Since I do have artificial /. limits on the number of posts per day, I will reply to you from my backup account. Don't worry, I won't pretend to be somebody else, that's not what this account is for, it's the same user, just under a different name.
Spending money on consumables does not grow the economy, especially the USA economy, which buys those consumables from abroad. It doesn't increase competitive pressures in the USA economy to produce, the only competitive pressures in the USA are in distribution and sales, but that's where a small number of very large economies of scale, such as WM dominate, specifically because they hire people at lowest prices and push suppliers to sell to WM at lowest prices as well.
Customers that get their income from welfare or from laws that steal that money from somebody else first are not real customers. The real trade is done between parties that produce, the so called trade between those, who live on welfare (or are benefiting from any type of theft, including taxes and borrowing that go towards minimum wages) is not real trade.
You see the point of trade is to exchange something, it makes sense for me to trade my productive output with others, who also have productive output, where I can get something from them I myself do not produce - comparative advantage is the name of the game.
When governments tell me (as an employer) that I must hit their artificial price floors, I cannot magically expand my overall earnings to provide any more money to anybody that I am already paying. I actually have a number of people that are paid below what you would consider a legal 'minimum wage', while vast majority of my employees are paid much more than any such price floor. The reason is very simple: productivity.
I don't throw people out if I can use their labour at the price, at which it makes sense for me to buy that labour. If the labour price is artificially raised, I would rather not hire anybody in that category at all, I would only be considering people that are definitely more productive than those, who are barely making it to the artificial price floor. There is a substantial difference between a worker that can produce high output and a worker that can barely move, however I can find use for those who barely move but they will not be making anywhere near what you think 'minimum wage' should be. They are fine with it, those are students and they do in fact need these jobs, they are getting experience that will help them to find better jobs later. Some of my student workers are very good, making more than what you think minimum wage should be.
My point is this: I will not have people at minimum wage, that doesn't even make sense. I will have people much below it and people much above it. Minimum wage is an artificial construct that has no meaning to me as an employer, there is nobody who is worth specifically that amount that I employ.
Now, the people that you are talking about, they are mostly in services industry, they are cleaners, stocking personnel, people with very little skills, not anybody with any real skills, those people command higher than minimum wage salaries. Placing artificial government price controls on labour price does a very simple thing: ensures that fewer people in that category are hired and those who are hired are going to be in higher categories of workers.
I definitely can see some business hiring an overqualified person with no job experience even to clean toilets, rather than hiring much less 'learned' counterparts, so the only thing that minimum wage does in that category is it prevents people without experience and without any extra qualifications from entering the work force.
Of-course the modern 'mainstream economists' will muddy the waters and try to sell you all sorts of nonsense as to how they think the economy works and how higher minimum wages will grow the economy, it's all nonsense and propaganda for the political elite that is in power, it has nothing to do with the actual economy and hiring and pricing. The actual economy will find a way to work around these price controls - hiring people that are much more qualified than necessary for jobs that shouldn't need those qualifications, ensuring that jobs go to the more connected people rather than considering people from the entire job market, etc.
As to your 'negative sum' and all that, sure, one way to deal with the increase in minimum wage is to raise your prices. Well, that IS happening. What do you think news like this are all about? It's inflation and all the price controls and laws and regulations, taxes, that's what it is. And Hershey's raising prices by 10% that just one tiny drop in a bucket of the overall prices going up, they are going up much faster than any government numbers indicate or admit to.
Product quality and portion sizes are going down, prices are going up, gov't can even claim that this is somehow indicating a 'growing economy'. But if you spend 10% more on Hershey's it doesn't mean your standard of living is better, the exact opposite is the case. To listen to the mainstream nonsense, you are in danger when prices fall. Well, I hope you are getting your fill of the great economic news, prices are not falling, they are going up just fine, so don't be scared, your wallet won't be emptied slower, it will be emptied faster, so you are all good.