Efficient tuition fees, examinations, and subsidies

We assume that students can acquire a wage premium, thanks to studies, and form a rational expectation of their future earnings, which depends on personal "ability". Students receive a private, noisy signal of their ability, and universities can condition admission decisions on the results of noisy tests. We assume first that universities are maximizing social surplus, and contrast the results with those obtained when they are profit maximizers. If capital markets are perfect, and if test results are public knowledge, then the optimal tuition fee is greater than marginal cost, and there is no sorting on the basis of test scores. Students optimally self-select as a result of pricing only. If capital markets are perfect but asymmetries of information are bilateral, i.e., if universities observe a private signal of each student's ability, or if there are borrowing constraints, then the optimal policy involves a mix of pricing and pre-entry selection on the basis of test scores. Optimal tuition can then be set below marginal cost, and can even become negative, if the precision of the university's private assessment of students' abilities is high enough.