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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. Further, 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 intra-family relations and focus on households as collections of roommates. The model's mechanism is that rising income leads to a falling expenditure 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% of the decline in the number of adults in a household between 1850 and 2000, and for 16% of the decline in the number of children.