Some Economic Models of Curriculum Structure
by Ralph F. Goldman, William H. Weber & Harold J. Noah - 1971
Two fairly speculative models presented in this paper illustrate some less restrictive techniques of economic model-building. The first model is the micro-economic type. It suggests that if a school district wishes to maximize student learning, there may exist an optimal teacher salary-level it should pay, given the student ability to learn, the distribution of abilities in the population of teachers currently "in-the-market," and certain other conditions of supply and demand. The second model is macro-socioeconomic, and suggests possible relationships among higher education curriculum, economic and technological change, and social change.
Ralph F. Goldman and William H. Weber, Ph. D. doctoral candidates in the economics of education program at Teachers College, co-authored this article. Harold J. Noah is professor of economics and education at Teachers College, and assisted wish the conception of this article.
Those interested in the economics of education have long concerned themselves with investigating the relationships which appear to exist between education and socioeconomic development. A number of studies have attempted to show the existence of a systematic relationship between school enrollment as a percentage of age group, or stock of educated manpower, and a nation's "stage of development." These studies search for systematic regularities across countries at a point in time and, in the case of individual countries, through time,i Most, if not all, such investigations suffer from their restricted formulation in terms of investment-in-human-capital models and their implicit assumption that, if economic and social development is to occur, educational patterns must be established which mirror those of developed Western nations. This approach, although capable of producing interesting results, fails to raise many more exciting questions which a somewhat broader application of economic model-building can generate.ii
The two fairly speculative models presented in this paper illustrate some less restrictive techniques of economic model-building. The first model is the micro-economic type. It suggests that if a school district wishes to maximize student learning, there may exist an optimal teacher salary-level it should pay, given the student ability to learn, the distribution of abilities in the population of teachers currently "in-the-market," and certain other conditions of supply and demand. The second model is macro-socioeconomic, and suggests possible relationships among higher education curriculum, economic and technological change, and social change.
Economic Aspects of Public Schooling
The public school curriculum, viewed in its entirety, appears to the economist as a community-purchased and distributed bundle of teacher-pupil interactions, carried out over a carefully defined period of time. Public provision to the school-age population of free access to these interactions is prescribe by custom, mandated by law, and justified by the contribution which pupil participation in these interactions is expected to make to the improvement of the milieu. The community provides the curriculum not as a final product, that is, not as an end in itself, but as an intermediate product, exposure to which is expected to produce within the pupil reactions commonly identified as knowledge, skills, and attitudes. These reactions are presumably transformed by the pupil, to a degree that varies with the individual, into that capacity for civilized thinking (and constructive action in accordance with that thinking) called education.
The community therefore does not provide education; it provides only the curriculum. Whether the pupil succeeds in transforming his exposure to the curriculum into the final good called education rest on other factors, such as general and school environment, family background, and the impact of these on the individual's genetic endowment. However, the pupil can gain access to the curriculum only upon condition of compulsory participation in, or at least exposure to, the institutionalizing process of schooling. The curriculum is imbedded in schooling and, therefore, for public purposes is inseparable from it. Hence, this paper speaks not of the "demand for (public) schooling."
The interactions which comprise the curriculum are produced by combining in varying proportions the traditional economic inputs of land, labor, and capital. In the schooling context, these scarce resources include school buildings, materials, and supplies (both instructional and noninstructional); time of administrators and auxiliary personnel; time of teachers; and time of pupils.
The time of pupils is considered to have zero money value since, at least until the age of sixteen, the pupil is not regarded as sacrificing earnings in order to attend school. The time of teachers, however, is recognized as having considerable money value, as reflected in the fact that teachers' salaries absorb about 50 percent of the total U.S. expenditure on public elementary and secondary schooling.
However, a curriculum is essentially a structuring of the time of all participants, pupils as well as teachers. The cost of structuring time to produce Curriculum Pattern A is reckoned in terms of the educational benefits that might have been enjoyed by pupils if the time had instead been structured to produce an alternative, Curriculum Pattern B. The cost of A can also be reckoned in terms of the inputs unproductively expended by failing to adopt alternative B.
Thus the structuring of time by which a given curriculum pattern is produced implies an economic trade-offthat is, certain curriculum features thought to be desirable are obtained at the expense of the efficient use of certain inputs. However, the inputs presently under consideration are not among those included in the traditional list. Rather they are the scarce human resource inputs which are always assumed to exist in sufficient quantity to guarantee the viability of each alternative curriculum pattern. However, these inputs are rarely included in analyses of the curriculum production function, even though they are at its very core. Despite the obvious difficulties of measurement, these inputs should at least be included as residuals, since not a single minute in the schooling process passes that does not somehow involve their expenditure.
