I’ve been trying to figure out what marginal tax rates would be if the so-called “Buffett Rule” were passed. There’s an actual Senate bill out there but, as with almost all bills, you have to look at previous law–and know how to read dense laws–to understand what it means.

Here’s a little background on tax law and economics to explain what I mean. When tax economists talk about marginal tax rates, they distinguish between a “notch” and a “kink.” Example: In 2010, Megan McArdle advocated eliminating “the tax-deductibiity of health insurance benefits for people making more than \$150K a year in household income, \$100K for singles.” If we take her literally, she was advocating a notch. Here’s my analysis at the time:

Imagine that you’re a married person with a family and you’re making exactly \$150K a year. Your employer pays \$10K toward your health insurance. Of course, it’s not subject to federal income tax, state income tax, or Social Security or HI tax. You and your spouse make a total of \$150K, split roughly evenly, so both of you pay the marginal payroll tax rate of 7.65%. You also pay a marginal income tax rate of 25% and a state income tax rate of 5%. So your total marginal tax rate is 25 + 5 + 7.65 = 37.65%.

Now you earn one more dollar. What happens? That whole \$10K employer contribution becomes taxable and so you pay tax on it at 37.65% or \$3,765. You made an extra buck and you paid \$3,765 extra in taxes. Oh, yes, plus \$0.3765. So you paid \$3,765.3765 in taxes. Your marginal tax rate on that dollar: 376,537.65%.

That’s a notch.

Now, my guess is that she didn’t mean what she wrote literally but, instead, wanted to phase out the deductibility over some income range. That would convert a notch to a kink. [Why these terms? Imagine drawing the Marginal Tax Rate on the vertical axis against income on the horizontal. If there is no phaseout, you get a big jump at the \$150,001 point and then a big drop at the \$150,002 point. If there is a phaseout over some income range, you get the MTR line kinking and becoming steeper at the \$150,001 point.]

Rather than speculate about what she might have meant to say, let me turn to the Buffett Rule. If I take literally the way Obama talks about the Buffett Rule, then, once your taxable income hits \$1,000,000 or \$1,000,001 [I’m not sure which], your average federal tax rate on income becomes 30%. Now let’s assume Buffett is right that there are a lot of high-income people paying, say, an average federal income tax rate of 20%. Imagine one of these people is making \$999,999 in taxable income and he is contemplating making an extra \$1 of income. Without the Buffett Rule, he pays \$200,000 [actually \$199,999,80] in federal income taxes. If he makes that extra dollar, getting him to the magic number of \$1,000,000 in income, he pays income taxes equal to 30% of his taxable income, or \$300,000. So he pays an extra \$100,000 in federal income taxes. His Marginal Tax Rate on that one millionth dollar is 10,000,000%.

Surely, Obama can’t mean that, can he? It’s hard to understand the proposed law, given how little analysis has been done. So let’s turn to the Joint Committee on Taxation, which has done revenue estimates. Not surprisingly, they seem to be aware of this problem and contemplate a phaseout. They write:

The tax would be phased in for taxpayers with AGI between one million dollars and two million dollars (\$500,000 and one million dollars for married individuals filing a separate return).

So that’s a kink, rather than a notch, for my hypothetical taxpayer at \$1,000,000 in taxable income. If he’s at an average tax rate (ATR) of 20%, we can figure out his new MTR. Over the next million, he will move from an ATR of 20% on \$1,000,000 to an ATR of 30% on \$2,000,000. In other words, over that additional \$1,000,000 in income, he will pay an additional \$400,000 in income tax. [30% of \$2,000,000 minus 20% of \$1,000,000.] So his marginal tax rate jumps to 40%. That’s bad, but not as horrific as it might first have seemed.

But wait; there’s more. What about the person making \$1,999,999 in income who makes an extra \$1? For him there’s NO phaseout. If he is currently paying 20% of his income in taxes, which is \$400,000 then, under the Buffett Rule, he would pay 30% of \$2 million, or \$600,000. So he pays an extra \$200,000 on that last dollar of income and his MTR is 20,000,000%.

This is as far as I’ve gotten. Has anyone looked at the details beyond what I have above?

UPDATE: My second last paragraph above, starting with “But wait; there’s more,” is incorrect. David W says why in the comments below:

The 1,999,999 taxpayer does indeed pay \$200K more – but that’s the result of the change in law, not the result of the earning an extra dollar. Marginal tax rates are a question of the change in tax by changing your income, keeping law constant. What you’re calculating is the effect of changing the law, keeping income constant. His marginal tax rate is certainly higher than current law, but it’s also not what you state.