> Only if you assume the current population of the city is held steady and you are not beaten out by new arrivals.
The population does not have to be held steady for the new high-end housing to lower prices for mid and low-end housing.
The only assumption the parent makes is that the aggregate desire of people not currently living in SF to move to SF is not affected by the increase in supply. This is an assumption, but I don't think an outlandish one.
Yes, of course some of the newly opened mid-level apartments (when their previous inhabitant moves to a high-end apartment) will be filled by new comers. But aren't those new comers going to compete for the existing space whether or not a more high-end space gets built?