1) Joe wants a backpack. The backpack bas to be of a minimum size so that it can hold his laptop. He also cares about how comfortable it is to wear as well as its cost. He is rick-neutral for cost. After initial consideration, he comes up with the following valuations for these attributes. Comfort Comfort Cost Size Value Abdominal Value | Shoulder Straps Value Value (width) Strap V. 6.5 None 0 Thin, unpadded $100 0 7.5 0 Present 100 Thin, padded 16.7 85 Thick, unpadded $67 33.3 9.5 100 Thick, padded 100 550 50 10.5 100 540 60 115 100 $33 66.7 $17 83.3 50 100 Joe now decides he is willing to pay the following amounts (as even swape) for each of the following backpack upgrades: * $100 to increase the size from 6.5 to 11.5 (independent of the presence of an abdominal strap and the kind of shoulder straps) * $40 to get an abdominal strap (independent of the size and the kind of shoulder straps) $5 to replace thin, umpadded shoulder straps with thin, padded straps (independent of the size and the presence of an abdominal strap) $15 to replace thin, umpadded shoulder straps with thick, unpadded straps (independent of the size and the presence of an abdominal strap) * $25 to replace thin, unpadded shoulder straps with thick, padded straps (independent of the size and the presence of an abdominal strap) 3) (10 points) Given Joe's even swaps, what values should his value function for shoulder straps Wax assign to thin, padded straps and to thick, unpadded straps?b) (10 points) To validate the model, you ask Joe to make some additional even swaps involving uncertainty about the shoulder straps: . Imagine you were choosing between one backpack that has thin, padded shoulder straps and another backpack about which you are uncertain about the shoulder straps - there's a chance p that it has thick, padded straps and a chance 1-p that it has thin, umpadded straps. The backpacks have the same size, abdominal strap, and cost. What value of p makes this an even swap? . Imagine you were choosing between one backpack that has thick, umpadded shoulder straps and another backpack about which you are uncertain about the shoulder straps - there's a chance q that it has thick, padded straps and a chance 1-q that it has thin, umpadded straps. The backpacks have the same size, abdominal strap, and cost. What value of q makes this an even swap? What answers to these questions (values of p and q) would be comeistent with the value function for shoulder straps that you identified in part a?() (20 points) Assume that Joe's even swaps are consistent. Identify a utility function that represents Joe's preferences. (You can refer to the single-attribute value functions defined numerically, you don't need to plug in equations for them. You do need to figure out the attribute weights.)d) (10 points) Suppose Joe goes to the store and sees the following three backpacks for sale: Abdominal Shoulder Backpack Size Strap Straps Cost Swiss Gear 9.5 Present Thick, unpadded $67 port. 8.5 Present Thin, padded 333 Kipling 10.5 None Thick, padded Which does he most prefer to buy