Consider a consumer who is deciding to buy insurance for his beachfront house. Suppose the probability that the house will get damaged by the rising sea level is 0.4. Let us assume that the valuation of the house is 100 (in thousand dollars) and in case of a natural calamity due to rising sea level, the valuation of the house would become 40. At the price of insurance of $0.5, what would the optimal level of insurance bought by the consumer if his vNM utility function is given by u(x) = In x? [Answer up to two decimal points.] Answer:
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- . Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = square root 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?Assume that the probability of having an accident in a year is 0.08. Suppose that your yearly income is 50,000 TRY and in case of an accident your income drops to 15,000 TRY. Your utility function is U(?) = ln (?) where C is consumption. a) What is your expected utility at the end of the year without insurance?b) Calculate an actuarially fair insurance premium for the full insurance. c) What would your expected utility be if you purchase a full insurance with actuarially fair premium? Will you buy this insurance, why or why not?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 insurance
- Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = square root 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. 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.. 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.
- Assume that you will earn $90,000 next year. The probability of having an accident in a year is 0.05 and your income will be $22,500 in that case. Your utility function is U(C)= C1/2 where C is consumption. a) What is your expected utility at the end of the year without insurance?b) Calculate an actuarially fair insurance premium for the full insurance. c) What would your expected utility be if you purchase a full insurance with actuarially fair premium? Will you buy this insurance, why or why not?Questions 4 & 5 Michelle owns a house in which she keeps valuables worth 100,000 which can get stolen with probability 1%. She can purchase coverage C of the amount C ∈ [0; 100,000] at premium π = 0.05 dollars for each dollar covered. Her Bernouilli utility function is u(w) = ln(w). Assume she has no other assets. 1. Set up her maximization problem. 2. How much insurance will she choose to buy? 3. How much profits does the insurance company earn on insuring Michelle? 4. Does the fact that the insurance company earn profits mean that Michelle is worse off com-pared to the situation in which she is not insured? Explain what is happening. 5. How much insurance will she buy if insurance companies charge an actuarially fair insurance rate?Explain how risk aversion makes a market for insurance possible
- Assume that your utility has a natural log function U(W)=ln(W), which is a concave function. Your car is worth $10,000 and your total wealth is $20,000 including the car. There is a 5% chance that a major accident occurs and you have a total loss of $10,000; a 10% chance that a minor accident occurs and you have a loss of $500; 85% chance you will not have any accident. Given these assumptions, how much are you willing to pay for an insurance that provides full coverage against car accidents? Thank you. Regards, Jim CarrollAbigail is a consumer whose utility is a function of her total wealth W. u(W ) = log W. Suppose that Abigail begins with initial wealth of A = 100 but will suffer a serious illness with probability π = 0.15 which will require extensive treatment costing L = 80. To hedge against this risk, Abigail considers buying a health insurance policy. She may buy as much insurance I as she wishes at a cost of p per dollar of coverage, so her payoffs in each state are Healthy Ill Probability 0.85 0.15 No Insurance 100 20 Claim 0 I Premium −pI −pI a) Show that Abigail is risk averse. b) Suppose that the insurance premiums are actuarially fair so that p = 0. Find Abigail’s expected wealth E[W ] and expected utility E[u(W )] as functions of how much insurance she buys I. c) How much insurance should Abigail buy?Abigail is a consumer whose utility is a function of her total wealth W. u(W ) = log W. Suppose that Abigail begins with initial wealth of A = 100 but will suffer a serious illness with probability π = 0.15 which will require extensive treatment costing L = 80. To hedge against this risk, Abigail considers buying a health insurance policy. She may buy as much insurance I as she wishes at a cost of p per dollar of coverage, so her payoffs in each state are Healthy Ill Probability 0.85 0.15 No Insurance 100 20 Claim 0 I Premium −pI −pI a) Now suppose that the insurance company raises premiums to p = 0.2 so that they are no longer actuarially fair. Find Abigail’s expected wealth E[W ] and expected utility E[u(W )]. b) How much insurance should Abigail buy now?