Screening while controlling an externality

We propose a tractable framework to introduce externalities in a screening model. Agents differ in both payoff-type and influence-type (ranking how beneficial their actions are for others). Applications range from pricing network goods to regulating industries that create externalities. Inefficiencies arise only if the payoff-type is unobservable. When both dimensions are unobserved, the optimal allocation satisfies lexicographic monotonicity: increasing along the payoff-type to satisfy incentive compatibility, but tilted towards influential agents to move the externality in the socially desirable direction. In particular, the allocation depends on a private characteristic that is payoff-irrelevant for the agent. We characterize the solution through a two-step ironing procedure that addresses the non-monotonicity in virtual values arising from the countervailing impact of payoff- and influence-type. Rents from influence can emerge but only indirectly, i.e. when the observed level of influence is used as a signal of the unobserved payoff-type.