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)
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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)
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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.AsapYou 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…
- Chris Traeger is trying to decide whether or not to purchase health insurance. Chris knows that if he is healthy, his wealth will be $2,000 this year. However, if he gets sick his wealth will only be $500. Chris knows the probability of getting sick is 40%. His utility function is written below. U = (2) What is utility if the individual purchases insurance at the actuarially fair price? 25.29 utils 26.46 utils 31.62 utils 18.97 utilsSeung’s utility function is given by 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. (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?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
- Dr. Gambles has a utility function given as U(w)=In(w). Due to the pandemic affecting his consulting business, Dr Gambles faces the prospect of having his wealth reduced to £2 or £75,000 or £100,000 with probabilities of 0.15, 0.25, and 0.60, respectively. Suppose insurance is available that will protect his wealth from this risk. How much would he be willing to pay for such insurance?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?Your utility function is U = In(2C) where C is the amount of consumption you have in any given period. Your income is $40,000 per year and there is a 2% chance that you will be involved in a catastrophic accident that will cost you $30,000 next year. Suppose that 25% of the population is comprised of individuals like you, who have a probability of a catastrophic accident, and the other 75% of the population will not face such a shock. The insurance company knows the incidence of catastrophic accidents in the aggregate, i.e., at the population level, but not to a person. Explain the conditions under which an insurance company might offer insurance (against income loss) to individuals, even if it could not determine who might be hit with a large negative income shock and those who might be hit with a small negative income shock.
- 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? ExplainYou are trying to decide between rescuing a puppy or an older dog. You decide to try to assign some numbers to your preferences so you can compare options. You estimate that your utility for a dog that will chew your furniture is 0.1 and your utility for a dog that can go on hikes with you is 0.8. You expect that a puppy will have an 70% chance of chewing your belongings and a 90% chance of going on hikes. What is your expected utility for getting the puppy?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?