Practice Question_Chap 16

Practice Question_Chap 16 - Uncertainty and Consumer...

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Uncertainty and Consumer Behavior Suppose   that   two   investments   have   the   same   three   payoffs,   but   the  probability associated with each payoff differs, as illustrated in the table  below: Payoff    Probabilities for Investment A Probabilities for Investment B $300 0.10 0.30 $250 0.80 0.40 $200 0.10 0.30 a. Find the expected return and standard deviation of each investment. The expected value of the return on investment A is EV  = (0.1)(300) + (0.8)(250) + (0.1)(200) = $250. The variance on investment A is σ 2  = (0.1)(300 - 250) 2  + (0.8)(250 - 250) 2  + (0.1)(200 - 250) 2  = $500. The expected value of the return on  investment B is EV  = (0.3)(300) + (0.4)(250) + (0.3)(200) = $250. The variance on investment B is σ 2  = (0.3)(300 - 250) 2  + (0.4)(250 - 250) 2  + (0.3)(200 - 250) 2  = $1,500. b. Jill has the utility function   U = 5 I , where I denotes the payoff.   Which  investment will she choose? Jill’s expected utility from investment A is EU=.1*(5*300)+.8*(5*250)+.1*(5*200)=1,250. Jill’s expected utility from investment B is EU=.3*(5*300)+.4*(5*250)+.3*(5*200)=1,250. Since both investments give Jill the same expected utility she will be  indifferent between the two. c. Ken has the utility function  U = 5 I .  Which investment will he choose? Ken’s expected utility from investment A is EU=.1*(5*300) 0.5 +.8*(5*250) 0.5 +.1*(5*200) 0.5 =35.32. Ken’s expected utility from investment B is
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EU=.3*(5*300) 0.5 +.4*(5*250) 0.5 +.3*(5*200) 0.5 =35.25. Ken will choose investment A since it has a higher expected utility.  Notice  that since Ken is risk averse, he will prefer the investment with less  variability. d. Laura has the utility function  U = 5 I 2 .  Which investment will she choose? Laura’s expected utility from investment A is EU=.1*(5*300*300)+.8*(5*250*250)+.1*(5*200*200)=315,000. Laura’s expected utility from investment B is
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Practice Question_Chap 16 - Uncertainty and Consumer...

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