DULUTH — The city of Duluth has worked hard to add jobs and make the city more attractive by nurturing its arts and outdoors scene. Now it’s coping with a problem caused by success: not enough housing for all those people moving in.

Duluth added more than 1,000 jobs between the fall of 2012 and 2013, according to the most recent state data.  Jobs in engineering and architectural services nearly doubled in the past decade.

“Folks are coming in and they’re making $50,000 a year,” Mayor Don Ness said.

“What they’re looking for is a nice, clean modern unit that they can spend somewhere between $600 and $1,200 a month,” he said. “So it’s not the very low income (but) it’s not the very expensive places.”

With Duluth’s rental vacancy rate below 2 percent, a recent study found the city needs to add 1,000 new housing units in the next three years, and another 1,300 by 2020.

Caralyn Stevens is one of the newcomers who struggled to find a decent place to rent. She joined LHB, an engineering firm that has added nearly 100 people in the past two years. Stevens, a designer who grew up in neighboring Superior, Wis., was eager to live in Duluth close to work and a short drive from the woods.

“I don’t need a castle,” Stevens said. “But I found myself in about a 300-square-foot studio apartment, on the third floor of an old building, paying between $550-600 for a 300-square-foot apartment. It just felt like robbery.”

Similar housing issues are being seen in other towns far from the Minneapolis-St. Paul area, from Roseau and Thief River Falls to Worthington. Digi-Key is busing workers to Thief River falls. The rental vacancy rate in Roseau, home to thriving snowmobile manufacturer Polaris, is almost zero.

Mary Tingerthal, commissioner of the Minnesota Housing Finance Agency, said developers are hesitant to rush into such traditionally low-rental-cost markets because they worry that people won’t be willing to pay enough rent for them to make enough on their investment. She said the state is encouraging developers to push up rents a little because new hires can often afford more than market rate.

The state is investing $10 million over two years to develop housing in communities with tight housing markets.