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- 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 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?5. You are a risk-averse decision maker with a utility function U(1) = VI, where I denotes your income. Your income is $100,000 (thus, I=100). However, there is a 0.2 chance that you will have an accident that results in a loss of $10,000. Now, suppose you have the opportunity to purchase an insurance policy that fully insures you against this loss (i.e., that pays you $10,000 in the event that you incur the loss). What is the highest premium that you would be willing to pay for this insurance policy?
- 12. Complete the following examples The Hotel California faces a risk that an earthquake will cause a $200 million loss; probability is 0.02. The owner of the hotel, Eddie Eagle, has a utility function of U= W05, where Wis the owner's wealth (as measured by the value of the hotel in millions of dollars). Suppose the initial value of the hotel is $225 million (W = 225). What is the expected loss for Eddie Eagle? What is Eddie Eagle's expected utility? Risk premium? o 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…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 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?
- # 4 Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?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?2. Cloneville is a town consisting on 100,000 identical citizens. Each citizen has a current total wealth of $160,000 and has a utility function given by u (w) = wż. In any given year, 10% of the citizens will lose 75% of their wealth to a fire. Since the citizens are identical, they are all equally likely to experience a fire. (a) Calculate the actuarially fair premium for complete fire insurance in Cloneville. How many citizens of Cloneville would purchase insurance if it cost this much? (b) Do you think insurance companies in Cloneville are likely to offer actuarially fair insur- ance? Why or why not? (c) Nearby Simville also has 100,000 citizens with the same initial wealth and risk of fire. While no citizens in Simville are risk-loving, some are more risk-averse than others. In fact, there are even a few citizens in Simville who are risk-neutral. i. Suppose insurance is supplied by a competitive industry made up of identical in- surance companies. Costs of providing insurance…
- 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?Zac has a current wealth of £400. He gets an email offering him the chance to enter a prize draw that gives £500 prize with a 25% chance and £0 the rest of the time. Zac is an expected utility maximiser with a von Neumann-Morgenstern utility in wealth w of u (w) = Vw. What is the minimum price at which Zac will sell his rights to enter the draw? £106.25 £506.25 O E31.25 £22.5 £56.25