6) Leia has $11,000 and she wants to invest in financial market. There are two types of assets. The first one guarantees 0.1 percent return next year. The second one is a risky asset which will yield 0.5 percent return in good times and 0.4 percent of loss in bad times. Suppose the chance of good and bad times is half-half and Leia's utility function is U(Y) = Y 0.5 a). What is the expected utility if she invest in the first asset? b). What is the expected utility if she invest in the second asset? Will Leia chooses the
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- 6) Leia has $11,000 and she wants to invest in financial market. There are two types of assets. The first one guarantees 0.1 percent return next year. The second one is a risky asset which will yield 0.5 percent return in good times and 0.4 percent of loss in bad times. Suppose the chance of good and bad times is half-half and Leia's utility function is U(Y) = Y 0.5 %3D a). What is the expected utility if she invest in the first asset? b). What is the expected utility if she invest in the second asset? Will Leia chooses the first or the second asset? c). Suppose that Leia can purchase a financial insurance which cost her $100 and cover all her lost when bad times happen. Will she purchase this insurance?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.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.
- Economics Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = Vc. -What is the expected value of Shawn's consumption? -What is his expected utility? -What is his certainty equivalent of having 10000 with probability 0.75 and 3600 with probability 0.25?5. Consider a weather forecaster who is paid based on her performance. Each day, she forecasts the probability q = [0, 1] that it will rain the following day. She is given a bonus that depends on her forecast and whether it rains. Assume that the forecaster knows the true probability, p, and when choosing her forecast, q, cares only about maximizing her bonus for that day (in particular, she may lie about the probability if doing so increases her pay). (a) Suppose the bonus is equal to the percentage the forecast assigns to what actually happens. For example, if the forecaster says there is a 72% chance of rain (i.e. q = 0.72), then she is paid $72 if it rains and $28 if it does not rain. If the forecaster is a risk neutral expected utility maximizer, what forecast will she make (as a function of p)? (b) Suppose instead that the bonus is equal to 100(1 − (1 − q)2) dollars if it rains and 100(1-q²) dollars if it does not rain. For example, if the forecaster says there is an 80% chance…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.
- Michael lives on an island and owns a beach house worth $400,000. Of that, $100,000 is the cost of land and $300,000 is the cost of the structure. The probability that a hurricane destroys his house is 3percent (he will still own the land). Michael can purchase hurricane insurance at the price of $2for each $100 of coverage. 1. What is Michael’s contingent consumption bundle if Michael does not purchase insuranceBecky is deciding whether to purchase an insurance for her home againtst burglary. the payoff for her is shown as follow: Net worth of her Net worth of her home: $ 20000 burglary(10%) Net worth of her Net worth of her home: $50000 burglary (90%) The insueance would cover all the loss from burlary and the insurance fee is $8000. Her utility funtion is given as u=w ^0.3 Should Beck purchase the insurance Explain.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. I Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. 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?