A theoretical and computational model with tax-financed, tuition-free public schools and competitive, tuition-financed private schools is developed. Students differ by ability and income. Achievement depends on own ability and on peers' abilities. Equilibrium has a strict hierarchy of school qualities and two-dimensional student sorting with stratification by ability and income. In private schools, high-ability, low-income students receive tuition discounts, while low-ability, high-income students pay tuition premia. Tuition vouchers increase the relative size of the private sector and the extent of student sorting, and benefit high-ability students relative to low-ability students

A theoretical and computational model with tax-financed, tuition-free public schools and competitive, tuition-financed private schools is developed. Students differ by ability and income. Achievement depends on own ability and on peers' abilities. Equilibrium has a strict hierarchy of school qualities and two-dimensional student sorting with stratification by ability and income. In private schools, high-ability, low-income students receive tuition discounts, while low-ability, high-income students pay tuition premia. Tuition vouchers increase the relative size of the private sector and the extent of student sorting, and benefit high-ability students relative to low-ability students.