Public good provision with redistributive taxation

A government sets the level of taxation to provide a public good valued by consumers. There are two groups of consumers, the rich and the poor. The government has redistributive preferences, but is initially constrained to use lump-sum taxation. This potentially leads the government to provide a very low level of the public good out of concern for not reducing private good consumption of the poor. In this context, allowing a small amount of redistribution from the rich to the poor may be Pareto improving. The loss in private consumption by the rich may be more than offset by the added utility from increased public good provision. I also analyze the extent to which a flat income tax can induce the government to choose a level of public good consistent with the Samuelson condition. When consumers have a survival constraint on private consumption, a progressive tax code is required to induce the government to choose the efficient level of the public good. Generally speaking, there is a trade-off between a desire to restrain the government's ability to redistribute income and a desire to induce it to choose the level of the public good implied by the Samuelson condition.