United States
             Environmental Protection
              Municipal Environmental Research
              Cincinnati OH 45268
EPA 600 5 78-008
             Research and Development
Planning Water
Supply: Cost-Rate
Differentials and
Plumbing  Permits


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
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      1.  Environmental Health Effects Research
      2.  Environmental Protection Technology
      3.  Ecological Research
      4.  Environmental Monitoring
      5.  Socioeconomic Environmental Studies
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      7.  Interagency Energy-Environment Research and Development
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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-
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 This document is available to the public through the National Technical Informa-
 tion Service, Springfield, Virginia 22161.

                                        May 1978
                  AND PLUMBING PERMITS
Haynes C. Goddard, Richard G. Stevie and Gregory D. Trygg
                 Department of Economics
                University of Cincinnati
                 Cincinnati, Ohio  45221
                     Project Officer
                     Robert M. Clark
             Water Supply Research Division
       Municipal Environmental Research Laboratory
                 Cincinnati, Ohio  45268
                 CINCINNATI, OHIO  45268

       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.

     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


     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

     °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.

     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.


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
   A.  Supplement to Section IV, Part A ................... 141
   B.  Residential Water Demand: A Literature Review
   C.  Commercial Water Demand: A Literature Review ....... 171

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

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

Number                                                      Page
  1    Summary of selected Mines'  statistical cost
         regressions	    31
  2    Summary of Ford-Warford's statistical cost            „
  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
 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

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

     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.

                           SECTION 1

                        INTRODUCTION TO

                    COST RATE DIFFERENTIALS

     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

     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.

     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-

     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

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.

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.


     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

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.

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.

                          SECTION II

                    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

      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).

     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

                          SECTION III



     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

     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.


     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
     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.

     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

     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


     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.

     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

     °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

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

     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.

 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

      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.
      W.L.  Patterson.  "Practical Water Rate  Determination".
 Journal  of  the American Water  Works Association. 54  (Aug.,  1962),
 p.  y04-12.	

     blbid,  p.  909.
      Ralph  K. Davidson, Price Discrimination  in Selling Gas
.and  Electricity.  (Baltimore:  John Hopkins  University Press,
       Chapter 8.


      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.


     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.

        R + C + I
= 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* = 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

     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.

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.

      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

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.


     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.


 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

      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
(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


     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

           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

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);
           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.


      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

      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.

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.


                                                 i   i   i i  i i i i
                       1.0                 10'
                    AVERAGE PRODUCTION (Q)- MGD.
 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)

     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.

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
                                     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

     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
      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.


      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.

Figure 4.  Step  cost functions

 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.

                            TABLE 1.


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 ($API,)
           (AFC)                 s.d.     (.30755)       (.000001428)
                                         (4.293)        (3.
     ii.) Average Variable Cost -209-7173 - 1. 4672 (%CU)-. 00001092 ($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

      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-
 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

 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  '




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)

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%

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.

 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.
      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.

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.


 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.

1-6 Total








Cost; 7-12
New Hampshire
Partially or
not metered-
New England
New Hampshire
Partially or
not metered-
New England
New Hampshire
Partially or
not metered-
New England
New Hampshire
Partially or
not metered^
New England
Ave. Cos




13-18 Total Cost




New Hampshire
Partially or
not metered,.
New England
New Hampshire
Partially or
not metered1
New England
1 . 3446



                                    Total gallons

                                    •.0721 (.0486.



Number of
.7227(.1842) .9449
.9694(.1176) .8861
.8226(.0296) .9354

Number of
b (standard
 ^ error)
         1 Excluding New Hampshire

1.0605(.0472)  .9387

1.1266(.0477)  .8827
1.0776(.0079)  .9517

     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

     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.



     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

     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.
                        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
 Figure  5.   System friction curve
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

     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.

 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

     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

         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.


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
     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.



