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### Practice Problem Set 1 part2 ans

Course: 320 322, Fall 2010
School: Rutgers
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Word Count: 286

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2010 Econ Spring 320 Intermediate Microeconomic Analysis Yoichi Otsubo 4. Consider the single-good utility function U ( y) = 2 y . a. What are this consumers utility for y = 1, y = 4, y = 5? Sketch the utility function. (You may use xz = x z , 2 = 1.1, 3 = 1.7, 5 = 2.2, 6 = 2.5) Ans. U (1) = 2 = 1.1, U (4 ) = 8 = 2 2 = 2.2, U (5) = 10 = 2 5 = 2.32 (Graph will be shown in class) b. Does this consumers...

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2010 Econ Spring 320 Intermediate Microeconomic Analysis Yoichi Otsubo 4. Consider the single-good utility function U ( y) = 2 y . a. What are this consumers utility for y = 1, y = 4, y = 5? Sketch the utility function. (You may use xz = x z , 2 = 1.1, 3 = 1.7, 5 = 2.2, 6 = 2.5) Ans. U (1) = 2 = 1.1, U (4 ) = 8 = 2 2 = 2.2, U (5) = 10 = 2 5 = 2.32 (Graph will be shown in class) b. Does this consumers preferences satisfy transitivity assumption? Explain. Ans. Yes. Let A, B and C denotes the consumption basket y=1, y=4 and y=5 respectively. B A and C B since U(4)>U(1) and U(5)>U(4). To satisfy transitivity condition, this consumers preferences has to be C preferences are transitive. A . Since U(5)>U(1), C A . Hence her c. Does this consumers preferences satisfy more the better assumption? Explain. Ans. Yes. Since U(5)>U(4)>U(1), C B A . And basket C contains most the units, B the second, and A the least. d. Derive this consumers marginal utility using derivative. What are this consumers marginal utility for y = 1, y = 4, y = 5? Sketch the marginal utility. (You may use 1 x = x x) Ans. MU y = 2 (2 y ) (Graph will be shown in class) -1- Spring 2010 Econ 320 Intermediate Microeconomic Analysis Yoichi Otsubo 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 U = xy , and his monthly income is I. Each unit of Pepsi costs Px and each unit of Pizza costs Py. Write a statement of the constrained optimization problem. Which variables are exogenous? Which variables are endogenous? Ans. max xy ( x, y ) subject to : Px x + Py y I Exogenous variables: I, Px, Py. Endogenous variables: x, y. -2-
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