高校收费问题的数学模型

Key problems for university’s charge are studied with aid of mathematical models. At first, several mathematical models are proposed for describing the problems of university’s charge under the theory on sharing in the educational cost and appropriate assumptions. Then, by analyzing the general model for the charge, some conclusions are obtained as follows: 1) A sufficient and necessary condition for preserving and stabilizing the charges is balancing the educational cost shared in by individual and incapability of payment of poverty students; 2) There exist minimum, maximum and stable values of university’s charge which can be attained by adjusting the proportion of the educational cost shared in by the individual and rising rate of incapability of payment of the poverty students. Finally, by analyzing particular models for charge, some conclusions are also given as follows: 1) Under the enlargement of recruiting students and unbalance, the increases and decreases of the university’s charge directly depend on a degree of the rising rate of incapability of payment of poverty students. 2) The university’s charge is a quadratic function of the students at the university. 3) Heightening and falling the university’s charge directly depend on a degree of the proportion of the educational cost shared in by the individual.