Why are big cities becoming expensive places to live? One answer is that they have good jobs and restrictions on housing construction. That may be right.
But one possibility I want to throw out there is that people want affluent neighbors. If I want an affluent neighbor, and an affluent neighbor is going to live in a neighborhood with high prices, then in some sense I want to live in a neighborhood with high prices. In the extreme, this makes my demand for neighborhoods upward-sloping. Higher prices make me want to live there.
I first considered this possibility many years ago when thinking about school vouchers. I thought that if what people really want for their children is to have them go to school with affluent children, then vouchers would not work as well. Instead of allowing non-affluent parents to send their children to good private schools, the result would just be that good private schools would raise prices so that only affluent children can attend.
I also think that some colleges that are not in the top tier may face upward-sloping demand. George Washington University, which is hardly an academic icon, may benefit from charging very high tuition. Affluent parents come and see a student population that is predominantly affluent, and this gives them comfort that sending their children to GW is a high-status thing to do.
Back to cities. Suppose that an important “urban amenity” is having a lot of affluent people around. Young singles may wish to meet potential marriage partners who are affluent. People who have acquired affluent tastes (sushi, yoga, wine) may want to be around people with similar tastes.
If that is the case, then there is not much that a mid-sized midwestern city can do to lure affluent people. The cost of living there is not high enough to create a barrier to non-affluent people living there. And that means that affluent people will not want to live there.