This might be the case but many jobs I feel like would no longer be worth paying anyone to do at that rate. That would suggest to me that the productivity of minimum/low wage workers has not increased at the same rate as productivity generally. Which would make sense given most of that increase is attributable to technology which isn’t distributed evenly through different sectors of the economy etc.
Right, this is where this sort of blanket extrapolation breaks down. Has the average productivity grown that much? Sure, I can believe that. Has the productivity at the lower margin grown that much? I seriously doubt that. The value created by stocking shelves at wal-mart just doesn't really change over time. There's a lot of labor on the lower end that is a solved problem with all the productivity wrung out of it de…
That's the problem. The minimum wage is a legal instrument, not just an economic process. It is designed for the lower margin to be "overpaid" over what they could get from the market otherwise.
It basically says "everyone working should get at least this much of our collective production". This is what we have decided our society should work like.
Our collective productivity increased much faster than minimal wage, making the minimal wage worker much poorer by comparison.