Jamal has autility function U=W1/2,where W is his wealth in millions of dollars and U is the utitlity he obtains from that wealth.Inthe final stage of a game show,the host offers offers Jamal a choice(A)$4 million dollar for sure,or (B) a gamble that pays $1 million with probability 0.6 and $9million with probability 0.4. a.Graph Jamal's utitility function.Is he risk averse?Explain. b.Does A or B offers Jamal a higher expected price?Explain your reasoning with appropriate calculations. c.Does A or B offer Jamal a higher expected utility? d.Should Jamal pick A or B? Why?

Jamal has autility function U=W1/2,where W is his wealth in millions of dollars and U is the utitlity he obtains from that wealth.Inthe final stage of a game show,the host offers offers Jamal a choice(A)$4 million dollar for sure,or (B) a gamble that pays $1 million with probability 0.6 and $9million with probability 0.4. a.Graph Jamal's utitility function.Is he risk averse?Explain. b.Does A or B offers Jamal a higher expected price?Explain your reasoning with appropriate calculations. c.Does A or B offer Jamal a higher expected utility? d.Should Jamal pick A or B? Why?

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter19: The Basic Tools Of Finance

Section: Chapter Questions

Problem 9PA

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Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?
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?
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?
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. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why? I would like help with the unanswered last parts of the questions.
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 (?)
# 4 Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?
Jamal has a utility function 1/2 U W5 , where W is hiswealth in millions of dollars and U is the utility heobtains from that wealth. In the final stage of agame show, the host offers Jamal a choice between(A) $4 million for sure and (B) a gamble that pays$1 million with probability 0.6 and $9 million withprobability 0.4.a. Graph Jamal’s utility function. Is he risk averse?Explain.b. Does A or B offer Jamal the higher expectedprize? Explain your reasoning with appropriatecalculations. (Hint: The expected value of arandom variable is the weighted average of thepossible outcomes, where the probabilities arethe weights.)c. Does A or B offer Jamal the higher expectedutility? Again, show your calculations.d. Should Jamal pick A or B? Why?
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2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.
2. Ronald has $18,000. But he is forced to bet it on the flip of a fair coin. If he wins he has $36,000. If he loses he has nothing. Ronald's expected utility function is 0.5x0.5 + 0.5y0.5, where x is his wealth if heads comes up and y is his wealth if tails comes up. What safe income would make him exactly as well off as this bet?
Jin's Utility Function Wealth Utility (Dollars) 60,000 4,000 61,000 4,110 62,000 4,209 63,000 4,288 Refer to Table 27-1. If Jin's current wealth is $61,000, then O his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is risk averse. his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is risk averse.