1) If someone has the utility function U = 1,000 + 2min {x, y}, then x and y are perfect complements for that person. 2) If there are two goods, if a consumer prefers more of each good to less, and if she has a diminishing marginal rate of substitution, then her preferences are convex. 3) If George has more classical records than rock and roll records, he is willing to exchange exactly 1 classical record for 2 rock and roll records, but if he has more rock and roll records than classical records, then he is willing to exchange exactly 1 rock and roll record for 2 classical records. George has convex preferences. 4) Noah has the utility function U(x, y) = max{x, y}. Noah's preferences are convex. 5) The utility function U(X1, X2) = 2|nX1 + 3|nx: represents Cobb- Douglas preferences 5) A consumer has preferences represented by the utility function U(x1, x2) = 10(x12 + 2x1x2 + X22) 50. For this consumer, goods 1 and 2 are perfect substitutes. Sharpen your pencils. Here we go. You can do this. 1) Max-a-million loves chocolate and always thinks that more is better than less. Max-a- million thinks that a few ukelele lessons would be worse than none at all, but if he had enough ukelele lessons to get good at playing the ukelele, he would prefer more lessons to less. Draw a graph with ukelele lessons on the horizontal axis and chocolate on the vertical axis. On your graph sketch two indifference curves for Maxa-million that would be consistent with this story. Label the better of the two indifference curves AA and the worse one BB. 2) Coach Steroid likes his players to be big, fast, and obedient. If player A is better than player B in two of these three characteristics, Steroid will prefer A to B. Three players try out for quarterback. Wilbur Westing house weighs 320 pounds, runs very slowly, and is quite obedient. Harold Hotpoint weighs 240 pounds, runs extremely fast, and is extremely disobedient. Jerry Jacuzzi weighs 150 pounds, runs at average speed, and is extremely obedient. Does Coach Steroid have transitive preferences? Explain your