2. Bob's wealth is $2500. However, he faces a 50% chance of suffering a S900 loss. Heis an expected utility maximizer and his utility function isU(w) = vw ,Where w is his wealth.(a) What is Bob's cost of risk?(b) If Bob can buy insurance against his loss for a price of $500, will he buy it?(c) What is the maximum amount Bob would be willing to pay for insurance?

Bob's Wealth = 2500 Probability of loss = 50% = 0.5 Therefore , probability of no loss = 0.5…

Answered: 2. Bob's wealth is $2500. However, he…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
A10.
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
Exercise 4: Insurance Fiona has von Neumann-Morgenstern utility function u(x) = VT and initial wealth 640, 000. She faces a 25% chance of losing L = 280, 000. 1. Is Fiona risk averse? 2. What is Fiona's utility if no loss occurs, what is her utility if the loss occurs? What is Fiona's expected utility? 3. What is the cost of fair insurance against the possible loss? Suppose Fiona is able to choose insurance with any coverage z E [0, 1] (i.e. 0 0 C(z) = if z = 0 4. Suppose co = 0 and c1 = 70,000. Is insurance at coverage level z > 0 fair insurance? What coverage level z* would Fiona choose? Explain. 5. Suppose co = 100 and c1 = 70,000. Is insurance at coverage level z > 0 fair insurance? What coverage level z** would Fiona choose? Explain. (Note that co = 100 is an "avoidable fixed cost" which is only paid if she chooses strictly positive insurance coverage. However, the "marginal cost" of additional insurance, c1 = 70,000, is the same as in the previous part.) 6. Suppose co = 100 and…
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.
2
The injection molding department of a company uses an average of 30 gallons of special lubricant a day. The supply of the lubricant is replenished when the amount on hand is 170 gallons. It takes four days for an order to be delivered. Safety stock is 50 gallons, wNch provides a stockout risk of 9 percent. What amount of safety stock would provide a stockout risk of 3 percent? Assume normality.
Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810,000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function ug (x) = VT. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able choose insurance with any coverage level z [0, 1] (i.e. 0 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?
1. Risk Premium: Assume your wealth is $100 and like in the Veritassium video you're offered a bet of a 50% chance of winning $10 and a 50% chance of losing $10. Assume you have square root utility. a. What is the utility you enjoy by holding the $100 of current wealth? b. What is the expected utility you foresee by entering the bet? Will you take the bet? c. What is your risk premium? Do you think someone would pay this to avoid the bet? d. Draw a diagram and label the relevant values.

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