Problem is demand is increasing at a far greater rate than the supply. In fact, I think this is -- among several other factors -- one of the primary causes of this migration.

The money an individual or a family has to spend is limited. For most, the rent is their single biggest expense: the less one makes, the more one has to give up (in terms of money that would go to savings, basic necessities, or food/entertainment) to live in a more desirable place.

Given that income distributions even with some amount of redistribution will still follow a power curve, it is quite possible that certain highly desirable areas -- themselves on a power curve of desirability -- might see great population growth, but -- on the whole -- the movement would not be to those areas. That is, unless, the supply of housing in those ares can keep up with the demand.