Last week a housing advocacy group released a report showing that many of the apartments built under Mayor Bloomberg's New Housing Marketplace Plan are not affordable to people living in the neighborhoods where the housing is located.

What's interesting is that this is so even though the mayor's initiative is serving more people at low incomes than his administration planned.

In its report, the Association of Neighborhood Housing Developers found that a third of units produced under the Bloomberg plan "have an upper income limit above the actual New York City median income"

What's more, in half of the city's 59 community districts, "the majority of units built in the community are too expensive for a household earning the local median income for the neighborhood." Finally, "two­thirds of New Housing Marketplace units are too expensive for the majority of local neighborhood residents."

But one key statistic cited by ANHD is that from fiscal year 2004 through fiscal year 2011, 82.9 percent of units produced under the mayor's plan served households making less than 80 percent of "area median income," or AMI.

Back in 2006, when Bloomberg increased his affordable housing goal from 68,000 units to 165,000 units, his plan aimed to devote 68 percent of its units to people making less than 80 percent of AMI.

In other words, the mayor's initiative has devoted a far larger share of its units to people making less than 80 percent AMI (83 percent) than was planned (68 percent). But they're still not affordable, according to ANHD. What's going on here?

For one thing, AMI— a regional income statistic tracked by the federal government and on which most housing subsidies are based—is a flawed measure because it takes into account incomes in wealthy suburbs. Right now the AMI for New York City about $83,000 for a family of four. According to the Census Bureau, the actual median income in 2011 for a family of four here was $61,401.

So that explains the statistical weirdness of the mayor's plan exceeding its numerical goals, while failing to deliver on actual "affordable" housing in many neighborhoods: The threshold the plan used for "low-income" has little to do with real low-income people in the city. But beyond the statistical oddities, why didn't the plan deliver more truly affordable housing?

In fairness, the mayor's plan from the outset aimed to serve income groups not typically helped by affordable housing, i.e. the middle class. And, as we've reported before, the units created under the plan are often hashed out in deals with individual developers, who will battle to get the highest rents (meaning, the highest-income tenants) they can.

More importantly, affordable housing isn't magic: Somebody has to pay the hefty cost of amortizing building costs and maintaining apartment houses (buying oil, taking out the trash, etc.) Since affordable housing rents are based on income, buildings that serve really poor people are harder to build and maintain because the rent roll can't offer very much. Bloomberg's plan always faced a steeper challenge than Mayor Koch's 10-year-plan because Koch could use the vast supply of tax-foreclosed property the city had on its books; Bloomberg never had as much of this "free" land to play with. And as City Limits reported in 2007, rising construction costs—due in part to the local development boom fed by other Bloomberg policies—squeezed the affordable housing plan. Ultimately, in the face of those costs, the city adjusted the plan to do less new construction and more preservation of existing housing and to span 11 years instead of 10.

Both the flaws in AMI and the math challenge underlying all affordable housing point to an underlying issue: The housing crunch in New York is as much an income problem as it is a housing problem.

In the past six years median income for a family of four in the city has increased 8.7 percent, while the inflation rate for housing has run about 16.7 percent. According to the Independent Budget Office, the top 1 percent takes home 34 percent of income in the city. The entire bottom half of the city's taxpayers earn only 9 percent of its income.

This squeeze on low- and moderate-income people is probably one reason why, according to the 2011 Housing and Vacancy Survey, more than half of New Yorkers pay more than the recommended 30 percent of their income in rent. A stunning 17 percent pay more than 80 percent of their income for shelter.

Of course, since before the time of Jacob Riis, there have always been people who couldn't afford decent housing in New York. And sure, some of the cost of the city's housing could be blamed on the city's complex building code or zoning rules. But while ANHD provides a list of interesting recommendations for how to better align the city's "affordable" housing with the people who most need help affording housing, one wonders if the housing crunch can be successfully addressed without looking at growing income inequality.