Tupper takes in a combined $3,700 a month from Social Security and her teacher's pension. She said one-room studios in her seven-unit building can go for as much as $3,000 a month.

The median monthly rent for unregulated apartments citywide was $1,369 in 2011; for rent-stabilized units it was $1,050, the city survey showed. Yet in Manhattan, average rents hit a record $3,418 in March, Citi Habitats, a real estate brokerage, said in an April 16 report.

New York's history of rent regulation goes back to 1920, when a post-World War I housing shortage prompted the state to enact temporary rules, upheld two years later by the U.S. Supreme Court. The federal government imposed emergency controls during World War II as part of a nationwide push to prevent rents from soaring in cities central to the war effort.

Rent Guidelines Board

The current system dates to 1969 when the state responded to rising rents and falling vacancy rates by enacting the Rent Stabilization Law, which now governs almost all the city's rent- limited apartments, including those of the Harmons.

Under the law, cities may limit rents if their vacancy rate is less than 5 percent -- a test New York easily meets. Its vacancy rate in 2011 was 3.12 percent, the city survey showed.

The system limits annual rent increases to a percentage set by the Rent Guidelines Board -- 3.75 percent for a one-year lease in the most recent adjustment. About 40,000 units are still covered under the older rent-control regime, which ties increases to a landlord's operating costs.

The law gives tenants broad rights to remain in an apartment or pass it on to a family member.

The Harmon family has owned the West 76th Street brownstone since 1949, when James's grandparents bought it with a $22,000 mortgage, according to court documents. James and his brother inherited the building in 1994, and James bought out his sibling's interest in 2005 for $1.5 million.

The Harmons live on the first floor. The three upper floors each have two units -- one rent-stabilized, one market-rate. The tenants in the low-rent apartments have all lived there since at least 1982. One owns a home in the Hamptons on Long Island, purchased for $320,000 in 2001, according to the Harmons' 2008 complaint.

The Harmons contend the rent-stabilization law is an unconstitutional "taking" of private property without compensation. They say previous Supreme Court decisions allow rent-control laws only for emergency situations and that New York's decades-old system has effectively become permanent.