As the movement for a $15-an-hour minimum wage has won victories in a series of cities across America, momentum has grown on the left for a national minimum wage that high. Both Bernie Sanders and Martin O'Malley have endorsed this idea, and Hillary Clinton's reluctance to do so has earned her the label "capitulator in chief" from Gawker's Hamilton Nolan.

This Pew Center map showing the cost of living in different metropolitan areas is a reminder that there is a powerful logic to Clinton's position that "what you can do in LA or in New York may not work in other places."

There are basically two ways you can think about what this map is saying, and they both point in favor of a differentiated minimum wage.

In humanitarian terms: You don't need such a high wage in Nebraska to achieve the same living standard as you need in New York City.

You don't need such a high wage in Nebraska to achieve the same living standard as you need in New York City. In business terms: A high minimum wage is much more of a disincentive to hire workers in Nebraska than it is in New York City.

Expensive labor is costly when other things are expensive

The first point should be obvious to anyone who's ever tried to buy anything in a big coastal metropolis rather than in the South or the Midwest. If you're going to try to get by on $12 an hour, you're going to have a much easier time finding a place to live in these cheaper cities.

But the second point is arguably more important. Economists talk about different "factors of production" coming together to create a viable business. You need workers, yes. But you also need land, and you need some buildings and some electricity. Your workers need some equipment to do their jobs, and they probably need some inputs — potatoes or giant vats of ketchup or what have you — to create whatever it is they are selling.

The reason the cost of living varies from place to place is that the price of these factors of production — especially land and buildings — varies considerably from place to place. In an area where land and buildings are cheap, cheap labor is likely to increase the employment level in a serious way. In an area where land and buildings are expensive, the employment level is likely to be less sensitive to the price of labor.

Regional differentiation used to be the left-wing position

It's worth noting that until very recently, Clinton's view of this — that the minimum wage should be hiked up to a high level in high-cost areas but not elsewhere — used to be the left-wing position in the debate.

University of Massachusetts economist Arindrajit Dube's Hamilton Project paper "Designing Thoughtful Minimum Wage Policy at the State and Local Levels" is the urtext of that era. It suggested a minimum wage of about $13 an hour in places like the Bay Area, Greater Boston, and the metropolitan area surrounding Washington, DC, while holding that something in the $9 to $10 range might be more appropriate for Atlanta or Dallas.

Far from a capitulation, Clinton's current position — a $12 national minimum wage going as high as $15 in high-cost areas — is a bit to its left, though arguably amounting to about the same thing when you consider delayed phase-ins and inflation.