Draw a graph with utility on the Y axis and income on the X axis for a risk averse person. Label the following points on the Y axis The expected value of utility while uninsured The expected value of utility with actuarially fair, full insurance The expected value of utility with actuarially far, partial insurance
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- Draw a graph with utility on the Y axis and income on the X axis for a risk averse person. Label the following points on the Y axis
- The expected value of utility while uninsured
- The expected value of utility with actuarially fair, full insurance
- The expected value of utility with actuarially far, partial insurance
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- 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.Continue from Question 16: You make $20,000 per year, and there's a $100 insurance expense to mitigate a 1% risk of a $10,000 accident. Utility without insurance and no accident = 2000 Utility without insurance with accident = 1500 What is the expected utility "without" insurance? Utility "2000" "1999" "1500" 1999 2000 1995 1500 $10,000 $19,900 $20,000Michael 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 insurance
- ease use utility of wealth function in the booK, 8-1 (see below). Certainty Utility B D 200 198 194 D' Total utility 170 of wealth C' Expected Utility A 140 10,000 15,000 19,000 20,000 Wealth FIGURE 8-1 Total Utility of Wealth and the Impact of Insurance Please explain the difference between the certainty utility line and the expected utility line b. Calculate your E(U), given an 80% change of being healthy and 20% of being sick, knowing that your income falls to $10,000 and your utility is 140 if you get sick. Calculate your E(W), given an 80% change of being healthy and 20% of being sick. d. Given that your Certainty Utility Function is U = 200Y-0.00154 and Y is your income, what is your Certainty Utility with insurance (if you are risk averse) What insurance premium will you pay to guarantee a utility of 197? Please provide a calculation.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?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?
- 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?Suppose that there is a 20% chance Malik is injured and earns $100,000, and an 80% chance he stays healthy and will earn $500,000. Suppose further that his utility function is the following (utility = square root of income) Malik is risk ____. He will prefer ____ (given the same expected income). a. lover; actuarially fair and full insurance to no insurance b. averse; no insurance to actuarially fair and full insurance c. neutral; he will be indifferent between actuarially fair and full insurance to no insurance d. lover; no insurance to actuarially fair and full insurance e. averse; actuarially fair and full insurance to no insuranceEconomics 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?
- Moral Hasard and Insurance The utility is U = W1/2 − 350S + 95S1/2 ; where W is wealth and S is care taken to avoid accidents. Probability of accident is 0.70 − S1/2 Wealth is ✩850,000 without accident and ✩300,000 with accident. Calculate S, EU and CE without insurance. Calculate S and EU with full insuranceQuestions 18 through 20 refer to the following information: 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. Question 18 What is the expected value of Shawn's consumption? Question 19 What is his expected utility?In the summer of 1984, Nicholai opened a small art gallery in the West Village and amassed a collection worth $2,60,000. An insurance company figured there was a 5% chance the collection would be destroyed and worth $0. Nicholai has utility u(x) = x0.5. If Nicholai purchases full insurance at a fair price, his expected utility would be ___. while if he declines the insurance he would face an expected utility of а. 1,487.5; 1,531.8 b. 1,487.5; 1,444.9 с. 1,571.6;B 1,531.8 d. 1,571.6; 1,444.9