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Fall 2010 Econ 201 Exam 1 Questions 1 to 8

Fall 2010 Econ 201 Exam 1 Questions 1 to 8 - ECONOMICS 201...

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Unformatted text preview: ECONOMICS 201 FALL 2010 EXAM 1 Instructions: Please mark your answers clearly. No class notes or other materials are allowed. 100 points total. Each question is worth 5 points with the exception of Questions 4, 8, 9, 10, and 15 (10 points). 1. Dora likes hugs (good 1) and kisses (good 2). To be able to consume any positive amount of good 1, she must pay $10. Once she pays this fixed cost, the price (per unit) of good 1 is $1. The price (per unit) of good 2 is $2. Her income is $100. Draw Dora’s budget set. Label the intercepts and slopes. 50". 2 30¢ a. 1 Let’s say that Lady Gaga is indifferent between bundles (5,10) and (9,2). Which of the following leads us to conclude that her preferences are convex? flint: The line connecting (5,10) and (9,2) is X 2 = -—2Xl + 20 ; her preferences satisfy monotonicity. (Please circle one response.) a. She strictly prefers (5,10) to (8,3). b. She strictly prefers (6,9) to (6,7). 0. She strictly prefers (7,7) to (5,10). d. She strictly prefers (6,8) to (9,2). Which of the following utility functions exhibit diminishing marginal utility with respect to good 1? (Please circle as many responses as necessary.) 1 a. u(X,,X,):2XE+5X, b. u(X,,X2)=3Xl+2X2 c. u(XI,XZ)=O.51nX1+03an1”2 Timon’s utility function is u(Xl,X2). Suppose that income, In, and both prices, P] and P2 , are multiplied by 6 , where 9 > 0 . (10 points) a. What is the Lagrangian of the UMP (Utility Maximization Problem)? What is the first-order condition (F DC} with respect to X 1 ‘? b. How does the value of the multiplier, A , change when we multiply income and prices by 6 ? True or False: Take a utility function that represents a consumer’s preferences. If we add 10 units of utility and divide the result by 2, we obtain another utility function that represents the same preferences. Explain your answer with a mathematical expression, graph, and/or one or two sentences. . True or false: Suppose there are two goods. If neither is inferior, the goods must be complements. Explain your answer with a mathematical expression, graph, and/or one or two sentences. . True or false: Suppose there are two goods. If they are complements and good 1 is not Giffen, good 1 must be normal. Explain your answer with a mathematical expression, graph, and/or one or two sentences. m: Remember that only relative prices matter in the sense that if we increased income and both prices by the same percentage, there would be no change in the consumption of good 1. . Rafael Nadai likes cereal (good 1) and oatmeal (good 2). Prices are P1 and P2 , and income is m. His utility function is u(X1,X2) = éln Xl + :lan. (10 points) a. What is his UMP (utility maximization problem)? b. What is the Lagrangian? What are the first-order conditions with respect to X1, X 2 , and/i. ? c. What is the demand function X1 (11,102,111)? (1. Take a derivative of the demand function to demonstrate that good 1 is ordinary. ...
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