Interim Efficiency in a Public Goods Problem

Abstract

We consider a Bayesian public goods environment with independent private valuations, where a public good can be produced at constant returns to scale, up to some capacity. We fully characterize the interim efficient allocation rules and prove that they correspond to decision rules based on a virtual cost-benefit criterion, together with the appropriate incentive taxes. Compared to the classical Lindahl-Samuelson solution there are generally distortions that depend on the welfare weights because the efficient way to reduce the tax burden on low-valuation (resp: high-valuation) types is to reduce (resp: increase) the level of provision of the public good. Second, we explore the implementation of efficient allocations by means of simple, dominant strategy voting rules, called referenda. In a referendum, individuals vote for or against production of the public good. If a sufficiently large fraction vote in favor, the good is provided at maximum capacity and costs are distributed equally across the population. Otherwise the good is not produced. We prove that for each interim efficient allocation rule there exists a referendum that approximates that achieves the same total surplus in large populations. Furthermore, if there is common value uncertainty in addition to the private valuations uncertainty, then the approximately optimal referendum is unique.