There is one thing that seems like it legitimately does work, but it requires a lot of time and a lot of expense. Have the the city (or some other organization interested in providing affordable housing) purchase and/or build so many non-profit housing rental units that it distorts the private market.
In Vienna, around 30% of the rental units in the city are offered through socialized housing programs that are incredibly secure, and low cost. There's so many of these units, that landlords in the private market have to compete with their prices. The for-profit rental units are more expensive than the socialized units, but the average price is still very low compared to comparable cities. As a result, Vienna is the cheapest major city in the German-speaking part of Europe, and Viennese people spend a much smaller portion of their income on housing than their peers spend pretty much europe-wide.
It's an interesting idea and I'm generally in favor of more social housing. I'd be even more in favor of it not being needed at all.
When market rent would be 1,200 yet you pay 800, somebody is paying for that 400. Typically the government, thus tax payers, and it will be subject to political turbulence. Ideally you want so much supply that the market value rent would be 800, as your idea illustrates.
The problem, at least over here, is that the naked price is still very high even without any profit motive. Land is expensive because cities are funded by that. And building that home really does cost 150-200K.
I'm sure you can find some 50K of wiggle room, but at the end of the day it's still going to cost 350K and rent/mortgage will reflect that.
While I somewhat agree with you, I feel compelled to mention that the most derisive term in the lexicon of Economics is "rent seeking behaviour" when they want to describe the behaviour of an actor in an economic system as non-productive, and parasitic, and that terminology is not an accident. It comes from the tendancy of land or property rental markets to quickly become non-productive exercises in wealth extraction by landlords.
While it's definitely possible to screw up a market via government intervention, I don't think it's really true that there's a fixed pie here that is being cut up and redistributed by this policy. I think it's better to be thought of as intervening to stop the rental market from going off the rails.
Buying land or property in Vienna is expensive, but it's actually not significantly more expensive than comparably sized German cities which don't have comparable social housing programs.
I should also note that the socialized housing in Vienna is not something that's just for poor people. People from every social class use it, and it's typically quite well maintained and high quality housing.
The nice thing about trying to follow Vienna's implementation too is that even at the very start, the city can help a lot of people by providing cheap, secure socialized housing to them, even if it will take a long time to benefit renters in the rest of the city.
I think this is a really nice example of how socialized policies can work really well when those socialized policies are aimed at taking advantage of market mechanisms, rather than resisting those market mechanisms.
In Vienna, around 30% of the rental units in the city are offered through socialized housing programs that are incredibly secure, and low cost. There's so many of these units, that landlords in the private market have to compete with their prices. The for-profit rental units are more expensive than the socialized units, but the average price is still very low compared to comparable cities. As a result, Vienna is the cheapest major city in the German-speaking part of Europe, and Viennese people spend a much smaller portion of their income on housing than their peers spend pretty much europe-wide.