The concept of a minimum wage ON IT'S OWN, is flawed. There also needs to be a maximum wage or you know what happens all those who were at $15 will want a ramp that places them in the same relative position versus all others as it was before.
It matters not if the minimum wage was $200 per hour if the UAW wage was then set at $800 - minimum wage earners would be just as unable to buy a new car as they are now. The group at minimum needs to ramp up, while the rest have a limit. That way purchasing power would broaden.
In Germany the organised labor does not get 5-10x what current fed minimum (~~$7.50) is. They say the UAW total package with benefits and perks is about $60 per hour, with less than half in wages the rest in pensions and benefits.