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Jamal has a utility function U = W 1/2 , 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. Graph Jamal’s utility function. Is he risk averse? Explain. b. Does A or B offer Jamal a higher expected prize? 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?

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Brief Principles of Macroeconomics...

8th Edition
N. Gregory Mankiw
Publisher: Cengage Learning
ISBN: 9781337091985
BuyFind

Brief Principles of Macroeconomics...

8th Edition
N. Gregory Mankiw
Publisher: Cengage Learning
ISBN: 9781337091985

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Chapter 9, Problem 9PA
Textbook Problem

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. Graph Jamal’s utility function. Is he risk averse? Explain.

b. Does A or B offer Jamal a higher expected prize? 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?

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