A "household equivalence" scale offers an answer to this question: How much more income is needed by a a household with more people so that it has the same standard of living as a household with fewer people? The question may seem a little abstract, but it has immediate applications.
For example, the income level that officially defines the poverty line was $13,064 for a single-person household under age 65 in 2018. For a two-person household, the poverty line is $16,815 if they are both adults, but $17,308 if it's one adult and one child. For a single parent with two children the poverty line is $20,331; for a single parent with three children, it's $25,554. The extent to which the poverty line rises with the number of people, and with whether the people are adults or children or elderly, is a kind of equivalence scale.
Similarly, when benefits the poor and near-poor are adjusted by family size, such adjustments are based on a kind of equivalence scale.
And bigger picture, if you are comparing average household income between the early 1960s and the present, it presumably matters that the average household had 3.3 people in the early 1960s but closer to 2.5 people today (see Table HH-4).
However, it often turns out that poverty lines and poverty programs are set up with their own logic of what seems right at the time, but without necessarily using a common household equivalence scale. Richard V. Reeves and Christopher Pulliam offer a nice quick overview of the topic in "Tipping the balance: Why equivalence scales matter more than you think" (Brookings Institution, April 17, 2019). Here's a sample of some common household equivalence scales:
But setting aside that particular issue, it's topic that matters to people planning a household budget, if they think about the question of whether living together will save money, or how much more money they will need if they have children. The commonly used "square root" approach, for example, suggests that a a household of two people will need 1.414 times the income of a single-person household for an equivalent standard of living, a household of three people will need 1.732 times the income of a single-person household for an equivalent standard of living and so on. Pick another household equivalence scale, if you prefer, but then plan accordingly.