3. In the second example, we will consider the case where the insurance contract involves a deductible this is an amount which is deducted from the final pay-out of the insurance firm in the case of a loss. In other words, the consumer bears this part of the loss herself. For this problem, assume a risk-averse, expected utility maximizing consumer with initial wealth wo who faces a potential loss of size L which will occur with probability p. Her utility-of-final-wealth function is denoted by u(.). Suppose that the consumer can purchase insurance coverage of C > 0 units of wealth from a perfectly competitive insurance firm at a premium of T per unit of coverage, but that the firm charges an additive deductible: if C units of insurance is purchased, the insurance firm pays out (C – d) if the loss occurs, where d >0 is a fixed amount independent of C. (a). For this problem, state the consumer's expected utility function. (b). Set up the consumer's utility maximization problem and find the optimal choice of C*. (c). If the price per unit of insurance is actuarially fair, i.e. if 7 = p, will the consumer choose to fully insure or under-insure? Provide reasons for your answer

3. In the second example, we will consider the case where the insurance contract involves a deductible this is an amount which is deducted from the final pay-out of the insurance firm in the case of a loss. In other words, the consumer bears this part of the loss herself. For this problem, assume a risk-averse, expected utility maximizing consumer with initial wealth wo who faces a potential loss of size L which will occur with probability p. Her utility-of-final-wealth function is denoted by u(.). Suppose that the consumer can purchase insurance coverage of C > 0 units of wealth from a perfectly competitive insurance firm at a premium of T per unit of coverage, but that the firm charges an additive deductible: if C units of insurance is purchased, the insurance firm pays out (C – d) if the loss occurs, where d >0 is a fixed amount independent of C. (a). For this problem, state the consumer's expected utility function. (b). Set up the consumer's utility maximization problem and find the optimal choice of C*. (c). If the price per unit of insurance is actuarially fair, i.e. if 7 = p, will the consumer choose to fully insure or under-insure? Provide reasons for your answer

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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6. for a large company (she travels by car). She earns 900 euros a week in fixed salary, but if she reaches the set for a week sales target, she receives a bonus of 325 euros that week. The probability of getting the bonus is 0.2. A person is a traveling salesman of goods Her utility function over money is given by U=√W, where W is the wealth in SEK per week. 6a 6b What is her expected weekly bonus? Her boss offers her another job within the same company. If so, she would work in an office with a certain personnel responsibility and receive a fixed salary per week (no bonuses). What salary per week must her boss at least offer her in order for her to accept new work? Justify your answer based on expected utility theory.
7. Consider an individual whose utility function over money is u(w) = 1+2w. (a) Is the individual risk-averse, risk-neutral, or risk-loving? Does it depend on w? (b) Suppose the individual has initial wealth ¥W and faces the possible loss of Y. The probability that the loss will occur is . Suppose insurance is available at price p, where p is not necessarily the fair price. Find the optimal amount of insurance the individual should buy. You may assume that the solution is interior. (c) Is there a price at which the individual will not want to buy any insurance? If so, find it. If no, explain.
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Janet's broad attitude to risk (risk averse, risk neutral, or risk loving) is independent of her wealth. She has initial wealth w and is offered the opportunity to buy a lottery ticket. If she buys it, her final wealth will be either w + 4 or w – 2, each equally likely. She is indifferent between buying the ticket and not buying it. Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally. Sam has another idea: They buy two tickets (that have independent outcomes) and share the costs and proceeds equally. Suppose that Janet's and Sam's utility of income is given by u(x) = In x and the initla wealth of each one of them is equal to w = 4. Which of the following statements is true? O a. Both agents prefer Sam's solutions to Janet's solution. b. Both agents prefer Janet's solutions to Sam's solution. The agents are indifferent between Janet's solutions to Sam's solution.…
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Suppose that Mary has a utility function U(W) W power of 0.5. Her only asset is the shares in the start-up e-com company. Next week she will learn the stock's value. She believes that it is worth $225 with the probability 1/3, $196 with the probability 1/2 and $144 with the probability 1/6. Write down the prospect and calculate the expected value and her expected utility.
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