2004MidtermSolutions

2004MidtermSolutions - API 111 / Economics 2020a /...

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API 111 / Economics 2020a / Government 2005 / HBS 4401 Midterm Examination November 8, 2004 1. [30 points] Consider a two-commodity world and consumer with the following utility function: () ( ) 2 1/2 12 1 2 , uxx x x =+ The prices of goods 1 and 2 are p 1 and p 2 , respectively, and the consumer has initial wealth w. a) State the consumer’s utility maximization problem [3 points] b) Will this consumer’s Walrasian demand functions satisfy Walras’ Law? Explain your answer? [3 points] c) Derive the consumer’s Walrasian demand functions and indirect utility functions. [12 points] d) Suppose that the consumer has wealth w = 260. Initially, prices are (p 1 ,p 2 ) = (6,8). Suppose prices change to (p' 1 ,p' 2 ) = (5,12). What is the (exact) equivalent variation of this price change? [12 points] 2. [15 points] Suppose a rational consumer’s Hicksian demand curves are given by: 2 11 1 1 1 22 2 2 , , p u hp u k a p p u p where a 1 , a 2 , k 1 , and k 2 are constants. a) What must be true of the constants a 1 , a 2 , k 1 and k 2 ? Explain your answer. [10 points] b) What is the consumer’s Walrasian demand for good 1? [5 points]
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3. [30 points] On-line betting services such as the Iowa electronic markets and Tradesports.com have gained tremendously in popularity in recent years. A typical trade in these markets is a purchase of a share in one political candidate for a price p which will be worth $1 if the candidate wins and $0 if the candidate loses. Suppose that candidates 1 and 2 each have probability ½ of winning an election, but that the price for a share of candidate 1 is p < ½ and that the price for a share of candidate 2 is 1 - p > ½. a) Suppose that a risk-averse consumer with wealth W is deciding whether to invest in shares of candidate 1. Assume that the consumer has VNM utility function for wealth u with u’(w) > 0, u’’(w) < 0. Write down the optimization problem for this consumer. [5 points] b) Does the consumer’s (expected) utility maximizing investment consist of a positive number of shares of candidate 1, no shares of candidate , or is it impossible to tell without knowing more about u ? Explain your answer. [5 points] For parts c) through e), suppose that exit polls will be revealed during the course of voting. With probability 1/2, the exit polls will reveal that candidate 1 has a 75% chance
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This note was uploaded on 04/12/2009 for the course HKS API111 taught by Professor Avery during the Fall '08 term at Harvard.

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2004MidtermSolutions - API 111 / Economics 2020a /...

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