U = ln(C), where C is consumption. She makes $30,000 per year and enjoy jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $15,000, and lose an additional $5,000 from missing work.
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(a) What is Seung’s expected utility without insurance?
(b) Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is her expected utility if she buys it?
(c) Suppose Seung can buy insurance that will cover her medical expenses and forgone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it?
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- Your Utility function of U = 5, where I is income. You receive an income of 1600 each week from your laundry delivery service in which you face a 50% chance each week of an accident that costs you $700. Calculate your expected income and expected utility.35. Your current disposable income is $10,000. There is a 10% chance you will get in a serious car accident, incurring damage of $1,900. (There is a 90% chance that nothing will happen.) Your utility function is U = √√T, where I is income. If this policy is priced at $40, what is the change in your expected utility if you purchase the policy rather than no insurance? b) 0.8 c) 0.2 d) 0. 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.
- Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.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. 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?. 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?
- AsapA person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. Calculate the actuarially fair insurance premium. What would your expected utility be if you were to purchase the actuarially fair insurance premium? b. What is the most you would be willing to pay for insurance, given your utility function?You are deciding whether or not to purchase insurance. Your income is $100,000 and the chance of you getting sick is 30%. The insurance company is offering you a coinsurance rate of 0. 15 and the utility that you get from your disposable income is U = VY. If you get sick, your medical bills add up to $80,000. Assume that the insurance company charges the actuarially fair premium, and assume that you would purchase the same amount of medical care whether you are insured or not (i. e. M ^ (i) = M ^ u = M ^ *). Economic theory predicts that you will purchase insurance if the expected gain in utility from receiving the insurance payout when you are sick is greater than the expected loss in utility from paying the premium and remaining healthy. Using an expected utility diagram, show your decision process regarding whether to buy insurance or not. then show on the diagram the following: Disposable income if you remain healthy and do not purchase insurance Disposable income if you are…
- Answer all questions. Imagine you are a person with a chronic disease. If the disease flares up, you will have to take substantial leave from work. The probability of the flare-up is 0.2 (or 20%). If you do not need to take leave from work, your income is $6400. If you take leave from work, your income is $1600. What is the expected value of your income? Expected utility E [= (U(1)] = pU (IS) + (1-p) U (IH) 1600 x 0.2 + 0.8 x 6400 = 5540 Assume that your utility function . What is the expected utility of your income? 0.8 √ 6400 + 0.2 √1600 = 72 utils Suppose a company is offering insurance where your premium is $500 and your payout is $2000. What is your expected utility from taking on this insurance? (Hint: you need to calculate your adjusted earnings in both states)2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.3. Let us consider a utility function: U(x) = (V2x -1. (200sxs800) We have LiL2 where L1=(1, Y) and L2=(0.3, 450, 0.7,648). a. Determine the value of Y. b. Determine RP (Risk Premium) of L2.