One thing I left out of my calculation the housing unit costs the other day in the interest of simplification was the efficiency of the building, but I probably shouldn’t have because it’s a huge factor. David Baker pointed out in a comment:
One thing, if the 800 Square foot is cost for the building overall the apartment size you are talking about is more like 640 (SF), Excluding corridors, stairs, etc.
This is exactly right- the units do not make up the entire building. Once space is subtracted for elevators, lobbies, mechanical equipment rooms, stairs and all of the other things that are necessary to make a building work, the building is usually only about 80% (or less) efficient- the percentage being what portion of the whole is comprised of the housing units.
Efficiency is a big factor on urban sites because there is often little freedom to optimize the dimensions of the building to fit the most number of units into the boundaries of the site while also staying under the height limits set in the planning code. Additionally, there are many code requirements regarding firefighter access and separation distances that further constrain the design.