> I think the extra factor is that rich people seem to attract more rich people. That is the number that I think can't be out built.

That isn't a real problem though. If people are coming who actually want to live there, let them. There are zero cities in the world that are entirely covered in buildings the height of the Empire State Building. Every time you sell a housing unit for more than it cost to construct, you have that much more money to construct more housing with.

The actual problem is that the existing residents pass zoning regulations preventing high density new construction, because they know it would reduce housing costs, but once they live there their housing costs are fixed and what they're worried about is increasing their property values.