How do you infer the economic well-being of individuals from household income? At one extreme, you could just divide household income by the number of people in the household. This is naive because there are some economies of scale. It doesn’t take twice as much energy to heat a house for two people as a house for one person, for example.
The other extreme is the two-can-live-as-cheaply-as-one philosophy. All that matters is household income; the number of people in the house is irrelevant. That’s too simplistic because while there are fixed costs to running a home, there are marginal costs per person.
So if you have a household of n people do you divide by the total income by n or by 1? Said another way, do you divide by n1 or n0? Some economists split the difference and use an exponent of 0.5, i.e. divide by the square root of n. This would say, for example, that the members of a family of four with a total income of $100,000 have roughly the same standard of living as a single person with an income of $50,000.
Dividing by √n is a crude solution. For one thing, it makes no distinction between adults and children. But for something so simple, it makes some sense. It makes more sense than dividing by n or not taking n into account.
Source: Burkhauser on the Middle Class