Economics 2159A/B Lecture Notes - Lecture 6: Insurance, Risk Premium, Weighted Arithmetic Mean

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ochrepug763

14 Dec 2015

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E(u), expected utility is the weighted average between two known point of utility. If you are not sure how much you can get, there must be somewhere the point fall on the curve, that is some point between a and b. we are not using the curve. Don t use the curve, use the straight line if you are not 100% sure how much you can earn. The individuals are better off under the insurance policy. For this case there is not risk that i have no income with the insurance. This is a gamble, and individuals hate gamble. Most insurance company charges more that the fair premium, which means plus the loading fee, the overhead expenses. The most that individuals pay is the fair premium + risk premium. Max wtp by an individual= fair premium + risk premium. If loading fee= 0, individual better off with insurance. If loading fee= risk premium, individual indifferent between insurance or not.

Related Questions

Darrell has a utility function for daily income given by u(I) = 10* I . Thus, an income of $36 a day would give Darrell a utility of u($36) = 10* 36 = 10*6 = 60.

Darrell has a job that pays him $100 a day. Darrell goes snowboarding on weekends, so with a probability of 10% (p = 0.10), Darrell has an accident that results in him breaking his leg and unable to work.

What is the actuarially fair price of an insurance policy that will pay Darrell $100 a day if he injures himself snowboarding and is unable to work (just think of this policy paying Darrell for a single day of missed work to simplify calculations)? What is Darrell's expected utility for a given day in the case that he doesn't have insurance (think of what he expects his utility to be on Monday when he leaves work on Friday)?

Would Darrell be willing to buy the insurance policy in part (a) at the actuarially fair price you calculated? Would Darrell be willing to pay more than this actuarially fair price? If so, what is the most that Darrell would pay for such a policy? What does this tell you about Darrell's risk premium given his preferences? Is he risk-averse?

Now consider Tommy who also likes to snowboard but is much more reckless and makes more money than Darrell. Tommy has the same utility function as Darrell but has a daily income of $225. Tommy will break his leg with a probability of 60% (so p = 0.6), and be fine for work on Monday only 40% of the time. What is an actuarially fair price of insurance for Tommy that will pay him $225 per day in the event of an accident? What is his expected income without insurance? Calculate the risk premium that Tommy would be willing to pay for insurance given this scenario. How does his risk premium compare to Darrell's?

pearmammoth754

(25 pts) Suppose that the market is comprised of 4 groups of people of differing risk categories. Individuals know their own risk, but insurers cannot tell which group a person belongs to. Each individuals has a current income equal to $40,000 and faces a risk of requiring medical treatment costing $7,600. Each individual has an utility function given by U = X1/2 Each groupâs probability of requiring medical treatment is as follows:

Group 1 2 3 4 # of People 1,000 1,000 1,000 1,000 Probability of Medical Treatment 0.20 0.40 0.60 0.80 a. (

5 pts) What is the most money each group will be willing to pay for an insurance policy that fully insures them in the event they require medical treatment (premium)?

b. (4 pts) What is the expected loss for each group? How does it compare to their maximum willingness to pay for insurance? Why are these different? c. (4 pts) What is the average riskiness of a person seeking insurance? If an insurance company were to charge all its clients the same premium to fully insure them, what would the fair premium be? Which group(s) would buy insurance at this price? Why?

c. (4 pts) What is the average riskiness of a person seeking insurance? If an insurance company were to charge all its clients the same premium to fully insure them, what would the fair premium be? Which group(s) would buy insurance at this price? Why?

d. (4 pts) What is the average riskiness of the persons now seeking insurance? (the group(s) identified in the last part of question (c) above). What would be the new fair premium that the insurance company would charge all its clients? Which group(s) would buy insurance at this price? Why? e. (4 pts) What is the average riskiness of the persons now seeking insurance? (the group(s) identified in the last part of question

(d) above). What would be the new fair premium that the insurance company would charge all its clients? Which group(s) would buy insurance at this price? Why? f. (4 pts) Is this an efficient outcome? Explain. Describe the different options the firm has to address this problem.

jadedonkey623

A health insurance company knows that there are two types of customers (smokers and non-smokers), each facing different health risks. The probabilities of getting sick and the healthcare costs in the case of illness for the two customer types is given in the table below.

Group	Healthcare costs	Probability of getting sick
Smokers	$1200	50%
Non-smokers	$1200	20%

Assume that each customer has a monthly income of $1600 and has a utility function given by U(x)=sqrt(x), where x is the remaining income after medical/health insurance expenses have been paid.

a. Explain the problem of âadverse selectionâ and the problem of âmoral hazard.â Give one example of a market in which adverse selection occurs and one example of a market in which moral hazard can be observed. What is the difference between the two information problems? Explain the consequences of adverse selection and moral hazard for the principal â agent relationship.

b. Discuss in detail the two ways (screening and signaling) in which the principal or the agent can try to resolve the problem of adverse selection. Give an example of screening and signaling and explain how the parties involved benefit from these strategies.

c. For the numerical example above construct the lotteries associated with the income that remains after healthcare expenses have been paid for smokers and for non-smokers (assuming agents do not have health insurance). Calculate the expected utility associated with the lotteries for smokers and non-smokers. Calculate the certainty equivalent of the two lotteries. What is maximum amount that smokers and non-smokers are willing to pay for full insurance? Calculate the actuarially fair health insurance premium for the two groups of customers (i.e. the expected healthcare costs).

dAssume the company cannot distinguish between smokers and non-smokers and offers a full insurance contract to all customers. How much should the company charge for the full insurance contract? Which customer group will purchase full insurance?

silverkangaroo356

Economics 2159A/B Lecture Notes - Lecture 6: Insurance, Risk Premium, Weighted Arithmetic Mean

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