> The problem is: why would you build more housing as prices fall?

Profitability is not black-and-white. Real estate investments can still be profitable if prices fall.

There are different types of real estate markets too. Working class homes in suburbs are not the same market as upper middle class apartments in an urban center.

A very interesting type of investment is high-density housing in catchment areas of new public transportation hubs. Those tend to be so profitable that they can even finance the investment in the public transportation service.

All you need is willingness to invest.