Inequality and taxes

While Dems and Repubs are fighting about how to manage the US's intentionally misnamed "fiscal cliff", we'll hear a lot about whether to tax the rich more. 

Repubs say the rich in the US pay more total taxes than the rich in most other OECD countries. 

They do. But not because their rates are higher. Their rates are lower than in most other OECD countries. 

The rich pay more in total taxes because they enjoy a much bigger slice of the US pie than the rich of most other OECD countries.

Here's the arithmetic (courtesy Brad DeLong). Suppose the top 10% pay taxes at a 40% rate, and everybody else pays 20%. If the top 10% have 20% of the country's income, their share of total taxes is  (20*40 / (20*40+80*20) = 33%. If they have 40% of the country's income, their share of total taxes is  (40*40 / (40*40+60*20) = 57%. Same tax rates, different total shares just because of more inequality.

Total share of taxes is a biased measure of the tax burden on the rich. You have to look at their rates. And on that score, Paul Krugman's argument from marginal utility stands: the rates should be much higher.