Peter Andrews - Reuters

Grover Norquist made headlines Monday night for saying that while he thinks a "carbon tax swap" — in which such a tax finances cuts to the income tax — is bad policy, he doesn't think it violates his anti-tax pledge. This isn't as big a deal as you might think, not least because the chances of a carbon tax were always slim, but it does raise the question: What would a carbon tax swap actually look like?

A paper in August by MIT's Sebastian Rausch and John M. Reilly — which Brad highlighted upon release — asks how much you could cut various taxes if you imposed a carbon tax, starting at $20 per ton in 2013 and increasing by 4 percent every year thereafter. The answer: not that much.

The first table below shows how much you could cut various taxes if 100 percent of carbon tax revenues are used to finance the cuts. The second table shows potential cuts if only half of the revenue goes to other cuts. The latter scenario seems likelier as part of a deficit reduction deal, as the former would be revenue-neutral and thus do nothing to balance the budget:

Source: Rausch and Reilly

In 2015, a 100 percent swap would only allow income tax rates to fall 0.59 percentage points, relative to all the Bush tax cuts expiring. So the top rate would be 39 percent rather than 39.6 percent. That's hardly a game-changer. The possible income tax cuts are barely perceptible when only half of revenue funds rate reductions.

The situation is a bit more promising for tax and corporate taxes. A full swap would finance a 1.59 point reduction in the payroll tax in 2015, almost as much as the two point cut in place for the past two years. Alternately, it would allow the corporate income tax rate to drop below 33 percent from its current level of 35 percent.

Rausch and Reilly found that cutting the corporate (blue line) or personal (red) income tax as part of a swap would be regressive, but using it to pay for a payroll tax cut (black) or social programs for the poor like Medicaid (green) would be highly progressive. Here's how each would affect the incomes of people across the income spectrum:

Source: Rausch and Reilly

The Medicaid option is a big boon for people making up to $75,000, and a net tax increase above that point. A payroll tax cut benefits everyone but those making over $150,000, while personal or corporate tax cuts help everyone but the very poor.

Another option, proposed by Gilbert Metcalf, a Tufts economist currently heading up the environmental tax division at Treasury, is using a carbon tax to fund an exemption in the payroll tax. Currently, Social Security taxes apply to the first dollar you earn, until you reach the cap (currently $110,100). Metcalf finds that a $15 per ton carbon tax would allow the government to exempt the first $3,660 a given worker earns from the payroll tax, similar to how personal exemptions allow all income tax payers to exempt the first few thousand dollars they earn.

Metcalf's plan would be more regressive than the ones Rausch and Reilly looked at. The bottom 30 percent of the income distribution would see taxes increase by as much as 1.1 percent of income, while middle class people would see modest tax cuts and the very rich would be unaffected. That suggests that policymakers concerned with progressivity would do better to use a carbon tax to fund entitlements or a payroll tax rate cut than an exemption.