Optimal provision of a public good with costly exclusion

We examine the problem of providing a non-rival and excludable public good to individuals with the same preferences and differing contributing capacities. Exclusion from the public good is costly in the sense that if two different quantities of the public good are consumed in the community, then the sum of the costs of providing the two quantities must be borne. By contrast, costless exclusion only requires the cost of the largest quantity consumed of the public good to be financed. We show that despite its important cost, providing public goods in different quantities is often part of any optimal provision of public good when the public authority is imperfectly informed about the agents' contributive capacities. In the specific situation where individuals have an additively separable logarithmic utility function, we provide a complete characterization of the optimal exclusion structure in the two-type case. We also show that the preference for such a costly exclusion is more likely when the heterogeneity in the population or income is large, and when the aversion to utility inequality is important.