Living arrangements have changed enormously over the last two centuries. While
the average American today lives in a household of only three people, in 1850
household size was twice that figure. Furthermore, both the number of children
and the number of adults in a household have fallen dramatically. We develop
a simple theory of household size where living with others is beneficial solely
because the costs of household public goods can be shared. In other words, we
abstract from intrafamily relations and focus on households as collections of
roommates. The model’s mechanism is that rising income leads to a falling expen-
diture share on household public goods, which endogenously makes household
formation less beneficial and privacy more attractive. To assess the magnitude of
this mechanism, we first calibrate the model to match the relationship between
household size, consumption patterns, and income in the cross section at the end
of the 20th century. We then project the model back to 1850 by changing income.
We find that our proposed mechanism can account for 37 percent of the decline
in the number of adults in a household between 1850 and 2000, and for 16 percent
of the decline in the number of children.
Keywords. Household size, living arrangements, roommates, economies of scale,
household public goods, fertility decline.