Innumeracy and the Fair Tax

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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The Fair Tax is a proposal popular on many conservative and libertarian Web sites, arguing for replacing the income tax with a flat sales tax of 23 per cent. The problem of the regressiveness of sales taxes would be eliminated by paying every taxpayer a monthly rebate.

The technical details of whether or not this is a good idea are outside the scope of my expertise. It's hard not to cheer for dismantling the present tax code; equally hard not to suspect tax evaders will find a raft of ways to evade the new tax, ways that will then require patches as complex as the present system.

But one aspect of the debate raises a red flag with me.

Many critics of the proposal have pointed out that the tax rate will be closer to 30 per cent because the 23 per cent refers to the rate after prices rise to accommodate the new tax. Defenders of the "fair tax" counter that existing income taxes are calculated on the basis of your before tax income, so an "inclusive" calculation is a fair comparison. Both calculations include the amount paid in taxes in the total.

Sorry, that's just not how percentages work. In describing percent changes, the change is always described with respect to the original amount. A tax of $30 on a $100 purchase is a 30% tax. It is not a 23% tax on a total of $130. The fact that prices rise from $100 to $130 and the tax comes out of the $130 doesn't change the fact that you're paying $30 more. If you work 100 hours to buy a big flat screen TV now, you will work 130 hours under the new system. You will work 30 hours longer, not 23. If you get a pay raise of $30 added to a $100 base, it's a 30% improvement in your present standard of living, not a mere 23%.

Likewise, if we had 200 crimes in a city last year, and 100 this year, it's a 50% decrease (100/200). It is not a 100% decrease (100/100). A sale that cuts prices from $50 to $40 is a 20% cut, not a 25% cut. Thus, increases are exclusive and decreases are inclusive, because you're interested in how things change relative to your present situation. Decreases are inclusive because you have the whole amount now, and are going to lose some. Increases are exclusive because you don't have the extra amount yet.

The whole inclusive/exclusive debate is a red herring. If you pay a 30% sales tax on $100, you pay $130, or $30 more. If you pay a 30% income tax on $100, you pay $30. In both cases the percentage indicates exactly what you pay. When it's calculated correctly.

This has nothing to do with the merits of flat versus graduated taxes. It's basic numeracy. Saying you get to choose which way to calculate percentages is like saying you get to decide whether or not to carry numbers when adding. There's a right way and a wrong way to do it. The right way gives you the right answer and the wrong way gives you the wrong answer.

The irony is that many of the folks arguing for the after tax calculation complain loudly about the quality of education in public schools. I don't know where them folks was educated, but it looks like they didn't learn math none too good.


The fatal flaw in the Fair Tax proposal has nothing to do with the technicalities of how much sales tax would be needed to replace the revenue from the present tax system. The legislation to create the fair tax system even requires the government to pay tax on its purchases, effectively taxing itself, but education expenses are exempt. So right off the bat, there's an exemption built into the system. Soon there will be others. Charities will surely not be far behind, and home purchases. Any commodity manufactured in some Congressman's district will be a prime candidate for exemptions. Is some business, say shipbuilding, in need of help? Cut them an exemption. Same pork, new name.

There's no inherent reason the income tax has to be complex. How much did you make? Send x per cent of that in. The very first income tax form used in the U.S. consisted of one page and had 13 pages of instructions. With minor adjustments, it could be used today. But very quickly, this, that, and the other interest groups moved in to argue that their income should be taxed differently or that taxpayers should be allowed to exclude payments to their particular interest.

Without legislation, or preferably a Constitutional amendment, mandating that taxes be uniform and applied equally without exception, the Fair Tax system will end up just as riddled with exceptions and inequities as the present system. Actually, the only thing it would take is for the Supreme Court to rule that unequal taxation violates the Fourteenth Amendment. That wouldn't be anywhere near as radical as some other rulings the Court has made invoking the Fourteenth Amendment, and would be a lot more beneficial.

The most obvious way to evade the Fair Tax would be to sell something and keep the tax. So there has to be some mechanism for verifying that people are reporting their entire sales revenue. There will have to be a reporting system, and auditing. The IRS has no reason to fear for job security.

Puff, the Magic Dragon

When Neal Boortz promised to take on a lengthy criticism of the FairTax posted on the conservative site Townhall.com, I was really looking forward to a detailed response. What we actually got (November 27, 2007) can be summarized as follows:

I gather that the principal justification for calculating taxes after the fact is the assumption that the new tax will be offset by a reduction in prices due to the end of all the embedded taxes now included in every purchase. That is, the farmer pays income taxes, but he will no longer have to, so he'll sell his produce for less, the trucker will no longer pay income taxes so he'll work for less, the processor will charge less because he's not paying income taxes, and the supermarket will charge less because they don't pay income taxes. This from a guy who thinks global warming is a figment of the imagination. Can somebody offer me the slightest evidence that the people all along the chain won't simply keep their tax savings? Wouldn't you?


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Created 12 March 2007;  Last Update 02 June, 2010

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