OK, folks, this is basically to scratch my own intellectual itch — later this week Senate Republicans either will or won’t enact the biggest tax scam in history, and analysis won’t make any difference. But inspired by the Furman-Summers beatdown of Republican economists lending cover to disgusting dishonesty by their political masters, I found myself looking for a simple analytical representation of the effects of cutting corporate taxes. By simple, of course, I mean for economists: for anyone else this may as well have been written in cuneiform. You have been warned.

OK, so the naive, super-optimistic version of what corporate tax cuts will do — roughly speaking the Tax Foundation version, without the incompetence — treats America as a small, perfectly open economy that faces an infinite, perfectly elastic supply of foreign capital at some given rate of return. It also ignores leprechaun economics — the potentially large difference between GDP and national income when foreigners own a lot of your capital stock. Meanwhile, America is neither small nor perfectly open, so that the rate of return to foreigners depends on how much capital we suck in — and since around a third of corporate profits already go to foreigners, they’re likely to collect a significant fraction of the gains from a tax cut.

So, can we put all of that in a simple framework? I think we can. In fact, just one diagram, although for those not raised on traditional trade geometry it may look a bit intricate, But it’s all very simple, believe me!

Starting point: we can think of a downward-sloping demand for capital, reflecting its marginal product. We can also think of an upward-sloping supply of capital, with the upward slope reflecting both the size of the US — we’re probably around half of the world’s capital market not subject to capital controls — and the imperfect nature of capital mobility, even now.

We can think of corporate taxes as putting a wedge between the rate of return to capital before taxes — which is assumed equal to its marginal product — and the after-tax return received by investors. So it’s kind of like an excise tax on capital, and looks like Figure 1:

Photo

Now imagine cutting the corporate tax rate. This narrows the wedge, as shown in Figure 2:

Photo

OK, a bunch of things happen.

First of all, the pre-tax return on capital falls as the capital stock rises. That reduced rate of return shows up in increased wages. So that part, shown as the green rectangle at the top, is the part of the tax cut that’s passed through to increased wages. How big that gain is depends on the relative elasticity of capital supply and capital demand.

As I’ve been arguing for a while, in the short run the supply of capital is likely to be pretty inelastic, because capital inflows have to take place via a strong dollar that in itself deters investment. So in the short run not much of the tax cut flows to wages. In the long run workers will get more of it, but the long run is likely to be measured in decades, not years.

Meanwhile, owners of capital gain. However, some — around a third — of these owners are foreigners, not U.S. residents, so about a third of the rise in after-tax returns — the red rectangle in Figure 2 — represents a welfare loss to the United States.

On the other hand — on the third hand? — more capital will come in, and this capital will pay taxes, representing an offsetting overall welfare gain — the yellow rectangle. Overall US national income can go either way; semi-realistic calculations suggest that it’s close to a wash.

So who benefits from this tax cut? There’s some wage gain, but also some revenue loss; if the revenue loss leads to cuts in programs that benefit workers (as it would), workers may well be worse off. Owners of capital, both foreign and domestic, gain.

Taken as a whole, this isn’t a slam-dunk case against corporate tax cuts: if the initial rates are very high and capital inflows sufficiently elastic, they could be a good idea. But they hardly look like the magic elixir Republicans are claiming.