to consumer
i in zone k;
KP
be "k*16 Piping station peak-load capital expendi-
tures for T&D;
p
KPk be the pumping station capacity available for the
peak-load in zone k;
KP KP / ~P
ACP be the TCP'1' averaSe capital cost per unit of
ikr
capacity during the peak-load in zone k;
73
-------
MP
TC., be the total maintenance cost for the pumping
station in zone k; and
MP / KP
WP^ be the TCj^r/Kpic » average maintenance cost per unit
of peak-load pump station capacity in zone k.
Therefore,
P TCP
(4-12) TCP^ - qlkr £ Hik [ACP^ + WPk].
This expression closely resembles that discussed in the section
on off-peak costs, equation (4-5).
The remaining element in off-peak costs is overhead. This
cost may be allocated to each account as similarly done for the
off-peak cost. Thus, A again represents the overhead cost per
customer.
A final element, not incorporated in the off-peak cost
equation, is storage cost. At certain times, the demand rate
may be greater than the peak-load capacity of pumping stations
and pipelines. For those occasions, storage facilities are
constructed to supply water and maintain pressure when the
system is overloaded. Storage cost is primarily a peak-load
cost allocable to peak-load users. Cost can be apportioned to
consumer i according to the amount of water demanded by consumer
i in relation to the total quantity of water supplied during the
period to the area in which consumer i resides.
Let:
QP,. be the quantity of metered water supplied to area r
in zone k;
q., /QPVv, be the proportion of water used by consumer i;
iKr Kr
q
TC£ be the total cost of storage to consumer i in area
r of zone k; and
Q Q
ACkr = TCkr>/'QPkr' avera£e c°st of storage per unit of
output supplied to area r of zone k.
Therefore,
(4-13) TCpfkr S qikr (*&.) .
The proportion
-------
Combining all terms involved in peak-load costs, the follow-
ing equation may be generated.
Let:
TCP-k be the total peak-load costs of supplying consumer
r i in area r of zone k.
Therefore, from (4-15), (4-17), (4-18), (4-19) and (4-20),
(4-14)
+ A.
Upon substituting into (4-14) for each TCP variable, this cost
function is generated.
OT
(4-15) TCP = q UC
. \ir x PPk 0/Ek tZikr/LJr + P\ x °'Ljr
J~ '
+ 4.8256 x 105 x (QPkr/n2gD4
-------
Equations (4-8) and (4-16) provide a complex framework in which
to estimate water supply costs for a given point. Both are
highly complex in formulation and use, but, as such, that does
not hiner the analysis. These two equations will be used to
generate data points that relate cost of water to distance,
altitude, and quantity supplied for two time periods; peak and
off-peak. Once the data points have been collected, statisti-
cal analysis of the relationship among the variables will be
performed .
76
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PART B: EMPIRICAL METHODOLOGIES
This part is devoted to a description of the study area
statement of the principal hypotheses to be investigated, pre-
sentation of the statistical equations to be estimated, the
estimation of scale economies in water supply in the study
area, and the framework for analysis of cost-rate differen-
tials.
The Study Area
The area studied consists solely of the service area of
the CW which is contained in Hamilton County, Ohio (see
Figure 8 ). The CWW is a self-supporting public utility
which has operated over one hundred years with the Ohio River
as the sole source of supply. Its treatment plant is located
in the southeastern corner of the County.a
Water is acquired from the Ohio River, and after treatment
is transported to the ten service zones of the supply area
(See Figures gand 10). These zones are defined essentially
on the basis of water flow and on the location of pump stations.
Since the direction of water flow is a variable, the zone
definitions are based on averages.
Empirical Framework
From the literature review ( Section 3) it was concluded
that virtually no empirical study has been performed on water
supply T&D costs of a metropolitan water system. Much of this
research has concentrated on the central plant functions of
water supply (AM!) only, and has neglected the measurement of
peak and off-peak costs. Furthermore, current water pricing or
rate setting methods, especially commodity demand or base-
extra capacity methods, neglect that inter-user relationships
that exist as a result of cross-subsidizations which result from
uniform or relatively uniform zonal or spatial charges.
To measure these impacts, it is useful to have fairlv
concise measures or representations of water supply costs
especially in order to measure scale economies in T&D. To
p
Construction was completed and operation began of a new
A&T plant in late 1976, supplied with ground water. The studv
period does not include the impact of this plant.
77
-------
CINCINNATI SERVICE AREAS
A. Cherry Grove
8. Ml Washington
C. California
D. Central
E. Eastern Hills
F Brecon
G. Western Hills North
H Western Hills South
MASTER METERED AREAS
1 Butler County
2. Warren Count/
3 Arlington Heights
4. Norwood
INDEPENDENT UTILITIES
5. Cleves
6. Addison
7. Wyoming
8. Loclcland
9. Reading
10 Glendole
11. Indian Hill
12. love/ond
13. Miltord
LEGEND
Service Area for Cincinnati Water Works
•••i Mastered Metered Areas
Independent Utilities
FIGURE 8. Cincinnati tfeter Works service area.
-------
VD
X--
FIGURE 9. Service area and zones of the Cincinnati Water Works
-------
C1b
C3b
C4b
oo
o
C1a
C2
C3a
C4a
Gravity
Tunnel
B1
Treatment
Acquisition
OHIO RIVER
B2
FIGURE 10. Schematic diagram of Cincinnati Water Works system,
-------
this end a number of statistical hypotheses were formulated
and estimated.
Manor Hypotheses; Cost Functions
There are alternative approaches to the estimation of cost
functions. Two discussed by Johnston are: (a) functions
estimated through the use of accounting and engineering records,
and (b) through explanatory variables or determinants of cost
variables.8
This research utilizes elements of both approaches. Water
supply costs traditionally have been examined in the framework
of quantity produced, capital invested, capacity available,
and/or the proportion of capacity utilized. This may be rep-
resented by: C = C(Q) in general or C = aQ specifically where
C = cost and Q = finish water produced. The data collected
usually consist of a cross-sectional sample of utilities' in-
tended to provide information about the shape of the long-run
cost curves (variable plant size). The interesting element in
such studies is the fact that water supply utilities consist of
two major components: A&T and T&D. Any measure of economies
of scale using aggregate data overlooks information on the
components of water supply in particular, the spatial aspects.
Therefore, through a comprehensive study of one utility, as
has been undertaken here, information on changes in T&D cost
over the service area of the utility may be generated.
To examine these spatial aspects then leads to the first
hypothesis HI:
H1: total water supply costs vary positively with
distance and altitude.
To examine any peak - off-peak cost differentials, we
state H^t
H?: peak period total costs exceed off-peak total costs.
A third hypothesis concerning costs is:
H,: Scale economies in T&D are mainly determined by
^ industrial water demands, as opposed to commercial
or residential.
Empirical Approaches To Cost Function Estimation
The empirical approaches to these hypotheses are essen-
tially the same. On the basis of the cost estimates generated
aj. Johnston, Statistical Cost Analysis. New York: McGraw-
Hill, 1960.
81
-------
from equations ( 4-8) and (4-15) above, the following relationship
was estimated:
(4-17) TC = f (Q, L, A)
where TC = total cost of water supply:
Q = quantity, hundreds of cubic feet, CCF;
L = distance from the treatment plant to a point in the
service area, feet; and
A = the altitude, feet.
The total cost function may be employed in testing all three
hypotheses for the data samples taken in each service zone for
each user group. In other words, all the consumers in a service
zone are stratified by customers class, thus permitting separate
analyses. Therefore, estimation of cost equation (4-17) above
may be performed for each user group in each zone for both peak
and off-peak periods. This is expected to provide information
on the effect of distance and topography on cost as well as
possible economies and diseconomies of scale, the variation in
cost between peak and off-peak periods, and the differences in
water supply costs among user groups.
An alternative empirical approach may also be taken for
estimation of their relationship which may provide a clearer
view of the impact of distance and topography on cost. By using
an average cost approach ($/CCF) as a method of holding the
influence of Q constant, more reliability from the estimates
may be obtained. Therefore, the alternative form of the above
equation is:
(4-18) AC = g (L, A),
where AC is average cost, $/CCF. Figures 11 and 12 graphically
depict the relationship of equation (4-18) to the traditional
textbook average cost curve. The concentration is not on the
traditional average cost, though the dimension is $/CCF.
Instead, the relationship represents total cost with respect
to distance and altitude for a hundred cubic feet of water.
This may provide a better view of the impact of distance and
altitude on cost.
^he appropriate, functional form of the equation will be
linear, logarithmic, or exponential depending upon the degree
of normality of the data after a transformation as seen in a
scattergram of the data points. A logarithmic transformation
of a multiplictive specification of the equations readily gives
estimates of the economy of scale parameter. In order to high-
light the spatial aspects of the relevant T&D cost function,
82
-------
$/CCF
D
ACo (D)
AC, (D)
AC (Q)
Pt. A0 represents the value of AC(Q), the traditional average cost relation-
ship, for which flow Q0 creates AC0 (D). A different flow, Qj, incurs a new
A, and AC((D).
Figure 11. Relationship of distance cost to a typical average
cost curve.
83
-------
$/
CCF
This graph depicts the same type of relationship for altitude at flows QQ and Q«.
Figure 12. Relationship of altitude cost to typical
average cost curve.
AC(Q)
-------
computer generated maps of the dependent variables will also be
presented. For the data points selected in the service area of
the CW, information on the following variables was collected or
generated: (a) the quantity consumed at each data point for
peak and off-peak periods, (b) the total cost of +hat quantity
supplied to each data point, (c) the cost per hundred cubic feet
of water for peak and off-peak periods, (d; the distance along
the pipeline between the treatment plant and the data point,
(e) and the change in altitude between the treatment plant and
the data point.
Manor Hypotheses; Cost-Rate Differentials
A policy of uniform zonal rate setting may allow signifi-
cant inter-areal and intra-areal subsidization, and user cross
subsidization within a customer class and perhaps among classes.
The possibility of subsidization increases if cost is signifi-
cantly affected by distance or topography. Thus, for a given
quantity, uniform zonal average cost pricing could lead to higher
rates than costs near the central treatment plant and lower rates
than costs farther from the treatment plant. Thus, one would
expect that those living closest to the treatment plant subsidize
(on a unit basis) those who live farther from it. It is hypo-
thesized therefore:
H/: the CW earns revenue surpluses on customers close to
the A&T facility, and incurs deficits on those farther
away.
Another hypothesis treats the question of the presence of cross
user or customer class subsidies, as where industrial users
might be subsidized by residential users, or vice versa.
HJ-: the CWW incurs revenue deficits on industrial and
0 commercial water supply, and surpluses on residential
supply.
It should be pointed out that such a result may occur not
so much because of cost differences, but because of the rate
structure (declining block rates), discussed below. For no such
subsidization to occur, rates would have to be tailored exactly
to costs.
Lastly, an examination of the costs of delivering water
during peak and off-peak periods, may reveal subsidies between
peak and off-peak periods. If significant differences exist in
the cost of supplying water between peak and off-peak periods,
with an unchanging rate structure, then the following hypothesis
may be supported:
Hg: Peak period water users are subsidized by off-peak
users.
85
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Of course, to some extent, these will be the same customers,
who may in fact prefer to have level billing.
Empirical Approaches to the Analysis of Cost-Rate Differentials
basic approaches to the analysis of cost-rate differen-
tials include (1) computer generation of maps for broad-brush
analysis of the spatial differentials uncovered, and (2) more
precise estimates for specific (unidentified) accounts (custo-
mers) as a function of the spatial variables and customer class.
This is performed for both peak and off-peak periods.
The maps and specific estimates are generated by comparing
revenues from the data points with the cost information generated
by the analyses discussed above.
data required for this analysis consists of four ele-
ments; revenue during the peak and off-peak periods for the data
points, the rate structure, the cost values for the data points
for peak and off-peak periods, and the statistical results of
the empirical work discussed in the section on cost functions.
Data Collection
We present a brief description of the data acquisition
procedures employed in this study as a guide to future studies
and to aid critics.
Data for this project was collected from the 1973 records
of the Cincinnati Water Works. Unfortunately, it was not
available in a form readily adaptable for this research.
The final data requirements as specified in the previous
section consisted of: revenue, quantity consumed, and cost of
supply information for each user group during the peak and off-
peak periods for the data points selected; the distance along
the pipeline and the change in altitude between the treatment
plant and each data point; and the rate structure existing for
the time of the study.
The preliminary data collection process was quite involved.
The process began by dividing the service area into ten zones on
the basis of direction of water flow and location of pumping
stations as noted earlier. This v/as justified because each zone
could be considered a small service area. This breakdown did
not facilitate computation, but did add greater depth and dis-
aggregation to the empirical analysis since cost curves could
then be estimated for each zone. Also, cost variation over the
area of the zone could be analyzed.
Once the zones were defined, a random sample of residential,
86
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commercial, and industrial users for each zone was drawn. This
initially involved the determination of which customer accounts
belonged in which group. Unfortunately, of the approximately
188,000 records, there was no clear.user group demarcation. At
the time of this study, the Cincinnati Water Works had two major
classifications of customers: commercial monthly billed and
quarterly billed. The commercial monthly billed accounts con-
sisted of the larger users numbering about 1700 in total. The
quarterly billed accounts could be broken into two groups based
upon a family unit coding system which identifies the number of
family units connected through that account (meter). If an
account possessed a number less than or equal to 98, it was
considered residential. For those classified 99, the customer
account either had 99 families or the user was industrial,
commercial or unclassifiable at the time of coding. The accounts
coded 99 totaled approximately 8300. This total group of 1700
commercial monthly billed accounts and 8300 quarterly billed with
a family units code of 99 were analyzed, categorized, and coded
with a four-digit Standard Industrial Code (SIC). Once com-
pleted, four divisions of the approximate ten-thousand accounts
could be made:
a) residential users to be included in the quarterly
accounts are those with a family unit code of 98 or less, SIC
code of zero or 6513;
b) commercial accounts with SIC code from 5000 to 8999;
c) industrial accounts with SIC code from 0100 to 4999;
and
d) other accounts with SIC code from 9100 to 9999.
The "other" accounts contained such users as schools, churches,
hospitals, parks, and government buildings. This segment was
not analyzed because of the wide diversity in water use among
the users.
From this demarcation of accounts, each user group could
be identified. The next step involved allocation of account
numbers to service zones. It was found that census tracts
could easily be associated to one zone or another and that the
account numbers of the Water Works corresponded to census tract
boundaries. On this basis, all the accounts particular to any
zone could be determined for sampling of the user groups in
connection with the SIC coding noted above. Once the records
were entered and stratified into segments, one for each of the
ten zones and three user groups, thirty random samples could be
drawn. In order to maintain a sample size of at least thirty,
samples greater than thirty records were taken. This allowed for
deletion of those records on which information was incomplete.
87
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Of the thirty samples, six were deleted. Three were dropped
because one zone was too small to be able to obtain any signi-
ficant variation in distance or altitude. The other three of the
six deleted samples, all industrial samples, did not contain
thirty users. In all cases, those samples dropped from the
analysis came from the smallest service zones of the Cincinnati
Water Works. Of the remaining twenty-four samples, there were
a total of 805 sample points, (see Table 4). Given the sampled
accounts, with specific addresses, it was then possible to com-
pute the cost of delivering water to the points, for peak and
off-peak periods.
The following procedure was used to identify the period.
Based on monthly records for total water pumped records for the
years 1965-1975, a monthly moving average was created to cal-
culate monthly indices of water pumpage. The resulting dis-
tribution (Figure 15) of the indices identified the peak and
off-peak periods as the third and first quarter, respectively,
of the yearly cycle. Quarters are identified here because no
finer time dimension in the records of the Water Works exists
for customer account records except the 1700 monthly billed
accounts. Based on this then, the consumption and revenue
records for the peak and off-peak periods could be collected
for each sample point.
Having obtained the sample sets and data points, the
remaining data needed for analysis were the cost of supply in
peak and off-peak periods. The preliminary data collection
process was also quite involved.
All transmission pipelines (greater than or equal to 16
inches in diameter) and their diameters were identified along
with all remaining capital facilities such as pumping stations,
storage tanks and the treatment plant. The historical cost of
each element was recorded. Distribution pipeline capital and
maintenance cost was included, but each line was not identified
in the same manner as transmission lines. This element was
ignored because of the inability to assign flows to those pipes.
Finally total metered water flow for the entire system for each
census tract was collected for the peak and off-peak quarters.3
Assuming that the demands of all the census tracts must be
supplied, representative water flow is each transmission pipe
could be determined for an average day in the peak and off-peak
quarters. Once the flows in each pipe were identified, costs
of supply could be calculated through the use of equations (4-8)
dimension of the water flow was converted from CCF/
quarter to CCF/day to facilitate comparisons, as some quarters
contain more days than others.
88
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TABLE 4
NUMBER OF DATA POINTS STRATIFIED BY
SERVICE ZONE AND USER CLASSIFICATION
Zone
Label
A
B1
B2
C1a
C1b
C2
C3a
C3b
C4a
C4b
Residential
D
31
32
32
28
30
39
30
30
39
Commercial
D
34
31
42
28
30
30
42
42
32
Industrial
D
D
D
36
D
33
36
32
33
33
Total in
Zone
65
63
110
56
93
105
104
105
104
Notes:
Total Sample Size user group:
1. Residential = 291
2. Commercial =311
3. Industrial =203
D s deleted sample
TOTAL 805
89
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MONTHLY INDICES
12O- •
115-
11O--
1O5--
1OO--
95--
9O--
I I
M
M
N D MONTH
Figure 13. Monthly indices based on water pumpage for 1965-1975.
-------
and (4-17) from the earlier discussion.
Given those equations, total cost was calculated for vary-
ing distances and altitudes by adding together the cost of the
separate components for both time periods for each sample point.
To ensure that all cost elements were included, the costing
procedure was made to balance with the annual report of the
Cincinnati Water Works. These cost calculations also required
simplyfying assumption for isolation of the effects of distance
and altitude on cost. This assumption sets selected engineering
factors constant. Specifically, by setting water pressure,
pump efficiency, and the Chezy coefficient of pipe friction
(C-factor) at a constant average value,5 inconsistencies in the
calculated data could be reduced if not eleiminated. If those
constants were allowed to vary, it is possible that conflicting
values of cost could be calculated for similar distances and
altitudes in the same service zone. Then, the relationship
between cost of water supply and distance/altitude would depend
upon the distribution of water pressure, pump efficiency, and
pipe quality. These variables do affect cost, but it was
judged that the cost of obtaining the additional information
would be greater than the increased precision would justify.
Capital costs per day for the peak period were calculated
on the basis of the cost of the existing system. Capital costs
per day for the off-peak period were calculated for a system
capacity scaled down by the ratio of off-peak flow to peak flow.
Once the proportion of capacity necessary was acquired, capital
costs for the off-peak could be determined. Specifically, the
capital cost for smaller transmission lines was calculated simp-
ly by using what it actually cost the Cincinnati Water Works for
pipes of that size. Capital costs for pumping station and treat-
ment were slightly more involved. Using the .6 rule of thumb
noted by Moore (see literature review) and the following formula:
TK = aK where TK = total capital cost,
K = capacity,
b = .6, and
a = a parameter; total off-peak capital
cost can be determined. First set K and TK at their peak period
values and solve for "a". Finally, substitute in off-peak K.
Using "a" and "b", off-peak capital cost is determined. In this
manner, two complete capital systems for water supply could be
established.
^Pressure was set at 100 psi, pump efficiency at 9096 and
C-factor at 100.
91
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The last data element is the water rate structure in effect
consists simply of the rate structure in effect during 1973,
(see Table 5). Only those rates referring to inside Cincinnati
and outside Cincinnati but inside Hamilton County are applicable
to this study.
92
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TABLE 5. CINCINNATI WATER WORKS WATER RATES EFFECTIVE APRIL 1, 1969.
MINIMUM CHARGES
Meter Size
5/8 inch
3/4 inch
1 inch
1-1/2 inch
2 inch
3 inch
4 inch
6 inch
8 inch
10 inch
12 inch
Number of
Family Units
2 or 3
4 or 5
6 thru 12
13 thru 20
21 thru 50
55 thru 115
116 thru 250
over 250
Inside Cincinnati
Outside Cincinnati
in Hamilton and
Clermont Counties
Butler and
Warren Counties
Monthly
$ 2.50
2.80
3.50
4.50
7.00
9.00
12.00
25.00
35.00
40.00
40.00
Quarterly
$ 4.50
5.40
7.50
10.50
18.00
24.00
33.00
75.00
105.00
120.00
120.00
Monthly
$ 5.00
5.60
7.00
9.00
14.00
18.00
24.00
50.00
70.00
80.00
80.00
Quarterly
$ 9.00
10.80
15.00
21.00
36.00
48.00
66.00
150.00
210.00
240.00
240.00
Monthly
$ 5.75
6.45
8.05
10.35
16.10
20.70
27.00
57.00
80.00
92.00
92.00
Quarterly
$ 10.35
12.40
17.25
24.15
41.40
55.20
75.00
170.00
240.00
270.00
270.00
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TABLE 5. CONTINUED
COMMODITY CHARGES
Outside Cincinnati
Inside in Hamilton and Butler and
Cincinnati Clermont Counties Warren Counties
Rate Rate Rate
Per 100 Cubic Feet
In excess of
1,000 cubic ft.
but not in excess
of 60,000 cubic ft.
In excess of
60,000 cubic ft.,
but not in excess of
1,000,000 cubic ft.
In excess of
1,000,000 cubic ft.
In excess of 2,000
cubic ft., but not in
excess of 180,000
cubic feet. 200
In excess of 180,000
cubic feet, but not in
excess of 3,000,000
cubic feet. 160
In excess of
3,000,000 cubic feet. 120
350
280
210
400
320
240
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SECTION V
EMPIRICAL RESULTS
GENERAL PURPOSES
This chapter presents and reviews the empirical results
generated in the quantitative phase of the study. Following
the division developed in the previous chapter, there are two
basic analyses presented: (a) cost functions and (b) cost-
rate differentials. Findings are presented on costs among
customer classes, peak and off-peak period costs, the relation-
ship of cost to distance and altitude, and the cost-rate
differentials.
PART A: COST ANALYSES
Cost Functions Disaggregated by Customer Class
For this analysis, 24 separate samples were drawn. The
data were extensively analyzed for normality. Both the square
root and logarithmic transformation improved the normality of
the data, but in general, the logarithmic transformation was
better.
With this data and the generated cost estimates, the
following relationships (from the hypotheses in Section IV)
were examined:
(5-1) TC1 = f(Q)
(5-2) TC2 = g(L,A,Q)
(5-3) TC5 = h(L,A)
where TC^ and TC2» are total costs;
Q is quantity (CCF);
L is distance in feet;
A is net altitude in feet;
95
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TC, is sum of A&T plus T&D per CCF (i.e., an average cost).
