Not handy, but use your common sense if you will: if you're surviving on $8/hour or whatever it currently is in the US, and your wage increases by a dollar per hour, then all things being equal you're going to be spending that extra buck on a range of things that had been delayed for a while: shoes for the kids, new tires for the car, and what not. This is consumption, and it's going to get recycled over and over again across the economy for the benefit of everyone.
The trouble is if you increase it to $50/hour. (Assuming the businesses survive, which is indeed a big if...) In this case you buy everything you ever needed or wanted, and...?, then what? You save it, put on debt to buy a huge mansion that you'll never actually be able to afford in the end, or otherwise contribute to some random asset bubble, snd you get booms and bust cycles. (See Steve Keen's research on the latter point, fwiw.)
The question you have to ask is, where does this extra dollar come from? (owners' margins? wages of workers who are now unemployed? consumers' budgets?), and how much extra consumption it generates in the still-employed workers' pockets, compared to where it was before?
I guess we can agree that the money is shifted downwards in the income spectrum relative to where it was before. Other things equal, lower-income households have a higher marginal propensity to consume. So shifting money downwards will boost consumption.
It's like you didn't even think through your example at all. If minimum wage is suddenly $50/hr, businesses begin to collapse.
The Fed, seeing this collapse, would massively inflate the dollar. Anyone with savings would have their savings destroyed, and the churn would make everyone poorer than before, quite specifically the same people you were trying to help.
The trouble is if you increase it to $50/hour. (Assuming the businesses survive, which is indeed a big if...) In this case you buy everything you ever needed or wanted, and...?, then what? You save it, put on debt to buy a huge mansion that you'll never actually be able to afford in the end, or otherwise contribute to some random asset bubble, snd you get booms and bust cycles. (See Steve Keen's research on the latter point, fwiw.)