Managerial Economics, 6th Ed Solution Manual

Type:

Solution Manual

Resource:

Managerial Economics

Edition:

6th Edition

Author(s):

Luke Froeb Brian McCann Michael Ward Mike Shor

CHAPTER ONE INTRODUCTION TO ECONOMIC DECISION MAKING OBJECTIVES 1.

To introduce Managerial Economics (pp. 1-2)

2.

To provide concrete examples of managerial decisions (pp. 2-6)

3.

To provide a framework for analyzing decisions (pp. 6-13)

4.

To compare decisions of the private firm (where maximum profit is the objective) to public sector decisions (where maximum societal net benefit is the objective) (pp. 13-16)

5.

To introduce the student to the book and its organization (pp. 16-19)

TEACHING SUGGESTIONS I.

Introduction and Motivation

The chapter begins by stressing concrete applications of managerial economics (the eight examples) rather than speaking generally about topics and methods. Our practice in class is to lead a brief discussion of some of the text examples (the three we like best) augmented with additional representative examples from the current business press.

A. Additional questions on text examples: 1.

Multinational Production and Pricing (Revisited p. 98 of Chapter 3 and Problem S2, p. 252, of Chapter 6). Why might the car company want to charge different prices home and abroad? (What if the John Wiley & Sons

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company had to charge the same price because of anti-dumping restrictions?) Why might it want to ship vehicles overseas?

2.

Euro Disney (Revisited p. 155 of Chapter 4.) Which factors most affect the success of the park? How would you go about collecting and analyzing the information needed to make forecasts regarding these factors?

3.

Market Entry (Revisited pp. 385 of Chapter 10). In a market that can support only one store, is there an advantage to being the first in? Are there strategic advantages to commitment? (Here you might tell the story of the game of chicken. Any advantage if one driver pulls off the steering wheel and throws it out the window?) How might a bookstore commit? What if both commit? (Both throw their steering wheels out the window?)

4.

Building a New Bridge. (Revisited pp. 445-447 of Chapter 11).

Building a bridge is usually a public responsibility (paid for out of public funds raised via taxes). Why is this the case? How might a public planner determine the need for a new bridge? How should tolls (if any) be set?

5.

A Regulatory Problem (See pp. 424-430 of Chapter 11). Does regulation put too great a cost burden on business? How should the benefits of environmental regulation be weighed against the costs?

6.

An R&D Decision (Revisited pp. 477-482 of Chapter 12). Might the pharmaceutical company be wise to pursue both R&D methods simultaneously?

7.

Texaco versus Pennzoil (Revisited p. 610 of Chapter 15). In light of the Texaco-Pennzoil dispute, is American business becoming too litigious?

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B.

Additional Vignettes. A good way to spice up the discussion is to (1) preview decision examples from later chapters or (2) take examples from chapters that are not assigned. Here are some suggestions.

• Airline price discrimination (Chapter Three, pp. 74 & p. 104) • Introducing New Coke (Chapter Four, p. 125) • The OPEC Cartel (Chapter Eight, p. 309) • Battle for Air Passengers (Chapter Ten, p. 370 & p. 397) • Regulating AZT (Chapter Eleven, pp. 415 and 451) • An Oil Wildcatter (Chapter Twelve, p. 469) • Predicting Credit Risks (Chapter Thirteen, p. 517) • Making a Tender Offer (Chapter Fifteen, p. 606) • Bidding to Televise the Olympics (Chapter Sixteen, p. 623 & p. 649) • Constructing an Optimal Portfolio (Chapter Seventeen, p. 660 & p.

689)

I. Teaching the “Nuts and Bolts” A. Issues deserving extra emphasis 1. The meaning of economic tradeoffs: • benefits versus costs.

• short-term profit versus long-term profit.

• risk versus return.

• tradeoffs among multiple objectives (For example in auto regulation: safety vs. emission reduction vs. fuel economy 2. The virtues of simple models (predictive models, the model of the firm) 3.

Coming to grips with uncertainty

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B.

The six decision steps mostly speak for themselves. (In our experience, students find them relatively easy to grasp.) The instructor may wish to reemphasize them by discussing some of the steps in class.

Alternatively, the six steps can be applied by discussing the decision vignettes in question 4 at the end of the chapter. In each instance, did the individual make a faulty decision? If so, in what step(s) did he or she go wrong? (See answers below).

C.

Guinea Pig Questions. An option that many teachers adopt is to involve students by posing short questions. We call these “guinea pig” questions. Students meet these questions “cold” without any advanced background or preparation. The main idea is to challenge them to think about possible solutions. By necessity, they usually rely on their general judgment or intuition rather than on any systematic analysis.

(It's a good idea for the teacher to tell the students that the questions are in some sense “unfair”; students don't have enough information or time to find the best solution. But neither do managers in real-life business decisions.)

1.

Locating a Shopping Mall. This is taken up in Chapter Two, p. 26.

2.

Finding the Best Item (Chapter Thirteen, Problem 12). Suppose that you will be shown three “prizes” in order. Ahead of time, you know absolutely nothing about how valuable the prizes might be. Only after viewing all three can you determine which you like best. You are shown the prizes in order and are allowed to select one. However, there is no “going back.” You must select a prize immediately after seeing it, and before seeing any subsequent prize. a) Your sole objective is to obtain the best of the three prizes.

(Second best doesn't count.) A random selection provides a onethird chance of getting the best prize. Find a strategy that provides a strictly greater chance (and compute the actual chance). b) What if there are a large number of prizes (say 10, 50, or 100)?

Describe in general terms the kind of strategy you might use.

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3.

Let's make a Deal (Thirteen, Problem 6). Consider the following simplified version of the game “Let's Make a Deal.” There is a grand prize behind one of three curtains. The other two curtains are empty.

As the contestant, you get to choose a curtain at random. Let's say you choose curtain three. Before revealing what's behind the curtain, the game show host offers to show you what's behind one of the other curtains. Suppose he shows you that curtain two is empty. In fact, he always shows you an empty curtain. (You know that's how the game works, the audience knows it, everybody knows it.) Now you must decide: do you stick with your original choice, curtain three, or switch to curtain one? Which action gives you the better chance of finding the grand prize?

4.

A Competitive Decision. Consider the following game involving two players. The players will alternate choosing the nine integers: 1, 2, 3, 4, 5, 6, 7, 8, 9. If the first player picks 4 (let's say), the second player can choose any one of the remaining digits, and so on. The first player that obtains three digits that add up to exactly 15 wins. For instance, the first player wins with the digits, 2, 3, 6, and 7 since 2 + 6 + 7 = 15. He would not win with 6, 7, 8, and 9 since no three of them add up to 15.

Ask for two volunteers to play this game (with the rest of the class free to kibitz). Questions to think about: How would you play? Is it an advantage to move first? What well-known game does this number game resemble?

5.

Bidding for an Item of Unknown Value. Tell the class that you will conduct a sealed-bid auction for a valuable item. The high bidder will pay his bid and win the item. The item is a jar of pennies. Actually its easier to fill a glass pickle jar with colored plastic Christmas ornaments

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(little pinwheels about penny size) to spare the bother of dealing with pennies. Fill the jar with a predetermined number of trinkets. (For instance, set the number at 483 by using two packs of 250 trinkets minus 17.) Tell the class that the winning bidder will receive the value of the jar where each trinket is redeemable for a penny. Thus, though the students don't know it, the jar is worth $4.83. A buyer with a winning bid of $3.50 would make a profit of $1.13. If the winning bid were $6.00, the “winner” would lose $1.17.

Ask each student to write down 4 items: (1) an estimate of the value of the jar (i.e. the number of trinkets translated into dollars); (2) a sealed bid for the jar; and (3) upper and lower bounds constructed to form a 90% confidence interval around the true value. (Remind students what a confidence interval is.)

D. Discussion of Guinea Pig Questions. Though these questions are deliberately set in non-business situations, almost all have interesting business counterparts. Question 1 demonstrates marginal analysis.

Questions 2, 3, and 5 involve decisions under uncertainty. Question 4 is a competitive decision.

1.

Siting a Shopping Mall. For discussion, see pp. 26-28.

2.

Finding the Best Item. For an arbitrary number of items (not only three), this is variously called the “secretary problem” (interviewing and selecting the best secretary), the “hotel problem” (deciding to stop at one of three hotels situated hours apart along a cross-country route), or the “art gallery problem” (in the gallery you are allowed to view paintings one at a time and choose only one). Your best strategy is as follows: Observe the first item but bypass it. Then, select the second item only if it is better than the first. If it isn't, go on to the third item and select it.

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This plan delivers the best item with probability 1/2, the second-best item with probability 1/3, and the worst item with probability 1/6. Here are the six equally likely orders in which the items might appear: First Item: Second Item: Third Item:

best 2nd best worst

best worst 2nd best

2nd best best worst

2nd best worst best

worst best 2nd best

worst 2nd best best

The bold-faced outcomes show the result of using the “wait and see” strategy. As shown, the strategy delivers three bests, two 2nd bests, and one worst. For more on generalizations of this example, see Chapter Thirteen of this instructor's manual.

3.

Let's make a Deal. Almost all students (if they have not seen the problem before) believe that either curtain offers a 50-50 chance of having the prize. This is incorrect. In fact, the chance is one-third that the grand prize is behind your chosen curtain and two-thirds that its behind the other curtain. After all, choosing your original curtain at random offers a one-third winning chance. The fact that you are shown an empty curtain does not change this prior probability (although it does eliminate one curtain from consideration). Since your winning chances are 1/3 if you “stick”, you should switch and gain a 2/3 winning chance.

Many students will still be unconvinced by this argument. One response is to challenge students (in pairs) to simulate the setup for themselves. The simulation could mean shuffling 2 black playing cards and one red card (the prize), and playing 60 times. Always “sticking” with one's original card after a black card has been revealed will produce only 20 wins on average. A second argument is to imagine that there are 100 curtains and one prize. After a curtain is chosen (say, curtain 1), the host reveals 98 empty curtains (all but curtain 71). Most students will easily see that the odds are 99 to 1 in favor of curtain 71 over curtain 1.

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This classic problem has been discussed among social scientists since the mid 1970s and has even made it to the front page of The New York Times: “Behind Monty Hall's Doors: Puzzle, Debate, and Answer,” NYT, July 21, 1991, p. 1. The discussion and analysis are recommended. Even in the 21st century, the riddle is still going strong.

4.

A Competitive Decision. This is a tough game because it involves mental arithmetic and keeping track of many possibilities. The “sneaky” way to play this game is by secretly using the following magic square: 8 1 6 3 5 7 4 9 2 In a magic square, all rows, columns, and diagonals add up to the same number (in this case 15). Using the magic square, we see that the number game is strategically equivalent to tic tac toe. The ways you can win in the number game are identical to the ways you can win in tic tac toe. There are many ways to play either game optimally -- block your opponent whenever he has a potential winning move and never let him set up two ways to win. The result of optimal play is a draw.

When students play, the first mover often wins because the second mover is apt to make the first mistake. A typical play of the game might be: 6, 9, 8, 1, 4, 3, 5, the first player wins with 6 + 4 + 5 = 15.

You can use this game to make two points. (1) Optimal competitive strategies (see Chapter Ten) often require looking ahead to anticipate competitors' moves and counter moves. (2) Often the best way to solve a new decision problem is to see that it is similar to a problem you already know how to solve.

5.

Bidding for an Item of Unknown Value. This example introduces complications posed by uncertainty. Each bidder is uncertain about the value of the jar and also about the level of competitors' bids. Before revealing the true value of the jar, ask a number of students to reveal their estimates. Students will be surprised by the wide dispersion of estimates. Ask the class what the distribution might look like if it were John Wiley & Sons

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plotted. A number of students are sure to suggest a bell-shaped normal curve. By shows of hands, find roughly the median of the class estimates and sketch a normal curve with this mean. Then ask students how they bid. Compare bids to estimates to emphasize the logic of placing bids below estimates. Note that the optimal degree of shading involves a tradeoff between the chance of winning and the profit from winning. (Finding an optimal solution is a complex problem.)

Superimpose the bid distribution next to the estimate distribution. Your graph should resemble Figure 16.2, p. 640.

Now is the time to suggest the possibility of the winner's curse by raising two hypotheses. First, suppose estimates are unbiased, i.e. centered around the true value of the item. (This seems reasonable.)

Second, suppose that estimates and bids are quite dispersed. (Also reasonable.) These two points imply that the highest bids (the shaded tail in Figure 16.2) are above the true value of the item. On average, the winning bidder loses money on the acquisition. At this point, you may ask some of the high bidders in the class, whether this argument worries them. (Do they still want to play for real?) Find the highest bid. Then, reveal the value of the item. With 20 or more students in the class, the winning bidder always will fall prey to the winner's curse, i.e. pay more than the item's value. The only exceptions occur if the class estimates are biased well below the true number of trinkets.

Having made the main point, you can raise some other questions.

What factors increase the likelihood and magnitude of the winner's curse? As discussed on pp. 639-641, the winner's curse increases with the degree of uncertainty and the number of bidders. Does the winner's curse happen in real life? Yes, bidding for off-shore oil leases, competitive tender-offers, and free-agent bidding for athletes are just three examples. How well did you (the student) gauge your degree of uncertainty? Most individuals are overconfident of their estimation abilities. Ask students if the true estimate fell between their lower and upper bounds. Typically, less than half the students answer in the affirmative by a show of hands. By construction, the intervals should bracket the true value 90 percent of the time. In short, students are surprised at how uncertain their knowledge really is.

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ADDITIONAL MATERIALS I.

Recommended Readings

M. Bazerman, Judgment in Managerial Decision Making, John Wiley & Sons, 2008 (especially chapters 1 and 9).

J. E. Russo, M. Hittleman, and P. J. Schoemaker. Winning Decisions. New York: Bantam Dell Publishers, 2001.

J. E. Russo and P. J. Schoemaker, Decision Traps, Fireside Publishing, New York, 1990.

G. Belsky and T. Gilovich. Why Smart People Make Big Money Mistakes and How to Correct Them. New York: Simon and Schuster, 2000.

N.R. Augustine, Augustine's Laws, Penguin Books, 1987. (A nice commentary on the foibles of managerial decision making) Mary Walton, Car, W.W. Norton, 1997, 360 pages. (This book is an inside look at Ford's decisions and mistakes in redesigning the Taurus.)

II.

Short Readings

D. A. Garvin and M. A. Roberto, “What You Don’t Know about Making Decisions,” Harvard Business Review, September 2001, pp. 108-116.

A. M. Hayashi, “When to Trust your Gut,” Harvard Business Review, February 2001, pp. 5-11.

D. Brooks, “The Behavioral Revolution,” The New York Times, October 28, 2008, p. A23.

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“Calculating the Irrational in Economics,” The New York Times, June 28 2003, p. A17.

“Brain Experts now Follow the Money, The New York Times, June 17, 2003, p. D1.

(The preceding three articles discuss the psychology of decision making.)

R. Trudel and J. Cotte, “Does Being Ethical Pay?” The Wall Street Journal, May 12, 2008, p. R1.

“Pharmaceuticals: A Gathering Storm,” The Economist, June 9, 2007, p.711.

J. Nocera, “The Paradoxes of Business Do-Gooders,” The New York Times, November 11, 2006, p. C1.

“The Good Company,” The Economist, January, 22, 2005, p. 11. (This and the preceding three articles discuss the social responsibility of business.)

“Where Borders Group and Barnes and Nobel Compete, It's a War,” The Wall Street Journal, September 3, 1996, p. A1.

D. Ekwurzel and J. McMillan, “Economics on Line,” Journal of Economic Literature, March 2001, pp. 7-10.

III. Cases Fighting Aids and Pricing Drugs (9-502-061), Harvard Business School, 2002.

Decision Making at the Top (9-398-061), Harvard Business School, 1997.

Canonical Decision Problems (9-396-308), Harvard Business School, 1997.

Teaching Note (5-396-313)

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IV. Quips and Quotes General maxims about decision making: There are three valid answers to making a decision: yes, no, or no decision right now. Only 20% of the answers should be an immediate yes or no.

Find two good reasons to do something. (You can always find one good reason.)

When making a decision of minor importance, I have always found it advantageous to consider all the pros and cons. In vital matters, however, such as the choice of a mate or a profession, the decisions should come from the unconscious, from somewhere within ourselves. (Sigmund Freud) Never, never use intuition (General Omar Bradley) When asked what he'd done during the terror of the French revolution, Abbe Sieyes replied, “I survived.” (An example of satisficing?)

If you don't know where you're going, chances are you won't get there.

We never make the same mistake twice. All our blunders are different.

I'd like to rush for 1500 or 2000 yards, whichever comes first. (Former Washington Redskin running back George Rodgers) In a choice between two evils, I make it my general rule to choose the one I haven't tried yet. (Mae West).

If the only tool you have is a hammer, you tend to see every problem as a nail.

The real objective of a committee is not to reach a decision but to avoid it.

It is better to know nothing than to know what ain't so.

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A decision is always a choice among alternative perceived images of the future. (Kenneth E. Boulding) Economic activity is rational activity . . . it consists firstly in valuation of ends, and then in the valuation of the means leading to these ends.

(Ludwig von Mises)

Here is a slightly exaggerated example from an Ann Landers column: Dear Ann, Our marriage was once so beautiful but things have changed.

My spouse treats me like a slave, never shows any affection, comes home drunk every night, slaps me around, and may be having an affair with my best friend. I alternate between loneliness and fear. I have gained weight and am severely depressed. My life is a living hell and I pray to get through the next day. Ann, what should I do?

(Ann Landers responded with a question. Are you better off with him or without him? That is, what are the outcomes associated with each alternative? Additional query: are these the only alternatives?)

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ANSWERS TO EVEN-NUMBERED PROBLEMS 2. i)

Multinational Production and Pricing. The global automobile company needs information on demand (how many vehicles can be sold in each market at different prices) and production costs.

ii)

Euro Disney. Disney should gather information on: a) the likely number of European visitors to the new park and the amount these visitors will spend on amusements, food, and lodging, b) costs of operating the park, and c) macroeconomic forecasts for the European economy.

iii)

Market Entry. Barnes and Noble and Borders not only need information on local market demand, they also need information on the ability and willingness of the other company to compete. This means gathering information on the rival's cost structure, sources of supply, access to capital, etc.

iv)

Building a New Bridge. The authority should estimate usage of the bridge over its useful life, the likely cost of building and maintaining the bridge, and other important side-effects, pro and con -- including positive effects on business activity and the impacts on air pollution and traffic congestion.

v)

A Regulatory Problem. Before deciding whether to promote the oil-to-coal conversion, regulators need information on how much oil would be saved (and the dollar value of savings) and the cost of the chain of side-effects -- not only the direct cost of electricity provision but also pollution costs and environmental damage.

vi)

An R&D Decision. The pharmaceutical company should quiz its scientists on the chances of success (and the timetable for completion) for each R&D approach. The company's marketing department would supply estimates of possible revenues from the drug; its production department would estimate possible costs.

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vii)

Texaco versus Pennzoil. An assessment of the ultimate monetary outcome of the suit (the chances of different possible court outcomes at different stages) is essential. Also important is an informed assessment of the terms at which the other side might be willing to settle.

4. Decision vignettes a.

A couple who buy the first house they view have probably sampled too few houses. Housing markets are notoriously imperfect.

Houses come in various shapes, sizes, conditions, neighborhoods, and prices. Personal preferences for houses also vary enormously.

The couple is likely to get a “better” house for themselves if they view a dozen, two dozen, or more houses over the course of time before buying their “most-preferred” house from the lot.

Circumstances justifying the first-house purchase include: (1) the house is so good that viewing others is a waste of time, (2) the house is so good and the commitment must be made now or another buyer will claim the house, (3) the couple must buy now (a job transfer has brought them to the area and schools open tomorrow), (4) they already have full information about the types of other houses available (the wife's best friend is a real estate agent).

b.

The company seems to be launching the product to avoid “wasting” the $6 million already spent in development. This “sunk” cost is irrelevant and should be ignored. What does matter for the reinvestment decision are the future revenues and costs of continuing. (Reinvest if the net present value of future profits is positive.) Some “close-to-home” examples of the sunk cost fallacy: i) A fellow pays $250 for a year-long tennis membership but develops severe tennis elbow after two months. He continues to play in great pain in order to get his money's worth. ii) Ms. K has a subscription to a series of six plays for $150. She braves a snow storm so as not to waste the $25 cost. On reflection, she admits that she wouldn't have gone had she been given the ticket for free.

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c.

It's in the individual motorist's best interest to drive on. (Stopping is risky and inconvenient). But it's in the collective interest of all the delayed motorists to have someone stop and move the mattress.

Here's an example of the potential conflict between private and public interests (between private profit and social welfare). In such circumstances, there is a potential role for government intervention.

d.

Allowing the use of thalidomide had a disastrous outcome and more importantly was a bad decision (besides its potential risk, the drug was of questionable benefit in aiding sleep). The thalidomide disaster prompted a much tougher stance toward prior drug testing in the U.S. and elsewhere.

e.

The frantic couple should choose separate lines to take advantage of whichever line is quicker. Whoever gets served first should check the baggage. The lesson here: DIVERSIFY.

f.

The cost per life saved is $400,000/20 = $20,000 for the ambulance service. It is $1,200,000/40 = $30,000 for the highway program.

Based on these average measures, its seems strange that the ambulance budget is being cut and the highway budget expanded.

However, the real issue is the impact on lives saved from budget changes at the margin. Perhaps, the ambulance budget has a lot of administrative “fat” in it. It could be cut by 40% with very little impact on lives. By the same token, a modest budget increase for highways might have a large impact on additional lives saved. In short, the average cost per life may not tell the real story.

g.

According to the counts of pros and cons, the individual prefers: Home over Beach, Beach over Mountains, but Mountains over Home. We have a cycle (i.e. intransitive preferences). The individual is left going around in circles. The obvious way out of this dilemma is to “score” each alternative by weighting the individual attributes. The more important the attribute the greater the weight. In addition, the individual could use a broader scale (1 John Wiley & Sons

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to 10) for each attribute as a way of measuring relative strength of preferences between alternatives. (For a related example, see Problem 4.4. In this context, the instructor may also wish to discuss voting cycles and the Condorcet paradox). h.

Compared to these extreme outcomes (abject surrender or fighting multiple open-ended wars against terrorism) any option looks good.

This is hardly an even-handed portrayal. The real question is whether adopting “Big Brother” policies to identify and stop potential terrorists is better than other relevant alternatives.

Discussion Question The six listed options for the Kendall School range from the status quo to the most radical option of razing the building and selling off the land.

Options d, e, and f mean that the town will no longer own and control the site. The best option for the town depends both on economics and the town's particular objectives. A purely economic objective might mean maximizing the sum of money the town receives for the school and land. Whether option d, e, or f is most profitable depends on whether the site is worth more after conversion to condominiums or sold as open land. One approach is for the planning board to make its own economic assessment and act accordingly. (For this task, it would need economic data on current land values, condominium prices, construction costs, and so on. It would also need to forecast future values, costs, and prices to decide whether it's better to sell now or later.) A different approach is to ask for competitive bids from the private sector.

Presumably, the highest bid reflects the maximum-value use of the land.

The board may also have non-economic objectives in mind: promoting the arts, maintaining open land in the town, retaining the option to use the space for its own purposes. Options a, b, and c address some of these objectives. But before adopting one of these options, the town would be well-advised to assess its opportunity cost -- the income it might be giving up by rejecting a more profitable alternative. Then they can decide if pursuing these non-monetary objectives is worth the cost.

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CHAPTER TWO OPTIMAL DECISIONS USING MARGINAL ANALYSIS

OBJECTIVES 1.

To introduce the basic economic model of the firm (pp. 29-30) - The main focus is on determining the firm’s profit-maximizing level of output.

- The main assumption is that there is a single product (or multiple, independent products) with deterministic demand and cost.

2.

To depict the behavior of price, revenue, cost, and profit as output varies. (pp. 31-36)

3.

To explain the notion of marginal profit (including its relationship to calculus) and show that maximum profit occurs at an output such that marginal profit equal zero. (pp. 36-40)

4.

To reinterpret the optimality condition in terms of the basic components, marginal revenue and marginal cost. (pp. 40-45)

5.

To illustrate the uses of sensitivity analysis (pp. 46-49)

TEACHING SUGGESTIONS I. Introduction and Motivation A. This is a “nuts and bolts” chapter. Because it appears up front in the text, it’s important to explain the motivation and assumptions. It is a good idea to remind students of the following points.

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1)

The model of the firm is deliberately simplified so that its logic is laid bare. Many additional complications will be supplied in later chapters.

The key simplifications for now are: • The model is of a generic firm. Although microchips are chosen to make the discussion concrete, there is no description of the kind of market or the nature of competition within it. The description and analysis of different market structures comes in Chapters 7 through 10.

• Profit is the sole goal of the firm; price and output are the sole decision variables.

• The description of demand and cost is as “bare bones” as it gets. The demand curve and cost function are taken as given. (How the firm might estimate these are studied in Chapters 4 through 6.)

B.

In general, our policy is to use extended decision examples, different than the ones in the text, to illustrate the most important concepts.

(Going over the same examples pushes the boredom envelope.) In the present chapter, we make an exception to this rule. It is important to make sure that students with different economic and quantitative backgrounds all get off roughly on the same foot. Reviewing a familiar example (microchips) makes this much easier.

II.

Teaching the “Nuts and Bolts”

A. Graphic Overview. The text presents the revenue, cost, and profit functions in three equivalent forms: in tables, in graphs, and in equations. In our view, the best way to convey the logic of the relationships is via graphs. (The student who craves actual numbers can get plenty of them in the text tables.) Here is one strategy for teaching the nuts and bolts:

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1.

Using the microchip example, depict the demand curve, briefly note its properties and demand equation (in both forms).

2.

Next focus on revenue, noting the tradeoff between price and quantity.

Present and justify the revenue equation. Graph it and note its properties.

3.

Repeat the same process with the cost function (reminding students about fixed versus variable cost). At this point, your blackboard graph should be a copy of Figure 2.8 (p. 44). Steps 1-3 should take no more than 20 minutes.

4.

Since the gap between the revenue and cost curves measures profit, one could find the optimal output by carefully measuring the maximum gap (perhaps using calipers). Emphasize that marginal analysis provides a much easier and more insightful approach. Point out the economic meaning of marginal cost and marginal revenue. Note that they are the slopes of the respective curves.

5.

Next argue (as on p. 45) that the profit gap increases (with additional output) when MR > MC but narrows when MR < MC. (On the graph, select quantities that are too great or too small to make the point.)

Identify Q* where the tangent to the revenue curve is parallel to the slope of the cost function. In short, optimal output occurs where MR = MC.

B.

Other Topics. The approach in part A provides a simple way of conveying the basic logic of marginal analysis using the components of MR and MC. Once this ground is covered, the instructor should emphasize other basic points:

1.

2.

3.

4.

The equivalence between M = 0 and MR = MC. Calculus derivations of M, MR, and MC. The exact numerical solution for the microchip example.

The graphs of MR and MC and an exploration of comparative statics effects (shifts in the curves) and the effects on Q*.

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C.

Applications. Besides the applications in the text (pp. 45-49), the following problems are recommended: Problem 1 (a quick but important check), Problems 6, 7 and 9 (numerical applications), Problem 13 (the general solution), and Problem 14. (If the class has a good grasp of this last problem, nothing else will seem difficult.) The following question gets students thinking:

1. a. For five years, an oil drilling company has profitably operated in the state of Alaska (the only place it operates). Last year, the state legislature instituted a flat annual tax of $100,000 on any company extracting oil (or natural gas) in Alaska. How would this tax affect the amount of oil the company extracts? Explain. b. Suppose instead that the state imposes a well-head tax, let’s say a tax of $10.00 on each barrel of oil extracted. Answer the questions of part a. c. Finally, suppose that the state levies a proportional income tax (say 10% of net income). Answer the questions of part a. What would be the effect of a progressive tax? d. Now suppose that the company has a limited number of drilling rigs extracting oil at Alaskan sites and at other sites in the United States.

What would be the effect on the company’s oil output in Alaska if the state levied a proportional income tax as in part c?

Answer. a.

This tax acts as a fixed cost. As long as it remains profitable to produce in Alaska, the tax has no effect on the firm’s optimal output.

b.

The well-head tax increases the marginal cost of extraction by $10.00 per barrel. The upward shift in MC means the new intersection of MR and MC occurs at a lower optimal level of output.

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c.

The income tax (either proportional or progressive) has no effect on the company’s optimal output. For instance, suppose that the company’s after-tax income is  = .9(R-C) under a 10% proportional tax. To maximize its after-tax income, the best the company can do is to continue to maximize its before-tax income. Another way of seeing this is to note that the tax causes a 10% downward shift in the firm’s MR and MC curves. With the matching shift, the new intersection of MR and MC is at the same optimal quantity as the old intersection.

d.

When the firm operates in multiple states with limited drilling rigs, using a rig in Alaska means less oil is pumped (and lower profit is earned) somewhere else. There is an opportunity cost to Alaskan drilling. Thus, one can argue that before the tax, the company should have allocated rigs so as to equate marginal profits in the different states. With the tax, the marginal profit in Alaska is reduced, prompting the possible switch of rigs from Alaska to other (higher marginal profit) locations.

D. Mini-case: Apple Computer in the Mid-1990s The mini-case reproduced on the next page provides a hands-on application of profit maximization and marginal analysis.

Answer a. Clearly, the period 1994-1995 was marked by a significant adverse shift in demand against Apple due to major enhancements of competing computers: lower prices, better interfaces (Windows), sales to order (Dell), and more abundant software. b. Setting MR = MC implies 4,500 - .3Q = 1,500, so Q* = 10,000 units and P = $3,000. Given 1994’s state of demand, Apple’s 1994 production strategy was indeed optimal. c. In 1995, demand and MR have declined significantly. Now, setting MR = MC implies 3,900 - .3Q = 1,350, so Q* = 8,500 units and P = $2,625. Apple should cut its price and its planned output.

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Apple Computer in the Mid 90s

Between 1991 and 1994, Apple Computer engaged in a holding action in the desktop market dominated by PCs using Intel chips and running Microsoft’s operating system.1 In 1994, Apple’s flagship model, the Power Mac, sold roughly 10,000 units per month at an average price of $3,000 per unit. At the time, Apple claimed about a 9% market share of the desktop market (down from greater than 15% in the 1980s).

By the end of 1995, Apple had witnessed a dramatic shift in the competitive environment.

In the preceding 18 months, Intel had cut the prices of its top-performing Pentium chip by some 40%. Consequently, Apple’s two largest competitors, Compaq and IBM, reduced average PC prices by 15%. Mail-order retailer Dell continued to gain market share via aggressive pricing. At the same time, Microsoft introduced Windows 95, finally offering the PC world the look and feel of the Mac interface. Many software developers began producing applications only for the Windows operating system or delaying development of Macintosh applications until months after Windows versions had been shipped.

Overall, fewer users were switching from PCs to Macs.

Apple’s top managers grappled with the appropriate pricing response to these competitive events. Driven by the speedy new PowerPC chip, the Power Mac offered capabilities and a user-interface that compared favorably to those of PCs. Analysts expected that Apple could stay competitive by matching its rivals’ price cuts. However, John Sculley, Apple’s CEO, was adamant about retaining a 50% gross profit margin and maintaining premium prices. He was confident that Apple would remain strong in key market segments – the home PC market, the education market, and desktop publishing.

Questions.

1. What effect (if any) did the events of 1995 have on the demand curve for Power Macs?

Should Apple preserve its profit margins or instead cut prices?

2. a) In 1994, the marginal cost of producing the Power Mac was about $1,500 per unit, and a rough estimate of the monthly demand curve was: P = 4,500 - .15Q. At the time, what was Apple’s optimal output and pricing policy? b) By the end of 1995, some analysts estimated that the Power Mac’s user value (relative to rival PCs) had fallen by as much as $600 per unit. What does this mean for Apple’s new demand curve at end-of-year 1995? How much would sales fall if Apple held to its 1994 price? Assuming a marginal cost reduction to $1,350 per unit, what output and price policy should Apple now adopt?

1 This account is based on J. Carlton, “Apple’s Choice: Preserve Profits or Cut Prices,”

The Wall Street Journal, February 22, 1996, p. B1.

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ADDITIONAL MATERIALS

I.

Readings

R. Chittum, “Price Points,” The Wall Street Journal, October 30, 2006, p.

R7. (How providers of consumer services compare extra revenues and extra costs.)

S. Waxman, “ ‘Crash’ Principals Still Await Payments for their Work,” The New York Times, July 25, 2006, pp. B1, B8.

C. Oggier and E, Fragniere, and J. Stuby, “Nestle Improves its Financial Reporting with Management Science,” Interfaces, July-August, 2005, pp.

271-280.

J. Thomas, W. Reinartz, and V. Kumar, “Getting the Most out of your Customers,” Harvard Business Review, July-August, 2004, pp. 117-123.

A. M. Geoffrion and R. Krishnan, “Prospects for Operations Research in the E-Business Era,” Interfaces, March-April, 2001, pp. 6-36.

R. Fourer and J. P. Goux, “Optimization as an Internet Resource,” Interfaces, March-April, 2001, pp. 130-150.

D. Ekwurzel and J. McMillan, “Economics Online,” Journal of Economic Literature, March 2001, pp. 7-10.

“Economics on the Net,” The Economist, March 13, 1999, p. 7.

W. Biddle, “Skeleton Alleged in the Stealth Bomber’s Closet,” Science, May 12, 1989.

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II.

Case

Colgate-Palmolive Co.: The Precision Toothbrush (9-593-064), Harvard Business School, 1993. Teaching Note (5-595-025). (Explores profit analyses of alternative launch strategies.)

III. Quips and Quotes Small mistakes are the stepping stones to large failures.

There was an old saying about our small town. Our town’s population never changed. Every time a baby was born a man left town. (Does this say something about the balance of marginal changes at an optimum?)

The head of a small commuter plane service reported that as costs rose, the company’s breakeven point rose from 6 to 8 to 11 passengers. “I finally figured we were in trouble since our planes only have 9 seats.”

Quotes about economics in general: If you laid all of the economists in the world end to end, they still wouldn’t reach a conclusion. (George Bernard Shaw) An economist is a person who is very good with numbers but who lacks the personality to be an accountant.

The age of chivalry is gone; that of sophisters, economists, and calculators has succeeded. (Edmund Burke) Please find me a one-armed economist so we will not always hear, “On the other hand . . .” (Herbert Hoover)

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2.

The revenue function is R = 170Q - 20Q2. Maximizing revenue means setting marginal revenue equal to zero. Marginal revenue is: MR = dR/dQ = 170 - 40Q. Setting 170 - 40Q = 0 implies Q = 4.25 lots. By contrast, profit is maximized by expanding output only to Q = 3.3 lots. Although the firm can increase its revenue by expanding output from 3.3 to 4.5 lots, it sacrifices profit by doing so (since the extra revenue gained falls short of the extra cost incurred.)

4. a.  = PQ - C = (120 - .5Q)Q - (420 + 60Q + Q2) = -420 + 60Q - 1.5Q2.

M = d /dQ = 60 - 3Q = 0 Solving yields Q* = 20 units.

Revenue = PQ = (120 - .5Q)Q = 120Q - .5Q2; MR = 120 - Q Cost = -420 + 60Q + Q2; therefore, MC = 60 + 2Q Equating marginal revenue and marginal cost yields: 120 - Q = 60 + 2Q, or Q* = 20 units. b. Here, R = 120Q; it follows that MR = 120 Equating marginal revenue and marginal cost yields 120 = 60 + 2Q or Q* = 30 units.

6. a. If videos are given away (P = $0), demand is predicted to be: Q = 1600 - (200)(0) = 1,600. At this output, firm A’s cost is: 1,200 + (2)(1,600) =$4,400, and firm B’s cost is: (4)(1,600) = $6,400. Firm A is the cheaper option and should be chosen. (In fact, firm A is cheaper as long as Q > 600.)

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b. To maximize profit, we simply set MR = MC for each supplier and compare the maximum profit attainable from each. We know that MR = 8 - Q/100 and the marginal costs are MCA = 2 and MCB = 4.

Thus, for firm A, we find: 8 - QA/100 = 2, and so QA = 600 and PA = $5 (from the price equation). For firm B, we find that Q B = 400 and PB = $6. The station’s profit is: 3,000 - [1,200 + (2)(600)] = $600 with firm A. Its profit is 2,400 - 1,600 = $800 with firm B. Thus, an order of 400 videos from firm B (priced at $6 each) is optimal.

