Pearson eText Economics -- Instant Access (Pearson+)
13th Edition
ISBN: 9780136879459
Author: Michael Parkin
Publisher: PEARSON+
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Chapter 20, Problem 7APA
To determine
Identify the expected utilities of J and Z.
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Text of the problem from 'An introduction to decision theory' by Martin Peterson:
You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in which you win $200 with a probability of 1/4, $50 with a probability of 1/4, and $10 with a probability of 1/2. You also prefer a fifty-fifty chance of winning either $200 or $50 to receiving $100 for sure. Are your preferences consistent with von Neumann and Morgenstern’s axioms?
The book proposes as solution 'No. Your preferences violate the independence axiom.' without proposing the steps to reach that solution and I don't know why it is correct.
.What is the probability of getting a king if a card is drawn from a pack of 52 cards?
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?
Chapter 20 Solutions
Pearson eText Economics -- Instant Access (Pearson+)
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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