Two months ago, a report issued by the Association for Neighborhood and Housing Development, a consortium of neighborhood housing groups, indicated that out of the 38,670 units developed by the Bloomberg housing plan from 2009 to 2011, only one-third of them were economically within reach of households making the median income or less for the typical household in their neighborhood. Of the units the city developed over the same period, only about 8 percent were intended for households making less than 40 percent of the metropolitan area’s median income, though they make up nearly one-third of all New York City households.

Another dimension to all this is what Alex Schwartz, a professor of urban planning at the New School, likens to a bathtub with a running faucet and an open drain. As the city builds new units of affordable housing, old units age out of the system. Much of the affordable housing isn’t meant to be affordable forever simply because it isn’t financially feasible, so rents go up, tax breaks expire and units nudge toward market rate. Last week, the housing development association issued new data indicating where existing affordable housing had disappeared or was threatened. In the University Heights section of the Bronx, 5,000 units of housing from 2008 to 2011 became unaffordable, with rents requiring incomes of more than 80 percent of the area’s median income.

The New York City Housing Authority, where the average monthly rent as of this year is $436, offers permanent affordability, of course, but there are currently more than 167,000 families on its waiting list (and more than 123,000 families on a waiting list, now closed, for Section 8 federal housing vouchers, which have had their financing reduced by sequestration). One partial solution to clearing the backlog would be to relocate older residents living alone in large apartments in public housing to smaller ones and give over two- and three-bedroom apartments to the families who need them. “It isn’t all that complicated,” Christine C. Quinn, the City Council speaker and a Democrat, said at the candidates’ forum, “even though it isn’t happening.”

Creating actual affordable housing, buildings that can pay for themselves in the absence of growing subsidies, will be a formidable challenge for the next mayor. John C. Liu, a Democratic candidate, proposes to do it with what he calls the People’s Budget, which he unveiled last week and which includes $27 million in housing vouchers for the homeless and $3.7 billion in capital funds to help create 100,000 units of affordable housing over a four-year period. He would finance these and other ambitions through tax increases on those making more than $1 million a year, charging rents to charter schools using city facilities and taxing private equity firms’ carried interest, to cite a few examples.

Advocates and analysts in the affordable housing world have talked about addressing some of this difficulty by cross-subsidizing buildings, a process that would have a mixed-income building in the Bronx, for instance, helping to offset the costs of a primarily low-income building in Brooklyn. I would propose another form of cross-subsidization called the You Don’t Need to Live in a $50 Million Penthouse Tax, which would require anyone buying a property for more than $10 million (of which there are currently about 280 listed in The Times) to pay a percentage of that cost to an affordable-housing fund. And then commit, in writing, to never complain about it.