Introduction

 In economic terms the concept of efficiency can easily be definedas the relationship between inputs and outputs, whereby economic efficiency is increased by a gain in units of output per unit of input.  This can occur by holding output constant and decreasing input or by deriving greater production from the same level of input.  In relation to education,then, we may say that various educational outcomes can result from a variety of different combinations of inputs such as teachers, buildings, classsize, curriculum, etc.  The problem that confronts economists andeducators, however, is how to mix the inputs in the right proportions toachieve the most efficient outcome.  But the problem is further compounded when we ask ourselves "What output should we measure?' According to Sheenan(1973:131), R is very difficult to specify a unit of output "because educational systems so often in practice have no single well defined function, so alsothey have no single well-defined indicator of output."

 Clearly, education serves many outcomes and some of these cannot be measured by using econometric techniques of orthodox economic theory.  For the typical profit-maximizing firm it is possible to put money values on the inputs of the production process and, in turn, assess its efficiency. Therefore, in a firm the right mix, or maximum efficiency, is achievedwhen the price of the resources used to make the commodity is equal tothe marginal cost of producing it; that is, p = MC.  In education,this is not feasible since many of the outputs are not quantifiable interms of market prices.  Historically, though, there have been effortsto increase educational efficiency.  For instance, during the earlynineteenth century an elaborate British system of tutors and monitors,the so-called Lancastrian system, was used in an effort to boost schooloutput (Tyack, 1974).  Similarly, in the early twentieth century,American schools were greatly influenced by the then prevalent scientific management movement founded by Frederick Taylor.  The hope was thatTaylor's principles of scientific management, which were popular in themanufacturing sector, could be applied to schools in order to enhance learningand reduce costs (Callahan, 1962).  In order to explicate the problemsinherent in the measurement of educational efficiency, it is necessaryto examine the research done on the most obvious input-output productionfunctions: namely, class size versus student achievement and size of schoolversus cost.
 

Class Size Versus Student Achievement

 From a theoretical standpoint, it would appear to be intuitively plausible to expect that the longer students are exposed to school-basedresources the greater would be their achievement.  Thomas and Kemmerer(1983) found that in this regard there is some evidence to show that 'learninggroup' size (a measure of access to resources) does increase student achievement.  However, even within the same classrooms, Thomas (1982) found that theamount of time teachers spend with each student varies considerably andis associated with differences in achievement for each student.  Moreover,there are important differences in quality and effectiveness among teacherswhich impact upon student achievement.  Research findings regardingthe relationship between teacher characteristics and student achievementseem to suggest that verbal aptitude, quality of university programs, andexperience are associated with gains in student learning (Summers and Wolfe,1977; Levin, 1969; Hanushek, 1981).  Nevertheless, Thomas (1977) pointsout that it is extremely difficult to separate the independent effectsof teacher attributes since highly qualified teachers are more likely towork in schools and communities that have more and better resources. Besides the foregoing, there are other difficulties involved in researchingthe relationship between class size and student achievement.  Forinstance, student achievement is obviously affected by the educational milieu of the home and the presence (or absence) of excellent communityfacilities and resources.  Differences in student learning appearto be associated with: differences in parental time spent in learning-relatedactivities (Leibowitz, 1977; Mumane et al., 1981); learning-related opportunitiesafter school hours (Medrich et al., 1982), and community-based resourcessuch as activities for children, better libraries and other community-basedcultural events (Benson, 1982; Medrich et al., 1982).

 In essence, then, it appears that no two investigations will havethe same input mix and, consequently, the outcomes of the investigations with regard to class size and student achievement will vary.
 

Size of School Versus Cost

 Controversy and doubt surrounds not only class size but school size as well.  For instance, a study done by Campbell (1965:3) onSchool Size:  Its Influence on Pupils showed that

 while students in large schools were exposed to a large number of school activities and the best of them achieved standards in many activities that were unequalled by students in the small schools, students in thesmall schools participated in more activities, their versatility and performance scores were consistently higher, they reported more and better satisfactions and displayed stronger motivation in all areas of school activities.

 However, when comparisons are made between small and large schoolsregarding cost, there appears to be enough evidence to suggest that schools,like firms, are able to achieve economies of scale; that is, as the schoolbecomes larger the cost per pupil drops.  But, according to Sheenan (1973:133), "the use of cost studies for comparing different kinds andlevels of education tells us nothing about efficiency as the goals andactivities are different; their main use is in the area of budgeting andfinance." After examining fifty years of research on economy of scale inhigher education, Brinkman (1985) concluded that the concept of economyof scale is not a clear-cut one.  He noted, for example, that thedefinition of scale is confused in theory and practice in that classicdefinitions relate scale to productive capacity, whereas most empiricalstudies define scale in terms of organization size or quantity of output. As well, Brinkman pointed out that economy of scale studies may be influencedby short-run versus long-run behavior.  Short-run effects may influenceresults in cross-sectional studies; or, conversely, short-run effects mightbe minimized in longitudinal studies based on performance over time. Similarly, educational organizations may be particularly prone to widefluctuations in important variables; for instance, with regard to enrolment,costs per student may at first decline with enrollment increases but laterrise with the consequent addition of staff and services, thereby givingdistorted results.
 

Conclusions

It appears, then, that organizational researchers investigating efficiencies in education tend to limit investigation to the distribution of resources within a single system and often examine the consequent effects in terms of cost per student.  Therefore, it might be argued thatthis approach is really an investigation of resource allocation ratherthan efficiency.  Hence, due to the obvious difficulties inherentin the measurements of efficiency with regard to the myriad of factorsthat impinge upon student achievement, one may conclude that we face apervasive ignorance about the production function of education; that is,the relationship between school inputs and outputs.  In this writer'sopinion, the production function must be used cautiously when applied toeducation, not only because of the many problems that plague it, such asmulticollinearity, simultaneity, etc., but also because what might be cheapestmay not necessarily be best.

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 Brinkman, Paul T. (1 985).  Economies of Scale in Higher Education: Fifty Years of Research.  A paper prepared for the 1985annual convention of the National Center for Higher Education ManagementSystems. 

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 Thomas, J.A. (1977).  Resource allocation in classrooms.  Final Report to the National Institute of Education, Grant #:  NIE-G-740037, Project 4-0794.

 Thomas, J.A. and Kemmerer, F. (1983).  Money, time, and learning. Final Report to the National Institute of Education, Contract #: 400-77-0094.

 Thomas, J.A. et al. (I 982).  Efficiency in educational finance:the classroom perspective.  In Financing Education: Overcoming Inefficiencyand Inequity (Edited by McMahon, W.W. and Geske, T.G.), pp. 100-118. Urbana, IL:  University of Illinois Press.

 Tyack, David B. (1974).  The One Best System.  Cambridge,Mass.:  Harvard University Press.