There's one point Greg Clark makes in The Son Also Rises which strikes me as plain wrong. It's this:
The world is a much fairer place than we intuit. Innate talent, not inherited privilege, is the main source of economic success (p14).
The problem here isn't merely that, as Rawls said, talent is arbitrary from a moral point of view and so should not be the basis for unequal incomes. (In fairness, Clark endorses this view). Instead, it's that a strong correlation between talent - innate or not - and economic success is no indicator of a just society.
Imagine a country run by a dictator, but one who is smart enough to see that it takes brains to run a centralized economy. He therefore selects apparatchiks according to rigorous tests of ability, and rewards them with wealth and power. Such a society will have a high correlation between talent and economic success. (It might also have a high correlation between soft skills and success, to the extent that success in a bureaucracy requires political and networking skills.)
Such societies are not purely imaginary. I'm thinking of Imperial China or the Soviet Union; it took intellect and skill to become commissar of tractor production.
However, I don't think Professor Clark would regard such societies as fair ones. And nor should he.
What's more, these societies would be unfair, whether the talented came from elite families or poor ones. In this sense, I agree with Matthew for a different reason; social mobility is no indicator whatsoever of a fair society.
Now, libertarians will object here that my argument is irrelevant to modern-day western societies because these are not centrally-planned dictatorships.
This, though, raises a paradox for libertarians who'd like to be meritocrats - though, as Hayek pointed out, you can't be both. It's that a just society for them is one in which people are free to give others whatever they choose. In such a society, though, we might well choose to reward people not because of their ability but for arbitrary whims. In this sense, the mark of a fair society is not that it rewards ability but that it does not do so. From a libertarian point of view, the evidence that our economies are fair is not that CEOs are paid millions - such people would probably succeed in centrally planned dictatorships too. It is instead that the likes of Kim Kardashian are well-paid.