These scarcer inputs are, on the teacher's side, the ability to teach and the desire to teach; and, on the pupil's side, the ability to learn and the desire to learn. The twin problems of pupil dropout and teacher turnover are only now focusing our attention on the urgent need for conserving, and possibly expanding, these very scarce human resource factors, which are coming to be recognized as inputs that are variable both upward and downward in the schooling process. Since economics concerns itself with the allocation of scarce resources of whatever form, these too deserve at least to be mentioned in any analysis of the demand for curriculum-qua-schooling, and to be given a priority rating on the list of topics for further research.
Analysis of the demand for schooling starts by considering the demand of individual private purchasers for that type of curriculum whose benefits would accrue primarily to them privately. In this private-consumer context, the demand for curriculum may be predicted from the traditional theory of consumer behavior. Thus in times of prosperity, as the relative price of education appears to decline, private consumers will demand longer periods of schooling. Even in times of general economic adversity, if consumers' information indicates that schooling is retaining or expanding its satisfaction-maximizing capacity, private consumers will demand more schooling, even if price rises.
However, the demand for schooling by a community, which is required to distribute it to the public, functions somewhat differently. Whereas the demand of the individual private purchaser is motivated by voluntarism, the demand of the community, the collective purchaser, is motivated by statutory compulsion. Moreover, the community is placed in the position of sole purchaser of the principal purchasable input to the processthe supply of certified teachers. As long as school enrollment remains fairly stable, the community as sole purchaser of this input is in a favored position and encounters no problem in meeting the demand for curriculum.
As school enrollment rises, however, the community's usage of certified teachers expands, and the price of this input increases. The community, however, is prevented by law from reducing its production of the schooling service which makes use of this input. If the community's production of schooling continues to expand, as made inevitable by rising enrollments, the additional expense of hiring one more teacher reaches the level at which quantitative demand for curriculum can be met only by purchasing lower-priced, lower-quality input. The community thus produces an output in period 2 which, though quantitatively "correct" from the standpoint of number of classes covered, is likely to be qualitatively below that of period 1. It is, therefore, apparent that the community is not as free as the individual consumer to reduce its demand for quantity-of-schooling-service-produced in response to rises in input price.
Nor is the community free to continue indefinitely lowering the quality of input, particularly in the form of labor. Negative output effects will soon evoke objections from pupils and parents on grounds of deteriorating quality of service. Objections will come, interestingly enough, from both the poor and the middle class, but for different reasons. The poor see the curriculum as a means for redistributing community wealth through the promise of additional earning power for their children as well as through the value of the service provided; the middle class see the curriculum as a means of maintaining their income lead and getting a proper return on their property tax. Political considerations will soon compel the community to substitute inputs of capital for the now excessively costly labor in an attempt to maintain quality as well as quantity of output. However, no relationship between resource input and curriculum output has yet been demonstrated. Hence the allocation pattern thus produced may be suboptimal, reminding us that the curriculum itself is often a suboptimal solution under a set of constraints which are not only economic but also social and political.
Generally, public schooling seems to be a "normal" good, with increase in money income leading to increase in consumption. Communities with higher per capita wealth commonly exhibit a willingness to purchase more units of curriculum for their schooling process than communities with lower per capita wealth. Even in communities with relatively low tax yields, however, external factors may increase the intensity of the local desire for schooling. Thus in the late 1950s, buying more units, and more expensive units, of curriculum became a way of demonstrating the community's patriotic determination to compete with the Soviets. Or, as an additional example, pressure in the job market may cause a rise in the demand for schooling. In response to a rapidly expanding labor force, as a result of demographic trends, employers set up increasingly, stringent schooling requirements as bases for selecting applicants. These rising expectations of employers are given wide publicity and are soon matched by rising local demand for schooling. As a third example of external forces, changes in public taste can also cause a decline in the demand for specific types of schooling, such as instruction in foreign languages.
Prices of related commodities also condition the level of demand for schooling. The rising cost of other public services has generated increasing resistance to school budget proposals, in effect communicating local desire to reduce the quantity of schooling to be purchased by the community. Nevertheless, the public insists, too, that this reduction not take place at the expense of curriculum quality. Accordingly, some school boards take this as a mandate for exchanging a large number of lower-quality teachers for a smaller number of higher-quality teachers, coupling this teacher redeployment with such innovations as modular scheduling, team teaching, technological devices for instruction, a loosely structured school day, and relaxation of behavioral standards requiring many teachers and much teacher time for enforcement. Other school boards have interpreted community resistance to school budget proposals as a mandate to hire young, relatively inexperienced, and hence lower-salaried teachers as less expensive inputs. Veteran tenured teachers who become aware of this trend in their districts have adopted the rule of thumb that when a salary of a tenured teacher reaches the level, under the automatic increment system, where it is equal to the salaries of two beginning teachers, the experienced teacher can expect to come under pressure to resign. The replacing of experienced by inexperienced teachers has brought in its wake a rising demand for instructional materials in "teacher-proof packages guaranteed to place minimum demand on the skill and inventiveness of the replacement.
