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Five of ten people earn $0, four earn $100, and one loses $100. What is the expected payoff? What is the variance of the payoff?
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- You have a 50 percent chance of making $0, a 40 percent chance of making $100, and a 10 percent chance of losing $100. Calculate the expected value and variance of the payoff.You are a hotel manager and you are considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the accompanying table. Project Boom (50%) Recession (50%) A $ 20 −$ 10 B −$ 10 $ 20 C $ 30 −$ 30 D $ 50 −$ 50 The variance in the returns of project D is Multiple Choice 1,600. 225. 900. 0.Solve the following problem using an excel spreadsheet. A tobacco company isinterested in hiring a salesperson to promote smoking cigarettes in nightclubs. The position pays a flat salary of $50,000, regardless of sales levels. The firm has two applicants, Predictable Patty and Risky Ricky. Predictable Patty can produce with 100% certainty $100,000 a year in sales. Risky Ricky, on the other hand, can produce $300,000 with probability of 50%. But if he turns out to spend his time drinking and dancing in the nightclubs instead of making sales, he could actually cost the firm -$100,000 per year.a) During their first year on the job, what are the expected sales of Patty and Ricky? What are the firm’s expected profits on each worker?b) Now assume both workers are currently 25, and they will work until the retirement age of 65. The firm has the option to fire its new employee after one year based on sales, but can only hire one employee. Assume that it takes only one year to discover whether…
- Consider a lottery with three possible outcomes: $100 will be received with probability .1, $50 with probability .2, and $10 with probability .7. What is the expected value of the lottery? What is the variance of the outcomes of the lottery? What would a risk-neutral person pay to play the lottery?A firm wants to maximize its expected profit. The firm must choose the production quantity q. The production cost is C=2q2 . However, the firm is uncertainty about the price consumers will be willing to pay for the product. With probability 75% the consumers will be willing to pay $24 per unit of output q. With probability 25% consumers will only be willing to pay $8. The firm must choose q before it learns if the price will be high or low. a) Compute the quantity q that maximizes the firm’s expected profit. Find the expected profit given this optimal quantity. b) Suppose that a consulting company knows exactly how much consumers are willing to pay. How much would the firm be willing to pay for this information?The following payoff table provides profits based on various posible decision alternativesand various levels of demand at Kmart Print Shop. Alternatives Low High Alternative 1 10,000 30,000 Alternative 2 5,000 40,000 Alternative 3 -2,000 50,000 The probability of low demand is 0.4, whereas the probability of high demand is 0.6.What is the highest possible expected monetary value?
- 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?In a game, there are three values 1, 000, 2.500 and 5,000 and the cost of the game is 1, 500 . If each outcome has an equal probability of occurring, then what is the expected value of playing the game?A risk-averse manager is considering two projects. The first project involves expanding the market for bologna; the second involves expanding the market for caviar. There is a 10 percent chance of a recession and a 90 percent chance of an economic boom. During a boom, the bologna project will lose $10,000, whereas the caviar project will earn $20,000. During a recession, the bologna project will earn $12,000 and the caviar project will lose $8,000. If the alternative is earning $3,000 on a safe asset (say, a Treasury bill), what should the manager do? Why?
- Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy. The fire statistics indicate that in a given year the probability of property damage in a fire is as follows: Fire Damage $100,000 $75,000 $50,000 $25,000 $10,000 $0 Probability .006 .002 .004 .003 .005 .980 If Burger Prince was risk neutral, how much would they be willing to pay for fire insurance? If Burger Prince has the utility values given below, approximately how much would they be willing to pay for fire insurance? Loss $100,000 $75,000 $50,000 $25,000 $10,000 $5,000 $0 Utility 0 30 60 85 95 99 100Company ABC holds an auction. Five bidders were invited. Company ABC estimates that each bidder has a value of either 15 or 25 for the item, and the probabilities attach to each value is 50%. What is the expected price? What is the price if three of the five bidders collude?The table below shows that a sales agent can work with either low, or high amount of effort. Low effort generates$30,000, $60,000 or $100,000 profit (with probability given below), while high effort generates 60,000; 100,000 or 150, 000 (with probability given below) depending on some random factors. Bad luck (P=0.3) Medium luck (P=0.3) Good luck (P=0.4) Low effort (a=0) $30,000 $60,000 $100,000 High effort (a=1) $60,000 $100,000 $150,000 The cost of low effort is 0 and the cost of high effort is $10,000 (Formally, c=$10,000a). The net wage is wage minus cost of effort and the net profit is total profit minus wage. Suppose the firm offers the repair person a fixed wage of 13,000, what will be the net wage of the repair person and the net profit of the owner? Suppose now the owner offers the repair person the following bonus arrangement What will be the net wage of the repair person? What will be the net profit of the owner? Specify…
