Student Number
ECON212 Quiz 3
1.
Consider a lottery with three possible outcomes, S1 , S 2 , and S 3 . If S1 occurs, the
payoff is 30; if S 2 occurs, the payoff is 10; if S 3 occurs, the payoff is 100. The
probabilities for S1 , S 2 , and S 3 are 0.4, 0.5, and 0.1.
a)
Compute the expected value of this lottery. 1 point
Answer
To compute the expected value, calculate the sum of the products of the
probabilities times the payoffs. This yields
EV  30(0.4)  10(0.5)  100(0.1)
EV  12  4  1  18
Page Reference: 631
b)
Calculate the variance of this lottery. 1 point
Answer
To calculate the variance, first square the difference between the payoffs
and the expected value of the lottery. Next, sum these squared differences
times their associated probabilities.
var  (30  18) 2 (0.4)  (10  18) 2 (0.5)  (100  18) 2 (0.1)
var  57.6  32  672.4  762
Page Reference: 631-634
c)
If the decision maker’s utility function is U  5I , what is the expected
utility associated with this lottery. 1 point
Answer
To calculate the expected utility, first determine the utility for each payoff
using the given utility function. Next, sum these utilities multiplied by
their respective probabilities. The utilities are U (30)  150 , U (10)  50 ,
and U (100)  500 . The expected utility is
E (U )  150(0.4)  50(0.5)  500(0.1)
E (U )  60  25  50  135
Page Reference: 640-641
Student Number
ECON212 Quiz 3
d)
If the decision maker had a choice between this lottery and a guaranteed
payoff of 27, which should she choose given her utility function from part
c)? 1 point
Answer
The guaranteed payoff of 27 has an expected utility of 5(27)  135 . Thus,
the guaranteed payoff has exactly the same expected utility as the lottery.
Since the person is risk-neutral, she is indifferent between the guaranteed
payoff and the lottery.
Page Reference: 640-641
2.
Consider two lotteries, A and B . With lottery A , there is a 20-percent chance
that you will receive $80, a 50-percent chance that you will receive $40, and a 30percent chance that you will receive $10. With lottery B , there is a 40-percent
chance that you will receive $30, a 30-percent chance that you will receive $40,
and a 30-percent chance that you will receive $50.
a)
Verify that these two lotteries have the same expected value but that
lottery A has a higher variance than lottery B . 1.5 point
Answer
EV A  80(0.2)  40(0.5)  10(0.3)
EV A  16  20  3  39
EV B  30(0.4)  40(0.3)  50(0.3)
EV B  12  12  15  39
Yes, both lotteries have an expected value of 39.
var A  (80  39) 2 (0.2)  (40  39) 2 (0.5)  (10  39) 2 (0.3)
var A  336.2  0.5  252.3  589
var B  (30  39) 2 (0.4)  (40  39) 2 (0.3)  (50  39) 2 (0.3)
var B  32.4  0.3  36.3  69
Lottery A has a higher variance than lottery B .
Page Reference: 631-634
b)
Suppose that your utility function is U  I . Compute the expected
utility for each lottery. Which lottery has the higher expected utility?
Why? 1.5 point
Student Number
ECON212 Quiz 3
Answer
E (U ) A  80 (0.2)  40 (0.5)  10 (0.3)
E (U ) A  1.79  3.16  0.95  5.9
E (U ) B  30 (0.4)  40 (0.3)  50 (0.3)
E (U ) B  2.19  1.90  2.12  6.21
Lottery B has the higher expected utility. In general, when two lotteries
have the same expected value but different variances, a risk-averse
decision maker will have a higher expected utility for the lottery with the
lower variance, lottery B in this case.
Page Reference: 637-638
3.
Consider the production function
Q  2K 3 L 3
1
a)
1
What is the equation of the isoquant corresponding to Q  10 ? 1.5 point
Answer
To find the equation of the isoquant, solve the production function for K
in terms of L .
Q  2K 3 L 3
1
1
10  2 K 3 L 3
1000  8 KL
125  KL
125
K
L
1
1
Page Reference: 229-230
b)
What is the equation of the isoquant corresponding to an arbitrary level of
output, Q ? 1.5 point
Answer
Perform the same exercise as in part a) leaving Q as a variable.
Student Number
ECON212 Quiz 3
Q  2K 3 L 3
1
Q 3  8 KL
Q3
K
8L
Page Reference: 229-230
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