Comment by AnthonyMouse

Probably the best thing you could do in terms of social housing construction would be to have the government put up some capital to buy land and build new housing on that land, then immediately sell it and use the proceeds to do it again and again with exponential growth because it's actually profitable.

But that's also what construction companies would be doing regardless except for the subsidy, at which point you might be better off doing something like exempting construction companies from property taxes for two years if they at least double the number of housing units on their land in that time.