On Tuesday, Metropolitan Life announced the sale of Peter Cooper Village and Stuyvesant Town to Tishman Speyer for $5.4 billion dollars. Stuyvesant Town was a state-subsidized project first planned in 1943, when rent control was imposed on New York. The two complexes are the embodiment of postwar New York’s two approaches to housing affordability: rent control and supply subsidies.

Both were built on the Lower East Side with the help of tax breaks and eminent domain, which were at that time the supply-side instruments of choice. The subsidies to private developers were accompanied by later handouts to tenants. Rent control and stabilization eventually made apartments in the project a great deal for the lucky few who got them.

The perversity of this situation on the Lower East Side, where rent control took from landlords and gave to tenants and subsidies then gave back to landlords, became an emblem of the perversities of residential planning in New York. Rent control and subsidized construction were a balancing act where public subsidies replaced the private incentives to build. The two interventions together managed to mimic the amount of construction that would have come from a free market, but inflicted a wide range of other harms on the city.

Rent control deterred building and also eventually reduced the supply of rental units by pushing landlords to convert rental units to cooperatives. As rent control eliminated the incentives for landlords to maintain and upgrade, grand edifices like the West Side’s Ansonia slipped into disrepair and decay.

Rent control turned off the price mechanism for allocating apartments, and units ended up in the hands of the well-connected or the fortunate, rather than in the hands of those were willing to pay most for them. Ken Auletta’s “The Streets were Paved with Gold” tells how world tobacconist, Nat Sherman, rented a six-room Central Park West apartment for $335 dollars a month in the mid-1970s, and declared, “it happens to be used so little that I think [the rent] is fair.” Since he didn’t value the apartment, he thought he wasn’t getting much of a deal, but many others would have paid in the low thousands for the same space.

The government’s adventures in housing supply were hardly more successful. Le Corbusier-inspired projects crammed large quantities of the poor into ultra-segregated high-rises. Violent crime and mismanagement were the most salient characteristics of many projects. Privately run, subsidized projects like Peter Cooper Village and Stuyvesant Town were more efficient, but their construction saw the ugly practice of using eminent domain to tear down existing neighborhoods to build racially segregated buildings.

Today, we have a chance for a better housing regime that can make Manhattan more affordable for everyone. Just as in 1947,high prices can be eased with more supply. But today, we don’t need subsidies to generate more housing. Today’s high housing prices can cover construction costs for almost any sort of project.

The problem this time is different. There are a host of regulatory barriers to construction. The brawl in Brooklyn over shortening the Atlantic Yards tower shows how effective community groups can be in limiting height and the supply of homes. As these community groups have grown since the 1970s, the heights of new residential buildings in Manhattan have plummeted.

The tenants association had tried to buy Peter Cooper and Stuyvesant on the cheap with government help. The sale to a private developer represents a victory for the free market over state control. It could be the start of a sensible housing policy that would replace rent stabilization with an affordability policy that emphasized eliminating the barriers to new construction. A supply-oriented policy could reduce prices without the pernicious negative effects of centrally managed prices. We could focus on reducing the barriers to building less expensive units, but any new housing increases supply and makes New York more affordable. Mayor Bloomberg should fight the community groups that make Manhattan unaffordable by restricting heights as avidly as he would fight someone lighting up a Marlboro in a saloon.

The Peter Cooper-Stuyvesant parcel offers a tempting place for a new supply-side policy to start. The new buyers have been saying soothing things about not disturbing any of the current rental arrangements. While this may sound nice, the status quo represents a terrible underutilization of a fantastic piece of Manhattan. A much better outcome would be for Tishman Speyer to vastly increase the total number of units in the complexes by gradually replacing the existing stock with taller buildings. Those 80 acres could easily hold many more units, which could boost Manhattan’s housing supply and ease prices.

If Mayor Bloomberg reduced the regulatory hurdles to construction and made it easier to deal with the current rent stabilized tenants, then Tishman Speyer would surely be happy to build up. The mayor might offer to help the new owner come to a reasonable buyout of the rent stabilized tenants in exchange for a commitment to build a significant number of units. Such a deal would exchange the false affordability of rent control, which has select benefits for a favored few, with true affordability of abundant supply, which makes the city more affordable for everyone.

Mr. Glaeser is the Glimp professor of economics at Harvard, director of the Taubman Center for State and Local Government, and a senior fellow at the Manhattan Institute.