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We might not need to argue about a minimum wage if we had UBI and Universal Health Care. If you have enough money to cover basic needs, a job is something you would do for other reasons. You might do it for very little money because you enjoy it. Or it might offer an opportunity to learn a craft.
On the other hand, if the job was digging ditches, you might want far more compensation. Or perhaps, if you could set your own hours, you’d consider it as exercise.
If the UBI was flat and not adjusted for local cost of living, employers might have to offer more pay where that cost of living is lower. Would all this tend to even out as populations moved to those places?
I don’t know. Maybe you have some thoughts?