Unformatted text preview: X such that v = a + bu for real numbers a and b, with b > , then (1) remains true with v in place of u. Exercise : Prove the last sentence of the Theorem. Write U ( p ) = ∑ u ( x i ) p i , so U ( e i ) = u ( x i ). Since p = ∑ p i e i , if follows that U ( ∑ p i e i ) = ∑ U ( e i ) p i , so the representation U of % is linear. The function U on L is called the von Neumann-Morgenstern (vN-M) utility . I will often abuse terminology and refer to the function u on X as the vN-M utility. 1 (A4) follows from (A0)-(A3) (proof?), but I assume it in my proof of the Theorem to save a few steps. 1...
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- Spring '10
- Microeconomics, Binary relation, real-valued function, pi ei