Your analysis is correct. Let's add one more factor:
At one point the prices become so high that people actually start getting out of the cities. That's what started happening in my country although it's going to be at least a decade until the consequences are felt (since the influx of people is still bigger than those who leave). But it did start happening.
At one point the prices become so high that people actually start getting out of the cities. That's what started happening in my country although it's going to be at least a decade until the consequences are felt (since the influx of people is still bigger than those who leave). But it did start happening.