In any case, it is a genuine question from someone living in a decent welfare state and happy to continue to do so. I don't really care to engage in debates of who has the moral high ground, just the practical question, if you have an answer.
technically in the U.S. there is a federal (nation-wide) minimum wage, then there are minimum wages for each state. I am not sure how they are defined, e.g. the federal one is certainly not automatically pegged to inflation. there is a movement to raise the federal minimum wage to $15/hour but even that is hard or impossible to live on in many areas.
You have not interpreted the comment correctly. This is deterministic. A capitalistic system or game has naturally emergent behaviors, but the propaganda excusing and defending the reluctance to add egalitarian rules is very much deterministic.