Size Economies in Local Government Services: a Review

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SIZE ECONOMIES IN LOCAL GOVERNMENT SERVICES: A REVIEW

r~ - .--. William F. Fox . m ■ 'ES

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U.S. Department of Agriculture Economies, Statistics, and Cooperatives Service

Rural Development Research Report No. 22 SIZE ECONOMIES IN LOCAL GOVERNMENT SERVICES: A REVIEW, by William F. Fox, Economic Development Division; Economics, Statistics, and Cooperatives Service; U.S. Department of Agriculture. Rural Development Research Report No. 22.

ABSTRACT

Expanding local government services to cover more people may lower costs per person served. Such savings could, however, be reduced substantially by other costs; among them, size of service area, transportation, and quality of service. Small- scale production technologies, such as cluster well systems for water services, could help lower costs. Savings from increasing the number of people served, although the savings may vary by service, can be achieved in fire and police protection, education, refuse collection, roads and highways, and water and sewer utilities.

Keywords: Economies of size. Economies of scale. Local government. Community development. Communities, Rural development. Cost functions. Costs, Education, Schools.

Washington, D.C. 20250 August 1980 CONTENTS

SUMMARY , ii INTRODUCTION. . 1 SOURCES OF SIZE ECONOMIES ^ Average Cost Curves.... ^ ..••. V Cost Curves for Local Government Services ^ HISTORY OF SIZE-ECONOMIES RESEARCH 3

ESTIMATION TECHNIQUES AND DIFFICULTIES ^ Common Approaches. ^ Cost Curve Analysis. •.. .^ ^ RESULTS OF SIZE-ECONOMIE S RESEARCH 8 Labor-Intensive Services... 8

Capital-intensive Services. 24 APPLICATION OF SIZE-ECONOMIES RESEARCH 30 LITERATURE CITED. 32 SUMMARY

Expanding local government services to reach more people may lower the per unit cost of providing such services as fire and police protection, refuse collection, education, roads and highways, and water and sewer utilities. Size economies (lower costs per unit) in fire protection are possible for towns with up to but probably not over 10,000 residents. For police protection, the increased service needed for more law enforcement may offset any savings derived from protecting larger areas. Cities with up to 20,000 residents could cut costs in refuse collection by increasing the number of people served. The amount of unit savings possible from large-scale provision of local government services depends heavily on other cost items, the most Important of which are population density, transportation, and quality of the service provided. Small-scale technologies suitable only for rural areas, such as cluster well systems for water services, could also save local governments money in providing services. Size Economies In Local Government Services: A Review

William F. Fox "

INTRODUCTION

Rising expenditures by local governments have created substantial public interest in how to cut costs and increase efficiency of providing public services. Research on limiting growth in local government expenditures has focused on costs. Analysts have attempted to determine if economies of scale or size exist in the production (provision) of goods and services by local governments. Economies of size are the reductions in the per unit costs of producing a good or service, reductions that accompany increased production of the good or service. This report shows that size economies are possible in provision of these government services. Rural areas have a substantial stake in research that shows whether size economies exist for local government services. With generally small, scattered populations, rural areas appear to be the most likely to benefit from reorganizations that provide services more efficiently. Local planners can use results of such research in deciding whether to consolidate certain functions, contract with another local government for services, or keep providing service in small units.

SOURCES OF SIZE ECONOMIES

The reasons size economies can exist and the types of local government services which are likely to permit size economies are discussed in this section.

Average Cost Curves

Size economies were determined by measuring the relationship between per unit costs of production and scale of output. This involved estimating an average cost curve for local government services. A generalized average cost curve can be written in the following form:

AC=f (I,P,S,T,N)

AC is the per unit cost of producing the local service. I is the number of input units employed; labor and capital would be the most prominent. P represents prices of the inputs. S shows service conditions, such as population density and weather. The state of production technology is T, and N is the scale of production or output. Size economies are evaluated by examining how N is related to AC.

— William F. Fox, an assistant professor in the Center for Business and Economic Research, at the University of Tennessee, was formerly an economist with the Econo- mics, Statistics, and Cooperatives Service. Size economies in production arise from either a unit of input per unit of output/volume of production relationship or an input cost/volume of production relationship* The unit of output per unit of input relationship can have as many as six expla- nations of why the number of input units necessary to produce an output unit falls with the level of output. First, increased specialization in the use of labor permits laborers to gain expertise in their functions and to spend a larger proportion of their time on tasks where their skills are appropriate. Second, increased specialization in the use of management will also permit managerial skills and time to be used more effectively. Third, large size may be necessary to permit governments to employ necessary technologies. Large scale is needed, for example, to permit meshing of several different machines each with different rates of output. Fourth, some factors of production are not sensitive to changes in scale. Fifth, large-scale producers are better able to utilize byproducts from the production process. Sixth, relatively fewer inputs may need to be purchased by large organizations because they may find it easier to hedge against uncertain demand for service (fire protection, for example). The input cost/volume of production relationship refers to the ability of a larger production unit to obtain favorable pricing for the inputs purchased. Volume purchases of police cars, for example, may lead to lower costs per car purchased. This relationship may also arise because internal ordering costs can be spread over the purchase of more inputs. These justifications suggest that average costs would continuously fall with expansions in output. As output continues to expand, however, diseconomies are expected and they offset the factors discussed above. Inability to effectively manage large organizations looms as the major limitation on achieving size economies. Costs of efficiently managing a large organization are thought to rise rapidly with size. Therefore, the overall average cost/volume of production relationship is expected to be U-shaped.

Cost Curves for Local Government Services

Hirsch categorized local government services«as horizontally integrated, vertically integrated, and circularly integrated (40).— Horizontally integrated services are those services provided by using a number of production plants at the same stage of the production process. Police and fire protection are examples. Hirsch also noted that 80 to 85 percent of all metropolitan government expenditures are for these services. Vertical integration characterizes the production of services which involve several different stages of production. Goods with separate production and distribution functions, such as water and electricity, are examples. These usually amount to 8 to 10 percent of all metropolitan expenditures. Finally, goods and services which complement one another in production are said to be circularly integrated (city hall is the example Hirsch gave). These services are estimated to represent 3 to 6 percent of a metropolitan government's expenditures. The average cost curve described here may accurately represent private industry costs or circularly or vertically integrated services. Hirsch noted, however, that size economies are unlikely to occur for horizontally integrated services. These services, because they are usually produced in small plants located near the consumer, offer few of the economies that are available from large-sized plants. Quantity purchase discounts are difficult to obtain because local governments purchase small amounts of needed inputs.

2/ — Underscored numbers in parentheses refer to items in Literature Cited at the end of this report. Labor is the only input generally purchased in large quantities. However, unionization of public employees can increase wage rates for large employers, which makes large size less economical. Further, legal restrictions on salary levels can preclude the hiring of the best qualified management, and political patronage can increase the diseconomies from management. Also, horizontally integrated services, which often are people oriented, must be produced in numerous locations near the consumers; this tends to keep the production plant small, Hirsch's conclusion that economies are unlikely for horizontally integrated services was based on consideration of metropolitan communities with populations exceeding 50,000. In these cases, full 24-hour service delivery is already provided and few economies are available as labor can be purchased in relatively continuous units and facilities have achieved the best, although small, size. However, size economies can be expected for many nonmetropolitan community services as movement is made towards continuous, full provision of services.

HISTORY OF SIZE-ECONOMIES RESEARCH

Early size-economies research focused on determining the optimal-sized city. Generally, local government costs were only one of several costs considered. One study, in England, concluded that the optimal-sized city would have approximately 32,000 residents (43). Ogburn, in a similar study, determined that the optimal city population ranged from 30,000 to 50,000 (61). He found that per capita local government expenditures rise with city population. Analyses of Montana County government costs by Renne and Voelker represent the earliest research applied specifically to size economies in local government (63, 74). Renne developed output indexes for each county office and used bar graphs to show that per unit costs fell with volume of work. Voelker, using Renne*s output indexes, fitted curvilinear relationships between units of work and labor costs and also found an inverse or U-shaped relationship. Government expenditure determinants analysis was applied to the questions of size economies that emerged from the Montana studies. Expenditure determinants analysis seeks to uncover the factors about people and governments which lead to expenditure differentials across governments. Population of the government unit, sometimes used as a surrogate for government output levels, was one factor examined. Fabricant, in one of the first studies, found strong relationships between current local government expenditures and population density, urbanization, and income (22). Brazer analyzed per capita expenditures for cities with populations greater than 25,000 (7)» Four population measures were employed: population size, population density, population growth rate, and the employment-population ratio. Population size was an insignificant determinant of expenditures for all services except police protection. Police protection and population size were found to be positively related. Most expenditure determinants research has supported Brazer by concluding that population size is unrelated to per capita expenditures. Expenditure determinants analysis, however, is inappropriate for examining size economies as demand and supply factors are mixed. As noted, size economies refer specifically to the supply side costs of producing and delivering services. Expenditure changes, which accompany increasing demand, must be excluded. For several reasons, demand will vary with population size. First, demand for local services tends to rise with population because of the problems associated with large population densities. Many services, such as police and fire protection, are designed to offset the problems resulting from population concentrations. Also, total service levels must be increased to offset the reduction in services available to each person îdiich accompany larger populations. The demand-induced expenditure increase may offset any reductions in supply-side production costs which occur when the level of production is increased (or may increase supply costs). The result could be incorrect inferences regarding size economies. Supply-side cost analysis (cost studies) was applied to utility companies during the fifties. An early example was Johnston's study of 40 electric stations in Great Britain (46). This study used ordinary least squares regression to find shortrun and longrun average cost curves for each station, ^camination of size economies through supply-side costs represents a significant theoretical improvement over previous work. Werner Hirsch first applied cost-curve analysis to the user-oriented, labor- intensive services which represent most of local government expenditures (37). Hirsch studied police and fire protection, refuse collection, and primary and secondary education in the St. Louis metropolitan area. Research on a wide variety of user-oriented, labor-intensive services expanded greatly following his work. An array of estimation techniques, cost measures, output and input proxies, and samples were applied and reported in the burgeoning literature. James Henderson was one of several researchers who provided additional theoretical breakthroughs (32). Welfare-maximizing behavior of local governments was explic- itly incorporated in his analysis. This led to better isolation of supply-side costs through recognition of the simultaneous determination of supply and demand. Henderson and others developed multiple-equation models and employed simultaneous estimation techniques to examine cost relationships. The models and techniques used by Henderson and others represent the most up-to-date research methods available (30). The Renne and Voelker work was oriented towards nonmetropolitan areas. However, during the 30 years which followed their analysis, most research was urban oriented or mixed urban and rural (26). The past 10 years have witnessed a significant trend towards research focused on nonmetropolitan areas. This has undoubtedly resulted because nonmetropolitan areas appear likely candidates for reorganization to reduce costs.

ESTIMATION TECHNIQUES AND DIFFICULTIES

The nianerous techniques which have been used to study size economies, together with data and related analytical problems, are reviewed in this section.

Common Approaches

Estimation of average cost curves of the same general form as equation (1) represents the most common method for examining size economies. Total cost curves and production functions have also been computed. Production functions have the same form as cost curves, except that they exclude input prices.

