Oh, elementary. The various sections of the housing market are interrelated
and hugely influence each other.

If there is a shortage of public housing, prospective tenants will have to try
their luck in the private sector. A small percentage will buy a house, thus
creating more competition for houses which in turn allows prices to rise. Most
people will enter the private rental market which now booms with two
consequences. Some people who planned to sell their home and move to
somewhere smaller or cheaper decide not to sell their home because they can
make more money renting it out. Running parallel is the buy-to-let sector
where people buy houses and transfer them from the for-sale sector to the
rental sector. Both contribute to a reduction in the number of houses to
purchase, and prices rise.

Building an adequate supply of public housing reverses that cycle and makes it
easier for prospective buyers to find a house at a price they can afford.