An econometric structure for cost functions with application to municipal water

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.