EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
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Question
Chapter 4, Problem 4.1P
a
To determine
To find:Whether gambles are fair or not.
b)
To determine
To know:Preference of gamble.
c)
To determine
To ascertain:Whether W will take a gamble if roulette game is not forcibly played.
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Alex has a utility function U = W2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a
game show, the host offers Alex a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million
with probability 0.6.
Use the blue curve (circle points) to graph Alex's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million.
Utility (Thousands)
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
0
2
4
6 8 10 12 14
Wealth (Millions of dollars)
16
18 20
V
Utility Function
(?)
Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?
Antonio has a utility function U = W, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage
of a game show, the host offers Antonio a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16
million with probability 0.6.
Use the blue curve (circle points) to graph Antonio's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million.
?
Utility (Thousands)
5.0
4.5
4.0
3.5
3.0
25
2.0
1.5
1.0
0.5
0
+
0
2
4
6
8
10 12 14
Wealth (Millions of dollars)
16 18
True or False: Antonio is risk averse.
20
20
Utility Function
Choice
True
O False
offers Antonio a higher expected prize. (Hint: The expected value of a random variable is the weighted average of the possible outcomes,
where the probabilities are the weights.)
Choice offers Antonio a higher expected utility.
Antonio should pick choice,
Chapter 4 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
Ch. 4.1 - Prob. 1MQCh. 4.1 - Prob. 2MQCh. 4.1 - Prob. 3MQCh. 4.2 - Prob. 1TTACh. 4.2 - Prob. 2TTACh. 4.2 - Prob. 1MQCh. 4.3 - Prob. 1TTACh. 4.3 - Prob. 2TTACh. 4.3 - Prob. 1MQCh. 4.3 - Prob. 2MQ
Ch. 4.3 - Prob. 3MQCh. 4.3 - Prob. 1.1TTACh. 4.3 - Prob. 1.2TTACh. 4.3 - Prob. 2.1TTACh. 4.3 - Prob. 2.2TTACh. 4.3 - Prob. 1.1MQCh. 4.3 - Prob. 2.1MQCh. 4.3 - Prob. 3.1MQCh. 4.4 - Prob. 1TTACh. 4.4 - Prob. 2TTACh. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - Prob. 7RQCh. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQCh. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - Prob. 4.8PCh. 4 - Prob. 4.9PCh. 4 - Prob. 4.10P
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