5. Jeff and Kyle jointly purchase the box of Neapolitan Ice-Cream (1/3 chocolate
ID: 3282238 • Letter: 5
Question
5. Jeff and Kyle jointly purchase the box of Neapolitan Ice-Cream (1/3 chocolate, 1/3 vanilla, and 1/3 strawberry) shown below. They will use the Divider-Chooser Method to divide the box. After flipping a coin it is determined that Kyle will divide the ice-cream into two pieces and Jeff will choose one. Kyle values chocolate five times as much as he values vanilla; however, he values strawberry four times as much as he values vanilla. As the divider, which of the divisions could Kyle make? Ice Cream None of the above.Explanation / Answer
From kyle's perspective
Let the value of Vanilla be $1 per unit division shown in figure.
So total value of Vanilla part will be $16.
Kyle values chocolate 5 times as much as Vanilla.
So value of chololate part = $80 ($5 per unit)
Similarly Value of strawberry part = $64 ($4 per unit)
So for Kyle total value of ice cream will be $16 + $80 + $64 = $ 160
As kyle is the divider (and he doesn't know about the preferences of Jeff), so he would want to make sure that he definitely gets half value out of the full ice cream .
As Kyle doesn't have the option of choosing better half, so Kyle would want to divide ice cream such that he definitely gets half i.e. $80 worth share.
(a) It is clearly wrong as left half has chocolate which is costlier than strawberry of right half and left half also has more of vanilla. So left half value is more than that of right half.
(b)Similaar to case (a)
(c) Value of chololate + Vanilla part = $5 x 12 + $1 x 12 = $72 < $80
So incorrect
(d) Value of part with more chocolate = $5 x 10 + $ 1 x 4 + $4 x 4 = $70 < $80
So incorrect
(e) This is the correct option
One possible correct division will be
Chololate part worth $80 in one part and Vanilla+Strawberry worth $64 + $16 = $80 as other part.
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