Which expected opportunity loss table is appropriate given the opportunity loss table below? The probability of a market rise is P = 0.7 and the probability of a market decline is P= 0.3 Act Opportunity Loss (S) Market Rise Market Decline Investment 1 4,000 Investment 2 3,000 Expected Opportunity Loss (S) 4,000 Purchase Investment 1 Investment 2 4,000 Expected Opportunity Loss ($) 1,200 Purchase Investment 1 Investment 2 1,200 Expected Opportunity Loss ($) Purchase Investment 1 Investment 2 1,000 Expected Opportunity Loss ($) 2,800 Purchase Investment 1 Investment 2 900
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- Question 3 Consider the following airline capacity allocation problem with buy-up. The total capacity is 100.There are three classes. All class demands follow normal distribution. The fare prices and demand statistics are given as follows: Class Fare Mean Std. Dev. 1 1000 17 6 2 900 45 15 3 500 90 20 Suppose that if a class 3 demand is rejected booking, each individual has a probability of 0.3 to become a class 2 demand; and if a class 2 demand is rejected booking, each individual has a probability of 0.2 to become a class 1 demand. The airline company needs to determine the nested protection levels. Use @risk simulation optimization tofind the optimal decisions. (Please round all the simulated numbers and solutions to the nearest integer.)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…Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]
- 8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow. probabilities and payoffs. S1 S2 S3 D1 500 100 -400 D2 200 150 100 D3 -100 200 300 Probability .2 .6 .2 Indifference Probability for Person Payoff A B C 300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89…Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 If an insurance company knows the probability of Tess experiencing an adverse event, what is the actuarially fair premium charged to Tess per $1 of benefit? Round to two decimal places
- Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do knowthe quality of the bike they sell. The price at which a bike is traded is determined by demand and supply.Each buyer wants at most one bicycle.(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price,and each seller is willing to sell their bike only if the price exceeds their valuation, what is theequilibrium outcome in this market?Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)If your worker works hard there is a 3/5 possibility that revenues will be $150 and a 2/5 probability that revenues will be $50. If she works at a lower level of effort, there is a 50% chance of each revenue outcome. Working hard costs her $6. Working moderately costs $3. Her outside utility is zero. She is risk-neutral, with utility equal to W - C , where W is the wage and C is the Cost of Effort (3 or 6 depending on whether she works with low or high effort, resp.) If you could contract for effort, would it be profitable to induce high effort? Explain why. What would your profits be? If you cannot contract for effort, find an incentive-compatible pay scheme that will induce high effort. Set up the incentive and participation constraints and find the z (payment when revenue is 150) and y (payment when revenue is 50) where both are exactly satisfied. Would it be profitable to use this scheme? Why? Now suppose that y can never be negative. What incentive compatible scheme will give…
- Setup from Question 1) An expected utility maximiser owns a car worth £60000 and has a bank account with £20000. The money in the bank is safe, but there is a 50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y) and they have no other assets. Setup from question 2)Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3 for every one pound of coverage. Question 3: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…Uncertainty and willingness to pay for insurance. Utility = (Wealth)1/3 Prob(flood) = .04 Prob(no flood) = .96 Total wealth if flood = $100,000. Total Wealth if no flood = $800,000. Find: (i) expected value, (ii) expected utility, (iii) certainty equivalent, and (iv) maximum willingness to pay for a policy that provides 100% flood insurance coverage. Draw the utility function and include all solved values on the diagram. What is the average gross profit per insurance customer, if each customer is charged his own maximum willingness to pay?