When Do Distortionary Taxes Reduce the Optimal Supply of Public Goods?

It is often argued that the optimal level of public good provision is below the first-best level as long as the government's expenditures have to be financed by distortionary taxes. I examine this hypothesis and show that it is correct in a representative consumer economy if (i) the public good is normal and (ii) private commodities are normal and gross substitutes. Otherwise, counterexamples can be constructed. These results hold also with heterogeneous households provided that equity considerations are ignored. In general, however, distributional objectives may lead to a higher level of public expenditures in second best than in first best.