I assume once you take the profit motive out and are providing cheap housing, rather than Manhattan Drive style housing, the rents pay for the cost incurred by the govt.
This is how the 20% is achieved. Basic housing with no profit motive but shelter for the people motive.
Those who want better housing can go private - nothing stopping them BUT the reduced demand of course due to the social housing provided helps keep costs down for everyone.
Whereas in Australia we have developers locking up land and deliberately not releasing it to keep supply low and prices high PLUS councils and state govts various zoning laws stopping cheap housing from getting built. We also NIMBY protests by people in expensive houses because they believe the cheap houses being built near them will make their own house price fall in value.
The profit motive on shelter is the problem. Remove it and things get fixed.
