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Midterm-2008 - Econ 6202 Fall 2008 Dmitry Shapiro Midterm...

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Econ 6202, Fall 2008 Dmitry Shapiro Midterm Exam October 21, 2008 There are 4 questions in the midterm. The exam is 75 minutes long and has 100 points. Be sure to allocate your time in proportion to the points (10 points = 7.5 minutes). The exam is closed-book. Be sure to explain your reasoning clearly for each answer, as most credit will be awarded based on your explanation rather than your final answer. Please turn off your cell phones and other sound-making devices. Good luck! 1
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1. [10 points] Suppose that a consumer chooses ( x 0 1 , x 0 2 ) = (9 , 2) at prices ( p 0 1 , p 0 2 ) = (2 , 3) and ( x 1 1 , x 1 2 ) = (4 , 5) at prices ( p 1 1 , p 1 2 ) = (3 , 2) . You can assume that in both cases the consumer spends his full wealth on a chosen bundle. Are these choices consistent with the Weak Axiom of Revealed Preferences? 2. [30 points] Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u ( x, L ) = xL , where x represents consumption of the good and L represents leisure. The total amount of time that the worker has is 1 unit, so L [0 , 1]. The time that is not spent on leisure is spent on work. In particular, for any L that the worker would choose she will receive income w (1 - L ), where w represents the wage rate. Let p denote the price of the consumption good. In addition, to her wage income, the worker also has a fixed income y 0 . (a) Write down the utility maximization problem for this consumer. (b) Find the Marshallian demands for the consumption good and leisure. Make sure to take care of the constraint L [0 , 1]. (c) Find the indirect utility as a function of p, w, and y . It is not necessary to simplify your answer.
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