Is partial privatization of universities a solution for higher education?

This paper accounts simply for the link between higher education and the productive economy through educated workers. We study a model of vertical successive monopolies where students/workers acquire qualification from a University then "sell" skilled labor to a monopoly which itself sells its final product to consumers, linking through quality the education sector to the labor and output markets. We determine the optimal share the State should keep in the University to compensate for the market imperfections, while taking into account the inefficiencies of public management. The resulting partially privatized University fixes the tuition fees so as to maximize a weighted sum of profits and social welfare. We derive the optimal public share under the hypothesis that the State may subsidize the tuition fees/University losses, then under the constraint that the University should make a nonnegative profit. We prove that in both cases, the State should keep a substantial share (higher under the first hypothesis) in the University, unless public management is too inefficient in which case the University's management should be completely private.