Last fall, Carmina Albaladejo Ochogavia came to New York to work in her family’s growing business, Carmina Shoemaker. She represents the sixth generation of cobblers in the family, which is from Majorca, Spain. The business was named for her grandmother, and so was she.

After graduating from Kingston University London last spring, Ms. Albaladejo, an only child, worked at the company’s factory and headquarters on Majorca. Then, with her father, she headed to New York for a week of apartment hunting before starting work at the family’s new store, just north of Grand Central Terminal. Their mission was to find her a home — preferably a spacious one-bedroom where visiting relatives could stay — for $2,400 a month or less.

They found a few listings and visited some crowded open houses. One agent suggested that Ms. Albaladejo hunt downtown, figuring her social life would be there. But the inventory was disappointing.

“In the East Village and West Village, maybe the streets were cute, but the apartments were super-small,” said Ms. Albaladejo, 22. “I thought that in such a city there would be a lot of supply. And there was, actually, but they weren’t right.”