An individual has 40,000 in income per year. The person will get sick with probability 0.1. If he does get sick, the medical bills will total 30,000. The following tables shows the utility derived from certain amounts of income: Income Utility 40,000 200 37,000 195 35,000 190 30,000 170 20,000 140 10,000 100 At the actuarially fair rate, will the person choose to buy insurance or face the risk of going uninsured? Explain why.
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- What is an actuarially fair insurance policy?An individual has 40,000 in income per year. The person will get sick with probability 0.1. If he does get sick, the medical bills will total 30,000. The following tables shows the utility derived from certain amounts of income: Income Utility40,000 20037,000 19535,000 19030,000 17020,000 14010,000 100Considering the probability of illness, what is the expected utility of income without insurance? Show your work.ASAP Consider an individual for whom utility is U = ln(I) There are two states of the world (G,B): Outcome G = 2000 with probability .4 Outcome B = 1000 with probability .6 W1 = 2000 L = 1000 π = .6 Option = invest $50 to lower π to .2 An insurance company is willing to offer a contract in which the individual pays a premium and gets full compensation for the loss (1000) in the bad state. a) With no insurance but the option of investing the $50, what is the utility of the individual? b) What is the first-best outcome for utility of the individual, insurance premium, and profits of the insurance company?
- Consider an individual for whom utility is U = ln(I) There are two states of the world (G,B): Outcome G = 2000 with probability .4 Outcome B = 1000 with probability .6 W1 = 2000 L = 1000 π = .6 Option = invest $50 to lower π to .2 An insurance company is willing to offer a contract in which the individual pays a premium and gets full compensation for the loss (1000) in the bad state. a) With no insurance but the option of investing the $50, what is the utility of the individual? b) What is the first-best outcome for utility of the individual, insurance premium, and profits of the insurance company?John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John’s utility function is U(c) = 5√c , where c is the value of consumption. Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that requires the farmer to plant corn. Here’s how the insurance contract works. At the beginning of the year, the corn farmer pays an insurance premium of $202.5. If the weather is GOOD, Mae makes no payment to the farmer. If the weather is BAD, Mae makes an indemnity payment of $675 to the farmer. a. If a farmer buys this insurance contract,what is Mae’s expected…An individual has the utility function U(I) = I^(1/2), where I is their net income. (Note that I to the exponent/power of 1/2 is the same as the square root of I.) The individual starts with $1600 in income. The individual has a 20% probability of being very sick, 30% probability of being slightly sick, and 50% probability of being healthy. If the individual is sick, they lose net income because they need to pay healthcare costs. The healthcare costs are $1600 if they are very sick, $700 if they are slightly sick, and $0 if they are healthy. Please use this information for the following parts of this question unless otherwise specified. What is the individual's expected utility? Suppose a health insurance company offers the individual a full insurance contract. What is the actuarially fair, full insurance premium for this individual? What is the individual's expected utility if they purchase a full insurance contract at the actuarially fair, full insurance premium?
- Do you think Canada's universal health care program can alleviate problems caused by moral hazard and adverse selection in the private insurance markets? Why or why not? John's utility curve over total wealth is given by U(W) =VW (i.e. square root of W). Suppose that he has a 50% chance of being healthy. If he is healthy, he gets all his wealth-$10,000. If he becomes sick, he only has $3,600 remaining after medical expenditures. Calculate John's wealth and utility when he does and does not get sick, his expected utility, expected wealth, and his expected loss. Now he has the option of buying health insurance Calculate the maximum amount John would be willing to pay to fully insure against the cost of the sickness. How much is the actuarially fair and risk premium? Suppose that society consists of large, equal numbers of identical male and identical female consumers. Male consumers are similar to John; female consumers differ only in that they face a 25% probability of being sick, but…Consider Bob's decision problem: Sunny Cloudy Rainy Beach 2 3 2 Park 3 3 2 Mall -1 1 x Suppose the probability of Sunny is 0.25, the probability of Cloudy is 0.25, and the probability of Rainy is 0.5. What is the smallest value of x for which Mall is an expected utility maximiser? Round your answer to one decimal place (e.g. 0.5).Question 1: Using Figure 11.1, illustrate the probability that someone will obtain insurance for treatment for: (a) a hangnail; (b) a broken arm; (c) a bad hair day; (d) viral meningitis
- Y5 Alfred is a risk-averse person with $100 in monetary wealth and owns a house worth $300, for total wealth of $400. The probability that his house is destroyed by fire (equivalent to a loss of $300) is pne = 0.5. If he exerts an effort level e = 0.3 to keep his house safe, the probability falls to pe = 0.2. His utility function is: U = w0.5 – e where e is effort level exerted (zero in the case of no effort and 0.3 in the case of effort).a. In the absence of insurance, does Alfred exert effort to lower the probability of fire?HINT: Calculate and compare the expected utility i) with effort, and ii) without effort. If effort is exerted, then the effort cost is paid regardless of whether or not a fire occurs.b. Alfred is considering buying fire insurance. The insurance agent explains that a home owner’s insurance policy would require paying a premium α and would repay the value of the house in the event of fire, minus a deductible “D”. [A deductible is an amount of money that the…Consider an individual with an expected utility function of the form u(w) = √wwhere wrep-resents this individual’s wealth. This individual currently has wealth of $100. This individualfaces a risk of losing $64 with a probability of (1/2). The maximum price that this individualwould pay for insurance that covers the entire $64 loss is?Imagine a market for used computers. There are two types of computers: good and bad. Also imagine that there are 50% of each on the market. Buyers can imagine paying 5,000 for a good computer and 1,000 for a bad computer Sellers want at least 4000 for a good computer and 1500 for a bad computer -What would happen in the market if the buyer thinks that there is a 50% probability that the computers are of poor quality? What type (s) would be sold and what would the price be?
