WASHINGTON — The gap between the wealthy and the poor is most extreme in several of the most prosperous and largest U.S. cities.

The economic divides in Atlanta, San Francisco, Washington, New York, Chicago and Los Angeles are significantly greater than the national average, according to a study released Thursday by the Brookings Institution, the Washington-based think tank. It suggests that many sources of both economic growth and income inequality have co-existed near each other for the past 35 years.

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A destitute man sleeps under a holiday window at Blanc de Chine, an elegant clothing store in New York. A Brookings Institution study found that inequality increased across cities even though incomes often fell for wealthy households from 2007 to 2012. The Associated Press

These cities may struggle in the future to provide adequate public schooling and basic municipal services because of a narrow tax base and “may fail to produce housing and neighborhoods accessible to middle-class workers and families,” the study said.

“There’s something of a relationship between economic success and inequality,” said Alan Berube, a senior fellow at Brookings. “These cities are home to some of the highest-paying industries and jobs in the country.”

At the same time, Berube noted, many of these cities may inadvertently widen the gap between rich and poor because they have public housing and basic services that make them attractive to low-wage workers.

The findings come at a delicate moment for the country, still slogging through a weak recovery from the Great Recession. Much of the nation’s job growth has been concentrated in lower-wage careers. Few Americans have enjoyed pay raises. President Obama is pushing for a higher minimum wage. And protesters in San Francisco have tried to block a private bus that shuttles Google employees from gentrifying neighborhoods to their offices in Silicon Valley.

Many wealthy Americans, from venture capitalist Tom Perkins to real estate billionaire Sam Zell, argue that the nation has tipped toward class warfare.

Incomes for the top 5 percent of earners in Atlanta averaged $279,827 in 2012. That’s almost 19 times more than what the bottom 20 percent of that city’s population earned. The ratio is more than double the nationwide average for this measure of income inequality. The top 5 percent of earners across the country have incomes 9.1 times greater than the bottom quintile.

Major chasms also appeared in the tech hub of San Francisco, the financial center of New York, the seat of the federal government in Washington and the home of the entertainment industry in Los Angeles.

“In San Francisco, skyrocketing housing costs may increasingly preclude low-income residents from living in the city altogether,” the study said.

Not all tech hubs have witnessed rising inequality.

Seattle, where Amazon and Microsoft are based, saw its income disparity decline since 2007. So did Denver. Austin, Texas, experienced a mild uptick.

“Both the tech boom and energy boom are inequality-reducing,” said Michael Mandel, chief economic strategist at the Progressive Policy Institute in Washington. “Tech introduces a path to good jobs.”

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