The reason it is an issue is because you can't just increase the cost of living while not increasing the wages of middle and lower end income earners. Now I'm not suggesting that we make Wal-Mart or other entry level jobs pay living wages but increasing the wages is definitely something to do in order to help. Now higher end wage earners won't be affected by some cost of living changes depending on how much they make and if they get more or less depending on how the social order changes.
But it's unreasonable to ask a person to live on 40K a year when it costs 36-38K a year to live (That's an example and not based on real life numbers), cause if all that's left over is 2-4K a year some would say that that is a lot of money left over however let's divide that into months, that's anywhere from 170-340 dollars extra every month. And everyone knows that in life things happen and sometimes you spend more than you make and 400 dollars a month maximum isn't a lot of money especially if you consider some potential accidents like injuries, car repair, theft, job loss, school, transportation, etc.
Most important thing in any society is equal distribution.Inequal income creates economic difference in a country.Although overall income of country seems high but per capita income becomea too low,example is India where, at least two out of top ten richest person of world are Indian and also country's 26% people are BPL.
Equality in income provides a uniform plateform and overall growth of the country
Income inequality is a red herring. If I'm making $150,000 a year and living comfortably, I couldn't give a flying crap if some rich celebrity makes $15 million dollars. It has zero effect on me. Economics is not a zero sum game. Just because somebody earns something doesn't mean value is taken away from what I have or what I could potentially earn. Austrian economics teaches that there is a thing called economic growth.