(1) AC=f (I,P,S,T,N)

Ordinary least squares regression analysis has been the most common statistical tool applied in size-economies research. However, several other statistical techniques have been used: two-stage least squares regression analysis, separable programming, mixed integer programming, linear programming, correlation analysis, maximum likelihood estimation, and principal ccmiponents analysis. Data derived from engineering studies of costs or ex post expenditures can be used to estimate cost curves. Researchers have usually applied expenditure data; however, for agricultural production efficiency studies, engineering cost studies outnumber ex post expenditure studies three to one (28). Engineering data are infrequently used for local government analysis because they are expensive to compile and require a much greater familiarity with the technical aspects of production. Further, they cannot account for managerial difficulties or government inefficiencies. Cross section expenditure data frequently form the sample for size-economies research, as sufficient years to perform time-series analysis are rarely available. One exception is Johnston's analysis of electrical utilities where time series data were used to estimate longrun and shortrun cost curves (46). Another example is the police protection production function estimated by Chapman, Hirsch, and Sonenblum (10). Cross section expenditure data can suffer from several problems. First, data on capital stocks or yearly capital costs are rarely available; therefore, all costs and inputs cannot be analyzed. Measurement of all costs and correct cost-curve specification are particularly vital when the analysis includes many local governments as is true of cross section work. Second, expenditure data reflect accounting costs rather than economic cost. Third, production functions can vary across geographic boundaries, particularly between metropolitan and nonmetropolitan local governments. Estimation techniques generally do not account for this difference in the ways of combining capital and labor. Using places from a wide geographic range increases the importance of accounting for demand differences that result from varying tastes and socioeconomic characteristics. Finally, divergent cost-of-living conditions across geographic boundaries can result in some governments appearing more (or less) efficient than in reality.

Cost Curve Analysis

Examined below are the common approaches and difficulties associated with each part of average cost curve analysis.

Cost Measurement

Average cost definition encompasses a series of data issues. The appropriate cost concept could include social or individual costs versus government costs. Each has been used for analyzing police protection. Morris used social costs, Popp and Sebold used individual costs measured by total expenditures plus total unrecovered losses, and Walzer employed agency costs (58, 62, 76). The appropriate concept of cost depends on the purpose for the research, even though most studies of size economies have focused on government costs. Social costs, which Include a measure of benefits or demand, are useful for measuring the impact of services on people. Individual costs are useful for examining effects on specific people. For analysis of budgets and optimal size of the production unit, however, government costs are more appropriate and are usually appropriate for size- economies research. The next basic cost question is whether the cost proxy should measure accounting or economic costs. Accounting costs will equal the cash outflows and possibly a depreciation measure for the time period. Economic costs are resources utilized during the time period. Economic and accounting costs will usually differ as inven- tories may be adjusted during the year and capital stocks will be drawn upon (which necessitates a measure of actual depreciation). Therefore, economic costs should be adopted to relate the true costs of government production with output. Accounting costs are the data usually available, however; and nearly every study reviewed used these costs. The final cost definition question is: Should current or total costs be the cost measure? Ideally, variable costs are appropriate for estimating shortrun average cost curves and total costs are appropriate for estimating longrun average cost curves. Current costs most closely resemble variable costs in practice. The ability of current expenditure to measure variable costs, however, suffers to the extent that current expenditures are made for fixed costs (debt retirement, for example). Total accounting costs, which include expenditures for current and capital purchases, represent a poor surrogate for total costs as capital expenditures occur infrequently. Therefore, accounting data can probably be used to estimate shortrun cost curves using current expenditures, but will probably be poor for estimating longrun average cost curves. Of 34 education studies, 27 used a measute of current expenditure and only 7 adopted total expenditures as the cost surrogate. Input Use Measurement

Input usage is the next component of average cost curves to be considered. For the user-oriented, labor-intensive services, inputs have generally been measured through the labor component. Capital proxies, as noted, are difficult to obtain. Some exceptions for education include the use of building value per pupil and percentage of classrooms built after 1950 (16, 65). Omission of capital from the average cost curve analysis leads to biased estimations if capital is an important input in the production process and if communities use different amounts of capital. Omission of capital from the labor-intensive services has often been defended because capital is relatively unimportant äs a production input. Yet, the production facility is frequently of greater interest for these services as the good is usually used at the facility (13). Education is transmitted in schools; justice is dispensed in courts, jails, and police stations; and health services are used and produced in hospitals and clinics. Conversely, with capital-intensive goods, the focus is on the outputs, almost to the exclusion of the facilities (transportation is an exception). The reason is that, in the view of consumers, buildings in which the services are provided are one canponent of output for labor-intensive services. Thus, not analyzing capital in studies of labor-intensive services is a more serious omission than has been thought. Capital inputs appear more frequently in cost-curve estimates for the capital- intensive, local government good. Capacity enters several electric power generation studies as a proxy for capital inputs (44, 55, 21). Miles of roads measure capital in every road study reviewed. Several techniques have been used to quantify labor quality and quantity. Chapman, Hirsch, and Sonenblum, in estimating a production function for police protection, separated labor into four inputs: motorcycle teams, field officers, nonfield officers, and civilian employees. Each type of labor was entered independently in the production function (10). Pupil-teacher ratio and expenditures were used as proxies to measure labor inputs for education (77, 50). Labor quality for education has been measured by teacher experience and percentage of teachers with masters degrees (57, 47). The basic difficulty with the surrogates for quantity and quality of labor inputs in the production of user-oriented services occurs because researchers have not found significant relationships between the inputs and output. For example, Katzman found a mixed relationship between teacher experience and student performance (47). Carr-Hill and Stern found a positive relationship between the offense rate and police per capita; they argued that this results from more crime being reported when more police are present rather than an actual increase in crime (9^). These nonintui- tive results probably arise because output and input proxies are inadequate.

Input Price Measurement

Input prices are the next component of an average cost curve. Most studies assume (at least Implicitly) that capital prices do not vary across geographic areas; therefore capital prices are not analyzed. An exception is the Christensen and Greene study of electric power generation (12). Wage rates were included in some, but not all, research. Teacher salary was used to measure labor costs for education (16, 65). Prices are frequently excluded because each service is provided with numerous labor inputs, each with its own wage rate or because the data are unavail- able. Again, to the extent that wage rates and other input prices vary across the chosen sample, research on the cost curves is biased if input prices are not included in the equation.

Service Condition Measurement

Service conditions, the next component of average cost curves, mirror geographic, demographic, or weather characteristics which influence the costs associated with producing a good or service. Examples are snow removal for.roads, transportation for water, electricity, and education, and, possibly, student's educational background. These factors have been accounted for with proxies, such as precipitation and snowfall for roads and pupil density for education (53, 54, 37).

Technology Measurement

Technology is usually omitted from cross section cost studies on the premise that the given state of technology is equally available to all local governments. The technology implemented in production processes appears more frequently in analysis of capital-intensive goods. For example, Johnston used time to account for technical change in his time-series analysis (46). Dhrymes and Kurz separated their analysis into four "technological periods" to examine the impact of technology on costs (21). Cost functions for almost any service, then, are implicitly assumed to come from a single technological approach. In solid waste, the technology may be a municipal or private collector with rear-loading compacting trucks, a transfer station, and a sanitary landfill. In health services, the technological approach may be a municipal hospital providing primary care through an outpatient department as well as secondary care through a range of self-contained secondary care departments (13). Associated cost functions are usually well developed. Their major shortcoming is that, as mainstream work, they concentrate on urban technology where sizable population concentrations exist (24). Seldom has there been much work with small- scale technology. Thus, as a whole, the research fails to provide policy-relevant information on appropriate technologies for small-scale production and on size economies for small-scale production techniques.

Output Measurement

Output or scale is the final element of average cost functions. Output measurement is important because output must be used to convert total costs to average costs. Also, the effects of size or production costs are determined by relating average costs to output. Yet, output measurement probably presents the most difficult data collection problem for analyzing user-oriented services. At one time, population served was used as a measure for local output. For a number of reasons, however, population performs poorly as an output surrogate. First, to the extent that local services are public goods, population and output are unrelated, so more people can be served without increasing total costs or reducing the services available to existing recipients (72). Next, to the extent that local services are private goods and price elastic in demand, a more serious problem develops. Suppose size economies exist for the service. If population increases, crowding out of the service will probably stimulate increased production of output leading to decreased unit production costs. But, as costs fall per user for a price- elastic service, quantity demanded responds so quickly that expenditures rise. Therefore, per capita expenditures may rise and lead to incorrect inferences regarding size economies (39). Finally, population served is an inadequate output surrogate because it fails to reflect differences in quality of services provided. Output can be thought of as a two-dimensional factor. It contains a quantity and a quality component. Recent work has sought to account for this. For education, quantity is often measured by the number of pupils in average daily attendance or enrollment. Quality has usually been measured by achievement test scores or an input proxy such as breadth of curriculum or student-teacher ratios. Fire protection output proxies have been population protected by the fire department and value of property protected (41). Quality has been measured with various input proxies. Proxies for hospital quantity have been patient days spent in the hospital, number of beds, admissions or cases, and an index of cases based on cost of production. Quality, to the extent researchers mean to include it, has been accounted for via input proxies and the availability of teaching programs. Police protection surrogates have been crimes solved, arrests divided by crime, predicted crime divided by actual crime, crime rates, and an index based on police inputs. Quantity of refuse collection has been measured with number of pickup units and amount of refuse collected, or population. Quality enters the analysis through pickup location and frequency. Output for capital-intensive goods is generally more easily measured. Electri- city can be quantified in kilowatt-hours. Quantity of roads has been measured by population and square miles of area. Output (or scale) of water services has been measured by water quantity and nimiber of customers. Quality surrogates for water have also included number of treatments and impurities ronoved.

RESULTS OF SIZE-ECONOMIES RESEARCH

The results of size-economies research for seven local government services are classified here into,(l) labor-intensive, user-oriented services and (2) capital- intensive services.— Education, fire protection, police protection, and refuse collection are included in the labor-oriented group. The capital-intensive services include roads and highways and water and sewer utilities. Potentially, two other services, hospitals and electricity, could be reviewed here, as both services are occasionally provided by local governments. However, most of the literature focuses on private market operations. Thus, these services are not formally reviewed here; only brief comments on the general implications of size- economies studies for these services are made. Berki's review of hospital cost studies included the work by Carr and P. Feld- stein, Cohen, M. Feldstein, Francisco, and Ro (¿,28, 14, 15, 23, 27, 66). Berki observed considerable diversity in both the approach and results. He concluded, "The exact general form of the literature is unimportant, but whatever its exact shape, and depending on the methodologies and definitions used, economies of scale exist, may exist, may not exist, or do not exist, but in any case, according to theory, they ought to exist." Four recent empirical studies of cost curves for electric power companies have been completed (_3, 12_,21_, 44). Each of the researchers concluded that size economies do exist for some range of electric power generation. Evidence also suggests that the fall in per unit costs declines with increased size of the firm, that there may be a substantial range of constant per unit costs, and that diseconomies may occur for very large firms. Further, Christensen and Greene concluded that fewer than half of the firms in the United States have unexploited scale economies. Municipally owned electric plants are more likely to have unexploited size economies, as they are usually small.

Labor-intensive Services

Size economies for the labor-intensive, user-oriented services are examined in this section.

