Math  /  Data & Statistics

QuestionQuestion 9
Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items - a desk and a vanity - using the method of sealed bids. The players' bids (in dollars) are:
| | A | B | C | D | | :---- | :-: | :-: | :-: | :-: | | Desk | 240 | 220 | 200 | 280 | | Vanity | 220 | 200 | 100 | 120 |
The original fair share of A is worth: $\$
In the initial allocation, player A: Select an answer and Select an answer the estate $\$
After all is said and done, in the final allocation, player A: Select an answer and Select an answer the estate $\$ Select an answer Gets no items Gets the desk Gets the desk and vanity Gets the vanity

Studdy Solution

STEP 1

1. The estate consists of two items: a desk and a vanity.
2. Each player bids on both items.
3. The fair share for each player is calculated based on their bids.

STEP 2

1. Calculate the fair share for player A.
2. Determine the initial allocation for player A.
3. Determine the final allocation for player A.

STEP 3

Calculate the fair share for player A by averaging their bids for the desk and vanity:
Fair Share of A=Bid for Desk+Bid for Vanity2=240+2202=230\text{Fair Share of A} = \frac{\text{Bid for Desk} + \text{Bid for Vanity}}{2} = \frac{240 + 220}{2} = 230

STEP 4

Determine the initial allocation for player A: - Player A bids the highest for the desk (\$240), so they get the desk. - The value of the desk is \$240.

STEP 5

Determine the final allocation for player A: - Player A keeps the desk. - Since player A's fair share is \$230 and they received an item worth \$240, they owe the estate the difference:
Amount Owed=240230=10\text{Amount Owed} = 240 - 230 = 10
In the initial allocation, player A gets the desk and owes the estate \$10. In the final allocation, player A keeps the desk and owes the estate \$10.

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