Tony Blair famously said:
“[It’s] not that I don’t care about the gap [between high and low incomes], so much as I don’t care if there are people who earn a lot of money. They’re not my concern. I do care about people who are without opportunity, disadvantaged and poor.”
Most people, including the Labour government, interpreted that as focusing on poverty rather than inequality. For an excelllent discussion of historic trends in inequality and how they were influenced, among other things, by poverty reduction programmes pushed by Labour (as well as how that may unwind in the near future) see this excellent discussion by Rick.
I recently saw a very clear defence of the position that poverty mattered more than inequality from Miles Kimball. His argument comes from surveys that quantify a basic principle of economics, which is diminishing marginal utility. He quotes results which suggest that a dollar of income means an awful lot more to someone earning half the average wage than someone who earns double the average wage. He suggests the results come close to validating the second principle of justice suggested by John Rawls. To put the idea at its most simple, we should not worry about the rich too much because their extra money buys them very little extra happiness, but instead focus on reducing poverty.
Now of course this point is irrelevant if we are talking about reducing poverty by taxing the rich. The rich are a very good source of money, because they will not miss it very much. The importance comes if we compare two societies. One has no poverty, but a significant number of very rich people. The other has no rich people, but still has poverty. Miles’s argument is that we should prefer the society with no poverty to the one with no super-rich. In a static sense I think that is right, but I have dynamic concerns that I will now come to.
Right at the start of Miles’s discussion is an interesting paragraph:
“Before going on, let me concede first of all that the amount of wealth held by the ultra-rich is truly astonishing, and that making sure that the ultra-rich do not convert their wealth into total control of our political system is important. Documenting and studying in detail all of the ways in which the ultra-rich influence politics is crucial. But short of the ultra-rich subverting our political system, the focus of our concern about inequality should be how well we take care of the poor; whether money needed to help the poor comes from middle-income families or the rich is an important issue, but still of secondary importance to how well we take care of the poor.”
I want to explore a point that Miles does not pursue. If money matters so little to the very rich, why would they want to become ultra-rich to an astonishing degree, and go on to try and control the political system to ensure they get even more? The answer comes from exactly the same logic as Miles uses. If £1000 means nothing to you because you are very rich, if opportunities arise you put effort into making that £1000 into £10,000 or £100,000. The fact that the ultra-rich have wealth that is truly astonishing may not be an accident, but may be a result of exactly the same principle that Miles explores: diminishing marginal utility. The rich are no different from everyone else in wanting more utility, except for them it requires huge amounts of money to get it. 
To see why this can matter, consider an argument put forward by Piketty, Saez and Stantcheva that I discussed here. Why has pre-tax income for the 1% risen so much in the two countries, the UK and US, that in the 1980s saw large reductions in top income tax rates? The argument these authors put forward is that with punitive tax rates, there was little incentive for CEOs or finance high-flyers to use their monopoly power to extract rent (take profits away) from their firms. It would only gain you a few thousands after tax, which as they were already well paid would not increase their utility very much. However once top tax rates were cut, it now became worthwhile for these individuals to put effort into rent extraction.
As I discussed here, the bonus culture may be the means of rent extraction that was incentivised by cutting top tax rates. If you want to see the kind of thing I have in mind in action, read this article by Ben Chu on what happened to Theresa May’s wish to see annually binding votes by shareholders on executive pay. That kind of lobbying takes effort. It worked, and as a result top executives at the builder Crest Nicholson can ignore a shareholder vote against changes to their compensation rules. No wonder executive pay seems to rise even when a company’s fortunes turn sour.
So it seems to me that I could take the same basic principle that Miles explores and write a very different conclusion. Once we allow those at the top the opportunity to earn very high incomes, and the only way these individuals can see to get additional utility is to embark on rent seeking, we can at the very least divert their effort from socially enhancing activities (i.e improving the company). When those efforts extend to influencing the political system, we are in serious trouble. These activities may culminate in taking over the political system, which after all is what has happened in the US, with potentially disastrous consequences. For that reason alone, inequality matters as well as poverty.
 Of course status linked to competitive consumption is also important.