That depends on a lot of factors. Manhattan is an example of a building boom not necessarily increasing supply or lowering prices: a lot of the building boom involved demolition of older, cheaper apartment buildings that were subdivided into small units, to be replaced with newer, higher-end apartment units subdivided into larger units. Net square footage increased, but square footage isn't identical to number of housing units. Which is why over the past 100 years Manhattan has gone from having cheap housing and 2.3 million people, to having expensive housing and 1.6 million people.
