Ya, this could be a case of induced demand that we see in freeway building. Making more housing in a hot area where people want to live could conversely encourage more people to move to that hot area. Unless you just have slow growth like Japan/Tokyo, or some kind of residency restriction, I don’t see a way to cheaper prices just by adding in more supply. The increased density is still a win, just don’t expect it to make housing much cheaper.

More housing doesn't create demand, the city's economy creates demand. This is exactly why people have kept pouring into NYC and SF over the last few decades while the rate of new construction has slowed down to a crawl and nothing is affordable.

> More housing doesn't create demand, the city's economy creates demand.

I doubt there is a simple one-way causation, it's a feedback loop.

The economy of a city only grows if more and more people and businesses move in, which means more housing and density which in turn grows the economy and prices even more.

Is there any example of a city where housing was quite expensive and over time housing became cheap merely by building more of it, while still remaining a thriving city?

As far as I can see, once a city is thriving and expensive it only becomes cheap through economic collapse (e.g. Detroit) which isn't the solution anyone wanted.

Yeah, and it’s a faulty assumption that all investors price housing on the basis of rents. I recall reading that in Vancouver, BC they had a large influx of foreign money pouring into their housing market because it was a way for foreigners to expatriate their money. Drove prices through the roof. They had to impose measures to discourage it. Those properties, I read, often sat empty because using them for housing was never the intent of the owners.

Manhattan and SF has built almost no housing over the past several decades, and demand has continued to rise anyway, causing skyrocketing prices. Those metro areas are proving the exact opposite point you are trying to make. Building more housing is not what is creating more demand.

One of two things is happening.

Either induced demand is real which implies if you bought a corn field in Idaho and built enough high density housing you could make the housing more expensive than Manhattan and walk away richer than god.

Or high demand drives housing density and high prices.

> bought a corn field in Idaho

For an example how trying to build something up artificially in the middle of nowhere can fail, see California City. OTOH, for a counterexample see Las Vegas.

> Or high demand drives housing density and high prices.

Yes, and it also drives even more demand and even higher prices.

The premise of the OP is that you can make housing become cheap in an expensive city by building a lot more of it. If that works, there ought to be a few success story cities where it happened. Which ones are they?