In his New York Times column this morning, Ross Douthat considers various ways of reducing income inequality. While not endorsing higher taxes on high-income people, Douthat’s takes it as given that such taxes would reduce inequality. Ignore the fact that he confuses income and wealth, referring to high-income people as the rich and low-income people as the poor. He makes an even bigger mistake: assuming an implausible supply curve for labor.

Note that the income inequality he talks about is before-tax. He says nothing about after-tax inequality. Then Douthat writes:

For one thing, the lazy liberal’s cure for income inequality — soaking the wealthy with higher tax rates and cutting taxes for everybody else — simply isn’t going to happen.

In part, this is because the Democrats have become as much the party of the rich as the Republicans, and parties rarely overtax their own contributors. (That’s why the plan to pay for health-care reform with a “surtax” on high earners found so many skeptics within the Democratic caucus.)

But it’s also because soaking the rich only makes a difference on the margins. The federal income tax is already quite progressive, and our corporate tax rate is one of the highest in the West.

He’s right that it would make a difference only on the margins. But he gets the direction of the difference wrong. If high-skilled (and therefore high-income) workers have even a slightly upward-sloping supply curve, then a higher marginal tax rate on their income will cause their rate of pay to rise. Assuming that the elasticity of demand for their labor is less than one, that higher rate of pay times slightly reduced hours will cause their pre-tax pay to rise. Therefore, inequality rises. Of course, their after-tax pay is likely to fall, but that’s not what Douthat’s discussing and it’s not what critics of income inequality point to. Virtually all of them point to pre-tax inequality.

What if these high-skilled workers have a vertical supply curve? Then there would be no effect on pre-tax income for them. But higher marginal tax rates on them would still not reduce measured pre-tax income inequality.

The only even-somewhat-plausible way Douthat could save his point is to assume that the demand for high-skilled labor has an (absolute value of) elasticity greater than one. Is that what he had in mind?

BTW, in trying to graph out the effect of a tax when there’s a backward-bending supply of labor, I realized that I have never seen this on standard supply and demand graphs. Does anyone have a cite showing how to do it?