The Utility fct is U = W2/3 + 1000 Flood occurs with Probabilities=1/20. The Value of house $540,000 if no flood. After a flood, the value is $40,000. Cost of insurance is 0.20 cents per dollar. a. Calculate EU b. Calculate EV c. Calculate CE d. Calculate RP e. Calculate the variance and standard deviation f. How much insurance should you buy? Assume your are paying premium in all event. g. What is the expected profit of the insurance company? h. Calculate the coefficient of absolute risk aversion i. Calculate the coefficient of relative risk aversion
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- Uncertainty The Utility function is U = W1/3Flood occurs with Probabilities=1/25. The Value of a house is $450,000 if no flood. Aftera flood, the value is $50,000. Cost of insurance is 10 cents per dollar.a. Calculate EU b. Calculate EV c. Calculate CE d. Calculate RP e. Calculate the variance and standard deviation f. How much insurance should you buy? Assume your are paying premium in all events.g. What is the expected profit of the insurance company? h. Calculate the coefficient of absolute and relative risk aversionThe Utility fct is U = W2/3 + 1000Flood occurs with Probabilities=1/20. The Value of house ✩540,000 if no flood. After aflood, the value is ✩40,000. Cost of insurance is 20 cents per dollar.a. Calculate EUb. Calculate EVc. Calculate CEd. Calculate RPe. Calculate the variance and standard deviationf. How much insurance should you buy? Assume your are paying premium in all event.g. What is the expected profit of the insurance company?h. Calculate the coefficient of absolute risk aversioni. Calculate the coefficient of relative risk aversionAn individual has 40,000 in income per year. The person will get sick with probability 0.1. If he does get sick, the medical bills will total 30,000. The following tables shows the utility derived from certain amounts of income: Income Utility40,000 20037,000 19535,000 19030,000 17020,000 14010,000 100Considering the probability of illness, what is the expected utility of income without insurance? Show your work.
- Joes initial income is y 10,000. Joe experiences illness with a probability of 20%. Jo's total medical costs associated with the illness are $1000. Joe's expected income without insurance isQ1) An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y)u(y)=ln(y) and they have no other assets. Q2) Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3π=£2/3 for every one pound of coverage. Q3) Consider the setup from Questions 1 and 2. How much profits, in expectation, does the insurance company earn on insuring the individual?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 insurance
- could you answer part b to this question or if you have time part a and part b but part is more important. thank you 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. 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?Consider an individual with an expected utility function of the form u(w) = √wwhere wrep-resents this individual’s wealth. This individual currently has wealth of $100. This individualfaces a risk of losing $64 with a probability of (1/2). The maximum price that this individualwould pay for insurance that covers the entire $64 loss is?Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]
- Uncertainty and willingness to pay for insurance. Utility = (Wealth)1/3 Prob(flood) = .04 Prob(no flood) = .96 Total wealth if flood = $100,000. Total Wealth if no flood = $800,000. Find: (i) expected value, (ii) expected utility, (iii) certainty equivalent, and (iv) maximum willingness to pay for a policy that provides 100% flood insurance coverage. Draw the utility function and include all solved values on the diagram. What is the average gross profit per insurance customer, if each customer is charged his own maximum willingness to pay?Deborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. a) The expected value of Deborah’s bet (after subtracting the $1.00 she bet) is $________________ b) Given that Deborah makes this bet, is she risk adverse, risk neutral, or risk loving?Suppose that the probability of low demand is 0.75. (a) What is the maximum Expected Monetary Value (EMV)? (show calculation steps) (b) What is the Expected Value of Perfect Information (EVPI)? Hint: EVPI=EVwPI-maximum EMV.