Q4. An individual with the utility function u(x) = 2 owns her wealth of $20,000. An expected profit maximizing company (or risk neutral company) 1 can make expected profit greater than $ 19,900. True or False? Explain it. If it is true, show the offer that gives the company such profit. If it is false, explain why the company cannot do it. The marks depend on your explanation.

Q4. An individual with the utility function u(x) = 2 owns her wealth of $20,000. An expected profit maximizing company (or risk neutral company) 1 can make expected profit greater than $ 19,900. True or False? Explain it. If it is true, show the offer that gives the company such profit. If it is false, explain why the company cannot do it. The marks depend on your explanation.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Monty Burns, the owner of the Springfield Nuclear Power Plant, owns many real estate properties. His last acquisition is a house worth €1,000, 000. Monty Burns considers purchasing an insurance for this new property. With probability 0.1, he will face damage reducing his property' value to €640,000 while with probability 0.9 his property will not be damaged and thus will remain at its current value. Burns' vNM utility for wealth is given by u°(w) = Vw. Miss b runs an insurance company in Springfield and is willing to insure Monty Burns. The insurance contract says the following: if Burns' new property is damaged, she will pay an amount q (the coverage) to Monty Burns in exchange for a payment r (the premium) that is due independently from the occurence of the damage. Miss b's vNM utility over her income y is u°(y) = y.
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Question a .Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this line
2. In the game between the manager and the stockholders of Ross (1977), the future value of the firm is random and uniformly distributed on the interval [0, t], where t is the upper bound of V1. The manager knows the value of t, but the stockholders do not, and this is the asymmetry of information. In observing the debt level F chosen by the manager, the stockholders think that the value of t is given by a[F]. In the lecture on the model of Ross, it was shown that a[F] has the following form: a[F] = 4 LF+c?. Yo Compute the debt level F that maximizes the manager's expected payoff.
3. The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions. (a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset? (b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expected return and standard deviation of the investor’s optimal complete portfolio?
A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. What is the consumer's expected wealth one year from now? b. An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? c. Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain situation. What is the maximum premium that the insurance company will be able to charge this consumer for its full insurance policy?
2. Consider an individual with a current wealth of $100,000 who faces the prospect of a 25% chance of losing $20,000 through theft of her car during the next year. If the person’s utility function is U(X) = ln(X), where X is wealth: a. calculate expected utility without insurance, b. calculate the actuarially fair premium for full insurance, c. calculate expected utility with full insurance at the actuarially fair premium d. calculate the maximum amount the individual would pay for full insurance.
Q4. An individual with the utility function u(x) = x² owns her wealth of $20,000. An expected profit maximizing company (or risk neutral company) facing the individual can make expected profit greater than $ 19,900. True or False? Explain it. If it is true, show
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Sarah has a utility function expressed as the square root of wealth (w). Currently, Sarah has an initial wealth of $2000 and faces a potential loss of $1500 with a loss probability of .15. What is Sarah's expected utility if an insurer charges her a pure (actuarially fair) premium? 63.75 41.37 42.13 225
Explain intuitively (or give a specific example) and show graphically what a risk premium is.
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