The UK is going through a rather traumatic reform of the finances of its higher education system. There is much debate, both public and among academics, on how much of the burden should be carried by the students and how. If we take as given that universities are funded by public grants, how to allocated them is still complex, in part due to the dual goals of universities: teaching and research. Research grants are now quality driven, while teaching grants are mostly quantity driven. Given that their is a budget constraint, either at the government or at the university level, any economist would tell you there is a trade-off and choices need to be made.
John Beath, Joanna Poyago-Theotoky and David Ulph discuss how universities choose whether to focus on research or teaching. Universities are funded according to a formula depending on the number of students taught, the number of academics and their research quality, which depends itself on the academic/student ratio, Every academic gets the same pay, and universities maximize an objective based on the quality-weighted volume of research and the quality adjusted number of students, where the quality of teaching is a consequence of the academic/student ratio.
It is clear there is not going to be a free lunch. A university cannot be good at both teaching and research. As one plays around with the funding formula, all sorts of equilibria can emerge. For example, if research is well rewarded and a minimum quality of research is required for it to be funded, a bifurcation occurs where a few universities concentrate on research and others on teaching. Which funding formula is best for society remains open, though.