Can state university fees increase welfare?: A mixed oligopoly approach

When students are unable to borrow, exams can be more efficient than fees in allocating students to schools. Optimal fees will then be zero for a monopolistic state university, but they can be positive when there is competition with a private, revenue-oriented university. The reason is that, by raising its tuition fees, the state university induces the private university to enrol more students. As a result, total enrolments and thus welfare can increase. For this to be possible we need the private university (i) to be of lower quality and selective, or (ii) to be of higher quality and not selective.