DETROIT — It’s a 21st century paradox: Detroit enters 2014 in bankruptcy, the largest public case in U.S. history and facing $18 billion or more in debt. Yet the Motor City’s resurgent auto industry is strong enough to host a show that by one estimate will generate nearly $400 million for the area’s economy.

The industrial city is looking to climb out from under decades of financial decline as its longtime industry revs ahead four years after General Motors and Chrysler, emerged from bankruptcies. The comeback can be measured in the North American International Auto Show’s economic impact, which is projected to rise 8 percent over last year, says David Sowerby, a portfolio manager and chief market analyst for Loomis Sayles, who authored a study of the show’s effect on the regional economy.

Sowerby says several factors favor increased spending tied to this show, which starts Monday.

“Economic activity is strong, the industry itself is stronger, there’s a modest increase in new models, and if you talk to hotel or lodging industry, the number of conferences is growing, as is business activity and travel.”

“The real Detroit has a long way to go,” said new Mayor Mike Duggan. “There’s no doubt there are a lot of great things happening, but we have not translated the success that people will see here into services for people living in the neighborhood. And that’s my job,” he says. “But that doesn’t stop everybody from enjoying the good things that are happening, like the auto show.”