In this paper, we analyze the equilibrium on the market for schooling where both public and private schools coexist and where individuals are differentiated by income and ability. We introduce a non linear in means model of peer effect by shedding the light on the fact that school quality is not solely dependent on mean ability but also on the dispersion of abilities. We study the distribution of students across sectors while examining the conditions for the existence of a majority voting equilibrium in the context of non single peaked preferences. Finally, we examine the presence of a hierarchy of school qualities. In the paper we shed the light on equity problems related to the access to educational quality while analyzing the functioning of the educational system.