NYC is probably not a good example to use here. Its median property prices are negative this year and flat for two years before that. It's likely (IMHO) that the post-recession building boom is a factor.
It's a perfect example for exactly that reason. NYC is expensive, but not as expensive as cities like San Francisco, precisely because we have more apartments here.
We should be building significantly more, but this shows the continuum. Tokyo > New York City > San Francisco
Another difference to consider is the superior transit infrastructure which allows for a much larger viable region to live in if you work in Manhattan, versus San Francisco within the Bay Area.
We should be building significantly more, but this shows the continuum. Tokyo > New York City > San Francisco