Thelma is indifferent between $100 and a bet with a 0.6 chance of no return and a 0.4 chance of $200. If U(0) = 20 and U(200) = 220, then U(100) =
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Thelma is indifferent between $100 and a bet with a 0.6 chance of no return and a 0.4 chance of $200. If U(0) = 20 and U(200) = 220, then U(100) = :
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- At a raffle, 100 tickets are sold for 1 prize of $100 and 3 consolation prizes of$20. If the ticket is worth $2, what would be the expected value?An investor with initial wealth W is given the opportunity to invest in a start-up (1) company. If the company does well, the investor will make a 200% profit in her investment, but if the company fails, the investor will lose all her investment. That is, if the investor invests X, she will get back 3x if the company succeeds and nothing if the company fails. The company will fail with probability 1/2 and will succeed with probability 1/2. The investor is risk-averse and has utility function u(x) wealth W should she invest in this company? Vx. What fraction of her initialMonty 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. 1. Considering that Monty Burns actually buys insurance from Miss b, express the wealth of Monty Burns and the income of Miss b as functions of q and r. You have of…
- A company owns an asset that is worth $245,000 and there is a 6% chance that it will lose $185,000 in value, otherwise it will not change. If the company has an expected utility functions with u(x) = x0.5, then the expected utility for the company is 480 464 460 456help meeeeeeSt. John's Brewery (SJB) is getting ready for a busy tourist season. SJB wants to either increase production or produce the same amount as last year, depending on the demand level for the coming season. SJB estimates the probabilities for high, medium and low demands as 0.32, 0.31, and 0.37 respectively, on the basis of the number of tourists forecasted by the local recreational bureau. If SJB increases production, the expected profits corresponding to high, medium and low demands are $800,000, $400,000 and $100,000 respectively. If SJB does not increase production, the expected profits are $550,000, $325,000 and $200,000 respectively. (NOTE: Text answers are case sensitive and the value of different parts of this question is indicated in square brackets [*/*]) Construct a decision tree for SJB. On the basis of the EV, what should SJB do? What is the expected value of increasing production? What is the expected value of not increasing production? Should SJB increase production (enter…
- A salesperson is trying to sell cars. The number of cars that she will sell depends on her effort "e" and her luck. Given her effort e, with probability 4e she is able to sell four cars, and with probability (1 - 4e) she is able to sell only one car. Her personal cost of effort is 100e². The dealership pays her a bonus b for each car sold. The salesperson is risk-neutral, and wants to maximize her expected utility, which is her expected income minus her effort cost. a) Given the bonus b, the salesperson's best response function is b) Suppose the dealership pays b = 2. Then the expected number of cars sold will be E(Q)=Adam is considering what skills to study in online school. Her utility function is based on the income she earns, and is defined by U(I) = I0.8. If she learns the skill of SPSS, she will earn $145,000 per year with probability 1. If she learns the skill of Tableau, she will earn $300,000 per year with probability 0.6 (assuming that she gets the certificate) and $30,000 with probability 0.4 (if she learns without earning a certificate and she has to find a waiter job). a. Is she risk averse, risk neutral, or risk loving? Explain.b. Write out the equation for her expected utility for each skill. c.Which skill will she learn? Show your work. d.Suppose someone offers her insurance for the possibility that she does not get a Tableau certificate. This insurance will provide her an amount of income in addition to the waiter job wages that makes her indifferent between learning SPSS and Tableau. What is this amount, and what is the cost of the insurance? (note: many possible answers)Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $600,000, a probability of 1/3 of valuing at $500,000, and a probability of 1/3 of valuing it at $200,000. Portsmouth Bank believes that these probabilities are independent among buyers. If Portsmouth Bank sells the house by means of a second- bidder, sealed- bid auction (Vicktey auction), what will be the bank's expected revenue from the sale?
- Your company has a customer list that includes 3000 people. Your market research indicates that 90 of them responded to the coupon. If you send a coupon to ONE customer at random, what’s the probability that he or she will use the coupon? Group of answer choices 3%. 9%. 30%. 90%. None of the above.At races, your horse, White Rum, has a probability of 1/20 of coming 1st, 1/10 of coming 2nd and a probability of 1⁄4 in coming 3rd. First place pays $5,000 to the winner, second place $4,000 and third place $1,350.Hence, is it worth entering the race if it costs $1050? Your company plans to invest in a particular project. There is a 40% chance you will lose $3,000, a 45% chance you will break even, and a 15% chance you will make $5,500. Based solely on this information, what should you do? On 1st Jan 2006, a business had inventory of $19,000. During the month, sales totalled $32,500 and purchases $24,000. On 31st Jan 2006 a fire destroyed some of the inventory. The undamaged goods in inventory were valued at $11,000. The business operates with a standard gross profit margin of 30%. Based on this information, what is the cost of the inventory destroyed in the fire?If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 50,000 bushels. The cost of pesticides is $30,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $9.00 with probability of 0.50 or it will be $11.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $10.00. If the farmer decides to sell the crop at harvest, then: a. He should not use pesticides because not using pesticides ensures greater expected profit. b. He should not use pesticides because not using pesticides ensures lower expected profit. c. He should use pesticides because using pesticides ensures greater expected profit. d. He should use pesticides because using pesticides ensures lower expected profit.