Why is Pigou Sometimes Wrong? Explaining How Distortionary Taxation Can Cause Public Spending to Exceed the Efficient Level

When a public good is financed by a proportional tax, the price distortion increases the marginal cost of the public good above its resource cost. Pigou (1928) conjectured that the higher cost lowers the second-best public good level below the first-best level. I explain why this conjecture is sometimes false. In particular, if the public good is financed by a commodity tax, the price distortion normally raises the marginal benefit, and I provide an example in which the increased benefit dominates the increased cost; the second-best public good level lies above the first-best level. In contrast, if the public good is financed by a wage tax and leisure is a normal good, the price distortion lowers the marginal benefit; if the wage elasticity is positive, the second-best public good level lies below the first-best level