8. a. First note that if marginal cost and marginal benefit to consumers both increased by $25, the optimal output would not change since MR(Q*) = MC(Q*) and MR(Q*) + 25 = MC(Q*) + 25 are equivalent. The price would rise by $25 but, since marginal costs rise by $25, the firm’s total profits would remain the same. If marginal costs rose by more than $25, profits would fall. Thus the firm should not redesign if the increase in MC is $30. b. If MC increases by $15 and MR increases by $25, the MR shift is greater than the MC shift and the new intersection of the curves occurs at a higher output. Output and price would both rise. Price, however, would rise by less than $25.

10.

The latter view is correct. The additional post-sale revenues increase MR, effectively shifting the MR curve up and to the right.

The new intersection of MR and MC occurs at a higher output, which, in turn, implies a cut in price. (Of course, one must discount the additional profit from service and supplies to take into account the time value of money.)

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12. a. The MC per passenger is $20. Setting MR = MC, we find 120 - .2Q = 20, so Q = 500 passengers (carried by 5 planes). The fare is $70 and the airline’s weekly profit is $35,000 - 10,000 = $25,000. b. If it carries the freight, the airline can fly only 4 passenger flights, or 400 passengers. At this lower volume of traffic, it can raise its ticket price to P = $80. Its total revenue is (80)(400) + 4,000 = $36,000. Since this is greater than its previous revenue ($35,000) and its costs are the same, the airline should sign the freight deal. *14.

The Burger Queen (BQ) facts are P = 3 - Q/800 and MC = .80. a. Set MR = 0 to find BQ’s revenue-maximizing Q and P. Thus, we have 3 - Q/400 = 0, so Q = 1,200 and P = $1.50. Total revenue is $1,800 and BQ’s share is 20% or $360. The franchise’s revenue is $1,440, its costs are (.8)(1200) = $960, so its profit is $480. b. The franchise maximizes profit by setting MR = MC. Note that the relevant MR is (.8)(3 - Q/400) = 2.4 - Q/500. After setting MR = .8, we find Q = 800. In turn, P = $2.00 and the parties’ total profit is (2.00 - .80)(800) = $960, which is considerably larger than $840, the total profit in part a. c. Regardless of the exact split, both parties have an interest in maximizing total profit, and this is done by setting (full) MR equal to MC. Thus, we have 3 - Q/400 = .80, so that Q = 880. In turn P = $1.90, and total profit is (1.90 - .80)(880) = $968. d. The chief disadvantage of profit sharing is that it is difficult, timeconsuming, and expensive for the parent company to monitor the reported profits of the numerous franchises. Revenue is relatively easy to check (from the cash register receipts) but costs are another matter. Individual franchises have an incentive to exaggerate the costs they report in order to lower the measured profits from which the parent’s split is determined. The difficulty in monitoring cost and profit is the main strike against profit sharing.

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Discussion Question Suppose the firm considers expanding its direct sales force from 20 to, say 23 sales people. Clearly, the firm should be able to estimate the marginal cost of the typical additional sales person (wages plus fringe benefits plus support costs including company vehicle). The additional net profit generated by an additional sales person is a little more difficult to predict.

An estimate might be based on the average profitability of its current sales force. A more detailed estimate might judge how many new client contacts a salesperson makes, historically what fraction of these contacts result in new business, what is the average profit of these new accounts, and so on. If the marginal profit of a sales person is estimated to be between $100,000 and $120,000 while the marginal cost is $85,000, then the firm has a clear-cut course of action, namely hire the additional 1, 2, or 3 employees.

ANSWERS TO SPREADSHEET PROBLEMS (You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1. a and b. Setting MR = MC implies: 800 – 4Q = 200 + Q. Therefore, Q* = 120 and P* = 560. c. Confirm these values on your spreadsheet by maximizing cell F7 by changing cell B7. Maximum profit in cell F7 is 16,000.

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S2. a. Given  = 20[A/(A+8)] –A, it follows that M = 20[8/(A+8)2] – 1.

Setting M = 0 implies (A+8)2 = 160, or A* = $4.649 million. b. Confirm this value on your spreadsheet by maximizing cell F7 by changing cell C7. Maximum profit in F7 is $2.702 million.

Additional Spreadsheet Problem The accompanying spreadsheet lists the compass positions of the eight coastal cities of Figure 2.1 and the possible position of the shopping mall.

By convention, the city positions are expressed in (x, y) coordinates. All cities are positioned “east-west” along the x-axis. Town A has coordinates (0, 0); Town B is located 3 miles due east, at coordinates (3, 0), and so on.

The shopping mall is tentatively located at (5.5, 0), i.e. a mile west of Town C (corresponding to position X in Figure 2.1.)

In the spreadsheet, column M lists the population of shoppers in each of the towns, while column Q computes the distance between the mall and the various towns. For example, cell Q7 contains the distance formula =((I7-D$7)^2 + (J7-E$7)^2)^.5, that is, distance is the square root of the sum of squared differences of the x and y coordinates. Finally, cell E11 computes the total travel miles associated with the mall’s location. a. By trial and error, vary the mall’s east-west location (cell D7) to minimize total travel miles. Use your spreadsheet’s optimizer to confirm the optimal location. b. More realistically, suppose the towns are scattered north-south as well as east-west. Set the y coordinates of towns B, C, E, F, and H to 11, 7.5, 15, 12, and 8, respectively. Answer again the questions in part a. c. Column U provides estimates of the fraction of each town’s shopping population that will actually frequent the mall. This fraction varies inversely with the square of the distance to the mall: F = 1 - d2/500.

Accordingly, the mall attracts 100% of the 10 thousand shoppers from nearby Town C but only 46% of the 15 thousand shoppers from Town H. Cell E14 lists the total number of mall visitors from all towns. (Be sure to check this formula.)

By trial and error and using your spreadsheet’s optimizer, find the mall location that maximizes total visitors (and thus revenue) for the town locations of part a and part b.

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A

B

C

D

E

F

G

H

I

J

K L

M

N O P

Q

R

S

T

U

V

1 2

Locating a Shopping Mall

3 4

Location

5

(x , y)

Towns

Location

Population

Distance

Fraction who

(x , y)

of Shoppers

from Mall

Visit Mall

6 7

Mall

5.5

0

A

0.0

0

15

5.50

0.94

B

3.0

0

10

2.50

0.99

C

6.5

0

10

1.00

1.00

D

8.5

0

10

3.00

0.98

E

11.0

0

5

5.50

0.94

F

15.5

0

20

10.0

0.80

G

17.5

0

10

12.0

0.71

H

22.0

0

15

16.5

0.46

8 9 10 11

Total Travel Miles:

742.5

12 13 14 15

Total Visitors:

78.4

16 17 18 19 20 21 22

Answer a. Using trial and error or the spreadsheet optimizer, we confirm that the optimal location for the mall is Town E, at coordinates (11, 0). b. Using the spreadsheet optimizer, we now find the optimal mall location to be (11.14, 7.3). c. Now the number of visitors varies with the square of the distance to the mall. Using the spreadsheet optimizer, our goal is to find the location that maximizes cell E14. For coastal cities, the optimal location is (11.05, 0). This is the mean of the one-dimensional distribution. For cities scattered north-west and east-south the optimal location is (11.05, 6.5).

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ANSWERS TO APPENDIX PROBLEMS 1.

When tax rates become very high, individuals will make great efforts to shield their income from taxes. Furthermore, higher taxes will discourage the taxed activities altogether. (In the extreme case of a 100% tax, there is no point in undertaking income-generating activities.) Thus, a higher tax rate mean a smaller tax base.

Increasing the tax rate from zero, the revenue curve first increases, eventually peaks, and then falls to zero (at a 100% tax). Thus, the curve is shaped like an upside-down U.

2. a. B(t) = 80 - 100t. Therefore, R = 80t - 100t2. Setting MR = dR/dt = 0, we find: 80 - 200t = 0, or t = .4. b. B(t) = 80 - 240t2. Therefore, R = 80t - 240t3. Setting MR = dR/dt = 0, we find: 80 - 720t2 = 0. Therefore, t2 = 1/9, or t = 1/3. c. B(t) = 80 - 80t.5. Therefore, R = 80t - 80t1.5. Setting MR = dR/dt = 0, we find: 80 - 120t.5 = 0. Thus, t.5 = 2/3, or t = 4/9.

3. a.  = 20x - x2 + 16y - 2y2. Setting d/dx = 0 and d/dy = 0 implies x = 10 and y = 4. b. The Lagrangian is L =  + z(8 - x - y). Therefore, the optimality conditions are: 20 - 2x - z = 0, 16 - 4y - z = 0, and x + y = 8. The solution is x = 6, y = 2, and z = 8. c. The Lagrangian is L =  + z(7.5 - x - .5y). Therefore, the optimality conditions are: 20 - 2x - z = 0, 16 - 4y - .5z = 0, and x + .5y = 7.5.

The solution is x = 6, y = 3, and z = 8.

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CHAPTER THREE DEMAND ANALYSIS AND OPTIMAL PRICING

OBJECTIVES 1. To take a closer quantitative look at demand starting with a multi-variable demand equation and continuing with a verbal description. (pp. 75-80) 2. To present the price elasticity of demand (pp. 80-85), other elasticities (pp. 85-88), and show how elasticities can be used to predict sales: Q/Q = EP(P/P) + EY(Y/Y) + . . .

3. To show the relationship between price elasticity and revenue changes i.e. marginal revenue. Maximum revenue occurs at EP = -1 or MR = 0. (pp.

88-93).

4. To demonstrate how the firm can maximize its profit by using optimal markup pricing and price discrimination. (pp. 93-100) 5. To examine the demand and pricing of information goods (pp. 101-104).

TEACHING SUGGESTIONS I. Introduction and Motivation A good teaching strategy is to introduce demand analysis by means of a realworld business application. Here is one example:

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A. Pricing Software. Consider a firm that produces a best-selling software program. The firm continues to spend a great deal of money revising and improving its software in an effort to maintain its market share lead over its next two or three strongest competitors. In fact, its last revision and update cost much more than the company expected. In light of these added development costs and any other relevant factors, how should top management determine its pricing policy for the updated program?

B. Pricing Software, Discussion. Based on intuition, many students offer pricing recommendations based on shaky logic. This deliberately “leading” question prompts the following student reasoning “Since development costs were higher than expected, the firm should increase the unit price of its software to help cover these costs.” Besides being incorrect, this reasoning misses the main point. The firm’s optimal pricing policy depends on how sensitive demand is to price changes -- in other words on the elasticity of demand. Because development costs are fixed (indeed largely sunk), they do not affect the pricing decision. Since the marginal cost of producing an extra copy of the software is trivial, the firm’s problem is essentially pricing to maximize revenue. Thus, the price and performance characteristics of competing spreadsheet software are extremely important factors affecting demand elasticity.

II. Teaching the “Nuts and Bolts” A. Teaching Approaches. As designed, the chapter combines two important topics: demand analysis and pricing decisions. This suggests two teaching approaches: 1. Teaching them together, or 2. Teaching demand analysis alone and postponing the discussion of pricing until after a discussion of monopoly. Though the second option is the traditional approach, we obviously favor the first method. In either case, the following “tried and true” points merit emphasis:

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1. The difference between a movement along a demand curve and a shift in the curve. Many instructors even make a distinction in terminology between “increased demand” and “an increase in demand.”

2. The definition and computation of price elasticity. The text’s presentation focuses on point elasticities (either discrete or continuous). The instructor may choose to extend the discussion to arc elasticities. Another option we recommend is to present actual elasticity estimates.

3. How elasticity varies along a linear demand curve and the relationship between elasticity and marginal revenue. If only demand analysis is covered, these points make a natural bridge into the empirical analysis of demand covered in Chapter 4. (The instructor may also wish to assign the appendix to Chapter 3.)

In turn, the discussion of pricing decisions emphasizes the following points: 1. Maximizing revenue in pure selling problems. (The instructor should continually emphasize that this is a special case of the general rule: MR = MC. Otherwise, the occasional student may mistakenly start to take MR = 0 as the monopolist’s optimal rule even when marginal costs are significant.)

2. The logic and application of the optimal markup rule. (Reemphasize that the firm’s current price cannot be optimal if demand is inelastic.

Thus, the markup rule does not apply for inelastic demand. Rather it tells the manager how high to push the price into the region of elastic demand.)

3. The logic and application of price discrimination.

B. Suggested Examples: Problems 4, 5, 6, 8, and 13.

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ADDITIONAL MATERIALS

I. Short Readings “The Irrationality of Product Pricing,” The Wall Street Journal, September 22, 2008, p. R2 T. Aeppel, “Seeking Perfect Prices, CEO Tears up the Rules,” The Wall Street Journal, March 27, 2007, pp. A1, A16 G. Anders, “In a Tech Backwater, A Profit Fortress Rises,” The Wall Street Journal, July 10, 2007, pp. A1, A19 The following articles provide examples of market segmentation and price discrimination.

J. Bailey, “Armed with Internet Bargains, Travelers Battle High Airfares,” The New York Times, November 23, 2006, p. A1.

D. Leonhardt, “Changes Ahead for a Theater Near You,” The New York Times, February 15, 2006, pp. C1, C15.

Hal R. Varian, “When it Comes to Complexity in Putting a Price on a Seat, Broadway Rivals the Airlines,” The New York Times, January 13, 2005, p.

C2.

T. Lewin, “Students Find $100 Textbooks Cost $50, Purchased Overseas,” The New York Times, October 21, 2003, pp. A1, A16.

J. Morell, “How Much for Tickets? You Need a Scorecard,” The New York Times, June 8, 2003, p. BU4.

“A Big Factor in Prescription Drug Pricing: Location, Location, Location,” The New York Times, September 21, 2000, p. C2.

J. Kronholz, “On Sale Now: College Tuition,” The Wall Street Journal, May 16, 2002, pp. D1, D6.

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D. Leonhardt, “Tiptoeing Toward Variable Pricing,” The New York Times, May 12, 2002, p. BU4.

“The Price is Wrong,” The Economist, May 25, 2002, p. 59.

“Things that Every Economist Takes for Granted Could Help a Lot of People Avoid Some Costly Mistakes,” The New York Times, January 3, 2002, p. C2.

“Apple, Digital Music’s Angel, Earns Record Industry’s Scorn,” The New York Times, August 27, 2005, p. A1.

“DVD Gains on Tape, But Economics have Hollywood in a Tizzy,” The Wall Street Journal, February 5, 2002, pp. A1, A6.

“Increased Spending on Drug is Linked to More Advertising,” The New York Times, November 21, 2001, p. C1.

“How Dell Fine-Tunes its PC Pricing to Gain Edge in a Slow Market,” The Wall Street Journal, June 8, 2001, p. A1.

“Second Chance for Aspirin is also One for Bayer,” The New York Times, August 9, 1997, p. 27. (Aspirin’s health benefit shifts the demand curve.)

“Apple Computer’s Choice: Preserve Profits or Cut Prices,” The Wall Street Journal, February 22, 1995, p. B1. (How should Apple respond to adverse shifts in demand?)

“Pennies that Add up to $16.98: Why CD’s Cost so Much,” The New York Times, July 5, 1995, p. C11. (This article illustrates: 1) demand-based pricing when MC is close to zero and 2) how stores determine retail prices by marking up the wholesale price they pay.)

“Retailers Try to Get Leg Up on Markdowns with New Software,” The Wall Street Journal, August 7, 2001, p. A1.

“Even in Good Times, Airlines Depend on a Hairline Balancing of Supply and Demand,” The New York Times, October 11, 2001, p. C2.

“So How Much Did You Pay for Your Ticket?” The New York Times, April 12, 1998, p. WK2.

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II.

Longer Readings

R. Metters et al, “The ‘Killer Application’ of Revenue Management: Harrah’s Cherokee Casino and Hotel, Interfaces, Vol. 38, May-June 2008, pp. 161-175.

C. Meyerhoefer and S. Zuvekas, “The Shape of Demand: What does it Tell Us about Direct-to-Consumer Marketing of Antidepressants?” The B.E. Journal of Economic Analysis and Policy, Vol 8, Issue 2 (Advances), 2008.

M. Connolly and A. Krueger, “Rockonomics: The Economics of Popular Music, in V.A. Ginsburgh & D. Throsby (ed.), Handbook of the Economics of Art and Culture, Elsevier Publishing, 2006, N. Economides, and V. B. Viard, “Pricing of Complementary Goods and Network Effects,” Research Paper, Stanford Graduate School of Business, June 2003.

W. Baker, M. Marn, and C. Zawada, “Pricing Smarter on the Net,” Harvard Business Review, February 2001. (Reprint R0102J) L. F. Ditt et al, “Pricing Strategy and the Net,” Business Horizons, MarchApril 2001. (Reprint BH059) R. Oberwetter, “Building Blockbuster Business,” OR/MS Today, June, 2001, pp. 40-44. (This article discusses revenue management by movie theaters.)

T. Jacobs, R. M. Ratliff, and B. C. Smith, “Soaring with Synchronized Systems,” OR/MS Today, August 2000, pp. 36-44. (This article discusses airline yield management.)

R. J. Dolan, “How do you Know when the Price is Right?” Harvard Business Review, Sept.-Oct. 1995, p.174.

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J. C. Hagarty and G. Russell, “Estimating Elasticities with PIMS Data: Methodological Issues and Substantive Implications,” Journal of Marketing Research, 1988, pp. 1-9.

R. Dorfman and P. O. Steiner, “Optimal Advertising and Optimal Quality,” American Economic Review, 1954, pp. 826-836.

III.

Cases

Virgin Mobile USA: Pricing for the very First Time (9-504-028), Harvard Business School, 2004.

Coca-Cola’s New Vending Machine (A) (9-500-068), Harvard Business School, 2000. Teaching Note (5-501-086).

Biopure Corporation (9-598-150), Harvard Business School, 1999, Teaching Note (5-599-094) Precision Pricing for Profit in the New World Order (9-999-003), Harvard Business School, 1998.

DHL Worldwide Express (9-593-011), Harvard Business School, 1997.

Teaching Note (5-594-094). (This is an excellent “pricing” case.)

American Airlines: Revenue Management (9-190-029), Harvard Business School, 1993, Teaching Note (5-190-192) IV.

Quips and Quotes

The universal law of hierarchical organizations: Rank x IQ = constant.

Can one desire too much of a good thing? (William Shakespeare) Because I cannot afford to buy a thing it does not follow that I have less need of it or less desire to have it than another man who can and does afford it. (Philip H. Wicksteed) John Wiley & Sons

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2. a. Q = 180 - (1.5)(80) = 60 pairs. R = P.Q = $4,800. b. At P=$100 and Q=30 pairs revenue falls to $3000 per month. c. EP =(dQ/dP)(P/Q). At P = $80, EP = (-1.5)(80/60) = -2; At P = $100, EP = (-1.5)(100/30) = -5.

Demand is much more elastic at the higher price.

4. a. This means that if the local population increases by 10 percent, ticket sales will increase by (.7)(10) = 7 percent. The actual population increase of 2.5 percent implies a sales increase of 1.75 percent. b. The 10 percent increase in ticket price implies a (.6)(10) = 6 percent fall in ticket sales. Because demand is inelastic, total ticket revenue increases. c. Here, the increase in total revenue per admission (from $18 to $19) is only 5.55 percent. This is outweighed by the decline in admissions (6 percent) causing total revenue to fall.

6. a. During this period, Mac computers, although technologically superior, were priced out of the range of many consumers. As a result of vigorous competition in the IBM PC clone market, prices of IBM PC clones were significantly lower and soon these clones dominated the market. As a result of network externalities (the phenomenon in which it is beneficial to have the same computer platform as everyone else) the Mac rapidly lost market share.

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b. Using the markup rule, we can see that with a price elasticity of -4 the profit-maximizing markup is 25%. And note that this only reflects short-term profit maximization. An even smaller markup may be optimal when one considers long-run demand. Thus the 50% markup goal was unrealistic and far from profit maximizing. c. It does make sense to concentrate in niche markets where demand may be less elastic and Apple already has significant market share.

Likewise, software (and even hardware) that make Apple compatible with PCs will help break the network externalities enjoyed by PCs and encourage consumers to buy Macs. However, since network externalities continue to exist even with these innovations, it may not be prudent to abandon the low end of the market. Indeed, the introduction of the iMac indicates that Apple has not given up on the consumer market.

8.

The key point here is that the optimal prices in summer and winter depend upon the relative elasticities. Higher winter prices are warranted as long as winter demand is more inelastic. There is no contradiction between more inelastic winter demand and a lower occupancy rate. For instance, it is likely that the overall volume of tourist traffic is lower in the winter (fewer people take extended vacations and this accounts for the lower occupancy rate) but also less price sensitive (skiing is for the relatively wealthy).

10.

If a firm can identify market segments with different elasticities, it can profit by charging different prices (even though marginal costs are the same.) It can set the price in each segment according to the optimal markup rule. The existence of substitute products should make demand for the firm’s product more elastic. Accordingly, the firm should reduce its markup.

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12. a. Frequent flier and frequent stay programs are primarily designed to induce strong allegiances and repeat business. It is also a subtle way of offering discounts (selectively) to enrollees (presumably, the most price sensitive customers). b. Discount coupons deliver lower prices to the most price sensitive consumers, while the average consumer pays the regular, full price. c. A guarantee to match a lower price is a way of winning sales from customers with the most elastic demand (who take the trouble to seek out a lower price), while maintaining higher prices for typical customers.

14. a. Because demand conditions differ, the operator can profit from a policy of price discrimination. She faces a pure selling problem. In order to maximize weekday revenue (and profit), management sets MRd = 36 - .2Qd = 0 implying Qd = 180 and Pd = $18 per round.

On weekends, we have MRw = 50 - Qw/6 = 0 implies Qw =300.

However, Qw = 240 represents full capacity of the golf course. This is the best that the operator can do. The optimal weekend price is PW = $30. b. To deter defections (and preserve revenue), the operator should narrow the price gap: raise weekday prices and lower weekend prices slightly.

Discussion Question a. With all farmers producing bumper crops (10% greater output), price is driven down. If market demand for the crop is inelastic, the percentage fall in price will be greater than the increase in output, causing total farm revenue to fall!

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b. Suppose that average court costs per case fall. One effect will be that more cases are brought to court. If the percentage increase in cases brought exceeds the percentage fall in cost per case, total court expenditures will increase. c. Here, the adverse feedback effect occurs over time. Other things equal, more numerous boats and the potential to catch more fish per boat would mean greater annual catches. But overfishing can deplete fishing stocks below levels at which they can reproduce themselves. Over time, the result might be a severe drop in the total catch of fish. d. Low-tar and low-nicotine cigarettes (because they might be perceived as “safe”) could actually spur some individuals to smoke or some current smokers to increase their daily number of cigarettes. (On the positive side, some smokers would switch from high-tar to low-tar with the attendant benefits.) The net health effect (pro or con) depends on the overall change in smoking behavior.

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley, Samuelson and Marks Website.)

S1. a. and b. Using the constructed spreadsheet, vary price in cell B7 until the markup rule is satisfied – that is, cells E12 and F12 are equal.

The combination of price and output satisfying the markup rule is P* = 560 and Q* = 120 (the same answer as we found in Problem S1 of Chapter 2 using MR = MC). c. Confirm this solution by using the spreadsheet’s optimizer.

Maximize cell F7 by varying cell B7.

S2. a. and b. Using the spreadsheet, we optimize total revenue by maximizing cell E13 (equivalently E18) by changing cells C9 and D9 subject to E9  E5 (i.e. the number of seats sold must be no greater than the total number available). The optimal solution is Q B = 240 seats, QT = 160 seats. The corresponding prices are PB = $420 and PT = $340, and total revenue is $155,200. At the optimal solution, we see that MRB = MRT (compare cells C14 and D14). c. If the airline sets a single “value fare”, solve the spreadsheet by including the constraint that price cells C11 and D11 must be equal.

The solution is QB = 347 seats, QT = 53 seats. The common price is $367, and total revenue falls to $146,667.

S3. a. The MC per seat is $20,000 per plane divided by 200 seats per plane, or $100. Setting MRB = MRT = 100, we have 540 – QB = 100 and 380 - .5QT = 100 implying QB = 440 seats, and QT = 560 seats. The corresponding prices are PB = $320 and PT = $240. To supply total demand of 1000 seats requires 1000/200 = 5 flights.

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b. and c. It is straightforward to confirm the algebraic solution using the spreadsheet. Invoking the optimizer, maximize total profit in cell E18 by changing cells C9, D9, and E2, subject to E9  E5.

ANSWERS TO APPENDIX PROBLEMS 1. a. Steep indifference curves mean that numerous units of Y must be gained to compensate for giving up a unit of X -- that is, the consumer’s marginal value for X is much greater than for Y. b. The optimal bundle (at the new tangency) will consist of numerous units of X and relatively few units of Y. It’s still true that MRS = 2.

2. a. If goods X and Y are both normal, the new optimal bundle will contain more of each good. b. To portray X as an inferior good, draw the new, higher indifference curve as much flatter than the inner curve.

3.

If one pivots the budget line so that PX/PY falls (X becomes cheaper), the new tangency along the same indifference curve must have the individual purchasing more X and less Y. This is usually called the pure “price substitution” effect.

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CHAPTER FOUR ESTIMATING AND FORECASTING DEMAND

OBJECTIVES 1. To introduce the “art and science” of empirical analysis.

2. To examine the sources of data. (pp. 124-127) 3. To give the student an intuitive feel for regression analysis. (pp. 128135) 4. To explain the statistics that are generated by regression analysis. (pp. 135-140) 5. To introduce the student to some of the problems encountered in regression analysis. (pp. 140-144) 6. To analyze time series models. (pp. 144-153) 7. To introduce barometric models. (pp. 153-154) 8. To discuss forecast accuracy and performance. (pp. 155-158)

TEACHING SUGGESTIONS I. Introduction and Motivation In the previous chapters we took demand and cost equations as given. In real life, however, they must be gleaned from experience. This chapter demonstrates some basic techniques for estimating demand. We like to emphasize that empirical work is always both an art and a science. In other John Wiley & Sons

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words, the outcome of a study is determined in part by the design of the study. If the study is poorly designed it will lead to “false” conclusions.

There are (at least) three important considerations in study design. First, the study design is motivated by the purpose to which the results will be put.

Before gathering data it is useful to consider possible outcomes and how they will affect decision making. If the study does not produce information relevant to the decision making process, then the study should be redesigned or abandoned.

Second, it is difficult to gather data without having some hunch about how things are likely to turn out. This hunch can be informed, of course. Theory is, in some sense, a well-thought-out hunch about the way the world works.

Also previous empirical studies can be useful in designing empirical studies.

Third, empirical studies cost money.

The above considerations yield two conclusions: 1) Empirical studies should be carefully designed with the decision making process in mind, and 2) the cost of the study should be compared to the expected benefits to determine whether the study is worth undertaking. (This latter conclusion we study in some detail in Chapter 13, The Value of Information, but a general discussion of costs and benefits of information is useful here.)

In analyzing empirical studies, we feel that, for the purposes of this course, the ultimate goal is not to become an expert in regressions but rather to be skilled in interpreting them. We spend more time on understanding what a regression is and very little time on the formulae for computing the outputs of regression analysis.

Finally, it is important that students approach the results with caution and that they exercise common sense. If the results do not make sense, then they should not be believed. Estimates as to the accuracy of the regression results should be used in performing sensitivity analysis in the underlying problem.

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In our discussion of forecasting, the main focus is on time-series models.

Time-series models have advantages and disadvantages when compared to demand-based models introduced in Chapter 3 and estimated in the earlier sections of Chapter 4. Time series models do not require much ex ante theorizing about economic relationships. On the other hand, they do not provide much information about these relationships.

The result is that time-series models can be quite accurate (even more accurate than structural models) provided that there are no bizarre twists in economic conditions. When unusual events occur that have profound effects on the economy (such as an oil embargo), time series models are often unable to forecast with any accuracy. Structural models, which allow the unusual events to be explicitly incorporated, usually do much better.

Another disadvantage of time series models is they do not account for variables that are under the power of the decision maker. For example, the trend models do not allow the decision maker to ask the question “What would happen if I increase my price?” or “What would happen if I increase advertising expenditures?” Structural models, on the other hand, are designed to answer these questions.

Often, time-series models and structural models are used in conjunction with one another. For example, an estimated demand equation may require information on the explanatory variables: consumer income, price and advertising. Price and advertising are under the control of the decision maker. However, a time-series model may be used to predict consumer income.

II. Teaching the “Nuts and Bolts” Sources of Information (pp. 124-127). In covering this section we like to emphasize the advantages of each technique. It is useful to put each technique on the board and have students call out the various advantages and disadvantages of each.

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Regression Analysis and the Interpretation of Statistics (pp. 128-140).

Here we try to give the student an intuitive feel for the least squares method.

One possibility is to put a scatter diagram on the chalkboard and to ask the students how we might go about finding a line that best fits the points. The distance between each point and the line can be shown and it is not too difficult to convince the student that squaring these distances and adding them is a reasonable (though not the only conceivable) way of measuring fit.

One way of explaining degrees of freedom is to use a diagram. With two data points one can estimate a line. However, it is impossible to tell how well this line fits the true underlying relationship. With three data points we can not only fit a line but also determine something about the distribution around the line. That is, with three data points we have a degree of freedom beyond what we need to determine a line. The more degrees of freedom we have the more we can determine about the distribution.

R2 is quite intuitive for most students. Its main shortcoming can be emphasized by exploring what happens when explanatory variables are added. Ultimately when there are as many explanatory variables (including the constant) as there are data points, then the fit becomes perfect. However, we have lost our degrees of freedom and with them any confidence we have in the specification. That is, adding explanatory variables has a cost in terms of lost degrees of freedom. The adjusted R2 is designed to take this cost into account.

For the F statistic we emphasize that it will have an F distribution if all of the coefficients are zero. Given the assumption that all the coefficients are zero, we can ask how likely it is that we get this value for F. If it is not very likely, then we reject the hypothesis that all of the coefficients are zero.

Potential Problems in Regression (pp. 140-144). We spend some time on what can go wrong in a regression. Our main emphasis is on equation specification and multicollinearity since these are most easily grasped by the student. Equation specification can be shown easily on the chalkboard by presenting a scatter diagram that looks well fitted to a curved demand curve.

Then the assumption of a linear demand curve can be shown. Two points John Wiley & Sons

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can be shown. The specification matters. However, it may not matter that much in many cases.

Likewise it can be shown that omitted variables can bias results. For example, suppose that income was omitted but it was positively correlated with price. Doing a simple regression on price could then show relatively inelastic demand when in fact it was quite elastic. This could lead to a disastrous pricing policy.

Multicollinearity can also be demonstrated fairly easily. Again, the price and income example can be used.

Though we do not spend much time on simultaneity, heteroscedasticity or serial correlation, the instructor may take the opportunity to cover these issues in greater depth.

Simple Time Series Models (The Trend Model). In this section we try to give the student a feel for time series models. The models are very simple and build on regression models. We let our students know that this is only the tip of the iceberg.

Seasonality. This is a refinement of the trend model that indicates how such a model might be complicated to take into account some commonly observed patterns.

Barometric Models. In a way, these are hybrids between structural and time-series models. They are more like time series models, however, in that they do not contain variables over which the decision maker has control.

Students should be encouraged to follow the index of leading indicators reported in the news.

Forecast Accuracy. All forecasting methods provide a point estimate of the forecast. It is equally important, however, to have some idea as to the accuracy of the forecast. More realistically, the forecaster should report a range within which the forecaster is reasonably confident that the outcome will fall. It is then important for the decision maker to do sensitivity analysis John Wiley & Sons

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over all reasonable forecasts. Only then will the manager have some idea whether a planned action is worth the risk.

Econometric Models. Though the text does not cover this important topic, instructors who wish to do so should refer to the short module found on the Samuelson and Marks website.

ADDITIONAL MATERIALS

I. Short Readings K. Yancy “Guests Put their Two Cents into the New Aloft Hotels,” USA Today, July 6, 2007, p. 12D. (Testing a new hotel concept on consumers.)

E. Porter and G. Fabrikant, “A Big Star May Not a Profitable Movie Make,” The New York Times, August 28, 2006.

“Opinions to Spare? Click Here,” The New York Times, July 2, 2003, p. E1.

“Use a Calculator to Help Find the Measure of a Manager,” The New York Times, October 17, 2004, p. Y8.

“Economists Wrestle with the Olympics,” The Wall Street Journal, July 16, 2004, p. A2. (Regression analysis predicts country medal counts.)

“Wine Equation Puts Some Noses out of Joint,” The New York Times, March 4, 1990, p. 1.

“More Great Wine Before Its Time,” The New York Times, December 12, 1990, p. D2.

(As the prior two articles show, economist Orley Ashenfelter’s regression equations, based on temperature and rainfall, rival wine tasters in judging the quality of French wines.)

“Test Marketers use Virtual Shopping to Gauge Potential of Real Products,” The New York Times, December 22, 1997, p. D3.

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II. Longer Readings J. H. Stock, and M. Watson, Introduction to Econometrics. Boston: Addison-Wesley, 2007.

R. S. Pindyck and D. L. Rubinfeld, Econometric Models and Economic Forecasts, New York: McGraw-Hill, 1997.

R. C. Fair, Predicting Presidential Elections and Other Things, Palo Alto CA: Stanford University Press, 2002.

J. S. Armstrong, Principles of Forecasting, Kluwer Academic Publishers, 2001.

D. Lovallo, and D. Kahnman, “Delusions of Success: How Optimism Undermines Executives’ Decisions,” Harvard Business Review, July-August 2003, 56-63.

J. S. Thomas, W. Reinartz, and V. Kumar, “Getting the Most Out of Your Customers,” Harvard Business Review, July-August 2004, 117-123.

Sam Savage, “Prices, Probabilities, and Predictions,” OR/MS Today, 31, June 2004, 22-29.

J. Yurkiewicz, “Forecasting at Steady State,” OR/MS Today, June, 2008, (This is a nice survey of forecasting software.)

Symposium on Event Markets, Journal of Economic Perspectives, Spring 2004, 107-142.

J. H. Stock and M. W. Watson, “How did Leading Indicator Forecasts Perform during the 2001 Recession?” Economic Quarterly, Federal Reserve Bank of Richmond, Summer 2003, 71-90.

V. Zarnowitz, “Theory and History Behind Business Cycles: Are the 1990s the Onset of a Golden Age?” Journal of Economic Perspectives, Spring 1999, pp. 69-90.

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S. A. Ravid, “Information, Blockbusters, and Stars: A Study of the Film Industry,” Journal of Business, 1999, 463-492.

S. K. McNees, “An Assessment of the ‘Official’ Economic Forecasts,” New England Economic Review, July-August 1995, pp. 13-23.

B. L. Bayus, “High-Definition Television: Assessing Demand Forecasts for a Next Generation Consumer Durable,” Management Science, November 1993, p. 1319.

G. L. Urban, J. R. Hauser, and J. H. Roberts, “Pre-launch Forecasting of New Automobiles,” Management Science, April 1990, p. 401.

J. Wind et al, “Courtyard by Marriott: Designing a Hotel Facility with Consumer-Based Marketing Models,” Interfaces, Jan.-Feb. 1989, pp. 25-47.

III. Short Readings S. Thurm, “Now, It's Business by Data, but Numbers still Can't Tell Future,” The Wall Street Journal, July 23, 2007, p. B1.

K. B. Yancy, “Guests put their Two Cents into the New Aloft Hotels,” USA Today, July 6, 2007, p. 12D. C. Bialik, “Relatively Small Number of Deaths Have Big Impact on Pfizer Drug Trial,” The Online Wall Street Journal, December.

IV. Cases Pilgrim Bank (A) (9-602-104), Harvard Business School, 2003.

Teaching Note (5-602-131).

Reyem Affiar (9-895-009), Harvard Business School, 1995.

Teaching Note (5-895-022).

Nopane Advertising Strategy (9-893-005), Harvard Business School, 1993.

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Colonial Broadcasting Company (9-894-011), Harvard Business School, 1993. Teaching Note (5-896-040).

Harmon Foods Inc (9-171-248), Harvard Business School, 1994.

Forecasting the Adoption of a New Product (9-505-062), Harvard Business School, 2005.

Tong Yang’s Cement (B): Demand Forecasting and Globalization (GS14B), Stanford Business School, 2004. (Available from Harvard Business School Publishing.)

Wal-Mart Neighborhood Markets (9-503-034), Harvard Business School, 2003.

GuestFirst Hotel (A) and (B) (9-602-099 and 9-602-111), Harvard Business School, 2003.

