Tuition fees and admission standards: how do public and private universities really compete for students?

We study a market where two universities, a public and a private one, compete for students by setting admission standards. Students di¤er in ability and receive a wage premium for participating in higher education. This wage increases with the quality of the university at- tended. The private university maximizes pro ts, the public university maximizes welfare. We show that there is no same-standard equilib- rium. In a speci c example we show that multiple equilibria can exist. In one equilibrium the private university sets a higher admission stan- dard, and in the other equilibrium the public university sets a higher admission standard.