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Question: show that a von neumannmorgenstern utility function u is linear...

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Show that a von Neumann-Morgenstern utility function U is linear in the probabilities, i.e.,
oU (p) + (1-a) U (p) for any p, p E P and α Ε Ο, 1 U(αp+(1−α)p′)=αU(p)+(1−α)U(p′)for any p,p′∈Pandα∈[0,1].

Remark: We used this linear property to prove that the indifferent curves of a preference relation which admits an expected utility representation U are parallel lines.

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