If people can't afford the rents then they'll just cram more people in. Currently have a "Joey/Chandler" style apartment form friends with 2 people in for $4k/month? Now you get 4. Or 6. Price increases to $6k/month but it's down on a per-person basis.

In some cities you get time-sharing beds. In 2003 I lived (for 3 weeks) in a house in London, I had my own room - the largest in the house. A smaller room had a couple with a baby, the loft had 3 mattresses in it but 4 people living there, time-sharing with the mattresses like you have in a nuclear submarine.

There's plenty of opportunity for landlords to increases costs even if peoples incomes can't support an increase.