In one example of economies of scale, households with multiple members are able to achieve the same standard of living at lower per capita expenditures on public goods than smaller households. For example, if two adults unite to form one household, the couple will be better off as they can share public goods--such as housing--lowering per capita expenditure on them. The couple can funnel these savings into increased consumption of public goods--more spacious housing than either could afford separately--making each member better off than they were when they lived by themselves. The basic idea has strong intuitive appeal; living standards for households of different sizes could be equated with lower per capita expenditures for larger households who are able to economize on public goods. Household economies of scale are therefore fundamental to the measurement of living standards. Measuring the distribution of income, the costs of children, the extent of poverty, and poverty thresholds necessitates an accounting for these economies of scale.
One difficulty with household economies of scale is that it can be difficult to estimate the size of the scale economy, and household economies of scale are not as well defined as scale economies in production. While economies of scale are a function of the size of the household, the demand for goods and services generally derives from both household size and composition. When researchers turned their attention to economies of scale in the household, they overcame the problem of detection and measurement by concentrating on adult-only households, as in Nelson (1988). Measuring economies of scale for households where all members are the same type, have identical tastes, and are treated equally will not aid in the measurement of poverty, the distribution of income, and the costs of children, where compositional heterogeneity matters.
A second difficulty lies in the income and substitution effects that scale economies have on private goods. While both the income and substitution effects imply increased consumption of public goods, the income and substitution effects work in opposite directions for private goods, and it is not possible to know which effect will dominate unless we know more about the private good. Private goods that have low own- and cross-price elasticities and sizable income elasticities are goods whose consumption is likely to increase with household size. The increased consumption of those private goods could be taken as a measure of household economies of scale where larger households are better off in terms of private consumption due to scale economies in public consumption. Using this insight, Deaton and Paxson (1998) suggested that food would be a good choice for a private good where the income effect will dominate because food has few substitutes and they argue that substitution away from food will be less likely for households close to subsistence. This implies that food expenditures should increase with household size--the savings realized on public goods would be funneled to food, a necessity that has few substitutes. Rather than increasing with household size, Deaton and Paxson found that food expenditure per capita decreases with household size. After considering and dismissing a number of possible explanations, they conclude that their empirical results are a puzzle.
A literature analyzing this "food puzzle" has developed (Deaton and Paxson, 2003; Gan and Vernon, 2003; Gardes and Starzec, 2000; Gibson, 2002; Gibson and Kim, 2007; Horowitz, 2002; Perali, 2001; Vernon, 2005), but research on household scale economies has yet to look at how or if scale economies change over time. Just as knowledge about scale economies at a point in time allows us to estimate the extent of poverty and inequality, knowledge about changes in scale economies are useful for analyzing changes in living standards over time. Even more, knowledge about changes in scale economies is important since average household size has changed over time. …