Roulan has wealth of $40,000 as long as his business does not burn down. However, there is a 50% probability that his business will burn down and cause a $30,000 loss, leaving her with $10,000 of wealth. Roulan's utility function is given by 0.5 U = W, where W is wealth. What is the maximum price that Roulan would pay for full insurance that covers the potential $30,000 loss? (Hint: The maximum price equals the actuarially fair premium plus the risk premium.) $17,500 $22,500 $12,500 $15,500

Roulan has wealth of $40,000 as long as his business does not burn down. However, there is a 50% probability that his business will burn down and cause a $30,000 loss, leaving her with $10,000 of wealth. Roulan's utility function is given by 0.5 U = W, where W is wealth. What is the maximum price that Roulan would pay for full insurance that covers the potential $30,000 loss? (Hint: The maximum price equals the actuarially fair premium plus the risk premium.) $17,500 $22,500 $12,500 $15,500

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

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The Anderson family lives in the Arizona wilderness. Their property is at risk for being destroyed by a forest fire. It is estimated that each year the Anderson face a 5 percent probability of a $500,000 loss. The Anderson family has a utility function of U = W 0.7, where W is wealth and measured in dollars. Suppose their current wealth is $1 million. What is the family's expected loss from fire? What is the Anderson family's expected utility? What is the maximum value the Andersons will pay for insurance to completely protect their home? What is the risk premium?
Yuri owns just one ship, he calls it Previt. The ship is worth $25 million dollars. If the ship sinks, Yuri loses $25 million. The probability that it will sink is .02. Yuri's total wealth, including the value of the ship is $50 million. He is an expected utility maximizer with utility U(W) equal to W?. What is the maximum amount that Yuri would be willing to pay in order to be fully insured against the risk of losing his ship? a. $4 million b. $ 1.96 million c. $ 0.39 million d. $ 3.9 million e. $ 5.96 million f. None of the above, the right answer is:
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?
The following table shows the relationship between your wealth (in thousands of dollars) and your utility: Wealth Utility. 15.0 10 23.0 15 30.0 20 36.0 25 41.0 30 46.0 35 50.0 You can invest in asset A, which offers a riskless payoff of $15,000 or in asset B, which pays $5,000 with 40% probability and $25,000 with 60% probaility. Which investment do you choose? A. B, because its expected utility of 31.6 is greater than the utility of A. O B. A, because it is riskless. OC. A, because its utility is greater than the expected utility of B, which is 28.4. O D. B, because its expected utility of 30.6 is greater than the utility of A.
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
Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810,000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function uf (x) = VT. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able to choose insurance with any coverage level z E [0, 1] (i.e. 0 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?
Exercise 7: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810, 000 and face a 40% chance of losing L = 450,000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function uê(x) = √x. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss?
Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is wealth. If Amy goes fast she gets an increase in utility equal to F. But when Amy drives fast, she is more likely to crash: when she drives fast the probability of a crash is 10%, but when she obeys the speed limit, the probability of a crash is only 5%. Amy's car is worth $2000 unless she crashes, in which case it is worth $0. If Amy doesn't have insurance, driving fast isn't worth the risk, so she will alway obey the speed limit. If Amy is offered an insurance contract with full insurance for a premium P with the deductible D, which of the inequalites below is her incentive compatibility constraint that makes sure that she will still obey the speed limit even when she is fully insured? 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.05U(0 – P – D + 2000) + 0.95U(2000 – P) 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.1(U(2000 – P – D) + F) + 0.90(U(2000 – P) + F) 0.05U(2000 – P – D) + 0.95U(2000)…
Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810, 000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = r and Eva has von Neumann-Morgenstern utility function uf(x) = VT. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able to choose insurance with any coverage level z E [0, 1] (i.e. 0 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?
Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810,000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function ug (x) = VT. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able choose insurance with any coverage level z [0, 1] (i.e. 0 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?
Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810, 000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function ug(x) = VT. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able to choose insurance with any coverage level z E [0, 1] (i.e. 0 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?
. 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?