Can other commodities be substituted for the curriculum so that a rise in the price of schooling would lead to a positive change in the consumption of substitutes? The legitimate possibilities for substitution are presently limited because schooling in the traditional form is required by law. However, if public opinion can be conditioned to accept the relaxation of the compulsory aspect, many substitutes will become available and will enjoy increasing demand. The avalanche of publicity now accorded to "free schools," "alternative schools," and other informal schooling agencies may well be a step toward relaxation of the compulsory aspect, at least on a de facto, if not a de jure, basis. In the meantime public school authorities may be expected to move with increasing alacrity to expunge those institutional aspects of public schooling which encourage young people to seek alternative agencies of schooling outside the public jurisdiction. Indeed, if fear of political unrest and social dislocation were not looming in the background to dampen efforts at fundamental school reform, public education authorities might well be inclined to discontinue production of traditional schooling with all the dispatch industry closes down its production of manufactured goods that are no longer in demand due to the invention of acceptable substitutes available at lower prices.
The public, however, has not been conditioned to accept the rate of change in social arrangements, especially those sponsored by local authorities, that it has come to accept for technical innovation. Hence it is possible that social changes will occur only as technological innovations make them inevitable. Substitute commodities for the traditional schooling-service can be expected to gain acceptance only where technological changes make relaxation of the compulsory aspect of public schooling seem reasonable.
A decline in demand for curriculum due to the availability of non-compulsory substitutes is a prospect for the long run. More immediate is the problem of the apparent declining demand for schooling on the part of its direct recipients, the pupils.
As reflected in classroom apathy and schoolwide unrest, the declining pupil demand for traditional schooling may well be the counterpart to the community's increased usage of lower-quality inputs, both instructional and physical, as substitutes for the more expensive inputs. Not infrequently the use of lower-quality inputs is justified on grounds that pupil performance does not warrant the use of costlier inputs. By this logic of self-fulfilling prophecy, community investment in schooling and pupil performance in the classroom must chase each other downward, presumably to the point at which the public recognizes that continued support of a nonfunctional "school" system is a misapplication of community resources. What is to be feared most, however, is not that a once-respected but now obsolete social form will disappear from the public scene; but that by the time society manages to overcome its social conservatism long enough to make the decision, it will have sustained irreparable damage to perhaps the scarcest of all human resourcespupils' ability and desire to learn, and teachers' ability and desire to teach.
Model I: Optimal Teacher Salary and the Production Function
As stated earlier, the economist looks upon the entire public school curriculum as a community-purchased and distributed block of teacher-pupil interactions performed over a specific time period and expected to produce knowledge and attitude changes in the minds of the students,iii The demands for teacher services and educational facilities derive from the community demand for the benefits which flow from living in an environment where some minimum level of educational attainment and set of attitudes can be presumed to be embodied in the individual members of the community. Thus the demand for free and required primary and secondary education is, at base, a demand for curriculum, where curriculum is broadly defined as teacher-pupil interactions so structured as to produce knowledge and attitude changes (socialization) in the minds of students.iv In this sense, the curriculum may be regarded as the production process whereby inputs are converted into desired outputs, and determination of the cost of an increment of desired output requires an understanding of the technical relationships which exist between productive inputs and desired (and, perhaps, undesired) outputs. This "technical relationship" economists refer to as the production function.
Economists working in the economics of education have given a great deal of attention to the problem of calculating the returns, both direct (as experienced by the educated individual) and indirect (as experienced collectively by the community), generated by various levels and distributions of educational investment (investment in human capital). However, virtually no attention has been directed to the "education production function" at the level of the individual firm (school). The common approach is to consider the problem from the aggregate standpoint: What are the costs, as "objectively estimated," in terms of resources absorbed, including student income foregone, and what are the direct returns in terms of income differentials attributable to a given level of educational attainment, as well as the indirect returns in terms of increased productivity for others, rate of economic development, improvement of the milieu, and so on? Comparison of investment costs with the estimated money value of the direct and indirect returns yields a rate of return which can be compared with the return being earned on other kinds of investments. If the rate of return to educational investment exceeds that earned in noneducational investment, it can then be concluded that community welfare (under the assumption that a greater dollar value of GNP is always "better") would be improved through a reallocation of the resources which the community has somehow determined to allocate to investment rather than to present consumption. Reallocation would continue until the rate of return on all investments is brought into equality. The investment pattern which equalizes marginal returns from all investments is an efficient pattern simply because it cannot be improved upon; however, this, as we hope v to demonstrate, is an incomplete analysis of the problem.
