I think these are two separate discussions. Indeed the floor effect of a minimum wage can have a negative impact on very low-value jobs, that's one of the issue

I think these are two separate discussions. Indeed the floor effect of a minimum wage can have a negative impact on very low-value jobs, that's one of the issues to be managed. One way is to try to orient your economy around more high-value jobs, with a generous safety net for those who can't reach it. It's a very difficult question