Empirical Estimate Of Educational Cost Function For Universities And Its Applications

Based upon the classical cost function theory, the university operation cost function model is constructed. While the variables concerning university input price and output specification are introduced, the function model reveals the relationship between output and cost of universities. Using the relevant data of 34 selective public universities, the paper establishes a quadratic cost function, and comes to some meaningful conclusion which can be summarized as follows:1. The theoretical model of college education cost function may be constructed like this: C = F (Q, P, S). Of which, C represents the higher education costs, Q represents the outputs of colleges and universities, P represents the price of colleges and universities' outputs, S stands for output specification. Based on this model, a quadratic cost function can be established as follows:Of which, C is operation cost of a University;αis a constant variable;β_i,γ_ij,δ_i,φ_? is the regression coefficients.Q_i,Q_jrepresents the various outputs of colleges anduniversities,P_? represents the price of colleges and universities' outputs;S_? stands foroutput specification;εis the random error term. This function reveals the relationship between output and cost of universities, when input price and output specification are considered.2. The Estimating Equation were built up as follows:Note: Of which, C is operation cost of a University, S represents the number of students, T stands for the prices of human capital, E stands for the price of material capital. Note: Of which,Q_R represents the number of research output; Q_G for the number of graduate students; Q_U for the number of undergraduate students;P_E represents the price of research and teaching equipments;S_M for the type of output,S_Q for the quality of output.3. we can come to some conclusions based on the equation 1:the elasticity of total cost C to College size S is 0.606, which means that each 1% increase of College size, will cause the total cost be increased by 0.606 %. Therefore, if the teaching quality can be ensured we shall be appropriate to expand the size of college. The elasticity increased from 0.600 to 0.621 during the years of 2001 to 2004. From the view of economics, we had made a retional use of economies of scale. In the same way, the elasticity of comprehensive universities, science and engineering college and foreign language college can be figured out as follows: 0.789, 0.748, 0.432. The results show that, compared to the comprehensive universities and science and engineering college, the foreign language college has more rooms to expand the size of the students in order to make better use of education resources. Further more, the comprehensive universities, relatively speaking, should pay more attention to control the speed of the expansion of the scale,4. According to the equation 2, we can come to some conclusions as follows:①the MC_R of sample universities' research output is 53,800 Yuan. That is to say, while other factors are controlled, the research output increase per unit will cause the total education cost increase 53,800 Yuan.②the MC_R of sample universities' graduate students output is 35,267 Yuan. That is to say, while other factors are controlled, every new graduate student will cause the total education cost increase by 35,267 Yuan,③the MC_R of sample universities' undergraduate students output is 2747 Yuan.. That is to say, every new undergraduate student will cause the total education cost increase by 2747 Yuan.④There are not enough evidence to say that a joint production of graduate students and undergraduate students can save cost.⑤Per unit joint production of the undergraduate students and research output will save 970 Yuan for the university.⑥Every Yuan' increased in the price of research and teaching equipment will cause 16124 Yuan' increasing in the total cost of the university .⑦Quality is an important factor for the increasing in total cost. The result shows that every unit increasing of quality will cause 10844680 Yuan' increasing in the operation cost of a university.⑧During the sample universities, the operation cost of science and engineering colleges are 85,470,000 Yuan more than other type universities.5. According to the equation 2, there exist ray economies of scale and global economies of scope. Of which, RE = 0.6007 and GE = 0.986371. But, the scale of graduate students output and research output have been the state of uneconomical, (E_G = 1.0737; E_R = 1.3194). The size of undergraduate students should not be more than 32,850. (that is, 200% of average size). Based on the equation, we calculated that the average variable cost of an undergraduate student is 4862 Yuan while the graduate student to be 32846 Yuan. It also suggests that per unit of research output may cost 40,800 Yuan. By analyzing the value of economies of scale and scope, we found that when the number of total student is expanded to 200% of average size, there will be a Ray Diseconomies of Scale. When the number of total student is expanded to 500% of average size, there will be Diseconomies of Scope upon the graduate students output.6. Gives such suggestions: For the first, the scale of graduate enrollment should be controlled. The size of undergraduate students output can be expanded moderately, on the condition of teaching quality is ensured and the ammount of students is less than 32,850. Secondly, it is necessary to strengthen the combination of research activities and undergraduate students' teaching. The third, a reasonable evaluation system for universities should be established as soon as possible. Of which, may give some space to cost-effective evaluation. We should also use the research and teaching equipment more effectively, and avoid the blind competition for facilities of university, only by doing so, could the university' development be faster and better.