Build a fifty lane wide highway in the wilds of Montana and it will carry about as many cars as the current freeway.

We see induced demand in highways because the thing highways provide is valued (land for private vehicle operation), but the price charged is almost always far far less, usually zero. So just like a Starbucks that started to offer free coffee, the result is going to be long lines.

If housing was being offered below value, then you would surely see induced demand in housing. Imagine for instance if a govt program committed to offering apartments of unlimited size for $0/month. People would absolutely decide they need a 5000 sqft apartment instead of a 2000 sqft apartment, just as today they decide they need to drive to a store 10 miles away, instead of walking to one around the corner.

There are other factors to consider like transportation and traffic, the quality of life of the inhabitants, business, tourism, future growth, climate resilience and so forth.

This isn’t a let’s cut down a bunch of trees and build a house out of low quality lumber in a week kinda situation.

It took 20 months to build the 380-meter Empire State Building, which is about 6 days per story, and it is not made of low-quality lumber. Nowadays we know how to build taller buildings than that, though it usually takes a little longer; 广州周大福中心 took 6 years to build (75 months) ending in 02016 and has 111 floors in 530 meters, thus requiring about three weeks per floor. Barcelona wouldn't even be able to do the paperwork to build a new building in 6 years.

You might object that skyscrapers are impractically expensive. They can be a bit expensive, but they don't have to be. 广州周大福中心 is half residential, consisting of just over 600 apartments and hotel rooms, so contains space for about 1200 residences, and was built on a budget of US$1.5 billion, about US$1.3 million per residence-equivalent. This is partly because the residences are large; the building's total floor area is 508k square meters, so we're talking about 400 square meters per residence-equivalent. If you'd carved it into 40-square-meter efficiency apartments it would hold 12700 of them and house 25000 people, at a cost of US$120k per apartment. Also, skyscrapers that aren't among the world's tallest buildings are generally cheaper per unit area.

Skyscrapers are not the only way to get high population density, just the least bad way. 广州市 has 2500 people per square kilometer and a per capita GDP of US$23k per year. Manhattan, where the Empire State Building is (but which has lost the ability to build) has 29000 people per square kilometer and a per capita GDP of US$550k per year. Giza has 45000 people per square kilometer, without many skyscrapers, and a per capita GDP of about US$7000 per year (nominal).

Note that 广州周大福中心 occupies a lot of 27k square meters. The hypothetical same-sized building of efficiency apartments would have a population density of a million people per square kilometer, 20 times Giza's and 6 times Imbaba, Giza's densest district. Even the actually existing luxury building has a population density of about 50k per square kilometer, probably denser than Giza.

Barcelona? Barcelona has 15000 people per square kilometer and a per capita GDP of US$103k per year. Barcelona's problem is not that there isn't space for all the people or that greater density would inevitably produce misery.

广州市 = Guangzhou

广州周大福中心 = Guangzhou Chow Tai Fook Center

Edit: and BTW I find it bizarre to use Chinese characters like this on an English language forum without providing an English translation. To most readers here, they're a meaningless string of unfamiliar characters.

  ((广州市, 广州周大福中心) => 广州市 < 2 ? 1 : 广州市 * 广州周大福中心(广州市 - 1, 广州周大福中心))(10, (广州市, 广州周大福中心) => 广州市 < 2 ? 1 : 广州市 * 广州周大福中心(广州市 - 1, 广州周大福中心))

For better or worse, perl is by default unwilling to parse them as Perl.

"we've tried not building any housing, and we're all out of ideas"

It does. Evidence: no large city in the US, Japan, or the Western Europe managed to lower housing prices long-term by increasing density.

Prices only go down if the city population goes down or stops growing.

Once the population growth returned, the prices went up as well. And no amount of new construction helped: https://www.globalpropertyguide.com/europe/austria/home-pric...

Again, perfectly fits my prediction and contradicts your model.