What if the people you're talking about are only skilled enough to produce $6 per hour of value to the economy?
Then no one will give them a job at any salary.
That's obviously not true. It's certainly possible to do $6 worth of work for a company. A small company, with little bureaucratic overhead when they hire someone, could find a reason to hire someone who did $6 worth of work.
The price of labor has nothing to do with productivity, it is completely driven by the market. If someone is generating $200k per year in benefit to a company, but the market salary for that person is $40K/year, they are going to get $40k/yr and if they don't like it, there are others willing to take $40k/yr to replace them (hence the market salary).
Quick aside, and then I will contest that.
You have you no idea how refreshing it is to hear you say that!
I studied Economics in college (although it was awhile ago), and there seems to be this idea going around the world of mainstream Economics that totally unregulated markets are perfectly fair, with no exploitation either way. "You get out what you put in..." etc.
With that said, I cannot agree. If John Doe produces $200k a year and gets paid $40k, and if he doesn't like it, then of course he will ask for more money! They're going to find someone else who's the bargain he is? I don't think so! The person who replaced him would probably produce only $40k of value for the company. And I say this because I do believe that at some point there is some positive correlation between the market rate for a type of labor and what that labor is actually worth to the company.
But that's not the whole story, of course. Big companies, with more financial breathing room than workers who are living paycheck to paycheck, can force workers to accept less than what they're worth. So yes, if enough laborers of a certain type are desperate for work, then that type of work will be underpaid.
I just think your statement that "the price of labor has nothing to do with productivity" is unfair to market capitalism. Productivity does not completely determine wages, but it partly determines them.
That is the real story with the women US soccer players. They are paid so little compared to the men because they have no where to go. If they want to play soccer, the very best paying job in the US is the Women's National Team. The best men in the US have a lot more options so US Soccer pays more. It doesn't matter that the women produce a better product and make more money.
Interesting riddle for economists...
"If female footballers are contributing more to US Soccer, why are their male counterparts paid more?"
It's late, and I'm too tired to think through that one now.
Seeing someone work 40 hours a week and have to supplement that with food stamps is sad. But I don't see how a $15 minimum wage is going to solve that. A minimum wage of $15 per hour doesn't force businesses to pay people $15 an hour; it tells them they have stop paying people $14 an hour.
...Often in the minimum wage debate, there is an assumption that just because labor is cheap, business owners will hire people they don't need and that if you raise the salary threshold, owners will fire people they require. Both assume that owners don't act in their best interests. Owners will hire the exact right number of people regardless of whether they cost $10 or $15/hour.
I don't think that if you raise the minimum wage, owners will "fire people they require". Of course they won't do that. What I think is that it may become the owner's best option to fold completely if the minimum wage goes too high for them. Or maybe, if they're a big business, they'll move certain divisions overseas or out of state.
A friend of mine is interested in working 48 hours a week, assembling semi-conductors, at $13/hr. He has no interest in starting a family, so $676 per week (almost $3000 per month!) is more than enough. But if the state no longer allows workers to get paid $13/hr, the company will move 1000 miles down the road to a state that does.