Elizabeth Warren's 68.7 Percent Tax on Capital Income

By David Henderson.

What about a 3% tax on wealth? If you have $100 and earn 3% on some investment, at the end of the year you have $103. Now you have to pay a wealth tax of 3%. The amount you pay is .03*103 = $3.09. Now divide 3.09/3 and you get 1.03. 3.09 is 103% of 3. A tax rate of 103% on income.

What about a 2% tax on wealth? If you have $100 and earn 3% on some investment, at the end of the year you have $103. Now you have to pay a wealth tax of 2%. The amount you pay is .02*103 = $2.06. Now divide 2.06/3 and you get .687. 2.06 is 68.7% of 3. A tax rate of 68.7% on income.

"Columbia University public finance economist Wojciech Kopczuk, who is also editor-in-chief of the Journal of Public Economics, arguably the top journal in public finance, has a first-rate critique of a proposal by Emmanuel Saez and Gabriel Zucman for taxing wealth. Saez and Zucman are professors of economics at University of California, Berkeley.

I’m working my way through the paper and found one statement up front that non-economist readers might find implausible but that is correct. Kopczuk writes:

An individual with this year’s stock of wealth W earning the return of r could be next year (assuming away any consumption) subject to a tax that is imposed on either (1+r)W or rW — a wealth or a capital income tax. It is immediate to see that absent any other considerations, a tax of t on wealth is revenue-equivalent to a tax of τ=(1+r)t/r imposed on capital income rW. This links the two bases and provides a straightforward comparison of the burden that a wealth tax would impose on capital income. If you consider a safe rate of return of, say, 3%, a 3% wealth tax is a 103% tax on the corresponding capital income and a 6% tax rate is a 206% tax. Obviously, even though wealth tax rates appear nominally small, they are in fact very heavy taxes on the corresponding streams of income.

Really? A 3% tax on wealth amounts to a 103% tax on capital income? Yes, it really does. It probably isn’t “immediate to see,” as Kopczuk writes. But it’s true.

My point here is to make his point clear by filling in the missing math.

If someone starts the year with wealth W and earns a rate of return of r on that wealth, at the end of the year she will have a wealth of (1+r)W. [Why do I say “she?” Because the tax that Saez, Zucman, and Senator Warren advocate is on the wealthy and the wealthy are disproportionately old, and the old are disproportionately female.]

So the tax will be t(1+r)W, where t is the tax rate on wealth.
But t(1+r)W = t(1/r +1)rW.

So the tax rate of t on W amounts to a tax rate of t(1/r +1) on rW
But notice that rW is the return on capital. QED.

Now plug in some plausible numbers.

Kopczuk starts with a 3% tax on wealth.

So the tax rate on income from wealth = 0.03(1/0.03 + 1) = 1 + 0.03 = 1.03. So indeed a 3% tax on wealth is a 103% tax on the income from wealth.

Start with Elizabeth Warren’s 2% tax on wealth. The tax rate on income from wealth, therefore, = 0.02(1/0.03 +1) = 0.687. That amounts to a 68.7 percent tax on the income from wealth."