Nathan Newman, the housing activist behind the group More NYC, offers another suggestion: straight up cash. In a recent report, he argued that the city should drop inclusionary zoning and instead offer developers additional density in exchange for cash payments that the city could use to finance affordable housing programs.

While Mr. Newman’s report overstates the amount of affordable housing a cash fund could create, its core insight remains: Inclusionary zoning generates fewer affordable housing units than a cash equivalent because luxury apartments make for an expensive form of affordable housing.

There is a recent precedent for a cash-for-density deal with developers. Near the end of his tenure, former Mayor Michael R. Bloomberg proposed charging office developers $250 a square foot to build bigger office buildings near Grand Central Terminal, money the city would then have spent on infrastructure improvements. Mr. de Blasio is expected to advance a revised version of Mr. Bloomberg’s plan.

A similar notion could work with residential development, but the difficulty would be turning development fee proceeds into new affordable housing. Benjamin Dulchin, executive director of the Association for Neighborhood and Housing Development, says inclusionary zoning is better than a fee because the scarcest resource for affordable housing in New York isn’t money — it’s land.

“Econ 101, money equals land, but not in New York City right now,” Mr. Dulchin said. If new dollars to subsidize affordable housing end up chasing fixed quantities of land and apartments, that could just drive up rents for middle-income New Yorkers.

Mr. Dulchin’s analysis assumes that the supply of buildable area in New York City is relatively fixed and that the number of added residential units would necessarily be low. Because of the political barriers to rezoning, and rent stabilization laws that make it difficult to tear down buildings to build taller ones, his assumption may be reasonable. Efforts to permit more land to be developed or to allow more development on a given piece of land often meet resistance from neighbors, who worry that noise will increase, light will be blocked and parking will become more difficult.

This isn’t universally true: At least one part of New York City, a cluster of Orthodox and Hasidic neighborhoods in northern Brooklyn, has welcomed increased density. As Stephen J. Smith has reported for The New York Observer, developers in South Williamsburg have aggressively pursued the right to build dense, boring apartment blocks to accommodate the area’s rapidly growing Hasidic population — and the added capacity has helped keep prices relatively modest, far below those on the north side of Williamsburg.