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The family is a remarkable institution. And a complex one. Indeed, so complex that much of economic theory proceeds as if no such thing exists. In the standard theory of prices and equilibrium (the most elegant version of which is to be found in the theory of general equilibrium), individuals and firms are visible, but definitely no families. The individual owns resources, sells them, earns an income, buys goods and services, and has utilities. The firm buys resources, makes commodities, sells them, makes profits, and gives incomes to individual owners. So the story runs, with no family in sight – and children neither heard nor seen.
Amartya Sen (Sat,) studied this question.