Abstract:
In an effort to determine empirical cost functions for municipal
water supplies in the United States, the writer found it necessary to
specify an acceptable mathematical form to represent the cost equation.
A preliminary search yielded no theoretically consistent expression
adaptable to the problem.
The primary concern in the studstimay thus became one of identifying
theoretically sound statistical etion procedures for interrelated
long- and short-run cost functions. Criteria were established
to recognize a mathematical form qualified to function as a generalized
cost equation.
The prescribed path wound its way through a traditional overview
of economic production functions, cost theory literature, and curve
estimation procedures; then it moved into a comprehensive review of
empirical cost studies. This empirical section first identified
studies of short-run cost relationships and gave examples of declining,
constant, and increasing marginal costs. Theoretical literature,
addressing possible reasons for these diverse shapes, was then cited.
The same format was maintained for long-run studies reporting diverse
shapes. Theoretical explanations followed. The last part of the
literature review inspected the explicit model structure of those
studies combining long- and short-run cost curves.
When no econometric model was found in the literature which
satisfied the pre-specified criteria for a generalized cost equation,
the study assumed the task of developing such a framework. The
resulting econometric structure exhibited the following properties:
(1) The adopted equation generates both long- and short-run cost
curves. (2) Two cost groups are retained in both the long- and
short-run—costs which vary proportionately with output (i.e.,
operating costs), and costs which are independent of output (i.e.,
plant costs). (3) Plant capacity is strictly defined, and all
short-run production of a plant is constrained to a quantity not
to exceed that capacity. (4) Operating cost is a function of production
and plant utilization while plant cost is a function of
plant capacity.
Once the general econometric structure was developed it was
then adapted to an empirical study of the cost for supplying water
to municipalities. A survey of operating data for water utilities,
collected by the American Water Works Association for the year 1965,
was used as the principal data source for the application. Other
independent variables, considered potentially important in determining
cost, were evaluated and added to or omitted from the model.
These characteristics included alternative treatments, types of
customers, sources of water, city density, etc.. The resulting
regression equations indicated the following industry structure:
(1) Although the major portion of the industry is facing economies-to-
scale, the long-run cost curve turns distinctly upward for large
water suppliers. (2) Over 95 per cent of the plants face downward
sloping short-run average cost curves. (3) With the available data
no statistical evidence could be found to indicate a plant's operating
cost is affected by the level of plant utilization.
The municipal water example was used to demonstrate the versatility
of the generalized cost function in accommodating cost studies
and hypothesis testing.
The author therefore asserts that the econometric structure
developed in this study is qualified to fulfill the pre-selected
requirements of a theoretically sound statistical estimation procedure
for interrelating long- and short-run cost functions.