That's the thing about minimum wage. All it really does is raise the floor, which in turn causes a corresponding upward shift in what higher level positions pay, which in turn is reflected in higher costs of goods and services. At the end, do they have any more purchasing power than before?
We get stuck with the Ebeneezer Scrooge image for pointing out this sort of thing. In some ways the political contest between us and the Left is like two parents at odds over how to raise the children. One parent wants to be responsible, knowing full well that means the child cannot be indulged all the time. The other parent is the permissive one -- hey kids, how about ice cream for dinner again! The permissive parent then has the nerve to tout the fact that the kids like them more than the stuffy "mean" parent.
With the whole minimum wage and "living wage" and all this stuff, the uncomfortable truth they refuse to acknowledge is that value is relative. It's always in flux. What's valuable today might not be tomorrow. What I'm able to do might be more valuable than what someone else is able to do, or vice versa.