To allow this building to come to be, the city had to waive current zoning and density rules that limit apartments to no less than 400 square feet.

The project is being watched with interest by both housing advocates and developers, and not just because of its modular construction. Housing advocates say the creation of more micro-apartments could open up many more reasonably priced living options. More units dedicated to singles could eventually bring down rent prices across the city, as more two- to four-bedroom apartments would then open up to families. Singles looking for larger apartments to share with others may have artificially inflated the rental market, as the combined incomes of roommates can be greater than those of families.

Some developers have a related idea on the drawing board, “micro-suites,” or apartments that are slightly larger than the legal limit — at, say, 500 square feet — but house two or three singles in separate, albeit tiny, bedrooms.

Whether New Yorkers can live (and happily, at that) in less than 400 square feet is not really in question — many New Yorkers already do. Micro-apartments that were built before the zoning rules were enacted in 1987 exist throughout the city. There are some 3,000 apartments under 400 square feet in Manhattan alone, according to Jonathan J. Miller, the president of Miller Samuel, a real estate appraisal and consulting firm.

Kelli Okuji, 27, a graduate student at Columbia University, lives in one, a newly renovated apartment of 313 square feet at the Greystone, a former hotel built in 1923 on the Upper West Side that has since turned its rooms into luxury rentals. Ms. Okuji occupies one of 26 efficiency units under 400 square feet, each of which comes with high-end finishes and appliances, a Murphy bed that tucks into the wall and access to a broad variety of building amenities, including a gym and a landscaped rooftop lounge.