Scattergrams of the data were constructed to choose
appropriate functional forms. The forms examined (in terms of
the independent variables) were linear, square root and multi-
plicative (log-linear). For each sample, and each customer
class (residential, commercial and industrial) 3 peak and 3 off-
peak equations were estimated, utilizing step-wise regression
analyses.
The multiplicative form will be emphasized here, as it
tends to fit the data best. An added advantage of this log-
linear form is that the estimated regression coefficients are
also the elasticity estimates, and are particularly useful in
an examination of cost economies with respect to quantity,
distance and altitudes.
Table 6 presents the estimates for total cost as function
of quantity alone (equation 5-1). The coefficients for lu Q
are the total cost elasticities, which are defined ad d lu TC/d
lu Q = €. For example, for equation 1 in Table 6, e = 0.2734,
which means that for the peak period, a 10% increase in quantity
of water consumed across the sample led to a 2.7% increase in
cost. This can be more readily seen by noting that in the
equation TC = aQ (as in Table 6), TC/Q = aQ^/Q = aQG"1 = SRAC
(shortrun average cost). Thus any € < 1 implies a negatively
sloped short run average cost curve, i.e. d(Ae)/dQ
= (€-1) aQ€~2 which is negative, for € < 1.
It is important to emphasize, that the estimates are based
on a system with fixed capital facilities, and so these esti-
mates are for short run total and average costs. The term
"scale economies", conversely, applies to situations in which
capital facilities are variable. The only insight into scale
economies presented in this study would come from a comparison
of peak and off-peak elasticity estimates.
A general finding here is that the estimated cost
elasticities for residential customers as a group are smaller,
meaning that average cost to residential customers as a group
declines more rapidly than to industrial or commercial customers.
While this does seem contradictory of what is usually expected,
it is plausible if one recognizes that, since we are considering
residences, industries and places of commerce as classes, the
total quantity of capital in place to serve residences is
greater than for the other sectors, and it is thus reasonable
for the cost economies to appear as they have. This finding
does need to be investigated further.
96
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TABLE 6. IMPACTS OF QUANTITY ON TOTAL COST OF DELIVERED WATER.
Zone C, „ - Peak Period
I 3.
1. Residential
Ln (TC,) = -2.2406 + 2.734 Ln (Q) DF = 30; R2 = .844
1 (.1079) (.0214)
2. Commercial
Ln (TO.) = -1.597 + .7075 Ln (Q) DF = 40; R2 = .862
1 (.5689) (.0447)
3. Industrial
Ln (TC,) = -1.576 + .8061 Ln (Q) DF = 34; R2 = .944
1 (.4674) (.0337)
Zone C, - Off-Peak Period
\ QL
4. Residential
Ln (TC,) = -2.5395 + .1191 Ln (Q) DF = 30; R2 = .140
1 (.2819) (.0539)
5. Commercial
Ln (TC,) = -1.634 + .6984 Ln (Q) DF = 40; R2 = .874
1 (.4683) (.0420)
6. Industrial
Ln (TC,) = -1.6215 + .8162 Ln (Q) DF = 34; R2 = .937
1 (.4827) (.0363)
Zone C2 - Peak Period
7. Residential
Ln (TC,) = -2.1903 + .2883 Ln (Q) DF = 28; R2 = .265
1 (.3689) (.0906)
8. Commercial
Ln (TC,) = -1.5554 + .6284 Ln (Q) DF = 28; R2 = .837
1 (.5273) (.0524)
9. Industrial
Ln (TC,) = -1.674 + .8074 Ln (Q) DF = 31; R2 = .888
' (.5587) (.0515)
97
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Zone C 2 - Off-Peak Period
10. Residential
Ln (TO.) = -2.0609 + .3542 Ln (Q) DF = 28; R2 = .408
' (.3393) (.0807)
11. Commercial
Ln (TCj = -1.692 + .7115 Ln (Q) DF = 28; R2 = .725
1 (.711) (.0829)
12. Industrial
Ln (TO.) = -1.4025 + .6483 Ln (Q) DF = 31; R2 = .862
(.5694) (.0466)
Note: all coefficients significant at 95% or higher.
98
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Another important finding can be seen by comparing peak-
period costs with off-peak. A usual expected result is to find
that costs decline more rapidly for the peak-period investments.
This would require the elasticity to be smaller for the peak
period equations. The results in Table 6 are mixed. In zone
C^ it is true for the industrial class (0.8061 vs 0.8162) but
i a
they are not significantly different statistically. Similar
conclusions apply to residential and commercial classifications
in zone C2» Conversely, for residences in zone C1, the off-
peak elasticity is less, and significantly so. This suggests
diseconomies of scale (the peak vs off-peak comparisons re-
present the only case in which we can draw inferences about
scale economies, as mentioned earlier). A pricing system which
did not take such scale diseconomies into account could be said
to be inefficient.
Estimation of equation 5-2 was performed to examine the
relative effects of quantity, distance, and net altitude, wo
statistically significant effects were found for the distance
and altitude variables, in spite of the fact that there was
little to no multicollinearity between the distance and altitude
variables. In virtually all cases the quantity variable
accounted for most of the explain variance. This occurred
because there is relatively much more variation in Q than in A
and L,, around TC.
c
Equation 5-3 represents an attempt to circumvent the unequal
variances by standardizing TC into TC per CCF (dividing by Q).
This makes the dependent variable an average cost measure, but
as a sum of A&T, T&D costs per CCF, with plant size fixed. As
before, the only scale implications that can be drawn are
from the comparison of peak and off-peak costs. These results
are presented in Table 7. There are a number of implications
of the results presented in Table 7. At present, it is not
possible to relate distance to total cost, as it would be
necessary to segregate the samples by TC and D, so that an
analysis could be performed for those sample points for which
the restriction &TC/6D > o holds.
First, net altitude, in general, is not an important deter-
minant of the average costs of delivered water for the CWW area,
but it is important where the typography is especially hilly, as
in zones C2 and C^b (see Figure 9). Another fact with respect
to the altitude variable present in Table 7 is that its magnitude
is less than the coefficient for distance, which reflects the
fact that, while the CWW supply area is hilly, it is not so
hilly as to cause altitude to rival distance in costs, especially
in transmission costs, where these two factors are principally
important.
99
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TABLE 7. IMPACTS OF ALTITUDE AND DISTANCE ON AVERAGE COSTS
OF DELIVERED WATER.
Zone C1t) - Peak Period
1. Residential
Ln (TC3) = -19.669 + 1.636 Ln (D) - .0341 Ln (A) DP = 25
(.006) (.088) (.0332)ns R2 = ,
2. Commercial
Ln (TC3) = -20.949 + 1.732 Ln (D) - .0028 Ln (A) DF » 25
(.001) (.0054) (.005)ns R2 = .999
Zone C1b - Off -Peak Period
3. Residential
Ln (TC3) = -25.515 + 2.171 Ln (D) - .0663 Lr (A) DF = 25
(.007) (.1126) (.0423)ns R2 = .964
4. Commercial
Ln (TC3) = -27.9695 + 2,3666 Ln (D) - .0294 Ln (A) DF = 25
(.0027) (.0170) (.0157)ns
Zone C2 - Peak Period
5. Residential
Ln (TC3) = -5.415 + .2994 Ln (D) + .0874 Ln (A) DF = 27
(.110) (.0314) (.0291) R2 = .794
6. Commercial
Ln (TC3) = -5.1693 •«• .2723 Ln (D) + .0891 Ln (A) DF = 27
(.114) (.0441) (.0271) R2 - .635
7. Industrial
Ln (TC3) = -4.2226 + .2161 Ln (D) + .0164 Ln (A) DF = 30
(.182) (.0730) (,0286)ns R2 . t
100
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Zone C2 - Off-Peak Period
8. Residential
Ln (TC3) = -5.9439 + .3618 Ln (D) + .0710 Ln (A) DF = 27
(.192) (.0548) (.0507)ns R2 = .635
9. Commercial
Ln (TC3) = -6.1139 + .3479 Ln (D) + .123 Ln (A) DF = 27
(.165) (.0637) (.0392) R2 = .585
10. Industrial
Ln (TC3) = -4.625 + .2522 Ln (D) + .0242 Ln (A) DF = 30
(.238) (.0954) (.0374)ns R2 = .192
Zone 0,^ - Peak Period
11. Residential
Ln (TC3) = -7.982 + .5128 Ln (D) + .1051 Ln (A) DF = 27
(.035) (.0458) (.0493) R2 = .830
12. Commercial
Ln (TC3) = -8.7062 + .5707 Ln (D) + .1174 Ln (A) DF = 39
(.0239) (.0322) (.0235) R2 = .904
13. Industrial
Ln (TC3) = -9.233 + .6228 Ln (D) + .103 Ln (A) DF = 29
(.0471) (.0887) (.0472) R2 = .630
Zone C5l3 - Off-Peak Period
14. Residential
Ln (TC3) = -9.475 + .641 Ln (D) + .1223 Ln (A) DF = 27
(.0503) (.065) (.070) R2 = .789
15. Commercial
Ln (TC3) = -10.0089 + .686 Ln (D) + .126 Ln (A) DF = 39
(.0271) (.0365) (.0266) R2 = .912
16. Industrial
Ln (TC3) = -10.785 + .7704 Ln (D) + .0914 Ln (A) DF = 29
(.063) (.1196) (.0637)ns R2 = .589
Note: All coefficients except those marked by ns are significant
at 95% level or more.
-------
A second major implication is that disuance is seen to be
a major determinant of the AC of delivering water, and the high
AC elasticities (up to 2.3) imply substantial diseconomies to
distance, (although we have no direct measure of the total cost
elasticity). The apparent finding of substantial diseconomies
with respect to distance indicates that there are rather definite
limitations to the economic size of water supply areas. Of
course, an economic area cannot be defined on the basis of one
set of cost estimates, as it would be necessary to compare the
costs with the costs of serving outlying areas from another
location in order to define the boundary of a service area. A
critical factor then will be the trade-off involving in A&T scale
economies with the diseconomies of T&D. A third finding of the
regressions in Table 7 is that off-peak AC elasticities are
greater than the peak elasticities for the distance variable,
that is, the diseconomies are greater for the off-peak users.
While more investigation of this point is in order, this in-
dicates "scale" economies in peak facilities with respect to
distance, meaning that the diseconomy for peak facilities rises
less rapidly than for off-peak.
In general, it appears that significant cost economies of
scale can exist in transmission of water in addition to the
economies usually associated with the treatment process. But,
these results also imply that cost elasticity varies over the
total service area (increasing with respect to distance) and
that limits do exist to the economic area of a water utility.
Aggregated Cost Functions
In this section, we examine various combinations of the
data. Such combinations, however, typically create statistical
problems, one of which is heteroskedasticity (unequal variances
among the observations) the presence of which violates least
squares assumptions. Upon examination of the data utilized
here, little to no variation was found in the extimate of var-
iance for distance and altitude variance from one sample to the
next. In addition, the differences among the variances that
do exist diminish after a logarithmic transformation of the
data is performed. Much variation in the variances for quantity
exists from one sample to the next and especially across user
groups. But, this also decreases upon a logarithmic trans-
formation, not only across user groups, but also over service
areas.
A total of 16 combinations of the 24 samples was conducted.
Nine of these involve aggregating all user groups within a zone.
Five of the remaining seven were divided into residential,
commercial, and industrial segments. Two of five were residen-
tial: one for the two service zones east of the treatment plant
(RES), the other for the seven service zones north and west of
the plant (RWS). Likewise, two other data sets (CES and CWS)
102
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TABLE 8. PEAK AND OFF-PEAK COST ELASTICITIES FOR QUANTITY.
Zone C1_ - Peak Period
d.
Ln (TC,,) = -1.5491 + .7253 Ln (Q) DF = 108
(.503) (.0236) R2 = .897
Zone C1Q - Off-Peak Period
a.
Ln (TC^ = -1.6341 -f .7238 Ln (Q) DF = 108
(.5367) (.0274) R2 = .866
Zone Bp - Peak Period
Ln (TO,) = -1.6974 + .5774 Ln (Q) DF = 63
(.524) (.0396) R2 = .771
Zone B2 - Off-Peak Period
Ln (TC,,) = -1.8841 + .5118 Ln (Q) DF = 63
(.4626) (.0459) R2 = .664
Zone B2 - Off-Peak Period
Ln (TC1) = -1.8841 + .5118 Ln (Q) DF = 63
(.4626) (.0459) R2 = .664
Note: All coefficients significant at the 95% level or more,
103
-------
were created by partition of the commercial data. The remaining
data set (DN) of the five included all industrial sample points
north and west of the treatment plant. No industrial samples to
the east had been collected. The final two data sets (TES and
T¥S) of the 16 contained all the data points east of the treat-
ment plant in one group and all data points north and west in
the other. Linear, square root and multiplicative specifications
were tested, but as before, the multiplicative form gave the
best results, and these are presented here.
Results from estimation of equation 5-1 in Table 8 indicate
the existence of cost economies with respect to distance for all
zones. Estimated cost elasticity values for the nine zones
range from .5596 to .7449 for the peak period and from .5118 to
.7238 for the off-peak period. In addition, though the peak
period values are greater than off-peak, they are statistically
not significantly different from one another.
For the other seven samples, the regression results show
that the cost elasticities of quantity for commercial and
industrial users are significantly greater than that for
residential samples for peak and off-peak periods, though all
of their estimates are very much below a value of one. The
regression equations in Table 9 for samples RWS (all residential
sample points to the west and north of the treatment plant) and
DN (all industrial sample points to the west and north of the
treatment plant) and DN (all industrial sample points to the
west and north of the treatment plant) indicate the difference
in cost elasticity estimates.
TABLE 9. RESIDENTIAL AND INDUSTRIAL SAMPLES.
Sample RVTS - Peak Period
Ln (TO,) = -1.925 + .4211 Ln (Q) DF = 226
(.3205) (.0233) R2 = .591
Sample RWS - Off-Peak Period
Ln (TC.,) = -1.988 + .3769 Ln (Q) DF = 226
(.3656) (.0259) R2 = .484
Sample DN - Peak Period
Ln (TO,) = -1.5074 + .7463 Ln (Q) DF = 201
(.606) (.0192) R2 = .882
104
-------
Sample DM - Off-Peak Period
Ln (TC,,) = -1.4795 + .7166 Ln (Q) DF = 201
(.609) (.0198) R2 = .867
Note: All coefficients significant at the 95% level or more.
Estimation of equation 5-2 again provided no information
on the relation between total cost and the distance/altitude
variables, as in general, the estimator of the distance/altitude
parameters were statistically insignificant. Quantity again
accounted for the greater part of the variance explained.
Estimation of equation 5-3 using the data from the 16
samples provides some interesting results. This form examines
only the association between cost per CCF and the distance/
altitude variables. The following five results appear the most
important.
First, for the nine zones, cost elasticity estimates in-
crease as the distance to the zone increases (see Table 10).
Using any of the paths through the nine zones as outlined in
Figure 9, it is easy to see that along each path, the cost
elasticity value increase.
Secondly, the difference between off-peak and peak average
cost elasticities increases for the more distant zones. This
implies that the diseconomies of distance increase more rapidly
for off-peak costs than for peak, which is consistent with the
earlier findings' of the AC elasticities.
Thirdly, no significant relationship between cost and
altitude was detected.
Fourthly, as seen in Table 11, industrial cost elasticity
based on the combined samples is found to be significantly lower
(at better than the 99% level) with respect to distance than the
cost elasticities for residential and commercial sample sets.
This was not evident in the zonal breakdown for user groups.
Fifthly, an examination of peak versus off-peak cost
differentials for samples TES (all sample points east of the
treatment plant) and TWS (all sample points west and north of
the treatment plant), reveals that a statistical difference
between peak and off-peak differentials exist for the system as
a whole (see Table 12;, but the numerical difference is not very
large. As shown in Table 13, the 95% confidence interval over-
lap.
105
-------
TABLE 10. AVERAGE COST ELASTICITIES ARRAYED BY DISTANCE.
Zone Paths Peak Off-Peak Difference
B1
B2
C1a
C1b
C3a
C3b
C4a
C4b
Note:
0.1367
0.3095
0.1735
1.7189
0.1482
0.5522
0.1159
0.2824
0.1656
0.2758
0.1813
2.3406
0.1681
0.6796
0.1152
0.3642
These coefficients are for the distance variable
All coefficients significant
-0.0289
0.0337
-0.0078
-0.6217
-0.0199
-0.1274
0.0007
-0.0818
in AC = f(A,D).
at 95% level or more.
TABLE 11. INDUSTRIAL AVERAGE COST ELASTICITIES.
Sample RWS - Peak Period
Ln (TC,) = -6.256 + .3976 Ln (D) + .042 Ln (A) DF = 225
(.149) (.0224) (.0052) R2 = .642
Sample RWS - Off-Peak Period
Ln (TC3) = -6.6428 + .4336 Ln (D) + .0459 Ln (A) DF = 225
(.176) (.0264) (.0062) R2 = .606
Sample DN
Ln (TC3) = -4.215 + .2158 Ln (D) + .0251 Ln (A) DF = 200
(.1051) (.0181) (.0035) R2 = .589
Sample DN
Ln (TC,) = -4.459 + .2387 Ln (D) + .0277 Ln (A) DF = 200
(.1276) (.0220) (.0042) R2 = .543
Note: All coefficients significant at the 95^ level or better.
106
-------
TABLE 12. PEAK AND OFF-PEAK AVERAGE COST ELASTICIES.
Sample TES - Peak Period
Ln (TC3) = -5.443 + ..3652 Ln (D) + .0169 Ln (A) DF = 125
(.0656) (.0154) (.0063) R2 = .820
Sample TES - Off-Peak Period
Ln (TC,) = -5.6377 + .3909 Ln (D) + .0067 Ln (A) DF = 125
(.1636) (.0149) (.0061) R2 = .846
Sample TWS - Peak Period
Ln (TCj = -5.4986 + .3321 Ln (D) + .0321 Ln (A) DF = 674
(.141) (.0128) (.0028) R2 = .576
Sample TWS - Off-Peak Period
Ln (TC^) = -5.854 + .3651 Ln (D) + .0356 Ln (A) DF = 674
(.1636) (.0149) (.0032) R2 = .576
Note: All coefficients significant at 95% level or better, unless
indicated.
TABLE 13. 9596 CONFIDENCE LIMITS FOR DISTANCE COST ELASTICIES.
Peak
Off-Peak
TES
Lower Limit
.3350
.3617
Upper Limit
.3954
.4201
TWS
Lower Limit
.3070
.3359
Upper Limit
.3573
.3943
107
-------
In summary, a significant positive relationship was found
to exist between distance and average cost, and less frequently
between altitude and average cost. In addition, the elasticity
of average cost with respect to distance was greater than one
for one service zone.
Industrial water supply cost elasticity estimates with
respect to quantity were found to be significantly greater than
estimates for residential water supply while with respect to
distance were lower than the residential estimates of elasticity
Estimates of commercial water supply elasticity were close to
those for industrial with respect to quantity, yet close to
residential estimates with respect to distance.
In examination of peak versus off-peak costs, the following
results were obtained. No significant difference exists between
peak and off-peak costs with respect to distance in a general
formulation all zones combined, but important differences do
occur in those zones most distant from the treatment plant.
Also, peak cost elasticity of quantity was found to be generally
greater than that for off-peak cost estimates.
108
-------
PART B: COST-RA'x.^ DIFFERENTIALS
For the analysis of cost-rate differentials, we have chosen
to examine the value of net revenue to the CWW for each account
examined in the sample. A net revenue differential (TRA - TC.^)
for each water account i is a cost-rate differential with its
signs reversed, and multiplied by Q, the quantity of water
consumed.
The current rate structure of the CWW does not differentiate
among users in terms of differential costs (peak, off-peak,
altitude, and for the most part distance), with the exception
that users outside of the city are charged a high rate (see
Table 5); but it does use a declining block rate schedule,
which is supposed to reflect the presence of scale economies in
water supply.
For an analysis of cost rate differentials, such a rate
schedule would lead us to expect the following:
1 - Off-peak users are subsidizing peak users;
2 - Those accounts closest to the A&T facilities are
subsidizing those more distant; and
3 - Small users are subsidizing large users.
However, despite the fairly detailed analyses conducted for
this study, unequivocal answers will be difficult to come by.
For example, when service zones were aggregated (Table 9), the
peak cost elasticities were greater than the off-peak, but when
disaggregated, as in Table 5, this pattern was sometimes reversed
(c.f. zone £2'* Nonetheless, we shall endeavor to draw whatever
generalizations seem valid.
Rate Structure and Overall Cost Elasticities bv Customer
Table 14 presents data on actual water use by customer class
for the CWW service area. This table averages peak and off-peak
water use, and thus shows each group in the top rate block of
Table 6. It is generally expected, however, that the incremental
cubic foot of water consumed by residential customers will fall
in the top rate block, commercial users in the second, and
industrial users in the third. This data, compared with the
109
-------
TABLE 14. MEAN WATER USE BY CUSTOMER CLASS.
User Group
Average Day Quarterly
Mean Water Consumption
Rate Block Applicable
for User Group
Residential
Commercial
Industrial
4266 cubic feet
50769 cubic feet
172224 cubic feet
Top
Top
Top
110
-------
findings in Table 9 suggests that (1) even if industrial users
paid the same incremental charge as residential consumers, since
the industrial cost elasticity is greater than the residential,
residential customers are subsidizing industrial users on an
incremental basis; (2), if the typical large industrial user
falls in the third (or lowest) rate block, then the subsidy is
greater still. The exact and full impact of the subsidies
would require more analysis. Thus, it appears that the CVTW
water structure does lead to such subsidization. Bringing rates
into line with costs would require the use of the cost functions
developed in Section IV.
Analysis of Computer Constructed Maps
In order to generate more detailed analysis regarding the
presence and distribution of cost-rate differentials, the costs
and revenues were computed for each sample point, and the result-
ing distributions were mapped. The boundaries of the resulting
regions were determined by pre-set ranges for the differentials,
and thus do not conform to the regions established for the
purpose of the cost analyses reported above. The contour maps
shown here have suppressed some of the detail in cost-rate
differentials in order to present a clearer view of the patterns.
Delivered Cost Comparisons
Figures 14 and 15 present the spatial distribution of off-
peak and peak period costs respectively for all classes combined.
The range of values for the 6 regions indicate that cost of
supply to region 4 is almost twice as much as that to region 1.
Region denoted as 5 and 6 are even higher in supply cost, but
represent a relatively small portion of the utility1 s service
area. It appears, then, that a significant spatial difference
in water supply costs does exist.
