Why does tuition keep rising? A flypaper effect?!

Just a brain-storm. Let's assume a very inelastic demand of university education. Consumers, i.e, students do not decide where to go based on price, i.e., tuition; other factors, such as fame, quality, and reputation of the institution matters more. Producers, i.e., universities, have substantial market power because there are only one or two universities in a city and information asymmetry exists in favour of producers. Its marginal cost curve is very flat, which means even if it has one more student, it does not incur such large extra cost. Without government intervention, the monopoly quantity of university education will be determined where marginal cost equals marginal revenue. Students should pay much higher than reservation price to the university. Now, the government offers every student with subsidies that have to be used to reduce tuition burden. As a result, the demand for university education will shift right. The new equilibrium output should be greater than monopolist quantity (but by a little because of inelastic demand). At the same time students' burden for the tuition will decrease. What if the government provides the equivalent amount of subsidies to the school. It will depend on how that money is assigned. If it is solely used to reduce tuition, the result will be the same as above. If it is unconditional, i.e. completely up to the university's discretion, things could be different. The university may use that money to reduce tuition, but it may use that money to renovate its old buildings, build more parking lots, hire more instructors to reduce the number of students per instructor or just raise employees' salaries. If these things happen, the marginal cost of university education will increase, and accordingly students' burden of tuition will remain the same or may rise. It may reduce the enrollment rate, but given the inelastic demand, the drop rate may increase by a little.

P.S. The flypaper effect, by the way, refers to a distortive effect of unconditional grants, summarized by "Money sticks where it hits."