Some Aspects of Scale Economies Among Missouri Area Vocational Schools

Abstract

O NE of the most significant contributions of the Vocational Education Act of 1963 was the authorization of federal funds for construction of area vocational-technical school facilities. In Missouri some 37 school districts have in operation or have secured approval for the establishment of area vocational-technical schools. During the 1966-1968 biennium some $42 million was spent on vocational-technical education in Missouri. This expenditure, from local, state, and federal sources, represented a 58 percent increase over the 1964-1966 biennium. Because of the magnitude of resources involved and their rapid growth, inquiry into scale economies in facilities for public vocational education has not received adequate treatment by researchers. This investigation of economies of size was confined to the regular day vocational program offered in the area vocational-technical schools of Missouri. Cost data collected pertained to shared-time type of secondary area vocationaltechnical schools with permanent separate plant facilities in operation during fiscal year 19681969. Fifteen schools met these qualifications. Costs incurred by these schools consisted of current operating expenditures (administrative costs, operation and maintenance cost) and capital outlay expenditures associated with equipment and physical facilities. Annual depreciation of plant and equipment was estimated by the straight-line method, then converted to a per student cost. Plant depreciation was distributed equally among total enrollment; equipment depreciation was allocated by enrollment with respect to curriculum and program area. Current expenditures per student ranged from $387 to $609. The mean and weighted mean were $468 and $455 respectively. Complete equipment inventories was a prerequisite for estimating total cost, and only seven schools had such inventories. Mean and weighted mean for total cost per student were $568 and $545 respectively; the range was from $464 to $735. In short, fixed cost per student was approximately $100. In order to quantify the relationship between expenditures per student and size, expenditures per student (dependent variable) were regressed on selected independent variables hypothesized to be correlated with expenditures. Stepwise regression techniques were used for the analyses. Number of students (X1), number of students squared (X2), average teacher salary (X,), tax levy (X4), assessed valuation per student (X5), studentteacher ratio (X6), and number of classes (X7) were the independent variables chosen. Two separate models were investigated. Model 1: This regression equation included only variables X1 and X2 (size of school and size of school squared). Estimated parameters for the equation were: Y = 764.65 1.808X1 + .00227X2. R2 was .51. The optimum size, or size with the least cost per student, was found to be 398 students, computed by taking the partial derivative of the above equation, setting it equal to zero, and solving for the number of students. Model 2: This model included all the selected