Envy-Free Pricing for Impure Public Good

In this paper, we study optimal public good provision with congestion and user fees to exclude some agents under lump-sum tax/transfer, constrained by the condition of reduction of envy. We adopt the λ envy-free constraint proposed by Diamantaras and Thomson(1990), and employ the exclusion technique used in Hellwig(2005), i.e., the policymaker decides the level of provision and user fee paid by people accessing a public good, as well as a uniform level of tax/transfer. We characterize the optimal public sector pricing rule that depends on utilitarian distributive concerns and envy reduction concerns, which are in conflict with each other. We show that if the social welfare function is strictly increasing and strictly concave and the government is not concerned with reducing envy, the user fee is greater than the marginal congestion cost. Additionally, we show that if the government reflects the notion of equality of opportunity under the reduction of envy, the user fee is lower than the marginal congestion cost. These results imply that the two fairness concerns are countervailing with regard to the surcharge fee. Furthermore, by numerical computation, we observe that both provision level of the public good and its user fee decrease as the intensity of envy increases under the binding ethical constraint