Neoclassical microeconomic theory finds investment to be efficient when incremental increases in investment in all areas yield identical returns; however, underlying this particular efficiency criterion are a number of assumptions, including the assumption of efficiency in production- The theoretical requirements for efficient industrial production have long been known, and this knowledge rests upon a large literature dealing with the characteristics of the industrial firm's production function. Although practical investigation of production functions in industry is logically the business of engineers, economists have never shown any disciplinary reserve about working in the theoretical aspects of input-output relations and, in fact, have made substantial contributions to this field. The results obtained from analyses of production functions in industry have not been used to help understand input-output relations in education. On the contrary, economists have been quite reluctant to engage in theoretical work on the school's production function. The result has been a "black box" approach to the education firm.v This is an unfortunate state of affairs, for a microeconomic analysis of the educational industry is both important and possible. The following is offered in the belief that such an analysis cannot be achieved in the absence of some theoretical generalizations concerning the nature of the educational firm's production function.
Figure LA. shows the supply and demand conditions facing a given educational firm, a school district. Given such matters as plant and equipment, past school performance, local economic conditions, state and federal aid, projected enrollment, and teacher turnover, there will be a demand schedule in the local market, DLM, for additional and replacement teachers.vi Given the existing "image" of the school district in the minds of prospective teachers, the district's recruitment effort, the output of teachers from regional colleges and universities, and the recruiting efforts and images of competing school districts, there is an effective supply schedule of teachers to the local market, SLM, such that at any given wage (or salary) a determinate number of teachers would offer themselves for employment. Under the temporary assumption that the wage paid to new teachers will not affect the wages of presently employed staff, W e, is simply a price paid to recruit new teachers. It is not the system-determined wage because DLM is not derived through marginal productivity analysis; that is, there is no school district analogue to marginal revenue product. Nor is there, for the moment, a school district analogue to the monopsonist's marginal supply price of labor.vii
It is important to note at this point that the effective supply of teachers at any wage, SLM, is not homogeneous as to quality, an index of which could be constructed from information concerning the selectivity of the college attended by the teacher, the teacher's academic record, and the information contained in the teacher's letters of recommendation.viii Figure 2 illustrates a hypothetical frequency distribution by quality level of teachers currently "in-the-market." Some of the more important factors affecting the area of the frequency distribution are the general market for teachers, regional capacity for producing teachers, and the level of college enrollment. Some of the more important factors influencing the shape of the frequency distribution are the quality of teacher education programs in regional colleges, state certification requirements, and the status system "controlling" recruitment to public school teaching.ix It may be supposed, for example, that the area under the curve might be reduced and the skewness also reduced by changes in state certification requirements which de-emphasized methods courses and emphasized preparation in the subject to be taught.
As the wage-level is increased, it is hypothesized that the number of applications from higher-quality teachers also increases, permitting, under conditions of excess applications, a higher average quality of teacher in the group employed. Given the beliefs of the school board concerning desirable teacher-student ratios and the conditions of supply and demand as indicated in Figure 1.A, the board determines to hire a teacher-group, size OH, of fairly high quality. To this end, it offers a wage of W6, and receives applications in W6 Q' quantity, or, looking at Figure 1.B, it receives OQ" number of excess applications. The selectivity function, OS, Figure 1.B, is determined by the influence of W6 on the number of applications received from the high quality end of the teacher distribution, Figure 2. The selectivity function will shift up and become steeper the greater the area of the frequency distribution to the right of the modal class.
With OQ" excess applications, a selectivity level of OS', Figure I.C, is attained. It is hypothesized that the higher the average teacher quality, the lower the time required to teach a given class of students a given "unit" of knowledge. The relationship between selectivity-level and teaching time/unit of knowledge is shown in Figure LC as Curve TT. It is hypothesized that increases in the selectivity level yield diminishing marginal returns in terms of reductions in teaching time/unit.x Nevertheless, it is predicted that teaching time/unit will fall absolutely as a function of increases in teacher quality.
Teaching time/unit falls, it is hypothesized, because the higher-quality teacher has both the ability and the inclination to present the unit at a higher level of conceptualization, emphasizing the operation of general principles and the broader implications of the "information" contained in the unit, rather than the "facts" approach characteristic of teaching at lower levels of conceptualization (Figure 1.D). It is also hypothesized that students respond positively, up to some point, to increases in the pace at which knowledge is presented; however, pace cannot be effectively increased, except when the reference pace has been quite low, without a concomitant increase in the level of conceptualization.xi Figure 1.E indicates the hypothesized "learning effect" of a more rapid delivery of the knowledge contained in the unit.
As indicated in Figure 1.E, for any group of students, given their abilities, school experience, socioeconomic environment, and school facilities, there is some optimal teaching time/unit, which implies some optimal conceptual level of the curriculum, such as OC', Figure 1.D. Figure 1.C indicates that level of selectivity consistent with these optima, and Figure LA indicates the level of wage, given conditions of supply and demand, which will lead to the achieve-merit of the postulated optima.
