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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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Principles of Macroeconomics (Mind...

8th Edition
N. Gregory Mankiw
Publisher: Cengage Learning
ISBN: 9781305971509
BuyFind

Principles of Macroeconomics (Mind...

8th Edition
N. Gregory Mankiw
Publisher: Cengage Learning
ISBN: 9781305971509

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Chapter
Section
Chapter 14, Problem 9PA
Textbook Problem
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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?

Expert Solution

Sub part (a):

To determine
Diminishing marginal utility.

Explanation of Solution

The utility function is W12 . Since the power function is less than one, the marginal utility will be diminishing. It implies that the person is risk averse.

Figure 1 illustrates the diminishing marginal utility

Expert Solution

Sub Part (b):

To determine
Expected value.

Expert Solution

Sub part (c):

To determine
Expected utility.

Expert Solution

Sub part (d):

To determine
greaterExpected utility.

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