Now make a law that makes construction cheaper. Or make a law that makes construction more expensive. What happens to rent and mortgages, even though productivity hasn't changed at all?
Productivity (or, rather, wealth) of the occupants is a very strong factor, but it is still just one of multiple factors.
No, you actually cannot do this in any lasting way.
The price of land would fall to the level required to make it construction viable again. Or the city would be abandoned, which is not generally the outcome since cities have so much shared capital investment that cannot be moved elsewhere.
Put the following prompt into your favourite AI and enjoy the reading:
"How do rents relate to productivity in the area? How does Vienna compare to San Francisco?"
Try this one: "Create a simple analysis approximating how much higher rents would be in Vienna if not for the aggressive public subsidization of supply"
In any case, Vienna has a good system! But it's not that it avoids high productivity → high rent, it's that it splits rent into subsidy costs and rent.
In other words, the amount of subsidy + rent required will grow with local productivity.
Yes, it can be done, and if we want to have a reasonable future, it should be done.
Vienna's solution is fine but has escalating costs and isn't necessary. Land Value Tax is better.
Manipulating the real estate market via direct economic manipulation, collusion, or regulatory capture is so common that the entire concept of manipulating the market to earn higher profits is called https://en.wikipedia.org/wiki/Rent-seeking.
It's not just that it can, it's that it does so often it's taught in Econ 101. That you don't know this implies you have never taken an economics class or that you forgot what you were taught, and in the meantime certainly have not spent any real effort in learning about economic theory. I think you read a lot of Ayn Rand and right wing libertarian popular books about the free market and how it's perfect. Stop posting confident nonsense.
The claim is not that rents are always at their optimal or most efficient level - they're not! The claim is that you cannot (at meaningful scale) charge people who earn $1,000/month in income $2,000/month in rent to live in a place. They will have to move.
Did you take any arithmetic classes?
And any case, you should stop mind-reading. You're bad at it. I'm not a Randian nor a right-winger nor a libertarian nor free-market idealist.
Your mistake was thinking that I, the corrupt landlord who pays bribes, cares about a macro analysis of every all the properties, or that some analysis about the current distribution of incomes and possible rents will stop me from doing exactly what you say is impossible. I don't own every property in the city, especially the ones that aren't built because I capture zoning, so arguments about average GDP and average rent and whatever else do not stop me. Your analysis is useless.
This is the only feature that's relevant. If productivity goes up, you can charge more. If it does not, you cannot.
You may do some corruption or some zoning or some whatever else you want, but at the end of the day, if productivity goes up you can charge more and if it does not you cannot charge more.
Hope that clarifies!