As we have developed the educational production function, it is a relationship between the quality of teacher input and output in terms of increased learning/ unit-of-time. Given SLM and DLM, teacher quality is seen as functionally related to the wage level. The L'L0 portion of the learning curve indicates that up to some critical point the rate of increase in learning/unit-of-time rises as teaching time/unit falls; however, Curve TT indicates that the rate of decrease in teaching time/unit falls as teacher quality increases. Although the interaction of these two relationships would differ from school to school and, for any one school, from one time period to the next, we will assume that for the "representative" school (the analogue to Marshall's "representative" firm)xii there is a period of increasing returns to unit increases in teacher quality followed by a period of decreasing returns, as illustrated in Figure 3.
Now, assuming that the quantity of teachers demanded responds very in-elastically to increases in the offered wage, the marginal cost of generating an increase in learning/unit-of-time can be approximated by multiplying the increase in offered wage necessary to generate the quality increase in learning/ unit-of-time by the number of teachers to be employed. The cost so calculated is marginal cost per unit increase in learning/ unit-of-time. From this information plus information concerning fixed costs, the Total Cost curve for the educational firm can be generated. Since the Total Revenue of a school varies with enrollment and not with quality of output, the school will operate at that level of learning/unit-of-time determined by the intersection of the horizontal Total Revenue Curve and the rising Total Cost Curve, that is, at the break-even point, as illustrated in Figure 4.
Total Cost is defined as the sum of fixed plus variable costs. Variable cost, in our case, is the sum of the marginal costs incurred in increasing the level of learning/ unit-of-time by one unit. Assuming that marginal product, measured in terms of the increase in learning/ unit-of-time per incremental increase in teacher quality, increases at a rate which exceeds the rate at which wages must be increased to generate the unit increase in teacher quality, marginal costs will be falling. This stage is likely to be followed by a stage of decreasing returns and increasing marginal costs. Such relationships will generate a Total Cost Curve such as that illustrated in Figure 4. Although LO is the maximum possible level of learning/unit-of-time (as in Figures 1.E and 3), the actual level of learning/ unit-of-time will be found to be L*, Figure 4. This is the level imposed by the break-even requirement, assuming that the break-even point occurs below the maximum level, at a level of selectivity below 5" and in the region of positive but diminishing marginal returns.
Given L*, we will also know the conceptual level of the curriculum which the interaction of all these forces calls into being. Assuming that the school superintendent has no control over the wage he can offer, and very limited control over who stays and who leaves his teaching staff, the conceptual level of his system's curriculum is determined by the system's passive adjustment to changes in variables over which little or no policy control can be exercised. To the degree that control is possible, it would appear that the only strategy really open to the superintendent is active recruitment of high-quality teachers when openings in his system occur.
To the extent that curriculum reformers have directed their efforts to surface changes in the curriculum complex, to the development of new texts and supplementary materials, they have not gone to the heart of curriculum improvement. Such reforms work only a cosmetic change, while fundamental change must depend upon changes in the socioeconomic mechanisms that control recruitment to primary and secondary teaching. In the final analysis, what we imply through our emphasis on the conceptual level of the curriculum is that, within limits, it does not matter what subjects are taught; what matters is that what is taught be taught at the highest level of conceptualization consistent with student ability to comprehend.xiii
Model II: Technological Change, Social Change, and the Higher Education Curriculum
Beginning with Plato's Republic, continuing with Adam Smith's Wealth of Nations and on to the present, social theorists, and economists in particular, have been concerned with the relationship between education and economic-and-social development and change. There are a number of modern studies which have attempted to establish a relationship between the curricular pattern of a nation and that nation's "stage-of-development." Studies of this type often attempt to establish the existence of a systematic relationship between school and college enrollment as a percentage of age-group and curricular "content" and the "resulting" stage-of-development by examining a range of countries at a point in time and/or several countries over time. The models used are, by and large, ones which see casualty as running first from education to development, and then back again through demand analysis from development to education through the effect of higher incomes on the demand for education. A rapid rate of economic development is assumed to raise the return-to-education as well as to increase the demand for education (as a capital good and as a consumer durable) often more than proportionately to the increase in incomes. Thus, education makes development possible, and economic development raises the demand for higher education as both an investment in human capital and as a source of present and future consumption benefits.xiv
During the early phases of development, it may be quite appropriate to operate with a model in which economic factors largely explain the growth and curricular composition of higher education; however, we will argue that at some point in a society's socioeconomic development, it is necessary to base models on a theoretical structure which makes some direct provision for the impact of the broader societal forces on the course of higher education and the higher education curriculum. Assuming that the developed quasi-market nations of the Western community have reached the point at which the broader social forces are beginning to swamp the narrower economic forces, we need to begin some disciplined speculation on the possible interconnections between education, economy, and society.
