Lottery A gives $2 million with 10%, $1 million with 80%, and $0 with 10%. ⚫ Lottery B gives $2 million with 12%, $1 million with 6%, and $0 with 82%. ⚫ Lottery C gives $2 million with 40%, $1 million with 20%, and $0 with 40%. ⚫ Lottery D gives $2 million with 3%, $1 million with 24%, and $0 with 73%. Show one example of preference relations which violate Independence of the expected utility theorem, and explain the reason.
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⚫ Lottery A gives $2 million with 10%, $1 million with 80%, and $0 with 10%.
⚫ Lottery B gives $2 million with 12%, $1 million with 6%, and $0 with 82%.
⚫ Lottery C gives $2 million with 40%, $1 million with 20%, and $0 with 40%.
⚫ Lottery D gives $2 million with 3%, $1 million with 24%, and $0 with 73%.
Show one example of preference relations which violate Independence of the expected utility theorem, and explain the reason.
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- You are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald’s or a Penn Station East Coast Subs franchise. McDonald’s indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be −$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and −$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.The conventional wisdom for urban economic development is: “Don’t put all your eggs in one basket. Diversify the economy.” To explain the idea of diversification, consider old McDonald, who must carry a dozen eggs from the barn to the house. The ground between the barn and the house is slippery, so there is a 50 percent chance that McDonald will slip on a given trip and break all the eggs in his basket. Consider two strategies: a one-basket strategy (a single trip with all 12 eggs) and a two-basket strategy (two trips, with 6 eggs per trip). INDEPTH ANSWERS. Questions= (1.)List all of the possible outcomes under each of the strategies. Question (2.)What is the expected number of delivered (unbroken) eggs under each strategy ? Question (3.)What are the trade-offs between the two strategies? If you were McDonald, which strategy would you adopt? Question (4.)What are the lessons for economic development strategies?An investor is considering three strategies for a $1,000 investment. The probable returns are estimated as follows: • Strategy 1: A profit of $10,000 with probability 0.15 and a loss of $1,000 with probability 0.85 • Strategy 2: A profit of $1,000 with probability 0.50, a profit of $500 with probability 0.30, and a loss of $500 with probability 0.20 • Strategy 3: A certain profit of $400 Which strategy has the highest expected profit? Explain why you would or would not advise the investor to adopt this strategy.
- Two partners start a business. Each has two possible strategies, spend full time or secretly take a second job and spend only part time on the business. Any profits that the business makes will be split equally between the two partners, regardless of whether they work full time or part time for the business. If a partner takes a second job, he will earn $20,000 from this job plus his share of profits from the business. If he spends full time on the business, his only source of income is his share of profits from this business. If both partners spend full time on the business, total profits will be $200,000. If one partner spends full time on the business and the other takes a second job, the business profits will be $80,000. If both partners take second job, the total business profits are $20,000. a) This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium. b) This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in…A risk-averse manager is considering a project that will cost £100. There is a 10 percent chance the project will generate revenues of £100, an 80 percent chance it will yield revenues of £50, and a 10 percent chance it will yield revenues of £500. Should the manager adopt the project? Explain. What will a risk-neutral and risk-loving manager do in the same situation?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?
- 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.The manager of XYZ Company is introducing a new product that will yield $1,000 in profits if the economy does not go into a recession. However, if a recession occurs, demand for the normal good will fall so sharply that the company will lose $4,000. If economists project that there is a 10 percent chance the economy will go into a recession, what are the expected profits to XYZ Company of introducing the new product? How risky is the introduction of the new product?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?
- Suppose a large bank has two openings for which it desires managers of different risk aversion. One position is the assistant vice president for commercial construction loans, for which the bank seeks a more risk averse manager. The other position is an assistant vice president to manage the venture capital loan portfolio, for which the bank seeks a manager who is more willing to take risks. The vertical scale of the following graph displays the guaranteed base salary, and the horizontal scale displays the profit-sharing rate—a percentage that represents what additions to or subtractions from one’s pay occur as a result of the profit-sharing agreement. The two hill-shaped curves represent expected profit-sharing payouts that would allow the firm to just break even on its incentive payments to the two managers. The graph also shows the indifference curves (IP and IQ) for two applicants. Which is the indifference curve of the more risk-neutral applicant? A. IQ B. IP Suppose…Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.BPO Services is in the business of digitizing information from forms that are filled out by hand. In 2006, a big client gave BPO a distribution of the forms that it digitized in house last year, and BPO estimated how much it would cost to digitize each form. Form Type Mix of Forms Form Cost A 0.5 $3.00 B 0.5 $1.00 The expected cost of digitizing a form is . Suppose the client and BPO agree to a deal, whereby the client pays BPO to digitize forms. The price of each form processed is equal to the expected cost of the form that you calculated in the previous part of the problem. Suppose that after the agreement, the client sends only forms of type A. The expected digitization cost per form of the forms sent by the client is . This leads to an expected loss of per form for BPO. (Hint: Do not round your answers. Enter the loss as a positive number.)