Macroeconomics
13th Edition
ISBN: 9780134735696
Author: PARKIN, Michael
Publisher: Pearson,
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Chapter 20, Problem 7APA
To determine
Identify the expected utilities of J and Z.
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Jamal has a utility function U= W1/2 where Wis his wealth in millions of 'dollars and Uis 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 $1million with a probability of 0.6 and $9 million with a probability of 0.4.
a. Graph Jamal's utility function. Is he risk-averse? Explain.
b. Does A or B offer, Jamal, a higher expected price? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.)
c. Does A or B offer Jamal a higher expected utility? Again, show your calculations.
d. Should Jamal pick A or B? Why?
Roger's utility/u as a function of wealth/w is
u = { ln w, w < 1600
w1/2, w >= 1600
Roger has $1000 and 3 options.
1. spend $400 to enter the game with probabilities of winning or losing:
Win/(Lose)
(500)
0
1000
3000
P(Win/(Lose))
0.2
0.1
0.6
0.1
a. Show with workings which option roger would choose.
Max Pentridge is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $10,000. With probability p = 0.9 the palace will succeed and Max's wealth will grow from $10,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $5,000, so that his wealth will be just $5,000.
What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $10,000 with certainty? ____
(Please round your final answer to the whole dollar, if necessary)
Chapter 20 Solutions
Macroeconomics
Ch. 20.1 - Prob. 1RQCh. 20.1 - Prob. 2RQCh. 20.1 - Prob. 3RQCh. 20.1 - Prob. 4RQCh. 20.2 - Prob. 1RQCh. 20.2 - Prob. 2RQCh. 20.2 - Prob. 3RQCh. 20.2 - Prob. 4RQCh. 20.3 - Prob. 1RQCh. 20.3 - Prob. 2RQ
Ch. 20.3 - Prob. 3RQCh. 20.3 - Prob. 4RQCh. 20.4 - Prob. 1RQCh. 20.4 - Prob. 2RQCh. 20.4 - Prob. 3RQCh. 20 - Prob. 1SPACh. 20 - Prob. 2SPACh. 20 - Prob. 3SPACh. 20 - Prob. 4SPACh. 20 - Prob. 5SPACh. 20 - Prob. 6SPACh. 20 - Prob. 7APACh. 20 - Prob. 8APACh. 20 - Prob. 9APACh. 20 - Prob. 10APACh. 20 - Prob. 11APACh. 20 - Prob. 12APACh. 20 - Prob. 13APACh. 20 - Prob. 14APACh. 20 - Prob. 15APACh. 20 - Prob. 16APACh. 20 - Prob. 17APACh. 20 - Prob. 18APACh. 20 - Prob. 19APACh. 20 - Prob. 20APACh. 20 - Prob. 21APACh. 20 - Prob. 22APACh. 20 - Prob. 23APA
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