This paper studies optimal taxation schemes for education in a search-matching model where the labor market is divided between a high-skill and a low-skill sector. Two public policy targets – maximizing the global employment level and optimizing the social surplus – are studied according to three different public taxation strategies. We calibrate our model using evidence from fourteen European countries, and compare our results with the target from the Europe 2020 Agenda for achievement in higher education. We show that, with current labor market characteristics, the target set by governments seems compatible with the social surplus maximization objective in some countries, while being too high for other countries. For all countries, maximizing employment would imply higher educational spending than that required for the social surplus to reach its maximum.