My earlier post Thursday on Herman Cain’s 9-9-9 plan was a bit theoretical. So I asked Edward Kleinbard, a tax law professor at the University of Southern California, to walk me through the tax burden for a typical family of four with an income of $50,000 in the current system and under Herman Cain’s plan. Before we get to the details, here’s the bottom line: Cain’s plan would increase the family’s tax bill by thousands of dollars.

Republican Herman Cain has surged in the polls since his appearance Tuesday at a Washington Post-Bloomberg presidential primary debate. (Evan Vucci/AP)

When it comes time to fill out their federal income taxes, they take the standard deduction ($11,400), plus four personal exemptions ($3,650 each), plus two child-tax credits ($1,000 each), which leaves them paying $766 in federal-income taxes.

Total tax bill? $8,416.

Cain’s plan, by contrast, acts like a 27 percent payroll tax with basically no exemptions. To understand why that is, read my earlier post, or, if you really want the details, see Kleinbard’s full analysis. So here, too, the calculation is fairly straightforward: $50,000 x 27% = $13,500.

And that leaves us with simple subtraction. $13,500 - $8,416 = $5,084. That’s how much more a family of four with $50,000 in income and a very simple tax return would pay under Cain’s 9-9-9 plan.

I want to stress that this is a simplified analysis. We can make it more complicated, of course. Most economists would argue that the employer is paying the family’s payroll tax out of a separate pot of money, so they’re really making a bit more than $50,000. That would increase the tax hike in Cain’s plan if we took it into account. But you could also argue that Cain’s consumption taxes are applying to $45,500 in income, as the worker won’t spend the portion that goes to the nine percent income tax. That would lessen the tax hike in Cain’s plan.*

That said, let’s look at the other side of this, too. Take a family of four with $1,000,000 in income. I wanted to stop bothering Kleinbard at this point, so I just ran these numbers myself. Assume again that the family files a very simple tax return: standard deduction, four exemptions. According to Turbotax, they would owe $311,208 under the current system.

Cain’s plan is a bit tougher to apply to them. Many of his taxes are consumption-based, and it’s likely that this family would hold on to much of their income in any given year. But as the tax professors will tell you, all income is eventually spent, so all the income they make this year will eventually be taxed under the 9-9-9 plan.

If you grant that premise, then the calculation is no harder than it is for the family of more modest means: $1,000,000 X 27% = $270,000. That means Cain’s plan is, for a household making $1,000,000, a tax cut of $41,208 (which I got by subtracting $311,208 from $270,000).

You can complicate this analysis, too. In the current tax system, a family making $1,000,000 would not take the standard deduction. They would likely hire an accountant and do some fancy footwork and end up paying a lower tax rate than I’ve assumed here, which would mean that the difference between Cain’s plan and the current system would, for the richer family, narrow a bit.

But this simplified calculation gets at the basic reality of Cain’s plan: He’s got what he says is a revenue-neutral tax proposal, so we can assume that it raises the same amount of money as the current system, but he replaces progressive taxes with regressive taxes. So the poor and middle class will face a big tax hike -- $50,000 is actually slightly above the median household income in America -- and the rich will get a huge tax cut.

*Update: Kleinbard got in touch to assure me his estimate accounted for the fact that some income would go to personal income taxes and thus would not be taxed by the two consumption taxes. He even provide the calculations. Here’s Kleinbard:

As an aside, you wrote:

“But you could also argue that Cain’s consumption taxes are applying to $45,500 in income, as the worker won’t spend the portion that goes to the nine percent income tax. That would lessen the tax hike in Cain’s plan.”

Actually, my numbers took that into account. My 27 percent (technically, 27.08 percent, I think) was not just 9 x 3! I converted everything into a wage-equivalent tax base.

If you want to get fancy, you can look at the Cain tax plan this way, where 100 is the starting corporate income before corporate tax, and T is his tax rate (9% in his actual proposal), expressed as a percentage:

CT = 100X

PT = X (100 - 100X)

= 100X - 100XX [I don’t know how to do superscripts in Outlook]

ST = X [100 - 100X - (100X - 100XX)]

=X [100 - 200X + 100XX]

= 100X - 200XX + 100XXX

Which in turn means that total tax = CT + PT + ST =

100X + 100X-100XX + 100X-200XX+100XXX

= 300X - 300XX + 100XXX

So for example when applied to a tax rate of 9 percent, total tax =

300(0.09) - 300 (0.09x0.09) + 100 (0.09 x 0.09 x 0.09)

= 27 – 2.43 + 0.07

= 24.64

And finally, to put total tax bill on a payroll tax equivalent basis, we have to compare it, not to 100 (the employer’s pre CT income), but to the wages paid the employee, which are: 100 – 100X

So the payroll tax equivalent rate (dividing both sides by 100 for clarity and restating the numerator) =

(3X - 3XX + XXX) ÷ (1 – X)

Which in his actual plan works out to 24.64/91 = 27.08%