Strangely enough, because of the way the EITC is tied with wages and already distorting the economics at the bottom, raising the minimum wage could result in net transfer of wealth from the rich to the poor and therefore reduce inequality.
Not all people are the same. Not all people are as equally productive, equally talented or equally motivated. Not all people want the same things.
You seem to subscribe to the aim of total income equality as a goal. To do this you would force the productive to hand over most of the product of their work to those who are less productive. Obviously, to do this, you need to force them using the apparatus of the state to do so.
In other words, they either spend the majority of their time working for others or they go to jail. They are not asked to share the product of their work, they are threatened to do so or be locked up.
Does that sound fair to you? That is a very perverse sense of justice, where you don't have a choice in how the output of your labour is divided.
Honestly I cannot understand after a century of misery from forced wealth redistribution and forced work and millions of deaths people still come up with these ideas.
There is a big gap between wanting "total income quality", and wanting to close the huge, and increasing, income equality gap in the US, and to increase the minimum wage (or undertake other means) to reach a point where people can reasonably buy a house and send their children to university without requiring crippling loans.
You can't force the minimum wage up any more than you can push on a piece of string. While you can certainly change legislation to make the minimum wage a set value, there will be offsetting measures felt elsewhere, usually an increase in unemployment and a general drop in living standards for all. You can't force someone to employ you anymore than you can force someone to be your friend.
Once houses have finished correcting lots of people will be able to afford them. Housing affordability is headed towards the best it's ever been.
I agree that things are bad, but going down the road of trying to force a solution by means of restrictions, price controls and regulations will only make the problem worse.
As I've posted in the past, places like Detroit should be cordoned off and turned into special economic zones like Hong Kong is to China. There should be a very low tax rate, no trade restrictions with other countries, and many other regulations, taxes and boondoggles dropped. There should be no (or very low, say 3%, for Military use) federal taxes and in turn they should receive no handouts or participate in any programs from the Federal government.
Do that I can guarantee that in 10 years the place will be booming, employment will be high and things will be moving in the right direction. With somewhere like Detroit, it's time people started thinking outside the box and experimenting with some rollback of the last 100 years of policy.
So do you believe removing the current minimum wage altogether would be beneficial to those people currently around that level of pay? Given the current high levels of unemployment I would expect to see a fairly substantial drop in wages, where it is already almost impossible to live on minimum wage.
Also, once Detroit is removed from all Federal programs, how does it pay to feed all the currently unemployed people there?
I had more relevant comments here: http://news.ycombinator.com/item?id=3120123