Building a Logic of Competition (9-798-072), Harvard Business School, 1999. Teaching Note (9-798-073). (This case asks students 30 questions about important macroeconomic and business trends and underscores popular misperceptions.)

Forecasting with Regression Analysis (9-894-007), Harvard Business School, 1996.

Science Technology Co. - 1985 (9-289-040), Harvard Business School, 1991.

Teaching Note (5-292-063) We provide three additional applications. The first illustrates the ways in which firms can employ consumer surveys. The second uses regression methods to measure the influence of economic conditions on U.S. Presidential elections. The third calls for a mining company to make crucial forecasts of demand for the resource it produces.

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Courtyard by Marriott

A classic example of the consumer survey method is illustrated by the design of the hotel chain, Courtyard by Marriott.1 Marriott Corporation undertook extensive market research before establishing (and subsequently introducing nationwide) its new hotel design: a small, quiet, informal, high-value hotel attractive to price-sensitive business and vacation travelers. The company surveyed over 600 consumers in four cities, paying people to come to a central location and complete a survey concerning some 50 hotel attributes related to room design, food, services, leisure activities, security, hotel location, price, and so on. Table 1, reproduced from the study, summarizes the alternatives subjects faced. Marriott market researchers designed the survey to check and cross-check subjects’ responses. For instance, after asking subjects to evaluate individual hotel features at given prices, they then asked subjects to reevaluate the total hotel package they had selected, indicating whether they found it attractive at the implied price or whether it could be improved further.

According to the survey results, respondents clearly preferred a type of hotel not then offered in the marketplace. Using information from the survey, Marriott estimated price and cross-price elasticities of demand with respect to major competitors, as well as expected market shares under different (what-if) assumptions. It turned out that the “optimal” hotel design differed significantly from what management had originally envisioned (a “smaller” Marriott offering features similar to the trademark hotel). The new hotel attracted so many customers that by the end of 1989, Marriott had opened some 150 new Courtyard by Marriott hotels. By 2008, the number had grown to some 700 nationwide allowing the company to continue a strategy of expansion and profitability. Predictably, at least five “clone” chains have been opened by other hotel groups.

1A discussion and analysis of this marketing study appears in J. Wind et al., “Courtyard by Marriott: Designing a Hotel Facility with

Consumer-Based Marketing Models,” Interfaces 19 (1989): 25-47.

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Table 1. Survey Results External Factors Building shape L-shaped w/landscape Outdoor courtyard Landscaping Minimal Moderate Elaborate Pool type No pool Rectangular shape Free-form shape Indoor/outdoor Pool location In courtyard Not in courtyard Corridor/view Outside access/ restricted view Enclosed access/ unrestricted view/ balcony or window Hotel size Small (125 rooms, 2 stories) Large (600 rooms, 12 stories) Rooms Entertainment Color TV Color TV w/movies at $5 Color TV w/30-channel cable Color TV w/HBO, movies, etc.

Color TV W/ free movies

Entertainment/rental None Rental cassettes/ in room Atari Rental cassettes/ stereo cassette playing in room Rental movies in-room BetaMax Size Small (standard) Slightly larger (1 foot) Much larger (2 feet) Small suite (2 rooms) Large suite (2 rooms) Quality of decor in standard room) Budget motel decor Old Holiday Inn decor New Holiday Inn decor New Hilton decor New Hyatt decor Heating and cooling Wall unit full control Wall unit soundproof full control.

Central H or C (seasonal) Central H or C (full control) Size of bath Standard bath Slightly larger sink separate Much larger bath w/larger tub Very large tub for 2

Sink Location In bath only In separate area In bath and separate Bathroom features None Shower massage Whirlpool (Jacuzzi) Steam bath Amenities Small bar soap Large soap/ shampoo/shoeshine Large soap/bath gel/ shower cap/ sewing kit Above items + toothpaste, deodorant, mouthwash Food Restaurant in hotel None (coffee shop next door) Restaurant/Lounge combo, limited menu Coffee shop, full menu Full-service restaurant, full menu Coffee shop/full menu and good restaurant None Restaurant nearby None Coffee shop Fast food Fast food or coffee shop and moderate restaurant

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Fast food or coffee shop and good restaurant Free continental None Continental included in room rate Room service None Phone-in order/ guest to pick up Room service, limited menu Room service, full menu Store No food in store Snack items Snacks, refrigerated items, wine, beer, liquor Above items and gourmet food items Vending service None Soft-drink machine only Soft-drink and snack machines Soft-drink, snack, and Sandwich machines Above and microwave Available In-room kitchen facilities None Coffee maker only Coffee maker and Refrigerator Kitchen in room

Lounge Atmosphere Quiet bar/lounge Lively, popular bar/lounge Type of people Hotel guests and friends only Open to public − general appeal Open to public − many singles Lounge nearby None Lounge/bar nearby Lounge/bar w/ Entertainment nearby Services Reservations Call hotel directly 800 reservation number Check-in Standard Pre-credit clearance Machine in lobby Check-out At front desk Bill under door/ leave key Key to front desk/ bill by mail Machine in lobby Limo to airport None Yes Bellman None Yes

Message service Note at front desk Message service Note at front desk Light on phone Light on phone and message under door Recorded message Cleanliness/upkeep/ management skill Budget motor level Holiday Inn level Nonconvention Hyatt level Convention Hyatt level Fine hotel level Laundry/Valet None Client pick up and drop off Self-service Valet pick up and drop off Special services (concierge) None Information on restaurants, theaters, etc.

Arrangements and reservations Travel-problem resolution Secretarial services None Xerox machine Xerox machine and typist

Car maintenance None Take car to service Gas on premises/ bill to room Car rental/airline reservations None Car rental facility Airline reservations Car rental and airline reservations Leisure Sauna None Yes Whirlpool/Jacuzzi None Outdoor Indoor Exercise room None Basic facility w/weights Facility w/Nautilus equipment Racquetball courts None Yes Tennis courts None Yes Game room/ entertainment None Electric games/pinball Electric games/ pinball/ping pong Above + movie theater, bowling

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Children’s playroom/ playground None Playground only Playroom only Playground and playroom Pool extras None Pool w/slides Pool w/slides and equipment Pool w/slides, waterfall, equipment Security Security guard None 11 a.m. to 7 p.m.

7 p.m. to 7 a.m.

24 hours Smoke detector None In rooms and throughout hotel Sprinkler system None Lobby and hallways only Lobby/hallways/rooms 24-hour video camera None Parking/hallway/ public areas Alarm button None Button in room, rings desk

Predicting Presidential Elections Every four years, United States citizens face the question: Which candidate and party will win the coming presidential election? Of course, political pundits and authoritative election predictions abound. Nonetheless, presidential elections are notoriously hard to predict. Reporters, commentators, and business leaders have turned increasingly to models created by political scientists and economists to explain and predict the patterns of election results. There are two customary ways of devising such forecasts. One approach relies on polling. A common poll question might be: “If the presidential election were held today, who would you vote for?” Such polls provide valuable information, but are subject to the same response errors and biases as other surveys.

Moreover, because likely candidates are known only six to eight months before the election, these predictions are necessarily very short term. A second approach is to make forecasts based on voting patterns from past elections. The most sophisticated models examine the past voting records state by state and combine this with an assessment of current party strength based on polls and incumbency considerations.

(Historically, Utah and Idaho have had the strongest tendency to vote Republican, Arkansas and Rhode Island to vote Democratic.)

In striking contrast to these traditional methods, analysts have applied economic models to election forecasting, incorporating key economic indicators as determinants of voter demand. The forecasting formula of Professor Ray Fair of Yale University has received much attention in the business press because it invokes a basic political tenet: Americans vote their pocketbooks.1 The Fair equation predicts the percentage of the popular vote (of the total two-party vote) for the incumbent party based on: the average rate of economic growth (both during the election year and during previous quarters), the average rate of inflation, the duration that the incumbent party has held office, whether the president is running for reelection, whether the party in power is Democrat or Republican, and whether the country is at war. Fair’s equation looks very much like an “incumbency demand curve.” According to the equation, high rates of inflation (higher prices) and reduced rates of economic growth (meaning lower income and higher unemployment for voters) lead to a lower popular vote for the incumbent party.

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To estimate his regression equation, Professor Fair considered elections from 1916 to 2000, using data on the percentage of the popular vote, the rate of economic growth, and the rate of inflation. The equation fits the past data quite well with an Rsquared of .947, and a standard error of the regression (for the incumbent party’s percentage of the popular vote) of 2.2 percent. Indeed, there are now numerous rivals to the Fair model. The most successful combine both economic and political variables. For instance, a popular equation includes the economy’s recent rate of growth and a measure of presidential job approval the May before the election.

These models and equations show that the state of the economy has an important impact on presidential elections. But other factors matter as well. Historical state voting patterns matter. Opinion polls, volatile as they are, matter. Personalities of the candidates matter. Unexpected events, such as the appearance of third-party candidates (Ross Perot, Ralph Nader) matter. Traumatic national events, such as the terrorist attacks of 9/11, matter. All of these factors are hard to gauge.

In the 1992 election, most of the leading models underestimated the strength of the Clinton challenge to President Bush. Relying only on economic factors, the Fair model mispredicted that the senior Bush would be reelected. Other models held that the election was too close to call (Bush leading 51 to 49 percent but with a 3 percent margin of error). The Fair model rebounded to make accurate predictions of the popular vote in the 1996 and 2000 races. Interestingly, foreseeing the popular vote does not always mean correctly predicting the presidential winner. For instance, on October 27, 2000 Fair predicted that Al Gore would receive 50.8% of the two-party vote. Gore actually received 50.3% of the vote. Though he won the popular vote, Gore lost in the electoral college.

(Of course, no expert or model could have foreseen the chaotic counts and recounts for Florida’s electoral votes.) For the 2004 election, Fair predicted on July 31, 2004 that George Bush would receive 57.48 percent of the two-party vote. Though Fair correctly predicted the presidential winner, his popular vote forecast turned out to be a significant overestimate. Bush ultimately received 51.3 percent of the two-party vote and was narrowly re-elected.

1. Ray Fair, Predicting Presidential Elections and Other Things, (Stanford, Stanford Business Books, 2002) and http://fairmodel.econ.yale.edu.

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Forecasting the Nickel Market Put yourself in the position of senior management of one of the world’s largest nickel mining companies in 1990. Currently your company has about a 30 percent share of world nickel sales, and your largest mine, in Canada, produces nickel more cheaply than anyone else. The company correctly predicted the high growth in demand for nickel in the 1980s and profited handsomely from it. Management has just completed a long-range forecast (for the next decade) of the nickel market. The forecast predicts that: 1. World nickel sales (in tons) will increase at an average rate of 6 percent per year during the coming five years and 4 percent for the remainder of the decade.

2. Nickel prices will remain strong, growing at an average of 7 percent per year, considerably faster than the overall rate of inflation.

3. Continuing the trend of the past five years, new competitors will expand into the industry. The likely effect is an erosion of the firm’s market share from 30 to 25 percent.

4. Together, input prices (labor, plant and equipment, energy), extraction costs, and transport charges will raise nickel’s cost per ton by an average of 4.5 percent per year over the decade.

In light of these forecasts, the company has decided to undertake a $1 billion investment to expand production facilities in Guatemala and Indonesia. With this expansion in capacity, the company should profit from growth in the nickel market and minimize the potential loss of market share. From its past record of forecasting accuracy, management is confident in its long-range plan. But a final evaluation of its strategy can be made only seven to ten years from now.

Discussion The large mining company was “bullish” on the prospects of world nickel sales during the 1990s after seeing its own shipments steadily increase during the 1980s. In fact, based on a linear time trend fitted to the past data, it estimated its own growth in nickel shipments roughly at an additional 12 thousand tons per year (see Exhibit 1.a). At this rate, demand would outstrip capacity in fewer than five years. Accordingly, the firm began expansion of its Indonesian and Guatemalan facilities. So long as actual nickel sales tracked the company’s projections, it would earn healthy (perhaps even “obscene”) profits and remain the world’s leading producer of nickel.

With 20-20 hindsight (Exhibit 1.b), one observes that the demand for the company’s nickel did not quite unfold as forecasted. Shipments in 1990 were 242 thousand tons and only 259 thousand tons per year a decade later. Shipments declined steeply in the early 1990s, recovered in the middle of the decade, then took a smaller dip before the decade closed. Used in many metal products (especially stainless steel), electronic products, and industrial processes, nickel demand closely tracked the business cycle falling during the 1990-1991 recession in the United States and collapsing further with the prolonged 1991 − 1994 European recession. With the worldwide recovery, nickel demand rebounded, only to fall again during the East Asian financial crisis and recession.

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Exhibit 1a 260 240 220 200 180 160 140 120

1982

1984

1986

1988

1990

1b 300 250 200 150 100 50 1980 2000

1982

1984

1986

1988

1990

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1992

1994

1996

1998

Not only did the company’s nickel shipments stagnate; the price of nickel during the decade dropped as well. Nickel prices dropped from $9,000 per ton in 1990 to as low as $6,000 a ton in 1993. Although prices recovered, they dipped again during 1998 and finally regained the $9,000 level by 2000. The price drops were due to cyclical declines in nickel demand, but also to over-capacity in the industry. The large nickel company was not alone in expanding capacity in the early 1990s. The third and fourth largest companies also expanded their production facilities, driving down prices. All three firms failed to make any profits in the early 1990s. The number one firm returned to profitability in the middle years of the decade, beginning to pay back its investment in expanded capacity. However, higher energy prices at present threaten profits.

(Processing the kind of ore found in the tropics takes one and one-half times as much energy as Canadian ores require.)

The large company’s myriad problems resulted from a combination of bad forecasting and bad luck. Could the company have planned better for the coming turbulence in world markets? The “bigger” picture of the nickel market depicted in Exhibit 1.b suggests that the answer is yes. The company’s 1980s time series of shipments (magnified in part a) appears in the small box in part b. The bigger picture suggests the following conclusions: 1. The company’s shipment history during the 1982 to 1990 period was unusually steady. However, during 1981 and 1982 (a time of worldwide recession), its shipments had fallen significantly. In fact, part of the company’s high growth probably represented recovery from previous depressed levels. Moreover, a look at the nickel industry as a whole would have revealed much greater volatility in demand year to year during the decade. Though the firm’s nickel sales grew steadily in the 1982-90 period, how long could the company remain shielded from the reality of global fluctuations?

2. A linear time trend probably overstates the company’s long-term growth prospects.

(A quadratic specification, allowing for slackening growth, probably would have fit the data better.) Whatever the specification, the company should be aware of the standard error surrounding its forecast. Had anyone asked, the standard error for the linear time trend was large − plus or minus 8 thousand tons around the annual forecast. This error will increase as forecasts become increasingly long range.

3. The time series did not take into account a key determinant of total nickel demand; the worldwide level of economic activity (especially steel production). Nor did it include an important factor influencing the company’s share of demand: the supply and prices of its leading competitors. These omissions increase dramatically the margin of error in the company’s forecast.

4. Japan’s decade-long recession, the East Asian financial crisis, and recent oil price shocks were all nearly impossible to predict. The company’s exposure to these adverse developments could well be attributed to bad luck.

The moral of this story? Often, the worst mistake a company can make is to ignore uncertainty. Even if its forecasts had been correct on average, the company faced the risk that nickel demand could fall well below its expected projection. Given the uncertainty surrounding nickel demand, such a scenario was a significant possibility.

Thus, the firm’s production planning should have taken uncertainty into account.

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V. Quips and Quotes It is a capital mistake to theorize before one has data. Insensibly, one begins to twist facts to suit theories, instead of theories to suit facts.

(A Conan Doyle) The only relevant test of the validity of a hypothesis is a comparison of its predictions with experience. (Milton Friedman) One accurate measurement is worth 100 expert opinions.

A straight line prediction is the shortest distance between two errors.

In economics, everything depends on everything else -- and in more than one way. (A simultaneity problem?)

He uses statistics like a drunken man uses a lamp post: for support rather than illumination. (Attributed to Benjamin Disraeli and Andrew Lang) The future is not what it used to be.

The great tragedy of science: the slaying of a beautiful hypothesis by an ugly fact. (Thomas Huxley) Beggar: I haven’t eaten in three days.

Statistician: How does that compare to last year?

A 17-year old dropped out of school and rode his motorcycle to […Fill in your choice of state], thereby raising the average IQ in both states.

The future is not what it used to be.

The best test of an expert in a given area is the ability to win money in a series of bets on future events in that area.

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The job of forecasters: to make the unknown, the unknowable, plausible to those who insist on knowing.

Economists are generally right in their predictions but wrong in their dates.

Forecasters: Often wrong, never in doubt.

Even a stopped clock is right twice a day.

Make 3 correct guesses consecutively and you will establish a reputation as an expert.

Two things one should never see in the making: sausages and economic forecasts.

He tortured the data until it spoke. (But was it telling the truth?)

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ANSWERS TO EVEN-NUMBERED PROBLEMS 2.a.

Coca Cola’s management is likely to conclude that consumers will prefer New Coke to Coke Classic. (However, as part b shows, they may be wrong.)

b. Yes, these rankings are consistent with the information in part a.

Consumers prefer Pepsi to Coke Classic by 58 to 42 (types A and C) and New Coke to Pepsi by 58 to 42 (B and C). However, a blind taste test between Classic and New Coke would have Classic preferred 84 to 16 (A and B)! c. It would be a big mistake to replace Classic by New Coke. The obvious strategy is to retain Classic but also offer and promote New Coke. New Coke will attract type C consumers away from Pepsi. As the text indicated, blind taste tests do not tell the whole story about consumer buying behavior; brand-name allegiance and loyalty is also important.

4.a.

False. A high R2 indicates that the equation closely tracks the past data, but this is only one part of performance. A complete evaluation would address these questions: i) Does the equation make economic sense? ii) Are the signs and magnitudes of the coefficients reasonable? iii) How well does it forecast, short-term and long-term?

b. Partly True. More data is better as long as the time-series relationship is stable. However, such behavior often changes over time. If two time periods (say, one decade versus another) show very different behavior, one should estimate separate time-series for each. c. False. Throwing in everything but the kitchen sink is bad on theoretical grounds and empirical grounds. Including irrelevant or insignificant variables will lower the adjusted R2 (a better measure of performance) and will typically worsen the equation’s forecasting accuracy.

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d. Partly True. But there are exceptions. i) Even forecasts that accurately track the past can produce implausible long-term predictions. See, for example, the prediction in problem 8 of Chapter 5 for the mile record in the year 2050. ii) No matter how good the past fit, an equation will generate poor forecasts if it relies on explanatory variables that are themselves difficult to predict.

6. a. Yes, the equation makes economic sense. Growth in tire sales is fueled by growth in miles driven and growth in new car sales. b. The equation performs well in explaining the past data (R2 = .83).

The coefficients of the two explanatory variables are highly significant, and the Durbin-Watson statistic indicates no serial correlation. c. The t-statistics for the respective coefficients are: (1.41 - 1)/.19 = 2.15 and (1.12 - 1)/.41 = .29. The first coefficient is significantly different than one; the second is not. If the second coefficient is taken to be one, this means that tire sales are proportional to new auto sales. d. The forecast is: .45 + (1.41)(-2) + (1.12)(-13) = -16.93. An actual drop of 18% would not be surprising; it’s well within the margin of forecast error.

8. a. The t-statistics for each of the explanatory variables are: Price -5.11 Comp. Price 4.97 Income 11.70 Population 1.29 Time 3.85

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Using a cutoff of 1.68 (41 degrees of Freedom), we see that all the explanatory variables are statistically significant except population.

The regression model explains 93% of the total variation. b. Price elasticity is (dQ/dP)(P/Q) = (-3590.6)(7.5/20,000) = -1.35.

Cross-price elasticity is (dQ/dPc)(Pc/Q) = (4,226.5)(6.5/20,000) = 1.37 c. According to the regression, pie sales should increase by approximately (4)(356) = 1424 pies next year. (Remember one year equals 4 quarters.) d. You might be fairly confident in predicting sales for the next quarter given that 93% of the variation is explained by the regression but only if accurate information about the explanatory variables can be obtained. Of course, you control your own price. However, competitors’ prices and other variables are not in your control. As for two years from now, predictions as to the values of the explanatory variables become even more difficult. Furthermore, the demand relationship itself is subject to change as tastes change over time. This makes prediction two years from now much more uncertain. e. Your confidence would depend on how well these test markets represent the national market.

10 . a. Focusing on years 3 and 4 exaggerates the growth trend (because sales were depressed in year 3.) b. The second manager is correct in principle. Using the average change over the period offers a better (more stable) prediction of annual growth.

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12.a.

As the economy improves, we would expect firms to stop laying off workers, then increase overtime hours, then begin hiring temporary workers, and finally initiate new permanent hiring.

b.

Yacht sales probably will not rebound until well after the upswing is in progress. The manager should not plan for greater yacht sales until employment, wage earnings, and consumer income have permanently increased.

Bonus Problem Over a span of 170 years, the men’s world record for the mile run was reduced from 4 minutes and 56 seconds in 1804 to Roger Bannister’s 3:59.4 in 1954 to John Walker’s 3:49.4 in 1975. A graph listing times by years suggests that a straight line provides a good fit. A time-series regression produces the equation t = 16.473 - .0064Y, where t is the time in minutes (i.e., t = 4.1 means 4 minutes and 6 seconds) and Y is the year. a. According to the equation, the passing of each decade should reduce the record by how many seconds? b. Steve Cram’s 1985 world record was 3:46.32. Hichman El Guerouj holds the current world record of 3:43.13 set in 1999. How accurate is the equation’s forecast for each of these times? c. What is the predicted world record time for 2010? Would it be reasonable to use the equation for 2050?

Answer a. The passing of each decade (Y = 10) implies: t = (.0064)(10) = .064 minutes = (.064)(60) = 3.84 seconds. This is a 3.84 second fall in the world record. b. For 1985, the equation’s prediction is: t = 16.473 - (.0064)(1985) = 3.769 minutes, or = 3 min., 46.14 sec. For 1999, the prediction is: t = 16.473 - (.0064)(1999) = 3.6794 minutes, or 3 min., 40.76 sec. The 1985 estimate is close to the actual record, (3:46.3), while the 1999 estimate is less accurate (3:43.1 is the 1999 actual record). c. In the year 2010, t = 16.473 - (.0064)(2010) = 3.609 minutes, or 3 min., 36.54 seconds. Since there is some limit to the amount that the mile time can be reduced, the linear prediction cannot continue to hold far into the future. The equation predicts a mile time of 3 minutes and 21 seconds in the year 2050. Can this be reached? Time will tell.

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Second Bonus Question The table below lists the Neebok Company’s sales in each of its five department stores. Management expects total sales to increase 10 percent in the coming year.

Store A 2004 8 2005 ?

Store B 9 ?

Store C 10 ?

Store D 11 ?

Store E 12 ?

Total 50 55

a. Provide forecasts of each store’s sales in the coming year. What assumptions underlie your forecasts? b. A fellow manager points out that last year’s sales pattern is typical; sales vary considerably across stores for unpredictable reasons. Sales at a particular store may vary up or down by 10 to 20 percent from year to year. A store may be a leader one year and a laggard the next. What effect might this have on your 2005 forecasts? Explain.

Answer a. Most students’ predictions are: 8.8, 9.9, 11.0, 12.1, and 13.2 for the respective stores. This assumes that last year’s differences in sales carry over exactly in the current year. b. The possibility of random fluctuations would call for more cautious predictions. For example, if differences were completely random, the best prediction for each store would be 11.0 (the overall average). Most likely, we would expect some “regression toward the mean” – Store E would have somewhat greater than average sales, and so on.

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Discussion Question One way of comparing the qualitative and quantitative approaches is to put them to a side-by-side forecasting test. Ask each approach to make forecasts of the average weekly revenues for a series of upcoming films. Then keep a careful track record of which forecasts are closer to the actual, realized figures.

Another powerful test is to combine the approaches in estimating movie demand. While human decision makers might be skilled at identifying important qualitative factors, they are less competent in estimating the magnitude of these factors’ impacts on demand. This is where statistical techniques excel. Fortunately, almost all the likely qualitative factors can be introduced in the regression analysis as measured variables or dummy variables. For instance, the director (or the script) could be rated on a one to four star scale, and this rating could be introduced as a explanatory variable in the regression equation. If the director makes a large difference in the quality of the film and its box office revenues, then the estimated coefficient for this variable should be positive and highly significant.

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley, Samuelson and Marks Website.)

S1. a. To estimate price elasticity, we compare 2001 and 2004, two years in which the level of income was the same: EP = [(1.90 – 2.00)/2.00]/ [(22 – 20)/20] = -5%/10% = -.5. b. Comparing 2001 and 2003 when prices were constant, we find: EY = [(1.94 – 2.00)/2.00]/ [(97 – 100)/100] = -3%/-3% = 1.0. c. dQ/Q = EP(dP/P) + EY(dY/Y) = (-.5)[(24 – 22)/22] + (1.0)[(105 – 100)/100] = -4.5 + 5 = .5 percent.

The forecast calls for a very slight increase in sales, whereas actual sales were unchanged. d. The OLS regression produces the equation: Q = 1 - .05P + .02Y with an R2 of 1.00! Surprisingly, this equation provides a perfect fit of the five years of observations. Obviously, this degree of accuracy is more than a bit unrealistic.

S2. a. The OLS estimated equation is: W = 18.25 - .41t, where the t-statistic associated with the “year” coefficient is -1.616. This t-value fails significance. We cannot reject the null hypothesis of a zero “year” coefficient. Thus, there is insufficient evidence to establish a downward trend in the water table. b. Average rainfall in the last 5 years was 46 inches compared to 38.4 inches in the first 5 years. Thus, accounting for variation in rainfall is crucial. Adding rainfall (R) as an explanatory variable would likely reveal a more pronounced yearly drop in the water table.

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c. The multiple regression equation is: W = 9.69 - .51t + .216R. This equation (with an R2 of .82) provides a much better fit to the data than the simpler part-a regression (R2 of .246). The t-values for the coefficients are –3.81 and 4.75 respectively, and both are highly significant. Notice that the equation identifies a stronger negative time trend.

S3. a. The estimated OLS equation is: Q = 332.5 – 506.6P. The equation is statistically significant (R2 = .941). If price is cut by $.10, quantity increases by 50.66 units. b. A careful plot of the points shows a slight degree of curvature. c. The Log-Log equation is: Log(Q) = 2.975 – 2.02Log(P).

This provides a better fit of the data (R2 = .992) than the linear equation. The Log-Log equation implies the demand equation: Q = 19.6P-2.02.

(The antilog of 2.975 is 19.6.) The price elasticity of demand is –2.02.

S4 a.

A regression of unit sales against the current level of advertising produces the equation: Q = 62.3 + .915A. The t-statistic associated with A is 3.6 and the equation’s R 2 is .37.

Advertising appears to account for a significant part of the quarterto-quarter variation in sales.

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b.

A regression of this quarter’s unit sales against the last quarter’s sales produces the equation: Q = 54.45 + .48Q-1.

The t-statistic associated with Q-1 is 2.55 and the equation’s R2 is .237. While this equation has explanatory value according to a standard F-test, it provides a poorer fit of the past data than the advertising equation estimated in part a.

c.

To test the lagged effect, we regress Q against A -1 (since three months constitute one quarter). The regression equation is: Q = 54.6 + 1.13A-1.

The t-statistic associated with A-1 is 5.20, and the equation’s R2 is .56. This last equation has the highest F-value and R2 and accounts best for the past pattern of sales.

S5 a.

The OLS regression equation is: Q = 95.0 + 4.68t. The coefficient for the time trend is highly significant (t-value of 35.3). The equation fits the past data very closely (R2 = .988).

b.

The constant-growth equation is estimated in the logarithmic form: Log(Q) = 4.6 + .03423Log(t).

The coefficient of Log(t) is highly significant. The growth equation provides a slightly better fit (R2 = .996) than the linear equation and appears to be an improvement. The growth equation coefficients are: b = Antilog(4.6) = 99.3 and r = Antilog(.03423) = 1.035. Thus, the growth equation is: Q = 99.3(1.035)t.

c.

The linear equation’s predictions are: 179.2, 183.9, 188.6, and 193.3.

The growth equation’s predictions are: 184.4, 190.9, 197.6, and 204.5.

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CHAPTER FIVE PRODUCTION

OBJECTIVES 1. To introduce the concept of production and to lay the groundwork for the later discussion about cost. (pp. 180-181) 2. To explain and contrast short-run concepts (fixed inputs, marginal product, diminishing marginal returns, etc.) and long-run concepts (returns to scale, output elasticity, etc.) (pp. 181-195) 3. To examine different types of production functions and their graphical representations. (pp. 196-200) 4. To explore optimization in the context of production using marginal analysis. (pp. 200-205)

TEACHING SUGGESTIONS I. Introduction and Motivation There seems to be a renaissance these days in the area of production. It has gotten renewed interest in the press, in business schools, in engineering departments and in industry. A lot of talk about "competitiveness" and "industrial policy" turns on issues of production. We feel it is very useful to motivate students as to the importance of production. It is the core of what businesses do.

This chapter gives an introduction to the economics of production and, even so, just scratches the surface. The main purpose is to lay the groundwork for a discussion of cost. In addition, this chapter provides another opportunity to discuss optimization and marginal analysis.

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II. Teaching the "Nuts and Bolts" Students often confuse short-run and long-run concepts (for example, the law of diminishing marginal returns and returns to scale). We find it is useful to highlight the differences by asking for concepts associated with each and putting these on the chalkboard. Here is an example: Short-run

Long-run

Some inputs are fixed

All inputs are variable

Law of diminishing marginal returns Returns to scale: constant, increasing or decreasing Marginal product

Input elasticity

Total product curve

Isoquants

Inputs and Outputs. Students sometimes get confused between inputs and outputs when dealing with marginal concepts. That is they get confused between marginal revenue and marginal revenue product. They also confuse marginal cost (per unit output) and marginal cost per unit input.

We suggest emphasizing this distinction over and over again. Here is one possible approach: What we say Marginal revenue

What we mean Marginal revenue per unit of output

Marginal cost

Marginal cost per unit of output

Marginal revenue product

Marginal revenue per unit of input

Marginal cost per unit of input, for instance, the wage

Marginal cost per unit of input

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It is also important to emphasize the following: 1. MRP is just MR times MP. If the firm is perfectly competitive in the output market then MRP=(P)(MP).

2. Marginal cost per unit of input is usually just the price of the input.

(That is, if the firm is too small to affect input price.)

3. When optimizing by equating marginal revenue and marginal cost it is important that both be per unit output or both be per unit input.

Isoquants. Some students have problems with the notion of isoquants. One way to approach this is to ask how a production function with output as a function of two inputs might be represented graphically. One way is with a family of total product curves. For example, each curve could graph Q as a function of L with a distinct K held constant. With this family of curves we could determine output for any given combination of K and L. (Of course, if there was not a curve for the chosen value of K we would have to interpolate.)

The other way to represent the production function is through isoquants. It is sometimes useful to get the students to view isoquants as they would a topographic map. Pretend that quantity values are elevations. Now consider the problem of maximizing output for a given level of cost. The cost constraint can be thought of as a fence with the goal to get to the highest elevation while constrained by the fence.

ADDITIONAL MATERIALS I. Short Readings Kate Linebaugh, “Honda’s Flexible Plants Provide Edge,” The Wall Street Journal, September 23, 2008, p. B1.

“Calling across the Divide,” The Economist, March 12, 2005, p. 74. (The link between cell phones and economic growth in the developing world.)

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Paul Glader, “For Rivals U.S. Steel and Alcoa, the Battle of Detroit Heats Up,” The Wall Street Journal, October 19, 2004, p. A1.

Varian, H. R., “IT May or May Not Matter; it Depends How You Use IT,” The New York Times, May 6, 2004, p. C2.

“Path to the Super Bowl No Longer Lined with Stars,” The New York Times, February 1, 2004, p. A12. (Building a winner under the salary cap.)

Postrel, V., “Lessons in Keeping Business Humming, Courtesy of Wal-Mart U,” The New York Times, February 28, 2002, p. C2.

“Incredible Shrinking Plants,” The Economist, February 23, 2002, pp. 71-73.

“A Long March,” The Economist, July 14, 2001, p. 63. (This article surveys the progress of mass customization.)

“For this Economist, Long-Term Prosperity Hangs on Good Ideas,” The Wall Street Journal, January 21, 1997, p. A1. (This article discusses Paul Rohmer's point that knowledge is the most important production input.)

II. Longer Readings Cookenboo, L., “Production Functions and Cost Functions: A Case Study,” in Managerial Economics and Operations Research, edited by Edwin Mansfield, W.W. Norton & Co., 1993.

III. Quips and Quotes Knowledge is the only instrument of production that is not subject to diminishing returns. (J.M. Clarke) Advice from the coach to his star player who has made four Fs and one D: “Son, look's to me like you're spending too much time on one subject."

Production not being the sole end of human existence, the term unproductive does not necessarily imply any stigma. (John Stuart Mill)

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IV. Mini-Case Designing the Boeing 777 When Boeing’s first twin-engine long-haul aircraft rolled out of the assembly hanger, it was in record time and represented the single most ambitious experiment in computer-aided design (CAD). Computer-aided design permits “virtual” manufacturing: realistic simulation of the most important aspects of products and processes.11 Instead of constructing countless mock-ups of the new aircraft to ensure that its millions of complex parts fit together and function as intended, Boeing uses CAD to create its mock-ups elsewhere: in the billions of bits of information faithfully stored in its computers. These computerized designs can be tested and modified at will − before materials, labor, and equipment are committed to actual production. For Boeing, CAD greatly enhances precision, allows designs to be transmitted instantly among company personnel and subcontractors, and dramatically cuts the time it takes to translate design into production. Indeed, for high-tech, complex systems such as aircraft, more than 50 percent of eventual life-cycle product costs depend on early design decisions.

Computer-aided design is changing the ways managers think about production. Beyond the customary, tangible production inputs (labor, capital, and materials), managers have come to recognize information as a fourth input. By using information more intensively, production managers can economize on the use of the other three inputs, as Boeing has done successfully. The exact trade-off managers choose between information and the other production resources depends on the relative costs of the inputs. As computing costs decline, managers will increasingly turn to CAD systems, particularly when they deliver significant savings on expensive labor and capital.

Moreover, information has two features not shared by other inputs.

First, information is not used up. Setting up information systems involves certain fixed costs, but, once established, information can be used and reused at relatively low marginal costs. Second, information enhances manufacturing flexibility. In modern information-based manufacturing, there are innumerable ways to produce a given quantity of output and myriad trade-offs among them. As the example of the Boeing 777 demonstrates, accelerated manufacturing and just-in-time production methods save time as well as money.

8For an account of Boeing’s experience, see “A Survey of Manufacturing Technology,” The Economist (March 5, 1994): 7-11.

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2.

Yes, this statement is consistent with diminishing returns. Average output declines with increases in the number of participants because the marginal product of additional workers keeps falling.

4.

In all likelihood, Chrysler's move to 24-hour production was prompted by the high capital cost of building new factories combined with a slowdown in wage growth. With labor cheap relative to capital, a switch to a greater ratio of labor to capital makes economic sense. Increased 24-hour production was in response to the soaring demand for minivans and Jeeps.

6. a. The marginal products for labor and capital are given by: MP L = 10 L and MPK = 24 - 2K. For L equal to K (in the range 0 to 10), capital's marginal product is greater than labor's. At the same input prices, the firm will use more capital than labor. b. Setting the price of each input equal to its marginal revenue product implies: 100 - 10L = 40, or L = 6, and 240 - 20K = 80, or K = 8.

8. a. In the short run, the restaurant should hire more wait staff (and possibly chefs) and squeeze in some extra tables so as to produce the maximum number of (delicious) meals per night. Clearly, given the restaurant’s small quarters (fixed capacity), applying extra labor inputs will quickly run into diminishing returns. b. In the longer run, the restaurant would be wise to increase its entire scale of operation. Perhaps, it could expand its space in the new building. If not, it might even consider opening a second restaurant in a carefully scouted location. In either case, it is much more efficient to produce gourmet meals using the “right” mix of culinary labor and distinctive restaurant floor space.

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10. a. Labor’s MPL is dQ/dL = 1 - L/400. Setting MRPL = wage implies 40 - .1L = 20, or L* = 200. In turn, Q = 150 and  = 2,000. b. With P = $50, MRPL becomes 50 - L/8. The new solution is L* = 240 and Q = 168. With the price increase, optimal output increases. If input and output prices change in equal proportions, there is no effect on any of the firm’s optimal decisions. c. The 25% increase in productivity implies: MPL = (1.25)(1 – L/400).

