Math 181 Quiz 6 Fall 2013 Name Solutions • You have 15 minutes • No calculators 1. Batman dies leaving behind this property to Robin and Batgirl. The as- sets include the Wayne Manor, the Batcave, the Batmobile, the Batwing, and the Batboat. Assume the points are assigned as follows: Robin's Batgirl's Asset Points Points Wayne Manor(WM) 20 40 Batcave(BC) 30 20 Batmobile(BM) 30 28 Batwing(BW) 18 10 Batboat(BB) 2 2 Use the adjusted winner procedure to determine a fair allocation of the property. Answer: Wayne Manor(WM) 20 40 Batcave(BC) 30 20 Batmobile(BM) 30 28 Batwing(BW) 18 10 Batboat(BB) 2 2 Robin Points: 78 points Batgirl Points: 40 points So the Batboat goes to Batgirl Total points: Robin Points: 78 points Initial winner Batgirl Points: 42 points Initial loser Point Ratio: BC 30=20 = 1:5 BM 30=28 = 1:07143 BB 18=10 = 1:8 1 So the Batmobile is the first item to be transferred. It can be transferred completely without making Robin the initial loser, so the item must be shared. 78 − (30)x = 42 + (28)x 36 = 58x 36 18 x = = 58 29 Robins gets the Batcave, Batwing and (11/29) of the Batmobile. Batgirl gets the Wayne Manor, Batboat and (18/29) of the Batmobile. 2 2. Alvin, Simon, and Theodore inherit a house, a recording studio and a car from Dave. They submit the following bids. How should they arrive at a fair division? Alvin Simon Theodore House $210,000 $180,000 $150,000 Recording Studio $150,000 $90,000 $120,000 Car $6,000 $12,000 $9,000 Answer: Alvin Simon Theodore House $210,000 $180,000 $150,000 Recording Studio $150,000 $90,000 $120,000 Car $6,000 $12,000 $9,000 So Alvin gets the House and the Recording Studio, and Simon gets the car. House: Alvin puts in (2/3)(210,000) = 140,000 Simon takes out (1/3)(180,000)= -60,000 Theodore takes out (1/3)(150,000) = -50,000 Record- 30,000 The split 30,000 (each gets 10,000) ing Studio: Alvin puts in (2/3)(150,000) = 100,000 Simon takes out (1/3)(90,000)= -30,000 Theodore takes out (1/3)(120,000) = -40,000 Car: 30,000 The split 30,000 (each gets 10,000) Simon puts in (2/3)(12,000) = 8,000 Alvin takes out (1/3)(6,000)= -2,000 Theodore takes out (1/3)(9,000) = -3,000 3,000 The split 3,000 (each gets 1,000) Alvin: House - 140,000 + 10,000 + Recording Studio -100,000 +10,000 + 2,000 + 1,000 = House + Recording Studio - 217,000 Simon: 60,000 + 10,000 + 30,000 + 10,000 + Car - 8,000 + 1,000 = Car + 103,000 Theodore: 50,000 + 10,000 + 40,000 + 10,000 + 3,000 + 1,000 = 114,000 Alvin pays $217,000 and receives the House and Recording studio. Simon receives the car and $ 103,000. Theodore receives $114,000. 3 3. Suppose that Calvin and Hobbes discover a sunken pirate ship and decide to take turns dividing up the loot. Assume that Calvin and Hobbes use the bottom-up strategy and that Calvin gets to choose first. Determine Calvin's first choice and the final allocation. Calvin Hobbes Sword Flag Cannon Sword Unopened Chest Unopened Chest Flag Anchor Anchor Cannon Answer: Calvin: Sword Unopened Chest Cannon Hobbes: F lag Anchor 4. When using divide and choose, when would you rather be the divider than the chooser? Answer: When you have knowledge of the other person's preferences. 4.