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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 Fall '08
 MINETTI
 Economics, Probability, Utility, Oliver, Expected utility hypothesis

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