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- J 4 a. Define an Indifference Curve (IC).We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactlyonce. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)A C Good X Good X Good X This picture shows three different indifference curve maps: A, B and C. All three represent different preference relationships between two goods; good X and good Y. Juliana has two friends, Hailey and Joana. For this problem, let good X be time spent with Hailey and good Y be time spent with Joana. When asked which friend Juliana wants to spend the most time with, she can't decide and likes both of them equally. Which of the three pictures represents these preferences? B. None of them. A poop A poop poop O0 00
- 9 True or False Explain If preference is monotonic but not strongly monotonic, indifference curves are upward sloping but may have flat portionsSanjana loves to read books(B) and likes to watch movies(M) as well. She derives double the satisfaction from reading a book than watching a movie. Her utility function is as followsU(B, M) = 2B + MWhere B and M are the number of books and movies respectively.a. Explain the shape of the indifference curve using diagrams. b. The income available with her is INR60. And price of movie ticket is INR 10 and that of a book is INR 15. Will she spend her entire budget and why? What will be her consumption, explain why?|When Matt is buying cards and toys (C, T), his preferences are well behaved and he is indifferent between (60, 16) and (30, 24). For the following combinations, determine which he prefers, or if he is indifferent between the two. Show how you know. A. (31, 25) or (59, 15) B. (60, 16) or (45, 20)
- Draw the indifference curves fort he preference indicated below. (Do not forget to represent the name of the axis) 1) Marry lives by the motto "eat, drink and be merry today, for tomorrow doesn't matter." (Hint: Today's consumption is measured on the horizontal axis and tomorrow's consumption is measured on the vertical axis) 2) Boris likes homework (H) but hates exercise (E). 3) Bianca's marginal utility of pizza equals 2 and her marginal utility of salad equals 4 always. ww www www 4)Adam is very picky about his tahin-pekmez. He always mixes one spoon of tahin with two spoons of pekmez. 5)Marty likes rap and rock music. Marty's preferences exhibit a diminishing marginal rate of subsitution between the two types of music. wwwwww 6) Beatrix hates studying both economics and history. The more time she spends studying either subject, the less happy she is.Q1: (I)Asma eats only apples and almonds. Her level of income is $36, Price of apple (Pa) is $2 per kg and price of almond (Pl) is $6 per kg. The preferences of Asma are represented by the following utility function Utility U= 10*Qa + 40*Ql where Qa and Ql are Asam’s consumption of Apples and almonds. (a) which kind of preferences Asma has? (b) Find Utility per dollar spent on apple and almond (c) Find Marginal rate of substitution and interpret it (d) Find utility maximizing values of apples and almond and show graphicallyIn case of the complementary goods what is the shape of the indifference curve ??
- We claimed in the text that if preferences were monotonic, then a diag-onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)D 3 Derive the Utility Function to find the equation for the indifference curve. U(x, y) = (.6T.5 + .4B.5)1/.5Consider the following equation for an indifference curve: y 20/x. At point A (2, 10), the MRS is? %3D