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Research on economies of scale and scope in the process of enrollment expansion in colleges and universities
-On the Moderate Scale of Universities Directly under the Ministry of Education
Abstract: The expansion of enrollment since 1999 has significantly improved the efficiency of running universities directly under the Ministry of Education. Most universities directly under the Ministry of Education have changed from diseconomies of scale to economies of scale, and the training and scientific research activities of undergraduates and postgraduates have changed from diseconomies of scale to economies of scale. At present, many universities still have room for enrollment expansion, but research universities and language universities should maintain their existing scale. In the future, we should seek a reasonable system supply and promote the formation of a moderate school scale through competition.
Keywords: institutions of higher learning, economies of scale, economies of scope
First, study motivation.
From 65438 to 0999 (Corning, 2000), there are three considerations in the introduction of the enrollment expansion policy: to meet the macro-social needs of the people and the national economic development for education; Stimulate residents' consumption, promote the development of education-related industries, increase social demand and reduce employment pressure; Promote the reform of the education system, get out of the traditional school-running mode under the planned economy system, and liberate hundreds of millions of students from "exam-oriented education." Since the expansion of enrollment, these three goals have been basically achieved, and now the gross enrollment rate of higher education has reached 15%. According to the classic classification of Martin Trow (1973), elite education has been transformed into mass education, which has met the social demand for higher education investment.
There have been many achievements in the macro-level discussion and analysis of the effect of the enrollment expansion policy, and positive conclusions have been drawn, but the analysis at the institutional level is still insufficient. This study mainly focuses on the institutional level, and intends to explore the following questions: 1, does the expansion of enrollment improve the efficiency of running colleges and universities? For a long time, colleges and universities have been regarded as an industry with slow progress in promoting various reforms in China, and there have been remarks that colleges and universities are inefficient in running schools. Whether the efficiency of running a school can be improved after the expansion of enrollment is also a concern of policy makers. To evaluate and measure the improvement of school-running efficiency, this paper thinks that it is a good idea to apply the theory of scale economy and scope economy. 2. Appropriate scale of running a school after enrollment expansion. Behind the implementation of the enrollment expansion policy in colleges and universities is the rapid expansion of the scale of running schools, which has become a common phenomenon. What needs to be considered is whether the existing school scale is appropriate, whether there is room for further enrollment expansion, and more importantly, whether it is appropriate.
Second, the relevant experience at home and abroad
The research of Verry and Layard( 1974) is an influential research, which directly adopts linear regression model, and its conclusion is that there is no convincing argument for the existence of economies of scale from the perspective of departmental scale.
The summary made by Brinchmann and Leslie (1986) is considered to be very comprehensive. After combing more than 40 related studies on the phenomenon of scale economy in American higher education, it is found that scale economy generally exists in all kinds of colleges and universities. For two-year colleges, when the number of students increases by three to four times, the average unit cost of students can be reduced by about 25%. The four-year university can reduce the unit cost by about 22%. They also believe that the unit cost of a school with a small number of students will be significantly reduced when the number of students increases. Differences related to scale can often determine the unit cost of students from 25% to 40%.