Setting MRPL (at P = $50) equal to the unchanged wage implies: 62.5 - .15625L = 20. Thus, L* = 272 and Q = 179.52.

12. a. Q = 100(1.01).5(1) = 1.005. Output increases by .5%. In general, the power coefficient measures the output elasticity with respect to the input. A 1 percent increase in labor produces a (.5)(1) = .5 percent increase in output. b. Since the sum of the power coefficients is .5 + .4 < 1, the production function exhibits decreasing returns to scale.

14.The optimal input condition is: MPK/MPL = PK/PL. The inputs’ respective marginal products are: MPK = ßLKß-1 and MPL = L−Kß. Thus, the ratio of the marginal products is: MPK/MPL = (ß/)(L/L-1)(Kß-1/Kß) = (ß/)(L/K).

Setting this equal to PK/PL and rearranging yields: L/K = (/ß)(PK/PL).

Other things equal, an input's use increases the greater its output elasticity or the lower its price.

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. The optimal quantity of labor is L* = 50. To find this solution by hand, vary the labor hours in Cell C5 until MRPL = MCL (compare cells C8 and C9). Using the spreadsheet optimizer, maximize cell I12 (profit) by changing cell C5. Output is 175 units and maximum profit is 250. b. In the long run, the firm should use L* = 64.64 and K* = 39.64 to produce 175 units (the output found in part a) at minimum total cost.

Using the spreadsheet optimizer, minimize cell I9 (cost) by changing cells C5 and F5 subject to cell I3 (output) being greater or equal to 175. Relative to the short run, total cost falls from 1,500 to 1,439 and profit rises to 311. At this optimal solution, MPL//MCL= MPK/MCK. c. After cutting its inputs by half, we have L* = 32.32 and K* = 19.82 implying an output of 105.8 units. Output has fallen by less than 50 percent indicating decreasing returns to scale. The firm’s profit has increased from 310.8 (part b) to 338.4. This is not a least-cost solution because MPL/MCL does not equal MPK/MCK. The former ratio is .1354 and the latter ratio is .1104. The firm could reduce the cost of producing 105.8 units by increasing L and decreasing K.

S2 a. (We assume that the student has created a new spreadsheet for this problem based on the format of the example on page 249 of the text.)

In the short run with a fixed price P = $10 and capital at K = 9, the optimal employment of labor is L* = 25. At this level, labor’s marginal revenue product is equal to the wage: MRPL = PL = 36.

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Total output is 180 units. To confirm this result, invoke the spreadsheet optimizer and maximize profit in cell I12 by changing cell C5. b. The firm seeks to produce 180 units at minimum cost. Using the spreadsheet optimizer, minimize cost in cell I9 by changing cells C5 and F5, subject to output in cell I3 being greater or equal to 180. The result is L* = 10 and K* = 22.5. Here, MPL/ PL = MPK/PK = .25. c. If PL falls to 18, we use the optimizer to find the new least-cost input mix: L* = 14.1 and K* = 15.9. The lower input price of labor induces the firm to increase its ratio of labor to capital.

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CHAPTER SIX COST ANALYSIS

OBJECTIVES 1. To explain relevant costs and related concepts. In particular, to contrast opportunity cost and fixed costs and to contrast accounting profits and economic profits. (pp. 213-222) 2. To explain the relationship between production and cost. To apply the concepts of the short run and long run to cost. (pp. 222-228) 3. To explore economies of scale and scope. (pp. 231-237) 4. To apply optimization concepts to cost minimization and optimal decision making. (pp. 238-244)

TEACHING SUGGESTIONS I. Introduction and Motivation The same motivation that applies to production applies to cost. However, cost is in some sense a broader concept than production in that 1) it summarizes the underlying production process and 2) it includes factors not taken into account by production analysis, that is, opportunity costs.

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II. Teaching the "Nuts and Bolts"

Opportunity Cost, etc. We begin by emphasizing the difference between accounting concepts and decision making concepts. One way to highlight the differences in class is to put the following on the board and to let the students fill in the yes's and no’s and to give reasons.

Type of Cost Fixed Cost Sunk Cost Variable Cost Opportunity Cost

Relevant to Accountant?

Yes Yes Yes No

Relevant to Decision Maker?

No No Yes Yes

From a discussion of opportunity cost one can go into the idea of economic profit. From our experience, we find it useful to continually reiterate the idea of economic profit as we do problems and examples. This is to prepare students for the idea of long-run equilibrium later in the course.

Cost and production. Here we like to discuss the shapes of the cost curves and how they depend on underlying assumptions about production. Again, we are careful to distinguish short-run and long-run ideas.

Returns to Scale and Scope. Students are very interested in these concepts.

The instructor might also choose to introduce the notion of the lee learning curve (not covered in the chapter) and take care to distinguish the learning curve from increasing returns to scale.

Optimization. Again, following the philosophy of the book, we present optimization yet again, this time in the context of cost. In this concluding section we introduce the shut-down rule. We also consider multiple products and transfer pricing.

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ADDITIONAL MATERIALS

I. Short Readings K. Linebaughu, “Honda’s Flexible Plants Provide Edge,” The Wall Street Journal, September 23, 2008, p. B1.

L. Hawkins and N. Shirouzu, “A Tale of Two Auto Plants,” The Wall Street Journal, May 24, 2006, pp. B1, B2.

N. Boudette nd N. Shirouzu, “Amid Price War, Chrysler to Revamp Manufacturing,” The Wall Street Journal, August 2, 2005, p. A1.

Evan Perez, “How Delta’s Cash Cushion Pushed it onto a Wrong Course,” The Wall Street Journal, October 29, 2004, p. A1.

“Wal-Mart: How Big can it Grow?” The Economist, April 17, 2004, pp. 6769.

“Intel Hopes Its Latest Chip Drives a New PC Generation,” The New York Times, February 2, 2004, p. C6.

Zaun, T., G. L. White, N. Shirouzu, and S. Miller, “Auto makers Get Even More Mileage from Third World,” The Wall Street Journal, July 31, 2002, pp. A1, A8.

“Incredible Shrinking Plants,” The Economist, February 23, 2002, pp. 71-73.

“Are Megabanks - Once Unimaginable, now Inevitable - better?” Business Week, April 27, 1998, p. 32.

“Call it Dumbsizing: Why Some Companies Regret Cost-Cutting,” The Wall Street Journal, May 14 1996, p. A1.

“The Vast Picture Show: Managing a Megaplex Often Takes an Epic Effort,” The New York Times, December 29, 1997, p. C1.

“The Supercollider: How Big Science Lost Favor and Fell,” The New York Times, Oct. 26, 1993, p. C1.

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II. Longer Readings P. J. Ferraro and L. O. Taylor, “Do Economists Recognize and Opportunity Cost When They See One?” Contributions to Economic Analysis and Policy, Vol. 4, 2005.

R. S. Kaplan and D. P. Norton, "Using the Balanced Scorecard as a Strategic Management System," Harvard Business Review, Jan.-February. 1996, pp.

75-85. (Reprint # 96107).

R. Cooper and R.S. Kaplan, "Measure Costs Right: Make the Right Decisions," Harvard Business Review, Sept.-Oct. 1988, pp. 96-103.

G. L. Baker et al, "Production Planning and Cost Analysis on a Microcomputer," Interfaces, July-August 1987, pp. 53-60.

III. Cases Fineprint Company (A), (B) and (C), (UVA-C-2193, 2194, and 2195), Darden Business School, University of Virginia, 2004.

Blackheath Manufacturing Company, (UVA-C-2197), Darden Business School, University of Virginia, 2004.

Blackheath Manufacturing Company Revisited, (UVA-C-2198), Darden Business School, University of Virginia, 2004.

Gibberson’s Glass Studio, (UVA-C-2205), Darden Business School, University of Virginia, 2004.

Wendy’s Chili: A Costing Conundrum (UVA-C-2206hgbkm), Darden Business School, University of Virginia, 2004.

Align Technology, Inc.: Matching Manufacturing Capacity to Sales Demand (9-603-058), Harvard Business School, 2002.

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Monster.com: Success Beyond the Bubble (9-802-024), Harvard Business School, 2002.

Chemical Bank: Implementing the Balanced Scorecard, (9-195-210), Harvard Business School, 1999. Teaching Note (5-198-090).

The Growth of Intel and the Learning Curve, (OIT27), Stanford Business School, 1999. (Available from Harvard Business School Publishing.)

Choice International, 1995 (9-795-165), Harvard Business School, 1996.

Teaching Note (5-796-073) Sony Corp.: The Walkman Line (9-195-076), Harvard Business School, 1997. Teaching Note (5-195-077).

Bridgton Industries: Automotive Component and Fabrication Plant, Harvard Business School, (9-190-085), 1993. Teaching Note (5-191-168).

IV. Quips and Quotes In the long run, we are all dead. (John Maynard Keynes) The easiest way to make money is to stop losing it.

If you start to take Vienna, take Vienna. (Napoleon Bonaparte) (Was Napoleon aware of the sunk-cost fallacy?)

On opportunity costs: There's not much to be said for old age except that it’s better than the alternative. (J.K. Galbraith) On the whole, I'd rather be in Philadelphia. (on W. C. Field's gravestone) Most people my age are dead. (Casey Stengel)

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If it wasn't for golf, I'd probably be a caddy today. (Professional golfer George Archer) Cost means sacrifice, and cannot, without risk of hopelessly confusing ideas, be identified with anything that is not sacrifice. (J. E. Cairnes) Costs merely register competing attractions. (Frank H. Knight) Cost [is] of two kinds, either (1) the endurance of pain, discomfort, or something else undesirable, or (2) the sacrifice of something desirable, either as an end or a means. (Henry Sidgwick)

V. Mini-Case Economies of Scale in Public Schools Over the last 20 years, there have been growing concerns about the quality and cost of public education. Parents, teachers, school administrators, and general taxpayers have an interest in maintaining quality schools while holding down costs. One crucial question is the extent to which economies of scale exist in public schools. Can schools with greater enrollments provide quality instruction at a lower cost per pupil?

Empirical studies of per-pupil costs across schools indicate the answer is yes. In a study of Maryland public elementary and middle-level schools, John Riew compared costs (in 1979) across a sample of schools of different sizes, using multiple regression analysis to measure the degree of scale economies.10 The basic regression equations were designed to measure the relationship between a school’s average operating costs per pupil (the dependent variable) and its enrollment (the main independent variable). The regression also included independent variables measuring teacher training, teacher experience, professional support staff, and teachers’ aides to account for the separate effect of “school quality” indices on cost. Finally, the regressions included the school’s utilization rate (the ratio of actual enrollment to the school’s capacity). If, as expected, shortrun average costs decline, increasing a school’s utilization rate should mean a reduction in its average cost per pupil.

The regression results confirm that economies of scale are present in both types of schools. For elementary schools, average cost per pupil John Wiley & Sons

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declines significantly over the range from 200 to 400 students before leveling off as enrollments approach 500 students. For a typical school, an increase in enroll-ment from 200 to 300 students, with all other variables held constant, affords a savings of $115 in average operating expenditures per pupil. In addition, if this increase also represents a rise in utilization (say, from 50 to 75 percent given a school capacity of 400 students), then there is an additional average cost reduction of $97. Thus, the combined average cost savings for this enrollment increase come to $212 per student.

For middle schools, economies of scale occur at higher enrollments, in a range between 500 and 900 students, and are exhausted as enrollments approach 1,000 students. An increase in enrollment from 600 to 800 students reduces the average cost per student by $142. The accompanying increase in utilization (say, from 60 to 80 percent given a school capacity of 1,000 students) produces an additional savings of $55. Thus, the combined average cost savings come to $197 per student.

The average cost savings are comparable with elementary and middle schools but occur at different enrollment levels and stem from a different mix of scale economies and utilization. For elementary schools, increasing utilization is the key to average cost savings. In this respect, massive enrollment declines during the 1970s and early 1980s contributed to cost escalation, whereas enrollment increases in the last decade should contribute to cost declines. For middle schools, scale economies are the most important factor. The efficient operation of these schools with their more varied programs, specialized teaching, and administrative functions requires a larger population of students.

See J. Riew, “Scale Economies, Capacity Utilization, and School Costs: A Comparative Analysis of Secondary and Elementary Schools,” Journal of Education Finance (Spring 1986): 433-446.

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2.

This statement confuses average quantities and marginal quantities.

Though average total cost is always greater than average variable cost, marginal cost certainly can exceed average cost. For instance, when short-run production is pushed past the point of diminishing returns, marginal costs tend to turn steeply upward and exceed average cost.

4. a. The firms, by combining the provision of several related services, hope to benefit from economies of scope on both the supply side and the demand side. On the supply side, similar services may take advantage of the same inputs. For example, it may be easier to train a financial services officer to do a number of related transactions than to train separate officers for each type of transaction. Additionally, the information to process one type of transaction, such as a customer's credit history, may also be relevant for other transactions. On the demand side, one-stop shopping allows consumers to conserve on transaction costs. Rather than going to several different firms for each type of transaction, the customer can do everything in one stop. b. It is possible for national banks to operate more efficiently than regional banks or state banks, but this depends on both production and transaction costs. Since banking is an information intensive industry, banks may be able to take advantage of economies of scope and scale in information collection and transmission. For example, national banks could provide a customer with access to his or her personal accounts nationwide and could use the same information for a variety of related transactions. On the other hand, the mortgage market depends on local information about the real estate market.

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National banks may not possess any informational advantages in these markets. In addition, national banks may have higher administrative costs associated with monitoring a large organization. Determining whether national banks have cost advantages requires a careful study of costs. c. Some of the mergers are based on economies of scope, particularly where the institutions have different but related products, such as banking and insurance. Other mergers are based on geographical expansion. Given that different products may be offered in different regions, these expansions could be said to represent economies of scope and economies of scale. Simple economies of scale may be driving some of the mergers.

6. a. The running shoe producer's demand is P = 48 - Q/200. and its costs are C = 10,000 + .0025Q2. We confirm the table entries simply by computing prices, revenues, and costs for appropriate levels of output Q. b. The firm maximizes profit by setting MR = MC. Therefore, MR = 48 - Q/100 and MC = .005Q. Setting MR = MC implies: Q* = 3,200. In turn, P* = $32.

8. a. Setting MR = MC implies 96 - .8Q = 16 + .2Q, or Q* = 80. In turn, P = 64 and  = 5,120 - 2,080 = 3,040. b. She is correct that Qmin = 40. At this output, AC = 960/40 = 24 and this exactly matches MC = 16 + (.2)(40) = 24. Her second claim is incorrect. Optimal output is Q* = 80 where MR = MC. c. Yes, it is cheaper to produce 80 units in two plants (each producing at Qmin = 40). Total cost is AC.Q = 24.80 = 1,920. This is cheaper than the single-plant cost (2,080) of part a.

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10. a. We have: MCE = 1,000 + 10Q and MC = 3000 + 10Q. Setting MR = MC implies: 10,000 - 60Q = 3,000 + 10Q. Thus, Q = 100 cycles and P = $7,000. b. Purchasing engines implies a marginal cost of 2,000 + 1,400 = $3,400 (compared to the MC in part a of $4,000). Again setting MR = MC implies Q = 110 and P = $6,700. However, the firm should continue to produce some engines itself (up to the point where MCE = 1,400).

Setting 1,000 + 10QE = 1,400 implies QE= 40 engines. The firm should produce 40 engines and buy the remaining 110 – 40 = 70 engines.

12. a. MPL = 120,000 watches/60,000 labor hours = 2 watches/hour. The marginal labor cost is: ($8/hour)/(2 watches/hour) = $4/watch. Total MC is: $6 + $4 = $10/watch. To maximize profit, the firm sets MR = MC. Therefore, 28 - Q/10,000 = 10, or Q = 180,000. However, the firm's capacity makes this output impossible. The best the firm can do is to produce up to its capacity, Q* = 120,000. To sell this quantity, the firm sets P* = 28 - 120,000/20,000 = $22. The firm's contribution is: (22-10)(120,000) = $1,440,000. b. Marginal labor cost on the night shift is $12/2 = $6. The relevant MC if the night shift is used is: MC = $6 + $6 = $12. Setting MR = 12, one finds Q* = 160,000 and P* = $20. Contribution is: R - VC = $3,200,000 - [1,200,000 + 480,000] = $1,520,000. c. Demand drops permanently to P = 20 - Q/20,000. A good bet is that the firm will now use only the day shift, implying MR = MC = 10. It follows that 20 - Q/10,000 = 10 or Q* = 100,000. In turn, P* = 20 100,000/20,000 = $15. Contribution is now $500,000. In the short run (when its $600,000 in costs are fixed), the firm minimizes its losses by producing 100,000 units. If these losses continue, the firm should shut down in the long run, i.e., when its lease is up.

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Discussion Question Most information goods are characterized by high fixed costs and low or negligible marginal costs. In this case, the firm’s average total cost will decline as output increases. Thus, minimum efficient scale will be very high compared with total demand, implying a small number of firm’s will split the market (each operating at a large, efficient scale).

Home grocery delivery (though it involves the internet for securing customers and defining the transactions) has a significant marginal cost component (physical delivery of the goods from warehouse to home). The demise of Internet grocery services seems to be due to the fact that most households would rather “do it themselves” the traditional way, than pay the higher cost of third-party delivery. (For the same reason, Amazon.com has enjoyed little success in expanding its business to bulky items such as electronics because of higher storage and delivery costs.)

Conversely, the lower transaction cost of e-commerce allows small sellers to cheaply transact with potential buyers (and allows buyers to find small sellers). A small seller of rare books or a provider of custom-made hiking boots can thrive by gleaning customers over the Internet. In each instance, the good or service is differentiated and does not exhibit obvious economies of scale, allowing small sellers to compete evenhandedly with large firms. See Chapter 10 for a full discussion.

Network externalities operate on the demand side to explain why bigger can be better. They simply reinforce the economic and strategy implications of (supply-side) economies of scale and scope. Network externalities imply a market dominated by a small number of large firms. The presence of network externalities provides a strong incentive for firms to attract customers – via advertising, joint partnerships, and (most important) price cuts.

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ANSWERS TO SPREADSHEET PROBLEMS (You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. and b. Varying labor usage in the spreadsheet from 1 thousand hours to 9 thousand hours traces out a U-shaped AC curve. In turn, SAC achieves a minimum of 4.00 at L* = 4.0. To confirm this, use the spreadsheet solver to minimize cell I10 (AC) by changing cell C5. c. At L = 9 and K = 9, the resulting output is Q = 108. What input mix should the firm use to produce this output at minimum cost in the long run? Using the spreadsheet solver, minimize cell I9 (cost) by changing cells C5 and F5 subject to output in cell I3 being greater or equal to 108. The result is L* = 6.0 and K* = 13.5. d. Doubling the inputs of part c (setting L* = 12 and K* = 27) generates twice the output (Q = 216). Thus, production exhibits constant returns to scale. e. The firm’s inverse demand curve is: P = 9 – Q/72. In the short run with K = 9, we invoke the optimizer to maximize total profit in cell I12 by changing labor usage in cell C5. Thus, L* = 9, K = 9, and * = 342. In the long run, the objective is to maximize total profit in cell I12 by changing cells C5 and F5. The result is K* = 22.5, L* = 10, Q = 180, and * = 450. Increasing the scale of operations (from K = 9 to K = 22.5) is the key to the significant increase in profit.

S2 a. Using the spreadsheet optimizer, we determine the multinational firm’s optimal plan: Maximize total profit in cell E20 by changing outputs and sales in cells C10, D10, C8 and D8, subject to cell F9 being greater or equal to zero. The solution is: QH = 150, QF = 70, DH = 90, DF = 130, and  = 19,000. At this solution, we see that MRH = MRF = MCH = MCF = 120.

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b. If the firm must charge a uniform worldwide price, we reoptimize the spreadsheet after adding the constraint that the price difference in cell C12 must be equal to zero. The new solution is: Q H = 150, QF = 70, DH = 106.67, DF = 113.33, P = 193.33, and  = 18,583.

ANSWERS TO APPENDIX PROBLEMS Transfer Pricing: 1. a. The transfer price should reflect the marginal cost associated with the input (the chip). Obviously, the chip is not free to the company (its marginal cost is positive). If a zero price is set, copiers will seem to be less costly (and more profitable) than they actually are. b. A markup policy maximizes the chip division's internal profit but at the expense of the company's total profit. Facing a transfer price that is too high, the copier division will perceive its product as less profitable than it actually is and will produce too few copiers.

2. a. Facing PT = $600, the copier division's profit is: A = RA - CA - 600Q = (4,000Q - 3Q2) - [360,000 + 1,000Q] - 600Q. Thus MA = 2,400 - 6Q, or Q* = 400 copiers (the same answer as in the text.) b. With the proper transfer price set, the copier division should simply maximize its profit; in doing so, it produces a level of output that is optimal for the company as a whole.

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3.

The chip division produces a quantity such that MCM = PM = $300.

Therefore, 200 + QM = 300, or QM = 100. Facing a $300 chip price, the copier division maximizes its profit by setting MR = MCA + 300.

The result is Q* = 450 and P* = $2,650. It buys 100 chips internally and the remaining 350 externally.

Short-Run and Long-Run Costs 1. a. Substituting K°=9,000 and Q=108,000 into Equation 7A.3 implies SAC = (16)(9,000)/108,000 + 108,000/[(4)(9,000)] = $4.33. Labor is given by L = Q2/144K° = (108,000)2/[(144)(9,000)] = 9,000. b. If Q = 108,000 and K° = 18,000, then SAC is $4.17. The 18,000 square-foot plant is the lower-cost option.

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CHAPTER SEVEN PERFECT COMPETITION OBJECTIVES 1. To examine supply and demand under perfect competition. (pp. 265-268) 2. To make a connection between a perfectly competitive market structure and managerial decision making. (pp. 269-271) 3. To examine equilibrium in the short run and long run and the dynamics of entry and exit. (pp. 272-275) 4. To study the efficiency of perfectly competitive markets. (pp. 275-285) 5. To examine issues in global competition and trade. (pp. 286-289)

TEACHING SUGGESTIONS I. Introduction and Motivation The present chapter is an introduction to perfect competition. Subsequent chapters consider monopoly and oligopoly. Thus, this is only the beginning of the inquiry into market structure. Students should be told to be on the lookout for how market structure might affect managerial decision making.

The introduction of perfect competition will establish a benchmark against which other market structures can be compared.

II. Teaching the “Nuts and Bolts” We begin by discussing with students their notions of competition. In particular, we discuss the consequences of raising price. In competitive markets the comment that “a rise in price will result in customers buying John Wiley & Sons

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from a competitor” can lead to a nice discussion about what this comment assumes about search costs and information, substitutability of products, number of competitors, etc.

It is reassuring to students to remind them that the principles of managerial decision making that they have already learned continue to be applicable given different market structures. In fact, they may be well served by reviewing Chapter 2 (Optimal Decisions Using Marginal Analysis). The only difference, in terms of optimization, is the specification of the demand curve. In perfect competition it is horizontal. In a pure monopoly (Chapter 8), the single firm faces a downward-sloping industry demand curve.

It is worth spending some time on long-run equilibrium because it gives the students a feeling for the dynamics of entry and exit and about how markets evolve. You may want to refer back to Chapter 6's discussion of economic profits on pages 215-217 and to emphasize that zero economic profit includes a normal rate of return on invested capital.

Finally, the instructor should spend some time explaining and illustrating the efficiency implications of perfectly competitive markets. Again, one should caution students that not all markets are perfectly competitive. Nonetheless, studying perfectly competitive markets establishes a benchmark and helps to identify sources of market failure.

III. Discussion Assignment The “southwest water shortage” reproduced on the next page makes for an interesting discussion vehicle. The instructor should distribute the page to students and can then pose the following questions: -

Is there a water shortage? What are the signs?

What is the cause of the shortage?

Is there currently a free market for buying and selling water?

What are the potential advantages of such a market (if it were created)?

What are the potential disadvantages?

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Suggested answers: The absence of a market for freely buying and selling water is at the heart of the seeming paradox of “waste amid shortage” in the Southwest. Presently opportunities to buy and sell water are limited and occur at wildly different prices. Farmers have historic rights to buy, but not sell, water at very low prices, while some users, such as chemical companies, cannot buy water at any price. Because many users pay a price well below the resource's replacement cost, the signs of waste and inefficient use -- open-ditch irrigation, cultivation of water-intensive, low-value crops -are hardly surprising. A first step toward a more rational program of water use would be for the government to end its subsidy programs and raise the prices it charges farmers for water. Higher prices would bring forth the expected economic reaction: water conservation and the withdrawal of marginal crops. Water waste would be reduced, and a fall in water demand would alleviate some symptoms of shortage.

The second crucial step is to institute a well-functioning, liquid (pardon the pun) market for water. Allowing current water recipients to sell their water would greatly swell and deepen the available water supply to others. (The small farmer or rancher would find it far more profitable to sell his or her water than to raise marginal crops or cattle.) This in itself would do more to eliminate the shortage than any number of costly new water projects. With buyers and suppliers facing the same market price, water would be directed to the users to whom it is most valuable. To date, some southwestern states have attempted to open up limited water markets. This effort has been strengthened by the end of funding for most new water projects on the grounds that they are not economic. However, establishing a widespread water market poses at least two problems, one economic and one political..

The economic problem concerns externalities. Any expected rise in the price of water increases the incentive to tap rivers and groundwater for a profit. The result is the destruction of the water table and the salinization of the region's major waterways. The political problem is that large windfall profits and losses accompany higher water prices -- profits for those who have grandfathered water rights and losses for those who no longer receive subsidized water.

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The Southwest Water Shortage

Water is the lifeblood of the American Southwest. Since the turn of the century, the growth of the West has depended on water supplied by federal projects such as dams, canals, and aqueducts. California's Imperial Valley, perhaps the richest agricultural area per acre in the world, was created and continues to depend on transported water. Today the Southwest's most valuable resource is being misused and wasted even as experts warn of impending and chronic water shortages. California's supply of water is estimated to fall well short of its need.

The same is true for most other southwestern states. Cities, farms, heavy industry, mines, electric power stations, and parks and other recreation facilities all compete for a limited amount of water. Moreover, by law (and historical accident) these various users pay sharply different prices for government-supplied water. Los Angeles residents pay in excess of $250 per acre foot (the quantity of water needed to cover an acre a foot deep), whereas farmers in many regions pay no more than $10 per acre foot. Many chemical companies, desperate for water, cannot acquire sufficient amounts at any price.

Yet there is waste amid shortage. Farmers use open-ditch irrigation methods and cultivate low-value, water-intensive crops. Homeowners douse their already emerald lawns with water. Industry fails to take full advantage of recycling waste water. Swimming pools and golf courses continue to proliferate. Not surprisingly, water users continue to demand that government provide an ever-increasing supply of cheap water. In a time of budget deficits, should the federal government continue to build expensive new dams, canals, and other water projects and charge the Southwest subsidized (below full cost) prices for water? Are there better economic solutions to the region's dual problems of waste and shortage?

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IV. Mini-Case Volatile Oil Prices: 1999-2005 The six-year period between 1999 and mid-2005 witnessed renewed volatility in the price of crude oil. Crude oil prices varied from $15 per barrel at the beginning of the period to over $60 by mid-2005. How do the basic economic forces of supply and demand explain these dramatic price fluctuations?

Consider the year 2002 (in the middle of this period) and a time of relatively stable prices. Strong economic growth in the United States and Europe and economic recovery in Asia boosted oil demand. At the same time, the Organization of Petroleum Exporting Countries (OPEC), comprising about 37 percent of total world supply, held fast to its production quotas in order to stabilize the average price of crude in the range of $25 to $28 per barrel. To get a quantitative understanding of the resulting price effects, consider the following bare-bones demand and supply model. Let normal worldwide oil demand in 2002 be described by the equation QD = 90 - .6P, and let normal oil supply be QS = 75 million barrels per day. Equating demand and supply, Q D = QS, implies 90 - .6P = 75, or P = $25 per barrel, a good prediction of the actual price. (In graphical terms, the downward-sloping demand curve intersects the vertical supply curve at a price of $25.)

Now backtrack to early 1999. The rock-bottom average crude prices at the beginning of that year stemmed from a combination of ample supplies and depressed demand. The aftermath of the 1998 economic slowdown in East Asia (the financial crisis and Japan’s continued recession) contributed to reduced overall demand. At the same time, OPEC was providing ample oil supplies (members were overproducing their supply quotas) and Western producers were also awash in oil. As an illustration, 1999 supply was about 76 million barrels per day, and 1999 demand was 5 million barrels per day less than in 2002, implying the demand equation Q D = 85 .6P. Now setting demand equal to supply implies a $15 per barrel equilibrium price (again firmly in the range of actual prevailing prices). In 1999, both depressed demand (a leftward shift in the demand curve) and extra supply (a slight rightward shift in the supply curve) combined to cause a large drop in price relative to the normal level of $25 per barrel.

(Check this qualitatively by constructing the appropriate graph with shifting demand and supply curves.)

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Finally consider events in 2004. Between 2002 and 2004 demand grew significantly, implying a new demand curve: QD = 104 - .6P. But in the first half of 2004, crude supply was about 80 million barrels per day, up only slightly from than the 2002 level. The continuing war in Iraq and oil worker strikes in Venezuela each cut about 2 million barrels per day of supply. These cuts were balanced by increased production by Saudi Arabia and other OPEC and non-OPEC producers. Increased demand and limited supply meant an oil price surge – namely QD = 104 - .6P = 80, which implied an actual price P = $40 per barrel. Oil prices continued to rise during 2005, fueled by surging demand (particularly from fast-growing China) and supply disruptions from natural disasters (Hurricane Katrina) and terrorists threats.

Because the crude oil demand and supply curves are inelastic, relatively small quantity changes can lead to large price fluctuations. It is easy to check that the 2004 crude oil demand curve is relatively steep. (Plot the curve for yourself.) Demand is quite price inelastic: E P = (dQ/dP)(P/Q) = (-.6)(40/80) = -.3, at P = $40 and Q = 80. Furthermore, we have been dealing with a vertical, perfectly inelastic supply curve. Although supply might vary little in the very short run (three months), higher prices will certainly induce some supply increase in the longer run (6 months and longer). Suppose that the long-run supply response in 2004 is estimated according to the equation QS = 70 + .4P. (This equation is consistent with supply behavior under the more stable price experience of 2003: 80 million barrels supplied at a price of $25 per barrel.) Now, higher prices induce greater oil supplies; the longer-run supply curve is not vertical.) Setting 2004 demand, QD = 104 - .6P, equal to supply implies 104 - .6P = 70 + .4P, so that the longer-run equilibrium price is $34 per barrel with a global output of 83.6 million barrels per day. According to this equilibrium analysis, the longer-run increase in supply would be expected to bring prices down from above $40 per barrel to the mid-$30 range.

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ADDITIONAL MATERIALS

I. Short Readings L. Lahart, P. Barta, and A. Batson, “New Limits to Growth Revive Malthusian Fears,” The Wall Street Journal, March 24, 2008, pp. A1, A12.

J. Tierney, “The $10,000 Question,” The New York Times, August 23, 2005, p. A23. (The economics versus ecology bet revisited.)

H. Varian, “Technology Levels the Business Playing Field,” The New York Times, August 25, 2005, p. C2.

B. Davis, “Finding Lessons of Outsourcing in 4 Historical Tales,” The Wall Street Journal, March 29, 2004, p. A1.

V. Postrel, “Selection Ranks above Price among the Benefits of Shopping Online,” The New York Times, April 22, 2004, p. C2.

V. Postrel, “When it Comes to Books, Internet Selling has not Led to Uniformly Lower Prices,” The New York Times, September 11, 2003, p. C2.

H. R. Varian, “The Usual Decorous Waltz between Prices and Sales Becomes a Lively Tango in the World of Online Sales,” The New York Times, December 19, 2002, p. C2.

H. R. Varian, “When Commerce Moves Online, Competition can Work in Strange Ways,” The New York Times, August 24, 2000, p. 38.

John Tierney, “At the Intersection of Supply and Demand,” The New York Times Magazine, May 4, 1997, p. 38. (This article discusses rent control in New York City.)

“Day Care: Quality vs. Equality,” The New York Times, December 25, 1996, p. D1.

“Malthus, Watch Out,” The Wall Street Journal, February 11, 1998, p. A22.

“When the Boomster Slams the Doomster, Bet on a New Wager,” The Wall Street Journal, June 5, 1995, p. A1.

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John Tierney, “Betting the Planet,” The New York Times Magazine, September 2, 1990.

“Frost Damage at French Vineyards Might Actually Help Glutted Market,” The New York Times, May 8, 1991, p. A8.

II. Longer Readings Brynjolfsson, E., Y. Hu, and M. D. Smith, “Consumer Surplus in the Digital Economy: Estimating the Value of Increased Product Variety at Online Booksellers,” Management Science, November 2003, 1580-1596.

Symposium on E-Commerce, Journal of Economic Perspectives, 15, Winter 2001, 3-80.

P. Evans and T. S. Wurster, “Strategy and the New Economics of Information,” Harvard Business Review, September-October 2000, 71-82.

P. A. Samuelson, “Where Ricardo and Mill Rebut and Confirm Arguments of Mainstream Economists Supporting Globalization,” Journal of Economic Perspectives, Summer 2004, 135-146.

Michael Pakko and Patricia Pollard, “A Big-Mac Guide to Purchasing Power,” Review: Federal Reserve Bank of St. Louis, November-December, 2003, 9-28.

C. N. Noussair, C. R. Plott, and R. G. Riezman, “An Experimental Investigation of the Patterns of International Trade,” American Economic Review, June 1995, 462-491.

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III. Cases The Aluminum Industry in 1994 (9-799-129), Harvard Business School, 2002. Teaching Note (5-700-014).

The Offshore Drilling Industry (9-799-111), Harvard Business School, 2001.

Teaching Note (5-700-016).

Economic Liberalization and Industry Dynamics (9-700-075), Harvard Business School, 2000.

IV. Quips and Quotes You can make even a parrot into a learned political economist -- all it must learn are the two words “supply” and “demand.”

Everything is worth what its purchaser will pay for it.

A cynic is a man who knows the price of everything and the value of nothing. (Oscar Wilde) If competition has its evils, it prevents greater evils . . . (John Stuart Mill) When the last of the Bourgeoisie are hung, a capitalist will sell the rope.

The business of America is business.

Happiness can’t buy money.

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2. a. At harvest time, supply is fixed (regardless of the price) so the supply curve is nearly vertical. b. At the beginning of the growing season, supply is quite flexible implying an upward-sloping supply curve. c. In the long run, the supply curve is nearly horizontal.

4. a. Setting the demand and supply equations equal to one another, we have 200 - .2Q = 100 + .3Q or Q = 200. In turn, we find P = 160. b. If a tax of $20 per unit is levied on suppliers, the industry supply curve undergoes a parallel upward shift. Increasing the curve's price intercept by 20 implies P = 120 + .3Q. Setting the demand curve equal to the new supply curve implies 200 - .2Q = 120 + .3Q or Q = 160. Consumers pay the price: P = 200 - (.2)(160) = $168. Eight dollars of the $20 tax increase (or 40%) has been passed on to consumers. The price that producers receive (net of the tax) is $148. c. If a tax of $20 per unit is levied on consumers, the demand curve undergoes a parallel downward shift and becomes P = 180 - .2Q. Setting the new demand curve equal to the supply curve, we have 180 - .2Q = 100 + .3Q or Q = 160. The price before tax is P = 180 - (.2)(160) = $148. The price inclusive of the tax is 148 + 20 = $168. The price and quantity results in parts b and c are identical.

Whether a given tax is levied on suppliers or consumers makes no difference in the ultimate competitive equilibrium.

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6. a. Setting P = MC implies 16 = 4 + 4QF, or QF = 3.  = (16)(3) - 80 = -32. b. QD = 200 - (5)(16) = 120. The # of firms = QD/QF = 120/3 = 40. c. Firms will exit the industry because all are making losses. In the long run, PC = min AC = 120/5 = $24. At PC = $24, QD = 80, and the number of firms = 80/5 = 16. d. Price increased enough to allow each remaining firm a zero economic profit, while QF increased from 3 units to 5 units (the point of minimum AC).

8 .a. Equating 70 - Q and 40 + 2Q, we find Q = 10 and P = $60. b. Now we use 70 - Q = 25 + 2Q to find Q = 15 and P = $55. The subsidy has increased output and (consequently) reduced price. c. While the subsidy helps producers and consumers, it is not “free.”

Taxpayers must finance the cost of the subsidy. Economists note that subsidies can lead to inefficient outcomes, encouraging output past the point at which MB = MC.

