Question

A linear utility function represents Hannah’s preference for a boyfriend. There are two relevant attributes – “looks” & “smartness” – of which she weights “smartness” one and half times more than “looks”. Each attribute is measured on a 1(=poor) to 7(=great) scale.

a. Whom does Hannah prefer, Tim (who she believes rates a 5 on looks and a 6 on smartness) or Sam (who she believes rates a 2 on looks and a 6 on smartness)? Explain. (Show Calculation) (5 points)

b. If Hannah has ideal points of 3 for “looks” and 5 for “smartness”, does that change the verdict? Explain. (5 points)

Answer 1

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Observe that TIm and Sam have same level of smartness (6) but TIm is better looking (5 > 2).

Hannah's ideal point is (3L, 5S) - which means that Hannah will prioritize Smartness after basic level of looks 3L has been achieved; on the flipside Hannah will prioritize looks when the basic level of smartness 5S has been achieved.

Since both TIm and Sam satisfy the minimum criteria for smartness (5S), Hannah prefers the one with better looks. TIm is not only as good as Sam on all counts (both Looks and Smartness), he's strictly better in the Looks department.

So verdict is still the same: Tim gets lucky.