SALT LAKE CITY — Stephanie Pappas and her brothers built their roofing supply company in this fast-growing region by promising next-day delivery, but lately they’ve been forced to tell some customers that tomorrow is impossible.

Their company, Roofers Supply, employs 28 drivers across Utah, and Ms. Pappas said she would need at least 15 more to meet the exploding demand for shingles and tiles. The company has raised its starting wage by 10 percent since the beginning of the year to $17.50 an hour, but it’s not enough.

“We never want to have to say, ‘We can’t do it,’ but we need people,” Ms. Pappas said.

After eight years of steady growth, the main economic concern in Utah and a growing number of other states is no longer a lack of jobs, but a lack of workers. The unemployment rate here fell to 3.1 percent in March, among the lowest figures in the nation. Nearly a third of the 388 metropolitan areas tracked by the Bureau of Labor Statistics have an unemployment rate below 4 percent, well below the level that economists consider “full employment,” the normal churn of people quitting to find new jobs. The rate in some cities, like Ames, Iowa, and Boulder, Colo., is even lower, at 2 percent.

That’s good news for workers, who are reaping wage increases and moving to better jobs after years of stagnating pay that, for many, was stuck at a low level. Daniel Edlund, a 21-year-old call center worker in Provo, Utah, learned Monday that his hours were changing. On Wednesday, he had his first interview for a new job.

“I’m trying to find a company that treats you well,” he said.

But labor shortages are weighing on overall economic growth, slowing the pace of expansion in northern Utah and other fast-growing regions even as unemployment remains stubbornly high in Rust Belt cities like Cleveland and in regions still recovering from the 2008 recession, like inland California.

To Todd Bingham, the president of the Utah Manufacturers Association, “3.1 percent unemployment is fabulous unless you’re looking to hire people.”

“Our companies are saying, ‘We could grow faster, we could produce more product, if we had the workers,’” he said. “Is it holding the economy back? I think it definitely is.”

President Trump continues to promise that he will accelerate job growth by cutting taxes and regulations. But the accumulating evidence that workers are getting harder to find, and that wages are rising more quickly, has convinced many economists that significantly faster growth is unlikely. The Federal Reserve has cited the trend as its reason for moving to wind down its own economic stimulus campaign. The Fed may raise interest rates again at its next meeting in June.

Qualtrics, which conducts online market research, is a prime example of the rapid growth of the Utah economy — and the sense that Utah is straining at the limits of its growth potential. Scott Smith started the company with his son, Ryan, and a college classmate in his Provo home in 2002. Qualtrics now employs 1,300 people, including about 800 in a new headquarters building opened in August at the mouth of Provo Canyon. And it is bringing workers to Utah as fast as it can.

Each…