EMERYVILLE, Calif.—The economy is booming in the Bay Area, but at Patatas Neighborhood Kitchen, located in this small city just north of Oakland, owner Marcos Quezada recently eliminated the dinner shift and laid off six of his 10 workers.

He struggled with the decision but felt he had no choice after Emeryville increased its hourly minimum wage in July from $15 to $16.30, the highest in the U.S. “I just didn’t see how I was going to survive it,” said Mr. Quezada, who opened the eatery in 2017.

This...