Elasticities of Substitution for Two-Digit Manufacturing Industries: A Correction

Abstract

There are two primary questions confronting program planners of educational facilities: 1) At what is the minimum cost per pupil achieved, i.e., what is the of school? 5 2) Ascertaining if economies of exist and the magnitude of such economics, i.e., at what rate does expenditure per pupil decrease as increases? Table 1 provides the results of expenditures per pupil regressed on selected independent variables. Use of the regression equation to find the net relationship between cost and is as follows for the different school sizes: 1) Change in cost from 200 to 500 pupils .0503 (500) + .00001121 (500)2 .0503 (200) + .00001121 (200)2 $12.74. 2) Change in cost from 500 to 1000 students is -$16.74. 3) Change in cost from 1,000 to 1,500 students is -$11.14 per pupil. 4) Change in cost from 1,500 to 2,000 students is $5.53. 5) Change in cost from 2,000 to 2,244 is -$.66 per pupil. In other words, the total net effect of increasing school from 200 to 2,244 students would result in a savings of approximately $47 per pupil. Riew, on the other hand, found the total savings would amount to well over $200 per pupil from a school with 200 to 1,675 students. A possible explanation for such a large discrepancy in the rate of decrease in per pupil expenditures is that Riew excluded transportation costs from his expenditure variable. The results of this analysis regarding the net relationship between current expenditures per pupil and of school provides guidelines regarding the added costs incurred if the optimum size school was not provided. Note that most of the economies had been realized as student numbers approached 1500. 5 DY/DX8 =-.0503 + 2 (.00001121) X8. Setting DY/DX8 equal to zero and solving for X8 yields 2,244 students. TABLE 1. REGRESSION RESULTS OF CURRENT PER PUPIL EXPENDITURES REGRESSED ON SELECTED INDEPENDENT VARIABLES MISSOURI SCHOOL SYSTEMS, 1966