Lets say I own 50 properties and I want to charge $2000 a month, and right now I can't because the people willing to rent my properties only make $1000 a month. I can bribe politicians to not allow any new construction of properties which rent between $2000 and $4000 per month. Then I wait 10 years. Now I can charge $2000 a month because I'm not renting to the people that made $1000 a month 10 years ago, I'm renting to the people who have $2000 a month to pay for rent but can't find any other units. This is called rent-seeking. You should read about it.

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.