Suppose that Lizzo's utility function U is given by U = w.53, where w is wealth. Lizzo has wealth of £21,500 but faces a probability of getting ill and being left with only £11,180. She has an 0.8 probability of being well and a 0.2 probability of being ill. a) To within two decimal places (e.g. 2.79), the expected value of Lizzo's wealth is £ 7 b) To within two decimal places (e.g. 1.21), Lizzo's level of utility at the expected value of wealth is c) To within two decimal places (e.g. 0.66), Lizzo's expected utility is
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- # 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?Suppose that Lizzo's utility function U is given by U = w.53, where w is wealth. Lizzo has wealth of £21,500 but faces a probability of getting ill and being left with only £11,180. She has an 0.8 probability of being well and a 0.2 probability of being ill.. 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?
- 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. 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.Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)
- a) Explain what is meant by risk aversion, and illustrate with the help of a figure out what we mean by the term "risk premium". Suppose Donald runs hotels and casinos, which makes one very insecure income. With probability 1 the income becomes 100 and with probability 1 the 64th Donald's expected income is thus equal to 82. Further assume that the utility to Donald is a a function of income, and that it is given by U (x) = 2x 12 x is the income level. b) Calculate Donald's expected utility.QUESTION 4 Mrs. Obaatanpa has a wealth of Ghe 3,500 for one year. There is a 35% probability that she will get sick and she estimates her loss from the illness to be Gh 1,600. Her utility function is given as U(Y) = VY, where Y is the amount of wealth she has. a) Comment on her utility function. Is she risk-neutral? b) Estimate the risk that she faces and explain. c) What is her expected utility? d) Suppose that she can buy an insurance policy that will cover the entire loss, what is the maximum premium she would be willing to pay?Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?
- Consider Ms Ayse who has an apartment in Istanbul. Ms Ayse thinks the probability of an earthquake in Istanbul next year is 0.3. In that case she would lose her apartment for sure which has value of 1000000TL right now, Suppose her utility function is u(x) = Vx. What is certainty equivalent of having an earthquake in Istanbul when Ms Ayse thinks her apartment (of course that would be terrible for anyone)? How much is she willing to pay for insuring her apartment?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?Suppose that Mira has a utility function given by U=2I+10√I. She is considering two job opportunities. The first job pays a salary of $40,000 for sure. The second job pays a base salary of $20,000 but offers the possibility of a $40,000 bonus on top of your base salary. She believes that there is a probability of p=0.50 that she will earn the bonus. What is the expected salary of the second job? Which offer gives Mira a higher expected utility? Based on this information, is Mira risk adverse, risk neutral, or risk-loving?