Abstract
Abstract Firstly, based on the charging theory of ‘education cost-sharing,’ under appropriate assumptions, two basic differential equation models are proposed to describe the problem of college education charges; secondly, through qualitative analysis of the basic model, it is concluded that colleges and universities maintain or impose several conditions for stabilising its education fees; finally, through the analysis of two basic models in three unique models under three situations, some new conclusions and suggestions on the macro-control of college education fees and enrolment scale are given. Also, three extended differential equation models are proposed.
Highlights
Relative to demand, resources are always scarce, so people need to integrate and efficiently use the resources so that they can somehow meet demand
If g (γ) = g0γ2 is changed to a quadratic function in model (2), it is easy to know that the scale of enrolment of colleges and universities whose education fees are positive is n < N ≤ n + 3δ (M − n)
It can be seen that the enrolment scale of colleges and universities can exceed the government’s Regulations, and fees increase slowly, this is an education fee and expansion model worth promoting
Summary
Resources are always scarce, so people need to integrate and efficiently use the resources so that they can somehow meet demand. The development of higher education and the school-running activities of universities conform to this law. Li et al Applied Mathematics and Nonlinear Sciences 2021(aop) 1–10 means to control unnecessary costs in the process of running colleges and universities while ensuring the quality of talent training, improving the efficiency of resource use, and improving the efficiency of running schools, which are important issues facing the development of colleges and universities [2]. Colleges and universities want to achieve leap-forward development by expanding enrolment and the scale of running schools. The popularisation of higher education [4], the gross enrolment rate, and universities with 10,000 people have become the boasting achievements of local governments. Some colleges and universities have to reduce student funding and office funding. Many school students could not take experimental courses, had no money for internships and the quality of education could not be guaranteed
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