     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

     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
     aJames B. Rishel, P.E., "Packaged Pumping Stations for
Suburban Water Distributions," Water and Sewage Works. 121
(1974) p. R-131-134.

                 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


     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),


     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


     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


     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.

      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
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;


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.



     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.


     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


     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)


     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;


    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


     Cu m cents per thousand gallons per mile;

     Qo = average yearly demand in gallons per day;


      C = total annual cost of conveying Qo through a pipeline of
          D inches for a distance of one mile.


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)


     CK » unit capital cost in dollars per thousand gallons per

      f m the capital recovery factor, i(l + i)n/(l + i)n - 1;

      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

    .75 * the load building factor, proportion of utilized

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

S consists of friction loss, Sf, and an average line slope, SL>

   is defined as
     aLinaweaver and Clark, "Costs of Water Transmission", p.

          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


 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,



     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.


     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.

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

     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



     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.


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

     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

     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^


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

     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


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 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.


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
     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.


     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;

     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;

  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-

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).


         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-

     Mathematically, energy cost per cubic foot for each linear
foot of pipe can be represented by the following expressions.


  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.)/

       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.


       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,

        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;
      PR.  is the pressure in zone k, Ibs./inch ;
        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
         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).


(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

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


 T).. = 1, if consumer i  resides in zone k or water to consumer
          i travels through zone k;

     = 0, otherwise;
  6.  =  1, if consumer i resides in area r or water to consumer
           i travels through area r;

       0,  otherwise; and


  *. .  is the length of pipe size j in area r, feet.
  I jr

                         K        R        n
(4-3)    TCOP £  = q.,   £    n .  E   6     E
             ikr     ikr       ik     ir
                                          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.


     The mathematical description of pipeline cost  relationships
appears similar to that for energy cost in general  formulations.


     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
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
      TCOPikr be  tne  total  off-Peak  capital  expenditures  for T&D
              pumping stations;


         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;

      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.


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.

            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.

     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       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.


 (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


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.
     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

    AC    be the average operating cost per unit of output;
   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.


(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

     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
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 .


     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;
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,

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

Combining the changes in (4-9) with equation (4-3) provides the

     aEquation number advanced from later in text.

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
Use of peak D.  may lower energy cost per foot of pipe since
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

     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.

     TCPvrr  be the total peak T&D pipeline capital and main-
             tenance expense in area r of zone k;

    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

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
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.
     TCP-k  be the total cost of maintenance and peak-load
            capacity for pumping station allocated to consumer
            i in zone k;
            be "k*16 Piping station peak-load capital expendi-
            tures for T&D;
        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
             capacity during  the peak-load  in  zone  k;

      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.

            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

     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.


     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
     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.


(4-13)   TCpfkr S qikr (*&.) .

The proportion 
     Combining all terms involved in peak-load costs, the follow-
ing equation may be generated.
     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),

               + A.
Upon substituting into (4-14) for each TCP variable, this cost
function is generated.

(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 .


     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-
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

      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.


   A. Cherry Grove
   8. Ml  Washington
   C. California
   D. Central
   E. Eastern Hills
   F Brecon
   G. Western Hills  North
   H Western Hills  South

    1 Butler County
   2. Warren Count/
   3 Arlington Heights
   4. Norwood

   5. Cleves
   6. Addison
   7. Wyoming
   8. Loclcland
   9. Reading
   10 Glendole
   11. Indian Hill
   12. love/ond
   13. Miltord
	Service Area  for  Cincinnati Water Works
•••i  Mastered Metered Areas
	  Independent Utilities
                                      FIGURE 8.   Cincinnati  tfeter  Works   service  area.


                     FIGURE 9.  Service  area and zones of the Cincinnati Water Works


                                            OHIO RIVER
                    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

     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.


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,


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.

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.

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

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

     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


     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,


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;


     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.


     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.

