## Thursday, April 12, 2007

### A Teachable Moment

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.

In other words, the income effect of taxes alters behavior, but that is the optimal response of behavior to the fact that the individual is poorer when the government takes away resources. The substitution effect measures the deviation from that optimal response. To see the distortion, you don't compare the tax and no-tax cases; you compare the tax and lump-sum cases.

Is that clear, knzn?