<p>We develop an evolutionary model to analyse the role of policymaker’s preferences on the amount and direction of funding in determining university trajectories. Results are four. First, the policies that maximise performance in certain dimensions do not require that funds targeted at those dimensions are maximised, due to the complementarities between research and teaching. In most cases, the Humboldt model in which a university commits to a balance between teaching and research tends to generate more robust performance patterns. Second, any policymaking that boils down to reduced competition in the research market and allocates most resources to top institutes might curtail research quality. Third, a generalised increase in funding is not effective if the distributive mechanisms are untouched and prioritise reputation, unless they target small institutes and sustain competition in the research domain. Finally, we have some evidence of the Baumol’s cost disease when a system-level wage rate combines with the emergence of technological advantages. At the best of our knowledge, this article constitutes the first endeavour to model the scientific and pedagogical trajectories of universities as emergent properties of the micro-dynamic that involves the <i>amount</i> and the <i>direction</i> of public funding, which is our way to formalise the third mission.</p>