Greg Mankiw has pointed to an old post of his on the deadweight loss of taxation that at first blush, sounds confusing:

The normally astute knzn is confused. In a comment on the previous post, he questions one of my assertions:

“according to standard theory, the distortionary effect of taxes depends only on the substitution effect”

Maybe I need a refresher course in public finance theory, but this doesn’t quite make sense to me. Suppose you have a large income effect and a large substitution effect, and the two are precisely offsetting, so that labor supply is perfectly inelastic. In that case, changes in labor taxation will not affect the quantity of labor supplied or the pre-tax wage. So in what sense can there be said to be a distortion?

Here is the logic:

Case A. No taxes. Andy earns \$10 an hour and works 40 hours a week, for income of \$400.

Case B. The government now levies a tax at 20 percent to fund a war. There are offsetting income and substitution effects. Andy still works 40 hours, now earning before-tax income of \$400 and after-tax income of \$320. The government collects \$80 to pay for the war.

Now you might say the tax has no distortion, because hours worked remain the same. But you would be wrong. Consider another situation:

Case C. The government funds the war with a lump-sum tax of \$80. Andy faces the same income effect as Case B (which makes him work more), but no substitution effect (which previously offset the income effect). Andy works 45 hours, for after-tax income of \$370.

Notice that welfare must be higher in Case C than in Case B. How do I know? Because in Case C Andy could have chosen to work 40 hours, earning \$320, the same outcome as Case B, but he chose not to. (By contrast, in Case B, if Andy had chosen to work 45 hours, he would have earned income of only\$360.) Thus, Andy is better off under the lump-sum tax than under the income tax that produced the same revenue. The difference in welfare between Case C and Case B is the deadweight loss of the income tax.

This is not intuitive to most people. Most people would assume that the deadweight loss of a tax is the reduced work output that results from taxing labor. In this case, it is appropriate to consider both the income effect (if you cut income tax rates across the board, people will tend to work less because they feel richer, and want to consume more of that luxury good, leisure); and the substitution effect (people want to consume less leisure, because the lower marginal tax rates effectively raise their pay, meaning that they now have to sacrifice more consumption of other goods in order to secure an hour's more leisure.) The argument over the effect of marginal rate cuts on output is, in essence, an argument over whether the income effect outweighs the substitution effect--or whether they are both trumped by factors like labor market rigidities.

But1 the issue is not that people have less money and therefore have to choose a different consumption bundle; what causes the deadweight loss is that the market is not clearing as efficiently as it could. There are, at current income levels, utility enhancing deals that would be made under a lump-sum tax that are not being made because of the substitution effect.

1Edited to make it clearer