Public Goods and Distribution under Multidimensional Heterogeneity

How should distributional concerns influence applied welfare analysis and its policy recommendations? Using a variational approach, we extend the classical problem of public good provision under optimal nonlinear income taxation to allow for multidimensional heterogeneity in abilities, preferences, and exposure to public goods. We derive a general policy rule where the deviation from the Samuelson condition is governed by the difference between the cross-sectional and within-individual income elasticities of the marginal willingness to pay for the public good. This novel sufficient statistic applies regardless of the structure of unobserved heterogeneities. Particular attention is paid to exposure heterogeneity, e.g., in terms of distance to the public good, which can generate substantial deviations from the Samuelson condition. The results suggest that it is often optimal to address distributional concerns explicitly in public good provision, rather than solely through the tax and transfer system.