For a more accurate model we would need:

* the actual number of people who wish to move to SF at any given time

* the number of people who pay rent control, but could pay more, and what that number is

* the actual rents that people pay under rent control

As obvious as parts of a toy model might be to people who are familiar with economics terminology, the toy model's conclusions are really quite 'new' to some people. For example: the rents in SF dont need to be 'supported' in the sense most of us think (by everyone). They merely need to be supported by a small amount of wealthy people bidding on a tiny amount of available apartments.

I think that's an important fact regarding how 'frothy' the market is. It can definitely go higher.