Public education in an integrated Europe : studying to migrate and teaching to stay?

An increasing international applicability of a given type of education encourages students to invest more effort when studying. Governments, on the other hand, face an incentive to divert the provision of public education away from internationally applicable education toward country-specific skills. This would mean educating too few engineers, economists and doctors, and too many lawyers. If the total tax rate is kept constant, then replacing part of existing wage taxes with graduate taxes, collected also from migrants, would improve efficiency. It could even allow for a Pareto-improvement.