So demand for cheap apartments fall and prices stagnate. But you can't just think about one step, you have to consider the implications of that step. For example, if people are moving out of their bad apartments into nicer apartments and homes, demand for nice apartments and homes will increase, driving prices higher. Which makes sense--suddenly there is much more money available for housing. But that's not the end of the story, either.

What is the incentive for the owners of small apartment complexes? It seems clear. They need to renovate their apartments so that they can capture the new up-market demand. Successful, mid-tier apartments could buy up cheaper complexes to renovate them and charge higher prices (this happens even now).

The low-demand, low-price alternatives will fade away, because the land owners can make more money with slightly nicer, more expensive units.