Education

The proliferation of size-economy studies in education probably results because education,remains the largest local goverranent expenditure, nearly half of overall budgets.— Also, the pros and cons of school consolidation, which still receive wide

3/ — A broader listing of the research is available in (26). 4/ — A technical review of education services can be found in (25). attention, have led to continued research on the costs of providing education and the potential savings from larger scale provision of education. Economies of size in education can potentially arise from several sources. One is that larger schools can have higher pupil/teacher ratios. Also, the cost of capital and shared facilities (gymnasiums, for example) can be spread across more students. An additional source is the relatively low unit cost of providing specialized training in larger schools (a variation on the previous two). Finally, there can be economies associated with spreading administrative expenses over more students. Tending to offset the factors leading to economies are the potential effects of larger size on quality of education and cost of transportation that are associated with large school districts. Some argue that, although larger schools may offer more selection, quality of education deteriorates with size because parents are frequently less involved in the educational process and because each student has fewer individual opportunities, so greater expenditures become necessary to offset the quality losses. Even if size economies exist, greater expenditures may also result if an area can develop a large school only through a geographically large district. . And, increased expenditures result from transporting students a greater distance. Existing education literature can be most intelligently reviewed in terms of the different types of size economies, because the type of facilities and outputs for elementary and secondary schools differ. Some authors have studied economies using district-level (or larger units) analysis. This can be satisfactory if the multidi- mensional nature of education is properly handled; however, this is seldom done. Also, the degree of economies is likely to vary with the level of school. Thus, we separate the studies according to those associated with elementary schools, those associated with high schools, and those associated with district-level administration. Size economies in administration are the most likely as administrative expenditures tend to be independent of the number of students. Economies for high schools are also likely because of the amount of shared space and specialized equipment in addition to the economies from achieving optimal pupil-teacher ratios. Economies for elementary schools are the least likely, once each grade level has achieved a reason- able pupil-teacher ratio as the use of shared equipment is less frequent. Economies for elementary schools have been infrequently studied (table 1). Hind, Katzman, and Michelson analyzed elementary schools separately from other schools (34, 47, 48, 57). Each found some evidence of size economies, though the evidence is mixed. Hind analyzed expenditures for 116 schools in New South Wales, Australia. Administration, instruction, and maintenance expenditures were examined separately with ordinary least squares regression. Economies of size were found throughout the estimated range for maintenance costs, though most of the economies were exhausted at the 200-pupil enrollment level. U-shaped cost conditions were found for instruction and administrative expenses. Most economies from these two cost elements were obtained at the 100-pupil level and they were all absorbed by the time a school reached 200 pupils. Diseconomies occurred above 600 pupils. Several difficulties with this study should be noted. The Hind study, as with most education cost-curve analyses, failed to consider the costs associated with the use of the capital and equipment. Also, the quantity of education (number of students) was examined without accounting for the quality of education. Katzman undertook two studies of elementary schools in Boston. He found evidence of size diseconomies in his initial study as costs were positively related with capacity utilization (47). Also, per pupil costs and enrollment were positively related. In the later study, two different forms of an average cost curve were estimated (48). One form, based only on enrollment and school capacity, yielded a U- shaped average cost curve with a minimum in the 1,400- to 1,800-pupil range. In the other equation, Katzman used a specification similar to the initial study, employing enrollment, teacher characteristics, and capacity utilization to estimate a cost curve. Enrollment was found to be negatively related with average costs. Taken together, Katzman's results seem to imply economies over a larger range than did the Hind work. Table 1—Summary of education size-economies research

Author Cost measure Output or Population Results scale measure range

Cohn (16) School costs. Average dally 377 Iowa high Economies of size attendance schools aver- with the optimal (ADA) measures aging 287 size high school quantity and pupils each. at approximately standardized test 1,500 students. scores measure quality.

Dawson (20) Total costs. ADA and ADA 377 school Economies of size or weighted by boards in constant returns for quality. Ontario. districts with single schools. Some diseconomies across all districts.

Hambor, Phillips, Teacher salaries, Performance on 42 States. Slight, though and Votey (30) selective ser- ins ignifleant, sIze vice exams. economies.

Hanson (31) Current Districts U-shaped average expenditures. with 1,500 cost curve with a to 846,616 minimum at about pupils. 50,000 pupils.

Heittich (33) Current Average enroll- Districts Slight economies expenditures. ment. with 150 or for elementary more students schools to 300 in New York pupils and disecono- and Michigan, mies above. Econo- mies for secondary schools to 600 pupils.

Hind (34) Separates ad- Average enroll- 9 to 928 Maintenance dis- ministrative, ment. students. plays economies instructional, throughout. Other and maintenance areas were charac- costs. terized by a U- shaped average cost curve with a minimum at 600 pupils.

Hirsch (36) Current expendi- ADA measures 27 St. Louis No significant tures plus debt quantity and an area public economies. service. index measures school dis- quality. tricts.

Hirsch (37) Administration ADA measures quan- 27 St. Louis U-shaped average cost. tity and an index area public cost curve with a measures quality. school dis- minimum at 44,000 tricts with pupils. 500 to 84,000 students.

Holland and Total costs. Not applicable. 77 to 457 Could save approxi- Baritelle (42) pupils. mately 1 percent of costs through consolidation.

Continued

10 Table l—Summary of equation size-economies research—Continued

Author Cost measure Output or Population Results scale measure range

Katzman (47) Both current and 56 Boston Finds diseconomies instructional elementary for instructional expenditures. school dis- costs. Finds econo- tricts. mies for reading and diseconomies for Latin education production.

Katzman (48) Both current and Number of stu- 56 Boston U-shaped average instructional dents. elementary cost curve for expenditures. school dis- high schools with tricts. a minimum between 1.400 and 1,800 pupils.

Kiesling (50) Current ADA is a scale School dis- Constant returns to expenditures. measure and tricts in scale. test scores are New York. an output proxy.

King and Total costs Number of pupils. 254 North School gymnasiums Wall (51) less administra- Carolina are significant tion. high schools. contributors to size economies.

Michelson (57) Test scores. 113 elemen- Size is positively tary schools associated with in Washington, pupil-teacher ratios D.C. but may harm outputs.

Ricker and Inschool costs ADA. Florida Size economies are Tyner (64) excluding trans- counties. found at a decreas- portation and ing rate. capital improve- ments.

Riew (65) School operat- Enrollment. 109 Wisconsin U-shaped average ing costs. high schools cost curve for high with 143 to school with a mini- 2,400 pupils. mum at 1,975 students.

Shapiro (68) Total expendi- Number of School dis- Finds size econo- tures net of pupils. tricts in mies. debt service Alberta, and contribu- t ions to building and loan funds.

Wales (75) Separates sala- Number of stu- Districts Size economies are ries, operating dents. ranging up indicated for each costs, and admin- to 74,000 cost component. istrative costs. pupils.

Cont inued

11 Table 1—Summary of equation size-economies research—Continued

Author Cost measure Output or Population Results scale measure range

White and ~ Admin is t ra t ive, ADA is the quan- Satisfied ' U-shaped average Tweeten (77) maintenance, tity proxy and sample of cost curve the building, test scores is Oklahoma form of which equipment, and the quality districts depends on desired transportation proxy. ranging program quality, costs are from under analyzed. 100 to more than 70,000 pupils.

12 Several difficulties with the Katzman work should be noted. First, the same basic data set yielded different results depending on the specification. This sensi- tivity to specification reduces confidence in the results. Another problem is the failure to hold quality of education constant, although several of the estimated equations did include teacher input quality. This is a particularly important limitation for analysis within a school district as all school expenditures are set by the school board and need bear no relationship with the costs necessary to attain a given quality of education. Michelson tested for size economies in elementary education by examining the relationship between the pupil-teacher ratio and the size of school (57). The pre- sumption was that higher pupil-teacher ratios mean lower per pupil costs for teachers. The remainder of the Michelson model included equations for the quality of third- and sixth-grade education and the quality of teachers. The pupil-teacher ratio was found to be positively related with size of school, meaning that lower teacher costs could result for larger schools. Yet the results suggested a negative relationship between the pupil-teacher ratio and the quality of education. Therefore, Michelson concluded that the costs necessary to offset the deterioration in quality would offset any savings from a higher pupil-teacher ratio. The main difficulty with the Michelson study is that it considered only economies associated with the pupil-teacher ratio. Other economies, although more limited for elementary schools, can result from the use of shared equipment and space and from shared school-level administration. Hettich used per pupil expenditures across the district to estimate a joint average cost curve for schools (33). Separate scale measures for elementary and secondary schools were included in the cost equation. The Hettich study is the district-level study most appropriate for individual statements on elementary and secondary education, although there are some difficulties with mixing elementary and secondary students in the same equation. Hettich found some evidence (not statistically significant) of economies in elementary education to 300 pupils. Diseconomies were found for schools with more than 300 students. Kiesling evaluated size economies for education by estimating an educational production function for 97 school districts in New York (50). He calculated the production functions for three sets of grade levels, even though the sample points were for school districts. Educational output was measured by achievement test scores. Explanatory variables in the production equation were student intelligence scores, expenditures per pupil, and school district size. Separate estimates were made for pupils by socioeconomic class and for large versus small school districts. Kiesling found no evidence of size economies for elementary or secondary grades. However, he did find a somewhat weak relationship between expenditures and performance. The Kiesling work must, however, be viewed with caution. The results showed that educational quality (test scores) falls when quantity (size of school district) rises, while inputs (measured by expenditures per pupil) remain constant. This fails to constitute a test of size economies. They are tested, not by examining the relationship between the two components of output (quality and quantity) but by examining the relationship between output and costs. Also, as school district size is used as the scale measure, economies for a school cannot be examined. In sum, the overall results of the six studies are that some size economies do exist for elementary education, generally for relatively small sizes—possibly up to the 300-pupil range. Size economies are more likely for high schools than for elementary schools, because of the increased number of specialized courses and a greater need for shared space and equipment. King and Wall provided some evidence of the availability of economies for better use of shared space (51). Using engineering data, they showed that gjrmnasiums are significant contributors to economies of size in high schools. The per pupil construction costs were shown to fall nearly 50 percent and per pupil yearly operating costs more than 20 percent as student populations increase from 400 to 2,200.

13 Economies for capital and equipment are infrequently researched. Dawson's study, which included depreciation in the total cost measure, is the only high school level analysis that included capital costs (20). Cohn and Riew included capital proxies in their cost equations but not in their cost surrogates (16, 65). Cohn examined economies of size in 377 Iowa high school districts (16). He estimated a per pupil cost equation and a production function with size, teaching, and building inputs, and educational quality as explanatory variables. Quality was measured by the change in standardized test scores from 10th to 12th grade. The size/per pupil .cost relationship was estimated as a parabola and as a rectangular hyperbola.— Minimum costs using the parabola are at 1,500 pupils, but Cohn concluded that as the rectangular hyperbola explains the data better, there "may be no basis for specifying an upper limit to optimal school size within the range of our Iowa data." Dawson estimated a cost curve for secondary school districts in Ontario, Canada (20). Only size was used as an explanatory variable, although it was weighted by quality in some regression equations. Separate equations were estimated for single- and multi-school districts. Also, separate equations were estimated for academic as well as commercial and vocational programs. Falling or constant average costs (depending on the cost-curve specification) were found for the two types of programs when the cost curve was estimated for districts with one school. A lazy "S" or inverted "L" cost curve resulted when all districts formed the sample. The Dawson study suggests two important results. First, the importance of examining individual schools (here, the single-school districts) is highlighted by the contrasting results. Second, the degree of economies appears to vary with the type of program emphasized by the school. The degree of savings from having larger schools may depend substantially on the type of students added to the school. The Dawson results are interesting; however, the specification of the cost curve is weak, and therefore the results must be assessed with caution. Riew estimated a per pupil cost curve for 109 high schools in Wisconsin (65). Schools were chosen for the sample if they were accredited, part of a one-high-school district, and not exceptionally high in quality. This technique was designed to choose schools with comparable quality of education. Least squares regression was used to estimate the cost curve with number of pupils, several input quality measures, changes in enrolIment, and proportion of new classrooms as the explanatory variables. Riew found declining average costs until school size reached 1,675 pupils. According to his estimates, per pupil costs would fall by $95.45 as enrollment rose from 200 to 500; costs would fall by $111 as enrollment rose from 500 to 1,000; and costs would fall by $54.67 as enrollment rose from 1,000 to 1,675. Riew did not include capital outlays (which comprise one-fourth of total expenditures) but he argued their inclusion would strengthen the conclusion that size economies exist. The consensus of these studies is that size economies also exist for high schools. Researchers, without consideration of the capital costs, report evidence of economies up to at least 1,500 students. Administration costs at the district level have been analyzed independently of other costs by three researchers. From the research, it is not clear whether the administrative expenditures occur at the district level or whether some of the expenditures arise from administration at the school level. The conclusion of each study was that per pupil district-level administration costs decline as the number of students in the district increases. However, none of the studies examined whether there are economies from increasing the number of schools within the school district. Hirsch provided the earliest study of administrative expenditures (37), using a sample of 27 St. Louis public school districts for two time periods. The estimated

— A parabola is a continuously declining curve and a rectangular hyperbola is a U-shaped curve.

