Actually it will - due to the ladder effect. When minimum wage goes up, the person in charge of the minimum workers has to have an increase to still be making more than the people he's in charge of - albeit at generally lower percentage than was the minimum wage increase. This happens all the way up the ladder with each level getting, generally, a slightly lower percentage increase than the one below, until a point is reached that the next level up is still making more than those below. So in addition to increased poverty by people being out of a job there's also increased "poverty level" employment by many now making proportionally closer to the minimum wage. Another result is that people with fixed resources - those on disability, retirees, pensioners, etc. - also end up hurt as their income will not increase by the same percentage as the minimum wage goes up, if it goes up at all. Some won't, and those that do are generally tied to a nebulous "cost of living" increase that both fails to reflect actual marketplace cost increases but also lags them by months to years. Not that it matters, it's the apple on the end of the stick that gets the "gimme" vote so it's going to happen and keep happening.
You are talking about 1.5 percent of American workers. You are stating that raising minimum wage would increase cost-push inflation, which it will not. 1.5 percent is not enough of the market to cause any of the things you are discussing. You are discussing an "Economies of scale" model and attempting to apply it to the nations economy. Also, cost-push inflation deals with worker that produce market products, which are not minimum wage workers. By the way, it is a ripple and not a ladder effect. What it will cause is automation, which causes unemployment.
If you are discussing raising minimum wage by $.50 and we are below or around the equilibrium point in the supply and demand's labor curve, then it could beneficial the market and cause employment because of an increase in aggregate demand. However, if you are above the equilibrium point then it would cause unemployment.
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