Two findings are of note. First, the peak and off-peak
cost regions generated by this analysis do not correspond. There
are substantial overlaps, but comparisons of the two maps show
considerable shifting in the cost contours. Secondly, where
region numbers do coincide, the peak-costs per CCF tend to be
less than the off-peak. It should be noted however, that more
variation exists on the peak map as well as a greater number of
higher cost areas. Thus, comparison of a specific point on the
two maps will frequently show the point experiencing higher peak-
costs than off-peak, often the same, and seldom less. The
equations for generating the cost estimates are equations 4-8
and 4-16, divided by the respective
These comparisons are complemented by Figure 16 and the
associated Tables 15, 16 and 17. Milepoints are indicated, and
the relevant peak and off-peak costs are noted—the information
is the same as contained in Figures 14 and 15. Resource
111
-------
TABLE 15. RESIDENTIAL NET REVENUES.
Mile-
Point
0-1
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Route C1
Off -Peak
.09 - .16
0.00 - .09
0.00 - .05
0.00 - .05
.05 - .09
.05 - .09
.05 - .09
.09 - .13
.09 - .13
.16 - .20
.16 - .20
.16 - .20
.16 - .20
.16 - .20
.16 - .20
.09 - .13
0.00 - .05
.05 - .09
-
-
-
i
Peak
.11 - .18
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.08 - .11
.11 - .14
.18 - .21
.18 - .21
.18 - .21
.14 - .18
.14 - .18
.18 - .21
.11 - .21
.08 - .11
.03 - .08
-
-
-
-
Route C^
Off -Peak
.09 - .16
0.00 - .09
0.00 - .05
0.00 - .05
.05 - .09
0.00 - .05
0.00 - .05
0.00 - .05
0.00 - .05
.05 - .09
.05 - .09
.09 - .13
.13 - .16
.09 - .13
.13 - .16
.13 - .16
.13 - .16
.09 - .13
.09 - .13
.09 - .13
.13 - .16
.09 - .13
Peak
.11 - .18
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.03 - .08
.08 - .11
.14 - .18
.14 - .18
.11 - .14
.14 - .18
.14 - .18
.11 - .14
.11 - .14
.11 - .14
.11 - .14
.11 - .14
.11 - .14
112
-------
TABLE 16. COMMERCIAL NET REVENUES.
Mile-
Point
0-1
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Route C.
Off-Peak
.06 - .10
.03 - .06
-.01 - .03
-.01 - +.03
.03 - .06
.03 - .06
-.01 - +.03
.03 - .06
.03 - .06
.10 - .14
.10 - .14
.10 - .14
.10 - .14
.10 - .14
.10 - .14
.03 - .06
-.01 - +.03
-.06 - -.01
-
-
-
-
Peak
.08 - .11
.02 - .05
-.02 - +.02
-.02 - +.02
-.02 - +.02
.02 - .05
-.02 - +.02
.02 - .05
.05 - .08
.11 - .13
.11 - .13
.11 - .13
.11 - .13
.11 - .13
.11 - .13
.05 - .11
-.02 - +.05
-.02 - +.02
-
-
-
-
Route C,
Off-Peak
.06 - .10
.03 - .06
-.01 - +.03
-.01 - +.03
-.01 - +.03
-.01 - +.03
-.01 - +.03
-.01 - +.03
-.01 - +.03
-.01 - +.03
-.01 - +.03
-.06 - -.01
-.01 - +.03
-.06 - .01
+.03 - +.06
+.03 - +.06
+.03 - +.06
+.03 - +.06
-.06 - -.01
-.01 - +.03
.03 - .06
.03 - .06
Peak
.08 - .11
.02 - .05
-.02 - +.02
-.02 - +.02
-.02 - +.02
-.02 - +.02
-.02 * +.02
-.02 - +.02
-.02 - +.02
-.02 - +.02
.02 - .05
-.02 - +.02
.02 - .05
.02 - .05
.02 - .05
.08 - .11
.08 - .11
.08 - .11
.02 - .05
.02 - .05
.05 - .08
.05 - .08
113
-------
TABLE 17. INDUSTRIAL NET REVENUES.
Mile
Point
0-1
1-2
2-3
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Route C^
Off -Peak
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.06 - -.03
-.03 - +.01
-.03 - +.01
-.06 - -.03
-.03 - +.04
.04 - .07
.04 - .07
.04 - .07
.01 - .04
.01 - .04
.01 - .04
.01 - .04
.01 - .04
-
-
-
-
Peak
-.04 - -.01
-.04 .-1
-.04 - -.01
-.04 .01
-.01 - +.01
-.04 - -.01
-.01 - +.01
-.04 - -.01
-.04 - -.01
-.01 - +.01
.04 - .06
.04 - .06
.04 - .06
.04 - .06
.01 - .04
.01 - .04
.01 - .04
.01 - .04
-
-
-
-
Route G^
Off -Peak
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.06 - -.03
-.06 - -.03
-.06 .03
-.06 - -.03
-.06 - -.03
-.06 - -.03
-.06 - -.03
-.06 .03
-.06 - -.03
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.03 - +.01
-.06 - -.03
-.06 - -.03
-.03 - +.01
-.03 - +.01
Peak
-.04 - -.01
-.04 - -.01
-.04 - -.01
-.04 - -.01
-.04 - -.01
-.04 - -.01
-.04 - -.01
-.07 - -.04
-.04 - -.01
-.04 - -.01
-.04 - -.01
-.07 - -.07
-.04 .01
-.01 - +.01
-.01 - +.01
-.01 - +.01
-.01 - +.01
-.01 - +.01
-.04 - -.01
-.01 - +.01
.01 - .04
-.01 - +.01
114
-------
VJ1
AREA
1
2
3
4
5
6
OFF-PEAK
COST RANGES
.14 to .18
.18 to .22
.22 to .25
.25 to .29
.29 to .3*»
.34 to .40
Figure 14. Spatial mapping of off-peak period costs for all classes combined,
-------
AREA
1
2
3
k
S
6
PEAK
COST RANGES
.]k to .17
.17 to .20
.20 to .22
.22 to .25
.25 to .29
.29 to .33
Figure 15. Spatial mapping of peak period costs for all classes combined.
-------
— CITY BOUNDARY
®= TREATMENT PLANT
Figure 16. Water main routes with indicated mile points.
-------
constraints prevented a more detailed analysis by sample point
instead of the fairly wide required analyses.
Figure 17 presents a mapping of peak minus off-peak costs
per CCF. Here region 6 (note changed definition) is the only
area where peak costs exceed off-peak cost while region 1, 2,
and 3 represent areas with off-peak costs significantly above
peak period costs. This result, as noted in previous discussion,
may occur because the peak period plant is larger in scale which
can provide lower unit costs.
Net Revenue Comparisons
Figures 18 and 19 present findings on what the cost-rate
differentials (analyzed here as net revenues to the CWW) would
be if it employed a uniform price of $.20/CFF (the average cost
per CCF of water supplied by the CWW). These maps indicate
that fairly significant cost-rate differentials would appear in
such a situation. In general, those closer to the treatment
plant would pay in excess of costs, and those more distant would
pay less than costs.
The remaining maps present information on the spatial
distribution of net revenues during peak and off-peak periods
for residential, commercial and industrial users. As mentioned
earlier, it is expected that the marginal unit of water con-
sumption for the typical residential user group falls in the
top block of the rate structure, commercial in the middle block,
and industrial in the lowest. Thus, rates for those levels
were assigned to each group for calculation of net revenue.
Therefore, the relevant rate for residential users in 1.20/CCF
for inside city users and $.35/CCF for outside city users,
where the $.35/CFF rate reflects the extra costs of providing
service to the more distant users. Commercial users fall in
the $.16/CCF and $.28/CCF brackets for inside and outside city
users respectively. And finally, industrial users are charged
$.12/CCF inside and $.21/CCF outside the city.
Figures 20 and 21 show that only for region 1, a very small
part of the two maps, is the net revenue negative, implying that
the cost is greater than the price. All other regions generate
positive net revenues, especially in the outlying areas. Figures
22 and 23 provide similar information for commercial users except
that the negative area increases as would be expected with the
lower rate.
Figures 24 and 25 present the mapping of industrial net
revenues. Here regions 5 and 6 remain as the only areas with
positive net benefits. Again, the areas with the lowest net
revenues are inside the city, though as mentioned before, this
results from the contrast between the city and the county rates.
118
-------
WATER RATES
PER CCF
MINUS DELIVERED
AREA COSTS
1 -.20 to -.I**
2 -.14 to -.09
3 -.09 to -.05
4 -.05 to -.02
5 -.02 to .02
6 .02 to .06
Figure 17. Water rates per CCF minus off-peak delivered costs.
-------
WATER RATES
PER CCF
MINUS DELIVERED
AREA COSTS
1 -.13 to -.09
2 -.09 to -.05
3 -.05 to -.02
A -.02 to 0.0
5 0.0 to .03
6 .03 to .06
Figure 18. Water rates per CCF minus peak delivered costs.
-------
PEAK MINUS
AREA OFF-PEAK COST
1 -.08 to -.06
2 -.06 to -.0^
3 -.Ol» to -.03
4 -.03 to -.02
5 -.02 to 0.0
6 0.0 to .01
Figure 19. Peak/off-peak cost differentials.
-------
I\J
REVENUES
MINUS PEAK
AREA COSTS-RESIDENTIAL
1 -.01 to .03
2 .03 to .08
3 .08 to .11
4 .11 to .14
5 .14 to .18
6 .18 to .21
Figure 20. Net revenues for peak period residential water use.
-------
REVENUES MINUS
OFF-PEAK COSTS
AREA RESIDENTIAL
1 -.05 to 0.0
2 0.0 to .05
3 .05 to .09
k .09 to .13
5 .13 to .16
6 .16 to .20
Figure 21. Net revenues for off-peak residential water use,
-------
REVENUES
MINUS PEAK
COSTS
AREA COMMERCIAL
1 -.06 to -.02
2 -.02 to .02
3 .02 to .05
A .05 to .08
5 .08 to .11
6 .11 to .13
Figure 22. Net revenues for peak commercial water use.
-------
ro
VJl
REVENUES MINUS
OFF-PEAK COSTS
AREA COMMERCIAL
1 -.11 to -.06
2 -.06 to -.01
3 -.01 to .03
4 .03 to .06
5 .06 to .10
6 .10 to .14
Figure 23« Net revenues for off-peak commercial water use.
-------
REVENUES
MINUS PEAK
COSTS
AREA INDUSTRIAL
1 -.11 to -.07
2 -.0? to -.01*
3 -.04 to -.01
k -.01 to .01
5 .01 to .Ok
6 .04 to .06
Figure 24. Net revenues for peak industrial water use,
-------
ro
REVENUES MINUS
OFF-PEAK COSTS
AREA INDUSTRIAL
1 -.14 to -.10
2 -.10 to -.06
3 -.06 to -.03
A -.03 to .01
5 .01 to .04
6 .04 to .07
Figure 25- Net revenues for off-peak industrial water use.
-------
The general implication of these findings is that residences
are subsidizing commercial and industrial uses of water, as
residential customers showed virtually no cases of costs exceed-
ing revenues, but this situation does occur for commercial and
industrial users. Tables 15, 16 and 17 present detailed infor-
mation on this point for the two water main routes presented
earlier, C^ and C,.
One final piece of information on the spatial variation
in net revenues is shown in Tables 18 and 19. Specific
residential customers with a 5/8" meter were selected along
routes Cx and C,, and calculations of total revenue and total
costs were made for each, based on the customers actual water
use, for both peak and off-peak periods.
As indicated in the tables, the magnitude of these net
revenues range from -1.67 to 3.5^ per off-peak quarter and -1.70
to 5.00 per peak quarter on route C^. Also, they range from
-1.52 to 3.26 per off-peak quarter and -1.76 to 2.50 per peak
quarter on route C,. Extending this to a year, the net revenues
may vary from $7.00 to $20.00 for a typical residential customer.
An interesting element is the change in the values along the
routes for inside and outside city users. For both routes, the
net revenues become more negative (cost exceeds revenue) as
distance increases for inside city users, while for outside
city users, the net revenues decrease though remain positive.
As noted before, this occurs because of the higher rate in the
county. The major point of these results is that costs increase
with respect to distance, use of the present quasi-distance
pricing does decrease the possible subsidization that could
occur from a return to a uniform zonal price. But, significant
subsidizations still existing could be diminished through a
redefinition of pricing zones to more accurately reflect water
supply costs.
128
-------
TABLE 18. RESIDENTIAL WATER USERS ROUTE C.
Customer
1
2
3
4
5
6
7
8
9
10
11
12
Rate
Inside
Inside
Inside
Inside
Inside
Inside
Out
Out
Out
Out
Out
Out
Distance
3.85
3.92
4.59
5.60
6.92
8.24
9.77
10.91
13.85
14.46
17.38
18.02
Quantity(CCF)
Off-
Peak
21
24
31
23
18
24
17
18
20
17
20
16
Peak
22
25
23
24
20
23
16
29
22
18
18
16
Total Revenue
Off-
Peak
$4.70
5.30
6.70
5.10
4.50
5.30
9.00
9.00
9.00
9.00
9.00
9.00
Peak
$4.90
5.50
5.10
5.30
4.50
5.10
9.00
12.15
9.70
9.00
9.00
9.00
Total Cost
Off-
Peak
$5.67
6.03
6.70
6.26
5.58
6.97
5.46
5.73
6.26
5.72
9.41
8.79
Peak
o
vo
-------
TABLE 19. RESIDENTIAL USERS ROUTE C-
Customer
1
2
3
4
5
6
7
8
9
10
11
12
Rate
Inside
Inside
Inside
Inside
Inside
Inside
Inside
Out
Out
Out
Out
Out
Distance
5.70
8.01
9.03
10.26
10.99
12.86
13.45
14.75
15.65
19.58
20.13
20.63
Quantity(CCF)
Off-
Peak
26
16
17
22
25
17
19
22
19
25
13
18
Peak
34
18
20
14
20
25
27
20
21
27
22
23
Total Revenue
Off-
Peak.
$5.70
4.50
4.50
4.90
5.50
4.50
4.50
9.70
9.00
10.75
9.00
9.00
Peak
$7.30
4.50
4.50
4.50
4.50
5.50
5.90
9.00
9.35
11.45
9.70
10.05
Total Cost
Off-
Peak
$6.34
5.45
5.64
6.16
7.02
5.71
5.94
6.44
6.89
9.14
6.44
7.56
Peak
$7.20
5.72
6.01
5.26
6.26
6.67
6.92
6.50
7.12
8.96
8.14
8.25
Net Revenues
Off-
Peak
$-.64
-.95
-1.14
-1.26
-1.52
-1.21
-1.44
3.26
2.11
1.61
2.56
1.44
Peak
$ .10
-1.22
-1.51
- .76
-1.76
-1.17
-1.02
2.50
2.23
2.49
1.56
1.80
-------
SECTION VI
INTRODUCTION TO PLUMBING PERMITS
AND WATER USE
INTRODUCTION
Planning is a problem for any unit of government and is
especially important for those activities characterized by
capital intensive facilities, such as water supply. The long
design and construction periods involved (up to 15 to 20 years)
make it imperative to plan much in advance if potential users
will find water available at a time and place where they are
willing to pay for it.
In the case of water supply systems, the planning problem
is to anticipate these three characteristics of development:
its geographic direction, its pace and its intensity. Typically
information of population movement and highway development is
coupled with the water system planner1s experience and pro-
fessional intuition, and these serve as the principal elements
of the planning process. The process ranges from the relatively
formalized and detailed engineering studies to informal, in-
tuitive or "seat of the pants" plans. The gathering of his-
torical data is a usual part of making predictions, and since
the development of a specialized data base as an input into water
system planning and analysis is usually an expensive undertaking,
it has been suggested that building permit data be utilized for
this purpose. The apparent benefit to water system planning from
employing such information lies in the fact that it is already
being gathered on a continuous basis, and thus should be obtain-
able at a relatively low incremental cost.
However, while data on plumbing permits are gathered on a
continuous basis, they are not gathered for water supply purposes,
and thus are not likely to be immediately suitable for water
system analysis. This was, indeed, one of the findings.
The question then is whether there is sufficient potentially
significant information in the data base to make it worthwhile
to modify it and/or supplement it in order to serve as a guide
for water system development. The suitability of these data for
this purpose would in large measure depend on the existence of
131
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sufficient lead time between the date of permit application and
the date of first water use in order to acquire and factor the
data into the planning process, and to carry out the necessary
construction to meet the predicted future demand.
For this purpose, two types of empirical analyses were
conducted in this study:
1. A simple analysis of the historical lags which have
existed in a recent period (1969-1974) between plumbing
permits (PP) applications and the date of_initial water
use. The statistics of the sample mean (x), srtandard
deviation (s) and coefficient of variation (x/s) are
presented as measures for these lags.
2. An attempt to estimate a lagged relationship between
system wide water use and PP, where other causal
variables are held constant. This work was incon-
clusive, as the variables of interest were not
statistically significant while the hypothesis examined
(that there exists a causal relationship between system
wide water use and PP) may in fact be unsupported, the
fact that the sample was drawn from a community which
has experienced little or no growth suggests that the
data base does not provide a good test of the hypothesis.
Also, the original scope of the research (with attendant
resources) precluded a further examination of whatever
econometric problems were implicit in the techniques
chosen to uncover the lags. We can say if there in
fact exists a significant relationship, it is not so
strong or obvious as to be insensitive to various
estimation techniques.
The objectives of the research reported here then are:
1. To estimate the time lags which exist between the date
of PP application and first water use at that address.
2. To test the hypothesis that these lags have a measureable
impact on system wide water use when other variables are
held constant.
132
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SECTION VII
METHODOLOGY, EMPIRICAL RESULTS AND RECOMMENDATIONS
GENERAL PURPOSE
'Ihis chapter presents brief descriptions of the empirical
methodologies employed for data collection and estimation of
relationships.
The Data Base
The data base was drawn from three basic sources: (1) the
City of Cincinnati building and plumbing permit applications and
permits, (2) the Cincinnati Water Works, and (3) the Census.
The period chosen for analysis was 1969 to 1974, and the data
gathered on a quarterly basis.
The City of Cincinnati, exclusive of the surrounding
suburbs and unincorporated county areas, was chosen for analysis
for a variety of reasons, principal among which are (a) the lack
of good and/or accessible record keeping outside the city and
(b) the differences among permit systems, such that comparability
is low among them.
The period of 1969-1974 was chosen because 1969 represented
the first year in which water consumption records were sufficient-
ly organized to be retrievable within the resource constraints of
this project. As water meters are read quarterly only, this
became the basic unit of data, and consequently the number of
permits also were aggregated to a quarterly basis.
Analytical Methodologies
As indicated earlier, there are two principal empirical
questions investigated in this report—(1; estimation of the lag
(in days) that exists between the first recorded data for a
building permit applicator (or plumbing permit) and the date of
first use and also continuous use of water at the observed
address; (2) estimation of the impact of building permits on
system wide water use for the observation period. For the first,
question, the lags were estimated by (a) drawing a random and
stratified sample (22 data points per quarter) for the time
period 1969-1974, (b) finding the date of building and plumbing
permit application, (c) matching the address on the building
133
-------
permit with the water consumption account, (d) estimating the
dates of first and continuous water use, and (c) calculating
the days lapsed between the dates. The statistics for these
computations appear later in this chapter.
The second question requires more complex methods in order
to investigate it. The objective is to estimate and test the
lagged impact of PP on system water use, holding constant other
variables which affect water use. These estimates would be
potentially useful as additional information regarding the
capacities of the various acquisition, treatment and distribution
systems by providing measures of the rate at which system and
sub-system capacities are being approached.
The estimation of lags between variables is done fairly
routinely in economics, especially where there is a need to
measure the effects of changes in fiscal and monetary policy
variables such as taxes, deficits, money supply, etc.
It was hypothesized that the impact on water use as earlier
reflected by PP would be distributed over several time periods,
instead of being concentrated in Just one or two periods. As
the basic unit of time chosen for analysis in this study is
the quarter, it was hypothesized that the dates of initial
water use associated with a specific period in which PP were
applied for would first rise, reach a peak, and then taper off
over time, as in Figure 26.
Frequency
0
Time in quarters
Figure 26. Distribution of initial water use,
134
-------
The distribution in fact follows this form for Cincinnati.
In terms of the impact on system water use, the weight to be
attributed to each subsequent time period in terms of impact
on water use will also decline. That is, the farther back one
goes in time prior to the time period in which water use is
measured, the less important will be the PP applied for in prior
periods, since their peak impacts will become increasingly
likely to have past. This concept is illustrated in Figure 27
where i is the time period, w* is the weight:
0 1 234 5 . . . i (lag)
Figure 27. Declining weights for plumbing permits.
The functional form for statistical estimation for such a
relationship is termed the Pascal Lag, and is given in equation
(1)
i * w2Xt-2 •*
in which the weights are estimated as:
w< » (i + r - l)!/i ! (r - 1)! (1 -
135
-------
where r is an integer to be chosen, and \ is estimated from the
data.*
In the analysis undertaken in this study, other variables
included in the regression equation were precipitation, price
of water, family income, population, and temperature. Exact
variable definitions are given below.
Empirical Findings
Simple Lags. This empirical analysis was conducted for the
three basic user classifications examined in this study: re-
sidential, commercial and industrial. The analysis was conducted
for new construction only, and does not apply to old construction
in which some form of plumbing replacement, modification or add-
ition took place. In Cincinnati, the preponderance of the permits
were for ,the classification of old buildings. The sampling pro-
cedure yielded 250 observations on new residences, 53 on new
commercial establishments, and 8 on new industrial plants. The
findings are summarized in Table 20.
This table shows the greatest lags for commercial use, the
industrial, and lastly, residential. The residential lag average
1.2 years, or about one year, three and one half months.
The commercial lags, however, exhibit the least variability,
as seen by the coefficient of variation, and industrial lags,
the most. This evidence suggests that the PP for commercial
uses of water may be the most useful, as they exhibit the
greatest lead or lag time, and the least variability—the re-
duced variability does reduce the risk and uncertainty associated
with them.
Pascal Lags
This analysis represents a first attempt to guage the impact
of PP on system-wide water use. The analysis was conducted in
two stages: (1) a regression with PP only (all for a given
quarter, not just the sample) and no attempt to control for other
exogenous influences on water use, and (2) all permits with
exogenous variables included. The regressions reported are not
the function in (1), but rather the relationship using instru-
mental variables. Equation (1) has not been derived due to the
inconclusive nature of the results. Also, the data was not
scaled to dimension it to \.
The results in Table 21 are for PP only, and do not support
the (simplistic) hypothesis that PP alone have an impact on water
*For a full discussion of the estimation technique, see
Jan Kmenta, Elements of Econometrics. MacMillan, 1971, pp.
487-491.
136
-------
TABLE 20. LAG TIME IN DAYS BY USER GROUP.
