In the paper entitled "Teaching versus Research: A Model of State University Competition" Del Rey (2000) develops a two-stage game of competition between two ex-ante identical non-profit universities. She assumes that a university aims at maximizing some measure of prestige positively affected by its number of enrolments, the quality offered to these students and its investment into research activities. A university's teaching cost decreases with the average ability of its student body and increases with its number of enrolments and the offered quality level. A university receives an exogenous budget consisting of a lump-sum amount and a per-student allocation, and spends these funds on teaching and research. In a first stage of the game, both universities simultaneously decide on the quality level they offer to their students. On the basis of these announcements students sort their preferences. In a second stage, the universities simultaneously set an admission standard and hence they determine their number of enrolments and the average ability of enrolled students. This game is solved by backward induction. Our paper deals with two important changes to this model of Del Rey and the consequences for the configuration of the subgame perfect Nash equilibrium of the game. First of all, in her model Del Rey assumes that attending a higher quality university always increases a student's utility independent of that student's ability level. We, however, assume that a higher ability student gains more from attending a higher quality university compared to a lower ability student (single- crossing property). Consequently, students with the same physical location do not necessarily prefer the same university. Secondly, Del Rey used a linear specification for a university's cost function. We use a non-linear specification in which the marginal cost of quality is increasing. Depending on the chosen parameter values we distinguish 4 types of resulting subgame perfect Nash equilibria: a single symmetric equilibrium, two asymmetric equilibria, a symmetric together with two asymmetric equilibria and no equilibrium in pure strategies. For instance, when mobility costs are very low, we find that one university announces a higher quality level compared to the other one. Due to this higher quality level the university attracts the highest ability students so that it is no longer necessary for this university to be selective. The best-reply of the lower quality university will be to admit as many students as possible; hence, to set its admission standard equal to zero. Notice that, despite its higher average ability, the higher quality university still needs to invest more into teaching than the lower quality university. Consequently, at this asymmetric equilibrium the higher quality university has fewer funds left to invest into research activities compared the lower quality university. When mobility costs are very high, however, a single symmetric equilibrium arises. In other words, both universities announce the same quality level, set the same admission standard and divide their funds over teaching and research in a similar way.