University of California at Berkeley's center on real estate and urban economics has taken a look at the costs of building low income housing and found that state-subsidized housing costs between 10% and 32% more to build than private housing projects!!
The short story is that state subsidies come with a lot of requirements that drive up costs--the biggest being prevailing wage requirements. So, as one of the Berkeley authors points out, state rules are just a means of shifting money from the low income housing program to unionized construction workers. Hmmm.
But not only is this another sleazy example of "hide the shift in wealth" politics, but it also exposes in part why new private housing development is the best way to increase the supply of housing and thereby create affordable housing.