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There's a free market idea that the market rewards those who provide value to society. I think I've found a simple counterexample.
Imagine a loaf of bread is worth 1 dollar to consumers. If you make 100 loaves and sell them for 99 cents each, you've provided 1 dollar of value to society, but made 99 dollars for yourself. If you make 100 loaves and give them away to those who can't afford it, you've provided 100 dollars of value to society, but made zero for yourself. Since the relationship is inverted, we see that the market doesn't reward those who provide value. Instead it rewards those who provide value to those who provide value! It's recursive, like PageRank!
That's the main reason why we have so much inequality. Recursive systems will have attractors that concentrate stuff. That's also why you can't blame people for having no jobs. They are willing to provide value, but they can't survive by providing to non-providers, and only the best can provide to providers.
I think you have to back up a step in your idea of "value". What makes the loaf worth $1 if you sell it for $0.99? Why isn't it worth $1M (to a theoretical starving rich person) and you're giving away HUGE amounts? Why isn't it worth $0.10 and the buyers gave you $890 in charity?
A thing's value is relative - different to every participant. And the relative values are only known (actually, not - they're bounded above by the seller and below by the buyer) by the transaction.