Are expensive cities economically threatened by an inability to house low-income workers?
Something missing from more traditional analyses is that a significant number of people may move to a new (expensive) location, take a job that pays a wage insufficient to cover living expenses, and burn through their savings until they're forced to relocate.  This happens quite often in "fashionable" locations such as San Francisco.

This is actually a strong argument in favor of a higher minimum wage in such places, even taking a "hard-line" position that such laws only result in the loss of low-paying jobs &mdash; because such jobs are a "trap" that lures people (with savings) into an unsustainable situation in which they are exploited until they run out of savings, at which point they are replaced by somebody else with savings to exploit.  Eliminating all jobs that pay wages insufficient to actually live (on an ongoing basis) in expensive markets guarantees that such "exploit the newcomers" economies cannot persist for very long.