Competition in Higher Education: Sorting, Ranking and Fees

We model student enrollment in markets for higher education where public universities, private non-profit universities, and private for-profit universities compete. Universities differ with respect to their capacity, graduation probability, and profit objective; students differ in ability. The value of a diploma at each university depends on its endogenous ranking based on average student ability.

In every equilibrium, the private for-profit university attracts the least able students. Under additional conditions, the private non-profit university attracts the top students. Paradoxically, a higher capacity at the public university might decrease its equilibrium market share as it incentivizes the for-profit university to compete more aggressively. The for-profit university benefits from an increased enrollment in higher education.