In othe words, the reason we care about inequality is that it reduces the happiness achievable from a given amount of income. How much depends upon the happiness/income relationship. Does the marginal utility of income fall rapidly? Or is the happiness from the 100,000th dollar almost as great as the happiness from the 100th?
I think that this question has an obvious answer. Anybody who has lived in poverty can immediately answer that just a few dollars for food can make a huge difference. But how many wealthy executives would feel happy all day over a $3 bonus?
Of course this curve is non-linear. The arguments for inequality that are interesting seem to involve: 1) Whether a class of wealthy investors can stimulate the economy through free market investment and 2) Whether differences in economic outcomes is needed to incentive unpleasant but necessary labor. Now, the later is unlikely to explain Bill Gates or Warren Buffet (are their jobs really so vile?). SO the former really has to do a lot of heavy lifting . . . and is likely overstated.
But an assumption that income effects are perfectly linear seems so contrary to experience that I presume that this post is to stimulate thinking!