There is no such thing as a fair minimum wage. There is no such thing as the right to have a job. A job is not charity, nor some sort of social duty.
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    Free men don't owe each other anything they haven't explicitly agreed upon. We're individual beings, and as individuals, we think and act to produce value for ourselves and those we love - who are, ultimately, a value to us. There is absolutely no valid reason why a random person would have a claim over the value produced by someone else.
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    A job is essentially profiting on someone else's idea and risk taking. An entrepreneur had an idea, and decided to take the risks and act on it. He cannot do everything himself, so he is willing to exchange part of his returns for other's people's work. A worker has value to his employer to the extent that he can help bring their idea to fruition. If you don't have an idea of your own, and can't help someone else concretize theirs, you don't get to have a job.
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    That's all there is to it.
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    Because of that, there is no moral obligation to pay someone above an arbitrary minimum. There is no sort of romanticized "brotherly bond", between random people, because random people, by definition, aren't each other's brothers. An employer has the moral claim to the most amount of value he can possibly get out of his idea. An employee has the moral claim to the most anyone is willing to pay for his time.
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    No more, no less. Anything else is a claim, but it's certainly not moral.