Since the research of Cohn et al. (1989), the multi-output quadratic model has been widely used in the study of economies of scale and scope in colleges and universities. Cohn et al. used the data of American universities with degree-granting qualifications in 198 1- 1982, and thought that when the number of undergraduate students in public universities increased, public universities often brought the corresponding increase in operating costs, while private universities were not significant. It is also considered that for public universities, training undergraduates and conducting scientific research at the same time has a compensation effect, while for private universities, there is no compensation effect for all universities, undergraduates and graduate students, graduate students and scientific research. Generally speaking, the simultaneous production of the three outputs has a compensation effect. From the perspective of economies of scale, for public universities, the production and scientific research of graduate students have economies of scale, and comprehensive universities are more efficient than junior colleges. Hashimoto et al. (1997) use the data of 199 1 94 private universities in Japan, and think that the output of graduate students and the output of science, undergraduate students and graduate students are complementary. However, the regression coefficient is not statistically significant. For small universities, undergraduate output and graduate output have economies of scale, while scientific research has economies of scale in large universities. For economies of scale, universities of different sizes always exist. Although Lloyd et al. (1993) still adopts the multi-output quadratic model, there are two biggest innovations in this study. When investigating the output of colleges and universities, in addition to undergraduate, graduate and scientific research outputs, it also includes five different disciplines as outputs. It is considered that the important factor affecting the cost of running a university is the combination of disciplines. Secondly, this study focuses on the changes of scale economy of Australian universities before and after the merger, and one of its purposes is to test the economic benefits and losses of the merger of universities. With 1988 as the boundary, the merged universities in Australia have brought about savings in operating costs, but there may be many reasons for this savings. A study recently completed by Laband and Lentz(2003) completely refers to the research system of Cohn et al. (1989) and also uses the data of the United States. Including 1492 private universities and 1450 public universities, the data year is taken from 1995- 1996. The main conclusions are as follows: (1) There are significant differences in the cost structure between public universities and private universities; Generally speaking, public universities show economies of scale and scope, but interestingly, undergraduate output does not show economies of scale, while other outputs show economies of scale; However, the overall and undergraduate output and scientific research of private universities show economies of scale. The most surprising thing about this study is that there is no economies of scale in the joint production of these three outputs in both public and private universities.
The models adopted by other research institutes are different. The research of Koshal et al. (1995) is quite different from Cohn's, which is reflected in the consideration of the factors of school quality. And it is estimated directly by quadratic model (without considering cross effect). The data used are1more than 90 universities with the right to award doctoral degrees 1990- 199 1 year. Research shows that economies of scale exist widely in universities. The most efficient scale varies from 1 1758 to 30957 according to different types. The study also believes that lowering quality standards will bring the most effective scale reduction when considering quality factors. If an institution wants to improve the quality of training, it is inevitable that the total cost of running a school will increase. Nelson and Hevert( 1992) completed this research by using transcendental logarithmic function. The most attractive part of their research is to consider the class size, focusing on the economies of scale and marginal costs of various outputs. Because it is only aimed at one institution, the study believes that there is no scale economy in running schools. The training cost of graduate students is almost twice that of undergraduate students, and experimental courses are more expensive than the courses explained in class. The study also believes that if colleges and universities want to achieve better economies of scale without considering the quality of training, they can try to expand the class size.
Domestic academic circles pay relatively little attention to economies of scale and scope in running colleges and universities, and systematic and standardized empirical research is even less. There are two reasons: first, the availability of data, the statistical data of foreign universities are relatively systematic, while the domestic statistical data have only been gradually established in recent years; Second, domestic research on economies of scale and scope in colleges and universities mostly adopts qualitative discussion.
Min Weifang (1990) applied the theory of scale economy to study the expansion form of higher equivalent education in China in 1980s. Through the data analysis of 1 16 institutions of higher learning, including national key institutions, provincial key institutions and ordinary local institutions, it is found that during the nine years from 1980 to 1988, the national and provincial level. However, the internal efficiency indicators of the higher education system (including the average size of the school, the ratio of students to all kinds of personnel in the school, etc.). ) there is no significant change. Therefore, in the past nine years, China's higher education system has developed and expanded mainly in accordance with the "extension" model; In the process of scale expansion, its internal efficiency has not been greatly improved. He pointed out that the expansion of college enrollment will take a development path based on "connotation", expand the scale of existing colleges and universities, and fully tap the potential of existing colleges and universities. Ding Xiaohao (2000) is probably the most systematic scholar who studied the scale benefit of Chinese universities by using the survey data of Shaanxi, Shanxi, Hubei, Guizhou and Yunnan provinces in 1988. His research conclusion can be summarized as follows: When. With the expansion of school scale, the use efficiency of various resources will show an upward trend. When the school scale exceeds a certain range, the improvement of the efficiency of the use of various resources brought about by the expansion of the school scale will be slower and slower. Compared with the scale, the average cost savings brought by the increase of student-teacher ratio are more significant. Other domestic scholars have also done some related research. Cao Liqun (2000) discussed the causes of scale economy in colleges and universities from different aspects; Chen Hongan (1996) analyzed the optimal scale of China's higher education by the method of survival of the fittest.
