In the Nuvotronics factory in Durham, N.C., small is beautiful. The firm, founded in 2008, uses a process resembling 3-D printing to make miniaturized 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 percent since 2001. By the same measure, North Carolina as a whole grew by just 3 percent 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. 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 percent more per head than America as a whole. Today's richest cities make 34 percent more.

Measured by total GDP, the decoupling is greater still, because prosperous cities are sucking in disproportionate numbers of urbanizing Americans. Between 2010 and 2014 America's population grew by 3.1 percent; its cities, by 3.7 percent. But the 50 richest cities swelled by 9.2 percent.

The Durham example

Durham, whose population grew by about 7 percent 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. Farsighted planning in 1959 led Durham and its close neighbors, Raleigh and Chapel Hill, to establish a research park between the three cities. The idea was to coax the universities' techies 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. Mayor Bill Bell hopes to develop a light-rail system for the city; in 2011 voters passed a sales-tax increase to help pay for it. Investment has also revitalized a deprived downtown area.

Durham is unusual for its failure to drag up statewide incomes. The state's labor-force participation rate, at 61 percent, is grim. Elsewhere, the presence, or absence, of rich cities determines economic fortunes. States with one of today's richest 50 cities have grown 13 percent in per-person terms since 2001. The 18 states without such a city saw growth of just 7 percent. As a result, inequality between states has risen for most of the past decade-and-a-half.

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 percent have more than doubled by one measure. Returns for middling performers have increased only a little.

A report by McKinsey attributes the divergence to the varying pace of digitization across industries. Highly digitized 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.

Wage gaps

This bears directly on the inequality that 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.

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 polarized. 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.

Cowen's predictions are already coming true. While successful cities grow, almost 60 percent of rural counties are losing population. With America's shale and manufacturing industries suffering, the pull of successful cities is becoming greater still.

Copyright 2013 The Economist Newspaper Limited, London. All Rights Reserved. Reprinted with permission.