Also, the value of min wage needs to be mapped on some topography of need. A $15/hr in SF or NYC is paltry due to the geographic localization of other prices--higher cost of living. Meanwhile, hiring 16 year in some middle-america towns probably shouldn't be dictated by "rich people's problems" imported from New York or California. All that being said, I also like the top-posters idea about adding a subsidy to basic negotiated/market wages. Because ultimately everything is simply a negotiation. And the non-work-related subsidy is something people can use to "walk"--so it's effective leverage as a tool of last resort.
If SF or NYC wants a higher wage, the city could augment the subsidy out of its own tax coffers.
I am however, very much against the idea of taxing a machinist in Alabama to subsidize wages in NYC.
I am also amenable to the idea of having the subsidy only be for those over 18, or people who are supporting families.
But I do think it is reasonable to provide $15 jobs in middle America. Right now, young people feel a compulsion to head to NYC/SF/DC to gain access to these job markets, which feed off the money surplus from winner-take-all-industries. I would rather that the money get spread around more, and that once again a decent middle class life would be easy to obtain in what is now known as the rust belt.