I've been thinking about this recently. If you look at places like California, where housing costs are through the roof, it's characterized by build-out---every plot of land that's close to anything already has something on it. Without density restrictions (zoning), the economics of the situation would have long-since compelled developers to build up. San Francisco would probably look like Manhattan by now.
But San Francisco has effectively prevented new development to preserve its character, and since freeways aren't being built like they were in the 50s and 60s, the end result is a housing shortage that pushes prices through the roof. Even in a place like Manhattan, we find a housing market distorted by BANANAs and rent controls rendered unable to meet demand.
Here, inner-city housing supplies have exploaded due to lax regulation, and the result is that housing isn't unaffordable in even the most trendy neighborhoods. Interestingly, if you compare two neighborhoods of equal trendiness, the Gold Coast and Lincoln Park, LP is actually more expensive even though it is further from downtown---in large part, I believe, because new units are coming on line significantly faster in high-rise GC than in low-rise LP.
Anyhow, my question is, are there any studies done on this? On the face it seems ipso facto, but I'd like to see if someone's proven it in a scientific paper for political reasons.