Self-selection in the state school system

With diminishing returns to the peer group, it is optimal social policy to mix chldren in schools. We consider what happens when, contrary to the outcome being determined by a social planner, schools and children are free to seek each other out: with some caveats, this leads to perfect segregation by child quality. It is shown that this is the worst possible outcome. We show also that a competitive system produces the optimal allocation of children to schools.