Gan and Vernon’s comment does not resolve the puzzle that we orig-inally posed. Their description of the puzzle is unclear, so we start by restating it. The essence of the matter is this. Imagine two households, one of which is larger than the other, for example, containing the same age and sex composition of people, but with twice as many of everyone. Imagine too that both households have the same level of per capita total house-hold expenditure so that, in the example, the household with twice as many people spends twice as much in total. If there are economies of scale, the second household is better off. While it is possible for it to maintain exactly the same expenditure pattern as the smaller household, with everyone having the same of everything, it can also rearrange its purchases to take advantage of the differential economies of scale in different goods. Because food is a normal good, we would expect the larger household to spend more per capita on food. This is especially so in poor countries, where there are few substitutes for food, so that there is limited opportunity for substituting away from food toward goods with greater economies of scale. The evidence contradicts this prediction. We looked at household survey data from the United States,

Household scale economics are plausibly attributed to shared household public goods that make larger households better off at the same level of per capita resources. larger households should therefore have higher per capita consumption of private goods, such as food, provided that they do not substitute too much toward the effectively cheaper public goods. The evidence shows exactly the opposite. Data from rich and poor countries indicate that, at constant per capita total expenditure, the per capita demand for food decreases with household size and that it does so most in the poorest countries, where substitution should be the least.

The permanent income hypothesis implies that, for any cohort of people, inequality in consumption and income should grow with age, a prediction that is here confirmed using data from eleven years of household survey data from the United States, twenty-two years from Great Britain, and fourteen years from Taiwan. In the permanent income hypothesis, the increase in inequality reflects the cumulative effect of luck on consumption. Other models of intertemporal choice--such as those with strong precautionary motives or liquidity constraints--can limit or even prevent the spread of inequality, as can insurance arrangements that share risk across individuals.

The well-known positive association between health and income in adulthood has antecedents in childhood. Not only is children’s health positively related to household income, but the relationship between household income and children's health becomes more pronounced as children age. Part of the relationship can be explained by the arrival and impact of chronic conditions. Children from lower income households with chronic conditions have worse health than do those from higher-income households. The adverse health effects of lower income accumulate over children’s lives. Part of the intergenerational transmission of socioeconomic status may work through the impact of parents' income on children’s health.