Monday, March 07, 2005

Reductio ad Absurdum

One way of doing a mathematical proof is to assume the opposite of what you're trying to prove. If you can show that it leads to a logical contradiction, then you've proven the original statement. If you can't show a contradiction, then the statement is false. It's called reductio ad absurdum; reduce to an absurdity.

This isn't done much in political argument. Usually, you try to show that some action will lead to Horrible Consequences. However, you could show that doing the exact opposite of the action will not result in HC.

What brought this up was the suggestion of replacing the income tax with a "consumption tax", ie a national sales tax. Its proponents say that we could replace the income tax with a sales tax of 20% - 24%. The numbers are bogus, of course; the "real" numbers range from 45% - 100%, depending on assumptions. The claimed advantage is that it would shift money from consumption to investment. Now, this seems odd to me; on one hand, you have to sell what you produce, and on the other hand, there's no shortage of investment capital floating around.

The big disadvantage, of course, is that if you're poor, you're going to spend all your money and invest very little if any. If you're rich, you're going to invest a lot and pay a much lower percentage of your income in tax. That's why sales taxes are the prime example of "regressive taxation"; taxes that hit the poor hardest.

The proponents of the "consumption tax" say no problem, we'll just give a tax rebate to poor people. This has two gaping holes: (1) you have an enormous job in keeping track of what everybody earns and (2) poor people don't have any financial reserves (duh!). Saying "you'll get the money back next April" doesn't help a bit right now.

OK, it's not a good idea. But now let's try reductio. Let's exempt consumption from taxes and tax only investments. What happens now?

Well, poor people don't pay any tax. Rich people pay a one- time tax on money they invest; if they take it out and spend it, they don't pay tax. It'll stimulate the economy; people will buy more stuff. Instead of every retail establishment in the country keeping track of the tax, it'll be collected by banks, stockbrokers, and so forth, who have to do a boatload of paperwork anyway. Interest? Capital gains? Details, details (:-).

The point is, not only is it not absurd, it actually looks better than the original idea! Poor pay low taxes, check. Rich pay higher taxes, check. Stimulates consumption, check. Easy to collect, check. Minimum paperwork, check. No funky rebates, check. "Supply side stimulus"? No, but I haven't seen a real economist who believes in "supply side economics" anyway.

Or, we could compromise. Ignore both and just tax income.

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