5) A person with a current wealth of $100,000 who faces the prospect of 25 percent chance of losing his or her $20,000 automobile through theft during the next year. Suppose this person's utility function is U(Y) = InY. a). If this person takes no action, what is the expected utility? b). What is the actuarially fair premium? What is his expected utility if he purchase this insurance. This
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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?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.5. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = √√x. 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 £10,000. 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?
- 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.. 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 £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.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.
- 5. You are a risk-averse decision maker with a utility function U(1) = VI, where I denotes your income. Your income is $100,000 (thus, I=100). However, there is a 0.2 chance that you will have an accident that results in a loss of $10,000. Now, suppose you have the opportunity to purchase an insurance policy that fully insures you against this loss (i.e., that pays you $10,000 in the event that you incur the loss). What is the highest premium that you would be willing to pay for this insurance policy?4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m7. She currently has $2025. a. Would she be willing to undertake a gamble that involves a gain $2875 with probability + and a loss of $1125 with probability ? Show your work and explain your answer. b. Would she be willing to undertake a gamble that involves a gain $2599 with probability and a loss of $800 with probability ? Show your work and explain your answer.Hello can any one help with this Economics question: A contractor spends Dollar 3,000 to prepare for a bid on a construction project which, after deducting manufacturing expenses and the cost of bidding, will yield a profit of dollar 25,000 if the bid is won. If the chance of winning the bid is ten per cent, compute his expected profit and state the likely decision on whether to bid or not to bid?
- # 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?5. Consider a decision-maker who expects to have a car accident with chance ; if this occurs, he will incur $L in damages. He can purchase as much auto insurance, q, as he likes, at a price of p per dollar of coverage: this means that if he pays pq upfront (as the insurance premium), he'll receive a payment of q from the insurance company if an accident occurs. (a) Write out his expected utility from purchasing insurance level q, assuming a utility-of- wealth function u(w) and initial wealth wo. 1 (b) Show that the optimal level of insurance, q, solves u' (wo - L + (1 - p)q)) u' (wo - pq) = p(1 - π) T(1-P) (c) Now assume that u(w) 1 - e-aw, where a > 0 (this is known as a "CARA", or "constant absolute risk aversion", utility function; a parametrizes risk aversion). Solve explicitly for the optimal insurance, and show that it does not depend on wealth.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?