Consider a health insurance market. The market has many insurers so that each insurance company offers insurance at the fair insurance premium. Each consumer has utility function, U(X)=√√X and has an initial wealth of $100. Consumers have access to a (magical) gym that reduces their probability of needing to go to the doctor from 90% to 10%. A gym membership costs $10. A trip to the doctor costs $75. Suppose insurance companies charge the fair insurance premium which assumes all consumers go to the gym. This fair insurance premium is $ ✓and the insurance company makes a profit of $ ✓ per consumer. Suppose insurance companies continue to charge the fair insurance premium that assumes all consumers go to the gym, but now charges a copay of $13 for a doctor's visit. The insurance company now makes a profit of $ ✓per consumer. By implementing a copay, the insurance company ✓ the ✓ problem.
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- Consider a health insurance market. The market has many insurers so that each insurance company offers insurance at the fair insurance premium. Each consumer has utility function, and has an initial wealth of $200. Consumers have access to a (magical) gym that reduces their probability of needing to go to the doctor from 90% to 10%. A gym membership costs $6. A trip to the doctor costs $120. Suppose insurance companies charge the fair insurance premium which assumes all consumers go to the gym. This fair insurance premium is $? and the insurance company makes a profit of $? per consumer. Suppose insurance companies continue to charge the fair insurance premium that assumes all consumers go to the gym, but now charges a copay of $15 for a doctor's visit. The insurance company now makes a profit of $ per consumer. By implementing a copay, the insurance company the problem.Joe's wealth is $100 and he maximizes his expected utility. Joe’s utility as a function of his wealth is U(W) = W1/2. Joe might oversleep his economics exam. He figures there is only a 1 in 10 5 chance that he will, but if he does, it will cost him $100 in fees to the University to take an exam later. Joe's neighbor, Mary, never oversleeps. She offers to wake Joe one hour before the test, but he must pay her for this service. What is the most that Joe would be willing to pay for this wake-up service? a. $10 b. $9 c. $19 d. $100 e. $12.7Consider a household that possesses $200,000 worth of valuables such as jewelry. This household faces a 0.02 probability of a burglary, where she would lose jewelry worth $70,000. Suppose it can buy an insurance policy for $15,000 that would fully reimburse the $70,000. The household's utility function is U(X) = 4X⁰.5 Should the household buy this insurance policy? The household should not buy this policy. What is the actuarially fair price for the insurance policy? If the insurance is fair, then the cost of the insurance policy is $ 1400. (Enter your response rounded to two decimal places.) What is the most the household is willing to pay for an insurance policy that fully covers it against loss? The most the household would pay for such a policy (p) is S (Enter your response rounded to two decimal places.)
- Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary's boat wins, Donna would give him $31. If Gary's boat does not win, Gary would give her $31. Gary's utility function is p1x^21+p2x^22, where P₁ and p2 are the probabilities of events 1 and 2 and where x₁ and x₂ are his wealth if events 1 and 2 occur respectively. Gary's total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). 1. Taking the bet would reduce his expected utility. 2. Taking the bet would leave his expected utility unchanged. 3. Taking the bet would increase his expected utility. 4. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. 5. The information given in the problem is self-contradictory.Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.
- Max is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)4. An individual's Bernoulli utility function is u(w) = Vw, and the individual has initial wealth 100. The individual might develop a health problem, which would reduce his or her wealth to 0. The individual might be "healthy" or "unhealthy." A healthy person develops the health problem with probability qL = 0.3, while an unhealthy person develops the health problem with probability qH = 0.7. The probability that the individual in question is healthy is 1/2. An individual knows whether he or she is healthy, but an insurer does not. Without insurance, a healthy person's wealth is 100 with probability 0.7 and 0 with probability 0.3. Without insurance, an unhealthy person's wealth is 100 with probability 0.3 and 0 with probability 0.7. Insurers only offer "full insurance." That is, if the adverse event occurs, they will pay back 100, restoring the individual's full wealth. Insurers set a price for this policy that is "actuarially fair." Insurance company makes no money on average.…Suppose a person chooses to play a gamble that is free to play. In this gamble, they have a 10% chance of $100.00, and a 90% chance of nothing. Their utility function is represented in the following equation: U=W 1/2 where W is equal to the amount of "winnings" (or the income). Suppose now Brown Insurance Company offers the person the option of purchasing insurance to insure they will win the $100. What is the minimum amount Brown Insurance would charge you to insure your win? 0.90 O. 99 01 O 10
- Max Pentridge is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $10,000. With probability p = 0.9 the palace will succeed and Max's wealth will grow from $10,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $5,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $10,000 with certainty? ____ (Please round your final answer to the whole dollar, if necessary)Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is wealth. If Amy goes fast she gets an increase in utility equal to F. But when Amy drives fast, she is more likely to crash: when she drives fast the probability of a crash is 10%, but when she obeys the speed limit, the probability of a crash is only 5%. Amy's car is worth $2000 unless she crashes, in which case it is worth $0. If Amy doesn't have insurance, driving fast isn't worth the risk, so she will alway obey the speed limit. If Amy is offered an insurance contract with full insurance for a premium P with the deductible D, which of the inequalites below is her incentive compatibility constraint that makes sure that she will still obey the speed limit even when she is fully insured? 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.05U(0 – P – D + 2000) + 0.95U(2000 – P) 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.1(U(2000 – P – D) + F) + 0.90(U(2000 – P) + F) 0.05U(2000 – P – D) + 0.95U(2000)…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?