Getting it Wrong

An encounter with a Landsburg.

The New Yorker arrived today, leading off with this letter to the editor about income tax rates:

…The very rich pay at significantly lower rates, because most of their income consists not of compensation for services but of capital gains and dividends, which are capped at a fifteen per cent rate.

This is wrong, wrong, wrong, wrong, wrong, wrong, wrong, and you can’t begin to think clearly about tax policy if you don’t understand why. Even if capital gains taxes were capped at one percent, income subject to those taxes would be taxed at a higher rate than straight compensation. That’s because capital gains taxes (like all other taxes on capital income) are surtaxes, assessed over and above the tax on compensation.

It always pays to think through stylized examples. Alice and Bob each work a day and earn a dollar. Alice spends her dollar right away. Bob invests his dollar, waits for it to double, and then spends the resulting two dollars. Let’s see how the tax code affects them.


First add a wage tax. Alice and Bob each work a day, earn a dollar, pay 50 cents tax and have 50 cents left over. Alice spends her fifty cents right away. Bob invests his fifty cents, waits for it to double, and then spends the resulting one dollar.

What does the wage tax cost Alice? Answer: 50% of her consumption (which is down from a dollar to fifty cents). What does it cost Bob? Answer: 50% of his consumption (which is down from two dollars to one dollar). In the absence of a capital gains tax, Alice and Bob are both being taxed at the same rate.

Now add a 10% capital gains tax. Alice and Bob each work a day, earn a dollar, pay 50 cents tax and have 50 cents left over. Alice spends her fifty cents right away. Bob invests his fifty cents, waits for it to double, pays a 5 cent capital gains tax, and is left with 95 cents to spend.

What does the tax code cost Alice? Answer: 50% of her consumption (which is down from a dollar to fifty cents). What does the tax code cost Bob? Answer: 52.5% of his consumption (which is down from two dollars to 95 cents).

So there you have it: A 50% wage tax, together with a 10% capital gains tax, is equivalent to a 52.5% tax on Bob’s income. In fact, you could have achieved exactly the same result by taxing Bob at a 52.5% rate in the first place: He earns a dollar, you take 52.5% of it, he invests the remaining 47.5 cents, waits for it to double, and spends the resulting 95 cents.

Why is this so terribly hard for so many intelligent people to understand? Here, I think, is why. They see a guy with a million dollar capital gain on his investment, and they forget that in the absence of wage taxes, he’d have invested twice as much and earned a two million dollar capital gain. In that sense, the capital gain is taxed in advance.

Let's review the bidding Alice makes $1, pays $0.50 in taxes and spends the rest. Bob makes $1 in wages and $0.50 in capital gains and pays $0.50 in income taxes and $0.05 in capital gains taxes. That, says Landsburg, is 52.5% of his consumption. Huh? #1 His consumption is $0.95, his total tax bill was $0.55 = 57.9% Not a huge error, but the logic from which it was derived, involving $2 mythical unrelated to the problem is weird. Now lets look at Alice. She consumed $0.50 and paid $0.50 in income taxes, (Huh? #2) so she paid taxes equal to 100% of her consumption, not 50% as Landsburg asserts.

Now I'm entirely too old a man to spend my time correcting the elementary arithmetic and logic errors of some economics prof, but I do feel some obligation to clarify the thinking of the idiots who read him - and yes, I do include myself in the description.

Some further words from the Master:

There’s plenty of room for reasoned debate about who should or should not be paying higher tax rates. But there’s no room for reasoned debate about the actual impact of the tax code. This is a matter of arithmetic: Anyone who pays taxes on capital income is effectively paying at a higher total tax rate than anyone who doesn’t. I’ve explained this before. Don’t make me have to explain it again!

Ok, there is a magic world interpretation in which the above reasoning can sort of make sense - that's a world in which investment automatically generates free money. If Bob had all of his dollar to put in the magic doubler, and Alice had had all of hers to spend, then she would have gained an extra 50 cents and Bob would have gained an extra dollar. It's the presence of free but delayed money that makes the machine work the way Landsburg would want it to.

Suppose Bob's investment is the lottery, and he wins $10. Then, with 10% capital gains tax, he has pays another buck in taxes, for a total tax of $1.50. To use SL math, he winds up losing not $1.50 but $11.50, because Landsberg math assumes that the next lottery ticket he bought would also be a winner. So taxes cost him, in Landoworld, $11.50, even though he only paid $1.50. Once you start using play money, Landsburg style, you can make the effective cost of capital gains taxes anything you like.