Home Chapter3: Quiz #2

# Quiz #2

This activity contains 15 questions.

Questions 1 and 3 refer to the following situation: Aaron and Brittney want to divide fairly the chocolate-banana cake shown in Figure 3.1 using the divider-chooser method. The total cost of the cake was \$6.00. Aaron values chocolate five times as much as he values banana, while Brittney values banana twice as much as she values chocolate.

In Aaron’s eyes, the piece shown in Figure 3.2 is worth

 \$2.00 \$3.50 \$2.50 \$3.00 None of the above

## In Aaron’s eyes, the piece shown in Figure 3.3 is worth

 \$1.75 \$1.00 \$1.25 \$1.50 None of the above

## In Brittney’s eyes, the piece shown in Figure 3.4 is worth

 \$2.00 \$2.50 \$3.50 \$3.00 None of the above

Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3). If the choosers declarations are Chooser 1: {s1, s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?

 Chooser 1 gets s1; Chooser 2 gets s2; Divider gets s3. Chooser 1 gets s3; Chooser 2 gets s1; Divider gets s2. Chooser 1 gets s2; Chooser 2 gets s1; Divider gets s3. Chooser 1 gets s1; Chooser 2 gets s3; Divider gets s2. None of the above

Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3). Suppose the choosers value the slices as follows:

 s1 s2 s3 Chooser 1 38% 32% 30% Chooser 2 29% 29% 41%

 Chooser 1 gets s2; Chooser 2 gets s1; Divider gets s3. Chooser 1 gets s3; Chooser 2 gets s2; Divider gets s1. Chooser 1 gets s2; Chooser 2 gets s3; Divider gets s1. Chooser 1 gets s1; Chooser 2 gets s3; Divider gets s2. None of the above

Questions 6 through 9 refer to the following example: Four heirs (A, B, C, and D) must divide fairly an estate consisting of three items – a house, a parcel of land, and a diamond ring – using the method of sealed bids. The players’ bids (in dollars) are:

 A B C D House 140,000 155,000 160,000 148,000 Land 80,000 90,000 100,000 75,000 Ring 40,000 35,000 36,000 25,000

The original fair share of player A is worth

 \$130,000. \$86,667. \$260,000. \$65,000. None of the above

## In the initial allocation, player A

 gets the land and pays the estate \$15,000. gets the house and pays the estate \$75,000. gets the ring and an additional \$25,000 from the estate. gets the ring and pays the estate \$25,000. None of the above

## After the initial allocation to each player is made there is a surplus of

 \$186,000. \$0. \$101,000. \$29,000. None of the above

## After all is said and done, the final allocation to player B is:

 \$99,000 in cash. \$77,250 in cash. the ring and \$32,250 in cash. \$70,000 in cash. None of the above

Questions 10 through 12 refer to the following: Four players (A, B, C, D) agree to divide the 12 items shown in Figure 3.5 using the method of markers. The player’s bids are as indicated.

Item 4

 is left over. goes to B. goes to C. goes to D. goes to A.

## Item 10

 goes to B. goes to A. goes to C. is left over. goes to D.

## Item 7

 goes to D. is left over. goes to A. goes to B. goes to C.

## Which player receives the largest number of items?

 B C All players receive the same number of items –3. D A

## Which of the following is a discrete fair division problem?

 dividing a chocolate cake dividing an collection of jewels dividing a gallon of milk dividing a liberated country None of the above

## Phil and Rick are dividing a business. Except for the factory, they own very little of value so they agree to divide the factory fairly using the method of sealed bids. Phil bids \$200,000 and Rick bids \$190,000. After all is said and done, the final outcome is

 Phil gets the factory and pays Rick \$95,00. Phil gets the factory and pays Rick \$97,500. Phil gets the factory and pays Rick \$100,000. Phil gets the factory and pays Rick \$105,000. None of the above