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- (a) Suppose we have preferences U(X, Y) = 10X²/³ Y¹/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). < (d) What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain.< (e)_From (d) we can show that optimal demands are: X=½ M/PX and Y = ½ M/Px. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands (X*, Y*) and utility if Px = 10, Px= 5 and income M = 1200. < (f)_Suppose Px falls to Px = 8 but Py and M are unchanged (Px = 5 and M = 1200). Calculate the new optimal demands…4We 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?)
- solve g, h please Thank youcan you please help me with questions c, d, e and f? Thanks!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?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.
- |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)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/.5
