Question: show that a von neumannmorgenstern utility function u is linear...
Show that a von Neumann-Morgenstern utility function U
is linear in the probabilities, i.e.,
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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