14 cost curve included pupil density, an index of quality of education, number of students, growth in number of pupils, and percentage of students in high school, A U- shaped average cost curve with a minimum at 44,000 pupils resulted. Wales estimated a per pupil cost curve for school district administrative costs, teacher salary costs, and other administrative costs in British Columbia (75)« Relating administrative costs to number of pupils in the district led Wales to conclude that administrative costs declined up to around 33,000 students, even though the decline in costs above 3,000 students was minimal. Slight evidence of diseconomies for districts above 33,000 in size was obtained. White and Tweeten used a sample of school districts in Oklahoma to examine economies associated with school administration (77). Large savings can be achieved with up to about 1,500 pupils. However, the costs probably include school-level as well as district-level administrative costs. Each of the three administrative expenditure studies found significant economies. The Wales and Hirsch studies suggested economies up to large sizes—30,000 to 40,000 pupils. Lesser economies were found in the White and Tweeten research, which included school-level administrative costs. Most other research testing for size economies has used inappropriate data and led to mixed results. Researchers used school district, county, or State data to study the economies associated with an individual school. Several researchers observed economies of size or a U-shaped average cost curve (31, 64, 68). Others found no significant evidence of school economies (30, 36). The conclusions cannot be viewed as being for or against the presence of size economies, although the research provides some conceptual direction and some thoughtful insights. Our conclusions, based on the research which examines appropriate data, are that (1) size economies exist for elementary schools, (2) size economies exist for secondary schools, and (3) size economies exist for district-level and administrative expenditures. This does not mean that all schools and districts should approach the same size. An analysis of school-level costs ignores several other important cost considerations, two of which we will consider. First, the statements on economies for school costs refer only to those costs specific within (and including) the building. However, the costs of transporting students to school can loom large in overall education costs. For example, Holland and Baritelle indicated that busing costs in Lincoln County, Washington, amounted to 16 percent of the total budget (42). Efforts to reduce costs through school consolidation are unlikely to result in savings for many less densely populated areas as the most important determinants of transportation expenditures are student population density and distance (77). Holland and Baritelle's analysis of remotely populated Lincoln County confiions this. Savings from the more efficient school sizes must be weighed against transportation costs. Another factor with implications for the minimum-cost school size is the desired quality of education. White and Tweeten used number and diversity of class offerings to measure quality of schools and found that the minimum-cost-sized school increased substantially with the number and diversity of class offerings (77). In sum, size economies exist in providing education services but the potential savings to a community must be weighed against other cost and quality factors. The gains or losses from consolidation must be considered case by case.

Fire Protection

Economies of size in fire protection may arise from two sources. One is size of the fire protection production unit, the economy associated with optimal plant size. Distance from a fire station must be kept short as rapid response time to alarms is essential for adequate fire protection, so there is limited potential for increases in the fire station size. Nonetheless, small towns may experience high unit costs of

15 maintaining a minimal production unit.— Economies may exist until sufficient size is attained to permit round-the-clock service by the company and equipment deemed necessary to provide adequate service.— The second area in which economies may occur relates to the costs associated with the fire department rather than the station. This may result when larger cities can locate stations more optimally because they locate nK)re stations and have a greater choice of available locations. Also, larger departments may be better able to draw upon equipment from other stations when backup equipment is needed rather than purchase backup equipment. Five studies of fire protection economies were identified for review (table 2). Hirsch, in the earliest fire protection study, used regression analysis to test for size economies (37). With population as a scale measure, he found the average cost curve to resemble a parabola with a trough (the low point on a statistical graph) at 110,000 residents. He concluded that economies result because larger cities could locate fire stations in more optimal locations. The economies, in other words, came from the fire department rather than the individual station. Will obtained cost measures from an engineering analysis by establishing a standardized unit of effort based on input measures and determining the costs of providing the standardized unit (79). Regression analysis was then used to relate population and costs per capita; economies of size were found for approximately 300,000 people. Will stated that the economies are not really a function of population size. Rather, they result from smaller cities being comprised of larger proportions of high-value districts. High- value districts require more service units per geographic area according to the rules Will applied to determine the number of service units necessary for each size. Therefore, the smaller cities use relatively more service units and this demand- related factor causes fire protection to appear more expensive per capita for small cities. Âhlbrandt regressed per capita expenditures on three output measures (population, area, and assessed values) several input measures, and other differential cost variables (1) • Scale effects were examined by evaluating how per capita expenditures adjust as all outputs (including quality) increased proportionately. He found no economies for fully paid fire departments and diseconomies for volunteer and paid volunteer fire departments. Hitzhusen employed multiple regression analysis to test for the existence of size econcxnies (41). Regression equations were estimated with five different cost proxies and two output measures. Cost proxies ranged from adjusted fire department operating costs to a surrogate for all private and public fire protection costs. Output was measured by population and full value of property protected. Quality of output was included through the American Insurance Association deficiency points which are assessed against public fire protection units. Significant size economies were not found for operating costs when either output proxy was adopted. However, significant economies were found when the best measure of public costs is employed 8/ (operating costs, depreciation, imputed volunteer effort, and water supply charges).— Most economies were exhausted when conmunity size reached 10,000.

— Alternative production techniques, such as volunteer fire departments, are frequently adopted to minimize costs in these cases. — Childs, Doeksen, and Drye listed some equipment which local fire chiefs felt was necessary for a volunteer fire department (11). 8/ — Volunteer effort charge does not represent an out-of-pocket expense. However, imputed labor costs are borne by the individuals and volunteer efforts must be considered to specify the production relationship properly.

16 Table 2—Size economies in fire protection studies

Author Cost measure Output or. Population Results scale measure range

Ahlbrandt (1) Adjusted opera- Quantity measured 900 to Constant returns ting costs plus by assessed pro- 536,000. to scale for fully depreciation on perty values. paid departments operating equip- area, and popula- and decreasing ment per capita. tion; fire insur- returns to scale for ance ratings and volunteer and paid input surrogates volunteer depart- were used to ments. measure quality.

Hirsch (37) Per capita total Population and 800 to Average cost current expendi- an index of 865,000. curve is a parabola tures plus debt scope and with a trough at service. quality of 110,000 residents. fire protection.

Hitzhusen (41) Five different Population and Under 2,500 Finds size economies cost measures full value of to over for population and are implemented. property pro- 100,000. property protected, The most inclu- tected measure although significant sive cost proxy output quantity. economies are not includes adjusted Output quality found when adjusted operating costs, is measured by operating costs are depreciation, American Insur- used. Most economies imputed volun- ance Association. are exhausted at teer labor cost, Deficiency points 10,000 people. annual charge assessed against for water, and public fire pro- private fire tection. insurance costs.

Morris (58) Per capita public Population mea- 7,787 to Sizable economies fire expenditures sures quantity 366,481. to 1 million plus per capita and the Standard population. outlays for fire Grading Schedule insurance. of the city's fire defense and physical condition is used for quality.

Will (79) Per capita Population. Over 50,000. Hyperbolic cost engineering curve with a cost estimated minimum at approxi- for providing mately 300,000. the necessary standard units of effort defined in the article.

17 Morris used per capita fire department expenditures and city size to predict fire protection class for each city (58). He calculated private insurance costs using the predicted class of fire protection and property valuations (based on a constant per capita wealth figure across cities). Constant per capita fire protection expenditures for all cities were added to the predicted insurance costs at each city size to yield an average cost curve. Cities of 1 million population or more had the lowest fire protection costs. The above studies fail to provide information on the relationship between costs of a single fire station and the number of people and geographic areas served. Instead, the studies were designed to evaluate the potential economies associated with city size. Furthermore, as a wide population range was employed in every case, the cities had different numbers of stations. Except for Will's, each study started with cities of fewer than 10,000 residents and ranged to cities of well over 100,000. The studies fail to examine the relationship between output (whether measured by population, area, or value) from a single fire station, population density, and the minimum costs for fire protection. General conclusions concerning economies associated with the size of fire departments are not Immediately clear. Âhlbrandt found no economies, Hitzhusen found small economies, and others concluded that size economies exist over a wide range. The two studies which found economies over the greatest range, however, did not examine economies associated with the public fire department. Size economies in the Morris research basically arise from private insurance costs; therefore, it did not provide information on costs associated with the fire department alone. Will indicated that the economies in his study are demand related; they arise because smaller cities have proportionately more high-value districts. Again, his study failed to provide information on the costs of the public fire department as size increases. Though size economies were found in the Hirsch study, they were small, only $1.24 per capita as population ranges from 1,000 to 100,000, Ahlbrandt, using operating costs plus equipment depreciation as the cost measure, found no economies. Hitzhusen also observed no economies for operating costs, but found economies with broader cost definitions. In sum, the research suggests that probably there are some economies to fire departments but these are limited and will yield small savings for cities above 10,000 in population.

Police Protection

Seven studies of police protection production or economies of size are presented in table 3. Hirsch's analysis represents the earliest work on size economies (37). Per capita police expenditures were found to have a statistically insignificant relationship with population. Schmandt and Stephens, in a study of 19 cities and towns in Milwaukee County, concluded that economies of size exist in the provision of police protection (67). A service index of 550 subfunctions (unweighted number of activities performed) served as the output measure. Service level, population, and per capita expenditures were correlated with each other. A positive correlation between population and service level and a negative correlation between service level and expenditures led to the conclusion that size economies exist. Morris and Tweeten examined the social costs of crime to determine if any economies occur with city size (59). The social costs of crime were measured by the outlay per capita for police necessary to hold the crime rate at a given level among all city sizes while city characteristics other than size were held constant. A two- equation system was estimated. One equation estimated the crime rate and one equation estimated police per capita. Next, the number of police per capita necessary to hold the crime rate at a constant number was determined while holding constant all city size characteristics other than population. The estimated number of police per capita was converted into dollars to yield cost of holding the crime rate constant. The resulting curve was U-shaped with a minimum in the range of 250,000 to 500,000 residents, and costs were found to rise sharply in populations above 1 million.

18 Table 3—Size economies in police protection studies

Author Cost measure Output or Population Results scale measure range

Carr-Hill and Population. Urban and Diseconomies. Stern {9) rural.

Chapman, Hirsch, Prevention and 82 California Increasing returns and Sonenblura punitive police cities. to the police (la) protection. agency as a whole.