10. a. The bookstore’s profit is  = (P – AC)Q = (9 – 5)(12) = $48 thousand.

Consumer surplus = ½(15 – 9)(12) = $36 thousand. b. From the demand curve, the chain sells 6 thousand books online at P = $12 and 10 thousand books in its stores at P = $7. Thus, its total profit is (12 – 4)(6) + (7 – 5)(10) = $68 thousand. Consumer surplus is the sum of triangles A and B: CS = ½(15 – 12)(6) + ½(12 – 7)(10) = $34 thousand. From the consumer’s standpoint, online selling has twin countervailing effects. In-store buyers benefit from lower prices brought by online competition. Online buyers actually pay a higher price than before (due to the chain’s skillful price discrimination).

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Price 15 12

A

B

9

P = 15 .5Q

7

0

6

12

16

Quantity of Books

Discussion Question a.

This does not contradict the law of demand, which states that price and quantity are inversely related given that everything else stays the same. A number of other determinants of demand may have changed (and most likely did change) during this period. For example, the number of students graduating from high school (the relevant population) may have increased. The value of a college degree also may have increased during this period as high school degrees have become more common and as job requirements have increased.

b. An increase in the population of high school graduates can be represented as a rightward shift in the demand curve. The increase in value of a college education can be represented as an upward shift in the demand curve. (The demand curve also represents the marginal benefit of an education to the marginal consumer.) The increase in cost can be represented by an upward shift in the supply curve. The result is an increase in the equilibrium price. Whether quantity increases or decreases depends on the relative shifts of the two curves.

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. and b. Using the spreadsheet optimizer, we find the short-run equilibrium price as follows: Set net demand (D-S) in cell F8 equal to zero by changing price in cell B8 and QF in cell B14, subject to (P – MC) in cell F14 equaling zero. The result is P = 11, Q F = 7.5, and D = S = 180. c. To find the long-run equilibrium price include the number of firms in cell C8 as an adjustable cell and add the zero-profit constraint, cell G8 must equal zero. The result is P = 6, Q F = 5, # firms = 56, and D = S = 280.

S2 a.

and b. Equating demand and supply implies: P = 160 – 2Q = 40 + Q. Therefore, Q = 40 and P = 80.

c. Using the spreadsheet optimizer, we maximize total trading gains in cell F10 by changing output in cell C5. The efficient level of output is Q = 40 (the competitive equilibrium found in part b).

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CHAPTER EIGHT MONOPOLY

OBJECTIVES 1. To examine price and output decisions under pure monopoly. (pp. 299-301) 2. To explore how monopolies are maintained through barriers to entry. (pp. 301-304) 3. To contrast competitive and monopolistic outcomes. (pp. 304-307) 4. To analyze cartel behavior. (pp. 307-310) 5. To discuss natural monopoly and regulation. (pp. 310-314).

6. To present a model of monopolistic competition (pp. 314-317).

TEACHING SUGGESTIONS I. Introduction and Motivation Market structure is studied in Chapters 7, 8, 9 and 10. The present chapter focuses on monopoly and monopolistic competition – a natural contrast to the analysis of perfect competition in Chapter 7. In turn, Chapter 9 considers oligopoly.

Through the comparison of competition and monopoly, it should become apparent that market structure is very important to decision making and profitability. This is one reason that we see expensive and protracted patent battles, why trademarks are so earnestly protected, and why so much advertising money is spent to establish brand loyalty. Thus any managerial

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decision must consider current market structure and how market structure is evolving or likely to evolve.

II. Teaching the "Nuts and Bolts" We begin by discussing with the students their notions of competition and monopoly. In particular, we discuss the consequences of raising price.

Students will often declare that "a monopolist can increase price as high as he or she wants and the consumer has no choice." Again, this can lead to a nice discussion about demand and elasticity, substitute goods, etc. You may want to refer back to the discussion of elasticity in Chapter 3.

In studying pure monopoly we like to begin by examining the optimization process (again, it is identical to that studied in Chapter 2) and also the determinants of profitability. Then we turn our attention to the many types of barriers to entry. It is helpful to get students to discuss these barriers and whether some may be socially useful (patents, scale economies, etc.) and which may be socially harmful (strategic barriers, control of resources, etc.) Note that there is a brief discussion of antitrust policy in Chapter 11. If you are not assigning Chapter 11 later in the course you may want to assign this short section now.

The comparison of perfect competition and monopoly on pages 304307 focuses on price and quantity effects. Again, social welfare implications are deferred to Chapter 11. However, if Chapter 11 is not assigned in the course then you might want to discuss the social welfare implications at this point. Cartels offer dramatic examples of the difference between competitive behavior and monopolistic behavior (achieved via cooperation). The regulation of natural monopoly provides a second contrast between monopolistic behavior and competitive behavior.

Finally, a discussion of monopolistic competition is provided. We emphasize that this structure combines the monopolistic assumption of a downward sloping demand curve, that is, differentiated products and some product loyalty, with the competitive assumption of free exit and entry.

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Mini-Case Monopolies, Past and Present For many managers, acquiring a monopoly position in a market is akin to an all-consuming search for the Holy Grail. However, it is worth remembering how few and far between monopolies are in the American marketplace. The adage “Many are called, but few are chosen” certainly applies to the monopoly quest. Here are three examples of “once, but not necessarily future” monopolies.

The Xerox Corporation accounted for over 95 percent of photocopier sales in the United States − a classic monopoly − until the late 1960s. In the 1970s, Xerox’s U.S. market share fell sharply. New firms, such as Canon, Sharp, Royal, and Savin successfully entered the copier market, particularly in the low- and medium-price segments. Currently, these four firms and Xerox make up this market with roughly comparable market shares. In the high-price, high-volume, copier-duplicator segment, Xerox, IBM, and Eastman Kodak divide the market (again roughly equally).

How did Xerox lose its monopoly position? During the 1970s, many of the company’s original patents expired, making it much easier for firms to market similar copiers. In 1975, Xerox was forced to sign a consent decree with the Federal Trade Commission agreeing to license its copier patents to other manufacturers. Perhaps more important, competitors were able to innovate around Xerox’s patents and develop comparable or superior copiers. In the early 1970s, Xerox stumbled by introducing a line of medium-volume copiers that proved unreliable. Finally, when the market moved from copier rental to copier purchase, new entry was facilitated because far less financial muscle was needed to sell copiers than to maintain a rental base.

Today, Xerox offers the widest product line and competes in more parts of the world than any other copier manufacturer. However, copiers have become much more of a “commodity” business, where numerous companies produce comparable copiers and where efficient assembly is as important as technological innovation. Instead of being a monopolist, Xerox is merely one of a dozen major players in the world copier industry.1 The American Medical Association (AMA) has the responsibility for overseeing the practice of medicine in the United States. Among its other activities, the AMA establishes procedures for licensing physicians and implementing guidelines for medical schools. In this latter role, the AMA has exercised control over the number of medical schools and the number John Wiley & Sons

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of medical students in the United States. Prior to 1965, the AMA influenced the number of doctors practicing in the United States by limiting the number of medical students and imposing formidable restrictions on the domestic practice of foreign-educated physicians. One result of this limitation was elevated incomes for physicians. In the 1960s, doctors’ earnings put them in the upper 20 percent of the income distribution.

Since the 1980s, the AMA’s control of the number of medical students has diminished and immigration laws for foreign doctors have been loosened, resulting in a greater-than-40-percent increase in the supply of doctors. By one estimate, this supply increase has “cost” the average doctor 20 to 25 percent in annual income.2 In short, the erosion of the AMA’s monopoly restrictions on the supply of physicians has meant a reduction in the excess returns earned by the medical profession.

The National Collegiate Athletic Association (NCAA) establishes and enforces the myriad rules governing intercollegiate athletics. Though intercollegiate athletics are certainly a part of the college experience and education, they are also “big business,” returning hundreds of thousands of dollars to universities with the most successful programs. Some top college coaches make seven-figure salaries. Athletic shoe companies pay top teams to wear their products. By its authority, the NCAA has monopoly control over this business. The organization determines the size and number of scholarships in different sports and the number of games played. It negotiates most of the lucrative radio and television agreements for major collegiate sports, such as football and basketball. Most important, the NCAA limits the “salaries” paid to athletes to the cost of tuition plus room and board. Of course, the NCAA and university presidents argue strenuously that student athletes should not be paid.

Whether one agrees with this view or not, a basic fact remains. The enormous profitability of intercollegiate sports is a direct result of the NCAA’s “monopoly-like” behavior − in particular, output restrictions that keep revenues high and scholarship rules that keep costs low.3

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ADDITIONAL MATERIALS I. Short Readings R. L. Rundle, “Botox Faces Worry Lines in Smooth Skin Game,” The Wall Street Journal, December 6, 2007, p. B1.

J. Carreyrou, “Inside Abbott’s Tactics to Protect AIDS Drug,” The Wall Street Journal, January 3, 2007, pp. A1, A10.

Lou, M., “New York Cabs can Charge More, but Riders can put it in Plastic,” The New York Times, March 31, 2004, pp. A1, A21.

Lipton, E., “Finding the Intersection of Supply and Demand,” The New York Times, November 23, 2003, p. A27.

Clark, D., “Big Bet Behind Intel Comback in Chips, Speed Isn’t Everything” The New York Times, November 18, 2003, pp. A1, A12.

“The Diamond Game, Shedding its Mystery,” The New York Times, April 8, 2001, p. BU1.

“Be True to Your Cola, Rah! Rah!?” The New York Times, March 10, 1998, p. D1. (This article describes soft drink sellers' exclusive deals with public schools.)

“Singing the Cartel Blues” The New York Times, March 29, 1998, p. WK4.

“As U.S. Trade Grows, Shipping Cartels Get a Bit More Scrutiny,” The Wall Street Journal, October 7, 1997, p. A1.

“Shipping Cartel to Seek 10% Rate Boost,” The Wall Street Journal, November 19, 1997, p. A2.

G. S. Becker, “There's Nothing Natural about 'Natural' Monopolies,” Business Week, October 6, 1997, p. 26.

“The Garbage Wars: Cracking the Cartel” The New York Times, July 30, 1996, p. 1.

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II. Longer Readings L. M. Kahn, “Cartel Behavior and Amateurism in College Sports,” Journal of Economic Perspectives, Vol. 21, Winter 2007, 209-226.

J. M. Perloff, “Cartels,” Journal of Industrial Organization Education, Vol. 1, 2006.

III. Cases Forever: De Beers and U.S. Antitrust Law, Harvard Business School, (9-700-082), 2000. Teaching Note (5-701-019)

IV. Quips and Quotes No one can earn a million dollars honestly. (William Jennings Bryant) Where does the monopolist gorilla sleep? Anywhere it wants.

United cartels stand, divided they fall.

There is unfortunately no good solution for technical monopoly. There is only a choice among three evils: private unregulated monopoly, private monopoly regulated by the state, and government operation. (Milton Friedman) The best of all monopoly profits is the quiet life. (J. R. Hicks) Like many businessmen of genius he learned that free competition was wasteful, monopoly efficient. (Mario Puzo, in The Godfather, Book III) Monopoly . . . is a great enemy to good management. (Adam Smith)

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Mini-Case Gasoline Price Gauging In 1981, a Boston-based gas station owner set the highest gasoline prices in the nation.8 During that summer, he charged $1.69 per gallon for unleaded gas during the daytime and $2.59 per gallon at night, when other downtown gas stations were closed. (His all-time high price was $3.99.)

Even at these extreme prices, however, the station owner sold an average of 3,000 gallons per week, half of this at night. Despite catcalls, pickets, and even vandalism from angry motorists during the gasoline crisis, the owner “stuck by his pumps”; he even charged $1 for air. As he put it, “People think of gas stations as public mammary glands, but they’re wrong. This is a business and it’s important to generate profits from every part of it. If I can use a resource, like air, to pay for the electric bill, so much the better. If you allow capitalism in its true form, it works beautifully.”

The station owner was an avowed profit maximizer, albeit not a very attractive one. How did he profit by his dual-price policy? The answer is price discrimination.1 Although his costs varied little day and night, the elasticity of demand varied greatly. He maximized his profit by charging a higher price at night, when demand is much more inelastic than during the day. In fact, we could go so far as to say that he operated under different market structures, day and night. At night, he appeared to have a pure local monopoly. Motorists desperate for gas had to drive miles to find another station open during those hours. Thus, the owner sold gas even at gouging prices. (Of course, at those prices the motorist may have preferred to buy five gallons rather than a full tank.) During the day, he faced a number of competitors within blocks and numerous stations in neighboring Cambridge. That is, the market resembled monopolistic competition. There was some product differentiation due to locational convenience and brand allegiance. Nonetheless, in normal times excess profits are limited by relatively free entry of new firms. (The gasoline crisis and accompanying supply shortage afforded sellers short-run, excess profits.)

1 E. Keerdojan, “There’s No Oil Glut for a Price Glutton,” Newsweek (July 6, 1981), 14.

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Question a. Suppose that, during the day, the station owner’s demand is given by PD = 2.06 - .00025QD. The marginal cost of selling gasoline is $1.31 per gallon. At his current $1.69 price, he sells 1,500 gallons per week.

Is this price-output combination optimal? Explain. b. The station owner sells an equal number of gallons at night, setting PN = $2.59. Suppose elasticity of demand is EP = -3. According to the optimal markup rule (in Chapter 3), is this price profit maximizing? c. The station owner is able to sell gasoline day and night at high prices.

Why aren’t there more gas stations in downtown locations in major cities? Explain.

Answer a. The combination, QD = 1,500 gallons and PD = $1.69, is profit maximizing. This quantity satisfies MR = MC: 2.06 - (.0005)(1,500) = 1.31. b. The $2.59 price at night is not optimal. According to the markup rule, the price should be: P = [-3/(1 - 3)]1.31 = $1.96 1/2. c. Although his contribution margin is very high, this does not mean that he is enjoying large profits. The high, fixed cost of downtown real estate is the main factor limiting his profit. This factor explains why one finds skyscrapers, not gas stations, in the downtown sections of major cities.

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2.

If the company is currently charging the optimal monopoly price, any cut will reduce its profit – the larger the price cut, the larger the profit reduction. Here is an illustration of how to compute the profit impact of a 10 percent price cut. Suppose the company's current price and output are P = $.20/pill and Q = 1 million pills and that MC = $.10/pill. Then, the company’s contribution is: (.20 - .10)(1) = $.1 million.

Suppose the company lowers price to P = $.18 and the elasticity of demand turns out to be EP = -1.5. Then dQ/Q = (-1.5)(-10%) = 15%, implying Q = 1.15 million. The firm's new contribution is: (.18 - .10)(1.15) = $.092 million, implying an 8% fall in profit.

4. a. A profit-maximizing cartel sets MR = MC. Thus, 500 - (2/3)Q = 200, or QM = 450 thousand trips. In turn, PM = 500 - 450/3 = $350 per trip. b. Under perfect competition, PC = LAC = $200. thousand trips.

Thus, QC = 900

6. a. We have P = 35 - 5Q and MC = AC = 5. Setting MR = MC, we find QM = 3 million chips and PM = 20. b. M = (20 - 5)(3) = $45 million Consumer surplus = .5(35 - 20)(3) = $22.5 million.

8. a. OPEC maximizes its profit by setting MR = MC. We have 115 - 4Q = 15. Therefore, Q* = 25 thousand barrels per day. In turn, P* = $65 per barrel.

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b. If it sets P = $50, then Q = 57.5 – (.5)(50) = 32.5 million barrels per day. Profit (per day) is:  = (50 - 15)(32.5) = $1.1375 billion. If it sets P = $65, its initial profit is:  = (65 - 15)(25) = $1.25 billion per day. In the second 5-year period, its optimal quantity and price are: Q2 = 18 million barrels per day and P2 = $60. (Check this by using the long-run demand curve and setting MR = MC.) Thus, 2 = (60 - 15)(18) = $.81 billion per day. OPEC’s average profit over the decade (ignoring discounting) is $1.03 billion per day – lower than $1.1375 billion from holding the price to $50 per barrel.

10.

The fact that the natural monopoly has earned zero economic profit on its capital investment is probably a sign that regulators have been successful in establishing rates (prices) that match the firm's long-run average cost.

*12. a. We know that P = 660 - 16Q1 and C = 900 + 60Q1 + 9Q12. Setting MR = MC, we have 660 - 32Q1 = 60 + 18Q1 or Q1 = 12. In turn, we find P1 = 468. The firm's profit is R - C = (468)(12) - [900 + (60)(12) + 9(12)2] = 5,616 - 2,916 = 2,700. b. If 10 firms each produce 6 units, total output is 60 and the market price is indeed P = 1,224 - (16)(60) = 264. Setting firm 1's MR = MC implies 1,224 - (16)(54) - 32Q1 = 60 + 18Q1, implying Q1 = 6 as claimed. Finally, the firm's average cost is C/Q = [900 + (60)(6) + 9(6)2]/6 = 264.

The typical firm earns a zero economic profit since P = AC. c. Under perfect competition, Pc = ACMIN. Setting AC = MC, we have that 900/QF + 60 + 9QF = 60 + 18QF, implying QF = 10 and ACmin = 240. Thus, Pc = 240 and Qc = 76.5 - (240)/16 = 61.5. The number of firms is found by dividing total output by each firm's

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output (QF): 61.5/10 = 6.15, or about 6 firms. The perfectly competitive market delivers a lower price and a slightly greater output with each firm producing at minimum average cost.

Discussion Question Under patent, the pharmaceutical company has a monopoly on the drug in question. The firm must still gauge overall demand in order to determine the profit-maximizing monopoly price. Upon the expiration of the patent, there is virtually free entry into the market, and numerous firms begin to produce generic versions of the drug. If the generic versions are seen as perfect substitutes for the monopoly drug, then vigorous price cutting would lead to the perfectly competitive outcome.

More likely, the former monopoly producer will have established some degree of brand allegiance for its drug. Because of new competition, it will be forced to lower its prices, but not all the way to the perfectly competitive level. (In addition to its branded version, the former monopolist might also choose to market its own generic version at a discount price to compete with rival generic versions.)

Figure 8.3 can be used to highlight the different pricing implications of pure monopoly and perfect competition. (However, Figure 8.3 depicts constant returns at the industry level, whereas the cost structure for pharmaceuticals exhibits significant sunk costs with AC steeply falling as output increases).

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. and b. Using the spreadsheet optimizer, we find the monopolist’s optimal plan in the short run: Maximize total profit in cell F8 by changing the typical plant’s level of output (Q F) in cell B14. The result is: QF = 4 and  = 450. Note that MR = MC at this optimal solution. c. To maximize the monopolist’s long-run profit, we include the number of plants in cell C8 as a variable cell. The new solution is: QF = 5, # firms = 20, and  = 500.

S2.

Use the spreadsheet created for Problem S2 of Chapter Seven. The monopolist’s objective is to maximize profit (cell F12) by changing the level of output in cell C5. The monopolist’s optimal output is QM = 24 and its maximum profit is 1,340.

S3 a. and b. Using the spreadsheet optimizer, we determine the short-run equilibrium under monopolistic competition as follows: Set the value of MR – MC in target cell G14 equal to zero by changing QF in cell B14. The resulting equilibrium is: QF = 8.95. c. To find the long-run equilibrium, set the value of MR – MC in target cell G14 equal to zero by changing QF in cell B14 and #firms in cell D8, subject to total profit in cell G8 being equal to zero. The equilibrium is: QF = 6, # firms = 10, and P = AC = 264.

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CHAPTER NINE OLIGOPOLY

OBJECTIVES 1. To provide an overview of Porter’s Five-Forces Framework. (pp. 328-330) 2. To compare market structures in terms of degree of concentration. (pp. 330-337) 3. To present the basic models of quantity competition (pp. 337-342) and price competition. (pp. 342-346) 4. To introduce the prisoner's dilemma paradigm. (pp. 346-349) 5. To explore other dimensions of competition: advertising (pp. 550-553), strategic commitments (pp. 353-355), and bundling (pp. 365-369).

TEACHING SUGGESTIONS I. Introduction and Motivation A. Points to Emphasize: Oligopoly is the most important domain for competitive strategy. (After all, a pure monopolist has no immediate competitors; each perfectly competitive firm is too small to affect the market by itself.)

1. In oligopoly, one firm's profit is affected not only by its own decisions, but also by the decisions of its competitors.

2. Therefore, a firm's profit-maximizing actions depend on the actions it expects its competitors to take. Game theory (taken up in Chapter 10) takes exactly this approach to competitive strategy.

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II.

Teaching the “Nuts and Bolts”

A. The Basics A traditional approach emphasizes the structural characteristics of markets and the well-known models of quantity competition and price competition.

Time permitting, the instructor may wish to expand the chapter's brief overview. Students find market concentration easy to grasp and interesting.

Concentration ratios from the Bureau of the Census are available online at http://www.census.gov/epcd/www/concentration.html The instructor may wish to present to the class ratios for other goods and services. In the business press, the ubiquitous “pie” charts depict market shares for the major players in various industries. Students might be asked to investigate the degree of concentration in a particular industry.

After covering the basics of quantity and price competition, the instructor may choose to discuss applied topics (advertising and bundling) or present additional game-theoretic examples. (If Chapter 10 is not assigned, it can be used as a source of stand-alone examples.)

Chapter Nine’s introduction has been expanded to discuss the elements of the five-forces model: 1. Threat of Entry; 2. Rivalry among Existing Competitors; 3. Pressure from Substitute Products; 4. Bargaining Power of Buyers; and 5. Bargaining Power of Sellers.

These concepts originated in: Michael Porter, “How Competitive Forces Shape Strategy,” Harvard Business Review, March-April 1979, pp. 137-145, available as Reprint 79209.

C. Recommended Problems Problems 3, 4, 6, 9, 10, and 11

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ADDITIONAL MATERIALS

I. Short Readings S. McCartney, “The Most Expensive City to Leave: Cincinnati,” The Wall Street Journal, December 11, 2007, p. B9.

“Two Upstarts Vie for Dominance in Satellite Radio,” The Wall Street Journal, March 30, 2005, p. A1.

“The Harder Hard Sell: The Future of Advertising,” The Economist, June 26, 2004, p. 69.

“Silver Linings Darkening Clouds: Airlines under Siege,” The Economist, March 27, 2004, p. 67.

“In Lean Times, Big Companies Make a Grab for Market Share,” The Wall Street Journal, September 5, 2003, p. A1.

“The War of the Razors,” The Boston Globe, August 31, 2003, p. E1, and “In Battle of Brands the Stakes are High,” The Boston Globe, August 31, 2003, p. E1.

“Dell Price Cut Puts a Squeeze on Rival H-P,” The Wall Street Journal, August 21, 2003, p. B1.

“In a Clash of Sneaker Titans, Nike Gets a Leg Up on Foot Locker,” The Wall Street Journal, May 13, 2003, p. A1.

“Videogame Giant Links with Sony Snubbing Microsoft,” The Wall Street Journal, May 12, 2003, p. A1.

“Mysterious Illness Opens a New Front in Amgen-J&J War,” The Wall Street Journal, January 29, 2003, p. A1.

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“Merged Hospitals Gain Both Power and Critics,” The New York Times, September 26, 2002, p. C1.

“Why the Sudden Rise in the Urge to Merge and Form Oligopolies?”

The Wall Street Journal, February 25, 2002, p. A1.

“Oligopoly,” The New York Times, June 11, 2000, p. WK1.

“Video Game Field Becomes Crowded and Highly Profitable,” The New York Times, December 17, 2001, p. C17.

“AOL’s Buddy Lists Spark Race to Harness the Power of ‘Presence’,” The New York Times, March 23, 2001, p. A1.

“How the Fiber Barons Plunged the Nation into a Telecom Glut,” The New York Times, June 18, 2001, p. A1.

“Makers of Generic Baby Formula Win Round in Court,” The New York Times, May 2, 2001, p. C5.

“Formula Fight: A Generic vs. the Giants,” The New York Times, September 26, 1999, p. BU1.

“A Matter of Trust,” The Economist, February 17, 2001, p. 78. (This article discusses cooperation in the prisoner’s dilemma.)

“Movers and Shakers,” The Economist, January 24, 1998, p. 63. (This article discusses theories of competitive strategy.)

“The Law as the Free Market's Rogue: Hostage to the Prisoner's Dilemma,” The New York Times, March 25, 1994, p. D1.

“How to Escape a Price War,” Fortune, June 13, 1994. p. 82.

“Tobacco Suit Exposes Ways Cigarette Firms Keep the Profits Fat,” The Wall Street Journal, March 3, 1990, p. 1.

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II. Longer Readings S. Borenstein and N. Rose, “How Airline Markets Work or do They?

Regulatory Reform in the Airline Industry,” in N. Rose (ed.), Economic Regulation and Its Reform: What Have We Learned? University of Chicago Press, 2009.

S. Berry and P. Jia, “Tracing the Woes: An Empirical Analysis of the Airline Industry, NBER Working Paper 14503, October 2008.

Akshay, R. R., M. E. Bergen, and S. Davis, “How to Fight a Price War,” Harvard Business Review, March-April 2000, 107-116.

T. Bresnahan, S. Stern, and M. Trajtenberg, “Market Segmentation and the Sources of Rents from Innovation: Personal Computers in the Late 1980’s,” Rand Journal of Economics, 1997, S17-S44.

III. Recommended Cases: Brief History of the Browser Wars (9-703-517), Harvard Business School, 2003.

Apple Computer-1999, (9-799-108), Harvard Business School, 1999.

Teaching Note, 5-799-150.

Competition and Business Strategy in Historical Perspective, (9-798010), Harvard Business School, 1998.

BMG Entertainment, (9-701-003), Harvard Business School, 2000.

Teaching Note, 5-701-049.

The Pharma Giants: Ready for the 21st Century? (9-698-070), Harvard Business School, 1998.

Cola Wars Continue: Coke vs. Pepsi in the 21st Century (9-702-442), Harvard Business School, 1995. Teaching Note (5-703-403).

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Strategic Countermoves: Coca-Cola vs Pepsi, (9-795-133), Harvard Business School, 1995.

IV. Quips and Quotes Advertising defined: Arresting the human intelligence long enough to get money from it.

People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices. (Adam Smith)

Putnam: Crandall: Putnam: Crandall: Putnam: Crandall:

Do you have a suggestion for me?

Yes, I have a suggestion for you. Raise your goddamn fares 20 percent. I'll raise mine the next morning.

Robert, we . . .

You'll make more money and I will, too.

We can't talk about pricing!

Oh [expletive deleted], Howard. We can talk about any goddamn thing we want to talk about.

(From a telephone conversation between Robert Crandall, CEO of American Airlines, and Howard Putnam, CEO of Braniff Airways, on February 21, 1982. The telephone call, unknown to Crandall, was taped. After finding out about the call, the Justice Department filed a suit accusing Robert Crandall of breaking the antitrust laws by proposing to fix prices.

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2. a. With the acquisition, three firms (rather than the original four) will account for 86% of the market. The four-firm concentration ratio (CR) will increase to 86% + s4, where s4 denotes the share of the 4th biggest firm. The 8-firm CR was 100% and of course remains 100%.

The “old” HHI is: 302 + 302 + 192 + 72 + [s52 + s62 + s72 + s82] = 2210 + [ ].

The “new” HHI is: 302 + 302 + 262 + [ ] = 2476 + [ ]. b. The HHI increased 266 points in a market where the original HHI exceeded 1800. Thus, the Justice Department's guidelines would call for possible prohibition of the acquisition. The acquisition was allowed in part because the resulting market would have 3 equally strong carriers who would be expected to compete vigorously against one another.

4. a. Each follower maximizes its profit by setting P = MC = 6 + QF. Therefore, each firm's supply curve is: QF = P - 6. With 4 followers, the total supply curve is: QS = 4QF = 4P - 24. b. The net demand curve of Firm A (the dominant firm) is QA = QD - QS = [48 - 4P] - [4P - 24] = 72 - 8P. Rearranging the leader's demand curve, we have: P = 9 - QA/8. The leader maximizes its profit by setting MR = MC: 9 - QA/4 = 6. Thus QA = 12. In turn, P = 9 - 12/8 = 7.5 and QS = (4)(7.5) - 24 = 6.

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6. a. The payoff table is

Firm M

$10 million $20 million

Firm N $10 million $20 million 50, 50 30, 60 60, 30 40, 40

b. Each firm's dominant strategy is to spend $20 million on advertising.

Yes, a prisoner's dilemma is present. c. If the firms could agree to limit spending to $10 million each, their profits would increase to $50 million.

8. a. The unique equilibrium has firm B setting a price slightly below $7.50 (the next lowest cost) and serving the entire market. b. No, firm B would continue to bid $7.50 to maximize its contribution toward its fixed cost. However, if B's fixed costs are so large so as to imply losses, the firm would exit the market in the long run.

10. a. Firm 1's price equation is: P1 = 150 - (2/3)Q2 - (4/3)Q1. Setting MR1 = MC to maximize profit implies 150 - (2/3)Q2 - (8/3)Q1 = 30, or Q1 = 45 - .25Q2. If a rival increases output, it causes an inward shift in the firm's demand and MR curves, thereby lowering the firm’s optimal output. b. Because both firms are identical, we can make use of the fact that Q1 = Q2 and set Q1 = 45 - .25Q1. Solving this equation, we find Q1 = Q2 = 36, P1 = P2 = 78, and 1 = 2 = (78 - 30)(36) = 1,728. c. In question 9, lowering one's own price induces the competition to follow suit. Thus, the equilibrium under price competition leads to lower profits than under quantity competition (where an increased quantity deters the rival's supply).

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12. a. We can write equation 12.7 as: [P-MC][Q/A][(dQ/dA)/(Q/A)] = 1, or [P-MC][Q/A] = 1/EA , after dividing each side by the last bracketed term. In the text example, [P-MC]Q/A = [1 - 0.8][10,000,000/1,000,000] = 2, which exactly equals 1/EA = 1/0.5 b. Divide the optimal price equation by the optimal advertising equation and cancel the common term (P-MC). The resulting expression is (A/Q)/P = (-1/EP)/(1/EA), or A/(PQ) = -EA/EP. In the example, A/(PQ) is 0.1, which is exactly equal to -EA/EP = -0.5/-5.0. c. To justify a much higher advertising ratio, Kellogg's sales must be very elastic with respect to advertising and/or very inelastic with respect to price.

Appendix Answers 1. Chez Pierre’s pure bundling strategy is profitable if diners’ preferences for different parts of the meal display some degree of negative correlation. If marginal costs are significant for some courses, Casa Pedro’s mixed bundling also can be profitable.

2. The optimal individual prices are PX = 20 and PY =20. The optimal bundled price is PB = $28, implying a total profit of (28 - 20)(3) = 24.

The optimal mixed bundling prices are PB = 28 and PX = PY = 20.

Consumer A buys Y, Consumer C buys X, and Consumer B buys the bundle. The firm's total profit is: (20 - 10)(2) + (28 - 20) = 28.

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. and b. For the typical small firm, MC = dC/dQ = 2q – 4. Setting P = MC, we have P = 2q – 4, or equivalently: q = .5P + 2. With 8 small firms, QS = 8q = 4P + 16. Taking into account this supply response, the dominant firm’s profit-maximizing price appears to be P = 10 or P = 11. c. We can invoke the spreadsheet optimizer to determine the leader’s optimal price. We maximize profit in cell I8 by changing cells B8 and B14, subject to P - MC in cell G14 being equal to zero. The solution is P = 10.5, q = 7.25 units, and QS = 58 units. The dominant firm’s output is 132 units and its profit is 656.

S2 a. With advertising spending fixed at A = 50, the firm maximizes its profit by changing its level of output. Using the optimizer, we find: Q* = 22.07 and  = 71.78. b. Now let us maximize profit, varying both A and Q. The optimal solution is: Q* = 20, A* = 25, and  = 75.

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CHAPTER TEN GAME THEORY AND COMPETITIVE STRATEGY

OBJECTIVES 1. To identify the similarities and differences among competitive situations. (pp. 371-375) 2. To introduce game-theoretic analysis: payoff tables and equilibrium strategies. (pp. 375-383) 3. To explore competitive strategies: entry deterrence and settings involving coordination and bargaining. (pp. 383-387) 4. To analyze sequential and repeated competition (pp. 388-397).

TEACHING SUGGESTIONS I. Introduction and Motivation There are numerous real-world examples of competitive situations that can be usefully analyzed using game-theoretic logic. A good source of examples is the current business press. (See the following list of suggested short articles.) Besides the applications in the chapter, the instructor can also draw on selected examples from Chapter 15 (bargaining) and Chapter 16 (competitive bidding). Another option is to engage students in stylized business games in class. See the competitive games described in Chapter 1 of this manual and, in the present chapter, the Battle for Air Passengers and the Shuttle Competition (Discussion Question).

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II. Teaching the “Nuts and Bolts” In our view, the most important ground to cover involves the creation and analysis of payoff tables. The instructor should carefully walk the class through the concepts of best responses, dominant strategies, and equilibrium strategies (in both zero-sum and non-zero sum settings). Students find the method of circles and squares particularly useful for finding equilibrium strategies. With a good grasp of these foundations, students can move on to the interesting “competitive strategy” applications. The analysis of game trees (extensive form games) can also be emphasized. The notion of a mixed strategy is an important optional topic presented in the appendix.

Suggestions 1.

The payoff table in Check Station 3 (depicting quantity competition) merits some discussion. (This is another look at the Cournot model introduced in Chapter Nine and provides a nice link.) The instructor should: a.

Walk through the firms’ best responses and establish the noncooperative equilibrium.

b.

Contrast the cooperative and non-cooperative outcomes. The collusive outcome is Q1 = Q2 = 6, where the firms’ total profits are maximized.

After these points have been brought out, it is easy to derive algebraic expressions for each player’s best response by setting MR = MC so that [30-Q2] - 2Q1 = 6, or Q1 = 12 - .5Q2. In turn, the (Nash) equilibrium is Q1 = Q2 = 8, after noting that Q1 must equal Q2 by symmetry.

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2. Market share competition (Problem 10). This constant-sum game requires students to construct the payoff table and identify the dominant-strategy equilibrium. Spreadsheet Problem 2 provides an advanced extension: If each firm has $10 million dollars to divide between the two markets, what is the equilibrium allocation?

Answer. Each should divide the $1 million in proportion to the size of the markets. Market I gets 30/48 of the total; Market II gets 18/48 of the total.

3.

Battle for Air Passengers. Additional remarks.

i)

As a “learning-by-doing” vehicle, this example can be played competitively by students in class. For instance, 30 to 40 students might be divided into 9 airline management teams with teams A, B, and C competing in one market; D, E, and F in a second market; and G, H, and I in a third. After 10 minutes of private discussion, each team writes down its number of departures. The first-round results for each market are posted on the blackboard, and profits are computed. With these results in view, teams make new decisions in a second round, the results are again posted, and then there is a third and final round. Since second and third round decisions tend to be reached quickly, the entire exercise (including discussion) takes about 45 to 60 minutes. Our rough track record of results is as follows: a.

About half the markets converge to equilibrium play (5,5,5) or near to equilibrium (5,5,4) by the second or third round.

b.

About 1 in 7 markets find their way to the tacit collusion outcome (3,3,4) or nearly there (3,4,4) or (3,3,3).

c.

About 1 in 5 markets converge to the zero-profit outcome (7,7,7).

d.

The remaining behavior is just plain random.

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There is an interesting explanation for the zero-profit outcome. This result inevitably occurs if teams look at relative profits rather than absolute profits. As long as total industry profit is positive, the airline with the most departures makes the most profit. (This is because both revenues and costs are proportional to the number of departures.) For example, if the first round result is (3,5,7), the respective profits are 30, 50, and 70. Looking at these profits, teams are often inclined to add flights to chase the market leader. A second round result might be (5,6,7) and a third round result (7,7,7). These outcomes usually prompt discussion of an airline’s “real” goal. Is it to maximize its absolute level of profit? Or is it to earn more than its rivals? We make it a point to emphasize at the outset of the exercise that all shareholders care about is the firm’s absolute level of profit. (However, the presumption could be quite different if the competition were modeled as a dynamic “war of attrition.”) ii)

The calculus derivation of the equilibrium is as follows: a = 450[a/(a + b + c)] - 20a.

Therefore, da/da = 450[(b + c)/(a + b + c)2 ] - 20 = 0.

By symmetry, a = b = c. Thus, we have: (450)(2a)/9a2 = 20, or a = 5.