(D (2) (3)
Mean 95% Confidence Limits Coefficient of Variation
Residential
Initial Water Use 469.332 431.912 < » < 506.75 1.55
Continuous Use 476.552 438.746 < p, < 514.358 1.56
Commercial
Initial Water Use 543.962 434.619 < n < 653.305 1.37
Continuous Use 547.453 438.449 < u < 656.457 1.38
Industrial
Initial Water Use 486.875 310.316 < p, < 663.434 2.25
Continuous Use 490.250 314.260 < ^ < 666.240 2.27
Total
Initial Water Use 482.501 447.085 < u < 517.917 1.51
Continuous Use 488.987 453.349 < u < 524.618 1.52
-------
use. There are no significant values for the coefficients, or
for the R2's as shown by the F statistic.
The objective of the analysis of these lags with other
exogenous variables was attempted, but it was not possible to
carry out the analysis to such a point so as to say that an
estimable lag does or does not exist in the experience of the
Cincinnati system studied. It was desired to control for such
influences as precipitation, price of water, income, population
and temperature. Of these variables, the preliminary analysis
showed that only temperature explain a statistically significant
amount of the variance in water use. PP showed no effect.
In sum, with the data base that was selected for use in
this study, it proved possible to estimate only the simple lags
(days lapsed) between the date of plumbing permit application
and the dates of first and continuous water uses. Attempts to
hold constant other exogenous influences on water use and to
estimate a weighted distribution of lags was not successful.
This lack of success was probably due as much to the presence
of greater intractability of the procedure that was anticipated
as to the fact that the study area did not exhibit enough growth
for PP to have any demonstrable impact on water use. Application
of the procedure to a more rapidly growing area might prove
successful.
138
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TABLE 21 . TOTAL WATER CONSUMPTION AND PLUMBING PERMITS: ANALYSIS OF PASCAL LAGS
f
4
X2<
Constant
;t
ieta.
1
B2
JBeta2
R2
F
Constant
(
X1j
'" B1
t
(Beta1
X
0.1
8266519.39862
1831.86822
0.4011
0.12128
1081.84735
0.2422
0.07324
0.03226
0.33334
0.2
7272677.31940
1565.57693
0.3443
0.10422
1231.92541
0.2770
0.08386
0.02989
0 . 30807
0.3
6278835.40407
1299.28356
0 . 2837
0.08600
1382.00527
0.3086
0.09354
0.02718
0.27942
0.4
5284992.59275
1032.99567
0.2215
0.06725
1532.08221
0.3360
0.10199
0.02434
0.24942
0.5
4291150.16468
766.70123
0.1599
0.04861
1682.16447
0.3588
0.10906
0.02153
0.22006
\
0.6
3297307.73632
500.40983
0.1007
0.03064
0.7
2303464.92500
234.12194
0.0451
0.01376
0.8
1309622.98855
-32.17137
0.0059
-0.00180
0.9
315780.74059
-298.46323
0.0522
-0.01593
1.0
-678062. 52825
-564.75475
0.0937
-0.02862
-------
X,
Beta
X*
R
F
0.6
1832.24365
0.3769
0.11473
0.01893
0.19292
0.7
1982.32059
0.3908
0.11910
0.01662
0.16903
0.8
2132.40056
0.4010
0.12232
0.01466
0.14881
0.9
2282.47985
0.4080
0.12458
0.01305
0 . 1 3224
1.0
2432.56087
0.4126
0.12607
0.01176
0.11902
Notes:
1. Y = Weighted change in water use from period to period, i.e.
2. X* = PP issued in previous period (t-1)
3. X~ = PP issued in current period (t)
4. 23 periods were examined (n = 23)
-------
APPENDIX A
SUPPLEMENT TO SECTION IV, PART A
The relationship of static, friction, pressure, and
velocity elements to head was established in Bernoulli's equa-
tion for head-loss. Briefly, total head, H, in feet, can be
estimated from:
(A-1) H a PRk x P + Zikr + V2/2g + HL represents friction
loss as calculated by the Hazen-Wilxiams or Darcy-Weisbach
formulae.8
S , the static head per foot of pipe, is formulated as:
oL
s = Zikr/L1kr* pressure and velocity head per foot of pipe,
S , equals: Sp = (PRk x p + v2/2g)/Ljkr» Since, V =
, V2 = 16(4.7 nV.
Therefore,
(A-2) Sp = (P\ x P + 8Qkr ^Vp/L^. But, Qkr is
measured in cu. ft. per sec. To obtain cu. ft. per day, multi
ply by 6.032 x 10 sec. /day.
As a result,
(A-3) Sp - (PRk x P + (4.8256 x 105 Qk2r)/(tT2gD^kr) )/Ljkr.
Finally, friction head, HL, may be added or defined in the
Hazen- Williams equation.*1
(A-4) HL - (4.72688)Ljkr x Qkr8518 x c'1'8518 x
Hazen-Williams and Darcy-Weisbach equations can be
found in any standard engineering text on water supply trans-
mission.
Since the study area for this project relies on the usage
of the Hazen-Williams equation, that formula will be used.
141
-------
U-5) Sf = HL/L..kr = (4.72688) Q^
..kr
Note that Q,,,, here is also measured in cubic feet per second,
4
Therefore, after multiplying by 6.032 x 10 sec. /day,
Sf = (2.85125 x 105) Q^8518 x C'1 '8518 x D^87. Combining
terms, S + Sf + Sn can be derived.
a i p
(A-6) Sa * Sf 4 Sp = Zikr/Ljkr + (PRk x P + (4.8256
x
(2.85125 x 105) Qk;8518 x C"1 '8518
x D'
X Djkr '
142
-------
APPENDIX B
RESIDENTIAL WATER DEMAND: A LITERATURE REVIEW
GENERAL PURPOSES
This appendix will examine the research that has been
conducted on the determinants of residential water consumption.
The kinds of statistical methods that have been used to explain
residential water use and the different variables that have been
associated with these different analyses will be discussed.
The traditional way of estimating future water consumption
is the requirements approach (Grima, 1973» P« 60), where a unit
variable, such as the number of persons or number of service
connections, was selected as the basis for estimating water
demand. The amount of water that each was assumed to use was
then multiplied by the total number present to determine the
total amount of water consumed. Often, water use has been
measured on a per capita basis, where population is correlated
with water pumped (Larson and Hudson, 1951, p. 603). Such
measures have included Hanson and Hudson's (1956, p. 1347)
proposed formula for establishing water use based on the
following:
Water Sold to Residential Users
(No. of Services; (No. of Persons per Service;
Sometimes the number of homes was used as the measure of
water demand, but then it was discovered that the number of homes
did not necessarily give an adequate picture of the total amount
of water consumed, since two areas with the same number of homes
could have very different rates of water consumption.
It became apparent that water consumption varied from place
to place not only because of the number of persons or homes
present, but also because of other factors. Certain economic
factors were identified as being influential in explaining area
differences in water use by the use of a variety of statistical
techniques. In 1939, Pond showed that per capita domestic water
consumption varied between residential areas containing different
housing types. Graphical comparisons were employed by Larson
and Hudson in 1951 to discover that, instead of daily per capita
water consumption being correlated with the population of Illinois
communities, it was correlated with disposable income. Least
143
-------
squares estimates were next introduced into analysis. Wolff
(1957, p. 230) used least squares estimates to discover the
correlation between the percentage ratio of maximum day con-
sumption to average day consumption and the population of the
city. Fourt (1958) employed multiple correlation to discover
the influence of different social, climatic, and economic
variables on per capita residential water use. Both cross-
sectional and time series regressions were used to derive
equations based on comparisons of residential areas over space
and over time. Recently Saunders (1970) used principal com-
ponents analysis to determine what social and economic variables
are similar in their variation between different communities and
across the service area of the Louisville water works.
There are many different variables that affect residential
water consumption; some of these can be identified by household
surveys, such as garden watering, and the length of family
holidays (Grima, 1972, p. 79). Still others are difficult to
identify, such as household plumbing leaks, and therefore, it is
possible that large errors will be present in any estimating
equation of water consumption derived. Instead of adding more
variables to the equation to increase the amount of variation
explained, it is more important to select the variables that are
most significant or are applicable to policy making.
Various social and economic variables have been mentioned in
the literature as being significant in explaining variation in
water demand. These variables are roughly divided into five
groups: climatic variables, variables that measure the ability
to consume water, variables that identify the presence of water
consuming devices, measures of population density, and deter-
minants of the price of water.
The Influence of Climate
Climate's main effect on residential water consumption is
on water used outside of the home. The influence of climate on
water use varies in intensity with the different seasons. Water
use tends to peak during the summer when water is used for a
variety of activities related to the warm weather, including
lawn-watering, car-washing, filling swimming pools, and operat-
ing air conditioners (Fourt, 1958, p. 5). Of these uses, lawn
sprinkling is probably the most important. The amount of water
devoted to lawn sprinkling is in large part determined by both
precipitation and temperature. Forges (1957, p. 204) reports
that the per capita water demand between states varies directly
with the annual precipitation. During periods of significant
rainfall, water is stored in the grass roots zone and is enough
to cover the loss of moisture to evapotranspiration. In con-
trast, during periods of little or no rainfall, sprinkling must
be employed to counteract the withdrawal of moisture in lawns by
144
-------
evapotranspiration. Linaweaver, Geyer, and Wolff (1967, p. 273)
reported that usually daily average lawn sprinkling is nearly
equal to daily evapotranspiration. The nature of evapotrans-
piration is determined by the temperature, the amount of sunlight,
wind velocity, type of soil, and humidity (Linaweaver, Geyer, and
Wolff, 1967, P. 273).
The traditional way to determine what portion of residential
water demand is used in lawn sprinkling is to find the difference
in residential water use between a wet day and a dry day, and to
assume that this difference is the amount of water devoted to
lawn watering (Wolff, 1961, p. 1254). Howe and Linaweaver (1967)
suggest a way of calculating the amount of water needed for a
lawn or other area subject to irrigation that includes the effect
of evapotranspiration. In its simple form, their equation is
(1967, P. 21):
- °-6rs)
where:
q a the average summer sprinkling demand in gallons per
s» dwelling unit per day;
b «= area subject to irrigation by dwelling unit;
W_ » the summer potential evapotranspiration in inches;
5
r a summer rainfall in inches.
s
Howe and Linaweaver recognized that these physical requirements
are also subject to the influence of the economic status of the
residents, and the price of water. Therefore, they have amended
the above equation to (1967, p. 21):
ps
B
3 vB4 • u
where :
p a the marginal commodity charge applicable to average
summer total rates of use;
v = the value of the dwelling in thousands of dollars.
The differences in sprinkling demand from one area to
another became apparent in their statistical analysis of summer
^sprinkling (Howe and Linaweaver, 1967, p. 28). They examined
sprinkling demands in twenty-one residential areas in the United
States, ten in the West and eleven in the East, where the
accounts were metered and sewered. They discovered that the
variables, irrigable area and climate, were not always signifi-
cant explanatory variables as had been theorized. These
145
-------
equations included the following (1967, p. 28):
for metered and sewered connections in the West:
q« e • 3.053 - 0.703 log PQ+ 0.429 log v R2 = .674
3, B &
t-statistica 2.19* 1.88*
for metered and sewered connections in the East:
Q0 = - -0.784 - 0.793 log b + 2.93 log (W0 - 0.6r )
8 9 S S S
t-statistic 3.65** 6.83**
-1.57 log p_ + 1.45 log v.
o
t-statistic 8.26** 4.74** R2 » .927
The two climate variables appear only in the equation explaining
sprinkling demand in the East.
Other research has produced mixed results when using cli-
matic variables in regression equations of residential water
use. Wong (1972, p. 38) included the effect of climate on water
consumption by using the average summer temperature for each
observation with a price variable, and an income variable. He
found that this climatic variable was significant in explaining
variations in per capita municipal water demand in metropolitan
Chicago for the years 1951-1961 (1972, p. 40). Fourt (1958)
measured the influence of climate in another manner. In the
equation that he derived, he found that the number of days of
rainfall in the summer months was significant in explaining
water consumption in forty-four cities when used with the two
variables: persons per meter, and price (1958, pp. 7-8).
In Young's (I973t p. 1070) work on identifying factors
significant in determining water demand, he used the two climatic
measures, temperature and evaporation. They were removed from
his equation when he found that they were not significant or had
a sign contrary to the one hypothesized. (1973, p. 1070).
The different aspects of climate, such as precipitation and
temperature, can be most useful in explaining variations in
residential water consumption in two types of situations; first,
aThe level of significance for the t-statistic in these
equations and those following is denoted by * for significance
at the .95 percent confidence level and ** for significance at
the .99 percent confidence level.
146
-------
between cities of different climatic regions, and second, for
any number of cities over a period of years. Since climate
generally does not vary appreciably across the service area of
a single water utility, it probably is of little use in explain-
ing the spatial variations of water consumption in a city for a
single year.
The Influence of the Cost of Water
A set of water utility practices as influential on water
consumption as climate, and even more so at the micro level are
those concerned with the price of water. These price variables
include metering and rate schedules. Metering may be the most
important of these in affecting water consumption. A water
account is either metered, where the user is charged according
to how much he consumes, or charged a flat rate regardless of
how much water is consumed.
Metering can change water use trends and the shape of
consumption peaks. It can lower per capita consumption and
change the future trends of water use (Flack, 1967» p. 1341).
The philosophy behind metering is not to restrict water con-
sumption, but rather to prevent the waste of water (U.S.,
Congress, Senate, 1960, pp. 13-16). It is supposed to provide
the incentive to repair water leaks in both domestic and
municipal water equipment (Howe and Linaweaver, 1967, p. 14).
Flack (1967) observed the effect that metering had on water use
in Boulder, Colorado during the 1960's. Based on his experience,
he suggests cities of similar size can expect about a thirty per-
cent reduction in water demand after all accounts are metered
(1967, P. 1343).
The metering of water accounts has its greatest influence
on reducing the amount of water used in lawn sprinkling. Lina-
weaver, Geyer, and Wolff (1964, p. 1128) found that water demand
in unmetered areas of small lots can nearly equal that in metered
areas containing very large lots. Howe and Linaweaver (1967, p.
14) report the annual average rates of use per dwelling unit in
eight flat rate areas to be 692 gallons per day, but only 458
gallons per day in ten metered areas. Their flat rate areas
used 420 gallons, per day, per dwelling, on the average, for
sprinkling compared to 186 gallons in the metered areas, but
the average annual figures for household water use were 236
gallons, per day, per dwelling, in flat rate areas and 247
gallons in the metered areas Q1967, p. 14). These results may
mean that domestic water use is more price inelastic than water
used for lawn sprinkling.
Hanke (1970) observed the effects that metering water
accounts had on both in-house water use and lawn sprinkling In
Boulder. He examined fourteen meter reading routes after water
meters had been installed and found that sprinkling declined
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dramatically. In most cases, the water consumption dropped to
levels below that required to maintain "the aesthetic quality
of one's yard; its green appearance" (Hanke, 1970, pp. 1255-56).
Domestic or in-house use of water dropped an average of thirty-
six percent after metering (Hanke, 1970, p. 1258). He also dis-
covered that the impact of the installation of meters on water
use did not wear off as time went on. In most cases, the amount
of sprinkling water used per capita continued to decrease, which
implies that the price elasticity for water is increasing over
time (1970, p. 1256). This decline in water use has occurred
while incomes have increased, suggesting that the income elas-
ticity is becoming more inelastic (Hanke, 1970, p. 1256).
The effect of metering varies between single homes and
apartments. Metering may be more influential in limiting water
use in areas where each home is individually metered in contrast
to areas where there may be only one meter for many dwelling
units. Apartment dwellers may not be directly metered, but
they are still indirectly affected by metering through the rent
they pay (Fourt, 1958, p. 3). But this is not a marginal charge
since their rent does not account for variations in water use.
Water rate structures are usually dependent upon metering
to help determine the cost of water to each consumer. The type
of pricing structure employed can be useful in helping to avoid
underuse and overbuilding of the system (Hanke and Davis, 1971
pp. 555-56). A wide range of different rate structures are used
in the water utility industry. In communities where water
accounts are not individually metered, a fixed charge or flat
rate for water is used. Unfortunately, this leads to waste and
excessive water consumption (Mann, 1970, p. 535). Increases in
water rates in unmetered areas may not lead to reductions in
water use, but rather can lead to increased demand "because the
customer has no incentive to save water, as he is paying more
he is inclined to use more" (Flack, 1967, p. 1343). '
When each account is metered, many different water rates
can be employed. The simplest is a uniform rate where the
customer is charged the same for each unit consumed, no matter
how much he uses (Mann, 1970, p. 534). A variation of this rate
system is where there is a minimum charge plus a per unit charge
made on all water consumed (Afifi, 1961, p. 43). These types of
rate structures ignore the possibility of cost variations in a
utility providing different amounts of water (Mann, 1970, p. 535),
A second type of metered rates is block schedules. Under
these rate schemes, the price per unit of water varies between
different quantities of consumption. In general, block schedules
are of a declining nature, where the cost of a unit of water
declines in each successive block (Afifi, 1969, p. 42). Mann
(1970, p. 535) criticizes this rate structure because it assumes
costs decline with increased consumption, but not enough cost
148
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data exists to accept or reject this theory. The declining block
rate may affect a water utility in numerous ways.
For example, the declining block schedule, on one
hand, may encourage water uses (sprinkling) which
are key contributors to peak demands, with the
result being a worsening of the utility's peak load
problems. On the other hand, large commercial or
industrial users, receiving water at a single out-
let (while making contribution to system peaks) may
be a prime example of declining supply costs with
increased usage (Mann, 1970, p. 535).
Another variation on block rates is a two-part rate which
is a combination of a declining block rate and a fixed demand
charge (Mann, 1970, p. 535). This type of pricing system may
suffer from the assumption that the demand charge is based on a
consuming group's contribution to peak demands, where in reality,
those users, whose contribution is biggest, may consume most of
their water at off-peak periods, while smaller users may consume
most of their water at peak user periods (Mann, 1970, p. 535).
Water rates should reflect the incremental costs incurred
in providing additional facilities. This is an issue when
comparing summer water use with winter water use. Since summer
water consumption is so much greater than winter consumption, the
cost of providing water increases. If rate structures do not
vary seasonally, to take account of these costs, then invest-
ments in new equipment and facilities, to account for peak water
demand periods, are "larger than economically justified" (Hanke
and Davis, 1971, p. 556).
The problem of equity is further intensified when it is
realized that summer customers are being subsidized in part by
winter ones, since the winter consumer is paying in part for the
additional plant capacity required by the summer users. In
general, inner city consumers, with little or no lawns, are
subsidizing the suburbanites with their large lawns and greater
summer peak demands (Hanke and Davis, 1971, p. 556). There are
pricing methods employed that are designed to overcome these
problems. Seasonal pricing is used to help keep peak water
demands under control and is useful in delaying capital invest-
ments to increase plant capacity (Hanke and Davis, 1971, p. 559).
Higher outside city water rates are frequently used, though
usually as a payment in place of municipal taxes or to provide
an incentive for annexation, instead of covering higher outside
city peak demand (Afifi, 1969, p. 45).
It may take more than special or seasonal water rates to
limit sprinkling use. In Kansas City, Hatcher (1956, p. 374)
found the ratio of maximum to average day lawn sprinkling to be
seven or eight to one, or much greater than the ratio of 1.25
149
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to 1 for domestic use. Howe and Linaweaver (1967, p. 29) point
out that a higher price for water may provide the incentive to
be more conservative in lawn sprinkling, but pricing alone does
not provide an incentive to avoid those times of very high rates
of water use. This is because the times available for watering
lawns are largely set by considerations other than price.
In addition to the water rates and special charges already
discussed, other charges have been employed by the water utility
industry. These include annual assessments on the width of the
customer's property, connection charges, and ad valorem taxes
which are levied to recover some or all of the costs of water*
utility operation and expansion (Linaweaver, Geyer, and Wolff
1964, p. 1127). In some communities, sewer charges are based*
on the amount of water consumed and may have an indirect in-
fluence on water demand (Linaweaver, Geyer, and Wolff. 1964
p. 1127). '
In the case of industry, some costs such as labor have been
increasing faster than the price of water so that the cost of
water has experienced a relative decline and water is sub-
stituted for labor in carrying off wastes (Seagraves, 1972
p. 476). This situation can also occur in the case of resident-
ial water use, where income and inflation can cause water charges
to decrease in relation to other prices, resulting in increased
water consumption (Young, 1973, p. 1072).
In statistical analyses, the price of water has been used
to explain residential water, consumption with varying degrees
of success. Fourt (1958, p. 8) found that the price of water in
dollars per 1000 cubic feet per month was significant in explain-
ing the amount of water used per person per year when used with
the two variables, number of days of rainfall in the summer
months, and average number of residents per water meter. Wong
(1972, pp. 38-39) used both cross-sectional and time series
regression to analyze water consumption data from Chicago and
its suburbs. He discovered that the price of water was a
significant predictor of average per capita water demand per
municipality. In his equations, he included the price variable
with average summer temperature and average household income.
Price was a significant explanatory variable in his cross-
sectional analysis for cities of populations over 5,000. But In
the time series regression of water consumption in Chicago, price
was not significant because Chicago charged a flat rate for water
(Wong, 1972, p. 39).
Grima (1972, p. 100) used three samples, one included in
the second, and both contained in the third, to test a series
of price-related variables and determine their individual
effectiveness in establishing annual water use in gallons per
day per dwelling unit. These variables were: the number of
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billing periods per year, the number of gallons per day allowed
to each dwelling in the minimum bill, the size of the minimum
bill* and the price of water in cents per 1000 gallons. In his
results, two of these variables, the amount of water allowed
with the minimum bill, and the number of billing periods per
year, were not significant in explaining water use (1972, pp.
101-2, 105). The variable, price in cents per 1000 gallons, is
a significant explanatory variable for accounts in only two of
the sample areas (Grima, 1972, p. 105). The most significant
price oriented variable was the fixed bill per period. It was
significant in explaining water use in each of the samples
(Grima, 1972, pp. 101-2, 105-6).
Gardner and Schick (1964) examined the effect that seven
different climatological and income related variables had on
water use in forty-three northern Utah communities. The final
equation which they derived contained only the price of water
and lot size as follows (1964, p. 13):
Log Y - 5.9504 - .7662 log X1 + .1506 log X^
t-statistic -11.70** 2.15* R2 = .83
where:
y = per capita daily water consumption;
X.. * average price of water per 1000 gallons;
XA * per capita lot area.
Estimating the price elasticity of demand for water has
become very important in studies of residential water use, since
it is helpful in determining how a rate increase or how diff-
erences in water rates will affect the demand for water. Under
former forecasting techniques, future water consumption was
determined by estimating population and multiplying it by the
current average per capita water consumption. This entirely
ignores the influence that changes in the cost of water and
subsequent changes in price have on demand, which must be es-
timated if accurate predictions are to be made (Hanke, 1970,
t> 1254). Price elasticity can be defined as the percent change
in quantity demanded compared with the percent change in price.
The price elasticity is inelastic when percent changes in price
are greater than percent changes in quantity demanded, and
elastic when percent changes in price are less than percent
changes in quantity demanded.