From the domestic empirical research, due to the lack of quantity, the research is based on the data of the 1980s, and the data collection and research methods need to be improved. Since 1990s, especially since 1999, the scale and speed of China's higher education expansion are rare in the history of higher education in the world. Under the new historical background, this study: 1 proves whether the enrollment expansion policy is effective in colleges and universities, and whether the implementation of the enrollment expansion policy has significantly improved the efficiency of running colleges and universities is of great significance. If so, it further proves that the enrollment expansion policy is effective. 2. The expansion of enrollment provides a good case for studying economies of scale and scope. The remarkable feature of the enrollment expansion of colleges and universities is the expansion of the scale of running schools, which is bound to be accompanied by the change of the cost of running schools, which makes it possible to study economies of scale. On the other hand, as an institution providing undergraduate, graduate and scientific research outputs, it needs to analyze from an empirical point of view whether the three outputs are more efficient by joint production or separate production. It is difficult to draw a definite conclusion from observation alone, which belongs to the research category of scope economy.
Thirdly, based on the multi-output quadratic model, this paper makes an empirical analysis of the economies of scale and scope in Chinese universities.
(1) Model selection: Multi-output quadratic model and its brief discussion.
1. Analysis premise. On the basis of the previous discussion, the following premises are put forward: (1) Colleges and universities are social organizations that provide undergraduate output, graduate output and scientific research output. In reality, colleges and universities not only provide these three outputs, but also include adult education, international student education and tertiary industry, but undergraduate training, postgraduate training and scientific research are the three most important activities in colleges and universities. It is reasonable to be limited to these three outputs. (2) The scale of running a school is mainly measured by the number of undergraduates and postgraduates. Strictly speaking, scale refers to a certain production capacity, but the production capacity is difficult to measure, so it is generally replaced by output capacity. For colleges and universities, output mainly refers to students. (3) The undergraduate output, graduate output and scientific research output of universities directly under the Ministry of Education are homogeneous. This is a strict assumption. However, considering that the distribution system of university education funds mainly adopts the form of "comprehensive quota plus special funds", that is, it is mainly distributed according to the number of students, and this paper mainly focuses on economies of scale and scope, it is acceptable to assume that the output of undergraduate and graduate students is homogeneous. As will be defined in the following variable description, this paper measures scientific research output by scientific research funds, so it can also be considered homogeneous.
2. Model definition. Because the research on economies of scale and scope in colleges and universities is basically based on the multi-output quadratic model (Baumol et al.1982; Cohen et al.1989; Lewis et al.1995; Hashimoto et al. 1997), this paper is based on this model. Theoretically, transcendental logarithmic model can also be used, and it is hard to say which model is better or worse. Theoretically, both of them are appropriate descriptions of the cost function, and they are also hot topics in the current empirical research. But from the measurement point of view, because the transcendental logarithmic function does not allow the independent variable to take the value of 0, the quadratic model allows the independent variable to take a wider value.
( 1)
Here, c represents the total cost, which is a constant term, and 0,0 is a regression coefficient, which represents various outputs, a virtual variable and a random disturbance term. If the first output is greater than 0, take it as 1, otherwise take it as 0. The basic meaning of this model is that the total cost of running a university can be explained by the output of undergraduates, postgraduates, scientific research and the cross effect of various outputs. Considering the cross effect of quadratic form is based on the understanding of quadratic form of cost function. It can be regarded as an approximation of the cost function, and the quadratic cost function does not need the specific form of the production function, which makes it possible to study the production function and determine the fixed form of university behavior.
In this paper, universities are limited to providing undergraduate, graduate and scientific research output. According to the research of baumol (1982) and others, the average incremental cost (AIC) of an output is:
(2)
Here is the cost of producing three outputs, and the total cost when the first output is 0. Similarly, the average incremental cost of j and k can be evaluated.
