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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.
Deaton et al. (Thu,) studied this question.