Re: Copley Place plan calls for condo tower
The city dictates what the affordable housing rates will be in these new projects. It's based on a percent of annual area median income. I don't remember off hand (surely there's an affordable housing expert in our midst on these forums), but who lives in these units is determined by a housing lottery and they pay the affordable rate for up to 50 years.
Affordable housing programs vary in both their income eligibility terms and their rent limits. There are local, state, and federal programs (multiple at each level), it's not always the city. Most affordable properties have multiple layers of support, which means multiple thresholds or tiers for qualification and rent limits. You're right that sometimes it's a lottery, not always though (very commonly it is in Boston given the extreme demand). A lot of the programs derive their income limits from annually updated HUD data, and then tweak it a bit. So they're not all exactly the same, but close.
I don't happen to know which programs this property has, so I can't say whether the City has a say. This web site has a useful introduction to what the limits look like in three MA cities for a range of programs (please note that some of these charts are for 60% AMI, some for 80% AMI, etc):
http://www.massresources.org/affordable-housing-financial-eligibility.html
So just for a taste of what the 60AMI implies: if you've got federal Low Income Housing Tax Credits, you've probably got a bunch of units at the 60% AMI level for a household of four in Boston is $56,460. That's total gross income for the family, before taxes. If there are two adults working equal hours, 40 hours per week base and averaging 10 hours overtime at time and a half, for 50 weeks, that gets to a ballpark base hourly wage of a tad over $10 per hour, just above minimum. Many households at this income level have far more patchy collections of income: multiple jobs, some more or less predictable in hours per week. These are folks often referred to as "the working poor", cause they're working, but feeding, clothing, housing four people on that sum of money in Boston is a real struggle.
The full source charts (deeper links within the link I've attached) break it down by household size, so there's different limits for differently sized households.
Note that the Tax Credit, and a number of other programs, are NOT operating subsidies. They help finance the project's construction, and in return the owner must meet program requirements for X years. Flat minimum term these days is 30 years, and I just about never see less than 50 in Boston; some go 99 years, a few try for "in perpetuity". Section 8 is an operating subsidy, by contrast.