You have no money in your pocket or in your bank account. You are proposed to pa
ID: 1189066 • Letter: Y
Question
You have no money in your pocket or in your bank account. You are proposed to participate in one of two lotteries A or B, which could alleviate your poverty. With lottery A, there is a 90 % chance that you receive a payoff of $0 and a 10% chance that you receive a payoff of $400. With lottery B, there is a 0.50 chance that you receive a payoff of $30 and a 0.50 chance that you receive a payoff of $50.
a. Verify that these two lotteries have the same expected value but that lottery A has a bigger variance than lottery B [Note: the variance is a measure of the risk of the lottery. If I have not defined it in class before you do your homework, look at the handouts which are on SmartSite for the definition of variance]
b. Suppose that your utility function for wealth is u(x) = x + 500 and that you are an expected utility maximizer. Which lottery do you prefer? Are you risk averse, risk neutral or risk lover?
c. Suppose that your utility function for wealth is u(x) = x + 500 and that you are an expected utility maximizer. Which lottery do you prefer? Are you risk averse, risk neutral or risk lover?
d. Suppose that your utility function for wealth is u(I) = (x+500)2 and that you are an expected utility maximizer. Which lottery do you prefer? Are you risk averse, risk neutral or risk lover
Please show all work
Explanation / Answer
a.
Calculation of expected values:
Lot. A:
Payoff (P)
Chance (C)
Expected value (P ×C)
$0
0.9
$0
$400
0.1
$40
$40
Total expected value of A (E1) is $40.
Lot. B
Payoff (P)
Chance (C)
Expected value (P ×C)
$30
0.5
$15
$50
0.5
$25
$40
Total expected value of B (E2) is $40.
Therefore, both A and B has same expected value.
Calculation of variance:
Lot. A:
Payoff (P)
Chance (C)
Expected value, (P ×C)
(P – E1)
(P – E1)^2
C(P – E1)^2
$0
0.9
$0
-$40
1,600
1,440
$400
0.1
$40
$360
129,600
12,960
$40 = E1
14,400
Variance of A is 14,400
Lot. B:
Payoff (P)
Chance (C)
Expected value, (P ×C)
(P – E2)
(P – E2)^2
C(P – E2)^2
$30
0.5
$15
-$10
100
50
$50
0.5
$25
$10
100
50
$40 = E2
100
Variance of B is 100
Therefore, A has bigger variance than B.
Payoff (P)
Chance (C)
Expected value (P ×C)
$0
0.9
$0
$400
0.1
$40
$40
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