You'll have seen the heartfelt cries around the place: income inequality is back up to Gilded Age levels and thus we've got to do something about it all. That something often being said to be raising taxes on capital. There's two reasons why we almost certainly don't want to do that (quite apart from the question of whether we want to do anything).
The first is that we actually have a list of taxes in their order of desirablness, courtesy of the OECD. All taxes have a deadweight cost: economic activity, growth, that doesn't happen because of the existence of this or that tax. But not all taxes have equal deadweight costs. The lowest costs are associated with property taxes (yes, Hello to all you LVTers!) and the highest costs in lost growth are with corporate and capital taxes. So if we were simply looking to raise the money necessary to run government we would have capital taxation as low as possible and property as high as.
But there is another part of taxation: that social engineering stuff. Perhaps our lefty friends are right here, that we should tax capital, that stuff owned and held by the rich, more highly for social reasons?
Well, no, for there's been a huge underlying change in who earns what where since the Gilded Age. It was true back then (these are Canadian figures but much the same is true for US and UK figures) that the majority of top incomes came from earnings from capital and also that the majority of capital earnings went to top income peeps.
This absolutely isn't true at all today. By far the majority of top incomes comes from labour income these days. And the majority of capital income goes to those further down the income scale: in Canada, 50% of investment income went to those earning less than $60,000 a year. It just isn't true (as it arguably was a century ago) that those with high incomes are making it from the interest and dividends they receive from owning everything.
So increasing capital taxation just isn't going to reduce income inequality: for the top earners are getting their income from their labour, not our labour.
As so often we find our lefty friends fighting the battles of a century ago. As it isn't true that high incomes are a result of capital concentration then taxing the returns to capital isn't going to either reduce high incomes nor income inequality.