Hirsch (37) Per capita total Population and 200 to No significant expenditures for index of scope 865,000. economies. police protection. and quality of police protection.

Morris and Per capita cost Per capita crime 25,000 to Economies of size Tweeten (59) of maintaining rates measure 1 million. are shown into the a constant crime police output. 250,000 to 500,000 rate. City size mea- size city. Dis- sures scale. economies.

Popp and Total expenditures Population, SMSA*s of Per capita total Sebold (62) plus uncovered 100,000 and costs rise with losses. more. population. Per capita police expenditures fall until population reaches 250,000 and then rise.

S chmandt and Per capita Number of acti- 1,200 to Economies of size Stephens (67) current vities performed. 750,000, are indicated. expenditures.

Walzer (76) Municipal police Index of services 23,000 to Economies of size expenditures. based on number 143,000, are found for the of offenses service index. No cleared, number significant rela- of accidents tionship between investigated, population and and miles per capita expendi- traveled by tures is found. police vehicles. Percentage of known offenses cleared by arrests is the quality surrogate.

19 However, the approach held constant the factors which affect the social costs of crime, such as population density, and it also held police salaries fixed across city sizes/ The results understated the social costs in large cities and had an undeter- mined effect on the average cost curve. Popp and SeboId sought to standardize a measure of police service by assuming that victims of crime are compensated fully for their costs (62). Each constituent, under this assumption, can be said to receive the same amount of protection of life and property. Government costs must then be measured by expenditures plus compensa- tion for crimes. With this definition of crime, the average cost curve is shown to increase as population increases. A U-shaped average cost curve with a minimum at 250,000 residents occurs when actual expenditures are used as the cost surrogate. However, Popp and Sebold's sample was 161 Standard Metropolitan Statistical Areas (SMSÂ), not police departments. Therefore, the results are inappropriate for evaluating size economies related to individual departments or stations. Walzer estimated an average cost curve for police services in 31 Illinois cities (76). Output was measured by a time-weighted composite of the number of offenses cleared, number of accidents investigated, and miles traveled by police vehicles. Percentage of known offenses cleared was the quality surrogate in the multiple regression analysis. Significant size economies were found using the service index; however, no size economies were observed when population served as the output surrogate. Determination of the level of crime statistics was modeled by Garr-Hill and Stern (9^). Their three-equation model included equations for the number of offenses per capita, the percentage of offenses solved, and the number of police per capita. Estimation of the model revealed that the population size^Qf the police district is inversely related with the percentage of offenses solved.— This led the authors to conclude that diseconomies were present in the provision of police protection. The finding of diseconomies by Carr-Hill and Stern must be viewed with skepticism once the offenses-solved equation is analyzed. The explanatory variables in their estimated equation included two input surrogates, the number of police per capita, and the total police expenditure per officer (a measure of equipment per officer). Therefore, the inverse relationship between population and proportion of offenses solved was found with inputs held constant. Thus, they found that the expected results — quality (proportion of offenses solved) and quantity (population protected) ~ vary inversely when inputs are held constant. Their results cannot be interpreted as a finding of size diseconomies for police departments. Chapman, Hirsch, and Sonenblum examined police department efficiency using the production function approach (10). Outputs were measured using several schemes for weighting a crime prevention component and a punishment component. Crime prevention was estimated as the difference between the actual crime rate and the predicted crime rate (calculated using multiple regression). Arrests divided by the crime rate formed the punishment surrogate. Five police protection production functions were estimated for Los Angeles with time-series data. Each function employed a different weighting scheme for output. The findings were that "a one percent increase in police employees and their associated equipment, on the average, increases output by substantially more than one percent—^often by two to four percent. Thus, there appears to be some indication of increasing returns to the police agency as a whole (10)." These seven studies, each with somewhat different results, can be combined to yield certain conclusions. Economies of size were not indicated by either study which relates police expenditures and population (37, 76). — Morris and Tweeten did

9/ — We argued above that population is a poor proxy for output. Nonetheless, it was used as an output or scale measure for five of the eight police studies — Similar results are generally found in the expenditure determinants literature (4, 7).

20 find a U-shaped average cost curve for social costs relative to population (59). Yet, this finding applies more to the question of optimal city size for police protection than to size economies for police departments. All studies which examine economies relative to a scale of services index found significant size economies (10, 67, 76). Thus, for a given size of city, costs of performing more of the same police services decrease—which means size economies are present. However, as city size increases, a sufficient number of new services must be (or are chosen to be) produced to offset the cost savings from performing more services. These demand-related increases in service levels absorb the cost savings derived from providing increased services. None of the reviewed studies examines the potential diseconomies associated with small-scale production of police protection or with single stations versus police departments. As noted, economies arising in the production of horizontally integrated services are most likely to occur in small towns. Hirsch and Schmandt and Stephens included small cities in their samples; however, the results are probably not specifically applicable to small cities as the samples covered such a wide size range that the results cannot be interpreted as representing the cost conditions for small cities (32.9 67). Using a sample of New Jersey cities, Beaton demonstrated that the population/expenditure relationship varies with city size (4^), Beaton's study suggests that analysis across wide population distributions may lead to biased results, even though his study is an expenditure determinants analysis rather than size- economies research.

Refuse Collection

Six refuse collection studies are reviewed in table 4, Hirsch argued that refuse collection is a horizontally integrated service and thus would not be expected to exhibit size economies (37). Kitchen accepted that refuse collection might be characterized by horizontal integration, but that a broader perspective of the service might reveal economies associated with vertical and circular integration (52). Any complementarity with street cleaning or other services would introduce circular integration and disposal, and recycling would introduce elements of vertical integration. Two of the six refuse collection studies included disposal and collection costs in the cost curve estimation. Disposal costs appeared to be less labor intensive than collection costs and more likely to exhibit size economies. Disposal costs for refuse have been estimated to represent 20 to 30 percent of total refuse costs (17, 60). Therefore, consideration of disposal costs may have a significant influence on whether economies or diseconomies are found, although an argument can be made that collection and disposal services can be separated easily so that an areawide government provides disposal and many small units provide collection. The potential for separation of collection and disposal is less for rural areas. Hirsch examined 22 municipalities in St. Louis ranging in size from 200 to 225,000 pickup units (35). He used multiple regression analysis to discern whether residential refuse collection and disposal costs per pickup unit decline with the number of pickup units served. He found no significant economies of size using a larger sample from an earlier study (37). Hirsch noted that the results must be interpreted with caution as the data refer to municipalities and the collection unit does differ from the municipality in some instances. Refuse collection and disposal costs in 32 rural Texas communities were examined by Hall and Jones (29). Total system costs, including collection and disposal, were used to measure costs, and population served as the scale surrogate. Effort was made to choose municipalities with similar service offerings, although there were some quality differentials between the communities. Multiple regression analysis was used to estimate a cost curve for the 22 communities in the sample with populations greater than 3,000, Economies of size were found for communities having up to 9,600 residents. Larger communities exhibited diseconomies.

21 Table ^—Size economies in refuse collection studies

Author Cost measure Output or Population Results scale measure range

Collins and Direct billings Pickup units mea- Under 500 to Economics available Downes (17) per pickup unit sure scale and 65,000. to at least 1,000 or total collec- pickup frequency pickup units (3,000 tion cost per and pickup loca- to 4,000 population), pickup unit. tions measure quality.

Hall and Operating costs Population. 3,000 to Economies of size Jones (29) for solid waste 25,000 are available to measurement sys- 9,600 residents. tems, including collection and disposal.

Hirsch (35) Residential Number of pick- 200 to No size economies refuse collec- up units measure 225,000 pick- are indicated. tion and dis- scale arid pickup up units. posal cost frequency and per pickup. pickup locations measure quality.

Kemper and Per ton and per Number of tons of Not No evidence of size Quigley (49) dwelling unit refuse measures applicable economies is found. collection quantity and fre- Argue that some costs. quency of pickup economies may be measures quality. available in towns under 2,000 population.

Kitchen (52) Total collec- Population mea- Cities Diseconomies occur tion operating sures quantity above 10,000. in move from costs plus and pickup loca- small to middle depreciation tion measures size, then attain per capita. quality. some economies from middle to large size (an inverted U-shaped average cost curve).

Stevens (70) Collection costs Cubic yards or 2,500 to Economies to city for municipali- tons of refuse 700,000. sizes of 20,000, ties and collec- measure quantity lesser economies tion revenues and pickup fre- to 50,000, and con- for private quency and pickup stant returns above firms. locations measure 50,000. quality.

22 There are two noticeable problems with Hall and Jones' study. One is the use of population as a scale proxy. Number of pickup units or refuse collected appear to be more appropriate output measures. Number of residences is included in the regression equation (a factor which is certainly highly correlated with population), but the regression coefficient is not reported. Also, the model appears to be misspecified. Quality differentials, although they are not accounted for in the regression analysis, are shown to exist between systems. Other cost factors, such as input prices, are also omitted. A sample of 128 Connecticut cities was used by Kemper and Quigley to test for size economies in refuse collection (49). Using only collection costs, an average cost curve was estimated with its scale measured by the number of dwelling units. Different equations were also estimated according to the institutional arrangement for providing refuse collection—whether municipal, contract, or private. No significant economies were found, although the authors concluded that economies may be available in cities having up to 2,000 residents (the size necessary to support one truck full time). Kemper and Quigley hypothesize that economies of density (tons per pickup mile) are likely for refuse collection. Pickup time per ton declined markedly in analyses of New Haven and Hartford, Connecticut, which shows economies of density. No such economies were found for the sample of 128 cities, even though the authors regarded this result as the product of poor data. Several problems in this study should be noted. First, failure to include disposal costs may lead to an understating of the overall economies in the handling of refuse. Kemper and Quigley argued that there are likely to be economies in refuse disposal, not collection. Also, input costs and production characteristics, such as crew size (number of workers per truck) are not included in cost-curve estimation. An average cost curve was estimated by Kitchen using data from 48 Canadian cities having populations over 10,000 (52). Multiple regression analysis was used to estimate the average cost curve using 17 (later reduced to 10) production, cost, and output characteristics. Data limitations forced Kitchen to employ population as the output quantity proxy, with pickup frequency and location serving as output quality surrogates. Kitchen included collection costs only and found an inverted U-shaped relationship between average costs and population. Average collection costs rise with population size, reach a maximum, and fall. He concluded that small firms, where the owner rides on the truck, are managerially efficient and large firms are efficient because they can use the most equipment and techniques. Middle-sized companies are caught in an efficiency squeeze. Kitchen's inverted U is difficult to justify. Examination suggests that maximum costs would occur at 324,000 residents. Communities near this size, which are served by only one firm, could hardly be classified as single-truck operations with efficiency resulting from owner operations. In fact, his sample did not include towns under 10,000, where direct owner involvement is most likely. Perhaps an inherent problem here is the inclusion of cities having populations widely different in size. The sample included cities having populations which ranged from 10,000 to over 300,000. The production functions may vary widely over the range examined. A related issue is that the service is provided by private firms in some cities and we are not clear whether more than one private firm produces refuse collection in some cities. If more than one firm produces the good, each firm must be examined as an individual supplier. A group of firms cannot be aggregated and examined as an individual producer. Finally, refuse collection, as used here, includes residential and nonresidential collection. Some firms will likely use private refuse collection. Also, costs for refuse collection would vary for residential and nonresidential collection so any potential economies would also differ according to the relative shares of these two. This is a particularly troubling difficulty when population serves as the quantity measure. Municipalities were asked to estimate the proportion of refuse coming from nonresidential sources and this variable was included in the analysis. It is questionable.

