4. Roman owns a football club. If Roman's club wins the Champions League, he will have wealth M = 625. If it does not win, he will have M = 400. The probability of winning is 0.20. %3D Roman has the utility function u (M) = 2\M. (i) What is Roman's expected wealth? (ii) What is his expected utility? (iii) Suppose that Roman could have money M* with certainty instead of facing the uncertainty. What is the minimum value of M* that Roman would accept?

4. Roman owns a football club. If Roman's club wins the Champions League, he will have wealth M = 625. If it does not win, he will have M = 400. The probability of winning is 0.20. %3D Roman has the utility function u (M) = 2\M. (i) What is Roman's expected wealth? (ii) What is his expected utility? (iii) Suppose that Roman could have money M* with certainty instead of facing the uncertainty. What is the minimum value of M* that Roman would accept?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

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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.
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?
3. Sarah's current disposable income is £90,000. Suppose there's a 1% chance that Sarah's house may be flooded, and if it is, the cost of repairing it will be £80,000, reducing her disposable income to £10,000. Suppose also that her utility function of income M is: U = VM (a)Calculate Sarah's expected income and expected utility given the risk of flooding. (b)For her to take an insurance that fully insures her in the event of house flooding, Sarah would have to pay a price for such an insurance, which would reduce her disposable income. What would be the minimum certain disposable income required for Sarah to take an insurance that fully insures her in the event of house flooding? Explain your answer.
12. Complete the following examples The Hotel California faces a risk that an earthquake will cause a $200 million loss; probability is 0.02. The owner of the hotel, Eddie Eagle, has a utility function of U= W05, where Wis the owner's wealth (as measured by the value of the hotel in millions of dollars). Suppose the initial value of the hotel is $225 million (W = 225). What is the expected loss for Eddie Eagle? What is Eddie Eagle's expected utility? Risk premium? o The Anderson family lives in the Arizona wilderness. Their property is at risk for being destroyed by a forest fire. It is estimated that each year the Anderson face a 5 percent probability of a $500,000 loss. The Anderson family has a utility function of U = W 0.7, where W is wealth and measured in dollars. Suppose their current wealth is $1 million. What is the family's expected loss from fire? What is the Anderson family's expected utility? What is the maximum value the Andersons will pay for insurance to completely…
2. Two individuals have the same income ($100,000), but different potential healthcare expenses. Person A's probability of having $80,000 in healthcare expenses is 0.5 percent. Person B's probability of having $800 in healthcare expenses is 50 percent. Assume your utility is U = VI where I is your income. Calculate each person's expected income and expected utility. Calculate each person's certainty equivalent. What does value of the certainty equivalent tell you about how much each person would be willing to insure against their loss?
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?
4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y ), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?
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?
Suppose that Mary has a utility function U(W) W power of 0.5. Her only asset is the shares in the start-up e-com company. Next week she will learn the stock's value. She believes that it is worth $225 with the probability 1/3, $196 with the probability 1/2 and $144 with the probability 1/6. Write down the prospect and calculate the expected value and her expected utility.
5) Philippina's utility of wealth function is VW. She has stocks, bonds and cash worth $360,000 and a house worth $280,000. There is a 1% chance of her house being completely destroyed by fire. Unfortunately, if she has insurance, she is less responsible and so the risk of her house being burned down rises to 2%. a. What is the most Philippina is willing to pay for insurance?
Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)