2. Bob's wealth is $2500. However, he faces a 50% chance of suffering a $900 loss. He is an expected utility maximizer and his utility function is U(w) = Vw , Where w is his wealth. (a) What is Bob's cost of risk? (b) If Bob can buy insurance against his loss for a price of $500, will he buy it? (c) What is the maximum amount Bob would be willing to pay for insurance?
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- 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?1. A customer has utility function u(x) = log(x + 1000). The customer’scurrent wealth is $28,000. The customer’s car has a value of $14,700. Theprobability of the car being stolen is 0.016. How much would the customerbe willing to pay for insurance against the car being stolen?Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
- 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.Sam, after taking a $200 loan from the bank to finance an investment that pays $1000 50% of the time and $0 50% of the time at a 100% interest, discovers another riskier investment that pays out $5,000 but only 10% of the time, while the other 90% of the time it pays zero. Would the he want to switch to the riskier investment? Question 4 options: Yes because his return has increased No because his liability to the bank has increased No because his return has decreased None of the above4) You are a financial professional working in a corporate loan department. A company named Mitch Hedberg Inc. (MH) comes to you for a loan. MH has debt from a previous loan (given by a different firm than yours) of 200. Your company analysts say that MH is likely to earn either 180, 240, or 300 this year - each with a probability of 1/3. MH wants you to lend them 100. MH could use this borrowed 100 to do either project X or project Y. Project X has a guaranteed return of 125 if the 100 is put there. Project Y may return either 0 or 210; each has probability of 1/2 and also costs 100 to do. a) Which project, X or Y, has the larger expected value? b) If you lend MH the 100, what will they do with the money? Why? Show your math. c) Should you lend MH the money or not? Show your math. d) Why did I choose the letters "MH" for this problem? What financial economic concept with initials "MH" is important in this problem?
- 4. Insurance You are pondering whether to buy insurance for your new car. The car is worth $50,000. Apart from that, your wealth sums up $40,000. Your utility takes the form u(w) = √w. There is 0.5% chance that your car will be stolen. With the insurance in place, you will get fully reimbursed if this tragedy happens. (a) If the insurance premium is $400, would you buy the insurance? (b) What is the largest premium you are willing to pay for the car insurance? (c) If your utility is instead given by u(w) = log(w), how does your answer to part (2) change?1. George maximizes expected utility and he has a von-Neumann-Morgenstern utility function u (c) = √e. He has an initial wealth of $1,000. He finds an investment opportunity. The project has a startup cost of $1000, and a 9% chance of success. If the project succeeds, the payoff is $100,000; if it fails, its payoff is $0. (a) Would George invest in this project? (b) Suppose George has an initial wealth of $100, 000 instead of $1,000. Would he invest in this project? (c) Comparing your answers in parts (a) and (b), how does George's risk appetite change? Why?1. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,00 A. Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. B. What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?
- 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…17. Suppose a risk-neutral power plant needs 10,000 tons of coal for its operations next month. It is uncertain about the future price of coal. Today it sells for $60 a ton but next month it could be $50 or $70 (with equal probability). How much would the power plant be willing to pay today for an option to buy a ton of coal next month at today's price? (Ignore discounting over the short period of a month.) а. 5 b. 4 с. 3 d. NOTE: I KNOW THAT THE ANSWER IS (A), BUT PLEASE INCLUDE ALL THE STEPS HOW TO SOLVE THE PROBLEM BECAUSE I NEED TO PRACTICE. THANK YOU.3) A risk-loving individual has $1000 to invest. The individual maximizes his/her expected utility and has a monotonic utility function. Show that he/she will never choose a diversified portfolio - that is, show that he/she will either keep the entire $1000 in a safe, or invest the entire $1000 in a risky assesst, for which each $1 invested yields $] with probability p, and SB with probability (1-p), where $B<$1<$J.