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particularly active this season involves betting on the winner of the U.S. presidential election. Thus, for example, if one trader buys one share of "Obama to win" from another trader, then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does not win the seller pays nothing; either way, the seller keeps the money paid by the buyer for the purchase of the share. (a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = In(x + 1) and initial wealth 4. Leila believes that Obama will win with probability 1/2. Find the highest price p, at which she is willing to buy at least one share. Solution: The price pa solves

particularly active this season involves betting on the winner of the U.S. presidential election. Thus, for example, if one trader buys one share of "Obama to win" from another trader, then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does not win the seller pays nothing; either way, the seller keeps the money paid by the buyer for the purchase of the share. (a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = In(x + 1) and initial wealth 4. Leila believes that Obama will win with probability 1/2. Find the highest price p, at which she is willing to buy at least one share. Solution: The price pa solves

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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please  only do: if you can teach explain steps 

 

 How does pb compare to the lowest price ps at which Leila is willing to sell at least one
share? Are they same? Explain.
Solution: Since Leila is risk averse, she will only agree to buy or sell if doing so yields
a positive expected value. Therefore, we must have

how to solve for this: ps > 1/2 > pb (and in particular,
ps > pb).


b) c

how to solve for this:
for Vadim is 4, and therefore p0
b < pb.

particularly active this season involves betting on the winner of the U.S. presidential election. Thus, for example, if one trader buys one share of "Obama to win" from another trader, then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does not win the seller pays nothing; either way, the seller keeps the money paid by the buyer for the purchase of the share. (a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = In(x + 1) and initial wealth 4. Leila believes that Obama will win with probability 1/2. Find the highest price p, at which she is willing to buy at least one share. Solution: The price po solves which implies that and therefore, This equation has solutions 1 In(5-ps) +: +In(6-pt) = ln 5, (5-Pb) (6-Pb) = 5, P² - 11ps + 5 = 0. 11 ± √101 Pb= 2 Since the price must clearly be less than 1 for Leila to buy, we obtain Pb= 11 - √101 2 (b) How does p, compare to the lowest price p, at which Leila is willing to sell at least one share? Are they same? Explain. Solution: Since Leila is risk averse, she will only agree to buy or sell if doing so yields a positive expected value. Therefore, we must have p. > 1/2> p (and in particular, Ps > Pb). (c) Vadim is more risk averse than Leila. He also believes that Obama will win with prob- ability 1/2. How does the highest price at which he is willing to buy at least one share compare to ps (i.e. to the corresponding price for Leila)? Prove your answer. Solution: Let p denote the highest price at which Vadim is willing to buy, and let L(p) denote the lottery associated with buying one share at price p. For Leila, the certainty equivalent of the lottery L(ps) is 4. Since Vadim is more risk averse than Leila, the certainty equivalent of L(P) for him is less than 4. But the certainty equivalent of L(ps) for Vadim is 4, and therefore p < P-
Transcribed Image Text:particularly active this season involves betting on the winner of the U.S. presidential election. Thus, for example, if one trader buys one share of "Obama to win" from another trader, then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does not win the seller pays nothing; either way, the seller keeps the money paid by the buyer for the purchase of the share. (a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = In(x + 1) and initial wealth 4. Leila believes that Obama will win with probability 1/2. Find the highest price p, at which she is willing to buy at least one share. Solution: The price po solves which implies that and therefore, This equation has solutions 1 In(5-ps) +: +In(6-pt) = ln 5, (5-Pb) (6-Pb) = 5, P² - 11ps + 5 = 0. 11 ± √101 Pb= 2 Since the price must clearly be less than 1 for Leila to buy, we obtain Pb= 11 - √101 2 (b) How does p, compare to the lowest price p, at which Leila is willing to sell at least one share? Are they same? Explain. Solution: Since Leila is risk averse, she will only agree to buy or sell if doing so yields a positive expected value. Therefore, we must have p. > 1/2> p (and in particular, Ps > Pb). (c) Vadim is more risk averse than Leila. He also believes that Obama will win with prob- ability 1/2. How does the highest price at which he is willing to buy at least one share compare to ps (i.e. to the corresponding price for Leila)? Prove your answer. Solution: Let p denote the highest price at which Vadim is willing to buy, and let L(p) denote the lottery associated with buying one share at price p. For Leila, the certainty equivalent of the lottery L(ps) is 4. Since Vadim is more risk averse than Leila, the certainty equivalent of L(P) for him is less than 4. But the certainty equivalent of L(ps) for Vadim is 4, and therefore p < P-
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