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Fall09MT2a

# Fall09MT2a - 1 Economics 420K(Microeconomic Theory Second...

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1 Economics 420K (Microeconomic Theory) Second Midterm Examination University of Texas at Austin, Fall 2009 YOUR NAME: Instructions Write your name in the space at the top of this page. This is a closed-book examination. A calculator will be useful. There are seven pages. Check that you have all pages. Answer each question in the space provided. The examination is worth 50 points. Points are indicated in parentheses at the beginning of each question. Provide all the information asked for by each question. No credit will be given unless clearly demonstrated reasoning is shown. Partial credit will be given for work in the right direction. Question 1 (22 points) A consumer called Vanessa has preferences over two goods, x and y, represented by the following utility function: U(x,y) = 3y + 2√(x) . Let p x and p y denote prices and let I denote income. Fix p y = 240 throughout the question. (a) (4 points) Assume that p x ≥ 6400/I . Use the method of Lagrange to show that Vanessa’s demand for x is x* = 6400/p x 2 . (You can get half points for using some method other than Lagrangeans. Further room for your answer on the following page.) 1

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2 (b) (2 points) Still assuming that p x ≥ 6400/I, what is Vanessa’s demand for y? (c) (2 points) Let p x = 10 and I = 1800. Find Vanessa’s optimal bundle (x,y) at these prices and income. Locate this bundle on a diagram with x on the horizontal axis, showing also Vanessa’s budget line (with slope and intercepts), and the indifference curve on which the optimal bundle lies.
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Fall09MT2a - 1 Economics 420K(Microeconomic Theory Second...

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