IN THE Nuvotronics factory in Durham, North Carolina, small is beautiful. The firm, founded in 2008, uses a process resembling 3D printing to make miniaturised radio chips for jets and satellites. Typically, such chips are the size of a chocolate bar; Nuvotronics’s widgets are smaller than a breath-mint. Such innovation is lucrative; every kilogram saved makes a satellite $15,000 cheaper to launch. Nuvotronics is part of a cluster of high-tech firms that have increased Durham’s GDP per person by 28% since 2001. By the same measure, North Carolina as a whole grew by just 3% over the same period. Durham’s success reflects an emerging trend: high-flying cities, and the successful firms they contain, are detaching from the rest of the economy.

Cities have long been the most productive places to do business, because they bring firms, customers and workers closer together. A banker in New York is only a taxi ride away from her clients; a new restaurant there immediately has 8.4m potential customers on its doorstep. Where clever people congregate, innovation results.

For the most successful cities, these advantages seem to be getting bigger. In 2001 the richest 50 cities and their surroundings produced 27% more per head than America as a whole. Today’s richest cities make 34% more. Measured by total GDP, the decoupling is greater still, because prosperous cities are sucking in disproportionate numbers of urbanising Americans. Between 2010 and 2014 America’s population grew by 3.1%; its cities, by 3.7%. But the 50 richest cities swelled by 9.2%.

Durham, whose population grew by about 7% in that period, provides some hints as to what makes a place flourish. The city thrives on its proximity to three leading universities—Duke, North Carolina State and the University of North Carolina. Far-sighted planning in 1959 led Durham and its close neighbours, Raleigh and Chapel Hill, to establish a research park between the three cities. The idea was to coax the universities’ boffins into business ventures. It worked; today 50,000 people work there.

Unlike much of America, the area has not shied away from infrastructure investment. Raleigh-Durham airport has been renovated with a helping hand from local businesses. The roads are well maintained, if a little crowded. Bill Bell, the city’s mayor, hopes to develop a light-rail system for the city; in 2011 voters approved a sales-tax increase to help pay for it.

Investment has also revitalised a deprived downtown area. For most of its history, Durham made tobacco and textiles. When those industries went into decline in the latter half of the 20th century, they left a vacuum in the city. But over the past decade the gap has been plugged. The tower of the old American Tobacco factory, emblazoned with the “Lucky Strike” logo, still stands—but the factory is now a “campus” featuring bars, restaurants and the kind of tech firms where staff ride around on scooters. The city’s performing-arts centre, across the road, is one of the four best-attended theatres in the country. Mr Bell says public-private partnerships account for much of the investment.

Durham is unusual for its failure to drag up state-wide incomes. The state’s labour-force participation rate, at 61%, is grim even by American standards. Elsewhere, the presence—or absence—of rich cities determines economic fortunes. States with one of today’s richest 50 cities have grown 13% in per-person terms since 2001. The 18 (mostly southern and south-western) states without such a city saw growth of just 7%. As a result, inequality between states has risen for most of the past decade-and-a-half (see chart). Rich cities typically attract successful, growing firms. Nuvotronics is young, employing fewer than 100 people, and did not move to Durham until 2013. But the city also plays host to well-established firms like Cree, which makes LED lighting, and giants like Quintiles, a consultancy which works on pharmaceutical trials. Attracting the right companies matters because America’s firms, too, are diverging. In the past two decades returns to investment at the most profitable 10% have more than doubled by one measure. Returns for middling performers have increased only a little (see chart). A recent paper by Jason Furman of the White House and Peter Orszag, a former budget chief, says this could be because the best firms are gaining market power (think of Apple’s dominance of the smartphone market). A report by McKinsey attributes the divergence to the varying pace of digitisation across industries. Highly digitised industries such as technology, media and professional services—all common in successful cities—have benefited from the juiciest increases in margins. Digital laggards, such as health care and offline retailing, are doing less well.

This bears directly on the inequality which matters most: that in wages. Two recent studies suggest that most of the increase in inequality over the past four decades is explained by wage gaps between firms rather than within them. A secretary will probably earn more working for Goldman Sachs than working for the local plumber; it is more lucrative to be a programmer at Facebook than in a corporate back-office. This means that bringing highly skilled workers to an area is not enough to guarantee high wages; the right firms must come to town, too.

The end of mediocrity

In 2013 Tyler Cowen, an economist at George Mason University, predicted in his book “Average is Over” that the fortunes of both people and places would become more polarised. Ambitious and talented workers, he argued, would want to work in a relatively small number of cities and regions. These vibrant clusters would then benefit from increasing returns to scale, cementing their advantages. Mr Cowen’s predictions are already coming true. While successful cities grow, almost 60% of rural counties are losing population. With America’s shale and manufacturing industries suffering, the pull of successful cities is becoming greater still.