• Rule 1: Paul Krugman is right.
• Rule 2: If you think Paul Krugman is wrong, consult Rule 1:

Paul Krugman: Some Misleading Geometry on Corporate Taxes (Wonkish): "There’s a fairly simple geometric way to see where the optimistic view that cutting corporate taxes is great for wages comes from...

...[Then] it becomes a lot easier to ask “What’s wrong with this picture?” (Answer: a lot).... Envision a small open economy with a fixed labor force (because labor supply isn’t of the essence here) that can import from or export capital to the rest of the world.... Saving... also isn’t of the essence: the stock of capital, we’ll assume, changes only through capital inflows or outflows.... Let’s... assume... factors of production are paid their marginal products. Then we can represent the economy with Figure 1, which has the stock of capital [per worker] on the horizontal axis and the rate of return on capital on the vertical axis. The curve MPK is the marginal product of capital, diminishing in the quantity of capital because of the fixed labor force. The area under MPK – the integral of the marginal products of successive units of capital – is the economy’s real GDP, its total output.... The economy faces a given world rate of return r*. However, the government imposes a profits tax at a rate t, so that to achieve a post-tax return r* domestic capital must earn r*/(1-t).... That... determines the size of the domestic capital stock.... In the initial equilibrium real output is a+b+d. Of this, d is the after-tax return to capital, b is profit taxes, and a – the rest – is wages.

Now imagine eliminating the profits tax (we can also do a small cut, but that’s harder and this is already sufficiently wonky). In equilibrium, the capital stock rises by ∆K, and... [GNP] to a+b+c+d... (e is returns to foreign capital).... Profit taxes disappear: that’s a revenue loss of b. But wages rise to a+b+c, a gain of b+c....

What’s wrong with this picture?.... Four reasons.... First, a lot of what we tax with the corporate profits tax is... monopoly profits and other kinds of rents. There is no reason to believe that these rents would be bid down by capital inflows.... Second, capital mobility is far from perfect. Third, the US isn’t a small open economy.... Finally... what we’re showing here is long-run equilibrium... [after] capital inflows take place as the counterpart of trade deficits, which in turn have to be created by a temporarily overvalued real exchange rate. And the kind of adjustment we’re talking about here would require moving a lot of capital, meaning very big trade deficits, meaning a strongly overvalued dollar, which would itself be a deterrent to capital inflows. So we’re talking about a slow process.... Long-run analysis is a very poor guide to the incidence of corporate taxes in any politically or policy-relevant time horizon...

Paul is, of course, 100% correct.

There is a footnote with respect to Mankiw to be written here...

Suppose that you cut the corporate tax rate in this model from its initial level t by an amount Δt. The reduction in revenue collected is then:

${k}\left(\frac{r}{1-t}\right){t} - {k}{\left(\frac{r}{1-t+Δt}\right)}{\left(t-Δt\right)}$

${\frac{krΔt}{(1-t)(1-t+Δt)}}$

By contrast, Mankiw miscalculates the "static" reduction in revenue as simply:

${\frac{krΔt}{(1-t)}}$

That is where the factor 1/(1-t) that puzzles him—"dw/dx = 1/(1 - t). I must confess that I am amazed at how simply this turns out. In particular, I do not have much intuition for why, for example, the answer does not depend on the production function"—comes from.

And do note that Alan Auerbach is right when he writes:

this result... is a combination of (1) the standard result that in a small open economy labor bears 100% of a small capital income tax...

and wrong when he writes:

the burden of a tax increase exceeds revenue collection due to the first-order deadweight loss...

The burden of a tax increase exceeds revenue collection due to the first-order deadweight loss, but Mankiw is claiming that even for an infinitesimal change in the tax rate—for which the deadweight loss term is infinitesimal relative to the distribution term—the ratio of revenue lost to wages gained is 1/(1-t). And that is simply a miscalculation of what the revenue loss is.