The Massive Inefficiency in San Francisco Public Housing

The San Francisco Chronicle reports on public housing in San Francisco.Things are quite inefficient.The Chronicle reports:

With aging properties that require more upkeep and union contracts that expire Sept. 30, it's a particularly tough time to be losing more money

Here are some numbers the Chronicle gives.There are 12,000 public housing residents with a budget of 221 Million dollars.That comes out to $18,416 a year or $1534 a month for each individual which includes children.So a mom with two kids is getting a subsidy of $4602 a month.Couldn't the private sector do this much cheaper? I guess when you have 400 employees monitering a system it's probably not that efficient.