For undergraduates, graduate students and scientific research output, the ratio of average incremental cost to marginal cost can be used to measure the change of scale economy. For the first kind of output, the economies of scale of a specific output are defined as (economies of scale of a specific product):
(3)
Here, it is the marginal cost of a certain output. If it is greater than 1, there is economies of scale for a certain output; Similarly, when it is less than 1, there is no economies of scale in output.
Overall economies of scale are defined as follows:
(4)
If it is greater than or less than 1, it can be said that the overall scale economy exists or does not exist.
In order to investigate whether there is scope economy phenomenon in universities directly under the Ministry of Education, this paper divides scope economy into two situations according to Dundar's definition (1995), namely, specific product scope economy. The definition of overall scope economy is as follows:
(5)
If it is greater than 0 or less than 0, it means that there is overall scope economy or there is no overall scope economy, that is, whether the cost of independent production of various outputs is greater than that of joint production is evaluated.
The definition of specific output range economy is:
(6)
For the output, whether the specific output interval is economical or not depends on whether it is greater than 0 or less than 0, that is, whether the specific output should be produced jointly with other products or independently.
(B) Empirical analysis results of economies of scale and scope after the expansion of schools directly under the Ministry of Education.
Definition and description of 1. variable. The data used in this paper are all from the Compilation of Basic Statistical Data of Colleges and Universities Directly under the Ministry of Education 1999, 2000, 200 1 year. For the cost of running a school, this paper calculates the income of all education funds in the school every year, including education funds, scientific research funds, other funds and higher-level funds. Operating income, contributions from affiliated units, etc. We consider a short-term variable cost to measure the cost of running a school with the income from education expenses. Only short-term variable costs are considered here, and fixed costs are not considered. The reason is that the fixed cost investment of colleges and universities is relatively stable in the short term, and the running cost mainly depends on the change of variable cost in the short term. The change of fixed cost often depends on large-scale random investment such as infrastructure investment, that is, for a college, infrastructure investment often increases substantially in a certain year or several years, but it is difficult to obtain most of the time. Because the fixed cost is not considered, this study avoids the problems of expanding the campus area and increasing the fixed cost in multiple campuses during the enrollment expansion. The advantage of only considering the income of education funds is that, theoretically, for a university with a fixed campus area, the cost of its teaching and research activities mainly depends on the income of education funds. Technically speaking, fixed cost data is not available, even if it is difficult to have an accurate evaluation of the fixed assets of each university. It is quite difficult to measure the output of universities. According to the ideas of Hashimoto (1997) and others, this study uses the number of undergraduates (including specialties) and postgraduates (including masters and doctors) to represent the output of undergraduates and postgraduates. Based on the consideration of sample size, there is no reference to undergraduates, junior college students and graduate students. Doctoral students are specifically distinguished, because in the past three years, there were 457 1 and 7 1 directly under the Ministry of Education. On this premise, even if 765,438+0 is taken as the calculation, if four levels are introduced and the quadratic crossover effect variables are considered, too many parameters to be estimated will also cause the loss of degrees of freedom and affect the accuracy of the model. Another level can also explain this problem well. However, compared with undergraduate students, the cultivation of master students and doctoral students has strong homogeneity, that is, they both emphasize research-based learning under the guidance of tutors. Scientific research output is measured by scientific research funds, because the scientific research achievements of colleges and universities are often not comparable, such as different projects undertaken, different grades of publications published, different forms of scientific research achievements of science and engineering colleges and humanities colleges, and scientific research funds often reflect the scientific research ability of colleges and universities. In the long run, colleges and universities with strong scientific research output ability can win more scientific research funds. There is a defect in the measurement of scientific research output, that is, the scientific research funds of humanities colleges can not be compared with those of science and engineering colleges. Of course, relatively speaking, the cost of scientific research output in science and engineering colleges should generally be higher than that in liberal arts colleges. Considering that an important factor affecting the cost of running a school is the teacher's salary, that is, the investment that the school uses for teachers. The most ideal way is to express it by the total salary of a school teacher. However, this data is not available. This paper is represented by the total number of full-time teachers. In the analysis, it can be regarded as the fourth output, and the above model can be adjusted accordingly. The total number of full-time teachers, not all teachers, is based on the following considerations: the total number of teachers in many universities includes employees engaged in the tertiary industry or even affiliated primary and secondary schools, which is not comparable among universities, and the tertiary industry and affiliated secondary schools are often relatively independent. On the other hand, in the process of enrollment expansion,
2. Description and analysis based on original data. The basic statistical indicators of 1999, 2000, 200 1 annual variables are shown in appendix1; At the same time, combined with the classification of Chinese universities and the needs of the following analysis, the basic statistical indicators of related variables of different types of universities such as comprehensive universities and universities of science and technology are also given, as shown in Appendix 2.