Economists are quite familiar with the heuristic usefulness of the assumption that in any system or subsystem there exists a tendency to equilibrium. The assumption serves the economists in much the same way that functional prerequisites serve the sociologists; that is, it is a conceptual device which performs a directing and ordering service. Although many types of equilibrium states are recognized by the economic model builder, he will usually organize his first approximations on the assumption that there exists a systematic interrelationship between the variables such that there is a tendency to equilibrium. In the model developed here, it is this assumption which "determined" the particular set of functional relationships connecting higher education curriculum with technological and social change which we show diagrammatically in Figure 5.
The assumptions of the model shown in Figure 5 are as follows:
1. In advanced Western countries the composition of the higher education curriculum (defined as the division of offerings between subjects of a highly specialized nature and offerings of a general-integrative nature) is related to the rates of technological and social change.xv
2. There exists a specifiable relationship between the percentage of offerings of a specialized nature and the supportable rate of technological change.xvi
3. Given the determinant rate of technological change, there is a rate of specialization (division of labor) and organizational differentiation which, in turn, results in the creation of new and the reordering of existing social positions (or statuses) such that a systematic alteration of moral, cognitive, and aesthetic norms occurs; that is, technological change induces social change, and a particular rate of technological change induces a particular rate of social change.xvii
4. If social order is to be maintained, a given rate of social change requires some minimum consideration of the unanticipated consequences arising out of that change; that is, a given rate of social change creates a social need for research in and the teaching of general-integrative (or interdisciplinary) studies.
5. There is a tendency for higher education to expand through increasing specialization and subdivision of knowledge and, hence, of subject offering.xviii
6. There is, on the other hand, a tendency for the higher education curriculum to respond to societal pressures for general-integrative studies, such as ecology or interdisciplinary social science.xix
Figure 5.A shows along the 45 degree line all possible combinations of percentages of general and specialized studies in the higher education curriculum. Figure 5.B indicates the general form of the functional relationship assumed to exist between the percentage of specialized studies and the rate of technological change, ceteris paribus. Figure 5.C shows the assumed relationship between the rate of technological change and the induced rate of social change, ceteris part-bus. Figure 5.D indicates the general nature of the relationship presumed to exist between the rate of social change and the societal need for general-integrative studies if social order is to be maintained at a given rate of social change.
Returning to Figure 5.B, it is assumed that, other things being equal, such as enrollment in higher education, the resources devoted to higher education, and the present state of the economy, increases in the percentage of the higher education curriculum (HEC) devoted to special studies at first induce increasing rates of technological change, but as the "specialized" emphasis continues to increase, the rate of induced change levels off. This particular specification of the relationship would seem "reasonable," and as its particular characteristics are not critical to the argument, a justification of this assumption need not be undertaken. That is, our results do not critically depend upon the shape of the Technology Function in Figure 5.B.
In Figure 5.C we indicate that higher rates of technological change induce increasing rates of social change. The reasoning behind this assumption is too complex to be elaborated here, but we would hold that our assumption is consistent with Talcott Parsons' analysis of this identical problem in Chapter XI, "The Processes of Change of Social Systems," of The Social System,
The particular relationship between the rate of social change and the "need" for general-Integrative studies is built upon a host of assumptions concerning the operation and adequacy of the society's socialization mechanisms and the mechanisms of social control. As indicated in Figure 5.D, the marginal increase in the functional need for general studies is presumed to be fairly constant over a rather extended range of variations in the rate of social change. For our model to operate, it is only necessary to make the rather weak assumption that the need for general studies does not decrease with increasing rate of social change. If the Need Function has either a constant or an increasing slope, the dynamic aspects of the posited system remain unchanged.
We have developed a dynamic equilibrium type model.xx It is dynamic because the path to equilibrium is, to some degree, specified, and it is of the equilibrium (or stable equilibrium) type because any exogenous force which displaces the system from equilibrium will set in motion forces which will return it to equilibrium, if at a different point. The model posits that, given the factors which determine the exact shape and position of the functions specified in Figures 5.B through 5.D, there is a combination of HEC composition, rate of technological change and rate of social change such that further system-induced changes in these variables will not take place.
If for purposes of discussion we assume instantaneous adjustment of all variables (when they are viewed as dependent variables) to the values called for by the value of their determining variables, we can trace the dynamic adjustment path illustrated in Figure 5.
Beginning with Figure 5.A, we assume a HEC composition where 80 percent of the studies are general and 20 percent are specific, as indicated by Point a. This combination induces a rate of technological change (RTC) of A/ and A induces a rate of social change (RSC) of A'; and A' induces a need for general studies (NGS) of a; and a' calls into being, following the tendency of higher education to be, so to speak, *as specialized as socially permissible," a new HEC composition, b. The process continues for a number of rounds until the equilibrium combination is determined.
