Take the analysis a step further though, population density matters, not median income. Take the ownership cost, and the total supply of housing, now align that with the households (groups who would live in one housing unit) and align it to the right side of the income distribution.

You will find that all housing is consumable by households for which their income exceeds the ownership costs. That is how the market works, the people who can afford houses buy them. If there are more people who can afford houses than there are houses, the prices adjusts upwards to capture that value, if there are more houses than people who can afford them, the price adjusts down to capture that value. There are no houses (typically) that are otherwise market acceptable that are not owned.

What is more, it has been shown that if you add houses, that widens the overlap with incomes, starting from the "high" end and moving down. That is why Sunnyvale has authorized the building of thousands of new houses and apartments. Even trying to artificially hold units out for "low income" people results in fraud where low income people "rent" those houses and then sublet them out at market rate to recapture the value. We just convicted a woman of doing that and she isn't the only one.