In basic consumer theory, there is an individual consumer who has a utility function, this function induces the individual's demand (given budget and prices), and this in turn determines the individual's final consumption.

But in reality, consumption is often done not by an individual but by an household/family. All household members live in the same house, use the same furniture and the same electricity equipment, etc. (of course there are also things that are consumed individually, such as food, but much of the consumption is done by the household). In contrast, the utility functions are still personal and belong to individual agents.

Gary Becker ("A theory of social interactions", 1974) settles this discrepancy in consumer theory by assuming that, in each family, there is an altruistic "family head", whose utility function takes into account the welfare of all family members:

"The head maximizes a utility function that depends on the consumption of all family members subject to a budget constraint determined by family income and family consumption...

a family with a head can be said to maximize "its" consistent and transitive utility function of the consumption of different members subject to a budget constraint defined on family variables.

The "family's" utility function is identical with that of one member, the head, because his concern for the welfare of other members, so to speak, integrates all the members' utility functions into one consistent "family" function...

That is, a "family's" utility function is the same as that of one of its members not because this member has dictatorial power over other members, but because he (or she!) cares sufficiently about all other members to transfer resources voluntarily to them...

Armed with this theorem, I do not need to dwell on the preferences of nonheads.

My questions are:

  • Are there more recent references (standard textbooks or papers) that make a similar assumption, speaking about "household utility function"?
  • Alternatively, are there recent references that provide a different solution to this discrepancy in consumer theory?

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