Inasmuch as social systems do not adjust rapidly to changes in societal variables, the path we have just described would never be experienced. We simply do not observe the radical shifts in fundamental societal variables suggested by the path just described. Using a period analysis approach to the adjustments in this model, we again begin at Point a, Figure 5.A. Given composition "a," the system of higher education is free to follow its tendency to expand through increasing specialization; that is, during the first period, Point a is consistent with unconstrained movement from Point a toward Point c, Figure 5.A. In the second period, the HEC composition is at Point c, with Functional Need at Point d, and the higher education system is still free to continue its growth, paralleling the general growth of the population and economy, through specialization and offering an increased percentage of specialized courses. In the third period, the higher education curriculum has reached Point e and Functional Needs are calling for a minimum indicated by Point f, Given the direction of movement in higher education, it may be expected that during the fourth period the system will "overshoot" the equilibrium combination and that a number of periods will be required for the system to settle down to its equilibrium point; however, the system operates to progressively dampen any oscillation about equilibrium. Looking at United States higher education, it would appear that a system of this type has been in operation for some fifty years and that we are now at Point d while the RSC stands at B, Figure 5.C, and Functional Need is calling for HEC combination Point c. This mismatch between our actual curriculum composition and the needed curriculum composition is the result of an "overshoot" of the equilibrium combination and the tardy response of higher education to societal forces calling for an increase in the percentage of general-integrative studies and research.
i Perhaps the best known of such studies is by F. Harbison and C. A. Myers. Education, Manpower and Economic Growth. New York: McGraw-Hill, 1964. The UNESCO publication, Readings in the Economics of Education, 1968, reprints a number of articles connecting economic growth with education. Those interested in a sociological approach to the problem of education and socioeconomic development are strongly directed to Joseph Ben-David's OECD Monograph, Fundamental Research and the Universities: Some Comments on International Differences. Paris, 1968.
ii Although there are many studies which make use of C.E.S. production functions, one of the more interesting is by Marcelo Selowsky, "On the Measurement of Education's Contribution to Growth," The Quarterly Journal of Economics, Vol. LXXXIII, No. 3, pp. 449-463. In this article international comparisons are drawn between Chile, Mexico, and India.
iii For a full discussion of what an economist means by "the production of knowledge," see especially Chapter II in Fritz Machlup. The Production and Distribution of Knowledge in the United States. Princeton: Princeton University Press, 1962.
iv A very interesting discussion of community demand for education is contained in Mark V. Pauly, "Mixed Public and Private Financing of Education," American Economic Review, Vol. LVII, No. 1, pp. 120-130. The literature on attitude change via a process of socialization is quite large. The following are representative sources of research: J. S. Coleman, ed. Education and Political Development. Princeton: Princeton University Press, 1965; A. H. Halsey, Jean Floud, and C. Arnold Anderson, eds. Education, Economy, and Society, New York: Free Press, 1961; C. H. Stember. Education and Altitude Change. New York: Institute of Human Relations Press, 1961; and "Socialization and Schools," Harvard Educational Review, Reprint Series No. 1, 1968.
v Two representative "black box" approaches are: Jesse Burkhead. Input and Output in Large-City High Schools. Syracuse: Syracuse University Press, 1967; and J. A. Kershaw and R. N. Mc-Kean. Systems Analysis and Education, RAND Corporation Monograph, Memorandum RM-2473-FF, October, 1959. Another, if quite different, approach to efficiency in public education is found in Chapter 12 in Andre Daniere. Higher Education in the American Economy. New York: Random House, 1964.
vi Two basic theoretical discussions of the derivation of the demand curve for a factor of production are contained in J. R. Hicks. Value and Capital New York: Oxford University Press, 1939, particularly Chapter VII and the Mathematical Appendix to Chapter VII; and Paul Samuelson. Foundations of Economic Analysis. Cambridge: Cambridge University Press, 1947. A particularly helpful discussion of the issues raised by Hicks and Samuelson is contained in R. R. Russell, "On the Demand Curve for a Factor of Production," American Economic Review, Vol. LIV, No. 5, pp. 726-32.
vii A good discussion of these matters is contained in most price theory (or microeconomics) texts; however, one of the clearest discussions is Chapter XVIII in George Malanos. Intermediate Economic Theory. Philadelphia: Lippincott, 1962.
viii Concerning the relationship between teacher and student performance, a relationship about which we will have more to say later in the paper, the Corazzini study, Higher Education in the Boston Metropolitan Area, Vol. VI, of the Board of Higher Education Series, State of Massachusetts, City of Boston, 1969, notes that: "Teacher qualifications, as expressed by the highest level of teachers' educational attainment, proved not only to be a significant influence on measured student aptitude, but also one to which improvement in pupil performance was relatively responsive." They also note that: "Schools that tend to spend the most also tend to employ the younger, less costly, teachers; an interesting trade-off in the expenditure of school dollars."
