On the optimal allocation of students and resources in a system of higher education

We model the social planner's decision to establish universities and populate them with students and resources, given a distribution of student ability and a limited pool of resources for higher education. If student ability and school resources are complements, and if there is a fixed cost to establishing a school, then the optimal allocation will involve a tiered system of higher education that sorts students by ability. In contrast to previous research, we show this tiered system is optimal even in the absence of peer effects. In considering where to locate students, the planner balances the benefit of providing students with more resources against the congestion costs of overcrowding schools. Nearly identical students who are close to the margin of entry to a higher or lower tier will experience discrete gaps in education quality. In considering how many universities to establish, the planner will balance the value of more precise tailoring against the cost of establishing additional schools. The planner's inability to perfectly tailor education quality will result in both winners and losers. Our model also makes predictions about how university systems that serve different populations should vary. Larger systems will produce more per dollar of expenditures and more education per student, due to economies of scale.