That is a good point, "demand" is never really just the # of potential "buyers", but also each buyers willingness to pay, which is of course highly influenced by their ability to pay. Once there's a shortage of anything, assuming prices are allowed to freely fluctuate, those with the most $$ are first in line. But that's capitalism for ya.

At least the government has a separate pool of income restricted housing units, where the selection is based not on wealth, but on (household size/dependents? seniority on the waitlist? being a lottery also...luck?)