Mankiw's Head Tax

I didn't take intro economics in college, but thanks to the distributed intelligence of the internet I can gain pearls of insight into what I missed by reading Greg Mankiw's blog on which we see the advice he would give to a politician interested in curbing inequality:

The tax system is probably the best vehicle to accomplish the Dems' goal. One possibility would be to reduce the payroll tax rate and to make up the lost revenue by increasing, or perhaps even eliminating, the cap on taxable payroll. That would benefit, approximately, the bottom 90 percent of the income distribution.

Fair enough. He also remarks that "This policy change would, of course, have an efficiency cost." How so? "By raising taxes on taxpayers who already face the highest tax rates, the deadweight losses of the tax system would surely rise." In other words, to maximize equality, we should make taxes on the wealthiest people as high as possible. By contrast, to maximize efficiency, we should make the highest tax rate as low as possible. He doesn't spell out the reasoning behind that view, but presumably that's why I should have taken the class. He also says earlier in the post that free-market economists like him typically don't care about inequality. He doesn't spell out the reasoning behind that view either, but my guess is it's because he thinks maximizing efficiency is the most important thing.

I think the implication of the combination of these views is that we should just divide federal spending (about $2.8 trillion) by the population (about 300 million) and then charge every person a $9,333 (or thereabouts) head tax. Is that right?