ix There has been a great deal of research done on the quality of teacher education programs and on the recruitment of undergraduates of teacher-training programs and undergraduates in other programs according to a number of factors, such as intellectual interest, motivation, and applied interests. See George C. Stern, "Student Ecology and the College Environment,'* Research in Higher Education. CEEB, 1965, pp. 35-52.
x The determination of teaching time/unit could be undertaken in the following way: Teachers of a given quality are asked to prepare an "academic unit" which will require two class-meetings of instruction. The "bench mark" unit, assuming it to be validated through the instruction of several matched classes of students (validated in the sense that it actually does take two class-meetings of instruction when taught by teachers of a given quality), is given to a group of teachers of a higher quality and they are asked to teach it with a minimum of modification to a group of students matched with those who participated in the establishment of the bench mark. It would be critical to the results of the experiment that the high-quality teachers not know that there was anything "special" about this assignment. It could be part of a series of experiments.
xi Although a great deal could be written concerning the particulars of the published research dealing with the hypotheses formulated in this paragraph, we will have to limit our "discussion" to the citation of works which we see as supporting our hypotheses. As we read Piaget in The Moral Judgment of the Child and in The Early Growth of Logic in the Child, particularly as these works are seen through the work of O. J. Harvey, D. E. Hunt and Harold M. Schroder. Conceptual Systems and Personality Organization. New York: John Wiley, 1961, we feel some confidence in the "reasonableness" of our formulation. As to what it is that we refer to when we speak of "the conceptual level of the curriculum," the following statement from Harvey et al. is offered: "We assume that an individual interacts with his environment by breaking it down and organizing it into meaningful patterns congruent with his own needs [which the teacher is acting to shape] and psychological make-up. As a result of this interchange, perceptual and behavioral constancies develop, which stem from the individual's standardized evaluative predilections toward differential aspects of his external world. We will refer to such evaluative tendencies as concepts. In serving as modes of relatedness or connecting ties between the individual and his environment, concepts thus provide the basis for understanding the joint effect of situational and dispositional factors." We argue that the curriculum of one school may quite usefully be distinguished from that of another based on the curriculum's efficiency in aiding the child to develop these subject-object ties, which we refer to as "the conceptual level of the curriculum."
xii Alfred Marshall. Principles of Economics, 8th ed. New York: Macmillan, 1920, Chapter XIII.
xiii In the matter of how a unit of secondary education may be organized to produce a curriculum having a high level of conceptualization, see William H. Weber, "The Central Program for Project Opportunity," Research in Education. April 1969.
xiv The most extensive study of this type which deals with developed nations is Edward E. Denison. Why Growth Rates Differ: Postwar Experience in Nine Western Countries. Washington, D.C.: The Brookings Institutions, 1967, particularly Chapter 8.
xv Concerning the notion of technological change and the measurement of such change, see Edwin Mansfield, The Economics of Technological Change. New York: W. W. Norton, 1968, particularly Chapter II.
xvi There is much in the Machlup study, op. cit., which supports this contention, although Machlup shows that in the original development of new technical knowledge, higher education plays only a small role.
xvii See, in particular, Talcott Parsons. The Social System. New York: The Free Press, 1951, Chapter XL On a more philosophical plane, the (uncertain) relationship between man, science and society as discussed by Floyd Matson. The Broken Image. New York: Anchor Books, 1966. In Matson we see "technological change" in the broader context of "applied social science," an application which depends to a great extent on the spread of this knowledge through higher education,
xviii For an account of how Harvard broadened its subject offerings while expanding in size, see Seymour E. Harris. The Economics of Harvard, New York: McGraw-Hill, 1970. If we take the appointment of (full) professors and associate professors as an index of the establishment of new teaching and research areas, it is interesting to note the increases in the percentage of professors and associate professors to total faculty at Harvard. These percentages have fluctuated widely over the years, but during the expansionary period from 1940 to I960, the percentage of expanding faculty at these high ranks increased from 45 percent to 64 percent, indicating the establishment of many new teaching and research specializations (see Table 10-3, p. 128.)
xix The response of engineering departments to the present circumstances, that is, a reduced interest in traditional engineering programs and a reduced market for the graduates of these programs, is interesting to note. For a report of the efforts of one "engineering" college, see the Lafayette Alumnus, January 1971, particularly the articles "Enrollment Slump Hits Engineering" and "'Arts and the Engineer."
xx The best short discussion of what economists mean when they talk about dynamic systems is contained in Fritz Machlup, "Statics and Dynamics: Kaleidoscopic Words," The Southern Economic Journal. Vol. XXVI, No. 2, October 1959, reprinted in Essays in Economic Semantics. New York: W. W. Norton, 1963. The "classic" book on the subject of dynamic models is William Baumol. Economic Dynamics, 2nd ed. New York: Macmillan, 1959.