In general, the equilibrium is: a = (R/c)(n-1)/n2, where R is total revenue, c is the cost per flight, and n is the number of airlines.

iii) We recommend that the instructor runs the exercise in class using different economic facts (so that knowledge of the text answer doesn’t dictate behavior), we suggest: R = $900,000, c = $25,000, and n = 3. In addition, let the capacity per flight be 300 passengers and the total number of passengers be 3,600. The collusive outcome is 3,600/300 = 12 total flights. From the formula above, the equilibrium outcome is 8 flights each (24 total). Finally, the zero-profit outcome occurs when there are 36 total flights.

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4.

The Shuttle Battle (Discussion Question). This takes less than 20 minutes to play and discuss in class and is another real “eye opener” for students. Be sure to prohibit students from any prior communicating.

Have students use a score sheet like the one on the next page. At each round, students write down their chosen prices, reveal these to their partners, and record profits.

Top performance occurs when both airlines aim for a collusive outcome ($139 fares) and neither defects to lower fares until near the end of the game. The worst performance occurs if one or both airlines engage in cut-throat pricing in the early periods. Once this occurs, it becomes nearly impossible to regain high-price ground.

Some benchmarks: $139 prices lead to payoffs of 612 and 684 respectively. In turn, $119 prices lead to a payoff of 396 for each airline. Finally, $99 prices lead to payoffs of 324 and 288 respectively.

C. Recommended Problems - Problems 3, 6, 7, 9, 10, and 13

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The Shuttle Battle Delta played by ______________ (Name)

Delta $139 Prices $119 $99

US Air played by ___________ (Name) US Air Prices $119 15, 42 22, 22 27, 9

$139 34, 38 42, 20 35, 7

$99 6, 32 10, 25 18, 16

Month

Delta’s Price

US Air’s Price

Delta’s Profit

US Air’s Profit

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

$ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___

$ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___ $ ___

___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___

___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___

Total Profits ___

___

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ADDITIONAL MATERIALS

I. Short Readings T. Burr, “Yanking ‘Harry’ Stirs the Plot Pot,” The Boston Globe, August 24, 2008, Pp. N9, N12.

K. Hudson, “Score One for Challenger in Phoenix’s Mall Bout,” The Wall Street Journal, March 13, 2008, Pp. B1, B2 R. Weisman, “X Games for Scientists Offers $10 Million Top Prize,” The Boston Globe, December 4, 2007, Pp. C1, C4.

Edward Wyatt, “Fighting for Ratings Dominance at the Same Time,” New York Times, October 28, 2006, p. B7.

“Can’t We all Just Get Along?” The Wall Street Journal, July 18, 2005, p.

R9.

“Boeing versus Airbus,” The Economist, June 25, 2005, pp. 67-68.

Carol Vogal, “Rock, paper, Payoff: Child’s Play Wins Auction House an Art Sale,” New York Times, April 29, 2005, p. A1.

Murray Chase, “Umpires are Getting Chance to Make Up for Bad Call,” The New York Times, December 28, 2004, p. C1.

“Summer Film Fight,” New York Times, April 26, 2004, p. B1.

“A TV Show Spurs Moves and Countermoves from CBS and NBC,” New York Times, January 13, 2004, p. C4.

“In Lean Times, Big Companies Make a Grab for Market Share,” The Wall Street Journal, September 5, 2003, p. A1.

“The New Card Shark,” New York Times, July 10, 2003, p. E1.

“Executives Ante Up, and Win Some Skills,” New York Times, February 9, 2003, p. BU14.

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“The Market Laboratory,” The Wall Street Journal, October 10, 2002, p. A14.

“And the Password is ….Waterloo,” The New York Times, December 27, 2001, p. D1.

“The Lemon Dilemma,” The Economist, October 13, 2001, p. 72. (George Akerlof, Michael Spence, and Joseph Stiglitz shared the 2001 Nobel Prize in economics for their pioneering work in game theory.)

“Now Comes the Gore vs. Bush Endgame, with 13 Toss-up States Left on the Board,” The Wall Street Journal, October 17, 2000, p. A24.

“How Economists Help Predict Behavior Online,” The New York Times, October 2, 2000, p. B1.

“QWERTY Spells a Saga of Market Economics,” The Wall Street Journal, February 25, 1998, p. B1.

“CVS Grows Rapidly, Using Shrewd Tactics and Ties with HMOs,” The Wall Street Journal, February 24, 1997, p. A1.

“The Only Campaign Number that Matters, 270,” New York Times, Sept. 26, 1996, p. 1. (This article describes the game of gaining the electoral votes to win the Presidency.)

“Shuttle Diplomacy, Airline Style,” The New York Times, October 25, 1996, p. D1. (This article describes how airlines compete for market share by adding daily departures.)

“Universal Studios’ Plan to Expand in Florida Moves Disney to Battle,” The Wall Street Journal, October 2, 1996, p. A1.

“Why the Best Doesn’t Always Win,” The New York Times Magazine, May 5, 1996, p. 60. (This article discusses the evolution of product standards.)

“How Wal-Mart Outdid a Once-Touted Kmart in Discount-Store Race,” The Wall Street Journal, March 24, 1995, p. A1.

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“Making Game Theory Work in Practice,” The Wall Street Journal, February 13, 1995, p. A14.

“How to Avoid a Price War,” The Wall Street Journal, May 10, 1993, p.

A10.

“The Games Economists Play,” The Economist, October 15, 1994, p. 96.

II. Longer Readings V.Suslow, “Entry Deterrence Strategies,” Journal of Industrial Organization Education, Vol. 1, 2006.

Silvia Nasar, A Beautiful Mind, Simon and Schuster, 2001.

This fine book chronicles the struggle with schizophrenia of 1994 Nobel Prize winner, John Nash (a developer of game theory). The film of the same name, starring Russell Crowe, is also of interest.

Symposium on Evolutionary Economics, Journal of Economic Perspectives, Spring 2002, 23-106.

J. K. Goeree and C. A. Holt, “Ten Little Treasures of Game Theory and Ten Intuitive Contrtadictions,” American Economic Review, 91, 2001, 14021422.

J. Berk, E. Hughson, and T. Vandezande, “The Price is Right but are the Bids?” American Economic Review, 86, 1996, 954-970.

Adam M. Brandenburger and Barry J. Nalebuff, “The Right Game: Use Game Theory to Shape Strategy,” Harvard Business Review, July-August 1995, 57-71.

Malcom Gladwell, “The Tipping Point,” The New Yorker, June 3, 1996, p. 32. (This article discusses the evolution and spread of disease and crime.)

J. Stavins, “Firm Strategies in the Personal Computer Business: Are Established Brands Better Off?” New England Economic Review, NovemberDecember 1995, 12-24.

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C. R. Morris and C. H. Ferguson, “How Architecture Wins Technology Wars,” Harvard Business Review, March-April 1993, 86-96. (Reprint 93203) R. H. Frank, T. Gilovich, and D. T. Regan, “Does Studying Economics Inhibit Cooperation?” Journal of Economic Perspectives, Spring 1993, 159-171.

F. M. Fisher, “Games Economists Play: a Noncooperative View,” RAND Journal of Economics, Spring 1989, 113-124.

John McDonald, The Game of Business, Anchor Books, 1977.

III. Cases A Note on Racing to Acquire Customers (9-803-103), Harvard Business School, 2003.

Judo in Action (9-703-454), Harvard Business School, 2003.

Hold or Fold? The War of Attrition (9-794-092), Harvard Business School, 1998. Teaching Note (5-795-166).

Toy Game (9-795-121), Harvard Business School, 1995.

Teaching Note (5-795-172).

Diaper War: Kimberly-Clark vs. Procter & Gamble (A), (92M003), Richard Ivey School of Business, 2000. Teaching Note (891MOV) (This case is available from Harvard Business School Publishing.)

Ready-to-Eat Breakfast Cereal Industry in 1994 (A) (9-795-191), Harvard Business School, 1997. Teaching Note (5-796-133).

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Bitter Competition: The Holland Sweetener Co vs. Nutrasweet, Parts A-G, (9-794-079, 080, 081, 082, 083, 084, 085), Harvard Business School, 1995.

Teaching Note (5-795-164).

R&D Race (9-190-108), Harvard Business School, 1992.

Teaching Note (5-191-165).

IV. Quips and Quotes It is a remarkable fact that [business strategies] are played largely in the mind. Only a small part of the play appears in overt action. Its full scope and depth lie in the players’ looking backward and forward and running through their minds their alternative moves and countermoves. (John McDonald, The Game of Business) A game is more than a sport, pastime, and amusement. It is also a model of the real world. (John McDonald, The Game of Business) Trust everybody but cut the cards.

If you’ve been in a poker game for thirty minutes and you don’t know who the patsy is, you’re the patsy.

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2.

It is never advantageous to move first in a zero-sum game. (The best one can do is choose one’s equilibrium pure strategy, if there is one.)

If there are multiple equilibria in a non-zero sum game, the first mover can select her preferred equilibria. A simple setting in which there is a second-mover advantage involves symmetric price competition. The second mover can do no worse than the price leader (it can always match the leader’s price) and can typically do better by undercutting it.

4. a. The players’ dominant strategies are R1 and C1. equilibrium.

This is the

b. The equilibria are (R1, C1) and (R2, C2). The first equilibrium is better for both players than the second and should be the expected outcome. c. The equilibria are the same as in part b. However, (R1, C1) becomes less certain as the actual outcome. If the second firm believes that the first might play R2 (intentionally or by mistake), it would hesitate to play C1 (at the risk of getting -100). If the first firm recognizes the second firm’s risk (and the fact it might play C2), it has a reason to play R2. In short, the -100 outcome may push the independent thinking of the players toward the (R2, C2) equilibrium.

6. a. The unique equilibrium outcome has firm A choosing High and firm B choosing Medium. (Use the method of “circles and squares” to confirm this.)

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b. The firms should coordinate their R&D strategies by selecting Medium and Low, respectively. Here the firms achieve maximum total profit, and each firm’s profit is greater than it was in the noncooperative equilibrium of part a.

8. a. There are no dominant nor dominated strategies for either player. b. The equilibrium strategies are R1 and C3; the equilibrium outcome is 10.

10. a. The payoff table below shows the total sales of the firms. (Carefully check these entries.) This is a constant-sum game. For any pair of strategies, the sum of the firms’ revenues is $48 million, the total revenue in the two markets. b. For Firm A, the strategies 3-0 and 0-3 are dominated by 2-1 and 1-2.

Firm A 3-0 2-1 1-2 0-3

Firm B 1-1 22.5, 29,19 27,21 13.5,

2-0 27, 21 33, 15 28, 20 18, 30

0-2 25.530,18 36,12 39,9 34.525.8,

22.2

But neither 2-1 nor 1-2 dominates the other. For Firm B, the dominant strategy is 1-1. Regardless of Firm A’s action, 1-1 gives better payoffs than 0-2 or 2-0. For this reason, Firm A should anticipate B’s play of 1-1. Accordingly, Firm A should play 2-1. The outcome (by iterated dominance) implies revenues of $29 million and $19 million respectively.

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12. a. The lure of the (10, 10) payoff would suggest that each party should cooperate at both its moves. b. Starting with B’s last move, B should move “down” to claim a payoff of 11. Anticipating this, A also would move “down” at its last move. In turn, B’s first move would be “down,” as would be A’s first move. The outcome is (2, 2). Given the logic of self-interested moves, there is no obvious way for the players to enforce the (10, 10) cooperative outcome.

Discussion Question a. In a one-time play, charging $139 is a dominated strategy; after its elimination, $99 dominates $119. The resulting payoffs are (18, 16). b. The only equilibrium is for each airline to charge $99 in every period.

Obviously, this results in poor overall payoffs for both airlines. With repeated play, the airlines have an incentive to reach an implicit cooperative arrangement -- both charging high ($139) fares.

However, as the 18-month horizon nears, each side has an increasing incentive to under-price the other. c. See Item 4 above.

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. The complete payoff table is shown below.

My Inventory

175

Average Auto Inventory of the Other Dealers 200 225 250 275 300

175

280.0

280.0

238.8

185.4

140.0

100.9

67.0

200

320.0

320.0

251.4

193.7

144.4

101.8

64.7

225

360.0

332.7

260.0

198.5

145.7

100.0

60.0

250

400.0

341.2

264.9

200.0

144.2

95.7

53.1

275

440.0

345.7

266.3

198.5

140.0

88.9

44.0

300

443.6

346.7

264.6

194.3

133.3

80.0

32.9

325

443.5

344.3

260.0

187.4

124.3

69.0

20.0

350

440.0

338.9

252.7

178.2

113.2

56.0

5.3

325

b. If each competitor’s inventory averages 325, then Dealer 1 should stock only 175 cars. For every 25 car decline in the average inventory per competitor, Dealer 1’s best response is to increase his inventory by 25. As in the earlier examples of quantity competition, the firm’s strategic actions can be thought of as “substitutes” -- the lower the competitors’ inventories, then the greater should be the firm’s. c. The unique equilibrium has: Q1 = Q2 = Q3 = Q4 = 250. (Check this using the payoff table.) Each firm’s profit is $200,000.

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d. Total demand is 800 cars per year. Therefore, the four dealers could split the market by holding 200 cars each in inventory. With all holding “lean” inventories, each firm’s profit is (4,000 – 2,400)(200) = $320,000. However, there is an obvious incentive to cheat on such an agreement. If each other dealer holds 200 cars, a typical firm maximizes its profit by holding 300 cars. (Check this using the payoff table.) e. Free entry would drive profits down to zero. Given that P = $4000, Qd = 800, and AC = $2,400, industry profits fall to zero when total inventories reach 1,333. Here, industry revenue ($3,200,000) just matches total industry cost (1,333 x $2,400 = $3,200,000). Of course, free entry might benefit consumers by inducing lower prices (in addition to expanded inventories).

S2. a.

With Firm A splitting its spending $6 million/$4 million and Firm B splitting $7 million/$3, the firms’ respective profits are $24.13 million and $23.87. Firm A earns the greater profit.

b. If Firm B spends $7 million in Market I, Firm A’s best response is to spend $6.27 million there. c. Using the spreadsheet optimizer, we find the following best responses for Firm A. Against $5 million spending, Firm A should spend $6.27. Against $6 million spending, Firm A should spend $6.25 million. Against $6.25 million spending, Firm A should spend $6.25 million. Against $9 million spending, Firm A should spend $6.90 million. Finally, against $9.5 million spending, Firm A should spend $7.48 million. The unique equilibrium has each firm spending $6.25 million in Market I and $3.75 million in Market II. Remember that Market I is worth $30 million and Market II is worth $18 million. In equilibrium, each firm allocates its spending in each

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market in proportion to the market’s revenue. For instance, the proportion of the total $10 million spent in Market I is: 30/(30 + 18) = 5/8 = .625.

Algebraic Solution.

Maximize  = 30[x/(x + y)] + 18[(1-x)/((1-x) + (1-y))]. with respect to x The optimality condition is: M = /x = 30y/(x + y)2 - 18(1-y)/((1-x) + (1-y))2 = 0.

By symmetry x = y, so that 30/4x = 18/[4(1-x)], or x = 30/48 = .625.

ANSWERS TO APPENDIX PROBLEMS

1.

Your proportions (x, 1-x) must leave your opponent indifferent between his pure strategies, implying -16x + 8(1-x) = 24x - 16(1-x) or 24 = 64x or x = 3/8. In turn, the opponent’s strategy proportion satisfies: -16y + 24(1-y) = 8y - 16(1-y) implying y = 5/8. Your overall expected payoff is -1; it is wise to walk away from the game.

2.

The Allies’ mixed strategy must satisfy: .6x + .8(1-x) = .9 + .6(1-x).

The German’s mixed strategy must satisfy: .6y + .9(1-y) = .8y + .6(1-y).

The respective solutions are x = 2/5 and y = 3/5. Germany is slightly more likely to defend Calais (where it is most vulnerable) and the Allies are slightly more likely to attack Normandy. The Allies’ winning chances are .72 in equilibrium.

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CHAPTER ELEVEN REGULATION, PUBLIC GOODS, AND BENEFIT-COST ANALYSIS

OBJECTIVES 1. To examine various market failures due to: monopoly (pp. 417-423), externalities (pp. 424-435), and imperfect information (pp. 435-438).

2. To identify the class of public goods and to determine the optimal amount of these goods. (pp. 439-441) 3. To introduce benefit-cost analysis and the net benefit rule. (pp. 442-447) 4. To discuss issues of benefit-cost implementation, including valuing benefits and costs. (pp. 448-451)

TEACHING SUGGESTIONS I. Introduction and Motivation In previous chapters we have discussed market structure. In this chapter we discuss the efficiency implications of different market structures and the implications regarding government intervention. This chapter can be motivated by asking students whether the government should ever be involved in private markets and, if so, why. Many students will bring noninterventionist views to the classroom that can be summarized by the statement that “markets are better”. From this point, the class discussion can turn on what we mean by “better” and this allows entry into a general discussion about the characteristics of markets. It is also possible to bring up examples where markets have broken down:

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What about the phone company? or the cable company? (natural monopoly) What about a polluter? (externalities) What about the harmful drug thalidomide? (imperfect information) What about defense? (public goods)

II. Teaching the “Nuts and Bolts” A. Market Efficiency.

The final section of Chapter 7 examines the characteristics of the ideal perfectly competitive market. It is worth some time reminding students that in the absence of externalities perfectly competitive markets deliver efficient levels of output. (Remind them that the marginal social benefit curve is the demand curve; thus, when demand equals supply, it follows that MB = MC.) This one idea can take the student a long way in understanding the effects of monopolization and externalities.

It is very important to emphasize to students that the type of efficiency that perfectly competitive markets guarantee is Pareto efficiency. That is, markets do not guarantee that the distribution of goods and services will be fair.

B. Monopoly and Externalities.

The instructor may wish to spend time reviewing the basics of market failure due to monopoly (Figure 8.3) and externalities (Figures 11.1 and 11.2). We also like to emphasize the basic point that whenever price diverges from marginal social cost there is a potential for inefficiency. This can be demonstrated to the students with the following simple example. Suppose that there are two goods and that a consumer is indifferent between them but has the resources only to purchase one of them. Call these goods widgets and gadgets. Suppose we have the following:

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Marginal Social Cost Price

Widget 100 150

Gadget 125 125

The Widget sells in a monopolized market so price is above marginal cost.

The Gadget sells in a competitive market with no externalities. The consumer will purchase the Gadget. However the consumer would have been just as happy with the Widget and at a lower cost to society. If both had been sold in competitive markets then the consumer would have purchased the widget.

Modify this example slightly:

Marginal Social Cost Price

Widget 150 100

Gadget 125 125

In this example the widget and gadget are both sold in competitive markets but widget production generates pollution while the gadget production does not. In this case the consumer purchases the Widget. Again, the Gadget gives just as much utility but at a lower cost to society. (One solution is to tax Widget makers. This would drive our consumer to buy the gadget. The consumer would spend $25 more but society, including this consumer, would gain $50 in reduced pollution.)

Advanced Example. Here is a problem discussed by Coase concerning the efficiency of taxes in resolving the problem of externalities.

Suppose that a train runs through farmland. The railroad has a choice of how many trains to run a day. If no trains run, the railway’s profit is zero, with 1 train its annual profit is $100,000, and with two trains its annual profit is $150,000. Farmers choose how many acres to plant: either 200 acres (this excludes acreage right next to the tracks) or 250 acres (including acreage next to the tracks). If no trains run, the farming profit is John Wiley & Sons

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$1,000 per acre per year. Unfortunately, sparks from the trains cause damage to the crops. How much damage depends on the number of trains running and the amount of acreage planted, according to the table below.

Annual lost farming profits due to sparks 0 Trains 1 Train 2 Trains

200 acres $0 $60,000 $120,000

250 acres $0 $120,000 $240,000

a. Summing the profits (and losses) of both farmers and the railway (taking into account spark losses), how many trains and how many acres maximize social efficiency (that is, maximize joint profits)? b. If the train company does not have to pay for the damage its trains cause the farmer, how many trains will it run and how many acres will the farmer plant? (Suppose that, because of the large number of farmers, negotiated side payments will not happen.) c. If the government imposes a tax on the train company equal to the dollar value of destroyed crops, how many trains will the train company run and how many acres will the farmers plant? (Again, assume no side payments.) d. Does imposing the tax result in social efficiency? Explain.

A Pollution Game. To convince students of the externality problem, the instructor might consider using the game described on the next page. Most students follow their self-interest and choose not to buy pollution control equipment. (Note that it is sometimes useful to play the game twice because some students do not get the hang of it the first time.) After students play the game, you might raise the issue of legislation requiring all persons to buy pollution control equipment and let the students debate this legislation.

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POLLUTION GAME Clean air is worth 100 to you. The amount of clean air that you get will be determined by the proportion of the class that chooses to buy pollution control equipment. For example, if half the class chooses to buy pollution control equipment then you will receive 50 points for clean air. Pollution control equipment costs 10. If you choose to buy pollution control equipment, 10 will be subtracted from your score. Thus your score depends on what you do and what your classmates do. For example, if you choose to buy pollution control equipment and 40% of the class buys pollution control equipment then you will receive 30 points. If you choose not to buy pollution control equipment and 35% of the class buys pollution control equipment then you will receive 35 points.

Make a choice (check one): _____I choose to buy pollution control equipment. _____I choose not to buy pollution control equipment Score:_______(to be determined later)

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C. Public Goods and Services.

A good way to introduce this general topic is to ask students to list examples of goods and services traditionally provided by government (and usually financed from tax revenues). Ask students to think of government at all levels -- federal, state, and local. A blackboard list should look something like the one on the next page. In the course of making the list, students usually suggest other government functions as well. Some functions – macroeconomic policy, and redistribution policies -- are beyond the present scope of concern. Others such as regulation (EPA, OSHA, and so on) occupy a middle ground between public provision and purely private markets. Regulatory examples can be listed on a separate blackboard.

With the list of goods and services in place, you can then ask questions aimed at exploring the economic basis for public provision. Which examples seem to be pure public goods (non-rival and non-exclusive)? In the absence of public provision, would private firms provide the good or service in a market setting? (Could firms do so profitably?) Remember to make the point that not all government provided goods are public in the economic sense. (Public housing is a case in point.) And not all public goods are supplied or built by the government. National highways are controlled by the government but built (and possibly operated) by private firms.

Examples of Public Goods and Services 1. National Defense 2. Police, Fire, and Sewer 3. The Criminal Justice and Legal System 4. Public Education (State and Local Level) 5. NASA, Government Sponsored Scientific Research 6. National Parks, Government-Owned Land 7. Public Transit 8. Public Housing 9. Entitlement (or Transfer) Programs Medicare, Medicaid, Social Security Unemployment Insurance, and so on.

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D. Benefit-Cost Analysis Public Investment in a Bridge. This example provides a nice “bridge” between the topics of public goods and benefit-cost analysis. The example shows that the public management of the bridge (at an efficient price, P = MC = 0) is superior to: (a) The “private” status quo (a monopoly ferry charging Pm = $2), (b) a regulated ferry (Pr = AC = $1), and (c) a privatelycontrolled bridge (which is unprofitable, see Check Station 5). Thus, it brings together most of the themes of the chapter. In addition, it provides plenty of practice in benefit-cost analysis -- calculating consumer surplus triangles and discounting. We feel that this is an example worth repeating in class.

Students do not have much of a problem with the net-benefit rule as a general principle. In fact, they have a tendency to accept it quite uncritically. Accordingly, it is useful to lead a discussion of the difference between efficiency and equity concerns. We believe that equity issues are important. Benefit-cost analysis assumes that such issues are unimportant because they will balance out in the long run or unimportant because equity issues should be addressed in some other arena, for example, through taxation. We feel it is important to check constantly to determine whether such assumptions are likely to hold. It is therefore good when doing benefitcost analysis at least to note what the likely distributional consequences will be. What are the benefits? What are the costs? What is the net benefit?

What are the equity consequences?

Consider the following hypothetical question. Suppose an anti-pollution agent could be released in the atmosphere and completely absorb all the air pollution in a metropolitan area. Would this be an unambiguously good thing for everyone? Most students respond with a loud and confident yes.

Obviously, eliminating all pollution at a nominal cost would generate enormous benefits in the aggregate. Nonetheless, some people might lose.

With pollution eliminated, urban rents would most certainly rise making

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low-income renters worse off. (Dry cleaners would be adversely affected and companies in the pollution abatement business would be devastated.)

The point is that almost any public program (even one unimaginably beneficial) can have some adverse equity consequences.

Valuing benefits and costs. In most cases, market prices provide the correct values for benefits and costs. One can get a good discussion going here. Usually market prices are the best we can do. However, they are far from perfect. Markets may not be competitive. If not, the price is likely to be higher than marginal social cost. There could be negative externalities.

In this case, price may be less than marginal social costs. Taxes, government regulation and liability rules may also cause price distortions.

Also, as mentioned in the text, the price of an unemployed resource may not reflect its cost. Labor, in the time of recession, is a prime example. Also, perfectly competitive markets do not guarantee equity. Prices in a market are more likely to represent the tastes of the haves and less those of the havenots. For example, in a society where resources are more evenly divided one would expect to find systematic price differences, for example, the prices of rare paintings could well be lower. Nevertheless, market price is usually the best we can do.

For non-marketed goods there are a variety of valuation techniques, including indirect market measures. One area that students are quite willing to debate involves risks to human life. In general, students feel that it is impossible to put a value on human life. A discussion will help to convince them that we make decisions every day that involve safety risks. For example, every time we get in a car to go to a movie we risk both our lives and others’ lives. The gain is the simple enjoyment of going to a movie.

Construction workers are exposed to risks (even of death) in building major projects (skyscrapers and bridges). When the government decides that cars do not have to be constructed out of 1/2” steel plate, we know that the result will be some additional fatalities. Students should eventually be convinced that the risk to human life can be priced.

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III. Discussion Assignment 1. Automobiles and Safety, reproduced on the next two pages makes for an interesting discussion assignment. The instructor should distribute the page to students and pose the question: Are the benefits of air bags worth the cost?

Suggested Answer: The information on numbers of lives saved and cost of installation implies a cost per life ranging between $625,000 ($5 billion/8,000) and $2,000,000 ($8 billion/4,000). Since most studies estimate the value of a life in the neighborhood of $1.5 million to $3 million, it would appear that an air bag program would generate a significant positive net benefit. This is before accounting for the benefits associated with injuries prevented. The valuation of injuries is complicated and painstaking. As a rough cut, however, we simply note that several studies have estimated that each fatality prevented is accompanied by reduced injuries equal in value of .5 of a fatality. Adding in this additional benefit further improves the benefit-cost calculation.

Installation of air bags would appear to generate significant net benefits. But this does not justify the immediate implementation of a mandatory program.

The real issue is whether safety is best served via air bags, by other competing programs, or through the private market. For instance, passive seat belts would save nearly as many lives as air bags -- assuming they are actually used and not disabled -- at a much lower cost. However, the case for or against passive constraints rests squarely on predictions of personal behavior -- whether a sufficient percentage of car owners will use the devices. A still more difficult question is whether the private market is best qualified to respond to the potential demand for safer automobiles. It is natural to ask: If air bags generate such large benefits, why aren’t consumers demanding, and suppliers delivering, air bags as an equipment option? Fifteen years ago, there seemed to be little response in this area by U.S. auto manufacturers. But since the early 1990’s, the “Big Three” automakers have made air bags as a standard feature of new models.

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Automobiles and Safety Since the late 1960’s, the National Highway Traffic Safety Administration has set increasingly stringent standards for automobile safety. Accident avoidance standards (pertaining to brake systems, tires, and steering mechanisms) have been effective in reducing fatalities at relatively little cost. Occupant protection standards also have been crucial in saving lives, but these are much more costly. These standards include requirements concerning head restraints, windshield glass, side door strength, and, of course, seat belts. The last decade has seen further safety initiatives: mandatory seat belt laws in many states, so-called “passive” seat belts, and air bags.

Automobile manufacturers and many car buyers see the cost of further regulation as too high. Safety advocates counter by arguing that the cost of doing nothing -- increased deaths and injuries from accidents -- is even greater. Thus, the argument rages concerning the “right” amount of automobile safety. Safety regulation of the automobile raises a chorus of questions: What are the costs and benefits of current auto safety programs?

What factors contribute to death and injuries in automobiles, and what safety decisions would most effectively save lives? How much is society -- that is, producers, consumers, and the government -- willing to pay for greater safety? the information needed to begin answering these questions depends on many factors, including factory costs, engineering studies and accident simulations, consumer purchasing (and driving) behavior, and societal value judgments.

As a concrete example of the issues involved, we choose to focus on a particular question: whether regulations requiring the fitting of air bags on new cares should be implemented. Numerous studies have attempted to value the benefits and costs of an air bag program.1 Consider the following question: If front seat air bags were fitted on all automobiles, what would be

1a

clear discussion and overview of these studies is provided by R. Crandall et al., Regulating the Automobile (Washington D.C.: The Brookings Institution, 1986). The present discussion (in a greatly simplified form) is drawn in part from this source.

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the predicted benefits in terms of lives saved and injuries prevented, and what would be the total costs?

First, let’s focus on lives saved. Despite differing methodologies, numerous studies have produced estimates in a manageable range of between 4,000 and 8,000 lives saved annually. (In all, some 50,000 to 55,000 lives are lost in automobile deaths each year.) For the moment, we will put aside the quantification of injuries prevented. What about the cost of air bags? Cost estimates range between $500 and $800 per car. Because about 10 million new cars are purchased in the United States each year, the total annual cost would be between $5 billion and $8 billion. (This is the cost of maintaining air bags in all U.S. cars. In all about 100 million vehicles are on the road.

Ten million cars are retired each year and replaced by 10 million new vehicles.)

Based on the information above, are the benefits of air bags worth the cost?

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2. A Gas Tax. In arguing for a 50-cent federal taxes on gasoline, economist Gregg Easterbrook lists some of the benefits: “The S.U.V. and pickup-truck crazes would not have occurred, or at least these vehicles would be much less popular; highway deaths would have been fewer; and gasoline demands would be lower as would oil imports. To continue, the world price of oil would have been lower, since petroleum demand in the United States is the first factor in oil markets; greenhouse-gas emissions in this country would be lower; Persian Gulf oil states would have less influence on the global economy and less significance to American foreign policy; fewer dollars would have flowed to oil sheiks; and the trade deficit balance for the United States would be smaller.” (Wall Street Journal, May 25, 2004) Do you agree with these arguments for the 50-cent tax?

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ADDITIONAL MATERIALS

I. Short Readings S. Castle, “Microsoft Gets Record Fine and a Rebuke from Europe,” The New York Times, February 28, 2008, p. C3.

E. Perez and C. Boles, “U.S. Fines British, Korean Airlines for Price Fixing,” The Wall Street Journal, August 2, 2007, p. A6.

J. Diamond, “What’s Your Consumption Factor?” The Wall Street Journal, January 2, 2008, p. A19.

M. L. Wald, “The Carbon Calculus,” The New York Times, November 7, 2007, pp. H1, H11 N. G. Mankiw, “One Answer to Global Warming: A New Tax,” The New York Times, September 16, 2007, p. BU6 L. Abboud and J. Clevstrom, “Stockholm’s Syndrome,” The Wall Street Journal, August 29, 2006, pp. B1, B8.

“The Rational Response to Terrorism,” The Economist, July 23, 2005, p. 72.

“Mixed Feelings as Treaty on Greenhouse Gases Takes Effect,” The New York Times, February 16, 2005, pp. C1, C3.

“The Anatomy of a Techno-Myth,” The Economist, March 26, 2005, p. 79.

“Are Too Many Unproven Drugs Receiving FDA Early Approval? Process Comes Under Scrutiny,” The Wall Street Journal, <March 1, 2005, p. B1.

“For 9/11 Families, Payments Ranged from Zero to Millions,” The New York Times, November 18, 2004, p. A26.

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Jane Brody, “The Real Risks to Children,” The New York Times, July 13, 2004, p. D7.

Greg Easterbrook, “The 50 cent a Gallon Solution,” The New York Times, May 25, 2004, p. A21.

“Life: The Cost-Benefit Analysis,” The New York Times, May 18, 2004, p.

WK14.

“How to Save the World? Treat It Like a Business,” The New York Times, December 20, 2003, p. A19.

“Pitting Fuel Economy Against Safety,” The New York Times, June 28, 2003, p. B1.

Robert Stavins, “Why not Trade Fishing Rights the Way Business Trades Pollution Credits?” Forbes Magazine, April 28, 2003.

L. Uchitelle, “Broken System? Tweak it, They Say,” The New York Times, September 28, 2002, pp. BU1, BU12.

R. Abelson, “Merged Hospitals Gain both Power and Critics,” The New York Times, September 26, 2002, pp. C1, C8.

V. Postrel, “Setting Fuel-Efficiency Targets for Vehicle Fleets Makes Little Sense,” The New York Times, December 6, 2001, p. C2.

“For Policy Makers, Microsoft Suggests Need to Recast Models,” The Wall Street Journal, June 9, 2000, p. A1.

Gary S. Becker, “Good-Bye, Tollbooths and Traffic Jams?” Business Week, May 18, 1998, p. 28.

“Capitalism is Giddy with Triumph; Is it Possible to Overdo It?” The Wall Street Journal, May 14, 1998, p. A1.

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“The Tax Credit for Research and Development: a Free Lunch,” The New York Times, February 5, 1998, p. D2.

“The Tale of the Secret Tapes,” The New York Times, November 16, 1997, section 3, p. 1. (This article describes price fixing by Archer Daniels.)

Arthur Schlesinger Jr., “In Defense of Government,” The Wall Street Journal, June 7, 1995, p. A14.

II. Longer Readings J. Baker and T. Bresnahan, “Economic Evidence in Antitrust: Defining Markets and Measuring Market Power,” in Handbook of Antitrust Economics, P. Buccirossi (Ed.) 2008.

W. K. Viscusi, “How to Value a Life,” Vanderbilt University Law School, Law and Economics Working Paper # 08-16, 2008.

M. Coate, “Economic Models and the Merger Guidelines: A Case Study,” Review of Law and Economics, Vol. 2, 2006, 53-84.

K. Arrow et al, “Are We Consuming Too Much?” Journal of Economic Perspectives, September 2004, pp. 147-172.

W. K. Viscusi, “Economic Foundations of the Current Regulatory Reform Efforts,” Journal of Economic Perspectives,” Summer 1996, pp. 119-134.

C. Winston, “Economic Deregulation: Days of Reckoning for Microeconomists,” Journal of Economic Literature, September 1993, pp. 12631289.

Charles Schultze, The Public Use of Private Interest, The Brookings Institution, 1977. (This classic is a very readable treatment on market failures and efficient regulatory remedies.)

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III. Cases Aviation Security after September 11: Public or Private? (9-702-021), Harvard Business School, 2004.

Antitrust Regulations in a Global Setting: The EU Investigation of the GE/Honeywell Merger (9-204-081), Harvard Business School, 2003.

A Note on Antitrust and Competitive Tactics (9-703-493), Harvard Business School, 2003.

Price-Fixing Vignettes (9-902-068), Harvard Business School, 2002.

Forever: De Beers and U.S. Antitrust Law (9-700-082), Harvard Business School, 2000.

Microsoft Corp.’s Pricing Policies (9-795-173), Harvard Business School, 1996.

New Jersey Solid Waste Crisis (9-792-002), Harvard Business School, 1992.

Teaching Note (5-793-026).

Many cases involving regulation, public goods, and benefit-cost analysis are available from the John F. Kennedy School of Government, Harvard University. These include: Buenos Aires-Colonia Bridge: The Project (#1400.0 & 1400.1) Harvard University JFK School of Government, 1997.

Implementing Electronic Road Pricing in Singapore (#1520.0 & 1520.1) Harvard University JFK School of Government, 1999.

Congestion Relief at Boston’s Logan Airport: Options and Controversies (#1341.0) Harvard University JFK School of Government, 1996.

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Post Office Square Park (#1231.0 & 1231.1) Harvard University JFK School of Government, 1993.

Dulles Toll Road Extension (#1276.0) Harvard University JFK School of Government, 1995.

Bridge over the Tempisque River (#1292.0) Harvard University JFK School of Government, 1995.

High Speed Rail Between Boston and New York (#1022.0) Harvard University JFK School of Government, 1991.

West Side Highway Proposal (#876.0) Harvard University JFK School of Government, 1989. Teaching Note (876.2) Massachusetts Water Resources Authority (#702.0) Harvard University JFK School of Government, 1986.

