There is indeed a huge shortage of housing and building in East Jerusalem. Of course, the shortage is for Palestinians, who are being systematically pushed out of Jerusalem. Israel delays or refusing to give them permits for new housing, and if they apply to add a level onto their existing homes, Israel refuses and then bulldozes the house if they build it anyway.
Palestinian girl, 17, arrested in Old City of Jerusalem with knife in her bag (Haaretz)
from the article: Netanyahu approves tenders for 238 homes east of Green Line