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:<math>X(p,m^1,\dots,m^n) = X(p, \sum_{i=1}^n {m^i})</math>
Under what conditions is it possible to represent the aggregate demand
Early results by Antonelli (1886) and Nataf (1953) had shown that, assuming all individuals face the same prices in a market, their income consumption curves and their [[Engel curve]]s (expenditure as a function of income) should be parallel straight lines. This means that we can calculate an income-consumption curve of an entire society just by summing the curves of the consumers. In other words, suppose the entire society is given a certain income. This income is somehow distributed between the members of society, then each member selects his consumption according to his income-consumption curve. If the curves are all parallel straight lines, the aggregate demand of society will be ''independent of the distribution of income among the agents''.
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