                            TABLE 4
Total in
Total Sample Size user group:
1.  Residential  = 291
2.  Commercial   =311
3.  Industrial   =203
D s deleted sample
                                                 TOTAL  805

        12O- •






                I     I
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

     ^Pressure was set at 100 psi, pump efficiency  at  9096 and
C-factor  at 100.

     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.

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
$ 2.50
$ 4.50
$ 5.00
$ 9.00
$ 5.75
$ 10.35

                                TABLE 5.  CONTINUED
                              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





                           SECTION V

                       EMPIRICAL RESULTS
     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


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

     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;


   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

     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.


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)


 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.

     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.

     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

              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

 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

     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)


Zone C1_ - Peak Period
     Ln (TC,,) = -1.5491 + .7253 Ln (Q) DF = 108
                 (.503)   (.0236)      R2 = .897
Zone C1Q - Off-Peak Period
     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,

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.


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

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

     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-

Zone Paths           Peak           Off-Peak           Difference

These coefficients are for the distance variable
All coefficients significant
in AC = f(A,D).
at 95% level or more.
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.


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

Lower Limit
Upper Limit
Lower Limit
Upper Limit

     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.


     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

     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


User Group
Average Day Quarterly
Mean Water Consumption
Rate Block Applicable
for User Group
     4266 cubic feet
    50769 cubic feet
   172224 cubic feet

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


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
.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
.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


Route C.
.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
.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,
.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
.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


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
-.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
-.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








.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,








.]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.

                                                                                     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.

                                                                                       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,

                                                                              MINUS  PEAK
                                                                    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.

                                                                                        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.

                                                                               MINUS PEAK
                                                                     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,

                                                                                       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.

                        TABLE 18. RESIDENTIAL WATER USERS ROUTE  C.

Total Revenue
Total Cost


Total Revenue
Total Cost
Net Revenues
$ .10
- .76

                          SECTION VI


                        AND WATER USE

     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


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.

                          SECTION VII



     'Ihis chapter presents brief descriptions of the empirical
methodologies employed for data collection and estimation of

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


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.
Time in quarters
             Figure 26.  Distribution of initial water use,

     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
                              i * w2Xt-2 •*

 in which the weights are estimated as:

      w< » (i + r - l)!/i !  (r - 1)! (1 -

 where  r  is  an integer  to  be  chosen,  and \  is  estimated  from the

     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.


                         TABLE 20.   LAG TIME IN DAYS BY USER GROUP.
                          (D                 (2)                          (3)
                          Mean	95%  Confidence  Limits	Coefficient  of  Variation

  Initial Water Use    469.332      431.912 < » < 506.75                1.55
  Continuous Use       476.552      438.746 < p, < 514.358               1.56


  Initial Water Use    543.962      434.619 < n < 653.305               1.37
  Continuous Use       547.453      438.449 < u < 656.457               1.38


  Initial Water Use    486.875      310.316 < p, < 663.434               2.25
  Continuous Use       490.250      314.260 < ^ < 666.240               2.27


  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








'" B1


0 . 30807
0 . 2837



-678062. 52825



0 . 1 3224

         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


     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

     S , the static head per foot of pipe,  is formulated as:
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.

(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-
       Since the  study  area  for this project relies  on  the usage
 of  the Hazen-Williams  equation, that  formula will be used.


U-5)   Sf = HL/L..kr = (4.72688) Q^

Note that Q,,,, here is also measured in cubic feet per second,

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
                       (2.85125 x 105) Qk;8518 x C"1 '8518
                     x D'
                     X Djkr  '

                          APPENDIX B



     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

                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


 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


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)
   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;

     r  a summer rainfall in inches.

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):
                                            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


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.

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.

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


 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


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


 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


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


     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


 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).


     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).

 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.

