Not to derail the conversation too far, but there are actually cases where a minimum wage has been used as a tool to eliminate certain jobs. For example, a big sticking point of the new NAFTA deal was the requirement that exported cars be manufactured in a factory with a $16/hr wage floor, with goal of making exports from Mexico uncompetitive and move some of those manufacturing jobs to the US.

Obviously, I don't think that's the common policy goal though.