Practice Problem Set 1 part2 ans

Practice Problem Set 1 part2 ans - marginal utility for y =...

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Spring 2010 Econ 320 Intermediate Microeconomic Analysis Yoichi Otsubo - 1 - 4. Consider the single-good utility function y y U 2 ) ( = . a. What are this consumer’s utility for y = 1, y = 4, y = 5? Sketch the utility function. ( ) 5 . 2 6 , 2 . 2 5 , 7 . 1 3 , 1 . 1 2 , z x xz use may You = = = = = Ans. ( ) ( ) ( ) 32 . 2 5 2 10 5 , 2 . 2 2 2 8 4 , 1 . 1 2 1 = = = = = = = = U U U (Graph will be shown in class) b. Does this consumer’s preferences satisfy transitivity assumption? Explain. Ans. Yes. Let A, B and C denotes the consumption basket y=1, y=4 and y=5 respectively. A B follows and B C follows since U(4)>U(1) and U(5)>U(4). To satisfy transitivity condition, this consumer’s preferences has to be A C follows . Since U(5)>U(1), A C follows . Hence her preferences are transitive. c. Does this consumer’s preferences satisfy “more the better” assumption? Explain. Ans. Yes. Since U(5)>U(4)>U(1), A B C follows follows . And basket C contains the most units, B the second, and A the least. d. Derive this consumer’s marginal utility using derivative. What are this consumer’s
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Unformatted text preview: marginal utility for y = 1, y = 4, y = 5? Sketch the marginal utility. ( ) x x x = 1 use may You Ans. ( ) y MU y 2 2 = (Graph will be shown in class) Spring 2010 Econ 320 Intermediate Microeconomic Analysis Yoichi Otsubo - 2 -5. Suppose David purchases only Pepsi and Pizza. Let x be the number of units of Pepsi, and y be the units of Pizza he purchases per month. Also suppose that his utility function is measured by xy U = , and his monthly income is I . Each unit of Pepsi costs P x and each unit of Pizza costs P y . Write a statement of the constrained optimization problem. Which variables are exogenous? Which variables are endogenous? Ans. I y P x P xy y x y x ≤ + : subject to max ) , ( Exogenous variables: I, P x , P y . Endogenous variables: x, y....
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