23 however, whether this variable would sufficiently account for the difference in production costs. Perhaps the most comprehensive and reliable study to date is the analysis of 340 cities by Stevens (7Q). The cities examined ranged from those having 2,500 to over 700,000 in population. Total cost curves were estimated separately for cities having under 20,000 in population, under 30,000, under 50,000, and over 50,000. Stevens also considered whether refuse collection was provided by a municipal monopoly, a private monopoly, or private competitive firms. The estimated total cost curve was derived from a Cobb-Douglas production function. Output was measured by quantity of refuse collected (in tons or cubic yards) and the costs were total costs to the households served for refuse collection. Quantity of refuse collected was found to be the most important determinant of total costs. Stevens concluded that there are economies of size "for populations up to 20,000, and that such economies are exhausted for populations in excess of 50,000 ...." The evidence for economies was mixed between populations of 20,000 to 50,000 but, potentially, some economies exist. Public monopolies were found to be sig- nificantly more costly than private monopolies for populations over 50,000. Private competitive firms were more expensive than public monopoly in the larger cities. Collins and Downes analyzed refuse collection in 53 suburban St. Louis cities ranging from those having under 500 to 11,000 pickup units (17). Pickup units were the output proxy and pickup frequency and location were the study's quality measures. Multiple regression analysis revealed a negative relationship between household costs per month and the number of pickup units (in logarithms), which suggests the presence of economies of size. Thus, based on observation, the authors concluded that economies existed up to at least 1,000 pickup units. Their model suffered from misspecification. Quality, quantity, and institutional characteristics of the services were accounted for but input and cost characteristics are ignored. Synthesis of the six studies suggests that economies of size are probably available in small communities. Each study that separately analyzed small communities observed some economies (17, 29, 70). Economies appear to occur in city sizes of 20,000 or possibly slightly more. Research examining a wide range of city sizes or only large cities found no economies or diseconomies (35, 49, 70). None of the studies specifically examined size economies in refuse disposal so no conclusion can be derived. Assuming economies do exist in disposal, Ochs and Hoover examined the possible benefits of setting up area stations to collect refuse and to transfer it in larger, one-person trucks to disposal sites (60). They concluded that such economies may exist, but obtaining a workable financing scheme requires a detailed specification of the costs and benefits for each community involved.

Capital-'Intensive Services

Capital-intensive services have a greater potential for size economies than do labor-intensive services. The capital-intensive services are reviewed below.

Roads and Highways

Potential size economies in roads and highways have received infrequent attention. Only three studies, two on rural roads, were found which specifically analyzed road and highway costs (table 5), Swanson studied the costs associated with providing Illinois with rural roads in 1956 (71), He divided the State into nine units to hold topographic and meterological conditions constant. Eight separate types of roads were identified and these were each used as regressors in estimating total cost equations for each of the nine districts. Size economies were found throughout the size ranges examined. The largest operating unit had 600 miles of roads and the largest construction project considered was 10 miles. These conclusions are limited in use as they refer only to rural

24 Table 5—Size economies in roads and highways

Author Cost measure Output or Population Results scale measure range

Lamb and Pine Total costs. Scale is measured Rural areas Noncounty roads (53) by square miles with 150 to exhibit a U-shap- of area; quality 1,443 square ed average cost surrogates are miles of curve and county miles of earth, area. roads were found gravel, and paved to have an invert- roads per square ed U-shaped aver- mile of area. age cost curve.

Lesher and Mapp Budget and/or Road mileage is 56 New York Significant econo- (54) expenditures. the scale measure counties. mies were found up and a quality to 400 miles of index of county county roads, up to roads is included. 590 miles for highway maintenance, and up to 490 miles for snow re- mo va 1. Admin istrative costs have a U-shaped average cost curve with a minimum at 465 miles.

Swanson (71) Maintenance, Mileage of eight Significant econo- adminis trat ion, types of roads. mies for rural and construction roads were found costs. for each cost component.

25 roads. Second, the results are at best suggestive because the regression equation fails to consider any input or cost variables. Finally, the results must be viewed with caution as they refer to the cost of a proportional increase in all road types. The results do not show economies or diseconomies for each road type. Lamb and Pine examined economies for rural roads in Kansas in 1974 (53); Cost curves for county and noncounty units were estimated separately with square miles of land area as an output proxy. A U-shaped average cost curve was found for noncounty roads and an inverted U-shaped average cost curve resulted for county roads. Lamb and Pine noted that road mileage would probably be a better output proxy, but they chose land area because several kinds of roads could not be aggregated. Mileage of three types of roads was included individually in the regression equation. Therefore, the scale analysis permitted examination of the impact on costs of providing highways over a larger area (lower highway density) while holding total highway miles constant. Land area would appear to bear no strong relationship with the road services the local government provides—whether seen as road miles, or people transpor- ted, or time saved. Thus, Lamb and Pine's conclusion is of dubious value, Lesher and Mapp examined administrative costs, maintenance costs, snow removal costs, and total costs for highway services in New York counties in 1974 (54). Multiple regression analysis was applied to estimate cost curves for each size class with road mileage used to measure scale. County roads were shown to be characterized by a downward sloping average cost curve with few economies available above 400 miles of roads. Both highway maintenance and snow removal demonstrated economies throughout the size range with most economies achieved at 590 miles and 490 miles, respectively, although economies for snow removal were found to be small. Finally, administrative costs exhibited a U-shaped relationship with minimum cost at approximately 465 miles. Each road study analyzed concluded that economies exist in the provision of roads. However, the costs associated with roads remains a relatively unresearched area. The three studies considered rural areas or county areas outside city limits. Also, previous research has failed to examine construction costs and how they inter- relate with other road costs.

Water and Sewer Utilities

Five studies of water utilities and two studies of sewer services were Identified (table 6). As these are capital-intensive services, economies of size might be expected (38). However, one offsetting factor is that a substantial share of the capital investment for water and sewer utilities is laying pipelines. The per unit costs associated with laying pipelines probably depend on density of consumers as much as scale of operation. Therefore, potential savings from consolidating several areas will be largely mitigated by any capital costs associated with laying more pipelines. Bourcier and Forste estimated shortrun and longrun cost curves for 10 water systems in New Hampshire and Maine (6), Three shortrun average cost curves were estimated for each of the waterworks corresponding to the use of replacement costs, replacement costs plus opportunity costs, and accounting costs as the cost proxy. The shortrun average cost curve sloped downward in every case. Longrun average cost curves were estimated for six waterworks which increased capacity over the time period studied, 1955-65. The trend line for average costs, measured using replacement costs, was calculated for each waterworks. It showed three waterworks with increasing trends and three with decreasing cost trends. The decreasing trend lines occurred for 1955-60 and the increasing cost lines for 1960- 65. The authors concluded that the longrun average cost curve is U-shaped because of the timing of the cost trends. Substantial questions arise as to the usefulness of this study's findings. First, the longrun average cost curves estimated by Bourcier and Forste appear to be a function of the time period when expansion occurred rather than a function of those elements of a longrun average cost curve which are useful for cost forecasting.

26 Table 6—Size economies in water and sewer utilities

Author Cost iifâasure Output or Population Results scale measure range

Andrews (2) Total costs and Gallons of water New England Finds significant costs per 1,000 and population waterworks. economies associat- gallons of water. are both used. ed with increasing water for a fixed set of consumers. Economies are offset if the number of consumers rise with water usage.

Broucier and Replacement cost Quantity of water. Each water All shortrun aver- Forste (6) less normal system age cost curves show returns. averaged economies. The long- approxi- run average cost mately 12,000 curve is U-shaped. people served.

Cosgrove and Operating and Water flow mea- 79 Ohio cities Declining marginal Hushak (18) maintenance sures quantity above 5,000 and average cost costs. and number of population. with significant treatments and savings beyond hardness removed 50,000 populations. measures quality.

Daugherty and Total utility Gallons of water 55 to more Significant size Jansma (19) cost per million sold and number than 42,000 economies for sur- gallons of water of customers customers. face water. Econo- sold. served. mies only result for ground water if the rate of water usage grows more rapidly than the number of customers.

Johnson and Annual fixed Number of users 23 to 686 Size economies were Hobgood (45) costs and annual measures scale. users. found for annual variable costs. fixed costs, annual variable costs, and total annual costs.

Marsden, Pingry, Costs other than Gallons treated. 0.2 to 60- Economies of size and Whinston maintenance and million- were indicated for (56) loans per gallon gal lons-a- wastewater treat- treated. day capacity. ment plants.

Young and Total annual Flow and propor- Economies of size Carlson (80) costs. tion of capacity exist for waste- used measure out- water treatment put and degree of plants. treatment is the quality surrogate.

27 Second, the minimuni cost production points appear to differ for each waterworks, some experience declining unit costs over output ranges in which others experience increasing unit costs. Finally, the authors do not state whether they standardized costs according to the time period. Andrews also examined waterworks in New England (2^) < He divided 112 New Hamp- shire utilities according to metered and nonmetered service to provide two separate samples. The combining of waterworks in five other states added another 951 utilities to the sample. Elasticities of cost for water volume were calculated for each of the three samples to test for size economies; revenues collected were the cost proxy. Large economies were found for expanding the water produced, while number of customers served was held constant. When the nimiber of customers served increased with water volume, however, no economies occurred. Some evidence of diseconomies is found when population is compared with expenditures. Andrews' study suffered most from data problems. As the author recognized, revenues may be a poor surrogate for costs, particularly when age of the utilities differs widely. Further, the author failed to consider other differential cost factors, such as aether ground or surface water is used and the geographic area served. An analysis of 79 water systems in Ohio cities having over 5,000 in population was undertaken by Cosgrove and Hushak (18). Both total variable cost and average variable cost curves were calculated while several differential cost factors were held constant. Output was measured by water flow, and the number of treatments and hardness removed were quality proxies. Separate cost curves were estimated for waterworks using surface water and ground water in addition to a cost curve for all waterworks. The cost curve estimates for all 79.cities revealed that marginal costs declined with increased size. The cost curves indicated lower costs for ground water when compared with surface water. Nineteen of the larger cities were used to examine economies associated with capital. Capital costs, including depreciation and opportunity costs, were estimated for these 19 cities and were used to estimate both a total and average cost curve. Average capital costs were much greater than variable costs ($336.10 versus $229 per million gallons, respectively). The cost curves, with only water flow and number of treatments as explanatory variables, indicated economies of size for the water systems. Marginal costs declined îIKDre rapidly with increased size when calculated from total costs than when calculated from variable costs. One drawback to the Cosgrove and Hushak study is that, although water flow was the output proxy, number of customers was not included in the total cost analysis. Presumably, capital costs for laying pipelines will depend heavily on the number of customers. Two proxies for customers (number of manufacturing plants and population densities) were included in several estimated forms of the variable cost curve. Another difficulty with the total cost curve analysis is the poor quality of capital data, a shortcoming observed by the authors. Pennsylvania water authorities constituted the Daugherty and Jansma study sample (19). Stepwise regression was used to estimate an average cost curve for waterworks serving 55 to 42,000 customers. Average costs were measured by using the sum of operating and nonoperating costs including debt service per unit of water. Size variables here were the number of customers served and total water sold. Other variables included such nonoperating expenses as proportion of total expenses and dimimy variables for the institutional, technical, and quality characteristics of the service. Elasticities were estimated for the size variables. Total number of customers had a positive elasticity of nearly one and total water sold had a negative elasticity nearly equal to one for ground water systems. This means unit cost reductions were small when number of customers and water sold increased in the same proportion. Surface water systems, though higher in cost, were found to exhibit substantial economies of size.