Appendix 1 shows that after three years of enrollment expansion, the scale of running universities directly under the Ministry of Education has expanded rapidly, among which four points deserve attention: (1) The enrollment expansion of undergraduates is greater than that of postgraduates. The average undergraduate scale of the school increased from 9855 in 1999 to 1403 1 in 2006. The average graduate size of the school increased from 2 194 in 199 to 3 127 in 2006, with a net increase of 933 students. The growth rate is 42.5%. (2) The growth of teachers is much lower than that of students. The average number of full-time teachers in the school increased from 1 0,999 to 1 0,434 in 2006, with a net increase of 1 0,654,38+0. The growth rate is only 8.6%. (3) The scientific research funds have increased significantly, which shows that the average scientific research funds of each school have increased from 6,543.8+99.74 million yuan in 1999 to 6,543.8+0,374.2 million yuan, with a net increase of 37.68 million yuan and a growth rate of 37.78%. (4) The state's investment in higher education has increased rapidly. The total cost of education in each school has increased from 654.38+.
Figure 1 directly reflects the growth trend of each variable, that is, the growth rate of total education expenses and undergraduates is faster than that of full-time teachers and research funds.
Figure 1 intuitively describes the speed of enrollment expansion of universities directly under the Ministry of Education, but further analysis is needed to answer whether the expansion of school scale has significantly improved the efficiency of running schools. A reference index is whether the average training cost per student has a downward trend with the expansion of the school scale. In this paper, the per-student training cost is defined as the total income of school education funds MINUS scientific research funds and then divided by the number of students. Note that the number of students here includes the number of graduate students. According to the relevant standards of the Ministry of Education, one graduate student is equivalent to two undergraduates. The smooth scatter chart of the average cost per student in 2000 and 20001year with the expansion of the school scale is as follows:
Figure 2: Scatter chart of annual average cost
From the scatter plot of the smooth line, the average cost per student shows a weak U-shape with the increase of the school size, that is, with the expansion of the school size, the average cost per student first shows a downward trend, and then shows a certain upward trend, which is particularly obvious in the scatter plot of the average cost per student and the school size in 1999 and 2000. That is, the average cost per student in a large-scale university is lower than that in a small-scale university. When it reaches a certain scale limit, the average cost per student will rise again, but within the sample range, the cost increase is limited. Note that the U-shaped feature here is different from the U-shaped feature of the long-term average cost curve in neoclassical economics. The U-shaped feature here refers to the phenomenon of "industry" in universities directly under the Ministry of Education, which is based on cross-sectional data; The traditional U-shaped feature is the relationship between the average cost of a single manufacturer and the change of long-term production scale. Generally speaking, based on time series data, the scatter plot of 200 1 seems to show a double U-shaped feature, that is, with the expansion of the school scale, the average training cost per student shows an upward, downward, upward, downward and upward trend in turn, which is a very interesting phenomenon. The preliminary explanation is that within a certain school scale,
3. Quantitative analysis results. The above analysis is based on the intuitive description of the original data, and further quantitative analysis is needed. According to the model (1), the regression coefficient of the total cost of running a school to various related variables can be estimated by OLS method. In order to evaluate whether the inclusion of teacher input will affect the goodness of fit of the model, there are two situations every year, namely, including teacher input and not including teacher input. The regression results are shown in Appendix 3.
