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Based on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low level of effort, or (3) put forth a high level of effort. Suppose for simplicity that each salesperson will sell $0, $5000, or $50,000 worth of brushes. The probability of each sales amount depends on the effort level as described in the file P07_71.xlsx. If a salesperson is paid w dollars, he or she regards this as a “benefit” of w1/2 units. In addition, low effort costs the salesperson 0 benefit units, whereas high effort costs 50 benefit units. If a salesperson were to quit Fuller and work elsewhere, he or she could earn a benefit of 20 units. Fuller wants all salespeople to put forth a high level of effort. The question is how to minimize the cost of encouraging them to do so. The company cannot observe the level of effort put forth by a salesperson, but it can observe the size of his or her sales. Thus, the wage paid to the salesperson is completely determined by the size of the sale. This means that Fuller must determine w0, the wage paid for sales of $0; w5000, the wage paid for sales of $5000; and w50,000, the wage paid for sales of $50,000. These wages must be set so that the salespeople value the expected benefit from high effort more than quitting and more than low effort. Determine how to minimize the expected cost of ensuring that all salespeople put forth high effort. (This problem is an example of agency theory.)
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Chapter 7 Solutions
EBK PRACTICAL MANAGEMENT SCIENCE
- The file P02_41.xlsx contains the cumulative number of bits (in trillions) of DRAM (a type of computer memory) produced and the price per bit (in thousandth of a cent). a. Fit a power curve that can be used to show how price per bit drops with increased production. This relationship is known as the learning curve. b. Suppose the cumulative number of bits doubles. Create a prediction for the price per bit. Does the change in the price per bit depend on the current price?arrow_forwardRework the previous problem for a case in which the one-year warranty requires you to pay for the new device even if failure occurs during the warranty period. Specifically, if the device fails at time t, measured relative to the time it went into use, you must pay 300t for a new device. For example, if the device goes into use at the beginning of April and fails nine months later, at the beginning of January, you must pay 225. The reasoning is that you got 9/12 of the warranty period for use, so you should pay that fraction of the total cost for the next device. As before, how-ever, if the device fails outside the warranty period, you must pay the full 300 cost for a new device.arrow_forwardThe IRR is the discount rate r that makes a project have an NPV of 0. You can find IRR in Excel with the built-in IRR function, using the syntax =IRR(range of cash flows). However, it can be tricky. In fact, if the IRR is not near 10%, this function might not find an answer, and you would get an error message. Then you must try the syntax =IRR(range of cash flows, guess), where guess" is your best guess for the IRR. It is best to try a range of guesses (say, 90% to 100%). Find the IRR of the project described in Problem 34. 34. Consider a project with the following cash flows: year 1, 400; year 2, 200; year 3, 600; year 4, 900; year 5, 1000; year 6, 250; year 7, 230. Assume a discount rate of 15% per year. a. Find the projects NPV if cash flows occur at the ends of the respective years. b. Find the projects NPV if cash flows occur at the beginnings of the respective years. c. Find the projects NPV if cash flows occur at the middles of the respective years.arrow_forward
- You are considering a 10-year investment project. At present, the expected cash flow each year is 10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last years actual cash flow and standard deviation 1000. For example, suppose that the actual cash flow in year 1 is 12,000. Then year 2 cash flow is normal with mean 12,000 and standard deviation 1000. Also, at the end of year 1, your best guess is that each later years expected cash flow will be 12,000. a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. b. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the value given in the file P11_60.xlsx. For example, suppose that year 1 cash flow is 4000. Then at the end of year 1, you expect cash flow for each remaining year to be 4000. This has an NPV of less than 62,000, so you should abandon the project and collect 62,000 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years are zero. So in this case the future cash flows after abandonment should be zero in your model.)arrow_forwardYou now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.arrow_forwardBased on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)arrow_forward
- Pls help ASAParrow_forwardWe all hate to bring small change to the store. Usingrandom numbers, we can eliminate the need for change andgive the store and the customer a fair shake.a Suppose you buy something that costs $.20. How could you use random numbers (built into the cash reg-ister system) to decide whether you should pay $1.00 or nothing? This eliminates the need for change!b If you bought something for $9.60, how would youuse random numbers to eliminate the need for change?c In the long run, why is this method fair to both thestore and the customer?arrow_forwardManagement of the Toys R4U Company needs to decide whether to introduce a certain new novelty toy for the upcoming Christmas season, after which it would be discontinued. The total cost required to produce and market this toy would be $500,000 plus $15 per toy produced. The company would receive revenue of $35 for each toy sold. Assuming that every unit of this toy that is produced is sold, write an expression for the profit in terms of the number produced and sold. Then find the break-even point that this number must exceed to make it worthwhile to introduce this toy. Now assume that the number that can be sold might be less than the number produced. Write an expression for the profit in terms of these two numbers. Formulate a spreadsheet that will give the profit in part b for any values of the two numbers. Write a mathematical expression for the constraint that the number produced should not exceed the number that can be sold.arrow_forward
- Which of the following statements is correct regarding the EMH form? Select one: None of the answers are correct If the market is weak-form efficient, then it is also semistrong and strong-form efficient. If the market is semistrong form efficient, then it is also strong form efficient If a market is strong-form efficient, it is also semistrong and weak form efficient If the market is strong-form efficient, it is also semistrong but not weak-form efficientarrow_forwardCLV = Profit per year X Number of years as a customer (lifetime) less customer acquisition costs And we can use the churn rate % to tell us how many years our average customer stay by dividing 1/churn rate. In our case that is 1/20% = 5 years = customer lifetime. A supermarket chain ran a social media campaign and they got 2,000 new customers. The TOTAL cost of the campaign was $250,000. These customers visited the supermarket 25 times a year. Each customer spends $100 per visit and the supermarket makes a 4% profit margin on the customer’s spend. The retention rate of the customers is 60%. What is their CLV? Assume that the profit margin is based on the customer’s non-discounted spend, then deduct the discount.arrow_forwardWhen it first debuted, Telsa was selling its Model 3 sedan for $35,000. The Model 3 was priced substantially less than Tesla’s other models at the time, however, it had similar quality and input costs. In charging such a low price, it is most likely that Tesla is trying to: A. Create more value without capturing more value B. Capture more value without creating more value C. Create and capture more value D. None of the abovearrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,