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 Considering the probability of illness, what is the expected utility of income without insurance? Show your work.
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- 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.Joes initial income is y 10,000. Joe experiences illness with a probability of 20%. Jo's total medical costs associated with the illness are $1000. Joe's expected income without insurance isAn 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?
- Wanda works as a waitress and consequently has the opportunity to earn cash tips that are not reported by her employer to the Internal Revenue Service. Her tip income is rather variable. In a good year (G), she earns a high income, so her tax liability to the IRS is $5000. In a bad year (B), she earns a low income, and her tax liability to the IRS is $0. The IRS knows that the probability of her having a good year is 0.6, and the probability of her having a bad year is 0.4, but it doesn’t know for sure which outcome has resulted for her this tax year. In this game, first Wanda decides how much income to report to the IRS. If she reports high income (H), she pays the IRS $5000. If she reports low income (L), she pays the IRS $0. Then the IRS has to decide whether to audit Wanda. If she reports high income, they do not audit, because they automatically know they’re already receiving the tax payment Wanda owes. If she reports low income, then the IRS can either audit (A) or not audit…Bob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.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…
- 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?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).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?
- If patient insurance inquiries arrive at Blue Choice insurance with a mean rate of 3.6 calls per minute, the exponential probability of waiting more than 0.5 minutes to get the next inquiry call is _____. Question 6Select one: a. 0.2407 b. 0.1222 c. 0.5000 d. 0.1653Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. How much utility does one lose if one loses the gamble?Suppose the market for auto insurance is made of up two types of buyers: high-risk and low-risk. Buyers’ willingness to pay (WTP) for auto insurance plans, and sellers’ willingness to accept (WTA) when selling plans to each type of buyer, are outlined in a photo Assume now that there is asymmetric information and that insurance companies do not knowhow risky an individual buyer is. In the face of this uncertainty, they determine that the probability that a “walk-in” is high-risk is 0.75. What is the minimum price sellers are willing to accept when selling aninsurance plan? At this price, will low- and high-risk buyers both be willing to purchase this insurance plan? Explain. Be sure the mention adverse selection in your answer. Returning to the conditions outlined in Q1, suppose that buyers of auto insurance (high- and low-risk) were offered a $1,000 subsidy to purchase coverage. This would raise their WTP by $1,000. Would the market for both insurance plans clear after the…