Optimal Taxation and Impure Public Goods

It has been shown that the introduction of a good that has portions of both private and public characteristics (an impure public good) can actually decrease the total level of the public characteristic provided. Using the standard impure public good model, I first isolate the conditions under which this occurs in a general equilibrium. I then introduce a central planner whose goal is to counteract this decrease. She chooses a tax rate for the purely private good, and spends the tax revenue generated to increase the provision of the public characteristic. In choosing the optimal tax rate, she minimizes the tax’s deadweight loss subject to the total public characteristic given the tax and the impure good being at least as large as it was in the absence of both. I then identify the properties both of markets and of impure public goods that tend to necessitate such a situation, thus also identifying those which necessarily increase the resulting deadweight loss. It is suggested that such properties are harmful to society, either through the decrease in the public characteristic absent a planner or through the resulting increase in deadweight loss if a planner is present