Private provision of public good and endogenous income inequality

We model a simple economy with privately provided public good and with two groups of individuals—rich and poor. Only rich people contribute to the public good and they own capital input that is used to produce varieties of private goods under monopolistically competitive market structure. Income inequality is endogenously determined in the unique Nash equilibrium of the economy. We show that government intervention in the form of higher tax rate and/or larger transfer of the tax-revenue from rich to poor would be able to reduce the degree of income inequality. However, the impact of such a policy on the aggregate provision level of the public good is, in general, ambiguous. Income inequality in the market economy is too high and there will be under provision of the public good compared to the planner’s economy even if the planner is only interested in maximizing the welfare of the rich people. We derived the optimal capital and wage income tax rate that implement the first best solution.