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Jack and Jill went up the hill and found an antique water pail. Jack and Jill must now make a fair division of the pail using the Knaster inheritance procedure. Jack bids $80 for the value of the pail and Jill bids $65.
-What is the outcome of the fair division?
A) Jack gets the pail and pays Jill $36.25.
B) Jack gets the pail and pays Jill $40.
C) Jack gets the pail and pays Jill $32.50.
D) Jack gets the pail and Jill gets $65.

Question

Quizplus · Accepted Answer

In the Knaster inheritance procedure, the item goes to the highest bidder, who then compensates the other party half the difference between the two bids. Jack's bid ($80) is higher than Jill's ($65), so Jack gets the pail. The difference between their bids is $15 ($80 - $65), and half of that is $7.50. Therefore, Jack must pay Jill half the sum of their bids ($145 / 2 = $72.50) minus his bid's half-value ($80 / 2 = $40), resulting in $72.50 - $40 = $32.50. However, the correct calculation for the payment should be Jack paying Jill the amount that makes both of their shares equal considering their valuation. Since Jack values the pail at $80, and Jill values it at $65, the total value is $145. Half of this is $72.50, which is what each should get in value. Since Jack takes the pail, he should compensate Jill so that her share equals $72.50 in value. Given Jill values the pail at $65, the compensation to Jill should be $72.50 - $65 = $7.50, which is not an option provided, indicating a mistake in the explanation. The correct approach is to ensure both parties receive equal value from their perspective, but without the exact formula provided in the options, the closest to a fair division based on the bids and the principle of the Knaster procedure is Jack getting the pail and compensating Jill to equalize their perceived values, which is misinterpreted in the provided options and explanation.

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