Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. A) Draw a game tree to represent this model.

Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. A) Draw a game tree to represent this model.

EBK HEALTH ECONOMICS AND POLICY

7th Edition

ISBN:9781337668279

Author:Henderson

Publisher:Henderson

Chapter4: Economic Evaluation In Health Care

Section: Chapter Questions

Problem 4QAP

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Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. h) What would β have to equal, in order for Celia to choose the socially optimal level of x in a Subgame Perfect Equilibrium ?…
Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. b) Write down Celia's expected payoff when she chooses x in step 1.
Consider the following steps: 1. Celia chooses how much care, x ∈ [0, 1], to take in programming her robot. This effort costs her x^2/2. 2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 − x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. - If there is no accident (the salamander is not stepped on), then Celia’s payoff is V − x^2/2. Peter and Luke both get zero. - If there is an accident, but Celia is not identified as the culprit, then Celia gets V − x^2/2. Peter gets −H. Luke gets zero. - If there is an accident, and Celia is identified as the culprit, then Luke (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V − (x^2)/2−D. Peter gets D−H. Luke gets −(βH−D)^2. h) What would β have to equal, in order for Celia to choose the socially optimal level of x in a Subgame Perfect Equilibrium ? We are…
Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10 percent chance of getting sick, and foreach the total cost of illness equals $50,000. Suppose person A has a total net worth of $100,000, and person B has a total net worth of $1,000,000. Both people have the option to buy an actuarially fair insurance contract that would fully insure them against the cost of the illness. a. Using expected utility calculations, show that person A would certainly buy full, actuarially fair insurance. b. Suppose an insurance company wants to maximize profits and wants to charge each customer the maximum price they are willing to pay. How much should the insurance company charge each client so that both buy the contract? c. What is surprising about your result in part b? What does this tell you about how insurance companies may be pricing health insurance contracts in the real world?
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
. 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.
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. 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?
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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?
Multiple Choice Adverse selection describes a situation where an individual's demand for insurance is positively correlated with the individual's risk of loss. Adverse selection occurs when someone increases their exposure to risk when insured. This can happen, for example, when a person takes more risks because someone else bears the cost of those risks. The relationship between smoking status and mortality provides a good illustration for adverse selection, especially in the case in which a life insurance company did not vary its premiums according to smoking status of its customers. To counter the effects of adverse selection, insurers may offer premiums that are proportional to a customer's risk.