Bloomberg is notorious for pretending government is the solution rather than the problem and housing is no exception. The problem of not enough cheap housing stems from several regulations and regulatory climates - not from income levels. It used to be that on the US Census records, many were listed as "Boarders" - ie people who stayed in someone else's home and paid a small fee to have their meals provided and laundry done. Government did away with this source of cheap housing by mandating hospitality permits for such activities at the behest of the hotel industry - who they then began to hit with large fees for water and energy consumption!

Next you have zoning boards, who decide whether or not a particular property can house a residential, industrial, or commercial entity. And they pay property taxes based on their zoning, incentivizing government to push people into the higher-tax commercial and industrial areas.

What other ways can you think of that contribute to the lack of affordable housing?