The world’s most basic math question about Romney-Ryan’s tax plan

I have the world’s most basic math question about the Romney-Ryan tax plan. It is so basic that I am embarrassed to ask it, but if I don’t know the answer then maybe that means that a lot of people don’t know it, so it’s worth asking.

Romney says his tax plan is to cut tax rates across the board by 20% and then to make up the difference in revenue by eliminating tax deductions and loopholes. He won’t specify which deductions he would eliminate until after the election, which is extremely unhelpful, but the subject for another post because my math question doesn’t depend in which deductions are eliminated. My question is about what Romneny means by cutting tax rates by 20%.

From Romney’s site, here is the description of “Mitt’s Plan”:

Make permanent, across-the-board 20 percent cut in marginal rates
Maintain current tax rates on interest, dividends, and capital gains
Eliminate taxes for taxpayers with AGI below $200,000 on interest, dividends, and capital gains
Eliminate the Death Tax
Repeal the Alternative Minimum Tax (AMT)

Usually in the real world, when you cut something by 20%, if you imagine getting a 20% off coupon, you would multiply by 0.8 to get the new amount. If you wanted to pay for a meal that that cost $20, with 20% off would save $4 and pay $16. I believe that is the mathematically correct definition of reducing something by 20%.

But I have noticed that when percentages get discussed in the news, politicians, pundits and reporters often just subtract the percentage. For a hypothetical example, say the news reported, “Death rates fell 2%, from 12% to 10%.” Mathematically, reducing a death rate from 12% to 10% is actually lowering the death rate by 16.7%, not 2%. (If in a population of 1000 people, 100 people die instead of 120, mathematically, 16.7% more survivors.)

So when Mitt Romney says “Make permanent, across-the-board 20 percent cut in marginal rates” I wonder whether he is saying, if your current income tax rate is 20%, will the new rate be 16% (20* 0.8), or 0% (20%-20%)? That is such a huge difference in terms of revenue impact you absolutely cannot evaluate his program without knowing that answer.

Here is an example using current tax rates–note that because of the way marginal tax rates work the example is a little more complicated than I would like but here goes:

Single taxpayer, no children, under 65 and not blind, taking standard deduction;

$40,000 gross income – $5,950 standard deduction – $3,800 personal exemption = $30,250 taxable income
$8,700 × 10% = $870.00 (taxation of the first income bracket)
$30,250 – $8,700 = $21,550.00 (amount in the second income bracket)
$21,550.00 × 15% = $3,232.50 (taxation of the amount in the second income bracket)
Total income tax is $870.00 + $3,232.50 = $4,102.50 (~10.26% effective tax)

So what would Romney’s tax rate cuts mean? If “across-the-board 20 percent cut in marginal rates” is accomplished by what I would consider a mathematically correct 20% reduction in tax rates, then the first income bracket tax rate goes from 10% to 8%, and the second income bracket tax rate falls from 15% to 12%. Then this citizen’s effective tax rate becomes 8.19%, and this individual saves $826.50.

Single taxpayer, no children, under 65 and not blind, taking standard deduction;

$40,000 gross income – $5,950 standard deduction – $3,800 personal exemption = $30,250 taxable income
$8,700 × 8% = $696.00 (taxation of the first income bracket)
$30,250 – $8,700 = $21,550.00 (amount in the second income bracket)
$21,550.00 × 12% = $2580.00 (taxation of the amount in the second income bracket)
Total income tax is $696.00 + $2580 = $3276 (~8.19% effective tax)

For this same taxpayer, if “across-the-board 20 percent cut in marginal rates” is done by subtraction, this taxpayer would actually pay no income tax at all because the tax rates were 10% and 15% to begin with–the effective tax rate is 0%! That may sound great in one way, but the government just lost $4102.50 in revenue that will have to be made up for elsewhere.

For a million dollars of income in the current 35% tax bracket, would the tax under Romney then become:

35% * 0.8 = 28%, new marginal rate of 28%?

or 35%-20%, new marginal rate of 15%?

That is the difference of a very wealthy person paying:

Current 35% marginal tax rate is $350,000 in taxes paid.
28% marginal tax rate would = $280,000 taxes paid
15% marginal tax rate would = $150,000 in taxes paid.

Either way this is a big tax cut, but I would like to know whether in this case the wealthy individual would pay $70,000 less, or $200,000 less!

And it all depends on understanding percentages, math that you probably bugged your sixth grade teacher about with eternal question, “When will we ever need to know this?” And the answer is, NOW!

***When I find the answer, I will share it here. I will reach out to the Romeny campaign and see if they can answer it for me. Even if I get the answer, I thought it was interesting and alarming that someone like me who is following the election very closely didn’t know the answer to this question.***