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This is why the raise in minimum wage should be compensated by also offering government jobs that do pay minimum wage or slightly less. Given enough time people will actually end up getting their minimum wage or even more than minimum wage.

However the talks about a $15 minimum wage actually have one very interesting detail. There are no plans for an immediate hike. It's going to be raised over time which means companies have enough time to adapt. It also sends a clear psychological signal to everyone that the times of cheap labor are going to be over because it is something that is happening year by year.