From the regression results, because the determinable coefficients of the model are all close to 1, the whole model has a good goodness of fit, that is, the variables contained in the model and their cross effects can explain about 95% of the total cost change. However, the significance level of regression coefficient of each variable in different models is different, which must be considered when analyzing each variable in detail. At the same time, the total determinable coefficient of the model is not affected by the addition of teacher variables. The comprehensive analysis shows that the model has the best goodness of fit after incorporating the teacher variables in 2000. Compare the regression coefficients of 1999 (column 2 of appendix 3) and 200 1 (column 6 of appendix 3), the output of graduate students, the cross effect between graduate students' output and teachers' input, and the output of graduate students and undergraduates. The quadratic regression coefficient between teacher input and undergraduate output has changed fundamentally (that is, from positive to negative or from negative to positive). This shows that the cost structure of running a university directly under the Ministry of Education has changed obviously after the enrollment expansion, indicating that its running efficiency may have changed. The following analysis will prove this point. After careful analysis of the regression results, we can also draw the following conclusions: (1) The influence of postgraduate training on the cost of running a school is gradually increasing. The regression coefficient increased from1-2.0780 in 1999, 1 1.6494 in 2000 to 12.2343 in 2006. (2) Correspondingly, the influence of scientific research output on the cost of running a school has gradually weakened, from 2.0828 in 1999 to 500006066 in 2000, which is consistent with the expansion of enrollment, that is, from the perspective of relative influence, scientific research has been affected by the sudden increase in the number of students, and its influence has shown a downward trend. (3) The influence of undergraduate output increased from-/kloc-0 in 1999 to 0.2672 5438+0 in 2006, which is the same as postgraduate training.
According to the mixed partial derivative of the cost function, we can also analyze whether the production of multiple "outputs" in colleges and universities has compensation effect, that is, whether the joint production of two outputs is more reasonable. As stated in the model definition, the criterion is that if
Table 1: Is there a compensation effect between outputs?
Undergraduate and postgraduate training
Undergraduate training and scientific research activities
Undergraduate training and teacher input
Postgraduate training and scientific research activities
Postgraduate training and teachers' input
Scientific Research Training and Teacher Investment
1999
-
-
-
-
Have compensation effect.
-
2000
-
No compensation effect
Have compensation effect.
No compensation effect
Have compensation effect.
Have compensation effect.
200 1
-
Have compensation effect.
-
No compensation effect
Have compensation effect.
-
Compared with three years, it is certain that postgraduate training and teacher investment are complementary, and the combination of them is more efficient, that is, there is a complementary relationship between increasing postgraduate training investment and increasing teacher investment, or increasing teacher investment is beneficial to postgraduate training. The reason is probably determined by the characteristics of postgraduate teaching, and postgraduate education generally adopts tutorial system. Teachers and students are highly complementary. However, there is no compensation effect between increasing investment in postgraduate training and increasing investment in scientific research activities. The reason may be that colleges and universities have exclusive effects on the funds or institutional arrangements for postgraduate training and increasing scientific research output, that is, increasing investment in one aspect will lead to decreasing investment in another.
-Analysis of changes in economies of scale after the expansion of enrollment. According to models (2), (3) and (4), we can examine the changes of overall economies of scale and specific economies of scale in the past three years, as shown in Table 2.
Table 2: Annual Economies of Scale
project
1999
In 2000,
200 1 year
Overall economies of scale
0.89 14
1.2258
1. 146 1
Economies of Scale of College Students' Output
-2.89 1 1
14. 1822
7.6482
Economies of scale of graduates' output
1.3367
0.8637
0.9599
Economies of scale of scientific research output
0.06 18
1.7830
2.8558
Table 2 shows that the expansion of enrollment has significantly improved the efficiency of running colleges and universities. Overall (line 2 of Table 2), undergraduates (line 3 of Table 2) and scientific research output (line 5 of Table 2) all changed from diseconomy of scale of 1999 to economies of scale of 200 1, especially the cultivation of undergraduates, and the variables representing economies of scale changed from -2.438+0638.
