In any given week, the housing crisis in New York City reveals itself through new but familiar anecdotes of deprivation, in fresh sets of grim statistics, in staggering contradictions. Several days ago, residents of the notoriously beleaguered Louis H. Pink Houses in the East New York section of Brooklyn rallied to protest a lack of heat and hot water in the buildings, a recurring condition, they said, that left children sleeping in parkas and hats and getting sick. Not long after, a report from the city’s Department of Investigation revealed that over a four-year period beginning in 2013, the Housing Authority failed to conduct mandatory lead paint inspections in its apartments but then falsely certified to the federal government that it had, potentially jeopardizing the health of young children of more than 4,000 families. Overcrowding in apartments of all kinds is escalating as well.

Among the poor, those with housing are the fortunate. During the past year the homelessness rate has been stagnant — more than 62,000 people sleep in shelters each night. Earlier this month, a study from the Citizens’ Committee for Children indicated that the number of families with children who had entered the shelter system between 2012 and 2016 increased by 22 percent and the average length of a shelter stay went up during the same period.

Throughout his campaign for re-election, Mayor Bill de Blasio directed our attention again and again to his housing initiative, one committed to preserving and building 200,000 affordable residences by 2022 with an additional 100,000 units targeted for completion by 2026. Three hundred thousand units would, as his administration has pointed out, supply enough housing for the entire population of Boston or Seattle. But housing advocates have been concerned all along that the plan provides insufficiently for those facing the most severe financial challenges.

In response to this criticism, the mayor, earlier this year, committed an additional $1.9 billion in capital funds to ensure that a quarter of the housing stock under the plan would go to New Yorkers with “extremely low” and “very low” incomes. Ten percent of the apartments are meant for those with “extremely low” incomes (a family of three earning about $26,000 a year or less, for instance) and about 15 percent are for those in the second category (a family of the same size with an annual income in the range of $26,000 to $43,000). This leaves a vast majority of “affordable” apartments in the hands of those who earn anywhere from 51 to 165 percent of the median income for the metropolitan area, or from $43,000 to upward of $141,000 for a family of three. Advocates maintain that the balance ought to be shifted to those further down the income chain and that the greatest need exists among those families making about $35,000.