28 With one drawback, the Daugherty and Jansma research appears to be a good effort toward estimating a cost curve. Expenditures, including debt, represented the cost proxy. However, expenditures inay fail as a cost proxy. Perhaps the most Important failure is that capital costs, a major consideration for water utilities, are infrequent. Further, debt expenditures are more likely to be a function of the facilities' age than the production costs associated with water. Johnson and Hobgood examined 62 rural water systems which served between 23 and 686 customers in Louisiana (45). Cost curves were estimated with stepwise multiple regression to test for size economies. Number of users was the scale measure; density of users, treatment, and storage type were also included in the cost equation. Separate cost equations were estimated for annual fixed costs, annual variable costs, and their sum. The sample was segmented in three groups according to user density because density was thought to be such an Important cost factor. Annual fixed cost curves were estimated for each segment and all three segments showed economies for fixed cost. Within the segments, user density was only significant in the low-density segment. Annual variable cost equations were also estimated for each user-density segment. Continuous economies were found for the range of analysis in the low-density and high-density segments. The cost curve appeared to be U-shaped for medium-density users. Cost economies were also found when annual fixed costs plus annual variable costs were used as the cost measure. The Johnson and Hobgood study is subject to several criticisms. First, the sample size was limited. Starting with 62 water systems, the sample was divided in such a way that one segment had as few as 14 water systems. Further, no conceptual or empirical evidence was provided to justify segmenting the sample in the way they did. An additional problem is that fixed costs were measured by debt repayment. Debt costs, rather than production costs, were substantially a function of the interest rate when the system was built. All of the systems were built during 1964-68, so the problem of varying interest rates was limited. Finally, this is the only study which did not use water volume as an explanatory variable. In two sewage studies, Marsden, Pingry, and Whinston used discriminant analysis to determine the Impact of workload, size, capacity utilized, and treatment level on average costs (56). Gallons treated represented the proxy for size of operation. Average costs were calculated from total costs less maintenance and loan charges. Fourteen sludge-activated plants ranging in size from 0.2 to 60 million gallons treated per day formed the sample. Marsden, Pingry, and Whinston observed that average costs appeared to be lower for plants with more gallons treated. The discriminant analysis approach did not, however, reveal any information about the savings from larger size. The authors saw their work as preliminary and stated that more work using this approach is needed. Young and Carlson used survey data for 52 cities located in the southern half of the United States to assess the availability of size economies in the treatment of wastewater (80). The authors used annual treatment costs as the cost measure and gallons of wastewater treated as the quantity surrogate. The total cost function was estimated separately for conventional in-plant treatment costs and for conventional treatment costs plus land treatment costs. Other variables in the cost equation were the prices of inputs, proportion of capacity used, and an index of treatment level. Significant size economies were found by Young and Carlson with a 1-percent increase in flow leading to only a seven-tenths of 1-percent increase in costs. Similar economies were reported for the two types of treatment, although the conventional treatment plus land treatment appears to cost less. One problem with the Young and Carlson study is that it did not examine explic- itly the possibility of diseconomies for large-scale production. Therefore, it failed to provide information on the plant size at which all economies will be exhausted. Also, this study did not consider the number of customers served, the density of customers served, or the collection costs for wastewater.

29 Each of the water and sewer studies reported the availability of operating cost econcmiies associated with larger volumes of water or wastewater treated. These economies were generally present throughout the range of outputs examined. Several water economy studies also examined the effect of the number of customers on costs, Andrews observed that economies associated with large volumes of water are offset if the increased volume is simply the result of more customers (2^). Daugherty and Jansma found the same result for ground water. But, for surface water, they found that greater volume and more customers provided some economies (9), Johnson and Hobgood's study of small water systems examined economies associated with numbers of customers and found significant size economies, although water volume was not held constant (45). Synthesis of the results suggests that operating cost economies are associated with larger scale provision of water. These economies are, however, likely to be substantially mitigated if the increased water comes because of more customers rather than increased water per customer. Potential economies from increased water service may be substantially offset because of the costs of laying new pipelines. The important consideration in costs of laying new pipelines is the density of customers. If new customers are densely located, then there may be economies. Both wastewater studies found economies associated with wastewater flow. Yet, both studies omitted the number of custaners from the analysis. Any operating cost economies are likely to be substantially eliminated when collection costs are considered unless the new customers are densely located.

APPLICATION OF SIZE-ECONOMIES RESEARCH

Size economies exist for every local government service, although there appear to be diseconomies for larger sizes. The policy implications stem from three issues: (1) Should service districts be consolidated? (2) What happens to service expenditures as populations grow or decline? and (3) What happens to costs if services are increased for the existing population? Usually, results from size-economies research are insufficient to answer these questions. Whether to consolidate service districts is one of the most frequent issues to which size-economies research has been applied. However, size-economies research cannot reveal all of the benefits and costs associated with consolidation. One reason for this is that size economies are not necessary in the range of consolidated output for cost savings derived from consolidation. Consolidations can be cost saving, for example, if a high-cost small school is consolidated with a low-cost school producing in a constant cost range. However, the knowledge of cost curves provided by size-economies research is usually insufficient to determine the actual cost savings derived from consolidation. Second, size-économies research presumes that other costs do not change with size, even though consolidation means that the geographic area for service provision increases. A wider area served frequently means increased costs. Transportation costs for education, for example, are directly related to the area served and student density (7£) . The interaction between potentially lower school costs and the higher transportation costs entailed when students are placed in the most "efficient" size school has recently been investigated. Holland and Baritelle examined the least-cost pattern of allocating students across the nine school districts in Lincoln County, Washington (42). They concluded (because of the large transportation costs involved) that the savings from consolidation would only be approximately 1.3 percent of total costs, clearly not a major economy. They further argued that as no value has been placed on children's time, their estimate is an upper limit because it ignores the value of this time. This finding, using a case study approach, is probably applicable only to such sparsely populated areas as Lincoln County which has a density of 4.08 per square mile and fewer than 10,000 residents. Nonetheless, transportation costs will generally offset some of the economies from larger size.

30 Similar relationships between service area or density and costs exist for other services. As noted, costs of laying pipelines can offset savings in providing water and sewer utilities and collection costs for solid waste decline with collection unit density. Consolidation can also influence service quality and must be factored into the consolidation decision. Some have argued that quality of education deteriorates as school size increases. Quality of police and fire protection depends on response time which is directly related to distance from the station. When changes in the institutional arrangements (consolidation, for example) for providing services are considered, small-scale production alternatives should also be examined. A number of small-scale technologies are available for most services, although increased research on small technologies is needed. Generally, size- economies research is based on services provided using urban technologies, so little is known about the comparative costs of choosing a small-scale technology versus trying to achieve lower costs by increasing the scale of output. Choosing an appropriate technology may permit relatively low costs of production and still allow for more local control of services. Size-economies research must be used cautiously when determining what happens to expenditures as population shifts because expenditures tend to respond to population shifts only after a time lag. Therefore, size-economies research probably under- states the initial changes in per capita expenditures which result when population grows in areas still able to obtain decreasing costs or when population declines in areas experiencing increasing costs. Initial changes in per capita expenditures are overstated in those population growth areas experiencing increasing costs and in those areas with declining population which are experiencing decreasing costs. This is, however, only a short term problem, as expenditures eventually adjust to the expected level. Size-economies research is also inappropriate for explaining expenditure respon- ses to population change as it deals only with the supply or cost side of the market. Population adjustments may affect local income levels, for example, and this means the demand for services is likely to increase or decrease leading to expenditure changes which would not be predicted by size-economies research. The final question is what happens to costs if services are increased for existing populations? For services such as water, this means greater flow but for most services this means Increasing quality for a given quantity of output. Economies result for water and sewer utilities when more output is provided for the same customers. Less is known about the economies from providing greater service quality for a given quantity (frequently measured by population) of output. Exceptions include police protection where there appear to be economies associated with the nimiber of services provided and an education study which showed that education economies occurred over a greater pupil range when quality was increased (77).

31 LITERATURE CITED

(1) Ahlbrandt, Roger, Jr., "Efficiency in the Provision of Fire Services," Public Choice, 16:1-15. 1973. (2) Andrews, Richard A., "Economies Associated With Size of Water Utilities and Communities Served in New Hampshire and New England," Water Resources Bulletin, 7 (5):905-912. 1971. (3) Barzel, Yoram, "Productivity in the Electric Power Industry," The Review of Economics and Statistics, 45(4);395-408. 1963. (4) Beaton, W. Patrick, "The Determination of Police Protection Expenditures," National Tax Journal, 27(2): 335-349. 1974. (5) Berki, Sylvester E., Hospital Services. Lexington, Mass.: Lexington Books, 1972. (6) Bourcier, David V., and Robert H. Forste, "Economic Analysis of Public Water Supply in the Piscataqua River Watershed" Bull. 1, Water Resources Research Center, Univ. New Hampshire, Mar. 1967. (7) Brazer, Harvey E., City Expenditures in the United States, Occasional Paper No. 66, New York, N.Y.: Nat. Bur. Econ. Res. 1959. (8) Carr, W. John, and Paul J. Feldstein, "The Relationship of Cost to Hospital Size," Inquiry, 4(2);45-65. 1976. (9) Carr-Hill, R. A., and N. H, Stern, "An Econometric Model of the Supply and Con- trol of Recorded Offenses in England and Wales," Journal of Public Economics, 2:289-318. 1973. (10) Chapman, Jeffrey I., Werner Z. Hirsch, and Sidney Sonénblum, "Crime Prevention, The Police Production Function, and Budgeting," Public Finance, 30(2): 197-215. 1975, (11) Childs, Dan, Gerald Doeksen, and Jack Drye, "Economics of Rural Fire Protection in the Great Plains." Agr. Inf. Bull. No. 407, Econ. Res. Serv., U.S. Dept. Agr. in cooperation with Ext. Serv. and Agr. Expt, Sta., Oklahoma State Univ., 1977. (12) Christensen, Laurits R,, and William H. Greene, "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, 84(4): 655-675. 1976. (13) Coelen, Stephen P., and William F. Fox, "Facilities for Rural Public Service Delivery." Paper prepared for the Rural Futures Committee, Farmers Home Admin., U.S. Dept. Agr., Oct. 1979. (14) Cohen, Harold A., ''Hospital Cost Curves with Emphasis on Measuring Patient Care Output," Empirical Studies in Health Economics, Baltimore, Md.: The Johns Hopkins Univ. Press, 1970. (15) , "Variations in Cost Among Hospitals of Different Sizes," Southern Economic Journal, 33(3):355-366. 1967. (16) Cohn, Elchanan, "Economies of Scale in Iowa High School Operations," The Journal of Human Resources, 3(4):422-434. 1968. (17) Collins, John N., and Bryan T. Downes, "The Effects of Size on the Provision of Public Services: The Case of Solid Waste Collection in Smaller Cities," Urban Affairs Quarterly, 12(3);333-347. 1977. (18) Cosgrove, Michael H., and Leroy J. Hushak, "Costs and Quality of Water in Ohio Cities," Res, Bull. 105 (2), Ohio Agr. Res. Devlpt. Cen., Columbus, Ohio, Apr. 1972. (19) Daugherty, Arthur B., and J. Dean Jansma, "Economies of Size Among Municipal Water Authorities in Pennsylvania," Southern Journal of Agricultural Economics, 5(2):1-6. 1973. (20) Dawson, Donald A., "Economies of Scale in the Ontario Public Secondary Schools," Canadian Journal of Economics, 5(2):306-309. 1972. (21) Dhr3nnes, Phoebus J., and Mordecai Kurz, "Technology and Scale in Electricity Generation," Econometrica, 32(3): 287-315. 1964. (22) Fabricant, Solomon, The Trend of Government Activity in the United Since 1900. New York, N.Y.: National Bur. Econ. Res., 1952,

