## 04 March 2009

### A fool and his money are soon parted

Did you know that there are people who think that by reducing their income from over \$250,000 to under \$250,000, they can take home more money? For those of you who aren't aware of this, President Obama is planning to increase taxes on families earning more than \$250,000 per year.

Of course, the way the US tax code is set up, the amount of tax you pay as a function of your taxable income is continuous, monotone increasing, and Lipschitz with parameter 1. That is, say that T(x) is the tax due if your taxable income is x. Let y > x. Then T(y) > T(x), and T(y) - T(x) < y - x. As you may note, you can derive from the second of these that

y - T(y) > x - T(x)

which tells us that if you make more money, you get to keep more of your money.

Note that T is actually not differentiable, because it's piecewise linear. Your "tax bracket" is in fact the amount of tax you pay on the last dollar of your income; that is, it's T'(x) where x is your income.

I'm not saying that there are no situations where this sort of thing might make sense. (The tax code is complicated.) But it's certainly not as common as these people would have you believe.

Original article from ABC News; I followed a link from The New York Times via The New Republic.

Jay said...

The only way in which the above really makes any sense is if he's referring to some kind of significant deduction that becomes unavailable at a certain income threshold, which would create an effective gap.

The quoted ranting certainly does imply that this is what he's talking about. But, since he claims to be an attorney, it's possible that he actually knows what's going on and is just being purposely sensationalistic.

Jay said...

certainly doesn't*, rather

Panos Ipeirotis said...

This is a general problem with the progressive tax rates. Almost nobody understands that you get taxed the higher rate only for the income that exceeds the threshold. And I am talking about people with university degrees and graduate education. So, I would not be surprised if more than 80% of the population believes that your "tax bracket" is applied to the total income.

John said...

It matters what you have to do in order to increase your income over \$250,000. If you are making \$250,000 in salary and your boss offers you a raise, then take it! But if you're contemplating an investment and computing your expected gain, you have to take the tax bracket into account because you keep less of the profit if your investment pays off.

What was a winning bet before the tax increase may become a losing bet after the tax increase, in which case the rational thing to do is not take the bet, i.e. to become more conservative in your investments.

Joseph said...

At high tax levels, it might make sense to take income in the form of expense accounts or more leisure time instead of salary. We might see revivals of the three-martini lunch or upper-middle-class people mowing their own lawns.

cwitty said...

The topic reminds me of http://dbaron.org/views/taxes-2007.html, which plots income vs. marginal income tax rates (that is, the derivative of T) under one particular simple set of assumptions. It's amazingly complicated.

(While T is not differentiable, the derivative is defined almost everywhere, which is enough for an interesting plot.)

CarlBrannen said...

Business takes effort. One typically has the choice of various fruit to pick. One first picks the low hanging fruit, the easy money. One then goes on to pick more difficult fruit only up to the point that it is personally worth one's time.

If the president taxes more of the stuff you earn beyond \$250K, there's less motivation to make the effort to get towards the top end of the tree. People cutting their income back to under \$250K aren't necessarily stupid; they may also be doing other, more rewarding, things with their time.

Another thing that should always be remembered is that rich people can afford good accountants. These can move accounts around so as to reduce taxes. When tax rates are changed, accountants respond with modification of accounting choices.

Veky said...

I think the answer lies here:

"Why kill yourself working if you're going to give it all away to people who aren't working as hard?"

His problem isn't he'll have less money after Obama's tax reform. His problem is poorer people will have more. :-]

unapologetic said...

The point is, ladies and gentlemen, that greed, for lack of a better word, is good. Greed is right. Greed works. Greed clarifies, cuts through, and captures the essence of the evolutionary spirit. Greed, in all of its forms -- greed for life, for money, for love, knowledge -- has marked the upward surge of mankind, and greed -- you mark my words -- will not only save Teldar Paper but that other malfunctioning corporation called the USA. Thank you.

-- Gordon Gekko, Wall Street

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