A model of vertically differentiated education

We analyze the allocation of students who differ in their ability to two school types. We assume that there are peer effects (students learn more the better their classmates) and that the expected income after school also depends on the average productivity of peers. We derive the allocation under free school choice and decentralized determination of the academic level; we show that, compared to the social optimum, the level is suboptimal and too many students attend the better school type. A social planner can improve on the allocation under free school choice by prescribing a higher academic level.