Control rights in public-private partnerships

This paper develops a theory of the allocation of authority between two parties that produce impure public goods. We show that the optimal allocation depends on technological factors, the parties' valuations of the goods produced, and the degree of impurity of these goods. When the degree of impurity is large, control rights should be given to the main investor, irrespective of preference considerations. There are some situations in which this allocation is optimal even if the degree of impurity is very low as long as one party's investment is more important than the other party's. If the parties' investments are of similar importance and the degree of impurity is large, shared authority is optimal with a greater share going to the low-valuation party. If the importance of the parties' investments is similar but the degree of impurity is neither large nor small, the low-valuation party should receive sole authority. We apply our results to a number of situations, including schools and child custody.