Economics+395+midterm+practice+questions

# Economics+395+midterm+practice+questions - Economics 395...

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Topics in Risk and Uncertainty Practice Questions Midterm Exam Fall 2008 Question One Anatole is given the choice between the following two lotteries: (i) Wins nothing with probability 0.54; loses \$1000 with probability 0.46. (ii) Wins \$100 with probability 0.48; loses \$1000 with probability 0.52. (a) Draw a diagram with probability of losing \$1000 on the horizontal axis, and probability of winning nothing on the vertical axis. Show in your diagram the full set of all possible lotteries over the three prizes V = {-\$1000, \$0, \$100}. Explain how you can capture such a lottery in a two dimensional diagram, when each lottery is specified as a sequence of three numbers. Identify the best lottery possible, and label it β. Identify the worst lottery possible, and label it ω. (b) In your diagram, show the two lotteries (i) and (ii), described above. (c) Suppose Anatole’s preferences satisfy the expected utility hypothesis. Also, suppose he prefers lottery (ii) over lottery (i). Draw a set of indifference curves that might represent his preferences. (d) Mark the following two lotteries on your diagram. (iii) Loses \$1000 with probability 0.2; wins \$100 with probability 0.8. (iv) Loses \$1000 with probability 0.1; wins nothing with probability 0.9. If Anatole were given the choice between these lotteries, which do you think he would choose? Explain why. (e) Consider a compound lottery which promises lottery (iv) as a prize with probability 0.6, and promises lottery ω as a prize with probability 0.4. If Anatole plays this lottery, with what probability does he lose \$1000? With what probability does he win nothing? With what probability does he win \$100? Mark that compound lottery on your diagram. (f) Can you describe a compound lottery, offering lottery (iii) and lottery ω as prizes,

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Economics+395+midterm+practice+questions - Economics 395...

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