Why "narrowly focused" middle-class tax cuts overwhelmingly benefit the wealthy

Since the White House finally got around to announcing the outlines of their tax reform plan today, I want to briefly address an issue that's generally ignored in discussions of income tax rates and brackets.

Marginal tax rates mean you pay taxes at lots of different rates

You often hear as shorthand that "the wealthy pay a 40% income tax." That's exactly wrong: the wealthiest Americans pay a 39.6% marginal income tax rate. If a single person reports a taxable income of $418,401 in earned income, they pay a 39.6% income tax...on exactly one dollar.On the first $470,700 in taxable income, the person pays 10% on $9,325, 15% on $28,625, 25% on $53,950, 28% on $99,750, 33% on $225,050, and 35% on $1,700. Only after paying all those tax rates does our single taxpayer begin to pay 39.6% on additional dollars of income.

Tax cuts disproportionately benefit people who fill up each tax bracket

Let's say that we decide the middle class is working longer hours for less pay and that the solution is a tax cut for hardworking middle class families (insert gagging sound effect here). $50,000 in taxable income seems like a good place to target our middle class tax cut, since that would imply about $60,400 in earned income, a solidly middle-class income. $50,000 in taxable income falls in the 25% tax bracket, so what happens when we cut the 25% marginal tax rate all the way down to 15%?Our solidly middle-class taxpayer saves $1,205 in federal income taxes: 10% of the amount of taxable income in excess of $37,950.Meanwhile, how much would someone making $100 million in earned income save? They'd pay $5,395 less in federal income taxes, 10% of the entire $53,950 bucket of earned income.And remember, this is the outcome of a federal income tax cut narrowly focused on middle-class taxpayers.But in this day and age, who can survive on $50,000 in taxable income? Let's raise the threshold for our narrowly focused middle-class tax cut all the way to $100,000, which puts our single middle-class taxpayer in the 28% tax bracket, and we'll cut the 28% tax bracket down to 15% as well.Now our solidly middle-class taxpayer gets to save the entire $5,395 in federal taxes our titan of industry saves, plus an extra $1,053: 13% of her taxable income in excess of $91,900.But sure enough, our hedge fund manager wins again, saving $12,967 (13% of $99,750) plus the $5,395 saved in the lower bracket.So much for narrow focus.

The only way to narrowly focus a middle-class tax cut is to raise marginal tax rates on higher incomes

This is a mechanical outcome of the nature of a system of progressive marginal income tax rates, and there's nothing that can be "done" about the savings the wealthy get from cuts to marginal tax rates in the lower income tax brackets.On the other hand, there's no secret to "narrowly focusing" a tax cut on the working or middle classes: you recoup the money saved by high earners through higher marginal income tax rates on the upper brackets.To recoup the $5,395 saved by high-income taxpayers by cutting the 25% rate to 15%, you can raise the 33% bracket by 2.4%. To recoup the $12,967 saved by lowering the 28% bracket to 15%, you could raise the 33% bracket by 5.8%.Note that this would still constitute a net federal income tax cut on everyone with taxable income up to $416,700, since only at that point will the entire tax savings in the lower brackets be recouped.

The idiocy of an "across the board" tax cut

To be clear, I'm not in favor of any of the above proposals because I don't think our middle class is suffering under the cruel yoke of an expropriating tax code. But even if you think taxes should be lower, even if it's out of pure greed, you have to understand that the wealthy receive a federal income tax cut when tax rates on lower incomes are lowered, even if the marginal tax rate on higher incomes is unchanged.You do not need an "across the board" in order to cut everyone's taxes. Cuts exclusively to the marginal tax rates of lower tax brackets not only benefit high-income taxpayers, they disproportionately benefit high-income taxpayers.