The estimates of price elasticity have varied considerably
from study to study. In Illinois, Afifi (1969, p. 41) found
the demand for water by residential customers to be highly
151
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inelastic. Young (1973, P. 1071) examined water data in Tucson
using a time series analysis and estimated the price elasticity
of water demand to be -.65 for the years 1946 to 1964, and -.41
for the years 1965 to 1971. This shift in the price elasticity
could have been caused by many factors. It coincided with
substantial price increase, and as the price of water increases,
the nonessential uses will be curtailed and essential uses will
become a larger share of the total demand. This will make the
demand for water more price inelastic (Young, 1973, p. 1072).
In Wong's (1972, p. 40) analysis, the price elasticity ranged
from -.26 to -.82 in his cross-sectional analysis. In his
time series analysis of water data, the price elasticity ranged.
from -.02 to -.28 (1972, p. 40). In northern Mississippi
communities, the price elasticity varied from -.26 to -.45
(Primeaux and Hollman, 1974, p. 142). In Kansas communities,
the price elasticity was found to be between -.66 and -1.24
(Gottlieb, 1963, p. 210). Finally, Gardner and Schick (1964,
p. 13) calculated the price elasticity to be about -.77 in the
communities which they examined in Utah.
The price elasticity of demand for water varies between
domestic use and sprinkling use. Of the water consumed for
residential purposes, the price elasticity for sprinkling water
is greater than that for domestic demands (Howe and Linaweaver,
1967, PP. 27-28). Howe and Linaweaver found the price elasticity
for domestic demands in metered and public sewered areas to be
-.23 (1967, p. 27). In the same areas, the price elasticity for
the demand of summer sprinkling water was -1.12 (1967, p. 25).
The influence of seasonal change on price elasticity has
been explored by Grima (1972). He developed three equations of
residential water consumption, one for average annual consumption,
one for average summer use, and one for average winter use (1972,'
p. 80). The price elasticity of demand for the entire year was
-.93, but it was -1.07 for the summer period, and only -.75 for
the winter period (Grima, 1972, p. 111).
These variations in the price elasticity may be due to a
number of reasons, including the type of price variable used.
For example, the price variable which Howe and Linaweaver (1967)
employed was "the sum of water and sewer charges that vary with
water use, evaluated at the block rate applicable to the average
domestic use in each study area" (p. 19). In contrast, Gardner
and Schick (1964, p. 14) used the average price per 1000 gallons
of water. Flack (1967) may have discovered a series of reasons
for differences in the price elasticity, by observing Colorado
Springs, Colorado, where "it was found that despite substantial
price increases, the effect on demand was obscured by larger
lawn areas and consequent larger sprinkler loads in new housing
developments, water use restrictions, and year-to-year climat-
ologic variations" (pp. 1342-43).
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Using information on expected rate increases to forecast
future water demand may not provide very accurate predictions
for a number of reasons. First, the range in the price of water
is not great enough between urban areas to provide knowledge on
the price elasticity of water at prices significantly greater
than currently charged (Saunders, 1969, p. 30). Second, the
cost of supplying more water to urban areas may increase at
different rates than in the past (Saunders, 1969, p. 30). Third,
building forecasting models can be hampered by not only trying
to estimate when future rate increases will occur, but also by
the change that new types of rate structures will be employed
(Hittman Associates, Inc., 1969, p. IV-12).
Measures of the Ability to Consume Water
Residential water consumption depends in large part upon
the ability to consume water. Two measures frequently used in
this context are the income of the consumer and the value of
his home. The effect of income has long been recognized as
being important in determining how much water consumers will
purchase. In 1939, Pond (p. 2008) reported that per capita
water consumption was greater in more prosperous neighborhoods.
Income was one of the first variables to be selected in place
of population in explaining residential water consumption
(Larson and Hudson, 1951, p. 603). In 1951, Larson and Hudson
(p. 606) found the greatest water consumption per person to be
occurring in communities in Illinois where incomes were greatest.
It was theorized in the 1950's (Hanson and Hudson, 1956, p. 1355)
that increases in income would correspond to increased water
consumption, because the higher the income of the consumer, the
greater the likelihood he would purchase more water-using
appliances. Increasing incomes not only means that more water-
using appliances are used, like washing machines and dishwashers,
but also that leisure time and water-related recreation time is
increasing (Sewell and Bower, 1968, p. 21).
To test the influence of income, it is usually difficult
to obtain data on per capita income. In these situations, proxy
variables are used.
Most studies tend to rely on the use of median
family income given by the census of population.
Few use average household income, which may be
obtainable from sales management or market surveys.
Where the later index is unavailable, proxy
variables namely, assessed property value, number
of water-using appliances (such as dishwashers and
automatic washers) in a household, size of lot,
number and type of automobile owned by family,
are used (Wong, 1972, p. 36).
153
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As an example of a proxy variable used in place of income, Youno-
(1973, P. 1069) employed retail sales per person per time period
in his study of water use in Tucson.
Income variables have been used frequently in studies of
water consumption and have been found to be important explanatory
variables. In Saunders' (1969, p. 20) principal components IJr
analysis of different variables influencing water use in ninetv
three American cities, he discovered that those that measured
urban area size and income have the most influence on water
usage. But, Whitford (1972, p. 830) complained that Saunders
did not separate residential water usage from the total consumed
and also failed to include many other important variables in hi
analysis, including average lot size and climate.
Wong (1972) included the effect of income in his analysis
of water consumption in the Chicago area in the form of the
average household income in each municipality for each year
under examination. In time series analysis, income was sig-
nificant in explaining only Chicago's average per capita water
demand and not the water demand of the other cities included in
his analysis (1972, pp. 39-40). In his cross-sectional analvsi**
the income variable was significant in explaining water con-
sumption in only those cities with populations of over 10,000
persons (1972, pp. 39-41). Unfortunately, the R2's for the
equations where income was significant in the cross-sectional
analysis were rather small, suggesting that the effect of other
variables must be explored (Wong, 1972, p.
Headley (1963) examined median family income and its effect
on water consumption in gallons per capita per day in fourteen
cities in the San Francisco Bay area, he determined the
correlation between these two variables for both 1950 and 1959
and derived the following equations (1963, p. 444):
for 1950: XQ » -30.24 + 2.16X1 R2 » .81
t-statistic 7.33**
for 1959: XQ - -18.77 + 1.27X., R2 . .80
t-statistic 6.86**
where :
= gallons per person per day;
= annual median family income in hundreds of dollars.
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A time series analysis of residential water use for each of the
fourteen cities was done for the ten years between 1950 and 1959
(Headley, 1963). The income variable explained a smaller amount
of the variance in the individual time series analyses than in
the one cross-sectional analysis (Headley, 1963, pp. 444-46).
An income variable was included in the study of sixteen New
Mexico communities done by Berry and Bonem (1974, p. 1239).
They examined the influence of four variables on average per
capita water consumption. These variables were: the price of
water, the population of each municipality, the sprinkling re-
quirements, and the per capita personal income (1974, p. 1239).
Their results showed only income to be significant in explaining
water demand (1974, p. 1240). Their final equation was (1974,
p. 1240):
g « 31.7 + 0.051y
t-statistic 3.00** R2 = .39
where:
g = water use in gallons per person per day;
y « annual per capita income.
Unfortunately, the coefficient of determination for this equation
was only .39 (Berry and Bonem, 1974, p. 1240).
A variable measuring income has proven to be of little
importance in at least one study of municipal water demand.
Gardner and Schick (1964, pp. 11-12) found that per capita
median income was not significant in explaining per capita
water use and that its regression coefficient had the wrong sign.
They (1964, pp. 16-17) explained these results as being caused
in large part by two problems. First, the results may be in-
dicative of only the study area and may have been different if
the range in median incomes had been greater. Second, since
their study compared differences in water consumption between
communities, it obscured variations within communities, possibly
minimizing the influence of income.
The income elasticity for water has been calculated by many
researchers and is useful in understanding how changes in income
will affect the demand for water. In California, Headley (1963,
p. /i/i/O found the income elasticity in his cross-sectional
analysis of fourteen communities to be 1.49 in 1950 and 1.24
in 1959* The income elasticities for each individual community
studied in a time series analysis ranged from .00136 to .4035,
with a simple average of about .25 for all the communities (1963,
p. 446). In comparing the income elasticities derived from the
two analyses, he says (1963, p. 446):
155
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In view of the historical information we have,
showing the increases in gallons per capita per
day of residential water purchases over time
from 1950 through 1959, the elasticities estimated
from the time series analysis seem to be more
reasonable.
The higher elasticities in the cross-sectional analysis may be
due to income being a proxy for other variables such as the
number of bathrooms per house, the presence of washing machines
or the average lot size, which may vary more between the cities
included in this study than within them (Headley, 1963, p. 448).
Wong's (1972) analysis was similar to headley's in that the
income elasticities were greater in the cross-sectional analysis
than in the time series analysis. In Wong's (1972, p. 40) cross-
sectional analysis, the price elasticity ranged from 1.03 to .58
while in the time series analysis, the price elasticity for '
Chicago was .20 and .26 for the other communities.
Howe and Linaweaver (1967) calculated the income elasticit-
ies for both sprinkling and domestic water in a cross-sectional
analysis, where they used property value as a surrogate for
income. They (1967, p. 27) calculated the income elasticity
for domestic water to be about .35 in sewered areas. The income
elasticities for sprinkling water were .4 in metered western
areas and 1.5 in the metered eastern areas (Howe and Linaweaver.
1967, p. 28).
A second variable indicative of the ability to consume water
is the value of the consumer's home. The value of the home is
assumed to be positively correlated with the size of the lawn
and the number of water-using appliances in the dwelling. Howe
and Linaweaver (1967, p. 20) suggest that the value of the home
"determines an approximate per capita usage through water com-
plementary appliances, baths, etc."
Howe and Linaweaver (1967) discovered that the value of the
home in thousands of dollars was a significant variable in
explaining both average annual domestic and average summer
sprinkling water consumption. They derived the following
equation to explain domestic water consumption in twenty-one
metered and public sewered areas, and thirteen flat rate and
public sewered areas containing apartments (1967, p. 24):
metered and public sewered areas:
<*a,d - 206 + 3
t-statistic
156
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flat rate and sewered area with apartments:
= 28.9 + 4.39v + 33.6p
t-statistic 7.87** 3.97**
where:
q = average annual water demand for domestic use in gallons
a»d per dwelling per day;
v « value of the home in thousands of dollars;
t> = water and sewer charges according to average domestic
W
w use.
In the case of water used for summer sprinkling in twenty-
one metered and public sewered areas and eight areas with flat
rates and public sewers, Howe and Linaweaver (1967, p. 25)
derived the following two formulas:
metered and public sewered areas:
a = 1.09 + 2.07 Log (w0 - 0.6r_) - 1.12 log ps
Hs, s s s
t-statistic 4.59** 5.00**
+ .662 Log v
t-statistic 3.06**
flat rate areas with public sewers:
q = 2.00 + .783 Log v
t-statistic 3.24** R2 = .635
where:
a a average summer sprinkling demand;
Ms,s
p = marginal commodity charge on average summer total rates
3 of consumption;
•w = summer potential evapotranspiration in inches;
s
r * summer rainfall in inches.
s
Linaweaver, Geyer, and Wolff (1967, p. 273) have calculated
correlation coefficient of .76 between the value of the home
and residential water use based on data from thirty-one residen-
tial areas. Their equation is (1967, p. 273):
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Sd/a = 157 + 3.46V R2 = .58;
where:
"Sj/a = average domestic water use in gallons per day for
each dwelling;
V » average value of the dwelling in thousands of
dollars.
Grima (1972) used the assessed sales value of the dwelling
unit in hundreds of dollars as a measure of housing value in
his research. This measure of housing value appeared in all of
his final equations, containing Just significant variables, as
follows (1972, p. 105):
average annual demand:
WUQ « 131.26 + 0.37V + 22.15Np - 2.14P - 0.16F
Q
t-statistic 3.20** 7.22** -4.5* -2.56** R2 » .52-
average summer demand:
WU0 * 152.28 + 0.41V + 26.15Np - 2.61P - 0.19F
O
t-statistic 3.51** 6.98** -4.5** -2.4** R2 » .50;
average winter demand:
WUW = 115.72 + 0.26V + 20.43NP - 1.74P - 0.13F
t-statistic 2.82** 6.9** -3.8** -2.07* R2 = .46;
where:
VU « annual average water use in gallons per day per
a dwelling;
¥U » summer average water use in gallons per day per
dwelling;
w
winter average water use in gallons per day per
dwelling;
V » assessed sales value of the dwelling unit in the
hundreds of dollars;
w = number of persons per residence;
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P = price of residential water in cents per 1000 gallons;
F = the fixed bill for each billing period in cents.
The value of homes has not always proven to be important in
determining water use. As with income, the value of homes did
not prove to be a significant variable in Gardner and Schick's
(1964) analysis of water use. They explain this result as being
similar to the results of the income variable, where the analysis
overlooked variations in home values within communities. (I9o4,
p. 18). Also, they felt that in-house use of water may not vary
significantly between homes of different value, since most homes,
no matter what their value, have certain water-using appliances
(1964, p. 18).
The Influence of Water-Using Appliances
The numbers and types of different water-using appliances,
present in each household, form a third set of variables
important in establishing residential water consumption. These
appliances are related to the consumer's median income and the
value of his home, since they are usually indicative of his
economic status. Per capita residential water use should in-
crease with their addition to the home (Wolff, 1957, p. 225).
The amount of water they consume depends on the consumer's in-
come level, the number of persons in the home, and the cost of
water (Grima, 1972, p. 79).
The rate of water use by each appliance (w^) is
dependent upon its technical efficiency. In the
case of residential water use, this efficiency
level is partly under the control of the user;
care of use and the repair of water-using appliances
(particularly the household plumbing system) are
relevant to the magnitude of WA» The rational
consumer adjusts to the marginal price of water
by using water more effectively (Grima, 1972,
pp. 79-80).
The use of domestic water-using appliances is essentially
different from lawn sprinkling in that it is not seasonal and
therefore has different peaking characteristics; also, daily
rates of domestic water use are generally the same in summer
as in winter (Howe and Linaweaver, 1967, p. 17).
Water-using appliances generally fall into the following
three groups: toilets and bathing facilities, home laundry and
kitchen appliances, and air-conditioning equipment. Water used
for bathroom equipment is a major source of in-house water demand.
Water use per toilet flush varies from 3.2 to 8 gallons or more
159
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(Howe and Vaughan, 1972, p. 118). Bathing is also very impor-
tant; thirty percent of domestic water use is devoted to it and
sixty percent of this is used in showers (Howe and Vaughan, 1972
p. 120). '
There has been a tendency, in recent years, to increase the
number of bathrooms in American homes. Seidel (1969, p. 490)
found that in Ames, Iowa, the size of homes had increased over
the previous ten to fifteen years and now many had additional
bathroom facilities. In spite of the increase in the number of
bathrooms, much of this is excess capacity that is used only
rarely (Wolff, 1957, p. 1256).
Home laundry equipment and automatic dishwashers have, over
the last few decades, become increasingly common in American
homes. The percentage of total water consumed within a home for
clothes-washing and dish-washing ranges between twenty and
twenty-seven percent of the total (Howe and Vaughan, 1972, p.
119). The amount of water used by these appliances varies
according to the amount of water they use in each operating
cycle. Consumer Reports (August, 1969, p. 443) found that
automatic home clothes-washers use between thirty-two and fifty-
nine gallons of water for each eight pounds of load. In a
study of water use in two homes in Louisville over a period of
seven days, it was discovered that, on the average, the washing
machine and dishwasher were used 0.7 and 0.8 times, respectively
per day (Anderson and Watson, 1967, p. 1235). Food disposers '
were used an average of 1.8 times per day in the same homes
(Anderson and Watson, 1967, p. 1235).
Peak in-house water demands have been increasing because of
the use of automatic appliances. It is now possible to have a
number of them running at the same time (Heggie, 1961, p. 264).
Household appliances can place a large demand upon a water
utility, but this does not need to be the case, since available
technology could reduce present domestic water use by thirty-two
percent® (tiowe and Vaughan, 1972, p. 121).
Sometimes incentives are employed to limit the use of water
for domestic purposes. An example of this has been in regard
to air-conditioning, which became a substantial problem to water
utilities in the 1950's because their consumption of water nearly
corresponded with the summer peak demands for water (Rynders.
1960, p. 1242). To solve this problem, two approaches were
aThis could be accomplished through the use of shower heads
with lower volumes of water flow, the installation of domestic
water reuse systems, and the selection of the most water-
conserving appliances available (Howe and Vaughan, 1972, pp.
118-21).
160
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taken. First, in some communities, special demand charges or
surcharges were enacted to control the amount of water used in
air-conditioning (Afifi, 1969, p. 45). In the case of demand
rates, the higher a customer's peak demand, the greater the
charge (Rynders, 1960, p. 1239). A second way of controlling
water use in air-conditioning was by ordinances. In the 1950's,
Kansas City passed an ordinance requiring new air-conditioning
units to be of the type that recirculated the condenser-cooling
water (Hatcher, 1956, p. 374). The use of ordinances, instead
of special charges, has been found in one study to be the most
common method employed to control water consumption by air-
conditioning equipment (Afifi, 1969, P. 45).
Air-conditioning's effect on water demand has declined in
recent years due to increased water rates and the use of
ordinances (Hatcher, 1965, p. 275). It has also experienced a
decline because of the increased use of air-cooled units and the
replacement of a number of smaller units in buildings with
central water-conserving units (Committee Report, 1965,
pp. 1456-57).
The Effect of Population and Housing Density
A fourth set of explanatory variables are related to
population and density; these variables determine both the water
demand per dwelling and per area. They include variables
measuring different characteristics of the consumers, like
population density, or characteristics of the dwelling units,
such as lot size. For water-using appliances, the frequency of
use is in large part determined by the number of persons in the
dwelling. The biggest use of residential water is for bathroom
purposes and this should be a function of the number of persons
per dwelling unit (Crima, 1972, p. 86). The number of persons
should also determine total annual domestic water use and reflect
any economies of scale present in water consumption (Howe and
Linaweaver, 1967, p. 20).
In Howe and Linaweaver's (1967) examination of domestic
water use in thirty-nine study areas, the variable, number of
people per dwelling unit, was used to explain water consumption
with mixed results. It was significant in explaining the average
yearly demand for domestic water by individual household for
dwelling units in apartment areas with flat rates and public
sewers, and was the only significant variable in metered areas
with septic tanks (Howe and Linaweaver, 1967, p. 24). They
derived the following equations for water use in these areas
(1967, P. 24):
flat rate and apartment areas with public sewers
q&td = 28.9 + 4.39v + 33.6dp R2 = .90
161
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t-statistic 7.87** 3.97**
metered areas with septic tanks
qa>d = 30.2 + 39.5dp R2 = .96
t-statistic 8.48**
where:
q d = annual average water use in gallons per dwelling per
a' day;
v = market value of the dwelling in thousands of dollars;
d « persons per dwelling.
Persons per dwelling were found to be insignificant, and
had the wrong sign when used to explain domestic water use in
metered and public sewered areas (Howe and Linaweaver, 1967,
p. 24). The poor showing in these latter areas may have been
due to the use of area averages as observations to produce the
equation (Morgan, 1973, P. 1065). Averaging the number of
persons per household for each set of observations reduces the
variance of this statistic in relation to the quantity of water
demanded (Morgan, 1973, p. 1065). Morgan suggests that water
use projections based on the Howe and Linaweaver model could
lead to inaccurate per capita water use estimates if the number
of people per dwelling unit is not approximately the same as the
sample mean (1973, p. 1067).
Morgan has conducted his own study to determine the influ-
ence of persons in each household on the amount of water demanded
(1973, P. 1065). tie examined ninety-two single family homes in
metered and public sewered areas for three different time periods
(1973, P. 1066). Also included in his equation was the assessed
value of each property in thousands of dollars as a second
independent variable (1973, P. 1065). Of the three equations
he derived, for the periods November to December, January to
February, and both periods combined, he found that the co-
efficients for both the number of persons per dwelling and the
assessed value were significant and had positive signs, but,
that the R2 was relatively low (Morgan, 1973, p. 1066).
The number of persons per dwelling was also significant in
explaining residential water use in Fourt's (1958) research. He
used this statistic with two other variables, the price of water
and the number of days of rainfall in the summer (1958, p. 7).
His analysis was conducted in three parts. First, he examined
twenty-three small cities, then, he looked at twenty-one large
cities, and finally, he combined both groups together (1958,
162
-------
p 7). In the results of his analysis, the number of persons
per meter was significant only for the large cities, and the
combined sample (1958, p. 8). The final equations for these two
samples were (1958, p. 8):
the large cities:
Xl « 5.829 - 0.4l4x2 - 0.026x3 - 0.339x4 R2 = .84
t-statistic 5.67** 3.71** 6.28**
the combined sample:
X. = 5.812 - 0.386x2 - 0.037x3 - 0.305x4 R2 = .68
t-statistic 5.22** 5.29** 4.77**
where:
x = annual quantity of residential water in thousands of
^ cubic feet used per person;
y. » price of 1000 cubic feet of water per month;
x, - number of days of rainfall during the months of June,
* July, and August, 1955;
XA - average number of persons per water meter.
Persons per dwelling may not be the only density variable
with significant influence on residential water consumption, as
the density of dwelling units may also be important. It has
been proposed to use the number of lots present to estimate the
amount of water used in a given area (Becker, Bizjak, and Schulz,
1972, p. 415)• The Per capita use of water increases as one
moves from rural to suburban areas, and then declines from the
suburban areas to the central city areas. The cause of this
phenomenon is the presence of large lawns in suburban areas and
multi-family dwellings and apartments in central city areas
(Flack, 1967, p. 1341).
The size of residential lots appears to be the best measure
of dwelling unit density, because it gives an indication of the
amount of area devoted to lawns. Linaweaver, Geyer, and Wolff
(1964, p. 1121) found that in an average neighborhood of middle
income families in Baltimore County, Maryland, each 8,000 square
feet of lawn area received an average of 8.5 inches of water in
the sprinkling season of 1963. They assumed lot size, as well
as weather and the amount of water metering, to be the most
important variables influencing sprinkling (1964, p. 1128).
Howe and Linaweaver (1967, p. 25) reported the amount of irrig-
able area between the observations (1967, p. 28). Wolff (1961,
163
-------
p. 1253) examined water consumption between dwelling units on
various sized lots. He found that the average day demand for
water increased as the size of the lot increased. His results
appear in Table B*
The ratio of peak hour to average day demand also increases
with lot size (Wolff, 1961, p. 1253). He found a linear re-
lationship between the size of a residential lot and the total
demand during periods of heavy sprinkling, and suggested that
when designing new distribution systems in residential areas, it
may be more profitable to examine lot size instead of population
(1961, p. 1253).
