Search and Satisficing. Andre wants to buy Sony earbuds online. There are four models sold online, denoted {x1, x2, x3, x4}. He cares mostly about the sound quality qk and the price pk of each of the four models, but he does not know qk unless he searches each of the models. The values of (qk, pk) are x1 = (3, 3), x2 = (2, 1), x3 = (9, 4) and x4 = (8, 2). When searching online for Sony earbuds the order in which models are shown changes after each search.

(a) (15 points) Assume that Andre's utility is given by u(xk) = qk pk but that he does not know (qk, pk) until she searches model xk online. If Andre uses an reservation stopping rule with reservation utility u , under which values of u would Andre be susceptible to violations of IIA when he chooses among the four models? Justify your answer.

(b) (15 points) A friend of Andre is a sound engineer and has told him that he should also check out Bose earbuds given they tend to have higher sound quality on average than Sony and a similar price range. If he decides to search both Sony and Bose earbuds, should his reservation utility u go up, go down or stay the same? Justify your answer.