If price goes up or down is complex. In an area that has a small amount of demand stopping building ensures that those who want to live there have to keep bidding higher. If those who want to live there have a lot of money only a few people who want to live there but don't can push prices up greatly. It may well be that the area only needs to build a small number of units to fill demand, and additional units will need to lower prices to get a buyer. Supply is limited of course, but so is demand - I wouldn't take a free house in the Bay Area as my job is several time zones away and so the free house is still a net cost to me (if only to replace the roof ever 30 years)