United States
Environmental Protection
Agency
Water Engineering
Research Laboratory
Cincinnati, OH 45268
Research and Development
EPA/600/S2-85/019 Apr. 1985
v>EPA Project Summary
Economic Modelling of Water
Supply: An Econometric
Analysis of the Multiproduct
Firm
Hak Youn Kim
Research was conducted to develop
a comprehensive economic model
that could use the neoclassical theory
of the multiproduct firm to analyze
the production structure of water sup-
ply. The project attempts to meet the
need for in-depth analysis of the cost
and economic structure of water sup-
ply.
The cost structure of the water sup-
ply industry was estimated using the
recently refined translog function.
Issues addressed included restrictive
specifications for water supply
technology, input demand function
for water supply, scale economies,
marginal costs and output supply, and
pricing of water and the presence of
cross subsidization among residential
and nonresidential users.
Findings of this research represents
the first attempt to apply the translog
production function in the water sup-
ply area. No comprehensive analysis
has been conducted before using the
econometric methodology adopted in.
this study.
This Project Summary was
developed by EPA's Water Engineer-
ing Research Laboratory, Cincinnati,
OH, to announce key findings of the
research project that is fully
documented in a separate report of
the same title (see Project Report
ordering information at back).
Nature of the Problem
The world's present water supply situa-
tion is substantially different from that of
the past. Scarcity of high-quality water is
evident in many locations in the United
States and in other countries. Per capita
consumption of water has continued to
rise with increasing affluence and ur-
banization, but many existing water
sources have become limited in availability
and degraded in quality. Increasing energy
costs coupled with inflation and high in-
terest rates have raised the costs of pro-
viding water. In addition, more stringent
environmental regulations (e.g., the Safe
Drinking Water Act of 1974) have the
potential for increasing water rates.
In recognition of growing water supply
problems, the United Nations has
designated the 1980's as the International
Drinking Water Supply and Sanitation
Decade. The primary goal is to provide
the world with safe water and sanitary
disposal of human wastes. In this period
of rising costs and impending regulatory
changes, the costs of water supply and
the factors affecting these costs have
taken on new importance.
The conventional solution to water sup-
ply problems has been to augment sup-
plies by expanding the system and acquir-
ing the resources as needed to meet the
full demand of customers. But the prob-
lems of supplying water of acceptable
quality are no longer simple. Issues
related to substitutabilities among water
supply inputs have become important for
the policy maker, who must understand
implications of increasingly scarce
resources. Knowledge of scale economies
and their limitations have implications for
"regionalization" policies. Also, utility
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commissions have begun to devote more
attention to rate structure reform. The
issue of public versus private water pro-
viders is becoming more important as
communities search for ways to improve
management and operation of water sup-
ply.
As the emphasis on water supply issues
grows, so does the need for an in-depth
analysis of the cost and economic struc-
ture of water supply. Previous research
efforts to meet this need have been
limited in scope and applicability. The
present research seeks to fill that gap.
Purpose of the Research
The object of this research is to develop
a comprehensive economic model that
could use neoclassical theory of the
multiproduct firm to analyze the produc-
tion structure of water supply. In this
study, the water supply utility is viewed
as a regulated multiproduct firm offering
multiple services to various classes of
consumers with spatial and temporal
variations. Particular attention is directed
to the production characteristics of the
multiproduct firm. This research project
assumes that many issues in water supply
can be resolved by applying some basic
neoclassical multiproduct production
theory. Specifications for the water sup-
ply technology used in this research were
derived in a manner that is entirely dif-
ferent from the neoclassical micro-
economic theory.
The following issues are addressed in
the development of the model: (1) restric-
tions posed by existing specifications for
water supply technology in view of the
neoclassical theory of production; (2) in-
put substitution and use in the production
process; (3) scale economies; (4) marginal
costs and the transformation function of
water supply; and (5) second best pricing
and the presence of cross-subsidization
among customer classes because of inap-
propriate pricing structures.
Though this research is primarily con-
cerned with the analysis of water supply
problems, it encompasses many practical
problems and issues faced by other
utilities and regulated industries. Thus the
analytical and empirical methods adopted
in this research should provide a useful
framework to study not only the water
supply industry but also the multiproduct
firm in general. Econometric analysis of
the general multiproduct firm is far from
complete in view of the fact that most of
the work in this area has been only
preliminary and suggestive without regard
to practicality and policy relevance.
Methodology of the Research
The approach of this research is to
estimate the cost structure of the water
supply industry using the recently refined
translog function. The translog function
can deal with multiple inputs and outputs,
variable elasticities of substitution among
inputs, variables elasticities of transforma-
tion among outputs, and variable
economies of scale. The theory of duality
is explicitly explored in the estimate of the
translog cost function.
