(taken from Osborne and Rubinstein, 2020.) Let X = R2. Describe each of the following preference relations formally, giving a utility func- tion that represents the preferences wherever possible, draw some rep- resentative indifference sets, and determine whether the preferences are monotone, continuous, and convex. Give a reason for your answer. (a) The consumer prefers the bundle (x1, X2) to the bundle (y1, y2) if and only if (1, X2) is further from (0, 0) than is (y1, y2), where the distance between (21, z2) and (z;, 22) is V(21 - 21)2 + (22 - 22)2. (Hint: Utility representation exists.) (b) The consumer cares first about the sum of the amounts of the goods; if the sum is the same in two bundles, she prefers the bundle with more of good 1. (Hint: Utility representation does not exist. Explain why.) (c) The consumer only cares about the maximum amount among all commodity amounts in a given bundle and wishes this maximum amount to be as large as possible. (Hint: Utility representation exists.) (d) The consumer has an ideal bundle which is (10, 10). She prefers a bundle x to a bundle y if and only if x is closer to (10, 10) than is y (where the distance between two bundles is measured as in (a)). (Hint: Utility representation exists. )