First of all, I'm talking about the inequality of income between the super-high-earners (1%) and the rest. Those people are not the ones pricing everyone else out of housing.

Secondly, it's not true that rent/house prices increased sharply everywhere, nor is it entirely due to income inequality between high-earners and low-earners.

For one, we had and have a lot of real estate speculation (a correction of which we experienced in 2007) but we also have policies and regulations in place that ensure the market can not provide for affordable housing. What prevents construction of an apartment highrise in the middle of San Francisco? It ain't neoliberalism, that's for sure...