Provision of public goods in a large economy

In this paper, I consider a large economy with a private and a public good where the distribution of costs (but not the individual costs) associated with the provision of the public good is known. A simple tax-subsidy policy, whereby all contributors get a subsidy funded by a tax on non-contributors, is shown to attain the first best allocation provided that the socially optimal amount of the public good is independent of the distribution of individual costs.