In the equations which Grima (1972, p. 105) derived to
explain residential water consumption for single family homes,
lot size did not prove to be a significant explanatory variable.
Grima (1972, p. 44) suggests that the amount of lawn watering
may be related more to income than to lawn size, since, in most
cases, lawns are greener where incomes are higher.
Gardner and Schick discovered that lot size was significant
in their study of daily per capita water use (1964, p. 12).
Their results show that if lot size increases one percent per
capita, water use increases 0.15 percent (1964, p. 12). The
small increase in water use with increases in lot size could be
due to the watering characteristics of cities in the study
containing large lots. Often in these communities, alternative
irrigation systems were originally employed for lawn and garden
watering. Today, in these areas, the residents often let much
of their land lay idle (Gardner and Schick, 1964, pp. 15-16).
The number of persons in an area residing in multi-family
units is also indicative of the amount of water used for non-
domestic uses. Linaweaver, Geyer, and Wolff (1967, p. 269)
found that the average annual water use, per dwelling unit, in
the five apartment areas which they examined, was 191 gallons
per day. This is much less than in residential areas of detached
homes, because of the smaller amount of lawn area per dwelling
unit associated with apartments (Linaweaver, Geyer, and Wolff,
1967, PP. 269, 271). Peak water use, per dwelling unit in
apartment areas, was found to be much less than in areas of
detached homes. Peak hourly water consumption in metered public
watered and sewered areas was 2480 gallons per day in the West,
and 1830 in the East, but only 960 in apartment areas (Lina-
weaver, Geyer, and Wolff, 1967, P. 269). In contrast to these
results, Grima (1972, pp. 103-15) found greater water use per
dwelling in townhouses than in single family dwellings.
Water use per acre may be greater in apartment areas than
in areas of detached homes. Maximum hour demands have been found
to be greater per acre in areas of group houses than in areas of
detached homes (Wolff, 1961, p. 1255). The results of Wolff's
164
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(1961, p. 1255) analysis showed maximum hour consumption to be
3.8 gallons per minute per acre for group dwellings, and between
1.8 and 2.9 gallons per minute per acre for detached dwellings.
These results suggest that the greater the density of dwelling
units in an area, the greater the total residential water con-
sumption. There are two reasons for this: first, dwelling units
in apartment buildings are usually not individually metered
and the residents may therefore use water more freely, and second,
the population density will be greater in apartment areas than
in areas of single family homes.
The literature of water consumption cites many other
variables that may have some influence on residential water
demand. Age of the dwelling may be indicative of the condition
of the water pipes and the possibility of water leakage (Howe
and Linaweaver, 1967, P. 20). Changing social tastes may have
an influence on water consumption by placing more importane on
cleanliness and personal hygiene (Sewell and Bower, 1968, p. 25).
Changing social tastes may also cause the public to prefer
products or services that increase the consumption of water
(Sewell and Bower, 1968, pp. 25-26). The growing number of
families with two or more automobiles has increased the per
capita demand for water (heggie, 1961, p. 264). Finally, the
water pressure in an area will affect the rates of water flow
and subsequent consumption (Howe and Linaweaver, 1967, p. 20).
165
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TABLE B
WATER CONSUMPTION BY TYPE OF DWELLING UNIT
Type of Dwelling
Lot size
(sq. feet)
Maximum Day
(gpcd)
Average Day
(gpcd)
Group House
Detached Dwelling
Detached Dwelling
Detached Dwelling
Detached Dwelling
2,000-2,400 93
5,000-7,500 64
9,000-12,000 163
15,000-25,000 278
40,000 or more 564
48
51
67
80
117
Source: Wolff, Jerome B., "Peak Demands in Residential Areas."
Journal. American Water Works Association. LIII (October, 1961)
1251-1260. *
166
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BIBLIOGRAPHY FOR APPENDIX B
Afifi* Hamdy, H.H. "Economic Evaluation of Water Supply Pricing
in Illinois." Journal* American Water Works Association,
LXI (January, 1969), 4-48.
Anderson, J.S. and Watson, K.S. "Patterns of Household usage."
Journal. American Water Works Association. LIX (October,
1967), 1228-37. '
Becker, A.E., Jr.; Bizjak, Gerald J.; and Schulz, James W.
"Computer Techniques for Water Distribution Analysis."
Journal. American Water .Work_s_As.spc_iation. LXIV (July,
1972), 410-17.
Berry, Dale W, and Bonem, Gilbert W. "Predicting the Municipal
Demand for Water." Water Resources Research. X (December,
1974), 1239-42. "—
Committee Report. "Trends in Air-Conditioning Regulation."
Journal. American Water Works Association. LVII (November,
1965), 1456-71.
Flack, J. Ernest. "Meeting Future Water Requirements Through
~ *• ^ I * || V "I A * •_# I . . - O
LIX
Reallocation." Journal. American Water Works Association.
(November, 1967), 1340-50. "~ "~~""
Fourt, Louis. "Forecasting the Urban Residential Demand for
Water." Agricultural Economics, Seminar. February 14, 1958.
Gardner, B. Delworth, and Schick, Seth H. Factors Affecting
Consumption of Urban Household Water in ^or-th^rn Utah
Bulletin 449.Logan:Agricultural Experiment Station
Utah State University, 1964.
Gottlieb, Manuel. "Urban Domestic Demand for Water: A Kansas
Case Study." Land Economics. XXXIX (May, 1963), 204-10.
Grima, A.P. Residential Water Demand; Alternative Choices for
Management. Unpublished Ph.D. dissertation, Department of
Geography, University of Toronto, 1972.
167
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Hanke, Steve H. "Demand for Water Under Dynamic Conditions."
Water Resources Research. VI (October, 1970), 1253-61.
Hanke, Steve H. and Davis, Robert K. "Demand Management Through
Responsive Pricing." Journal. American Water Works Assoc-
iation, LXIII (September, 1971), 555-60.~~ "
Hanson, Ross, and Hudson, Herbert E. "Trends in Residential
Water Use." Journal. American Water Works Association.
XLVIII (November, 1955), 1347-59.
Hatcher, Melvin P. "Basis for Rates." Journal. American Water
Works Association, LVII (March, 1965), 273-8. """
Hatcher, Melvin P. "Kansas City, Missouri in Panel Discussion:
The Lawn Sprinkling Load." Journal. American Water Works
Association. XLVIII (April, 1956), 373-6."
Headley, Charles J. "The Relation of Family Income and Use of
Water for Residential and Commercial Purposes in the
San Francisco-Oakland Metropolitan Area." Land Economics.
XXXIX (November, 1963), 441-9. "~
Heggie, Glen D. "Sizing of Residential Service Lines and Meters
in Detroit." Journal. American Water Works Association.
LIII (March, 1961), 253-b.
Hittman Associates. Forecasting Municipal Water Requirements.
Vol. I; The Main II. System.Columbia, Maryland.Hittman
Associates, Inc., 1969.
Howe, Charles W. and Linaweaver, F.P. Jr., "The Impact of Price
on Residential Water Demand and its Relation to Systems
Design and Price Structure." Water Resources Research.
Ill (First Quarter, 1967), 13-32^~
Howe, Charles W. and Vaughan, William J. "In-House Water Savings."
Journal. American Water Works Association. LXIV (February,
1972), 118-21.
Larson, Brent 0. and Hudson, H.E. Jr., "Residential Water Use
and Family Income." Journal^ American Water Works
Association. XLIII (August, 1951), 603-11.
Linaweaver, F. Pierce Jr., Geyer, John C., and Wolff, Jerome B.,
"Progress Report in the Residential Water Use Research
Project." Journal. American Water Works Association,
LVI (September, 1964), 1121-8.
168
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Linaweaver, F.P. Jr., Geyer, John C., and Wolff, Jerome B. ,
"Summary Report on the Residential Water Use Research
Project. " Journal .American Water Works Association.
LIX (March, 1 9b7 ; , 2b7-b2 .
Mann, Patrick C. "A New Focus in Water Supply Economics — Urban
Water Pricing. " Journal. American Water Works Association.
LXII (September, 1970), 534-7.,
Morgan, W. Douglas. "Residential Water Demand: The Case from
Micro Data." Water Resources Research, IX (August, 1973),
1065-7.
Pond M.A. "Urban Domestic Water Consumption." Journal. American
Water Works Association. XXXI (December, 1939), 2003-1**.
Forges, Ralph. "Factors Influencing Per Capita Water Con-
sumption." Water and Sewage Works. CIV (May, 1957),
199-204.
Primeaux, Walter J. Jr. , and Hollman, Kenneth W. "Factors
Affecting Residential Water Consumption: The Managerial
Viewpoint." Water and Sewage Works. CXXI (April, 1974),
R-138-140-, R-142-144.
Rynders, Arthur. "Demand Rates and Metering Equipment at
Milwaukee." Journal. American Water Works Association.
LII (October, 1960), 1239-43.
Saunders, R.J. "Forecasting Water Demand: An Inter- and Intra-
Community Study. " West Virginia University Business
Economic Studies. XI (February, 1969), 1-30.
Seagraves, J.A. "Sewer Surcharges and their Effect on Water
Use." Journal. American Water Works Association. LXIV
(August", 1972), 476-80.
Seidel, Harris F. "Trends in Residential Water Use." Journal.
American Water Works Association. LXI ( September , 1 9b9 ) ,
Sewell, W.R. Derrick, Bower, Blair T. , et. al. Forecasting the
Demands for Water. Ottawa: Policy and Planning Branch,
Department of Energy, Mines, and Resources, 1968.
U.S., Bureau of the Census. Census of Population and Housing:
1970 Census Tracts. ~' " ~ ' ~~ '^ • • -- -
Ohio - %. Ind. SMSA.
±f\f\* *•• ^*^t ** ••* «^*« W V •W«*lv> W« V V VWM M*»V *^ •— • ^fff^*,^ VA ^-l^^^** "^« "«• *- * A^XWft^ Alt If-, •
1970 Census Tracts. Final Report PHC (1) - 44 Cincinnati,
hio - """"
169
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U.S., Congress, Senate. Select Committee on National Water
Resources. Water Resources Activities in the United States;
Future Water Requirements for Municipal Use. Committee
Print No. 7.Washington, D.C.:Government Printing Office
1960.
"Washing Machines." Consumer Reports. August, 1969, 436-40.
Whitford, Peter W. "Residential Water Demand Forecasting."
Water Resources Research. VIII (August, 1972), 829-39.
Wolff, Jerome B. "Forecasting Residential Requirements for
Distribution Systems." Journal. American Water Works
Association. XLIV (March, 1957), 225-35.
Wolff, Jerome B. "Peak Demands in Residential Areas." Journal,
American Water Works Association. LIII (October, 1951),
1251-60.
Wong, S.T. "A Model on Municipal Water Demand: A Case Study of
Northeastern Illinois." Land Economics. XLVIII (February,
1972), 34-44.
Young, Robert A. "Price Elasticity of Demand for Municipal
Water: A Case Study of Tucson, Arizona." Water Resources
Research, IX (August, 1973), 1068-72. "—
170
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APPENDIX C
COMMERCIAL WATER DEMAND: A LITERATURE REVIEW
BACKGROUND
Commercial water use is a second major source of water
demand in America. In 1960, the United States Senate (Committee
Print, No. 7, p. 9) reported that eighteen percent of the average
daily per capita consumption of municipal water was devoted to
commercial uses.
The literature of commercial water use is not as extensive
as that for residential use, but a few significant pieces of
research have explored much of the water use activity of different
commercial establishments. The most important was Wolff, Lina-
weaver, and Geyer's (1966) survey of water use by various
commercial and institutional water users in the Baltimore area.
They determined the average day, maximum day, and peak hour water
demands of these activities and calculated the 95 percent con-
fidence limit of water use for each. They identified a single
parameter for each consuming group "... which could describe
the design requirement for that establishment as a simple unit
of water use" (1966, p. 2).
Water Use by Commercial and Institutional Activities
The different commercial activities and institutions that
Wolff, Linaweaver, and Geyer (1966) examined included schools,
office buildings, stores, restaurants, social organizations,
health care facilities and different service oriented businesses.
Many of the institutions included in their study have also been
examined in other research. In this section, the different
estimates for a variety of commercial activities will be compared.
The analysis of commercial and institutional water use pre-
sented here relies heavily on the work done by Wolff. Lina-
weaver, and Geyer (1966), and Searcy and Furman (1961). Wolff,
Linaweaver, and Geyer (1966) examined 186 commercial establish-
ments and institutions in the Baltimore area. Their data sources
included quarterly billing records, daily and hourly visual
readings of water meters, and water consumption recorders in-
stalled on water meters (1966, p. 4). Recordings of water use
were made between 1963 and 1965. Si some cases, an establishment
171
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was observed twice to determine seasonal variations in water
consumption (Wolff-, Linaweaver, and Geyer, 1966, p. 5).
Searcy and Furman (1961) conducted their research on water
use by commercial establishments and institutions in Gainesville,
Florida. They calculated the monthly, daily and hourly water
consumption of the establishments in their sample. The monthly
rates of water use were obtained from records covering the
period of October 1, 1958 to April 1, 1960. Daily and hourly
readings of water meters of the accounts under observation were
made in February and March, 1960 (Searcy and Furman, 1961, p.
1113).
While residential water use is measured on a per capita
basis or a per dwelling unit basis, commercial and institutional
water use is based on many different parameters, depending upon
what is the most applicable parameter for each activity. This
makes it difficult to compare the water use by different
activities, since they may each be based on a different para-
meter.
Water use by educational institutions varies according to
grade level. The parameter used to measure water use by these
institutions is gallons per day per student. However, Searcy
and Furman did not find this parameter to be completely adequate
because:
"... there is not always a direct relationship
between water consumption rates and the number of
students in attendance. Variations in water con-
sumption appeared to be more nearly related to
special activities of the school. These include
lawn watering, sports events, construction work,
and other water consuming activities" (1961, p.
1115).
Searcy and Furman (1961, p. 1114) examined nine elementary
schools, two junior high schools, two senior high schools and
one school containing kindergarten through twelfth grade. The
monthly average rates of water use by type of school were 5.8
gpd/student for elementary schools, 6.0 gpd/student for junior
high schools, and 15.8 gpd/student for senior high schools. The
maximum monthly rates were 12.9 gpd/student for elementary
schools, 16.2 gpd/student for junior high schools, and 36.8 gpd/
student for senior high schools. Maximum day recorded demands
were 10.6 gpd/student for elementary schools, 12.2 gpd/student
for junior high schools and 61.3 gpd/student for senior high
schools (Searcy and Furman, 1961, p. 1111).
Wolff, Linaweaver, and Geyer (1966) compared water use by
both public and private primary and secondary schools. They
found the mean annual water use for public schools to be 5.38
172
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gpd/student for elementary schools, 5.64 gpd/student for junior
high schools, and 6.63 gpd/student for senior high schools. The
mean annual water use for private schools was 2.27 gpd/student
for elementary schools, 10.4 gpd/student for senior high schools,
and 8.49 gpd/student for combined schools containing grades one
through twelve. The maximum day recorded rates of consumption
in public schools were 6.84 gpd/student for elementary schools,
and 15.2 gpd/student for senior high schools. The maximum day
recorded consumption for private schools was 3.10 gpd/student
for elementary schools, 15.7 gpd/student for senior high schools,
and 16.8 gpd/student for combined schools (Wolff, Linaweaver, and
Geyer, 1966, p. 9).
Water use in schools occurs primarily in one limited period
of the day, and the peak water use at certain specific times.
Ninety-three percent of the water consumed in elementary and
junior high schools is during a ten hour period (Searcy and
Furman, 1961, p. 1116). Most water use in schools appears to
occur between 6:00 a.m. and 6:00 p.m. on weekdays. (Wolff,
Linaweaver, and Geyer, 1966, p. 13; Searcy and Furman, 1961,
pp. 1114-15). Peak water use in elementary schools and junior
high schools occurs around noon. High schools experience two
peaks, one around noon, and another in the late afternoon.
(Wolff, Linaweaver, and Geyer, 1966, pp. 12-13; Searcy and
Furman, 1961, pp. 1114-15). "The effect of showers following
the sports program explains the second peak in the consumption
rates of the high schools. . ." (Searcy and Furman, 1961, p.
1116).
Other variables beside grade level and whether they are
public or private affect water consumption in schools. The
age of a school is such a variable. Searcy and Furman (1961,
p. 1112) found that, in general, the older the school, the
smaller the water consumption per student. It has also been
reported that the presence of showers and cafeterias in schools
have significant influence on water consumption (Public Works,
1957, P. 108).
Water consumption in colleges is dependent upon whether
students live on campus or not. The range in water consumption
for colleges with resident students was 63.3 gpd/student to 169
gpd/student, but only 2.05 gpd/student to 15.2 gpd/student for
colleges without resident students (Wolff, Linaweaver, and Geyer,
1966, p. 15). The mean school year water consumption for colleges
was 106 gpd/student for institutions with resident students and
only 5.4 gpd/student for colleges without students in residence.
(Wolff, Linaweaver, and Geyer, 1966, p. 16). The above results
for schools without resident students should be approached with
caution as they were derived from a sample containing only two
schools, one of which had limited water using facilities (Wolff
Linaweaver, and Geyer, 1966, p. 15). '
173
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The parameter selected by Wolff, Linaweaver, and Geyer
(1966, p. 18) to explain water use in hospitals was the number
of beds present. The data showed that as the cost of patient
care increased, so did water use. The cost of patient care was
not used to predict water use because it was difficult to obtain
cost data (Wolff, Linaweaver, and Geyer, 1966, p. 17). They ex-
amined nine hospitals and found the average annual water con-
sumption to be 346 gallons per day/bed (1966, p. 18). Maximum
day recorded consumption was 551 gpd/bed (Wolff, Linaweaver and
Geyer, 1966, p. 19). Searcy and Furman (1961, p. 1117) dis-
covered average water use in hospitals to be only 275 gpd/bed.
Peak water demands in hospitals occur in the late morning, the
early afternoon, and the late afternoon or early evening. (Wolff,
Linaweaver, and Geyer, 1966, p. 21).
Water consumption in nursing homes and special institutions
like orphanages or mental institutions were also measured in
gallons per day per bed. The average annual use in the institu-
tions observed was 133 gallons per day per bed with a range of
92.2 gpd/bed to 210 gpd/bed (Wolff, Linaweaver, and Geyer, 1966,
p. 22). The period of peak water use in these institutions
occurs between two and five in the afternoon (Wolff, Linaweaver,
and Geyer, 1966, p. 23).
Two types of apartments, four high-rise apartment buildings,
and five garden-type apartment buildings, were included in the
commercial water use research project (Wolff, Linaweaver, and
Geyer, 1966). The parameter selected to explain water use in
apartments was water use per occupied unit. The average annual
use was 218 gpd/unit occupied for high rise apartments and 213
gpd/unit occupied for garden apartments (Wolff, Linaweaver, and
Geyer, 1966, p. 25). The maximum day recorded demand was 426
gpd/unit occupied in high rise apartments and only 215 gpd/unit
occupied for garden apartments (Wolff, Linaweaver, and Geyer,
1966, p. 25). Peak water use in high rise apartments occurs from
ten in the morning to three in the afternoon and from six to
seven in the evening. In contrast, peak water use in garden
apartments occurs between seven and nine in the morning and six
to seven in the evening. The evening peak water demand in
garden apartments increases as lawn sprinkling increases .in the
summer (Wolff, Linaweaver, and Geyer, 1966, p. 26).
Water use in two downtown Baltimore hotels was measured in
gallons per day per square foot. The mean annual water use in
the two hotels was 0.256 gpd/square foot, and the maximum day
recorded demand was 0.294 gpd/square foot (Wolff, Linaweaver,
and Geyer, 1966, p. 28). According to Wolff, Linaweaver, and
Geyer (1966, p. 30), water use in motels is very much like that
in hotels. They.used the same parameter for motels as they did
for hotels and found mean annual water use was 0.224 gpd/square
foot and the peak recorded demand was 0.278 gpd/square foot
(1966, p. 31). Though they found water use per square foot to
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be greater in hotels than motels, this situation is due to
the presence of more public rooms in hotels than motels. Water
use per living unit is much higher in hotels than motels (1966,
p. 30).
Data on motel water use has also been collected on a per
guest basis. (Searcy and Furman, 1961, p. 1117). The average
monthly water consumption in the six motels Searcy and Furman
examined was 63 gpd/guest, and the maximum monthly consumption
was 181 gpd/guest (1961, p. 1112). In 1961, the average water
use in motels per dwelling unit in ten cities and counties
varies from 50 gpd/housing unit to 196 gpd/housing unit ("Water
Demands of Decentralized Community Facilities", 1961, p. 104).
When measuring water use in office buildings, Wolff, Lina-
weaver and Geyer (1966) differentiated between general purpose
office buildings and medical offices. The parameter used to
measure water use in both was consumption per square foot. The
general purpose office buildings were divided into two groups,
those ten years or older, and those younger than ten years.
Average annual water use was 0.093 gpd/square foot for office
building less than ten years old, 0.142 gpd/square foot for
office buildings over ten years old, and 0.618 gpd/square foot
for medical office buildings (Wolff, Linaweaver, and Geyer,
1966, p. 34). Only two observations were made of medical office
buildings, but both had substantially higher water use than
general office buildings. The greater water consumption in
older office buildings as compared to younger buildings could
be due to leakage in the older water systems, discharge of water
in their cooling units, and more inefficient utilization of
water (Wolff, Linaweaver, and Geyer, 1966, p. 33).
Sales area was used as a design variable for department
stores. Mean annual water use in five department stores in the
Baltimore area was 0.216 gpd/square foot of sales area and the
maximum day recorded use was 0.388 gpd/square foot (Wolff,
Linaweaver, and Geyer, 1966, p. 38). Water use in department
stores is subject to the types of amenities they offer, such as
restaurants, and restrooms (Wolff, Linaweaver, and Geyer, 1966,
P. 38).
Gross floor area was selected to describe water use in two
shopping centers in Towson, Maryland. The average annual water
use for both was 0.169 gpd/square foot, and the maximum day
recorded demand was 0.232 gpd/square foot (Wolff, Linaweaver,
and Geyer, 1966, p. 41). Searcy and Furman (1961) also used
gross floor area to describe water use in a shopping center.
They found the average monthly consumption was 0.209 gpd/square
foot, and the maximum monthly use was 0.278 gpd/square foot
(1961, p. 1113). Water use per square foot in shopping centers
may be influenced by the presence of restaurants, cafeterias, and
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self-service laundries ("Water Demands of Decentralized Community
Facilities", 1961, p. 103).
Water use in a single car wash was measured by the floor
area of the building. Mean annual water use was 4.78 gpd/square
foot and the maximum day recorded use was 8.72 gpd/square foot
(Wolff, Linaweaver, and Geyer, 1966, p. 43). They discovered the
maximum demands for water at the car wash included in their study
was in the winter (1966, p. 45).