In this study, we believe that there are several reasons to consider the economies of scale caused by the expansion of colleges and universities:
(1) Teaching cost saving. Before the enrollment expansion, the resources of colleges and universities were not fully utilized. At this time, the scale is expanded, and the marginal cost of its unit output, including undergraduate and graduate students, will be far lower than its average cost. This is determined by the particularity of the teaching process. For example, a teacher teaches 20 students and 50 students, only considering classroom teaching. There is not much difference. In a sense, when the number of students increases from 20 to 50, the increase of per capita unit cost, that is, marginal cost, can be ignored. In this sense, the expansion of scale will inevitably lead to the decline of average cost, resulting in economies of scale. This study believes that this is one of the main reasons for the phenomenon of economies of scale since the expansion of colleges and universities in China. 1999, including before 1999, because the average size of schools is generally small, in the so-called "elite education" stage, even in the undergraduate teaching stage, the class size is generally around 30 to 40 students, and after the expansion of enrollment, the class size of ordinary universities will reach more than 60 students. In this expansion process, because the investment is often fixed, such as using a classroom or a teacher to attend classes, the only thing that may increase the cost is the time value of the teacher correcting the homework.
(2) Save management costs. Before the enrollment expansion of colleges and universities, there have been criticisms about the lagging reform of colleges and universities, focusing on too many non-teaching staff, which will inevitably lead to an increase in management costs, especially in the case of a small scale, and the management costs allocated to each student are also quite high. Min Weifang (1990) and Ding Xiaohao (2000) think that small-scale colleges and universities also have "institutionalization" in social organizations. Small-scale schools still need to set up corresponding management departments, and the management scope is insufficient. After the enrollment expansion, the expansion of management radiation can improve the use efficiency of each student's management resources, that is, the scope and level of management of each management institution have expanded. In the process of enrollment expansion, the main teachers, corresponding managers and logistics personnel have not increased significantly, which will inevitably lead to a decline in the average management cost per student.
(3) saving transaction costs. On the one hand, the expansion of scale will increase the cost of organization and management, such as office expenses and conference expenses, on the other hand, it will also help to save transaction costs. Coase (1937) believes that manufacturers are born to save transaction costs, and the reason why scale expansion has economies of scale is that the saved transaction costs are greater than the increased organization and management costs. The main transaction in colleges and universities is knowledge products. The special nature of knowledge products attached to people makes them only transfer the right to use, but not the ownership, which leads to high transaction costs in the knowledge product market. By expanding the scale, colleges and universities internalize knowledge products as much as possible, thus saving transaction costs. As long as the saved transaction costs are greater than the increased organization and management costs, the expansion of colleges and universities will have economies of scale. The transaction of knowledge products in colleges and universities can be understood as two processes. One is that schools buy corresponding knowledge products from teachers, and the other is that students buy knowledge products from schools. Because the pricing of knowledge products is quite expensive, and there are many kinds of knowledge products traded in colleges and universities, colleges and universities have the incentive to make the transactions happen internally as much as possible instead of buying them from the market, which provides the possibility for the expansion of the scale of colleges and universities.
(4) economies of scale brought by "division of labor". Adam Smith believes that division of labor can improve efficiency, and division of labor and specialization are the source of economic growth. The three advantages of division of labor are: first, the improvement of workers' proficiency will inevitably increase the workload they can complete. Because of the division of labor, because each worker's business is limited to simple operations for life, of course, the proficiency can be greatly improved. Second, because one job is transferred to another, usually, a lot of time will be lost, and this loss can be avoided through division of labor. With the division of labor, this loss can be avoided. The benefits of saving this time are much greater than we thought. Third, many simplified and labor-saving mechanical inventions are also caused by division of labor, so that one person can do many things.