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People didn't used to need a second income to afford a house. Now they do.
Household income doesn't show that change. Individual income does.
The median income for a single-income family is $78K. That's enough to afford a house that costs $310K-$390K.
The average individual income in Michigan, where houses are actually selling for around $300k, is $34,768. https://www.census.gov/quickfacts/fact/table/MI/INC110221
That doesn't give the median, but it's lower. Those numbers are always thrown off by a few rich people.
When everyone needs a separate individual house that they refuse to share, then per capita income will be relevant.
But in the real world, people buy houses because they want to share them with their family. On average, 2.5 people live in a single house. And the median household income is $63K in Michigan.
So if you really want to look at per capita income, that means there is $87.5K (2.5 x $35K) available to buy a house, which is easily enough to afford a $300K home.
Again, families didn't used to need 2 incomes to buy a house.
Saying that households can still afford houses is tautological. Of course they can, or they wouldn't be a household.
Who said they need two incomes?
You insist on using per capita income for some reason. That means that even in a single earner family, the income is considered to be divided equally among the family members.
If you are a single earner making $160K in a family with two adults and two kids, then when using per capita income you consider all four family members as making $40K each. That's the definition of per capita.
And that's why it's nonsense to say that per capita income of $40K is not enough to afford a house. A family of five with per capita income of $40K would be in the top 10%.
Household income is total family income, regardless of whether there is one earner or more than one. And it's not tautological. If your household income is very low, then your family may not be able to afford to buy a house.
If your family can't afford to buy a house, then your family doesn't get counted as a household.
That's absolutely not true. A household is one or more people who live in a housing unit. They can be homeowners or renters.