This paper evaluates the behavioural responses of multitask agents to the provision of incentives skewed towards one task only. In particular it studies the case of strong research incentives for university professors and it analyzes their effects on the way university faculty members allocate effort between teaching and quantity and quality of research and on the way they select into different types of universities. I first obtain different individual level measures of teaching and research performance. Then, I estimate a difference in difference model, exploiting a natural experiment that took place at Bocconi University, which heavily strengthened incentives towards research in 2005. I find evidence that teaching and research efforts are substitutable in the professors' cost function: the impact of research incentives is positive on research activity and negative on teaching performance. The effects are driven by career concerns rather than by the monetary incentives and are stronger for low ability researchers. Moreover, under the new incentive regime lower ability researchers tend to leave the university. Since I estimate that teaching and research ability are positively correlated, this implies that also bad teachers tend to leave the university. These results are consistent with a model of incentives where agents allocate effort between two substitute tasks and ability is multidimensional. An appendix shows how the author solved the model (for internal solutions) and shows the equilibrium effort level.