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where the function <math>U</math> satisfies the equality:
::<math>(U')^{-1}(p) = \sum_{i=1}^n{(v_i')^{-1}(p)}</math>
In the special case in which all agents have the same utility function <math>u(x,m)=u(x)+m</math>, the aggregate utility function is:
::<math>U(x,M) = n \cdot u({x \over n}) + M</math>
=== [[Homothetic preferences]] ===
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