In this paper we investigate the optimal choice of prices and/or exams by universities in the presence of credit constraints. We first compare the optimal behavior of a public, welfare maximizing, monopoly and a private, profit maximizing, monopoly. Then we model competition between a public and a private institution and investigate the new role of exams/prices in this environment. We find that, under certain circumstances, the public university may have an interest to raise tuition fees from minimum levels if it cares for global welfare. This will be the case provided that (i) the private institution has higher quality and uses only prices to select applicants, or (ii) the private institution has lower quality and uses also exams to select students. When this is the case, there are efficiency grounds for raising public prices