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Unformatted text preview: 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 1. [10 points] Suppose that a consumer chooses ( x 1 ,x 2 ) = (9 , 2) at prices ( p 1 ,p 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 ≥ . (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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This note was uploaded on 10/20/2010 for the course ECON 6202 taught by Professor Shapiro during the Fall '09 term at UNC Charlotte.
- Fall '09