Mitt Romney and House Budget Committee Chairman Paul Ryan (R-Wis.) are both pushing “tax reform” plans that would lower marginal tax rates while broadening the base (curbing tax deductions, credits, and exclusions). Romney’s plan, for example, would reduce all individual income tax rates by a fifth—e.g., the top 35 percent rate would fall to 28 percent—and the revenue loss would be made up by limiting or eliminating unspecified tax expenditures. And he says he would do this without cutting taxes for high-income households (beyond continuing their Bush-era tax cuts), meaning that he would more or less preserve the progressivity of the current tax code (i.e., tax burden distribution).

For the moment, let’s leave aside the fact that these plans neglect to raise a dollar in additional revenue at a time when we need more revenue to put the government on a sustainable fiscal path. Why are these proposals pure folly?  First, because they’re obviously not serious—if they were, the plans would lead with the tax expenditure reform rather than the rate cuts. Instead, they’re sold in manner suggesting that Romney and Ryan wanted to propose big across-the-board tax cuts but didn’t want to be seen as blowing up the deficit, so they included vague language on base-broadening in order to ignore the monumental cost of slashing tax rates.

But most importantly, these plans aren’t serious because their stated intent isn’t mathematically possible. In an analysis released Wednesday, researchers at Brookings and the Tax Policy Center analyzed a plan that is consistent with Romney’s proposal, including lowering rates by a fifth and eliminating the Alternative Minimum Tax. The researchers then attempted to construct a base-broadening approach to both make up the revenue lost from the rate cuts and maintain the progressivity of the current tax code.

Turns out, they couldn’t. The figure below shows even under the best case scenario, taxpayers with income under $200,000 (95 percent of all taxpayers) would pay more under the tax reform plan, and the top 5 percent would necessarily get a tax cut.

Why can’t progressivity be maintained? For one thing, the initial tax cut is intrinsically regressive, providing a larger rate cut for high-income taxpayers: tax units between $50,000 and $75,000 would get an initial tax cut of under $1,000 (before losing tax preferences), while a taxpayer making over $1 million would get an initial tax cut over $175,000. This is partly because the taxpayers at the top have more income subject to taxes in the first place, but also because the 20 percent rate cut provides greater percentage-point cuts the higher the marginal rate. For example, a 20 percent reduction in the top 35 percent rate translates into a 7 percentage-point reduction, while the same reduction in the 25 percent rate translates into a 5 percentage-point reduction.

The second reason tax reform like this is inherently a losing proposition for the bottom 95 percent is that while tax expenditures do skew towards higher-income taxpayers, they also benefit middle- and upper-middle-income taxpayers. Furthermore, Romney and Ryan both explicitly exclude savings preferences—notably the preferential rate on capital gains and dividends—from the tax expenditures that they would be willing to curtail. As the figure below based on Tax Policy Center data shows, overall tax expenditures do provide a disproportionate benefit to the top income quintile, particularly the top 1 percent of earners, but this effect is completely driven by savings preferences, which are the only tax expenditures that Romney and Ryan won’t touch. Exclude them, and the distributional impact of the remaining tax expenditures is quite flat—meaning the middle class would feel a big bite from their elimination.

So the next time you hear Romney or Ryan talking about how they’re going to cut rates and broaden the base, keep in mind that there’s one element of the plan that they’re leaving out: the rich will pay less and everyone else will pay more.