The water supply firm produces mul-
tiple outputs for different customer
classes such as residential and
nonresidential users. Capital, labor, and
energy are considered as the major inputs
into the production process for the
delivery of water and to meet customer
demands. Interaction among outputs and
inputs is taken into account in the
estimate, and various hypotheses of the
production structure are tested. The data
used represent a cross section of water
utilities in the United States for the year
1973.
An unusual feature of the methodology
used here is the direct incorporation of
the firm's operating characteristics into
the specifications for the technology.
Operating characteristics include capacity
utilization and service distance, which are
considered important for production and
delivery of water supply. With the
generalized cost function (which includes
operating characteristics in addition to
conventional arguments of ouputs and in-
put prices), it is possible to obtain insights
into the quantitative relationship between
costs and operating conditions.
Estimates of the translog cost function
by ordinary least squares would be im-
precise because of possible multi co-
linearity resulting from a large number of
regressors interacting with one another.
Thus our estimates use the iterative
Zellner efficient method, which jointly
estimates the translog cost function and
the input demand functions derived as the
first order conditions of cost minimization.
The iterative Zellner efficient method is
asymptotically equivalent to the maximum
likelihood method.
Major Findings of the Research
Parameter Estimates and Tests
of Restrictive Specifications
for Technology
Estimates of water supply costs
presume nonhomotheticity that prescribed
differences exist among outputs (residen-
tial and nonresidential water supply), in-
put prices, and operating variables
(capacity utilization and service distance).
The translog multiproduct cost function is
an adequate description of the technology
of water supply. The tests of homogene-
ity of outputs, input-output separability,
nonjointness, and a Cobb-Douglas form
produce results that are significantly dif-
ferent from the unconstrained translog
cost model. This result suggests that ex-
isting specifications placing arbitrary
restrictions on the translog multiproduct
cost function are inappropriate. In addi-
tion, our findings reject the hypothesis
that the operating variables should be ex-
cluded from the model. Attempts to
analyze water supply costs without con-
sidering the operating variables would
lead to false conclusions about the struc-
ture of water supply.
Input Demand Function for
Water Supply
No previous studies have been per-
formed to estimate the input demand
function for water supply. Capital is a
substitute for labor and energy. Substitu-
tion between energy and labor is limited
to a great extent. Substitution between
capital and energy is consistent with the
findings of studies in other areas. Energy
is an input that requires intensive use in
the production process in response to
changes in the demand for water and
capacity utilization. Furthermore, capacity
utilization and service distance have
significant effects on input requirements.
Thus the inability to account for these
variables would lead to a serious problem
in estimating of input requirements for
water supply.
Scale Economies
Water utilities experience substantial
economies of scale for both residential
and nonresidential water supply. The
water supply industry is experiencing
marked economies associated with the
treatment of water, but it suffers from
diseconomies with increasing size of
distribution network. The economies in
treatment override the diseconomies in
distribution, however. Furthermore, scale
economies are mainly determined by
nonresidential water users as opposed to
residential users.
Marginal Costs and
Output Supply
Marginal costs of residential and
nonresidential water supply are much
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lower than the actual prices charged.
Marginal costs are quite sensitive to
changes in outputs, input prices, and
operating variables. Marginal costs are
estimated from the transformation func-
tion of water supply. The latter is convex
and illustrates decreasing real opportunity
costs of residential and nonresidential
water supply. This observation implies an
advantage to specializing either in residen-
tial or nonresidential water supply.
Pricing of Water and
Cross-Subsidization Among
Customer Classes
The economies of scale experienced by
water utilities suggest that marginal cost
pricing is not feasible. The second best
pricing rule has been proposed as an
alternative scheme through which prices
can be calculated for residential and
nonresidential water supply. Surprisingly,
the existing price structure is close to the
second best pricing optimum. The fact
that marginal costs are less than the ac-
tual prices indicates that real costs of
water supply are much lower than ex-
pected. In addition, this study finds no
evidence of cross-subsidization among
residential and nonresidential users.
Empirical findings in this research repre-
sent first attempts in the water supply
area. No comprehensive analysis has been
conducted in the past using the
econometric methodology adopted in this
research. However, before sweeping or
definite conclusions can be drawn from
these findings, it is important to verify
them using different data. This step is
necessary because of the limitations im-
posed by the data currently available.
Nevertheless, the methodology used in
this research should provide fruitful lines
of inquiry into the various issues
associated with water supply.
The full report was submitted in fulfill-
ment of Cooperative Agreement No.
CR808102020 by the University of Cincin-
nati under the sponsorship of the U.S.
Environmental Protection Agency.
Hak Youn Kim is now with Western Kentucky University, Bowling Green, KY.
Robert M. Clark is the EPA Project Officer (see below).
The complete report, entitled "Economic Modelling of Water Supply: An
Econometric Analysis of the Mult/product Firm," (Order No. PB 85-176
899/AS; Cost: $20.50, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Water Engineering Research Laboratory
U.S. Environmental Protection Agency
Cincinnati, OH 45268
r U.S GOVERNMENT PRINTING OFFICE: 1985-559-016/27035
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