So why do some big corporations lobby the government for a higher minimum wage? Because it destroys their less established competition. And naturally, this has a devastating effect on those who work for those smaller businesses.
Of course big business won’t support a minimum wage increase if it’s too high (they could not compete with companies in other countries if they did). But they will support a wage increase if it’s just enough to hurt their much smaller and less established competition, helping them to establish a monopoly.
Some believe that the problem is capitalism itself, not just crony capitalism. Yes, capitalism has its problems; but it's also important to note that all economic systems financially reward some people and punish others—including communism. (For a good example see what happened in China.* See also chapter 8 in Capitalism by George Reisman. No system provides economic equality for all.)
But what about the very wealthy? Do they serve any useful purpose? See here.
Some tough questions about the minimum wage.
* If you wish to understand why communism cannot work even on paper, read The Government Against the Economy by George Reisman. The more the government sets the prices of good and services, the greater the economic decline. The situation in China became so bad, that they had no choice but to adopt capitalism. See here.