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.
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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.3. Consider a home energy storage (battery) system that can store up to 2 units of energy. At every time step, there is a demand for energy in the home which is drawn from 0,1,2 units with equal probability independent of the demands in the previous time steps. At every point in time, you have to satisfy the demand either by discharging the needed energy from the battery or purchasing power from the grid (or a combination of the two). You could also choose to purchase power from the grid to charge your battery. The grid energy price is either H(igh) or L(ow) according to a Markov chain (Price moves from H to L with probability p, and from L to H with probability q). (a) Model the decision making as an infinite horizon MDP where the objective is to minimize the discounted cost of energy purchased over an infinite horizon. (b) Write down a policy a of your choosing. Perform two steps of the operator T, for your policy, followed by one step of T..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?
- 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?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?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.
- 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?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?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.
- Becky 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.Q1. A farmer believes there is a 50-50 chance that the next growing season will be abnormally rainy. His expected utility function has the form Expected utility = 0.5lnYNR + 0.5lnYR Where and represent the farmers income in the state of ‘normal rain’ and ‘rainy’ respectively. Suppose the farmer must choose between two crops that promise the following income prospects Crop YNR YR Wheat $83,000 $10,000 Maize $83,000 $15000 What mix of wheat and maize would provide maximum expected utility to this farmer?6. for a large company (she travels by car). She earns 900 euros a week in fixed salary, but if she reaches the set for a week sales target, she receives a bonus of 325 euros that week. The probability of getting the bonus is 0.2. A person is a traveling salesman of goods Her utility function over money is given by U=√W, where W is the wealth in SEK per week. 6a 6b What is her expected weekly bonus? Her boss offers her another job within the same company. If so, she would work in an office with a certain personnel responsibility and receive a fixed salary per week (no bonuses). What salary per week must her boss at least offer her in order for her to accept new work? Justify your answer based on expected utility theory.