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) = Vx. 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?
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- 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?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?
- 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 up (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?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?
- Question 3: Jane has utility function over her net income U(Y)=Y2 a. What are Jane's preferences towards risk? Is she risk averse, risk neutral or risk loving? [Briefly explain your answer] b. Jane drives to work every day and she spends a lot of money on parking meters. She is considering of cheating and not paying for the parking. However, she knows that there is a 1/4 probability of being caught on a given day if she cheats, and that the cost of the ticket is $36. Her daily income is $100. What is the maximum amount of she will be willing to pay for one day parking? c. Paul also faces the same dilemma every single day. However, he has a utility function U(Y)-Y. His daily income is also $100. What is Paul's preference towards risk? Is he risk averse, risk neutral or risk loving? d. If the price of one day parking is $9.25, will Paul cheat or pay the parking meter? Will Jane cheat or pay the parking meter?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; 1,444.95. Larry, who has wealth (w) of 100, faces a 25% probability that a catastrophe will eliminate all of his wealth. Larry's utility function is u(w) = In (w + 1). We will cover insurance on 12/2 in case you want to hold off on parts (b) and (d) until then. Characterize Larry's preference over risk. Is he risk-averse, risk-loving, or risk-neutral? а. Explain. b. What is the highest premium that Larry would accept for full insurance? C. Alternatively, suppose that Larry's utility is u (w) = e". Characterize his preference for risk and explain your answer. d. Under this alternative utility function, what is the highest premium that Larry would accept for full insurance? Explain.
- 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?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:An 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 Utility 40,000 200 |37,000 195 35,000 190 30,000 170 |20,000 140 10.000 100 A. Is this person risk neutral, risk loving or risk averse? Why? B. Considering the probability of illness, what is the expected income without insurance? Show your work.