Theory Seminar - presented by Takuro Yamashita (TSE)

Abstract: This paper considers a planner's problem of dividing a unit-mass of students with heterogeneous abilities into a finite number of schools. Each student's final payoff is a function of his own ability and the peer effect, the average ability (or the average of a function of abilities) of the students in the same school. Perhaps due to this endogenous allocative externality, in the literature, the optimal assignment mechanism has been characterized in a relatively restricted set of environments (e.g., with binary ability types or with specific payoff functions such as Cobb-Douglas). This paper characterizes the optimal assignment mechanism with continuously many types and a much milder assumption on the payoff function, which may be interpreted as a monotonicity condition for the planner's preference of having more diversity in each school. The optimal mechanism is shown to have a simple cutoff structure, allowing for clean comparative statics.