Households differ in size, age composition, educational level and other characteristics and, in general, we would expect households with different characteristics to have different expenditure patterns. Just as we are interested in modeling the effects on demands of differences in prices and budget levels, so is it legitimate and useful in summarizing a great deal of information to model the effects of household characteristics. In cross-section studies, either rather aggregated data for a few household types are available or, more rarely, a great deal of truly microeconomic information. Modeling the effects of household characteristics is useful in both situations provided that the model is plausible: in the former case, we obtain more precise estimates of the price and budget responses by pooling scarce data; in the latter, the model provides a convenient way of summarizing information that otherwise would take the form of a different demand system for each of the many household types.

In general, we can model differences in behavior by making demand depend not only on prices and total expenditure but also on some list of household characteristics. Most frequently modeled are the effects of household composition, the number, types, and ages of household members, but in principle any other characteristics can be included. As we shall see, this can be done in a wide variety of ways. One of the crudest, other than ignoring such effects altogether, is to deflate both demands and total outlay by household size so that, in per capita terms, consumption is the same function of the budget and prices for all households.