Well, I haven't received a straight answer yet.
That's weird, since I hear about this so often.
Seems like a reasonable question.
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Well apply some simple logic. 1) i am not sure you will find actual evidence, because frankly who would admit to it? 2) for sake of argument we know sexism happens. We know that some men feel women shouldnt be in the work force, doing certain jobs, and are not at the same level as other men. ( see military or fireman as an example.) So the idea that their are some men who reluctantly hire women, would pay them less. Its not that far of a stretch.
As for income inequality. Well again like everything else on this planet, there has to be a balance. No i dont mean everyones wage has to be equal. I am talking ratios. There will always be rich, middle and poor classes, but if you dont have that balance things will get wonky for any nation. We are seeing a surge in the separation of rich to poor. Thats an issue that needs to be fixed.
There is nothing wrong with being rich, nobody has ever made that argument that you shouldn't have that money.( at least in any majority, one person here or there is nothing to worry about)
The issues come with the idea that some rich rig the game, they give out bonuses after taxing tax payer bailouts, or use tax loopholes to keep out of paying taxes ( see rigging the game).
Once you get past the stupid left vs right thing the OP and a few others are playing at you can actually see the issues at hand, but some people can't get past being a partisan.