We address the following question: how does a higher education funding system influence the trade-off that universities make between research and teaching? We do so by constructing a model that allows universities to choose actively the quality of their teaching and research when faced with different funding systems characterised by the pivotal role of the university funding budget constraint. In particular, we derive the feasible sets that face universities under such systems and show how, as the parameters of the system (the research block grant element, the research quality premium and the incentives-triggering quality threshold) are varied, the nature of the university system itself changes. Different ‘cultures’ of the university system emerge such as the ‘research elite’ and the ‘binary divide’.