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QUIZ 3
Econ 212-Section B
Question 1. [10 marks] Consider two lotteries A and B. With A, you win $60 with
probability 0.5 and $ 100 with probability 0.5. With lottery B, you win $ 200 with
probability 0.4 and $ 0 with probability 0.6. Assume that this lottery costs you nothing
and that you have no wealth to start with.
a) [4 marks] Compute the expected value and variance of A and B. Which lottery is
more risky? Show your work.
Answer:
EV of B = 0.4*200 = 80
EV of A = (.5)*60 + 0.5*100 = 80
Variance of A = (.5)*(60-80)^2 + 0.5*(100-800)^2 = 200 + 200 = 400
Variance of B = (.6)*(0-80)^2 + 0.4*(200-80)^2 = 9600
Lottery B is more risky.
b) [3 marks] If the decision maker’s (your) utility function is U  I  100 , what is the
expected utility associated with lotteries A and B? Given a choice to pick between the
two lotteries, which lottery would you pick and why? Show your work.
Answer:
The expected utility of A is
E (U )  (0.5) * 60  100  0.5 * 100  100
 13.396
The expected utility of B is
E (U )  (0.6) * 0  100  0.4 * 100  200  12.93
Lottery A has higher expected utility than lottery B, So you would prefer lottery A.
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c) [3 marks] If the decision maker’s (your) utility function is U  I ^2 , what is the
expected utility associated with lotteries A and B? Given a choice to pick between the
two lotteries, which lottery would you pick and why? Show your work.
Answer:
Expected Utility of A given above utility function is
E (U )  (0.5) * (60) 2  0.5 * (100) 2
 6800
Expected Utility of B given above utility function is
E (U )  (0.6) * (0) 2  0.4 * ( 200) 2
 16000
You would choose lottery B as it gives higher expected utility. Note that the preferences
in this part exhibit ‘love for risk’. So you prefer lottery which is risky in terms of returns.
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