Show your work. An MBA applies for a job in two firms X and Y. The probability of his being selected in firm X is 0-7 and being rejected at Y is 0-5. The probability of at least one of his applications being rejected is 0-6. What is probability that he will be selected in one firms?
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- Many decision problems have the following simplestructure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow.s1 s2 s3d1 500 100 -400d2 200 150 100d3 -100 200 300probability.2 .6 .2Indifference Probability for PersonPayoff A B C300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89 .60 .22-100 .75 .45 .10a. Plot the utility function for each decision maker.b. Characterize each decision maker's attitude toward risk.c. Which decision will each person prefer?Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!
- Joes initial income is y 10,000. Joe experiences illness with a probability of 20%. Jo's total medical costs associated with the illness are $1000. Joe's expected income without insurance isSubject 2 A bottle company ALPHA, is considering creating a new bottle of 0.25 lt. To decide whether to invest in this projector not, they performed market research that costed €5,000. The results indicated two possible scenarios that depend on the competitor's reaction to create a similar product and on the percentage of the faithful customers of ALPHA. ScenarioA has a 45% chanceto be realized, while scenarioB has a probability of 55%. For the project's realization the company must purchase specialmachinery that cost €80,000, while transportation and installation costs amount to €2,000. The useful life of the project is two years, and the machinery can be sold at the end of the useful life for €30,000.Table 1 presents the pertinenteconomic data. At the end of the second year the working capital is going to be recaptured. The tax rate is 25%, the weighted average cost of capital is 10% and the company fully depreciates fixed assets for tax purposes, using the straight-line depreciation…. If you examine the decision tree in Figure 9.12 (orany other decision trees from PrecisionTree), you willsee two numbers (in blue font) to the right of each endnode. The bottom number is the combined monetaryvalue from following the corresponding path throughthe tree. The top number is the probability that thispath will be followed, given that the best strategy isused. With this in mind, explain (1) how the positiveprobabilities following the end nodes are calculated,(2) why some of the probabilities following the endnodes are 0, and (3) why the sum of the probabilitiesfollowing the end nodes is necessarily 1.
- The investor is considering how to optimally invest 1000 euros in stocks and bonds. Let's assume that the optimal decision is made based on expected utility. Suppose the investor has a utility function u(x)=ln(1+x), where x is their wealth. Let y be the proportion invested in stocks and 1−y be the proportion invested in bonds. By investing in stocks, the investor earns 1% with a probability of 39.5% and 4% with a probability of 60.5%. By investing in bonds, the investor earns a certain 2.8%. What proportion of the investment will the investor allocate to stocks and what proportion to bonds?The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?6.33 Statistics released by the National HighwayTraffic Safety Administration and the National SafetyCouncil show that on an average weekend night, 1 outof every 10 drivers on the road is drunk. If 400 driversare randomly checked next Saturday night, what is theprobability that the number of drunk drivers will be(a) less than 32?(b) more than 49?(c) at least 35 but less than 47?
- ONLY SOLVE D An investor with a total wealth of $100 is faced with the following opportunities. First, he may invest $100 now and receive $144 if there are good times, but receive $64 if there are bad times. The investor estimates that good times happen with 50% probability.He can also buy an investor newsletter whether good times or bad times will occur. (a) Draw the decision tree that illustrates the options available to the investor and the payoffs to the different options. Define P as the price of the newsletter. (b) If the investor is risk-neutral with U(M) = M, where M is income, how much would he be willing to pay for the subscription to the newsletter? (c) If the investor is risk-averse with utility U(M) = M0.5, where M is income, how much would this investor be willing to pay for the subscription to the newsletter? (d) Suppose that the owner of the newsletter estimates that there are 75 risk-averse investors like those of part (c) and 25 investors like those of part(b). If…An electronics company gives a warrantee on a $150 eReader that covers accidentaldamage (AD) and theft (T). Due to the costs associated with fixing an eReader, it ischeaper for the company to credit the buyer the full price of the product to purchaseanother one. In any given year, there is a 5.1% chance that an AD claim is filed. Assumeonly one claim can be filed (not one of each type).If a customer reports an eReader as stolen, the company will credit the customer 80% ofthe product's full price. In a given year, there is a 3.5% chance that a T claim is filed.If the warrantee costs $15.95 for one year, what is the company's expected financialgain/loss on each contract?(NOTE: Remember that a customer will pay for the warrantee up-front, whether or not aclaim is filed.)A plaintiff believes that there is a 30% chance that he will winIf he wins, he will gain $50,000. It costs him $5000 in non‐recoverable litigation costs to take the case to court. If the plaintiff is risk‐neutral, which of the following is true? A) The plaintiff will take the case to court with an expected net‐gain of $10,000 B) The plaintiff will take the case to court with an expected net‐gain of $15,000 C) The plaintiff will not take the case to court because he is afraid of losing. D) None of the above
