Texas now has more Fortune 500 corporate headquarters than any other US State. No doubt helped by the fact that their receptionists, etc find living in Texas much more affordable than living in California or New York: look at the relevant housing prices (pdf). While Texas job growth is much better than the US national trend.
Texas is a case where population growth spurs the economy (and the economy spurs population growth) but housing prices do not shoot up because housing supply can react directly to housing demand.
The geography helps: flat land means there are limited geographical positional goods in housing. Places like San Francisco, with hills and beaches, mean there are strong geographical positional goods in housing, which encourage land regulation to protect said positional goods. (The same thing happens in Sydney.) Once you start that game, then housing landowners generally want it to continue since it boosts the value of their houses. If cities have lots of non-citizens who are new arrivals, this aggravates the process because housing market entrants are disproportionately not part of the political process, tilting regulation further in favour of housing market incumbents and against housing market entrants. So cities with geographical positional goods (hills, beaches) and lots of foreign migrants will tend to have high housing prices.
Cities with few geographical positional goods (flat land away from beaches) and lots of citizen-migrants (or foreign migrants well-connected to existing citizen networks—such as Hispanics in Texas) will tend to have lower housing prices.
Working out inequality implications from this is more complicated. Washington DC has by far the highest (pdf) level of income inequality as measured by the gini coefficient of any State/Territory in the US, New York is worse than Texas which is on par with California. Alaska, New Hampshire and Utah have the most equal income distributions. But US inequality is also directly connected to its higher per capita income, as one can see from comparing the income distribution of Swedish-Americans to Swedes.
ADDENDA In his response to my comment, Scott Sumner makes some thoughtful points (including a really nice compliment):
Lorenzo, As usual, you know far more about American housing than any Americans I know. Regarding the flat land in Texas, I think land use patterns also play a role. In the midwest there are many farms of roughly a square mile, which can be easily divided up into large housing developments. There is actually a fair bit of land around Boston that is undeveloped, but you don’t have large, easily divided farms or ranches. Instead you have older towns scattered across the western suburbs of Boston, and the residents of these towns try to preserve their semi-rural characteristics. Some midwesterners who visualize a densely populated East Coast might be shocked at how thinly populated many Boston suburbs are. Look on a map at how close places like Weston and Lincolm are to Boston and the Route 128 office belt, and yet large parts of them are quite rural, with horses walking down country lanes. This is true to a lesser extent of many other suburbs.That seems right to me, with semi-rurality being another positional good to be defended.