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Ch05 Textbook Answers

Ch05 Textbook Answers - Chapter5 Exercises1,3,5,7and9 1....

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Chapter 5 Exercises 1, 3, 5, 7 and 9 1.  Consider a lottery with three possible outcomes:  $125 will be received with probability .2 $100 will be received with probability .3 $50 will be received with probability .5 a. What is the expected value of the lottery? The expected value,  EV , of the lottery is equal to the sum of the returns weighted by  their probabilities: EV  = (0.2)($125) + (0.3)($100) + (0.5)($50) = $80. b. What is the variance of the outcomes? The variance,  σ 2 , is the sum of the squared deviations from the mean, $80, weighted by  their probabilities: σ 2  = (0.2)(125 - 80) 2  + (0.3)(100 - 80) 2  + (0.5)(50 - 80) 2  = $975. c. What would a risk-neutral person pay to play the lottery? A risk-neutral person would pay the expected value of the lottery: $80. 3.  Richard is deciding whether to buy a state lottery ticket.  Each ticket costs $1, and the  probability of winning payoffs is given as follows: Probability Return 0.50 $0.00 0.25 $1.00 0.20 $2.00 0.05 $7.50 a. What is the expected value of Richard’s payoff if he buys a lottery ticket?  What is  the variance?
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The expected value of the lottery is equal to the sum of the returns weighted by their  probabilities: EV  = (0.5)($0) + (0.25)($1.00) + (0.2)($2.00) + (0.05)($7.50) =  $1.025 The variance is the sum of the squared deviations from the mean, $1.025, weighted by  their probabilities: σ 2  = (0.5)(0 – 1.025) 2  + (0.25)(1 – 1.025) 2  + (0.2)(2 – 1.025) 2  +  (0.05)(7.5 – 1.025) 2 , or σ 2  = 2.812. b. Richard’s   nickname   is   “No-Risk   Rick”   because   he   is   an   extremely   risk-averse  individual.  Would he buy the ticket? An extremely risk-averse individual would probably not buy the ticket.  Even though  the expected value is higher than the price of the ticket, $1.025 > $1.00, the difference  is not enough to compensate Rick for the risk.  For example, if his wealth is $10 and he  buys a $1.00 ticket, he would have $9.00, $10.00, $11.00, and $16.50, respectively,  under the four possible outcomes.  If his utility function is  U  =  W 0.5 , where  W  is his  wealth, then his expected utility is: EU = 0.5 ( 29 9 0.5 ( 29 + 0.25 ( 29 10 0.5 ( 29 + 0.2 ( 29 11 0.5 ( 29 + 0.05 ( 29 16.5 0.5 ( 29 = 3.157. This is less than 3.162, which is his utility if he does not buy the ticket ( U (10) = 10 0.5  =  3.162).  Therefore, he would not buy the ticket.
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