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 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 existence of a hierarchy of school qualities, as a consequence of the discriminating pricing strategy used by private schools to internalize the effect of peer groups.