The Department of Transportation and Airport Landing Slots (#781.0) Harvard University JFK School of Government, 1987. Teaching Note (781.2)

IV. Quips and Quotes When you can measure what you are speaking about and express it in numbers, you know something about it. Otherwise your knowledge is of a meager and unsatisfactory kind. (Lord Kelvin) The age of chivalry is gone; that of sophisters, economists, and calculators has succeeded. (Edmund Burke) Generally speaking, there is no one who knows what is in your interest so well as yourself. (Jeremy Bentham) For every action, there is an equal and opposite government regulation.

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Under capitalism, man exploits man. Under socialism, it’s just the reverse.

When the last of the bourgeoisie has been hanged, a capitalist will sell the rope.

The world will always be governed by self-interest. We should not try to stop this. We should try to make the self-interest of cads a little more coincident with that of decent people.

Govern a nation as you would cook a small fish -- do not overdo it.

No more good must be attempted than the people can bear. (Thomas Jefferson) The man who believes in “laissez faire” would allow his garden to run wild so that the roses might fight it out with the weeds and the fittest might survive. (John Ruskin) The business of America is business.

Law (government) is like sausage. If you like it, you shouldn’t watch it being made. (Chancellor Bismarck) Government creates scarcely anything. A government could print a good edition of Shakespeare’s works. But it could not get them written. (Alfred Marshall) One cabinet minister, two agency heads, and three congressmen wired in a series produces near infinite impedance.

He’s the kind of politician who could cut down a redwood tree, climb the stump, and make a speech about conservation.

(Adlai Stevenson about Richard Nixon)

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2. a. If management and workers have perfect information about job risks in mining, there is no externality. The two sides should be able to negotiate working conditions that provide the efficient amount of safety. However, if information is imperfect and asymmetric (workers are not aware of all safety risks), there is an externality. b. The competitors of these large brokerage firms receive a positive externality: more productive new hires whose training was paid for by someone else. Larger firms are well aware of these “lost” hires but still profit from these training programs. c. Spam is an obvious externality. Spammers send out millions of mass emails at an exceedingly low marginal cost. The idea behind the 5second requirement is to increase greatly the cost of sending email by the millions, without imposing any real cost on normal email users. d. The couple incurs an adverse effect, but this is not an externality.

Rising house values are a price effect – an effect occurring within a well-functioning market – not a side effect occurring outside the market.

4. a. Do families make well-informed, rational decisions concerning purchases of toys, cereal, and so on? If not, government paternalism might justify regulation of advertising. b. One point of view is that workers and employers already structure efficient labor contracts -- ones providing the optimal amount of workplace safety (at the least total cost). According to this argument, regulating additional safety is unnecessary. Deregulation is called for.

However, if information about work place risks is imperfect, government regulation might be warranted to insure an “optimal amount” of safety.

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c. By law, there must be access for the disabled. However, the cost of modifying existing buildings and transport is often very high. In some locals, offering shuttle-bus and taxi service to the disabled has proved more convenient and cost-effective than modifications to transit systems. d. The Department of Agriculture should tradeoff the benefits of pesticides (in increasing crop yields) against the costs (their risks as possible carcinogens). e. Maintaining the infrastructure should be a matter of benefits and costs, not dictated by budget worries.

6. a. Yes, this is a prisoner’s dilemma. It does not pay for any block to unilaterally reduce emissions. (For instance, for the DNs, the benefit is 10 and the cost is 12.) b. A multilateral .2 reduction does not quite work; for the U.S., the extra benefit is 18 and the extra cost is 22. However, if the DNs block reduces by .4, all blocks benefit: U.S. (24 > 22), Europe (32 > 18), and DNs (38 > 30). c. The efficient scheme has EUS = 1.2, EEU = .8, and EDN = .8, implying total emissions of 2.8. The net benefits (relative to the status quo are: U.S. (24 - 0), Europe (32 - 18), and DNs (38 - 48). Suppose the U.S. and Europe paid $15 billion and $5 billion per year to DNs as compensation. Then the net gains would be $9 billion, $9 billion and $10 billion for the respective blocks.

8. a. This rule makes sense when deciding whether or not undertake a single program. Note that B/C > 1 is equivalent to B - C > 0.

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b. The benefit-cost ratio does not reveal any information about the scale of either project. Therefore, it cannot be used to decide between the two. For instance, suppose the library’s total benefit is $1,500,000 and its total cost is $1,000,000. The garage’s total benefit is $1,400,000 and its total cost is $700,000. The garage has the greater net benefit and the better benefit-cost ratio. Now suppose that the garage were one-half as large (with correspondingly lower benefits and costs). Its benefit-cost ratio would be unchanged (and still better than the library’s), but its net benefit would be only $350,000, making it an inferior choice compared with the library. c. This strategy makes great sense. The state should repair bridges where the benefit is greatest per dollar spent, i.e., where the “bang is biggest for the buck.” In this way, the state maximizes the total benefit it can achieve with its limited budget.

10. a. The developer’s maximum profit is at site A; profit is 12 - 6 = 6. But the final agreement will be reached at site E, which provides the greatest total net benefit, NB = (12 - 8) - 2 = 2. b. If only sites A, B, and D are feasible, no negotiated agreement is possible because, in each case, the town’s cost exceeds the developer’s potential profit. However, in terms of statewide benefitcost analysis, the facility should be sited at A. Here, the total net benefit is 4 + (12 - 6) - 7 = 3. Together, the state and developer must pay the host town at least 7 to induce it to agree to the facility.

Discussion Question Imperfect information might be the main reason for lax security at airports.

Until 2002, airlines contracted with private companies to provide security.

Before September 11, air travelers were much more concerned with convenience and speeding through airports than with security risks. By underestimating real risks, air travelers downplay the value of security.

Accordingly, they are unwilling to pay the costs (in dollars, inconvenience, John Wiley & Sons

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and delay) of increased security. A related source of market failure is a lack of incentives on the supply side. Barely profitable airlines have low incentives to pay for more scrupulous security. The security companies themselves might care more about minimizing costs (by hiring minimumwage, low-skilled, high-turnover labor) than maximizing security.

Government regulation was also lax. A third source of market failure might be lack of competition between the small number of dominant firms supplying airport security nationwide.

After September 11, the main issue was whether screening should be done by private employees under strict rules and regulations or by federal employees Congress opted for the latter alternative. Government provision brings with it the potential problems of inefficiency, elevated costs, and lack of competition. Whether U.S. airport security is elevated to the levels found in Europe remains to be seen.

Bonus Question Some years ago, the governor of Maine assembled a task force to evaluate several oil company proposals to develop a deep-water harbor for tankers and to build a refinery at Machias, a seaport at the northeast end of the state’s rocky and unspoiled coast. Following are miscellaneous facts that may (or may not) be relevant to a benefit-cost analysis of the proposal.

(1) The harbor and refinery would process 30,000 barrels of crude oil per day into home-heating oil, gasoline, and other fuels.

(2) The complex would provide cheaper oil to the state and to the northeast in general. (Neighboring New Hampshire imports much of its oil from Canada.)

(3) Recently, a tanker broke up off the Maine coast, causing a major oil spill. Coastal property owners believe the harbor and refinery would jeopardize the value of their land.

(4) Industries in the region, including utilities, construction companies, and the state’s railroads, vigorously support the project.

(5) Unemployment in the region is 3 percent above the national average.

(6) The growth of Maine’s tourist industry (the state’s biggest industry) has leveled off in recent years.

(7) Several oil companies are competing for the project.

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a. Outline a benefit-cost analysis of the proposed project. b. Select three or four benefits or costs and explain how they might be valued. Describe some of the major uncertainties inherent in the benefitcost analysis. What additional information about these risks would be useful?

Answer a. Here is a sample benefit-cost outline of the Machias oil refinery.

Affected Group Benefits Oil consumers Oil Companies Other Business Unemployed workers

Costs

Consumer Surplus (more oil, lower prices) Added profit Added profit Wage income (net of lost leisure)

State & City Tax Payers Tourism

Capital and Operating Costs Lost tourist industry profit Lost consumer surplus Environmental cost of oil spills, oil pollution

Society

b. Valuing benefits. The benefit to consumers of more abundant oil at lower prices would be estimated by the increase in the consumer surplus triangle. A regional macroeconomic model would be useful in estimating the potential increase in business activity (business profits).

The value of new jobs should be based on estimated market wages.

Estimates of capital and operating costs depend on engineering and economic information (how much concrete at what prices). Key uncertainties surround the long-term forecast of oil demand, the cost of the facility, environmental costs, and the potential adverse effect on tourism.

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ANSWER TO SPREADSHEET PROBLEM

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1. a. and b. We can use the spreadsheet optimizer to confirm the results of each of the analyst’s recommendations. To confirm the monopoly outcome (the result of analyst A’s policy of laissez faire), maximize industry profit in cell C15 by changing industry output in cell B10. The result is QM = 17,500 and PM = 325. To confirm the result of analyst C’s tax policy, enter a tax of 100 in cell C10, and again maximize industry profit in cell C15 by changing cell B10.

The result is QM = 12,500 and PM = 375. To confirm the perfectly competitive outcome (Analyst B’s recommendation), maximize consumer surplus in cell B15 by changing cell B10, subject to industry profit in cell C15 being greater or equal to zero. Now the result is QC = 35,000 and PC = 150. Finally, to identify the optimal regulatory policy, maximize total benefit in cell G15 by varying output in cell B10. The result is Q* = 25,000 and P* = 250. c. To find the optimal output, tax, and quantity of pollution cleaned up, we maximize total benefits in cell G15 by changing output in cell B10, the tax in cell C10, and the level of cleanup in cell D10, subject to the firm’s cleaning up to the point that the MC equals the tax (cell E19 equal to zero). The result is Q* = 25,000, P* = 250, tax* = 100, and cleanup = 10. Maximum total benefits come to 3,625.

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CHAPTER TWELVE DECISION MAKING UNDER UNCERTAINTY

OBJECTIVES 1. To review the notions of uncertainty, probability, and expected value. (pp. 466-469) 2. To show how to draw decision trees and average them back. (pp. 469477) 3. To explore sequential decisions. (pp. 477-484) 4. To introduce the concept of risk aversion. (pp. 484-487) 5. To show how the manager can use the (more general) criterion of expected utility. (pp. 487-495)

TEACHING SUGGESTIONS I. Introduction and Motivation A. Business Risks.

An easy way to introduce this topic is to ask students to prepare to answer the discussion question at the end of Chapter 12. The discussion can begin with the case of Olestra, Procter & Gamble’s miracle no-fat substitute and then move on to a categorization of business risks in general. (See the suggested answer to the discussion question in the answer section.)

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B. Guinea Pig Questions 1. $500,000, Take it or leave it? a. In 1975, a 22-year women sued a New York hospital and two doctors for administering too much oxygen following her birth (two months premature). The woman grew up nearly totally blind. The case went to trial, and while the jury was deliberating its verdict, the hospital’s lawyers offered a settlement of $165,000. Would you advise her to accept this settlement? b. In 1976, the parents of a seven-year old boy sued a Maryland hospital for $3.5 million in a similar case. Born two weeks premature, the boy was blinded shortly after birth allegedly because too much oxygen was given. Again, the case went to trial, and during jury deliberations, the family received a settlement offer of $500,000. Would you advise them to accept?

2. Escalating Investments in R&D (Presented and analyzed in Chapter 13, pp. 524-526). An electronics firm can initiate an important R&D program by making a $3 million investment. There is a 1/5 chance that the program will meet with immediate success (i.e. within the year) earning the firm a return of $10 million (for a net profit of $7 million). If success does not come, the firm can invest another $3 million and raise its success chances to 1/4. If this second stage fails, the firm can invest again, and so on, up to a total of five investments. The investment cost for each stage is $3 million, the ultimate return from a successful completion of the program (sooner or later) is $10 million, and the chances of success are 1/5, 1/4, 1/3, 1/2, and 1 for the investments. As the manager in charge of this decision, would you make the initial $3 million investment and if so, at what stage (if any) would you stop?

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3. Which Cab Did It? Two taxi companies, Blue Cab Co. and Green Cab Co., serve a city. Blue cabs make up 85% of all taxies. A witness to a hit-and-run accident at twilight believes he saw a green cab leave the scene. The witness is found to be 80% accurate in distinguishing green and blue cabs (under twilight conditions). What are the chances that a green cab did it? (This question relies on probability revisions taken up in Chapter Thirteen.)

4. Monday Morning Quarterbacking. In the 1984 Orange Bowl game, Nebraska trailed Miami by 14 points in the second half. Nebraska scored a touchdown and kicked the extra point to close the gap to seven points.

Then, in the closing seconds of the game, Nebraska scored a dramatic touchdown to draw within one point. If it successfully kicked the extra point, the game would end in a tie. If it attempted a two-point conversion, it would win or lose the game depending on whether or not the attempt succeeded. Nebraska attempted to pass for the two-point conversion. The pass failed, and Nebraska lost the game and the mythical national championship of college football.

Analyze Nebraska’s decisions to attempt the one-point and two-point conversions after its first and second touchdowns in the second half. In your analysis, assume that (1) kicking a one-point conversion is a certainty; (2) a two-point conversion has a .5 chance of succeeding; and (3) Nebraska is indifferent between a tie and a 50-50 chance of winning or losing. What is Nebraska’s optimal strategy?

C. Guinea Pig Questions, Discussed 1. In either instance, your decision to accept or reject the settlement depends on your assessment of the expected monetary award (net of legal fees) in court. You would be wise to question your lawyers closely about the strength of the case, the chances of various court outcomes (including appeals), and the possible monetary awards. In each instance, the

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plaintiff accepted the settlement. After accepting $165,000, the woman learned that the jury would have awarded her $900,000. In the family’s case, the jury would have awarded them nothing. This is a good example to show the difference between good and bad decisions versus good and bad outcomes.

2. See the discussion and decision tree in Chapter 13, pp. 524-526.

3. Most students believe that the chances are 60% or greater that the green cab did it. Many think that chance is 80% (reflecting the witness’s degree of accuracy). The correct answer is 12/29 or about 41%. To see this, suppose that cabs of one company are no more prone to such behavior than the cabs of the other. If we imagine 100 such accidents, 85 would involve blue cabs and 15 green cabs. The green cab accidents would generate (.8)(15) = 12 correct green sightings. The 85 blue cab accidents would generate (.2)(85) = 17 incorrect green sightings. Thus, of 29 green sightings, 12 are actually caused by green cabs.

4. Consider two of Nebraska’ possible strategies: (1) kicking after each touchdown secures a tie; (2) kicking now and trying the two-point conversion after the second touchdown offers a 50/50 chance of winning (if the conversion succeeds) or losing (if the conversion fails). According to the coach’s stated preferences, Nebraska is indifferent between these two options. However, there is a third and better option: (3) attempting the two-point conversion now. If it succeeds, kick the point after the second touchdown (for a one-point win). If it fails, go for two points after the second touchdown (in the hopes of salvaging a tie). This strategy offers a 50 percent chance of a win (whenever the first conversion succeeds), a 25 percent chance of a tie (the first attempt fails, the second succeeds), and only a 25 percent chance of a loss (if both attempts fail). This strategy “dominates” the second strategy, i.e., it provides a lower chance of a loss and the same chance of a win.

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II.

Teaching the “Nuts and Bolts”

A. The basic oil drilling problem implies the simplest possible decision tree: one safe action, one risky action with only two possible outcomes.

It is a good vehicle for talking about: a) probabilities (that they are subjective and subject to revision, i.e. not etched in stone) and b) the meaning of expected value. Check station 2 extends the example to a sequential decision.

B. Developing an anti-clotting drug is a more complicated sequential decision. We usually present a streamlined discussion which includes: a) comparing the expected profits of each separate method; b) drawing the decision tree for simultaneous development (reminding students of the product rule for independent probabilities and that the company will only commercialize the more profitable method, not both); c) showing via a decision tree that an optimal sequential decision is to try the riskier R&D method first.

C. Launching a new product Here is an alternative extended example that can be used in class to cover the “nuts and bolts” of Chapters Twelve and Thirteen. A firm faces the decision as to whether to launch a new product. The decision tree is: booming economy $20 million .36 Launch 5.92

Not

moderate economy .40

$10 million

recession -$22 million $0

.24

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The firm’s business economists think the most likely outcome is moderate growth (a 40 percent chance). If moderate growth does not materialize, they see a booming economy as more likely than a recession by odds of 3 to 2.

Note: If you wish, you can supply a complete economic explanation for the launch payoffs. Here is one possible example: The firm’s fixed cost is $30 million and its MC is $2/unit.

Demand is: P = 12 - .5Q in a boom economy (so that Q* = 10 and P* = 7), P = 11 - .5Q in a moderate economy, (so that Q* = 9 and P* = 6.5) P = 6 - .5Q in a recession (so that Q* = 4 and P* = 4).

Here Q is in millions of units. The respective profits are $20 million, $10.5 million, and -$22 million, close to the round numbers above. As the decision tree shows, the best course of action for a risk-neutral firm is to launch the product.

To carry out the analysis if management is risk averse, let utility values be: U(20) = 100, U(-20) = 0, U(10) = 90, and U(0) = 70.

It follows that: E(Ulaunch) = (.36)(100) + (.4)(90) + (.24)(0) = 72, which is just slightly better than the utility of not launching, U(0) = 70.

D. Suggested Problems Problem 4 (European Consortium) Problem 6 (Producing a Movie) Problem 8 (A Legal Decision) John Wiley & Sons

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E. Risk Aversion and Expected Utility. Here is an important topic that in some respects is hard to handle. The presentation in the text takes the middle road -- by discussing risk aversion in general terms and then showing how a manager can quantify his attitude toward risk by assessing utility values. i) For an instructor who wants to devote minimal time to this topic, we suggest omitting the discussion on pp. 487-495. The instructor can stress the consequences of risk aversion (the demand for insurance, the tradeoff between risk and return, the evaluation of safety risks) and note that risk aversion implies declining marginal utility. ii) An instructor who wants to do more on this topic might look more closely at the assumptions underlying expected utility and discuss actual choices under uncertainty (which often violate the expected utility axioms).

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ADDITIONAL MATERIALS

I. Short Readings P. Barta, R. Mathews, and A. Batson, “Giant Mines Scramble to Cut Output,” The Wall Street Journal, November 17, 2008, pp. A1, A15.

J. A. Trachtenberg, “In Era of Blockbuster Books, One Publisher Rolls the Dice,” The Wall Street Journal, October 16, 2006, p. A1.

Eric Lipton, “U.S. Report Lists Possibilities for Terrorist Attacks and Likely Toll,” The New York Times, March 16, 2005, p. A1.

Andrew Higgins, “In Path of Tsunami, Giant Cement Maker Struggles to Recover,” The Wall Street Journal, February 11, 2005, p. A1.

“Citibank Takes Risk by Issuing Cards in China,” The Wall Street Journal, March 10, 2004, p. C1.

“Burned Once, Brewers Return to China – with Pint-size Goals,” The Wall Street Journal, March 10, 2004, p. A1.

“How Two Economic Gurus Think about Risk,” The Wall Street Journal, February 2, 2004, p. A2.

“By Learning from Failures, Lilly Keeps Drug Pipeline Full,” The Wall Street Journal, April 21, 2004, pp. A1, A12.

“Risk Management for the Masses, The Economist, March 22, 2003, p. 7071.

“A Blaze in Albuquerque Sets off Major Crisis for Cell-Phone Giants,” The Wall Street Journal, January 29, 2001, p. A1.

“How Burger King Got Burned in Quest to Make the Perfect Fry,” The Wall Street Journal, January 16, 2001, p. A1.

“Anatomy of a Recall: How Coke’s Controls Fizzled out in Europe,” The Wall Street Journal, June 29, 1999, p. A1.

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“Microsoft’s Universe of Risk,” CFO Magazine, March 1997, p. 69.

“When Uncertainty is Constant, You can Still Plan for Surprises,” The Wall Street Journal, April 9, 1998, p. B1.

“A Wildcatter on the Tame Side: Replacing Roughnecks with Computers,” The New York Times, 1998, p. D1.

“Why ‘Waterworld’ with Costner in Fins is Costliest Film Ever,” The Wall Street Journal, January 31, 1995, p. A1.

“Maker of Simplesse Discovers Its Fake Fat Elicits Thin Demand,” The Wall Street Journal, July 31, 1991, p. 1. (A good illustration of multiple risks) “Ignoring Big Chances, Bumblebees just Seek Small, Reliable Gains,” The New York Times, September 3, 1991, p. c10. (Even bumblebees are risk averse.)

II.

Longer Readings

Daniel Maxwell, “Decision Analysis: Aiding Insight VII,” OR/MS Today, 46, October 2008. (A nice survey of decision tree software.)

D. von Winterfeldt and T. M. O’Sullivan, “Should We Protect Commercial Airlines Against Surface-to-Air Missile Attacks by Terrorists?” Decision Analysis, Vol. 3, June 2006, 63-75.

M. Baucells and C. Rata, “A Survey Study of Factors Influencing Risk-Taking Behavior in Real-World Decisions under Uncertainty,” Decision Analysis, Vol. 3, September 2006, 263-276.

R. L. Keeney, “Making Better Decision Makers,” Decision Analysis, Vol. 1, December 2004, 193-204.

D. N. Sull, “Disciplined Entrepreneurship,” MIT Sloan Management Reivew, 46, Fall 2004, 71-77.

S. A. Lippman and K. F. McCardle, “Sex, Lies, and the Hillblom Estate: A Decision Analysis,” Decision Analysis, 1, September 2004, 149-166.

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Keefer, D. L., C. W. Kirkwood, and J. L. Corner, “Perspective on Decision Analysis Applications, 1990-2001,” Decision Analysis, March 2004, pp. 4-22.

Kirkwood, C. W., “Approximating Risk Aversion in Decision Analysis Applications,” Decision Analysis, March 2004, pp. 51-67.

Ulvila, J. W., and J. E. Gaffney, “A Decision Analysis Method for Evaluating Computer Intrusion Detection Systems, Decision Analysis, March 2004, pp. 35-50.

Lovallo, D. and D. Kahnman, “Delusions of Success: How Optimism Undermines Executives’ Decisions,” Harvard Business Review, July-August 2003, 56-63.

Watkins, M. D. and M. H. Bazerman, “Predictable Surprises: The Disasters You Should Have Seen Coming,” Harvard Business Review, April 2003, 7280.

Kahneman, D., “Maps of Bounded Rationality: Psychology of Behavioral Economics,” American Economic Review, 93, 2003, 1449-1475.

Stonebraker, J. S., “How Bayer Makes Decisions to Develop New Drugs,” Interfaces, 32, November-December 2002, 77-90.

Dillon, R. L., R. John, and D. von Winterfeldt, “Assessment of Cost Uncertainties for Large Technology Projects: A Methodology and an Application,” Interfaces, 32, July-August 2002, 52-66.

Hunink, M. G. et al, Decision Making in Health and Medicine: Integrating Evidence and Values, Cambridge UK: Cambridge University Press, 2001.

S. A. Gurusami, “Ford’s Wrenching Decision,” OR/MS Today, December 1998, pp. 34-39. (The auto giant uses decision analysis to choose suppliers.)

Friedman, D., “Monty Hall’s Three Doors: Construction and Deconstruction of a Choice Anomaly,” American Economic Review, 88, 1998, 933-946.

J. Weisberg, “Keeping the Boom from Busting,” The New York Times Sunday Magazine, July 19, 1998, p. 24. This article examines the risk John Wiley & Sons

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calculations and decision methods of Robert Rubin, Treasury Secretary in the Clinton administration.

H. Courtney, J. Kirkland and P. Viguerie, “Strategy under Uncertainty,” Harvard Business Review, November-December 1997, pp. 67-79. Reprint 97603.

P. L. Bernstein, “The New Religion of Risk Management,” Harvard Business Review, March-April 1996, pp. 3-6.

J. Kluger, “Risky Business,” Discover Magazine, May 1996, p. 44. (The entire Discover issue is devoted to risky decisions,) R. D Behn, “The Shed Load Decision,” Duke University, Institute of Policy Sciences and Public Affairs, 1993.

W. E. Balson, J. L. Welsh, and D. S. Wilson, “Using Decision Analysis and Risk Analysis to Manage Utility Environmental Risk,” Interfaces, 22, 1992, pp. 126-139.

J. Hosseini, “Decision Analysis and its Application in the Choice Between Two Wildcat Oil Ventures,” Interfaces, March-April 1986, pp. 75-85.

D. E. Bell, “Bidding for the S.S. Kuniang,” Interfaces, March-April 1984, pp.

17-23.

III. Cases Blackout: August 14, 2003 (9-804-156), Harvard Business School, 2004.

Align Technology, Inc.: Matching Manufacturing Capacity to Sales Demand (9-603-058), Harvard Business School, 2002.

Merck & Co.: Evaluating a Drug Licensing Opportunity (9-201-023), Harvard Business School, 2001. Teaching Note (5-202-001) Complexity and Error in Medicine (9-699-024), Harvard Business School, 2000.

Canonical Decision Problems (9-396-308), Harvard Business School, 1997.

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Teaching Note (5-396-313) Amgen Inc.: Planning the Unplannable (9-492-052), Harvard Business School, 1997. Teaching Note (5-492-054) Value at Risk (9-297-069), Harvard Business School, 1997.

Biotechnology Strategies in 1992 (9-792-082), Harvard Business School, 1992.

Arundel Partners (9-292-140), Harvard Business School, 1992. Teaching Note (5-295-118) Strategic Response to Uncertainty (9-391-192), Harvard Business School, 1993.

Freemark Abbey Winery, Harvard Business School, (9-181-027), 1981, 2 pages. (A winery must decide when to harvest its grapes in light of uncertain weather conditions.)

Key West Fisheries. (See the following mini-case and teacher note). A small tuna fishing outfit must decide whether to i) contract with a Spanish importer to sell a portion of its catch at a fixed price, or ii) reject the contract and sell all its catch at uncertain domestic prices. Both the total size of the fishing outfit’s catch and the domestic price are uncertain.

IV. Quips and Quotes I was expecting this but not so soon. (Written on a Tombstone in Boot Hill) You can get more with a kind word and a gun than you can get with a kind word. (Gangster Al Capone on the virtues of diversification) I never knew what true happiness was until I got married. But by then it was too late.

What men really want is not knowledge but certainty.

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Education is the process of moving from cocksure ignorance to thoughtful uncertainty.

If Hell is paved with good intentions, it is largely because of the impossibility of foreseeing consequences. (Aldous Huxley) So far indeed are men in business from knowing the conditions on which future prices and profits depend that they are often ignorant after the event of the causes of their past profit and losses. (Thomas Leslie) They couldn’t hit an elephant from this dis-. . . (The dying words of Civil War General, John Sedgewick) Ready, fire, aim. (A confused sequential decision?)

The best way to have a good idea is to have a lot of ideas.

A man jumps from a skyscraper. As he passes the 20th floor, “So far, I don’t see any problems.”

What do you do when you see a banker jumping out the window? Follow him. There must be money to be made down there.

The contempt of risk and the presumptuous hope of success are in no period of life more active than at the age at which young people choose their professions. (Adam Smith) The gambling known as business looks with austere disfavour upon the business known as gambling. (Ambrose Bierce)

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Key West Fisheries In March 1997, Harry Morgan, the founder and president of Key West Fisheries faced a difficult decision. The company has been in the tunafishing business for twelve years, operating a single boat. Morgan has seen the company’s fortunes rise and ebb, mainly depending upon the price of tuna. When prices are high, tuna fishermen prosper. When prices fall, they face tough times. He is uneasy about the company’s future because of uncertainties about prices and the size of future catches.

Earlier in the week, Morgan received a Fax from a Spanish tuna importer to whom he has sold fish in the past. The importer is offering to make a oneseason contract with Key West Fisheries to deliver 150,000 pounds of tuna at a price of $1.10 per pound. The tuna is to be delivered by October 31.

Morgan has to decide in the next 10 days whether to accept or reject the Spanish contract.

In considering this decision, Morgan has gathered the following information.

The tuna season in the south Atlantic runs from the beginning of April to the end of October. (Not all of this time can be devoted to fishing; time in port or traveling to fishing grounds means lost fishing days.) At the risk of some over-simplification, Morgan foresees two different types of seasons, good and bad. (The type of season depends upon ocean currents, tuna migration patterns, the number of competing boats, and so on.) In a good season, the total Atlantic catch will be large, and the company can catch 300,000 pounds of tuna. In a bad season (small catches), Morgan will be able to catch only 240,000 pounds. Before the beginning of the season, it is impossible to tell whether it will be good of bad. Based on his past experience, Morgan sees good and bad seasons as equally likely. However, after the first four weeks of the season, Morgan can discern the prevailing pattern (large or small catches).

Copyright 1990 © Boston University. This case has been adapted from Edgartown Fisheries (A).

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Tuna is caught not only in the Atlantic but also in the Pacific, primarily by US, Russian, and Japanese fishermen. Therefore, the price of Atlantic tuna depends not only on whether the Atlantic catch is large or small but also on the size of the Pacific catch. The expected price of tuna depends upon the catches in the respective oceans as follows: Atlantic Large/Pacific Large: Atlantic Large/Pacific Small: Atlantic Small/Pacific Large: Atlantic Small/Pacific Small:

$.50 per pound $.80 per pound $.70 per pound $1.00 per pound

Morgan considers each of these four possibilities to be equally likely. (The type of Pacific season is fifty-fifty, and the outcomes of the two seasons are independent of one another.) As with the Atlantic catch, the size of the Pacific catch cannot be predicted prior to the season. However, the type of Pacific season will be known after the first three or four weeks of fishing.

If Morgan accepts the contract, there are two options for delivering the fish to Spain. He can hire a commercial freighter to take all or part of the 150,000 pounds at a cost of $.44 per pound. Alternatively, Morgan can use his own boat to deliver the fish. This would require two round-trips since his boat can carry only 75,000 pounds. (The cost difference between operating the boat for shipping versus fishing is insignificant.) However, if the company delivers the fish itself, it will lose about 1/3 of the available fishing days (meaning a 1/3 reduction in its total catch).

Revenues, Costs, and Assets. The company’s revenues in the coming season consist of its domestic sales (at uncertain prices) plus revenues from the importer (if the contract is accepted). The company’s total cost for the entire fishing season is $180,000 (the sum of crew’s wages, interest expenses, office rent, etc.) regardless of how much fish is caught. Besides its boat, the company currently has $30,000 in liquid assets.

Morgan has decided to sketch a decision tree to help him determine whether to accept the contract (and if so, how to deliver the fish). He has decided to John Wiley & Sons

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measure outcomes in terms of end-of-season liquid assets. For example, if he rejects the contract and there are large catches in both oceans, his end-ofseason assets are: 30 + [($.50)(300) - 180] = $0 thousand. (The low price results in a $30 thousand dollar loss reducing his assets to zero.) If he accepts the contract, uses the freighter, and both catches are large, his assets are: 30 + [165 - 66 + 75 - 180] = $24 thousand, and so on.

Assuming Morgan is risk neutral, what is his best course of action?

Additional questions.

1. Suppose that Morgan is able to delay his contract decision until after the first of May (when he will know the types of Atlantic and Pacific season). How much is this postponement worth to him?

2. Suppose instead that Morgan can hire the services of a marine biologist who will be able to give him a perfect forecast of the Pacific season (large or small) immediately. How much is this forecast worth?

3. Morgan is risk averse. He has provided the following certainty equivalents for fifty-fifty gambles. Sketch his utility curve, and use this to determine his preferred course of action:

50-50 Gamble a) $90,000 and $0 b) $90,000 $24,000 c) $24,000 and $0

and

Certainty Equivalent

50-50 Gamble

Certainty Equivalent

$24,000

d) $90,000 and $52,000

$69,000

$52,000

e) $52,000 and $24,000

$35,000

$6,000

f) $24,000 and $6,000

$13,000

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Key West Fisheries Teaching Note A decision tree describing Harry Morgan’s basic problem is shown below. If Morgan rejects the contract, his monetary position at the end of the year depends on the price of tuna and the size of his catch. The expected value of this option is $49,500 after averaging over the four equally likely outcomes.

If Morgan accepts the contract, he locks in a fixed price for 150,000 pounds of his catch, but the profit from his domestic sales is still uncertain. Thus, he faces the same chance branches as in the reject decision. After learning about the type of season(s) and the going price of tuna, he decides how to ship the fish. Thus, there is a decision square at the end of each of the four chance branches. He is free to make different shipping decisions in different types of seasons.1 (This decision is simple since it is made after all uncertainty has been resolved.)

The decision tree shows that his most profitable shipping decision depends on the price of tuna. If the going price is $.80 or $1.00 (when the Pacific catch is small), hiring the freighter is the more profitable option. If the going price is $.50 or $.70 (when the Pacific catch is large), using his own boat more profitable. There is an easy intuitive explanation for this result. When domestic prices are high, the opportunity cost of using his own boat exceeds the explicit cost of hiring the freighter. Accordingly the freighter is the better option. Conversely, when domestic prices are low, doing it yourself costs little and is the better option.

Comparing the expected values of the alternatives, we see that a risk-neutral decision maker should reject the contract.

1 We have not shown one possible shipping option: transporting half the catch by freighter and half by

one's own boat. The value of this option always lies midway between the values of shipping all by freighter and all by own boat. Thus, it is always worse than one of the “all or none” alternatives and can be eliminated from consideration.

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Freighter

$.50 40

.25

Boat Freighter

$.80

Accept

69

.25

Boat Freighter

42.5 $.70

22

Boat

.25

Freighter

$1.00

39

.25

Boat

24 40 69 55 12 22 39 25

49.5 $.50 .25 Reject

$.80

0

90

.25 49.5 $.70

18

.25 $1.00

90

.25

The following questions are typical vehicles for leading a class discussion of this decision: 1. What are Morgan’s options? What are the associated risks? If he accepts the contract, does he face an additional decision?

2. How does one use the answers above to draw the outline of Morgan’s decision tree? At what point in the tree does the shipping decision occur?

(This last question is important since many students incorrectly put the shipping decision “up front” -- at the same time the contract is signed.)

3. What are the monetary values to be listed at the branch tips?

4. Where should Morgan begin solving the tree? (This is another important question. The analysis of any tree should begin with the last decision -- that is, the tree should be solved from right to left. Students who forget this point are inclined to begin with the first decision.)

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Additional Questions: 1. The option to postpone effectively gives Morgan perfect information about price and catch before having to make the contract decision. The appropriate decision tree is shown below. From the tree, we see that if the domestic price is $.80 or $1.00 (when the Pacific catch is small), Morgan should reject the contract. If the domestic price is $.50 or $.70 (when the Pacific catch is large), Morgan should accept the contract and use his own boat. The overall expected value is $60,500. Therefore, the expected value afforded by this additional information is 60,500 - 49,500 = $11,000.

Freighter 24 $.50

40

.25

Boat Reject

40 0

Freighter 69 $.80 Delay signing

90

.25

Boat Reject

60.5

55 90

Freighter 12

$.70 22 .25

Boat Reject Freighter

$1.00 .25

40

Boat Reject

22 18 39 25 90

2. The decision tree below shows the situation when Morgan can acquire perfect information about the Pacific catch (from a marine biologist) before making his contract decision. Knowing that the Pacific catch is large, Morgan should accept the contract and use his own boat. Knowing that it is small, he should reject the contract. The expected value is $60,500. This is exactly the same expected value as in question 1. After a little reflection this should be no surprise. It happens that Morgan’s best course of action depends only the Pacific season (and the resulting prices).

Knowing the Atlantic outcome as well (as in question 1) makes no John Wiley & Sons

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difference. Since the same decisions are made in either case, Morgan obtains the same expected value.

Freighter

Atlantic Large .5

Accept

40

31 31

Freighter

Atl. Small

Pacific Large

22

.5 31 .5

Boat

Atlantic Large .5

Reject

Boat

24 40 12 22

0

9 Atlantic Small

18

.5 Marine Biologist 60.5

Accept 54

Pacific Small .5

Freighter

Atlantic Large .5

69

Atl. Small

39

.5

90

Atlantic Large .5

Reject

Boat

39

Boat

25

90

90

.5

Extra Point. For different amounts of information, Morgan’s expected values are: --- --$49,500 Atl --$54,250 --- Pac $60,500 Atl Pac $60,500

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55

Freighter

90 Atlantic Small

69

Knowing the Pacific outcome, Morgan obtains no additional benefit from also knowing the Atlantic. But what if Morgan does not know the Pacific outcome? In this case, would information on the Atlantic outcome be of any value? The answer is yes. As the tree below shows, Morgan’s expected value is $54,250 (which is greater than $49,500).

