Bernie Sanders has introduced legislation to boost the federal minimum wage to $15. The NY Times has a good article comparing $15 per hour with the median wage in various U.S. cities. Roughly speaking, the higher the ratio of the mandated minimum to the median, the more "binding" the minimum, and the more likely it is to lead to job losses as low-skilled workers are priced out of the local market.
Of course, there is no magic ratio at which the minimum wage becomes "too high." And even if the adverse employment effects became significant, those effects would have to be weighed against the benefits to those receiving the pay boost. But it is definitely worth thinking about whether a much higher uniform national minimum wage (Bernie's proposed $15) makes sense, when $15 is only about 50% of the median wage in some places (e.g. San Francisco) but more than 75% in others (Miami).
Furthermore, from a justice perspective, the goal of a legal minimum is to help the lowest-paid workers afford a reasonable minimum standard of living. But the cost of living varies dramatically across locations. For example, according to this widely used calculator, the cost of living in Miami is about 75% of the cost of living in my area, San Jose. In Miami, then, an hourly wage of about $11.25 would support the same standard of living as $15 here.
Regardless, Sanders's $15 minimum is a political non-starter in the U.S. Congress, so we will no doubt continue to see a low (in my view too low) federal minimum, and a wide range of much higher local minimums. A fantastic set of natural experiments for smart young economists like Arindrajit Dube.