This is what the Republicans are talking about when they say something like 53% of households pay no taxes... because a family with $17K in income has a deduction of about $5700 per adult and $3750 per child... not to mention the possible other deductions such as the $1K per child tax credit, child care tax credits, credits for monies invested in retirement plans (such as 401Ks), etc. and then the fact that after all the deductions one then has a window of income which is below the threshold for taxation.
I could do the numbers, but without bothering I'd say that $17K for an individual is liable to lead to an effective tax rate of about 2-4%... with a (non-working) spouse... or children, you're looking at 0% (the 10% deductions from paychecks will ALL be refunded).
With Cain's plan NONE of it would be refunded (well, 10% of it wouldn't be collected... you'd have 9% rather than 10% deducted... but you would get NONE of it back). Further, under Cain's plan you would have an extra 9% federal sales tax added on top of your state/county/local sales tax (assuming you have state sales tax). This is a tax that would have no deductions and would have no exemptions... unless you buy used food, for instance (I'll leave the meaning of that to your imagination).
Meanwhile, the rich who are currently basking in the loophole wonderment of having to only pay 15% on capital gains and preferred dividends, will be able to get away with only 9%... and rather than the 15-35% marginal tax rates (applied to incomes of various levels, but increasing as the totals get higher)... they will just pay a straight 9% on all income...
And, meanwhile, corporations will pay 9% on everything, rather than rates that average about 35%...
As for the "hidden tax" that Cain suggests won't be adding to the costs of goods... what he hasn't admitted is that he's adding new "hidden taxes" that he might not even realize. Sure, the corporations will only be paying 9% income tax, and only 9% income tax for all the employees along the supply chain... and theoretically it MIGHT be possible that corporations would reduce prices as a result of the income tax expenses saved along the supply chain... but what isn't being mentioned is that Cain's plan doesn't include any accommodation for the writing-off of any of the other expenses of production or distribution. No wages expense deductions, no fuel deductions, no rent or depreciation of facilities or equipment deductions... and without these deductions, compared to which the tax expenses for generally under-paid employees along the distribution line pale and shrink to insignificance... the "hidden taxes" that Cain is expecting business will be "unburdened of" hardly compare to the one that business will become "reburdened of".
A 9% flat corporate tax rate that allows no deductions means prices WILL GO UP. A 9% corporate flat tax rate that allows deductions to continue as they are now means that the government will go bankrupt (sales tax revenue can't possibly make up for this loss)... and it also means that businesses will be allowed to continue writing off "stuff" even as individuals will be prohibited writing off "stuff"... unless Schedule C filers (sole proprietorships) are also allowed to write-off "stuff"... in which case the flat tax will be solely for laborers.
As a general rule, if you rent and work for wages, then the 9-9-9 plan will screw you or, if you're at the top edge of the bracket, it will not make things worse for you.