32 Feldstein^ Martin S«, Economic Analysis for Health Service Efficiency. Amster- dam, The Netherlands: North Holland Publishing Co., 1967. Foster, John E., "City Water: Rural Water System Design," Water Well Journal, (1): 26-27, 53--55. 1974. Fox, William, "Relationships Between Size of Schools and School Districts and the Cost of Education," Econ., Stat., Coop. Serv., U.S. Dept. Agr., Tech. Bull. 1621, 1980. Fox, William F., et. al., 1979. "Economies of Size in Local Government: An Annotated Bibliography," Econ., Stat*, Coop, Serv., U.S. Dept. Agr., Rural Devlpt. Res. Rpt. No. 9, 1979. Francisco, Edgar W., "Analysis of Cost Variations Among Short-Term General Hospitals," Empirical Studies in Health Economics, edited by Herbert E. Klarman. Baltimore, Md«: The Johns Hopkins Univ. Press, 1970. French, Ben C«, "The Analysis of Productive Efficiency in Agricultural Marketing: Models, Methods, and Progress," A Survey of Agriculture Economies Literature, Vol. 1, St. Paul, Minn.: Univ. Minn. Press, 1977. Hall, J. Patrick, and Lonnie L, Jones, "Costs of Solid Waste Management in Rural Texas Communities," Southern Journal of Agricultural Economics, 5(1):115- 119. 1973. Hambor, John C, Liad Phillips, and Harold L, Votey, Jr., "Optimal Community Educational Attainment: A Simultaneous Equation Approach," The Review of Economics and Statistics, 55(1): 98-103. 1972. Hanson, Neis W., "Economy of Scale as a Cost Factor in Financing Public Schools," National Tax Journal, 17(l):92-95. 1964. Henderson, James M., "Local Government Expenditures: A Social Welfare Analy- sis," The Review of Economics and Statistics, 50(2): 156-163. 1968. Hettich, Walter, "Equalization Grants, Minimum Standards, and Unit Cost Differ- ences in Education," Yale Economic Essays, 8(2):5-55. 1968. Hind, Ian W., "Estimates of Cost Functions for Primary Schools in Rural Areas," Australian Journal of Agricultural Economics, 21(l):13-25. 1977, Hirsch, Werner Z., "Cost Functions of an Urban Government Service: Refuse Collection," The Review of Economics and Statistics, 47(l):87-92. 1965. , "Determinants of Public Education Expenditures," National Tax Journal, 13(2):29-40. 1960. ___, "Expenditure Implications of Metropolitan Growth and Consolidation," The Review of Economics and Statistics, 41(3): 232-241. 1959. ___, "Local vs. Areawide Urban Government Services," National Tax Journal, 17(4):331-339. 1964. 3 "Output and Costs of Local Government Services," National Conference on Nonmetropolitan Community Services Research, Columbus, Ohio, Jan. 11-13, 1977. U.S. Senate Committee on Agriculture, Nutrition, and Forestry, 95th Congress, 1st Session, July 12, 1977, pp. 307-319. , "The Supply of Urban Public Services," Issues in Urban Economics. Baltimore, Md.: The Johns Hopkins Univ. Press, 1968. Hitzhusen, Frederick J., "Some Measurement Criteria for Community Service Output and Costs: The Case of Fire Protection in Texas," Southern Journal of Agricul- tural Economics, 4(1):99-107. 1972. Holland, David W., and John L. Baritelle, "School Consolidation in Sparsely Populated Rural Areas: A Separable Programming Approach," American Journal of Agricultural Economies, 57 (4):567-575. 1975. Howard, Ebenezer, Garden Cities of Tomorrow. London, England: Faber and Faber, 1902. Huettner, David A., and John H. Landon, "Electric Utilities: Scale Economies and Diseconomies," Southern Economic Journal, 44(4); 883-912, 1978. Johnson, R. B., and W. P. Hobgood, "Cost Analysis of Rural Water Systems in Louisiana." Working Paper No. 483, Dept. Agr, Econ., La. State Univ., April. 1973.

33 (46) Johnston, J., "Statistical Cost Functions in Electrical Supply," Oxford Economic Papers, 4(1):68-105. 1952. (47) Katzman, Martin T., "Distribution and Production in a Big City Elementary School System," Yale Economic Essays, 8(1):201-256. 1968. (48) , The Political Economy of Urban Schools. Cambridge, Mass.: Harvard Univ. Press, 1971. (49) Kemper, Peter, and John M. Quigley, The Economics of Refuse Collection. Cambridge, Mass.: Lippincott and Ballinger, 1976, (50) Riesling, Herbert J., "Measuring Local Government Services; A Study of School Districts in New York State," The Review of Economics and Statistics, 49(3):356- 367. 1967. (51) King, Richard, and Bryan Wall, "Estimation of Cost-Quality-Quantity Relation- ships," National Conference on Konmetropolitan Community Services Research, Columbus, Ohio, Jan. 11-13, 1977. U.S. Senate Committee on Agriculture, Nutri- tion, and Forestry, 95th Congress, 1st Session, July 12, 1977, pp. 321-41. (52) Kitchen, Harry M., "A Statistical Estimation of an Operating Cost Function for Municipal Refuse Collection," Public Finance Quarterly, 4(l):56-76. 1976. (53) Lamb, Steven W,, and Wilfred H. Pine, "Influence of Size and Administrative Organization on Costs of Rural Roads," Southern Journal of Agricultural Econom- ics , 6(2):157-160. 1974. (54) Lesher, William G., and Harry P. Mapp, "Economies of Size in Highway Maintenance and Administration: A Preliminary Analysis for the Counties of New York State," Journal of the Northeastern Agricultural Economics Council, 3(1):90-111. 1974. (55) Lomax, K. S,, "Cost Curve for Electricity Generation," Económica, 19(74): 193-197. 1952. (56) Marsden, James R., David E. Pingry, and Andrew Whinsto, "The Large-Scale Regional Plant Hypothesis; Discriminant Analysis, Water Resources Research, 2(6):1013- 1017. 1975. (57) Michelson, Stephan, "Equal School Resource Allocation," The Journal of Human Resources, 7 (3): 283-306. 1972. (58) Morris, Douglas E,, "Economies of City Size: Per Capita Costs pf Providing Community Services." Ph.D. dissertation, Okla. State Univ., 1973. (59) Morris, Douglas E., and Luther Tweeten, "The Cost of Controlling Crime: A Study in Economies of City Life," The Annals of Regional Science, 5(l):33-49. 1971. (60) Ochs, Jack, and Edgar M. Hoover, "On Exploiting Scale Economies," Journal of Urban Economics, 4(l):30-44. 1977. (61) Ogburn, W. F., "Social Characteristics of Cities." Chicago, 111.; International City Managers Assoc, 1937. (62) Popp, Dean 0., and Frederick D. Sebold, "Quasi Returns-to-Scale in the Provision of Police Service," Public Finance, 37(1):46-61. 1972. (63) Renne, Roland R., '^Montana County Organization, Services and Costs." Bull. No. 298, Montana State College, Apr. 1935. (64) Ricker, William D., and Fred H. Tyner, "An Analytical Approach to the Consolida- tion of Counties in North and West Florida Based on Educational Efficiency Criteria," Southern Journal of Agricultural Economics, 4(l):79-84. 1972. (65) Riew, John, "Economies of Scale in High School Operations," The Review of Economics and Statistics, 48(3): 288-287. 1966, (66) Ro, Kong Kyun, "Determinants of Hospital Costs," Yale Economic Essays, 8(2):185- 257. 1968. (67) Schmandt, Henry J., and Ross G. Stephens, '^Measuring Municipal Output," National Tax Journal, 13(4):369-375. 1960. (68) Shapiro, David, "Economy of Scale as a Cost Factor in the Operation of School Districts in Alberta," Canadian Journal of Economics, 6(1): 114-121. 1973. (69) Sher, Jonathan P., and Rachel B. Tompkins, "Economy, Efficiency, and Equality: The Myths of Rural School and District Consolidation," Education in Rural America: A Reassessment of Conventional Wisdom. Edited by Jonathan P. Sher, Boulder, Colo.: Westview Press, 1977.

U.S. GOVERMENT PRINTING OFFICE 1980 -0- 310-945/224

34 (70) Stevens, Barbara J,, '^Scale, Market Structure, and the Cost of Refuse Collec- tion/' The Review of Economics and Statistics, 60(3): 438-448, 1978. (71) Swanson, Earl R. , "Rural Road Costs and Size of Road Unit," Current Econoinic Comment, 18(3)^25-32. 1956. (72) Tiebout, Charles M,, "Economies of Scale and Metropolitan Governments," The Review of Economics and Statistics, 42(4)•442-444* 1960, (73) U,S. Bureau of the Census, Census of Governments, 1972, vol, 6, Topical Studies No, 4, Historical Statistics on Governmental Finances and Employment, Govt, Frint. Off,, Dec, 1974, (74) Voelker, Stanley Wo, "Possibilities of Farm Tax Reduction Through County Consol- idation in Montana." Unpublished masters thesis, Mont. State College, June 1936. (75) Wales, Terence J., "The Effects of School and District Size on Education Costs in British Columbia," International Economic Review, 14(3): 710-720. 1973. (76) Walzer, Norman, "Economies of Scale and Municipal Police Services: The Illinois Experience," The Review of Economies and Statistics, 54(4): 431-438. 1972. (77) White, Fred, and Luther Tweeten, "Internal Economics of Rural Elementary and Secondary Schooling," Socio-Economic Planning Sciences, 7(4)^353-369. 1973. (^^) , "Optimal School District Size Emphasizing Rural Areas," American Journal of Agricultural Economics, 55(l):45-53. 1973. (79) Will, Robert E., "Scalar Economies and Urban Service Requirements," Yale Economic Essays, 5(1):3-'61. 1965. (80) Young, C* Edwin, and Gerald A. Carlson. "Land Treatment vs. Conventional Treat- ment of Municipal Wastewater," Journal of Water Pollution Federation, 47(11): 2565-2573. 1975.

35 UNITED STATES DEPARTMENT OF AGRICULTURE POSTAGE AND FEES PAID WASHINGTON, D.C. 20250 U.S. DEPARTMENT OF AGRICULTURE AGR 101 THIRD CLASS

ES Economics, Statistics, and Cooperatives Service The Economics, Statistics, and Cooperatives Service (ESCS) collects data and carries out research projects related to food and nutrition, cooperatives, natural resources, and rural development. The Economics unit of ESCS researches and analyzes production and marketing of major commodities; foreign agriculture and trade; economic use, conservation, and development of natural resources; rural population, employment, and housing trends, and economic adjustment problems; and performance of the agricultural industry. The ESCS Statistics unit collects data on crops, livestock, prices, and labor, and publishes official USD A State and national estimates through the Crop Reporting Board. The ESCS Cooperatives unit provides research and technical and educational assistance to help farmer cooperatives operate efficiently. Through its information program, ESCS provides objective and timely economic and statistical information for farmers, government policymakers, consumers, agribusiness firms, cooperatives, rural residents, and other interested citizens.