[celtain]

>They moving there because they want to be in a big city - with friends, jobs, museums, and nightlife.

Sure

>So I don’t understand why Matt believes that building a few new apartments in some city - a very small move along that spectrum - would do anything other than make local prices go up.

Huh? Other than friends, none of the previously mentioned amenities are provided by apartment buildings.

Adding commercial real estate to a city adds jobs and amenities that make it more desirable, and thus more expensive.

Adding more housing does not.

That said, adding more housing raises the demand for commercial real estate (more available workers and customers), hence the cycle that leads to very dense, very expensive places like Manhattan. Strictly speaking though, adding apartments alone isn't enough to keep that cycle going.