1) (4 points) Weakly and strongly convex preferences Suppose Mindy and Tulip are roommates. Mindy works part-time at Roberto’s and can bring home four carne asada burritos for free every week. Tulip works part time at Tapioca Express and can bring home eight steamed pork buns for free every week. Use x to denote the number of burritos, and y to denote the number of pork buns. 

a. Suppose Mindy is always willing to trade one burrito (x) for two pork buns (y), regardless of how many she has.

i. Draw a couple of her indifference curves in the graph. ii. Are Mindy’s preferences convex? b. Tulip is also indifferent between having 4 burritos and no pork buns and having 8 pork buns and no burritos. However, she would prefer to have 2 burritos and 4 pork buns instead. i. Draw a couple of Tulip’s indifference curves (what they might plausibly look like – you don’t have enough information to draw them precisely) ii. Are Tulip’s preferences convex? c. Might the girls decide to share/trade food with each other? Find one possible exchange so that neither of the girls is worse off, and at least one of them is strictly better off. d. Consider the following possible specifications of utility functions: 𝑈1 = √𝑥 + √ 𝑦 2 𝑈2 = √2𝑥 + 𝑦 𝑈3 = (2𝑥) 2 + 𝑦 2 𝑈4 = 𝑥 2𝑦 𝑈5 = 𝑥𝑦 2 𝑈6 = min (4𝑥, 𝑦) 𝑈7 = min (𝑥, 2𝑦) 𝑈8 = 2𝑥 − 𝑦 𝑈9 = 𝑥 + 2𝑦 𝑈10 = 𝑥 + 𝑦 2 i. Which of these functions is/are consistent with Mindy’s initial preferences? ii. Which utility function(s) is/are consistent with Tulip’s preferences? [Hint: consider that indifference curves may look different from the way you drew them.

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