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- In an insurance system, would you expect each person to receive in benefits pretty much what they pay in premiums or is it just that the average benefits paid will equal the average premiums paid?What is an actuarially fair insurance policy?Economics 2. Suppose that a farmer usually makes profit of $120,000 per year. Let's say that there is a 2% chance that a tornado will hit the farm. This would strongly hurt farmer's profit, leading to losses of $96,000 with 2% probability. a. What is the actuarially fair insurance? b. Assume that the farmer utility is given by u = 7 0.5 where 7t represents profit. What is the farmer's expected utility with no insurance? c. How much would the farmer be willing to pay to have insurance? d. Assume that the farmer expects that the tornado's effect to your farm is lower, only leading to losses of $70,000. i. What is the actuarially fair insurance? ii. What is the farmer's expected utility with no insurance? iii. How much would the farmer be willing to pay to have insurance? iv. What is the risk premium?
- 2. Suppose that a farmer usually makes profit of $120,000 per year. Let's say that there is a 2% chance that a tornado will hit the farm. This would strongly hurt farmer's profit, leading to losses of $96,000 with 2% probability. a. What is the actuarially fair insurance? b. Assume that the farmer utility is given by u = T 0.5 where t represents profit. What is the farmer's expected utility with no insurance? c. How much would the farmer be willing to pay to have insurance? d. Assume that the farmer expects that the tornado's effect to your farm is lower, only leading to losses of $70,000. i. What is the actuarially fair insurance? ii. What is the farmer's expected utility with no insurance? iii. How much would the farmer be willing to pay to have insurance? iv. What is the risk premium?Explain what is the risk premium?ease use utility of wealth function in the booK, 8-1 (see below). Certainty Utility B D 200 198 194 D' Total utility 170 of wealth C' Expected Utility A 140 10,000 15,000 19,000 20,000 Wealth FIGURE 8-1 Total Utility of Wealth and the Impact of Insurance Please explain the difference between the certainty utility line and the expected utility line b. Calculate your E(U), given an 80% change of being healthy and 20% of being sick, knowing that your income falls to $10,000 and your utility is 140 if you get sick. Calculate your E(W), given an 80% change of being healthy and 20% of being sick. d. Given that your Certainty Utility Function is U = 200Y-0.00154 and Y is your income, what is your Certainty Utility with insurance (if you are risk averse) What insurance premium will you pay to guarantee a utility of 197? Please provide a calculation.
- Nathan's income in a typical year is 75,000. There is a 10 percent chance that Nathan will be seriously ill next year, incurring 15,000 in medical expenses. Samantha also earns 75,000 in a typical year. Her chance of becoming seriously ill next year and incurring ur 15,000 in medical expenses is 20 percent. a. Calculate the actuarially fair premium for full insurance for (i) Nathan and (ii) Samantha. b. Suppose that a private insurance firm cannot distinguish between Nathan and Samantha in terms of their risk and assumes the risk of being seriously ill in the general population is 10%. In this context, discuss the adverse selection problem the firm might face. c. Can a compulsory, government - run health insurance program avoid the problem of adverse selection? Explain why or why not.Develop a graphical representation of the choice to buy insurance. Define and highlight on the graph diminishing utility of wealth, expected utility curve, pure premium, amount you'd pay above it. What are you comparing in order to decide whether to buy insurance?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.
- 1: A risk-averse individual is offered a choice between a gamble that pays £2000 with a probability of 25% and £200 with a probability of 75%, or a payment of £650. Using a diagram explain which he would choose? What if the payment was £640?1. 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 £10,00 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?2. Two individuals have the same income ($100,000), but different potential healthcare expenses. Person A's probability of having $80,000 in healthcare expenses is 0.5 percent. Person B's probability of having $800 in healthcare expenses is 50 percent. Assume your utility is U = VI where I is your income. Calculate each person's expected income and expected utility. Calculate each person's certainty equivalent. What does value of the certainty equivalent tell you about how much each person would be willing to insure against their loss?