The floor area of the garage and office was the parameter
used by Wolff, Linaweaver and Geyer (1966) to measure water use
in six service stations. The mean annual water use for the six
was 0.251 gpd/square foot and the range in water use for the
stations was 0.159 gpd to 0.443 gpd/square foot (Wolff, Lina-
weaver, and Geyer, 1966, p. 45). The ratio of peak hour water
demand to mean for days recorded was 19.5—this probably denotes
the effect of car washing (Wolff, Linaweaver, and Geyer, 1966,
p. 45).
Other measures have been made of service station require-
ments. In a survey of sanitary engineers ("Water Use and Sewage
Volume Away from Home", 1957, p. 108), to determine the design
requirements of different commercial and institutional activities,
suggestions were made as to how much water should be allowed for
use by service stations. One recommendation was to allow five
gallons of water per day for each car. Another also suggested
five gallons per car, but also thirty gallons per day for each
employee ("Water Use and Sewage Volume Away from Home." 1957,
p. 108).
Two types of laundries were included in the Commercial
Water Use Research Project. Wolff, Linaweaver, and Geyer, (1966)
combined commercial laundries and dry cleaners, and laundromats.
The design parameter for both was floor area. The average annual
water use was 0.253 gpd/square foot for commercial and dry clean-
ing establishments, and 2.17 gpd/square foot for laundromats.
Peak water use was available for only laundries and dry cleaners;
the ratio of maximum day recorded water use to the mean for days
recorded was 1.29 (Wolff, Linaweaver, and Geyer, 1966, p. 48).
A great many estimates have been made for water use in
restaurants. A survey made in 1961 ("Water Demands of Decen-
tralized Community Facilities", p. 105) stated water use per
seat in restaurants across America vary from 20 gpd to 120 gpd.
The same survey also reported water use on the basis of meals
served, where water use varied from 2.6 gallons to 15 gallons
per meal (1961, p. 105). An earlier survey of v/ater use made in
1957 ("Water Use and Sewage Volume Away from Home", 1957, p. 109)
reported much the same type of water use in restaurants, but it
also allowed for an additional two gallons per person served in
bars and cocktail lounges. Searcy and Furman (1961, p. 1113)
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measured water consumption in two restaurants and one cafeteria
based on per meal use. They found the average monthly consumption
was 7.7 gpd/meal and the maximum monthly consumption was 17.3 gpd/
meal. (1961, p. 1113).
Wolff, Linaweaver, and Geyer (1966) divided the restaurants
in their sample into three groups, drive-in restaurants with
seating facilities, drive-in restaurants with little or no
seating, and traditional restaurants. The parameters they used
for design purposes were water use by car space for drive-in
restaurants with little or no seating, and water use by seat
for drive-ins with seating and traditional restaurants. The
mean annual use for these three types of restaurants was 109
gpd/car space for drive-ins without seating, 40.6 gpd/seat for
drive-ins with seating, and 24.2 gpd/seat for traditional re-
staurants (Wolff, Linaweaver, and Geyer, 1966, p. 51).
Social clubs examined included golf clubs, swimming clubs,
and boating clubs. The parameter used to describe water use in
each was the number of the family or individual memberships.
The mean annual demand for water by golf clubs was 66.1 gpd/
membership, for swim clubs, it was 16.5 gpd/family memberships,
and 10.5 gpd/membership for boating clubs. (Wolff, Linaweaver,
and Geyer, 1966, p. 54).
The number of members was selected as the design parameter
to describe water use for churches. Mean annual use in two
churches was 0.138 gpd/member, and maximum day recorded use was
0.862 gpd/member. (Wolff, Linaweaver, and Geyer, 1966, p. 55).
Water consumption by barbershops was measured in use per
chair. In six barbershops, the average annual use was 54.6
gpd/chair. (Wolff, Linaweaver, and Geyer, 1966, p. 56).
An activity similar to barberships are beauty salons where
the number of stations was used as the predictor variable for
water use. The mean yearly water use for eight salons was 0.269
gpd/station (Wolff, Linaweaver, and Geyer, 1966, p. 58).
Supermarkets vary considerably in the amount of water they
consume in their operation. In a survey of sixty supermarkets,
ranging in size from 4,600 to 35,000 square feet, water con-
sumption per 1,000 square feet ranged from 24 to 3,370 gpd
("Water Demands of Decentralized Community Facilities," 1961,
p. 104). This wide variation in water demand must depend upon
many different effects including: "Degree of business activity,
number of employees, clean-up practices, butchering conditions,
form of air-conditioning and washing and repackaging of veget-
ables." (Water Demands of Decentralized Community Facilities,"
1961, p. 104).
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Water use on highways refers to the restrooms and restaurants
serving these transportation routes. Total water use per service
area has been estimated at 25,000 gpd on the Sunshine Parkway in
Florida, and 10,000 gallons per day at rest areas in Georgia
("Water Demands of Decentralized Community Facilities", 1961,
p. 103). The average number of persons per vehicle stopping
at rest areas has been estimated to be between 1.5 and 3.5. The
percentage of those stopping at rest areas and using the
restaurants has been estimated at both 15 percent and 80 percent.
Between 90 and 100 percent of those people stopping at rest areas
use the rest rooms. ("Water Demands of Decentralized Community
Facilities", 1961, p. 103).
Many other commercial activities have been examined to
determine their water use. These activities and estimates have
included the following: Drive-in theaters, 3 and 7^ gpd/car;
airports 3 to 5 gallons per passenger; trailer camps, 100 to 150
gpd/trailer space; and theaters, 1 to 5 gallons per seat ("Water
Use and Sewage Volume Away from Home," 1957, pp. 108-9, 210).
Forecasting Models
Few forecasting models of commercial water use have been
developed, but the ones presented here are either based upon
extending past trends into the future or using Wolff, Linaweaver
and Geyer's (1966) data as a basis for forecasting water use by
individual commercial activities. Strand (1966) provides a four
step method of forecasting future daily commercial water use
based on past consumption trends. The four steps are: First,
plot past annual water sales and extend the line that best fits
the data to the desired year and find the future daily demand;
second, plot the past number of meters present and the use in
gallons per day separately, extend these trends into the future,
and combine the results to get future water use; third, plot
annual water sales per capita per day, then estimate the future
daily water demand by using an estimate of future population;
and fourth, after examining the above estimates, select a figure
of water use that is a compromise between the various estimates
(1966, p. 523).
A second approach examines each commercial and institutional
activity separately, using data obtained by Wolff, Linaweaver,
and Geyer (1966). Hittman associates (1969) in their Main II.
system devised water forecasting equations for twenty-eight
categories of institutional and commercial water users (p. V-1).
These forecasting equations used data obtained by Wolff, Lina-
weaver, and Geyer in the 1960fs. The water demand for each of
commercial and institutional activities, Hittman associates
examined, were estimated using the following equations (p. V-3):
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Mean annual requirements:
% -
Maximum day requirements:
' CmxdyPd
Peak hour requirements:
(nrO = C PC
vq 'pkhr pkhr
where: "qc = mean annual water requirement for category c.
(qc)jnx(i = maximum day water requirement for category c.
(qc) ^nr = peak hour water requirement for category c.
"C = mean annual coefficient for category c.
C , = maximum day coefficient for category c.
Cpkhr = peak hour coefficient for category c.
PC = value of water use parameter for category c.
Growth models of commercial water uses were based on
projections of past consumption as measured by the parameters.
The values of these parameters are projected to the desired
future year and water use is estimated in that year. (Hittman
associates, 1969, p. V-5). Unfortunately, they found it very
difficult, in most cases, to get data on the values of these
parameters for past years. They selected an alternative method
for projecting the parameter values by using employment data.
They explained this choice as follows (p. V-6):
"The basic assumption implicit in this method can be
stated: For a specific category, in a specific
place, the relationship between employment and the
water use parameter is presumed constant over time.
If the water use parameter is a valid measure of the
activity within the category, this amounts to a
constant productivity assumption, with the impor-
tant qualification that it applies individually to
each category and each place."
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The following procedure was employed to estimate the future
values of the parameters for each commercial activity when the
data on the past value did not exist (Hittman Associates, 1969,
p. V-6):
First, a statistical model is developed for employment in
each activity—
EMEM = f(EMP±, X1, X2, etc.)
where
EMP. = number of employees in category i;
X1, X2 = other right-hand, variables in the growth equation.
ETC.
(') = the project value
Second, the parameter value is projected—
PAR1. = (EMPj/EMPj) PARi where: PAR. = parameter value for
cateogory i.
This method of predicting the parameter value was not
employed for elementary and secondary schools because the actual
parameter values were available (Hittman Associates, 1969t P.
V-6).
They found the employment information for some of the
categories were grouped together with other commercial categories,
This caused them to group these activities together and derive
growth equations for the entire group.
These derived growth equations are used to project the
future values of the individual parameters in the following
manner (Hittman Associates, 1969, p. V-14):
4EMPi/t = f (X1, X2, X3, etc.)
EMPi' = AEMPi/At At + EMPi
PAR1. = PAR. EMP!/EMP. WHERE:
J J •*• *•
El-IPi = number of employees in category group i
t = calendar year
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X1, X2 = right - hand variables
X3, etc. in growth equation
PAR- = parameter value for category j
0
(') = projected value.
The growth equations of the ten groups are similar in the types
of variables they contain. Except for the equations for schools,
they all contain some measure of population change, whether it is
historical or projected change, though none of the equations
contain both terms. "The historical term suggests that growth
in correlated categories follows increases in population by
some log time, but the growth in laundries and total services
employment apparently tends to be coincident with population
growth". (Hittman Associates, 1969, p. V-14).
A second set of important variables in these equations are
the historical and the projected rates of change in total service
employment. Those equations that contain negatively correlated
historical rates of change in total service employment, also
contain the projected total service employment variable which is
more heavily weighted." This may demonstrate the tendency of
individual entrepreneurs to balance expected future business
growth against recent increases in capacity". (Hittman
Associates, 1969, p. V-15).
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BIBLIOGRAPHY FOR APPENDIX C
Hittman Associates. Forecasting Municipal Water Requirements,
Vol. I.; The Main II. System. Columbia, Maryland. Hittman
Associates, Inc., 1969.
Searcy, Phillip E. and Furman, Thomas de S. "Water Consumption
by Institutions." Journal, American Water Works Association,
LIII (September, 1961), 1111 - 9.
Strand, John A. "Method for Estimation of Future Distribution
System Demand." Journal, American Water Works Association,
LVIII (May, 1966), 521-5.
U.S., Congress, Senate. Select Committee on National Water Resources,
Water Resources Activities in the United States; Future
Water Requirements for Municipal Use. Committee Print No. 7.
Washington, D.C.:Government Printing Office, 1960.
"Water Demands of Decentralized Community Facilities." Public Works.
XCII (September, 1961), 102 - 5.
"Water Use and Sewage Volume Away From Home?" Public Works, LXXX
VIII (March, 1971), 108 - 9, 210.
Wolff, Jerome B.; Linaweaver, P.P. Jr.; and Geyer, John C.
Report on the Commercial Water Use Research Project; Water
Use in Selected Commercial and Institutional Establishments
in the Baltimore Metropolitan Area. Baltimore;The John
Hopkins University,1966.
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APPENDIX D
INDUSTRIAL WATER DEMAND: A LITERATURE REVIEW
INTRODUCTION
Industrial water consumption is a third major source of
water demand on municipal water utilities and is second in
importance to that of residential users. In contrast to re-
sidential and commercial users, most industries fill demands for
water from their own sources. Water use between individual
residential and commercial consumers does not vary as much as
between different industrial users. This extreme variation is
caused by the wide range of activities and manufacturing pro-
cesses engaged in by industry. Explaining present water use and
forecasting future consumption by industry is made difficult by
this great variety in industrial processes. Usually, projections
of industrial water use are made according to the type of indus-
try involved and by using employment figures.
Water Use in Industry
The percentage of total water demand in America devoted to
industrial purposes is substantial. Analyses of municipal water
utilities have found that about one fourth of their water is used
by industry (Forges, 1957, p. 1577; and U.S. Senate, 1960,
Committee Print, No. 7). Municipal water utilities are not the
only source of industrial water—many industries have developed
their own source of supply. It was estimated in 1965 that
industry supplied 1.70 billions of gallons per day of their
water needs themselves (Murry, 1965, p. 4). The percentage of
fresh water consumed by industry obtained from municipal sources
was only about ten percent in the 1960's (Kollar and Brewer,
1968,-p. 1130).
The sources of industrial water are varied and changing
over time. Kollar and Brewer (1968, pp. 1129-30) summarized
these various sources of water in their study of the industrial
that account for 97 percent of all industrial water consumed.
"In 1964, fresh water withdrawals accounted for
11,200 bil-gal. of the total 14,000 bil gal.
withdrawal. Company controlled sources pro-
vided 9,800 bil gal. of which 8,500 bil gal.
were obtained from surface supplies, and
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1,360 bil gal. from wells. The remaining 1,380 bil
•jal. were purchased from public water systems."
(Kollar and Brewer, 1968, p. 1130).
The remainder of water withdrawn for industrial purposes in
1964 was brackish containing 1,000 ppm dissolved solids (Kollar
and Brewer, 1968, p. 1130). Though industries were using more
water in 1964 than in previous years, the percentage of total
industrial water provided by municipal utilities declined.
(Kollar and Brewer, 1968, p. 1133)• The relatively minor
dependency of industry on municipal utilities is because water
from company owned sources and brackish water is lower in cost
than municipal water (Kollar and Brewer, 1968, p. 1131).
Industry may obtain relatively little of its water from
municipal sources at present, but this may change in the coming
years. There are two reasons why this change may occur. First,
with water becoming more scarce, new and expensive facilities
will be needed to capture and transport it to consumers. Public
water authorities may be the only ones able to afford the
development, of such facilities. Second, as the regulations
controlling effluent become more stringent, it may induce in-
dustries to connect themselves to municipal water treatment
and sewer systems (Howe, 1968, pp. 54-55).
The uses for water in industry are varied, but they can
be summarized into four classifications (Kollar and Brewer,
1968, pp. 1132-33). The first classification is process water,
which is water used directly with the materials used in the
production process. The second classification contains water
used for cooling and condensing in stream electric generating
plants. The third classification is water employed to cool
machinery used in the production process, or the materials under-
going processing. The fourth classification is water used for
sanitary purposes and boiler feedwater. Another category can
also be included containing water used for sprinkling systems
and fire protection. The percentage of water in a factory
devoted to each of these categories varies according to the
size of the plants. Larger plants devote a greater percentage
of the water they use to cooling than smaller plants, but water
used for sanitary and service purposes is more important in
small plants than large ones (Green, 1951f p. 595).
In 1964, major industrial users of water consumed 3»700
billion gallons in process operations or over 26% of the total
water they demanded (Kollar and Brewer, 1968, pp. 1129, 1134).
Water for all cooling and condensing purposes accounted for
9,400 billion gallons in 1964 or about two-thirds of all the
water used by manufacturers. In some industries, over &5% of
all water demanded is devoted to cooling and condensing purposes
(Kollar and Brewer, 1968, p. 1133). Hurry (1965) reported water
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used in cooling was even more important than this. According to
him, 97$ of all water used in thermoelectric plants is for
cooling purposes, and for all industrial water combined, 90% is
for cooling purposes (1965, p. 4). Sanitary demands for water
are small compared to water use in other industrial processes.
It has been found to range from twenty to thirty gallons per
day per employee (Dickerson, 1970, p. 612). The heaviest demand
for sanitary water is usually during the day shift when the
office staff is present and the laboratory and maintenance crews
are at their maximum size (Dickerson, 1970, p. 612). The amount
of water set aside for fire protection varies according to the
type of industrial process and hazard involved. Since fire
demands often are greater for industrial plants than commercial
or residential structures, the water pressures are nearly twice
as great. Usually a factory must maintain its own water storage
and fire water distribution system. (Dickerson, 1970, p. 612).
Most industrial water is consumed by only a relatively few
industrial plants and by a few major industry groups. Less than
three percent of all the major industrial water users in the
United States consume more than ninety-seven percent of all the
water used in industry (Kollar and Brewer, 1968, p. 1130). Five
industries, metals, chemicals, pulp and paper, petroleum and
coal, and food processing use about eighty-five percent of the
water used in industry (Ruble, 1965, p. 831.). Data reported by
Feth in 1973 showed an even greater concentration of water use
in these five industry groups (p. I 12). He reported primary
metal industries annually withdrew 3»899 billion gallons; paper
and allied products withdrew 2,078 billion gallons; petroleum
and coal products withdrew 812 billion gallons (1973, P. 112).
Water use for an industry group can vary substantially from one
factory to another. Pulp and paper mills use between twenty and
sixty million gallons a day. (Guthrie, 1969, p. 533). Chemical
plants consume between a few hundred thousand gallons a day to
several million a day (Dickerson, 1970, p. 612).
McGregor (1968) analyzed water use in different industries
in Northern Georgia to discover how it was employed in various
production processes. Forty-four four-digit standard industrial
code industries were selected for analysis (McGregor, 1968,
p. 66). Water users were broken down into five categories based
on the amount of water withdrawn annually per employee. (Table
C-1).
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TABLE C.
INDUSTRIAL WATER USER CATEGORIES
CATEGORY PER EMPLOYEE REQUIREMENT NUMBER OF FOUR-
(THOUSANDS GALLONS;DIGIT INDUSTRIES
I. 1-9 23
II. 10-99 10
III. 100-199 5
IV. 200-299 3
V. 300 or more 3
Source: McGregor, John R. "An Approach to the Regulation of
Water use in Manufacturing: A Study of North Industries."
Proceedings of the Indiana Academy of the Social Sciences.
(1968), p. 70.
Water used in Category I. industries was nearly entirely
used for drinking, washroom, and sanitation purposes. The major
use of water in Category II. industries was for drinking, wash-
room, and sanitation purposes, as a material in the production
process, and for washing and cooling machinery. Water use in
groups III., IV., and V. was similar to that in categories I.
and II. except for significant use of water in rinsing, scalding,
cooking, and sterilizing in food processing (McGregor, 1968,
pp. 69-72).
Water use in separate elements of the production process
may be subject to changes in social taste. If consumer pre-
ferences change from one product to another, this can cause
increases in water used in production (Sewell and Bower, 1968,
pp. 25-26).
Seasonal variations can also cause fluctuations in the
amount and types of water use. Climatic changes through the
year can affect how much water is used for cooling (Sewell and
Bower, 1968, p. 35). The rate of production may vary according
to the time of the year, as in the automobile industry, where
more cars are produced in the first half of the year (Sewell and
Bower, 1968, p. 36). The type of product produced may vary by
the season of the year. The demand for gasoline is greatest in
the summer, whereas for heating fuel, the peak demand occurs in
the winter. (Sewell and Bower, 1968, p. 36). Daily water use
can be affected by fluctuations in the rate of the incoming raw
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materials, or by equipment failures. (Sewell and Bower, 1968,
p. 39).
Each production process involved in industry may require a
specific grade of water. Industry may demand one quality of
water for boiler water, another for cooling water, and one each
for the different processes involved in the production line
(Guthrie, 1969, p. 533). Industrial production is generally of
two types—either simple, where there are just a few different
processes involved, or complex, where there are many different
processes present—each requiring a different quality and quan-
tity of water (Brewer, 1968, pp. 90, 93). Vaughn (1971, pp.
144-46) has summarized the types of water involved in industrial
production into three categories. First, is high quality water
that is relatively unaffected by the production process. An
example of this is cooling water which many times is maintained
in closed systems and does not experience any significant change
in quality. Second, is low quality water whose quality is
significantly altered by the production process. Third, is a
high quality water that is also significantly affected by the
production process. The most important requirement of industrial
water is the uniformity in its quality level. "It is usually
possible to compensate for deficiencies in the desired standard,
but it is nearly impossible to adjust for unexpected variations."
(Guthrie, 1969, p. 533).
Since completely pure water is not needed in some industrial
processes, industry engages in the recycling of water. Kemmer
(1970, p. 708) describes three approaches taken by industry in
recycling water. First, some industries employ the effluent
from municipal sewage plants for use in their production pro-
cesses. A second older method is for a plant located downstream
from other plants and cities to collect their discharges. Though
this is easily accomplished, it means the industry collecting the
effluent may be exposed to contamination of various strengths and
types. Finally, many plants recycle their own water, employing
the highest quality water in the most sensitive processes, and
recycling the poor quality water into less sensitive areas.
The recirculation of water within a plant is very common
and has been increasing over time. The rate of recirculation is
defined as the ratio of the gross water used in a plant over the
water pumped into the factory (Kollar and Brewer, 1968, p. 1133).
The recirculation rate in 1964 for large water using industries
was 2.18; in 1954, it was 1.86 (Kollar and Brewer, 1968, p. 1133)
The recirculation ratios of the five largest water consuming
industries, chemicals, petroleum, pulp and paper, food process-
ing, and primary metals, increased at an annual rate of 1.8
percent between 1954 and 1964. (Stewart and Metzger, 1971, p.
156). The recirculation of water by industry has been found to
be greater in areas where water is scarce (Kollar and Brewer,
1968, p. 1135).
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An industry's decision to recirculate water depends on the
grade of water to be recycled, and the costs incurred. It is
usually profitable to recycle low grade water whose quality is
significantly affected by an industrial process, where high
quality is not demanded (Vaughn 1971, p. 146). High quality
water, which may be used in closed cooling systems not affected
by the industrial process, demands little more than to be cooled
to a lower temperature for reuse. (Vaughn, 1971, pp. 144-45).
In contrast, it may be very expensive to recycle a high grade
water whose quality is severely affected by an industrial
process, since the necessary facility may be more advanced than
normal sewage treatment plants (Vaughn, 1971, p. 146). Water
whose quality has been significantly affected can be recir-
culated back into a factory, but it may be employed in a process
not demanding a high standard of quality.
The extent of water recirculation depends on what process
it has been employed in. Except for refineries, where cooling
water may be recirculated over twenty times, few factories re-
circulate substantial amounts of cooling water, and most is
discharged. (Kollar and Brewer, 1968, p. 1133). About one
third of the factories surveyed in 1964 recirculated boiler
feedwater and sanitary water, but since this is a small portion
of the water used in manufacturing, the amounts recirculated
are not very significant. (Kollar and Brewer, 1968, p. 1134).
Large amounts of water used in process operations are recir-
culated in part to recover materials and products. The re-
circulation rate of process water may be about 4.5 (Kollar and
Brewer, 1968, p. 1135).
Recirculation is a function of technology which is an
influential variable on many aspects of industrial water use.
Technological change can manifest itself in many ways, such as
new products, new industrial processes, new kinds of raw
materials, and new methods in handling water. (Sewell and
Bower, 1968, p. 24). The influence of technology is difficult
to measure for two reasons. (Sewell and Bower, 1968, pp. 24-25).