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


     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):


      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

 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


     flat rate and sewered area with apartments:
          = 28.9 + 4.39v + 33.6p
t-statistic        7.87**   3.97**
   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   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
    a    a  average  summer sprinkling demand;
      p  = marginal commodity charge on average summer total rates
       3   of consumption;
      •w  =  summer potential evapotranspiration in inches;
      r  * summer rainfall in inches.
      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):

     Sd/a = 157 + 3.46V                     R2 = .58;


     "Sj/a = average domestic water use in gallons per day for
            each dwelling;

        V » average value of the dwelling in thousands of

     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

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

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;


    VU  « annual average water use in gallons per day per
      a   dwelling;

    ¥U  » summer average water use in gallons per day per
winter average water use in gallons per day per
      V » assessed sales value of the dwelling unit in the
          hundreds of dollars;

     w  = number of persons per residence;

      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


 (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.

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


 t-statistic         7.87**     3.97**

      metered areas  with septic  tanks

      qa>d = 30.2 +  39.5dp                             R2  =  .96

 t-statistic         8.48**


    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,


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**


     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,


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


(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).

                          TABLE  B

 Type of Dwelling
  Lot size
 (sq. feet)
Maximum Day
Average Day
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
Source:  Wolff, Jerome B., "Peak Demands in Residential Areas."
Journal. American Water Works Association. LIII (October,  1961)
1251-1260.                                                     *

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

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.

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.

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),

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),

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 -          """"

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

"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),

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.                  "—

                           APPENDIX C


     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


 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.

      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-

      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

     "... 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.

      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


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.

     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).                            '


      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


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


 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)


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).

     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):

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."

     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.)


     EMP.   = number of employees in  category i;

     X1, X2 = other right-hand, variables in the growth equation.

     (')    = 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.

     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

     X1,  X2  = right - hand variables
     X3,  etc. in growth equation

     PAR-    = parameter value for category j

     (')      = 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).

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.

                           APPENDIX D

     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


      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

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

                           TABLE C.


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


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).


     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.

    "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


     T  = pounds of B.O.D. per $1,000 value  added in manufactur-

     S  = surcharge in dollars per  1,000 Ib. of  B.O.D.


      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

      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

     Pr1t = Price o:C recycled water

     G..L.  = gross water use

          = quantity of intake water

     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


      F  = ratio of future to present industrial  water use.

      E  = ratio of future employment in industry to  present

      0  = ratio of future industrial output  per  employee  to  the
          present  value

      R  = ratio of future use of recirculated  water  to present

      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..
     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.

     N. = sum of employment in ith two digit standard industrial
      1   code.

     Employment by firms:

     S, = L./R,


     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):

      Equation 1
      X =  T-D
      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
      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),
      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

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
                     pkhr Pn
           qn =  average  annual water  requirement for industrial
                 category n;

      (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


         ' = 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


     EMPn = employment in category n, within indusgry group m.

     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
= 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.

He correlated  this index with per capita  water  production  for  the
years 1928 to  1950, and derived the following equation  (1951,  p.

     W = 0.365 I + 07;


     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.

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.

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),

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.

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.

                                 TECHNICAL REPORT DATA
                          (Please read Instructions on the reverse before completing}
                                                        6. PERFORMING ORGANIZATION CODE
                                                         3. RECIPIENT'S ACCESSION NO.
                                                         . REPORT DATE
                                                          May  1978  (Issuing Date)
 Haynes C. Goddard, Richard G.  Stevie,  and  Gregory D.
                                                         8. PERFORMING ORGANIZATION REPORT NO.
 Department of Economics
 University of Cincinnati
 Cincinnati, Ohio  45221
                                                         10. PROGRAM ELEMENT NO.

                                                         11. CONTRACT/GRANT NO.

 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
                                                         14. SPONSORING AGENCY CODE


 Project Officer:  Robert M.  Clark
      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.
                               KEY WORDS AND DOCUMENT ANALYSIS
                                            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-


                           21. NO. OF PAGES

                                             20. SECURITY CLASS (This ptgej
                                                                       22. PRICE
   form 2220-1 (9-73)