Monopolistic group design with peer effects

In a range of settings, private firms manage peer effects by sorting agents into different groups, be they schools, communities, or product categories. This paper considers such a firm, which controls group entry by setting a series of anonymous prices. We show that private provision systematically leads to two distortions relative to the efficient solution: first, agents are segregated too finely; second, too many agents are excluded from all groups. We demonstrate that these distortions are a consequence of anonymous pricing and do not depend upon the nature of the peer effects. This general approach also allows us to assess the way the `returns to scale' of peer technology and the cost of group formation affect the optimal group structure.