That's an economic multiplier theory that, in execution, never seems to come to pass. Probably because it assumes that the money rolls right back into those offering the minimum wage and that there's somehow a demand gap that's not really there for that wage level.
It's basic economics. If a person making minimum wage gets a raise, they'll spend that on things they need or want but couldn't afford before, which is good for the businesses where they spend it, promoting job, wage, and economic growth.
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