Suppose treatment for traumatic brain injuries allows treated children to live an additional 25 years with an average utility or QALY weight of .65. Draw a QALY graph and indicate the QALY's gained from treatment both without discounting and discounting using a 3% rate
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- Suppose Diane's utility function is U=- Vincome . Diane earns an income of $102,400, but there is a 15% chance that she will get sick and have a $62,400 medical bill. The health insurance company, DenialCare, will offer her a health insurance policy to pay for her medical bills. What would an actuarially fair premium be and what is the maximum she would be willing to pay for the insurance?Show that a decision maker who has a linear utilityfunction will rank two lotteries according to their expectedvalue.If a person lives for 3 years with a disease and the current standard of care for that disease means he/she lives with a utility level of 0.7.-What is the QALY? Answer in not less than 300 words
- 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 utilsShow that a decision maker who has a linear utility function will rank two lotteries according to their expected value.An individual has the following utility function: U = Z!/2 H/2, where Z is a composite good and H is the level of health. The individual has income, m = $100. The price of the composite good, Z, is Pz = 1. The price of health, H, is PH = 4. What is the optimal consumption bundle of H and Z that maximizes utility? Show your steps and show the decision graphically (which includes finding the endpoints of the budget constraint).
- Billy John Pigskin of Mule Shoe, Texas, has a von Neumann-Morgenstern utility function of the form u(c) = √c. Billy John also weighs about 300 pounds and can outrun jackrabbits and pizza delivery trucks. Billy John is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If an injury ends his football career, he will receive a $10,000 contract as a refuse removal facilitator in his home town. There is a 10% chance that Billy John will be injured badly enough to end his career. If Billy John pays $p for an insurance policy that would give him $1,000,000 if he suffered a career-ending injury while in college, then he would be sure to have an income of $1,000,000 − p no matter what happened to him. Write an equation that can be solved to find the largest price that Billy John would be willing to pay for such an insurance policy. Here is my question: Why is Billy's income 1,000,000 - p even…Rosario has to finish her dissertation within 10 days, that is, at time t = 1, t = 2, ..., or t = 10. It takes one day to finish the dissertation, and on the day Rosario does so, she incurs an instantaneous disutility cost equivalent to $10. Rosario is a hyperbolic discounter with β = 0.85 and δ = 1. Her (instantaneous) utility function is u(x) = x.(a) Suppose the university has a system in which it charges Rosario $1 in fees for every day she does not finish her dissertation (paid each day that it is incurred). E.g., finishing on day 2 incurs a cost of $1 paid on day 1. When does Rosario finish if she is naive? How much does she pay in penalties? (Hint, past penalties are sunk, e.g., from the perspective of t = 2 self, any penalties paid in t = 1 are sunk, and do not factor into decisions or utilities going forward.)(b) Still in the $1/day system, when does Rosario finish if she is sophisticated?(c) Now suppose that the university has a deadline system: Rosario incurs a penalty of…Seung’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?
- . 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?When Shalini is sick, she values wealth according to the utility function US(w) = ln (w). When she is healthy, she values wealth according to UH(w) = 1.1 ln (w). Shalini allocates wealth of $1,000 for each week and has a 5% chance of getting sick. a) Would Shalini be willing to spend $30 of her of her $1,000 wealth in order to guarantee avoiding getting sick, if it were possible for her to do so? (b) Would Shalini be willing to spend $30 of her of her $1,000 wealth in order to buy an (actuarially fair) insurance policy under which she receives $600 in indemnity if she gets sick? (c) How do you explain your answers to parts a and b above? How do the answers compare and how you can intuitively explain them in this context?Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.