Building a lot of housing in an expensive city will not lower rents there; it lowers them in the cheaper places that were absorbing its spillover demand.

In fact — and this is a point that is, in my opinion, underappreciated by the pro-housing side — building a bunch of housing in Santa Monica would probably not lower rents in Santa Monica. It would bring more people to Santa Monica, creating lower rents elsewhere in Greater Los Angeles as the spillovers from Santa Monica lessened.