First, forecasts of technological change are difficult to make,
especially beyond five or ten years. Second, the adoption rate
of new technology is unknown. "We have a basis in past history
for estimating the rate of innovation, but recognized urgency,
higher costs of water, or other causes contributing to concerned
efforts may introduce a new trend." (U.S. Senate, Committee
Print, No. 32, 1960, p. 32).
Water use and water recirculation are also dependent upon
the presence of effluent charges levied on industry.
188
-------
"Increased use of sewer rental charges, based on the
amount of water used as a method of financing sew-
erage and sewage treatment, has a tendency to in-
crease water conservation and reduce the use of
water. On the other hand, when sewer service
charges are based on the strength of the sewage,
there is a tendency to use more water for trans-
portation of the wastes than is really needed, in
order to reduce the strength of the sewage." (U.S.
Senate, Committee Print, No. 7, 1960, p. 16).
Elliot (1973) conducted a statistical analysis to determine
the influence of surcharges on industrial wastes. He found a
ten percent increase in sewage surcharges caused a decrease of
around eight percent in the amount of wastes discharged by
industry. A similar increase in sewage surcharges caused a
decrease of six percent in the water used in industry. (1973,
pp. 1127, 1129).
The effect of price on water demand is large enough to
influence industry's consumption. Afifi (1969, p. 41) reported
that the demand by large industrial consumers for water is more
elastic than for residential consumers. Industries that produce
more expensive products per 1000 gallons of water will find their
production process less affected by increases in the price of
water than industries producing goods lower in price in relation
to the cost of water. (Kollar and Brewer, 1968, p. 1137).
Usually, the cost of water is a small portion of the per unit
cost of a product, ranging from about 0.1 to 5.0 percent.
(Sewell and Bower, 1968, p. 22).
Statistical analyses have shown the price of water to be
significant in determining the demand for industrial water.
Elliot (1973) found the price of water to be significant in
explaining both the amount of industrial wastes discharged and
the amount of water consumed. His derived equations are as
follows (1973, PP. 1128-29):
For waste treatment:
T = 13.11 - 1.46S - 120.00 G + 36.20 P
For water:
W = 2.22 - 36.79 N - 0.52 S + 8.63 P + 75.10 FK
Where:
T = pounds of B.O.D. per $1,000 value added in manufactur-
ing
S = surcharge in dollars per 1,000 Ib. of B.O.D.
189
-------
G = gross marginal cost of water and normal sewer in
dollars per 1,000 gallons
P = price of labor in dollars per hour
YJ = gallons of water per day per $1 , 000 value added to
manufacturing
N = net marginal cost of water and normal sewer in dollars
per 1,000 gals.
FK = proportion of city value added, accounted for by food
and kindred products
The difference between variables G and N in the above
equations has to do with the amount of sewage discharge, indus-
tries are permitted. The sewer charge included in variable G is
a fixed percentage of the water charge. However, for variable
N, the sewage surcharge does not account for all the sewage
discharged, but only that above a certain minimum level of
concentration (Elliot, 1973, p. 1123). The coefficient of
determination for the two equations by Elliot are quite low,
only 0.17 for his waste treatment equation, and 0.32 for his
water equation (1973, pp. 1128-29).
Another analysis of the effect of price upon industrial
demand for water was conducted by De Roog (1974). He divided
industrial water into four types; cooling, processing, steam
generation and sanitation and measured the impact of price on
the first three. His price variable (pGjt) is a weighted mean
and takes into account the price of both new water and recycled
water. This price variable is defined in the following equation
(De Roog, 1974, p. 404):
PGjt - ^Pwjt + Swjt + Prjt
where :
P ., = price of new water
wjt
Pr1t = Price o:C recycled water
G..L. = gross water use
J^
= quantity of intake water
190
-------
The cost of new water and recycled water includes many
different costs such as maintenance costs, the cost of water
brought from a public water utility, and capital costs (DeRoog,
1974, P» ^04). The equations he derived included three var-
iables, the price variable, a value of output variable, and a
technology index which measures capital and labor inputs. (1974,
pp. 404-5). His results showed that as the cost of water in-
creases, its use in cooling, processing, and steam generation
declines (1974, pp. 405-6).
Increases in the price of water may in some instances not
cause declines in water consumption, if other costs to industry
are increasing at a faster rate. Seagraves (1972, p. 476)
suggests this may occur where the cost of labor is increasing
faster than the cost of water, so that water is substituted for
labor in dealing v/ith industrial wastes.
Forecasting Industrial Demand for Water
To project future industrial use of water requires an
understanding of many different variables. Some simple fore-
casting equations have been developed to project industrial
water consumption, but they overlook many of these influential
variables that are discussed in only a few forecasting models.
Projections of water demand by manufacturers are often just
extensions of present water use trends. Strand (1966) offers
one such forecasting model. His procedure for estimating future
average daily industrial water demand involves three steps as
follows: "(1) plotting annual sales (not including large users)
and reducing to future daily demand, (2) discussing with large
industrial users their needs for water in the future, including
determination of present hourly use on maximum day by field
study, and (3) adding the two estimates to determine future
demand" (Strand, 1966, p. 523).
Forecasting methods have become more sophisticated in
recent years with the addition of the study of employment in
industry and examining industry groups separately. The amount
of water withdrawn by a plant appears to be a function of the
number of employees working in the factory (Green, 1951, p. 594).
Stewart and Metzger (1971) produced a ratio forecasting future
industrial water based not only on changes in employment, but
also changes in recirculation and output. Their ratio is the
following (1971, p. 155):
F = EO/RT
191
-------
where:
F = ratio of future to present industrial water use.
E = ratio of future employment in industry to present
employment.
0 = ratio of future industrial output per employee to the
present value
R = ratio of future use of recirculated water to present
recirculation
T = ratio of present gross water use per unit of production
to the gross water requirements in the future.
Stewart and Metzger (1971) have estimated what the values
of the variables in their equation will be. They report in-
dustrial employment is increasing at a rate of about one percent
annually (1971, p. 156). The measure of industrial productivity,
variable 0, is increasing at an annual rate of almost three
percent, and for the large water using industries, the rate is
between two and four percent annually. (Stewart and Metzger,
1971, p. 156). The recirculation ratios of the five largest
water using industries increased 1.8 percent between 1954 and
1964. They estimate that for industry in general, recirculation
will increase at a rate of two percent annually (1971, p. 156).
Finally, they forecast the value of T will be about 1.5 in fifty
years and will almost eliminate the influence of increases in
industrial employment. (1971, p. 157).
Mercer and Morgan (1974) used an approach also considering
employment, but broke industry down into categories defined by
two digit standard industrial codes. They derived two equations,
one for estimating water use per employee for each industry
category, and one for estimating employees in firms not covered
by the census of water use. These equations were (Mercer and
Morgan, 1974, p. 797):
Water use per employee:
= OT./N..
where:
W. = water use per employee in the ith two digit standard
industrial code.
OT. = sum of water use by firms in the ith two digit
standard industrial code.
192
-------
N. = sum of employment in ith two digit standard industrial
1 code.
Employment by firms:
S, = L./R,
where:
S. = the average employment of a firm in the ith industry
L. = total employment in the ith industry minus the employ-
1 ment of the firms included in the census of water use;
R. = number of firms in the ith industry minus those inclu-
ded in the census of water use.
The second equation was employed only to gain information
on industries too small to be contained in the census of
manufacturing. If their model is used to calculate water use
for a number of years, trends may be observed and can be useful
in planning future water facilities (Mercer and Morgan, 1974,
p. 800).
A related technique was employed by Rollins, Allee, and
Lawson (1969) to project industrial water use per employee in
hydrological areas in the North Atlantic Region. They used
three forecasting procedures. In the first, they multiplied
water intake and discharge by employee by estimates of employ-
ment change. The second was output based where the water intake
and discharge per employee was multiplied by estimates of
employment and output by employee. The third equation was simi-
lar to the second, but included projected changes in the amount
of water recycling. (Rollins, Allee, and Lawson, 1969, pp. 36,
AO). Projections of employment based on past experience may be
dangerous, especially if based on a short time period, because
the employment rate may have made dramatic changes with fluc-
tuations in the economy. (Staley, 1960, p. 12).
Staley (i960) derived a model for estimating what portion
of total water consumed in a city would be devoted to industrial
activities. The purpose of his model was to determine how much
industrial employment a river basin can support. Not all water
in a river basin can be devoted to industrial consumers, since
residential and commercial users must also be supplied. He
derived three simultaneous equations to obtain, estimates of the
amount of industrial employment, the amount of water used by
industry, and the amount of water used in homes and commercial
establishments. (Staley, 1960, p. 7). His first equation
determines industrial water consumption (i960, p. 8):
193
-------
Equation 1
X = T-D
where:
X = industrial water use
T = total water use
D = domestic water use
The second equation determines industrial employment (Staley,
1960, p. 8):
Equation 2
M = is1
where:
M = industrial employment
ai = percentage of industrial water used in industry
i (i = 1...,n)
Bi = gallons of water per employee in industry i;
X = industrial water use.
The third equation determines the-amount of domestic water
use. (Staley, 1960, p. 8).
Equation 3
D = (M + \M + yM + xyM),
where:
D = the amount of domestic water use
M = amount of industrial employment
y = induced employment
6 = consumption of water per person per year
X = the dependent/employee ratio
194
-------
He assumed: y = 1 , or that each new industrial worker provided
for one secondary employee, 5 = 10,950, and x = 1.5 (1960, p. 8).
Thus, the third equation can be written as follows (Staley,
1960, p. 9):
Equation 3*
D = 54,750 M
He solved the simultaneous equations in the following mannei
(1960, p. 9). First, he substituted equation 3' for D in equa-
tion 1 :
X = T - 54,750M; then, he substituted equation 2 for M to
der,ive equation 4:
Equation 4
X = T - 54,750 (a1X/B1 + a2X/B2 +....+ aJ1X/Bn)
The solution to equation 4 is:
X = T/(54,750a1/B1 + 54,750a2/B2 + . . .+54,750an/Bn + 1)
This model is designed to tell how much industrial employ-
ment can be supported in a city with a given river flow. Given
a rate of employment growth, it is possible to estimate when the
maximum employment level will be reached. (Staley, 1960, p. 9).
Employment data was used by Hittman Associates (1969) to
forecast water use by different industry groups. Water use per
employee was the parameter they used to measure consumption.
This approach is best suited for industries that receive most of
their water from municipal utilities. Unfortunately, industries
that require large amounts of process water usually develop
their own sources of supply. (Hittman Associates, 1969, p. VI- 1)
The water use equations they used are (1969, p. VI-2):
«n ' Un pn
= ^ n' mxdy n
where
pkhr Pn
qn = average annual water requirement for industrial
category n;
195
-------
(q ) = maximum day water requirement for industrial
n mxay category n.
(Q ) vv, = peak hour water requirement for industrial
n pKnr category n;
U = average annual water usage coefficient for
industrial category n;
(U ) = maximum day water usage coefficient for indus-
x n'mxdy tr.1ft1 0«^o-rt-rv n
(U ) ,,hr, = peak hour usage coefficients for industrial
n plcnr category n
P = water use parameter (category employment) for
industrial category n.
The statistical models that were developed to project
employment were based on data from the same sample of cities.
The models were derived for two-digit standard industrial code
categories. Because of difficulties encountered in collecting
employment data, similar two-digit S,I.C. industrial categories
were grouped together so that ultimately eleven groups were
formed. (Hittman Associates, 1969, p. VI-6).
The following equations were used to project employment in
each group. (Hittman Associates, 1969, p. VI-8):
INDm/P = !WDm/P + At A(INDm/P)/At
lNDffl = P1 lNDm/P
where:
' = projected value
IwDm = employment in industrial group m
P = resident population
t = calendar year.
The employment change in the different categories contained
in the major groups can be found as follows (Hittman Associates,
1969, p. VI-8): EMPn = EMPn INDm/IWDm
where:
EMPn = employment in category n, within indusgry group m.
196
-------
Though employment data appears very helpful in explaining
water use, other water forecasting approaches attempt to in-
tegrate many different economic, political, and social influences,
Economic base studies have been proposed as methods of under-
standing the nature of growth in an area. This includes an
understanding of the growth potential of industries present in
an area and the attractiveness of the area to other industries
(Sewell and Bower, 1968, p. 22). One such technique is the
export-base approach. This technique identifies a region1 s
major export oriented industries, their existing and potential
markets, and their expected success in these markets. It also
determines how much local service industry will be needed to
support the exporting industries and the local population.
(Howe, 1968, pp. 64-65). In such an analysis, it may be
possible to predict a region1 s future industrial activity, and
hence, project industrial water use.
Bower (1968) has attempted to identify the variables that
establish water use in manufacturing. These variables are
indicative of such things as the production process, raw
materials employed, output, level of production, and pollution
controls. These influences are presented in the following
function (Bower, 1968, pp. 88-89):
QIt* Ut' QEt' WDt' WEt = f(CI» PP " PM» RM» OR» R'
HP, CE)
where :
QIt = time pattern of water intake
U. = Consumptive use
Q_. = final effluent
£
-------
MR
BP
= possibilities of the recovery of materialsand by-
product production
= cost of handling and disposing of final effluent
The variables included in Bower's function can be grouped
into different categories (Bower, 1968, p. 89). The first group
is the technology of production and refers to how many steps are
involved in the manufacturing process, and the effect of tech-
nology on production (Bower, 1968, pp. 90, 94). The second
group is concerned with regional industrial location and the
difference in the industrial environment between regions, in-
cluding markets, raw materials, and transportation. (Bower,
1968, pp. 99, 103). The third group is in—plant water utiliz-
ation variables. These variables determine the amount of water
used in processing and cooling uses, the quality standards of
the water required, and the amount of recirculation possible.
(Bower, 1968, pp. 107, 117). The fourth group is the water
environment. These variables include the availability of water
effluent controls, and the availability of areas for the dumping
of waste materials. (Bower, 1968, pp. 120-21). The final group
is the influence of government policy on the cost of water and
disposal of wastes. (Bower, 1968, p. 125).
Finally, a forecasting model put forward in 1951 by Elder
also weighs many different variables, but these are more bus-
iness oriented than the ones mentioned previously. This model
attempts to explain all municipal water use and contains measures
of residential, commercial, and industrial activity. It is based
upon his observation of how water sales have fluctuated with
changes in the state of the economy (1951, p. 129). To measure
the effect of the economy on water use, he used the "Index of
Business Activity in Southern California" produced by the
Security First National Bank of Los Angeles (1951, p. 129).
"This index is a weighted average of ten seasonally
adjusted business series. With their respective
percentage weights, these are as follows: depart-
ment store sales, 15; building permits, 5; Los
Angeles bank debits, 20; residential city bank
debits, 5; agricultural city bank depits, 5;
industrial employment, 20; industrial power sales,
13; railroad freight volume, 6; telephones in use,
7; and real estate activity, 4" (Elder, 1951, p.
129).
He correlated this index with per capita water production for the
years 1928 to 1950, and derived the following equation (1951, p.
129):
198
-------
W = 0.365 I + 07;
where:
W = regional water production in gallons per person per day;
I = business activity index.
The coefficient of correlation for this equation was
.94 - .02. There was a lag of two years between the values for
per capita water consumption and the business activity index.
The effect of changes in business seem to take two years before
it affects water consumption (Elder, 1951» pp. 129-130). It
appears that if it is possible to forecast the economy, then one
may be able to predict changes in industrial water demand.
199
-------
BIBLIOGRAPHY FOR APPENDIX D
Afifi, Hamdy, H.H. "Economic Evaluation of Water Supply
Pricing in Illinois.'» Journal. American Water Works
Association. LXI (January, 1969), 41-8.
Bower, Blair T. "Industrial Water Demands." Forecasting the
Demands for Water. Edited by W.R. Sewell and Blair T.
Bower. Ottawa:Policy and Planning Branch, Department
of Energy, Mines and Resources, 1968.
DeRooy, Jacob. "Price Responsiveness of the Industrial Demand
for Water." Water Resources Research. X (June, 1974), 403-6,
Dickerson, Bruce W. "Selection of Water Supplies for New
Manufacturing Operations." Journal, American Water
Works Association, LXII (October, 1970), 611-5.
Elder, Clayburn C. "Determining Future Water Requirements."
Journal, American Water Works Association, XLIII
(February, 1951), 124-35.
Elliott, Ralph D. "Economic Study of the Effect of Municipal
Sewer Surcharges on Industrial Wastes and Water Usage."
Wa£er Resources Research, IX (October, 1973), 1121-31.
Green, Roy R. "Water Use in Industry." Journal, American
Water Works Association, LXIII (August, 1951), 591-9.
Guthrie, J.L. "Tailoring Water Treatment for Industrial Use."
Journal. American Water Works Association, LXI
(October, 19b9), 533-8.
Hittman Associates. Forecasting Municipal Water Requirements.
Vol. I; The Main II. System. Columbia, Maryland.
Hittman Associates, Inc., 1969.
Howe, Charles W. "Municipal Water Demands." Forecasting the
Demands for Water. Edited by W.R. Sewell and Blair T.
Bower. Ottawa:Policy and Planning Branch, Department
of Energy, Mines and Resources, 1968.
Kemmer, Frank N. "The Influences of Water Pollution on
Utility of Water by Industry." Journal. American
Water Works Association. LXII (November, 1970). 708-10.
200
-------
Kollar, Konstantine L. and Brewer, Robert."Water Requirements
for Manufacturing." Journal. American Water Works
Association. LX (October, 1968), 1129-40.
McGregor, John R. "An Approach to the Regulation of Water Use
in Manufacturing: A Study of North Georgia Industries."
Indiana Academy of Social Sciences; Proceedings of the
Annual Meeting. C1971). 64-78.
Mercer, Lloyd J. and Morgan, Douglas W. "Estimation of
Commercial, Industrial and Governmental Water Use
for Local Areas." Water Resources Bulletin, X (August,
1974), 794-80.
Forges, Ralph. "Factors Influencing Per Capita Water
Consumption." Water and Sewage Works. CIV (May, 1957),
199-204.
Rollins, N.W., Allee, D.J. and Lawson, Barry. "Industrial
Water Use in the North Atlantic Region: Projections and
Methodology," Cornell University Water Resources and
Marine Sciences Center; Technical Report No. 17, Ithaca,
New York, October, 1969.
Ruble, Earl H. "Industrial Water Requirements." Journal.
American Water Works Association. LVII (July, 1965), 831-3.
Seagraves,'J.A. "Sewer Surcharges and Effect on Water Use."
Journal. American Water Works Association, LXIV (August,
1972), 476-80.
Sewell, W.R. Derrick; Bower, Blair T., et.al. Forecasting the
Demands for Water. Ottawa: Policy and Planning Branch,
Department of Energy, Mines, and Resources, 1968.
Staley, Charles E. Municipal and Industrial Water Requirements
of the Kansas 'River Basin. Lawrence, Kansas; Center
for Research in Business, The University of Kansas,
October, 1960.
Strand, John A. "Method for Estimation of Future Distribution
System Demand." Journal, American Water Works Association,
LVIII (May, 1966), 521-5.
Stewart, Robert H. and Metzger, Ivan. "Industrial Water
Forecasts." Journal, American Water Works Association,
LXIII (March, 1971), 155-7.
201
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Thompson, Russell G. and Young, H. Peyton. "Forecasting
Water Use for Policy Making: A Review." Water Resources
Research. IX (August, 1973), 792-9. "~~
U.S., Congress, Senate. Select Committee on National Water
Resources. Water Resources Activities in the United
States; Future Water Requirements for Municipal
Use. Pursuant to S. res. 48, 86th Congress, 1960,
Committee Print No. 7.
U.S., Congress, Senate. Select Committee on National Water
Resources. Water Resources Activities in the United States;
Water Supply and Demand. Pursuant to S. res. 48. 8bth
Congress, I960, Committee Print No. 32.
U.S. Department of the Interior. Estimated Use of Water
in the United States. 1965. by C. Richard Murry.
Geological Survey Circular 556. Washington, D.C.:
Government Printing Office, 1968.
U.S. Department of the Interior. Water Facts and Figures
for Planners and Managers. by J.H. Feth. Geological
Survey Circular 601-1. Washington, D.C.: Government
Printing Office, 1973.
Vaughn, Stuart H. "Water for Industrial Needs: What, Where,
When?" Journal. American Water Works Association,
LXIII (March, 1971), 142-7.
202
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
REPORT NO.
EPA-600/5-78-008
TITLE AND SUBTITLE
PLANNING WATER SUPPLY: COST-RATE DIFFERENTIALS
AND PLUMBING PERMITS
6. PERFORMING ORGANIZATION CODE
3. RECIPIENT'S ACCESSION NO.
. REPORT DATE
May 1978 (Issuing Date)
AUTHOR(S)
Haynes C. Goddard, Richard G. Stevie, and Gregory D.
8. PERFORMING ORGANIZATION REPORT NO.
"PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Economics
University of Cincinnati
Cincinnati, Ohio 45221
10. PROGRAM ELEMENT NO.
1CC614
11. CONTRACT/GRANT NO.
R-803596-01
I. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Laboratory—Cin.,OH
Office of Research and Development
U.S. Environmental Protection Agency
Cineinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/14
5. SUPPLEMENTARY NOTES
Project Officer: Robert M. Clark
513-684-7209
This study is concerned with measuring the cost of water supply and net revenue
differences among customers by user class and location, and analyzing future water
demand on the basis of plumbing permit application data. For water supply, a method-
ology based upon engineering principles was employed to collect data on distance,
altitude, and costs of water delivery to sampled customers in a water utility service
area. Estimates of cost elasticity were obtained. Altitude was not significant, but
distance was found positively correlated with cost. In one location, at an extreme
of the service area, this total cost elasticity became greater than one. Thus, cost
economies for transmission of water exist, but are limited as indicated by this cost
elasticity estimate. In addition, these costs were compared to the revenues collecte
from each customer sampled. The pattern of costs and computed net revenues were then
examined through the use of computer mapping techniques. All this information become
useful for examining water rates and system expansion.
Also examined is the hypothesis that future water use can be predicted through
the use of plumbing permit records. It was concluded that the evidence for this
same supply area does not support the hypothesis.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
Cost Analysis; Cost Comparison; Demand
(Economics); Econometrics; Economic
Analysis; Forecasting; Prices; Public
Utilities; Rates (Costs); Regional
Planning; Utilities; Water Consumption;
Water Distribution; Water Pipelines;
Water Services; Water Supply
Building Permits; Cost
Rate Differentials, Dis-
:ance Costs; Plumbing Per-
nits; Regionalization;
Jater Demand; Water Demand
forecasting; Water Supply
osts; Water Supply Econo-
13B
91J
. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
Unclassified
21. NO. OF PAGES
215
20. SECURITY CLASS (This ptgej
Unclassified
22. PRICE
form 2220-1 (9-73)
203
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