tutorial_12ans - ECOS 2001 Tutorial 12 1. Clarence Busen is...

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ECOS2001 Tutorial 12 1 ECOS 2001 Tutorial 12 1. Clarence Busen is an expected utility maximiser. His preference among contingent commodity bundles are represented by 1/2 12 1 2 1 1 2 2 (, , , ) . () . uc c c c ππ π =+ Hjalmer has offered to bet Clarence $1000 on the outcome of the toss of a coin. That is, if the coin comes up heads, Clarence must pay Hjalmer $1000 and if it is tails Hjalmer must pay Clarence $1000. It is a fair coin toss (prob of each is 1/2 .) If he doesn’t accept the bet Clarence will have $10000 with certainty. Let Event 1 be heads and let Event 2 be tails a. If Clarence accepts the bet, then in Event 1 he will have how many dollars? What about with Event 2? In Event 1 gets 9000; Event 2 gets 11 000 b. If Clarence gets c1 with Event 1 and c2 with Event 2, what is the formula for Clarence’s expected utility? What is his expected utility if he accepts the bet? 12 11 22 EU c c Accepting the bet EU = 99.8746 c. If Clarence decides not to bet, what is his income under Event 1 and 2? What his expected utility be under each Event? EU = 100 d. Does Clarence take the bet? No 2. The certainty equivalent of a lottery is the amount of money you would have to be given with certainty to be just as well-off with that lottery. Suppose that your expected utility function with income in the case of Event 1 and Event 2 is x and y respectively is (, , ) ( 1 ) Uxy x y , where π is the probability of event 1. a. If π = 0.5, calculate the utility of a lottery that gives you $10 000 if Event 1 happens and $100 if Event 1 doesn’t happen. 55 = 0.5(100) + 0.5(10)
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ECOS2001 Tutorial 12 2 b. If you were sure to receive $4900, what would your utility be? U = 70 c. Given this utility function and π = 0.5, write a general formula for the certainty equivalent of a lottery that gives you $x if Event 1 happens and $y if Event 1 does not happen 1/2 21 / 2 1 / 2 2 11 22 () EU x y UCE EU CE EU x y =+ = == + Certainty equivalent CE is such that: = So that / 2 1 / 2 2 CE EU x y + d. Calculate the certainty equivalent of receiving $10 000 if Event 1 happens and $100 if Event 1 does not happen.
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This note was uploaded on 04/20/2010 for the course ECOS 2001 taught by Professor None during the One '09 term at University of Sydney.

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tutorial_12ans - ECOS 2001 Tutorial 12 1. Clarence Busen is...

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