If Alice prefers P to Q, it means that 1 4 2a > q 2a >...

 

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If Alice prefers P to Q, it means that 1 4 2a > q 2a > 4q If Ben prefers P to Q, it means that 2³ > 4q. (1) This means that 2a > 4q implies 28 > 4q for all values of q. This is only true if 2³ ≥ 2ª or > a. (2) Risk aversion for Ben means 3 ≤ 1. Thus, a ≤ 1 so Alice is also risk averse. (3) We know a ≤ 1, but that says nothing about whether 3 is greater or less than 1. Thus, we do not know. If Alice prefers P to Q, it means that 1 4 2a > q 2a > 4q If Ben prefers P to Q, it means that 2³ > 4q. (1) This means that 2a > 4q implies 28 > 4q for all values of q. This is only true if 2³ ≥ 2ª or > a. (2) Risk aversion for Ben means 3 ≤ 1. Thus, a ≤ 1 so Alice is also risk averse. (3) We know a ≤ 1, but that says nothing about whether 3 is greater or less than 1. Thus, we do not know.

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