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Midterm-2006 - Econ 6202 Fall 2006 Dmitry Shapiro Midterm...

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Econ 6202, Fall 2006 Dmitry Shapiro Midterm Exam September 21, 2006 There are FOUR questions in the midterm. You need to do all four of them. The exam is 75 minutes long and has 75 points. Be sure to allocate your time in proportion to the points. The exam is closed-book. Please turn off your cellphones and other sound-making devices. Good luck! 1. [25 points] Consider a consumer with the following utility function: u ( x 1 , x 2 ) = x 1 + x 2 . Denote by p i , i = 1 , 2, the price of commodity i and by y the consumer’s income. (a) Derive the Marshallian demand functions x i ( p 1 , p 2 , y ) , i = 1 , 2. (b) Suppose that originally prices are p 1 = 2 , p 2 = 2. The consumer’s income is y = 24. Denote the utility of consumer given this prices and income as u . Now suppose that price changed to p 0 1 = 4 and p 0 2 = 2, but the income has not changed y = 24. Denote the utility that consumer receives given the new prices as u 0 . Compute e ( p 1 , p 2 , u 0 ) - e ( p 1 , p 2 , u ). [Your answer should be a number.] 2. [20 points] A consumer has initial wealth W = 64. His von Neumann-Morgenstern utility function over nonnegative levels of wealth is u ( y ) = ln y . (a) In period 0, the following class of lotteries is available. If the consumer pays x , he receives nothing with probability ˆ p and 3 x with probability 1 - ˆ p . Notice that regardless
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