Abandoned houses with overgrown yards may be the image most people associate with Detroit, but the city’s downtown and midtown neighborhoods have the opposite problem: a shortage of rental apartments to meet a growing demand for an urban lifestyle.

Developers say occupancy rates in these areas are at least 96 percent, spurred by young professionals, students and empty nesters who want an easy commute to school or work and a short walk to local cafes and bars.

“To us it feels like there’s an insatiable demand,” said Fred Beal, manager of Motown Construction Partners, which led the recent renovation of the 124-unit Broderick Tower downtown.

Built in the late 1920s, the 34-story building near Comerica Park had been vacant for decades, but is fully leased after opening in November. Penthouse units that are 2,300 square feet command $5,000 a month, Mr. Beal said, though most of the studios and one- and two-bedroom apartments rent for $2,000 or less.