If "affordable housing" means "under market price", in practice AH means that it goes to the connected at that price. If they can, they resell at market later, if they can't, well, they just got subsidized housing.
Remember, housing prices in high-priced areas are driven by location, location, location, location, location (yes, two more locations than ordinary housing), so "it's small" doesn't translate to "the market price is low." (It's just less expensive than big.)
When the "market price" exceeds the cash price, the folks who get to buy are the ones who have some way to pay outside the system.
Some countries have what's called "buyer-funded development". Property buyers invest into shares of the development company which then uses the funds to buy land and build housing.
Investors get much cheaper prices, developers get easy liquidity. The downside is that you have to wait a year or two before moving in, and some theoretical risk. (Which can be managed with proper legislation.)
But the scheme works if you want affordable housing.
No, that scheme doesn't do what you think it does (and that scheme is occasionally done in the US, especially for luxury residences).
Suppose that the residences will be worth $1000 when built and it costs $500 to build them.
The pay-in-advance price will be around $1000 - interest.
The pay-in-advance price won't be significantly less than $1000-interest because the builder can borrow the $500, and sell for $1000 when built, repaying the bank and pocketing the rest.
The pay-in-advance price won't be significantly more than $1000-interest because if it is, folks who want to buy will wait and pay $1000 when the units are built (forcing the builder to borrow $500).
In other words, pay in advance doesn't result in below market prices.
If you add in some units which would sell for $500 but you're forcing the builder to sell them for $250, the question is "who gets them?" The answer to that question does not depend on when the payment is made.
In the US, the vast majority of the "below market" units will be split between friends of the local govt and the developer.
Yes, it would be nice if that wasn't true, but it is absurd to behave as if it isn't true (in the US).
With "buyer-funded development" the developer gets free liquidity, with no interest and no obligation to pay anything back. (Just an obligation to build something.) Obviously more profitable than having a bank take a cut for a loan.
The property is cheaper for the buyer because there are obvious risks involved for those in on the scheme at an early time. (And yes, it can be significantly cheaper, both because of the risk and due to opportunity cost while the property becomes attractive on the second-hand market.)
Remember, housing prices in high-priced areas are driven by location, location, location, location, location (yes, two more locations than ordinary housing), so "it's small" doesn't translate to "the market price is low." (It's just less expensive than big.)
When the "market price" exceeds the cash price, the folks who get to buy are the ones who have some way to pay outside the system.