The long cycle of “lose jobs, gain jobs, lose jobs” that kept Georgia’s unemployment rate at 10.2 percent in August — the same as it was a year earlier — is illustrated by Union City, a small city on the outskirts of Atlanta.

It suffered a blow when the last store in its darkened mall, Sears, announced that it would soon close. But the city had other irons in the fire: a few big companies were hiring, and earlier this year Dendreon, a biotech company that makes a cancer drug, opened a plant there, lured in part by state and local subsidies.

Then, this month, Dendreon said it would lay off more than 100 workers at the new plant as part of a national “restructuring.”

Union City, with a population of 20,000, now calls itself the place “Where Business Meets the World” and has been trying to lure companies by pointing out its low business taxes, various incentive programs and proximity to Hartsfield-Jackson Atlanta International Airport.

Steve Rapson, the city manager, said that the challenge there, as in much of America, has been to get employers to hire again. “It’s hard to get your mind around what can you do as a city to encourage future jobs and jobs growth,” he said.

The reordering of the nation’s economic fortunes can be seen in the Brookings analysis, which found that many auto-producing metropolitan areas in the Great Lakes states are seeing modest gains in manufacturing that are helping them recover from their deep slump, while Sun Belt and Western states with sharp drops in home values are still suffering. The areas that have been hurt the least since the recession, the study said, rely on government, education or energy production. Places that were less buoyed by the housing bubble were less harmed when it burst.

In Pennsylvania, the analysis found, the Pittsburgh area — which is heavily reliant on education and health care — is weathering the downturn better than the Philadelphia area. In New York, areas around long-struggling upstate cities like Buffalo and Rochester are recovering faster by some measures than the New York City metropolitan area. And the rate of recovery in Rust Belt areas around Youngstown and Akron, two Ohio cities that were hit hard, has outpaced that of former boomtowns like Colorado Springs and Tucson.