Freighter

Pacific Large .5

Accept

40

31 54.5

Freighter

Pac. Small

Atlantic Large

.5 Pacific Large .5

54.5 .5

Boat

Reject

69

Boat

24 40 69 55

0

45 Pacific Small

90

.5 Marine Biologist 54.25

Freighter Accept Atlantic Small .5

69

Pacific Large .5 30.5

22

Pac. Small 39

.5

54

Pacific Large .5

Reject

Boat

39

Boat

25

18

54 Pacific Small

90

.5

This demonstrates an important point explored in Chapter Nine. The value of additional information depends in part on the amount of information a manager starts with.

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55

Freighter

3. Set U(0) = 0 and U(90) = 100. Then, Morgan’s certainty equivalents for the 50-50 gambles establish the following utility values: U(24) = 50, U(52) = 75, U(6) = 25, U(69) = 87.5, U(35) = 62.5, U(13) = 37.5 In the graph below, we have drawn free hand a smooth utility curve going through these points. Then, we have reproduced the original decision tree with utility values at the end points (as read roughly from the graph). The tree shows that accepting the contract delivers the higher expected utility.

For the risk-averse Morgan, this is the better course of action. By reading from vertical axis to horizontal axis on the graph, we find the certainty equivalent of accepting the contract to be about $40,000. (Because rejecting the contract is very risky, its certainty equivalent is lower than the CE of accepting the contract, even though its expected value is higher.)

Utility

100

75

50

25

0 0

10

20

30

40

50

Wealth ($ Thousands)

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60

70

80

90

Freighter

$.50 CE = $40 K

67

.25

Boat Freighter

$.80 Accept

87.5

.25

Boat Freighter

67.1 $.70

48

Boat

.25

Freighter

$1.00

66

.25 $.50 .25

Reject

$.80

Boat

0 (0)

90 (100)

.25 61 $.70

18 (44)

.25 $1.00 CE = $34 K

.25

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90 (100)

24 (50) 40 (67) 69 (87.5) 55 (77) 12 (36) 22 (48) 39 (66) 25 (51)

ANSWERS TO EVEN-NUMBERED PROBLEMS

2.a.

Whether the parents should accept or reject the $500,000 settlement depends on their assessment of the expected monetary award (net of legal fees) in court. The parents would be wise to sketch a decision tree and get input from their lawyers about the strength of their case, the chances of various court outcomes (including appeals), and the possible monetary awards. Suppose that the couple (after averaging back the “litigation tree”) estimate an expected value of $800,000. If they are risk neutral, they should reject the settlement. If they are sufficiently risk averse (a plausible assumption), they prefer to accept the certain $500,000 settlement.

b. The defense lawyers should undertake a similar analysis on behalf of the hospital. (In fact, there may be the involvement of a third party -the insurance company obligated to pay part of any malpractice award. This may alter the defendant’s calculations.) If plaintiff and defendant assess similar decision trees, they will come up with similar expected values concerning the court outcome. In this case, the sides should be able to reach a mutually beneficial settlement. (Of course, if both sides are over-optimistic about their court chances, a settlement may be doomed.)

4.

According to the decision tree below, the consortium’s most profitable decision (on average) is to redesign the aircraft.

Success .6

Redesign

$100

80 Failure .4

.5 50

80 No Restrictions

.5 $125

.5

Do Not 75

Restrictions .5

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$100

$25

$0

6. a. The film is not worth launching.

High Demand

80

.4

38

Low Cost

.6 10 Low Demand

.5

Produce

-4

High Demand

.5

0

.4

-42

High Cost

0

.6

-70

Low Demand Do Not

0

b. The termination option is worth: 4 – 0 = $4 million.

High Demand .4

Continue

80

38

Low Demand

.5 Launch

4

4

.6

38

Low Cost

Terminate

Low Demand -30

.5

High Demand 0

Continue

High Cost

-42

-30

.4 .6

Terminate Do Not

Low Demand

-70

-30

0

8.

10

The decision tree below shows that the best strategy is to attempt a settlement, accept the $400,000 settlement if this is offered, and otherwise go to court. (Note that the expected cost of rejecting an offer, $650,000, is the expected value of going to court plus the $50,000 cost of trying to settle.) The optimal “try-to-settle” strategy has a $550,000 expected cost, which is less expensive than always settling or always going to court.

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Accept $400 K offer .5

$450

450 Reject

Attempt to Settle

$650

550 Accept $900 K offer 550

650

.5

Reject

600

$650

$1100

.2

Go to Court

$950

$700

.5

$100

.3

10. a. The firm should not develop the medicine; the expected loss from doing so is $13 million.

B Succeeds

.4

Devel Medicine

$75

.3

A Succeeds

267.5 B Fails

-13 A Fails

$0

.7

$350

-$200

.6

b. The firm should go ahead if it learns that B has failed (expected profit of $20 million); otherwise it should not invest. Its overall expected profit is: (.7)(20) = $14 million.

Success B succeeds

Develop

0

.4 -90

.3

Failure

Not

0

14 B Fails

.7

20

Develop

.6 Success .4

0

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-$200 350

20 20 Failure

Not

$75

.6

-$200

c.

i) In the joint venture, the chance that both programs fail is (.6)(.7) = .42. Thus, according to the decision tree, developing both is losing proposition.

Success .58

$200

-31 Failure .42

-$350

ii) Developing A alone is best: (.4)(350) + (.6)(-200) = $20 million.

(Developing B alone yields: (.3)(400) + (.7)(-150) = $15 million.)

12. a. “Improbable” might mean a 10 percent chance, a “long shot” might mean a 5 percent chance, and “somewhat likely” a 25 percent chance.

Adding these chances would imply a 40 percent probability (at best) of the system functioning. b. This implies that U(50% power) > 50 (i.e., is better than half as good as 100% power.) c. The operator should shed 50% load. The expected utility of not shedding load is (.4)U(100% power) + (.6)U(0% power) = 40. From part b, 50% power is clearly preferable to risking a total blackout.

14. a. u(50) = 50, u(112) = 75, u(13) = 25, u(153) =87.5 u(75) = 62.5, u(28) = 37.5, u(50) = 50 b. The function u = 7.1y = 7.1y.5, closely tracks the utility values in part a. For instance, if y = 50, then u = (7.1)(50 .5) = 50.2. If y = 153 then, then u = (7.1)(153.5) = 87.8, and so on. In this sense, the function embodies management’s attitude toward risk. The firm is moderately risk-averse. Thus, its CE for a 50/50 gamble between $200 million and $0 (a significant risk) is $50 million---well below the expected value of the risk ($100 million). For less risky outcomes, the gap between its CE and the expected value is smaller.

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Discussion Question The case of olestra makes for an interesting discussion. Olestra is a zero-fat cooking oil approved by the FDA to use in producing snack foods: primarily chip snacks and pop corn. Eighty percent of subjects cannot taste any difference between Olestra snacks and snacks made with normal (fatty) cooking oil. However, Olestra causes stomach cramps and diarrhea in a small percentage of consumers. It also inhibits the absorption of carotenoids (which are believed to reduce the risk of cancer and heart disease). In pursuing olestra, Procter & Gamble faces a number of uncertainties: the extent of regulatory approval, the ultimate magnitude of consumer demand, and possible liability risks. (Canadian regulators have rejected olestra; nor has it yet been approved in the United Kingdom.) If granted U.S. approval, olestra could be used in cooking oils, salad dressings, even ice cream.

After discussing olestra (see also the suggested reading on Simplesse), the instructor should ask students for other examples of business risks. The instructor can list these (by type of risk) on the blackboard. A typical list might look something like this (with categories listed in no special order): Bonus Problems 1. a. You are given $1,000 to keep. You then are offered a choice between receiving an additional $500 for certain or taking a 50-50 gamble with outcomes of $1,000 and $0. Which would you choose? b. You are given $2,000 to keep. You then are offered a choice between paying $500 for certain or taking a 50-50 gamble with outcomes of $0 and -$1,000. Which would you choose? c. The majority of individuals choose the sure $500 in part a but select the gamble in part b. Show that this combination of choices is inconsistent. What does this suggest about the way in which decision makers should think about risks?

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Answer a. The majority of subjects (slightly risk-averse) choose the sure $500. b. If you are like the majority of subjects, you choose the 50/50 gamble.

With $2,000 in hand, you figure it is worth risking the $1,000 loss (even if you lose, you will still be ahead and you are hoping you won’t lose) rather than paying back a certain $500. c. Although they are described differently, the situations in parts a and b offer identical choices. In part a, you can choose to walk away with a total of $1,500 for certain or to gamble on receiving either $2,000 or $1,000. Part b has exactly the same ultimate outcomes. Thus, consistency requires you to make the same choice in each case. The best way to think clearly about risky choices is not in terms of profit or loss but in terms of the ultimate consequence for your wealth.

2. Firm A is about to embark on a risky development project that offers a .2 chance of a $4 million profit and a .8 chance of a $0 profit. Unexpectedly, firm B proposes a joint venture. In return for its expertise, firm B will receive 25 percent of any profit. With firm B aboard, the chance of success is expected to rise to .25. After much deliberation, firm A decides to turn down the joint venture and continue on its own.

Two years pass, and firm A has overcome most of the development hurdles. The estimated chances of success are now .8. Now firm C offers to pay firm A $3 million for all rights (and profits) concerning the development project. Deciding to take the sure $3 million, firm A now sells out.

Show that whatever firm A’s attitude toward risk, the pair of decisions just outlined are contradictory. (Hint: There are only three outcomes across the two decisions: $4 million, $0, and $3 million, with the associated utilities 100, 0, and u, respectively.) Show that no value of u is consistent with firm A’s pair of choices.

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Answer In the first decision (see tree), the company chooses to continue on its own, implying 20 > .25u. Thus, u < 80. $4 (100) Alone

20

.2 .8

$0 (0)

$3 (u) Partnership

.25U

.25

.75

$0 (0)

In the subsequent decision, the company sells out, implying u > 80. These two inequalities (and, therefore, the two decisions) are contradictory. $4 (100) Alone

80

.8 .2

$0 (0)

Sell Out $3 (u)

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Business Risks I. Macro risks: • GNP growth: boom or recession; how this affects firm’s future sales.

• Inflation: effect on input and output prices and wage demands • Interest rates: given future movements in interest rates, when is the best time to borrow to meet the firm’s investment needs?

• Exchange rate changes: important for overseas sale and production II. Micro Risks • Predicting demand: for a new product, the impact of advertising • Predicting costs: R&D cost, cost of building a new facility, day-to-day operating costs, changes in input costs and/or availability.

III. Competitive Uncertainty • Will new competitors enter the market?

• Will current competitors cut prices, increase output, raise advertising, and so on?

• Will ours be the winning bid for a valuable procurement contract?

• Will a competitor sue for patent infringement? If so, at what terms might the competitor be willing to settle? Should the firm fight the suit in court?

IV. Government/political uncertainty.

• Regulation: will it be imposed and at what cost? Tax treatment?

• International relations and political risks V. Scientific (or Natural) Uncertainty • Will the firm’s well strike oil?

• Are we winning or losing the war on cancer?

• Will the firm’s scientific approach lead to a successful R&D outcome?

• Natural disasters, war, acts of God, the weather, global warming.

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CHAPTER THIRTEEN THE VALUE OF INFORMATION

OBJECTIVES 1. To show how to incorporate new information into the manager's decision tree. (pp. 507-511) 2. To show how to revise probabilities using joint probability tables and Bayes rule. (pp. 512-516) 3. To present applications (pp. 516-519) and examples of prediction pitfalls (pp. 519-523).

4. To demonstrate optimal sequential decisions (pp. 523-527) and optimal search (pp. 527-530).

TEACHING SUGGESTIONS I. Introduction and Motivation A. Information Sources. Ask students to think about the myriad kinds and sources of information that decision makers might use. Here is a possible (partial) list:

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Types and Sources of Information Business: 1) Macro-forecasts, Futuristic forecasts (MegaTrends), demographic data (population data by zip-code), sociological trends, marketing surveys.

2) Budget projections, cost information of all kinds.

3) Political risk assessments, credit histories 4) Workplace: job interviews, drug testing General: 1) Scientific evidence (medical, geological, meteorological, actuarial) Predicting earthquakes, hurricanes, global warming, and so on 2) Legal evidence 3) Statistical information 4) Polls and political surveys 5) Educational testing (standardized tests) 6) Encyclopedia-type information

B. Guinea Pig Questions. Three intuitive prediction problems -- “Steve's occupation”, “The three box problem”, and “Is it cancer?” are discussed on pp. 520-521. These can be used in class before they are formally assigned for reading.

1. Is it Cancer? In the text example, the prior probability of the disease is 1 in 1000 and the test is 95% accurate. In light of a positive test, the revised probability is 1 in 51 (about a 20 fold upward revision).

2. Let's Make a Deal (Problem 6). Consider the following simplified version of the game “Let's Make a Deal.” There is a grand prize behind one of three curtains. The other two curtains are empty. As the contestant, you get to choose a curtain at random. Let's say you choose curtain three. Before revealing what's behind the curtain, the game show host offers to show you what's behind one of the other curtains. Suppose

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he shows you that curtain two is empty. In fact, he always shows you an empty curtain. (You know that's how the game works, the audience knows it, everybody knows it.) Now you must decide: do you stick with your original choice, curtain three, or switch to curtain one? Which action gives you the better chance of finding the grand prize?

3. Predicting Sales. Last year, sales at 5 department stores in a chain were: Store A Store B Last Year

Store C

Store D

Store E

Total

8

9

10

11

12

50

?

?

?

?

?

55

Next Year

Your job is to predict sales at each store in the coming year. The overall forecast is for total regional sales to grow by 10 percent (from 50 to 55).

What are your predictions?

4. Odds and Urns. There are two urns -- one contains 40 red balls and 20 white balls and the other contains 40 white balls and 20 red balls. The urns are identical from the outside. After choosing an urn at random, you are allowed to reach in and take out a ball, note its color, then return it to the urn. In ten such picks, you observe 7 red balls and 3 white balls.

What are the chances that you originally selected the “red” urn?

5. The Cocoa Game. (We have summarized and paraphrased the original account which appeared in Adam Smith, The Money Game.)

“Cocoa,” said the Great Winfield. “There isn't any cocoa. The world is just about out of it.” And he proceeded to explain that the price of cocoa depends on how much cocoa there is and that a shortage of cocoa means a sky high price. “My informant in Ghana tells me there is no cocoa. The game then is to buy futures contracts in cocoa, betting that the price of cocoa will go up. And when it does, we make a killing.”

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And so they bought cocoa futures and waited and watched events in Ghana. Revolution in Ghana: Cocoa up 2 cents. Civil war. The Hausers are murdering the Ibos. Who is going to harvest the crop? Cocoa up 2 more cents. The main railway has been blown up. How will the cocoa, if there is any, get to market? It was then that the Great Winfield decided to send his man Marvin to West Africa to find out if it was raining (bad for the crop) and whether the dreaded Black Pod disease was spreading.

Twenty-four hours after buying out Abercrombie and Fitch, Marvin is cabling messages from the darkest cocktail lounges of Ghanian hotels: RAINING OFF AND ON. Three days later: BRITISHER IN HOTEL SAYS CAPSIO FLY SPREADING. IT HAS STOPPED RAINING. All the time, the prices of cocoa futures continued to rise.

Until strange things began to happen to the price of cocoa. The price began to fall, first slowly, then disastrously. By the time the price of cocoa had stopped falling, the followers of the Great Winfield were busted and Winfield himself had lost two-thirds of his cocoa contracts.

6. Escalating Investments in R&D (Discussed on pp. 324-326). An electronics firm can initiate an important R&D program by making a $3 million investment. There is a 1/5 chance that the program will meet with immediate success (i.e. within the year) earning the firm a return of $10 million (for a net profit of $7 million). If success does not come, the firm can invest another $3 million and raise its success chances to 1/4. If this second stage fails, the firm can invest again, and so on, up to a total of five investments. The investment cost for each stage is $3 million, the ultimate return from a successful completion of the program (sooner or later) is $10 million, and the chances of success are 1/5, 1/4, 1/3, 1/2, and 1 for the investments. As the manager in charge of this decision, would you make the initial $3 million investment and if so, at what stage (if any) would you stop?

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7.

Finding the Best Item (Problem 12). Suppose that you will be shown three “prizes” in order. Ahead of time, you know absolutely nothing about how valuable the prizes might be. Only after viewing all three can you determine which you like best. You are shown the prizes in order and are allowed to select one. However, there is no “going back.” You must select a prize immediately after seeing it, and before seeing any subsequent prize. a) Your sole objective is to obtain the best of the three prizes.

(Second best doesn't count.) A random selection provides a onethird chance of getting the best prize. Find a strategy that provides a strictly greater chance (and compute the actual chance). b) What if there are a large number of prizes (say 10, 50, or 100)?

Describe in general terms the kind of strategy you might use.

C. Guinea Pig Questions, Discussed 1. Is it Cancer? This example shows how difficult it is to estimate probabilities. Students can get a good feel for the effect of prior probabilities by trying other priors: a) With prior probability 1 in 100, the revised probability is 1 in 6 (about a 17 fold upward revision). b) With prior probability 20 in 100, the revised probability is 19 in 23 or 83 percent (representing about a 4 fold upward revision). c) With prior probability 50 in 100, the revised probability is 47.5 in 50 or 95%. In this case, Pr(cancer|+) = Pr(+|cancer) = .95 because of the fact that Pr(cancer) = Pr(health) = 1/2.

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Related Example Stress tests (with an electrocardiogram monitoring the heart) have become popular to screen for signs of possible heart disease. Unfortunately, these tests not only frequently fail to detect heart problems, they also produce a high rate of false-positive tests -- a rate of 15 to 20 percent for healthy men and 40 to 50 percent for healthy women.

2. Let's make a Deal. Almost all students (if they have not seen the problem before) believe that either curtain offers a 50-50 chance of having the prize. This is incorrect. In fact, the chance is one-third that the grand prize is behind your chosen curtain and two-thirds that its behind the other curtain. After all, choosing your original curtain at random offers a onethird winning chance. The fact that you are shown an empty curtain does not change this prior probability (although it does eliminate one curtain from consideration). Since your winning chances are 1/3 if you “stick”, you should switch and gain a 2/3 winning chance.

Many students will still be unconvinced by this argument. One response is to challenge students (in pairs) to simulate the setup for themselves: shuffling 2 black cards and one red card, let's say, and playing 60 times). (Always “sticking” after a black card has been revealed will produce only 20 wins on average.) A second argument is to suppose their are 100 curtains and one prize. After a curtain is chosen (say, curtain 1), the host reveals 98 empty curtains (all but curtain 71). Most students will easily see that the odds are 99 to 1 in favor of curtain 71 over curtain 1.

After 20 years, this classic problem finally made it to the front page of The New York Times: “Behind Monty Hall's Doors: Puzzle, Debate, and Answer,” NYT, July 21, 1991, p. 1. The discussion and analysis are recommended. Eighteen years later, the conundrum is still going strong.

3. Predicting Sales. Most students do what comes naturally making the predictions: 8.8, 9.9, 11, 12.1, and 13.2, i.e. raising last year's sales for each location by 10%. This prediction would be correct only if differences in sales between locations were due entirely to “real” and persistent factors. The contrary hypothesis is that last year's differences were completely random (i.e. due to chance elements). In this case, the same prediction, namely 11, would be suitable for all locations in the The Dryden Press

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coming year. What can one say about reasonable forecasts? Only that they lie somewhere between the two extreme hypotheses (since sales differences are neither entirely deterministic nor entirely random). If these components were equally important, the best forecasts would be 9.9, 10.45, 11, 11.55, and 12.1 (half way between the extreme forecasts). This example illustrates regression toward the mean. A component of the best store's sales (or the worst store's) is due to luck. Next period's results will not be as good (nor as bad) but rather will move toward the overall mean.

4. Odds and Urns. Most students guess probabilities between 60 and 80 percent that the draw of 7 red and 3 white is from the “red” urn. The actual probability is 16/17 = .94, much higher than most people expect.

Students recognize that the sample is a likely one from the red urn. What they tend to overlook is how unusual the sample would be from the white urn (where white balls outnumber red ones two to one). The calculation via Bayes theorem is: Pr(7r&3w|Red)Pr(Red) Pr(7r&3w|R)Pr(R) + Pr(7r&3w|W)Pr(W)

Pr(Red|7r&3w) =

=

(2/3) 7(1/3) 3(0.5) (2/3) 7(1/3) 3(0.5) + (2/3) 3(1/3) 7(0.5)

=

2 713 (.5) 2 713 (.5) + 17 2 3 (.5)

=

27 27 + 23

=

128 128 + 8

= .94. the calculation, we have used the fact: Pr(Red) = Pr(White) = .5. After cancellation, these equal priors disappear from numerator and denomin-ator.

(We've also canceled all factors of 3.)

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Remark. Here, the revised probability depends on the difference between the number of reds and whites, not the ratio. Thus, 15r&10w is stronger evidence for the red urn than 7r&3w, which in turn is stronger than 4r&1w.

To see this intuitively, note that 15r&10w is equivalent to 10r&10w (which calls for no revision) followed by 5r.

Some other results: Pr(Red|1r) = (2/3)(.5)/[(2/3)(.5) + (1/3)(.5)] = 2/3.

Pr(Red|2r) = (4/9)(.5)/[(4/9)(.5) + (1/9)(.5)] = 4/5.

This last probability can also be computed one ball at a time. After 1 red, the red urn is two-thirds likely. Use this as the new prior to be revised after drawing a second red: Pr(Red|2nd r) = (2/3)(2/3)/[(2/3)(2/3) + (1/3)(1/3)] = 4/5 = .8 (the same answer as above).

5. The Cocoa Game. What went wrong? There were revolutions in Nigeria and Ghana and outbreaks of Black Pod disease and torrential rain and railways blown up. But something like this happens almost every year in Ghana, and there is still a cocoa crop. Just a large enough crop to satisfy demand at “normal” prices. The lesson here is to know which information is meaningful and which should be “discounted” or ignored.

A Related Question: Yesterday, Company A reported that its earnings were up 14 percent over last year. Today, the price of the company's common stock fell by two points. The explanation? Stock watchers had expected earnings to be up by 15 to 20 percent and the stock's previous price reflected this. Thus, announced earnings (though solid) were a disappointment relative to expectations; this prompted the price drop.

6. Escalating Investments in R&D. See discussion and decision tree on pp. 324-326.

7. Finding the Best Item. See the answer to Problem 12.

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II. Teaching the “Nuts and Bolts” A. General Tips. Assessing the value of information involves: 1) incorporating new information into the manager's decision tree, and 2) revising probabilities using joint probability tables or Bayes rule.

We place at least as much emphasis on the first point as on the second. For instance, it is worth having students practice building one or two decision trees with all revised probabilities already supplied. Once the logic of the tree has been laid bare, more complicated decisions can be tackled.

B. Launching a new product. An alternative to using the oil drilling example in the text is to revisit the example of launching a new product (see Chapter Twelve of this manual). Version 1 is simpler and should be presented first.

1. Suppose that the firm can purchase a macro-forecast concerning the course of the economy, before making its launch decision. The forecast is one of two kinds: positive (+) or negative (-). In light of a positive forecast, the probabilities of the different scenarios are: Pr(Strong|+) = .5, Pr(Moderate|+) = .4, and Pr(Recession|+) = .1.

In light of a negative forecast, the chances of the different scenarios are: Pr(Strong|-) = .15, Pr(Moderate|+) = .4, and Pr(Recession|+) = .45.

Finally, the chance of a positive forecast is .6 (and a negative forecast .4).

The decision tree below shows that the firm should launch the product in light of a positive forecast but abandon (or postpone) the launch if the forecast is negative. The expected profit from this course of action is $7.08 million -- $1.16 million greater than the expected value of launching the product without the macro-forecast (see Chapter Twelve of this manual).

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11.8

+

Strong .5

Launch

.6

Moderate

11.8

.4

20

10

No

7.08

Recession $0

-

.1

Strong .15

0 Launch

.4

Moderate

-2.9 No

.4 Recession .45

$0

-22

20

10

-22

2. The situation is as in version 1, but instead of being given the revised probabilities, the manager must calculate them. Management starts with the following information about the accuracy of the macro-forecast. In 5 of 6 strong economies, the forecast has been positive, Pr(+|S) = 5/6. In 6 of 10 moderate economies, the forecast has been positive, Pr(+|S) = 6/10.

In 3 of 4 recessions, the forecast has been negative, Pr(-|R) = 3/4. Recall that the prior probabilities are: Pr(S) = .36, Pr(M) = .4, and Pr(R) = .24.

Combining these facts, we can generate the following joint table:

+ Total

Strong .30 .06 .36

Moderate .24 .16 .40

Recession .06 .18 .24

Total .60 .40

From this table, we can compute the revised probabilities of version 1 above. For instance, Pr(S|+) = Pr(S&+)/Pr(+) = .3/.6 = .5, and so on.

Then, the decision tree and decision recommendation are as above.

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Additional variations.

1. Suppose the joint table is:

+ Total

Strong .216 .144 .36

Moderate .24 .16 .40

Recession .144 .096 .24

Total .60 .40

In this case, the information is worthless. The outcomes + and - are independent of the future course of the economy. Revised probabilities are no different than the prior probabilities: Pr(S|+) = .216/.6 = .36, and so on.

2. Suppose that Pr(+|Strong) = 8/9, Pr(+|Mod) = 1/2, and Pr(-|Recession) = 1/2. The resulting joint table is

+ Total

Strong .32 .04 .36

Moderate .20 .20 .40

Recession .12 .12 .24

Total .64 .36

Computing revised probabilities and putting them into a decision tree shows that this test is also worthless! Regardless of the forecast (even if it is negative), launching the product is the best course of action.

D. Suggested Problems

Problems 3, 7, 8, and 9.

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ADDITIONAL MATERIALS

I. Short Readings S. Banjo, “Doing Your Home Work,” The Wall Street Journal, December 11, 2007, p. R6.

J. W. Miller, “Why Miners Look for Buried Treasure in Belgian Museum,” The Wall Street Journal, March 20, 2007, pp. A1, A13.

J. W. Miller, “Gumshoe’s Intuition: Spotting Counterfeits at Port of Antwerp,” The Wall Street Journal, December 14, 2006, pp. A1, A18.

T. Parker-Pope, “Web Site Tallies your Risk of Disease and Tells You What You Can do About It,” The Wall Street Journal, October 31, 2006, p. D1.

No Author, The Economist, “Secrets of the Digital Detectives,” September 23, 2006, pp. 32-33.

J. Nocera, “The Future Divined by the Crowd,” The New York Times, March 11, 2006, “Ratings Take on Political Risk,” The Wall Street Journal, June 21, 2004, p.

C1.

“Afraid to Fly after 9/11, Some Took a Bigger Risk – in Cars,” The Wall Street Journal, March 23, 2004, p. B2.

Varian, H. R., “A Market in Terrorism was a Good Idea; It just got Bad Publicity,” The New York Times, July 31, 2003, p. C2.

“What are the Chances?” The New York Times, February 6, 2003, p. B1.

“Looking to Improve Your Credit Score? Fair Isaac Can Help,” The Wall Street Journal, March 19, 2002, p. A1.

“New Futures Could Help Folks Insure Against Economic Risks,” The Wall Street Journal, September 5, 2002, p. A2.

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A. Barnett, “It’s a Crime What Some People Do with Statistics,” OR/MS Today, October 2000, p. 18.

“Casino Chain Mines Data on its Gamblers, and Strikes Pay Dirt,” The Wall Street Journal, May 4, 2000, p. A1.

“Value of Second Opinions is Underscored in Study of Biopsies,” The New York Times, April 4, 2000, p. D7.

“How the Tire Problem Turned into a Crisis for Firestone and Ford,” The Wall Street Journal, August 8, 2000, p. A1.

“Firestone Engineers Offer a List of Causes for Faulty Tires,” The New York Times, December 19, 1999, p. C1.

Daniel Kopans, “An Unacceptable Degree of Risk,” The Boston Globe, October 4, 1998, p. C1. (This article suggests that women as young as 40 benefit from annual mammograms.)

“How Shell Hit a Gusher Where No Derrick had Drilled Before,” The Wall Street Journal, April 4, 1996, p. A1.

“Loans Granted by the Megabyte,” The New York Times, April `18, 1995, p. D1.

“Compiling Data and Giving Odds on Jury Awards,” The New York Times, Jan. 21, 1994, p. B18.

Marilyn Vos Savant, “Tests for AIDS and Drugs: How Accurate are They?”

Parade Magazine, March 28, 1993, p. 24.

“Behind Monty Hall's Doors: Puzzle, Debate, and Answer,” The New York Times, July 21, 1991, p. 1. (After 20 years, this classic problem made it to the front page of The New York Times.)

“Too Many Bugs in Screening Measures,” The Wall Street Journal, April 14, 1986. (Why false positives make rare diseases hard to identify)

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“Study Raises Serious Doubts About Commonly Used Methods of Treating Back Pain,” The New York Times, July 14, 1994, p. A 16. (This study shows that 2/3 of normal subjects have spinal abnormalities and concludes that the link between actual back pain and abnormal disks may be sheer coincidence, not cause and effect.)

“How to Campaign with Statistics without Really Cheating,” The Economist, April 14, 1979, p. 110. (An Oldie but Goody)

II.

Longer Readings

D. N. Sull, “Disciplined Entrepreneurship,” MIT Sloan Management Review, 46, Fall 2004, 71-77.

J. W. Ulvila and J. E. Gaffney, “A Decision Analysis Method for Evaluating Computer Intrusion Detection Systems, Decision Analysis, March 2004, 3550.

E. Urbanovich. et al, “Early Detection of High-Risk Claims at the Workers’ Compensation Board of British Columbia,” Interfaces, July 2003, 15-26.

Watkins, M. D. and M. H. Bazerman, “Predictable Surprises: The Disasters You Should Have Seen Coming,” Harvard Business Review, March-April 2003, 72-80.

J. E. Smith and R. L. Winkler, “Casey’s Problem: Interpreting and Evaluating a New Test,” Interfaces, May-June 1999, 63-76.

J. Weisberg, “Keeping the Boom from Busting,” The New York Times Sunday Magazine, July 19, 1998, p. 24. This article examines the risk calculations and decision methods of Robert Rubin, Treasury Secretary in the Clinton administration.

T. O. Tengs et al, “Five-Hundred Life-Saving Interventions and Their Cost Effectiveness,” Risk Analysis, 1996, 369-390.

N. A. Nichols, “Scientific Management at Merck,” Harvard Business Review, January-February 1994, 89-99. (Reprint 94106).

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“Decisions, Decisions,” Discover Magazine, June 1985, p. 23. (This is a survey of the pitfalls of intuitive decision making and highly recommended.)

M. G. Morgan, “Risk Analysis and Management,” Scientific American, July 1993, 32-41.

L. D. Stone, “Search for the SS Central America: Mathematical Treasure Hunting,” Interfaces, Jan.-Feb. 1992, 32-54.

III. Recommended Case Exercises on the Value of Information, Harvard Business School, (9-893-006), 1994. Teaching Note (5-396-275)

IV. Quips and Quotes Grace is given by God, but knowledge is bought in the market.

Risk varies inversely with knowledge. (Irving Fisher) The race is not always to the swiftest, nor the battle to the strong -- but that is the way to bet (Damon Runyon) I know the records of the horses, the abilities of the jockies, the condition of the turf. I probably know more about what horse should win than anybody in the country. But there's one thing I don't know -- how the horse was feeling when he got up in the morning. (McCarthy explaining why he didn't bet on horse races.)

In gathering information before making an important decision, be prepared to spend about 1 percent of what is at stake. (Ronald Howard)

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Test everything. The most important word in the vocabulary of advertising is test. Twenty-four out of twenty-five new products never get out of test markets. Manufacturers who do not test market their products incur the colossal cost (and disgrace) of having their products fail on a national scale instead of dying inconspicuous and economical deaths in test markets.

(David Ogilvy, Confessions of an Advertising Man) It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth. (A. Conan Doyle) After his team lost 73-0 in the 1940 NFL championship game, quarterback Sammy Baugh was asked if things might have been different if his team had scored first. “Sure, it would have been 73-6.”

Always get a second opinion.

If you can tell the difference between good advice and bad advice, you don't need advice.

If three people call you an ass, put on a bridle.

Doctor: As your physician, I have to tell you that you are seriously overweight. Patient: I'd like a second opinion. Doctor: OK you're ugly too.

If at first you don't succeed, try, try again. Then stop. No use being a damn fool about it. (W.C. Fields) If you don't catch anything after seven casts for trout, move on to the next likely spot in the stream.

If you start to take Vienna, take Vienna. (Napoleon Bonaparte)

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ANSWERS TO EVEN-NUMBERED PROBLEMS 2. a. The assessment is subjective in the sense that different “experts” or “odds makers” would come to different judgments about the team's World Series chances. Prior to the season, one's assessment rests mainly on determining the strength of the team's hitting, pitching, and defense relative to their division-, league-, and cross-league rivals. b. Since there are 30 teams in the Major Leagues, a “naive” assessment would assign each team an equal, one-in-32 chance of winning the Series. An avid sports fan would modify this assessment by taking account of the factors in part a. He would revise his assessment as teams posted win-loss records over the season, and in light of team performances, injuries, and so on.

4. a. No. The reason this age group accounts for the greatest proportion of accidents is because they comprise half of all drivers. (Add across the table rows to see this.) b. The accident rate for Age 17-30 is: (12,050 + 1,822)/(90,243 + 12,050 + 18,22) = .133.

The accident rate for the other two age groups are .091 and .112. The middle age group are the best drivers; the youngest age group are the worst. c. The comparison is misleading because the older group drives many fewer total miles than the middle group. A more even-handed evaluation would compare accident rates per miles driven.

6.

The chance is 1/3 that the grand prize is behind your chosen curtain.

The fact that you are shown an empty curtain does not change this prior probability (although it does eliminate one curtain from consideration). Since your winning chances are 1/3 if you “stick”, you should switch and gain a 2/3 winning chance.

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8. a. Based on the loan officer's assessments reported in the problem, we can construct the following joint probability table: Performing Loan .225 .270 .360 .045 .900

Category A (“zero risk”) B (solid) C (uncertain) D (high risk) Total

Defaulted Loan .020 .025 .045 .010 .100

Total .245 .295 .405 .055 1.000

Therefore: Pr(Def|A) = .02/.245 = .08 Pr(Def|B) = .025/.295 = .085 Pr(Def|C) = .045/.405 = .11 Pr(Def|D) = .01/.055 = .18 b. The loan officers' assessments of default risk range between 8% and 18%. The scoring system's assessments range between 5% and 25% and appear to be better at discriminating between “sound” and “problem” loans. The scoring system provides more valuable information.

10.a. According to the decision tree, the agency should not take the case to court: Prove .75

Pad .2

Go to Court

1 Not

-.2

.25

Not

-.5 .8

0

Do Not

$0

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1.5

-.5

b. The joint table is Q C

Padding .15 .05 .20

Not .16 .64 .80

Total .31 .69 1.00

In turn, Pr(P|Q) = .15/.31 = .484 and Pr(P|C) = .05/.69 = .07 c. According to the decision tree below, the agency should investigate and go to court if Q but drop the case if C. Its expected benefit is $70 thousand.

Prove .75 Pad Court

.4

Not

Not .6

Q

1 .25

31 .226

1.5

-.5

-.5

.226

.31

No $0

Investigate .07 million

Prove

1.5

.75 Pad Court

.07 31 -.40

0 .69

.25 Not

-.5 .93

C No $0

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1 Not

-.5

12. a. Here is a strategy that improves upon random choice. Observe but bypass the first prize. Select the second prize only if it is better than the first; otherwise go on and select the third prize. We list below the six distinct (equally likely) orderings of the prizes: First Prize

best

best

2nd best

2nd best

worst

worst

Second Prize

2nd best

worst

best

worst

best

2nd best

Third Prize

worst

2nd best

worst

best

2nd best

best

The italicized items show the prizes selected in each ordering following the suggested strategy. In three cases out of six, the individual obtains the best prize, in two cases the second-best prize, and in only one case the worst prize. Observing the relative merits of the prizes and making a contingent choice (even though there is no going back) improves your outcomes. b. For a large number of items, the optimal strategy is to observe but bypass a certain fraction of the total, then select a subsequent item if and only if its the best item of all you have seen.

Remarks. For an arbitrary number of items (not only three), this is variously called the “secretary problem” (interviewing and selecting the best secretary), the “hotel problem” (deciding to stop at one of a number of hotels situated hours apart along a cross-country route), or the “art gallery problem” (in the gallery you are allowed to view paintings one at a time and choose only one without going back to a previous painting).

For a large number of items, a remarkable result has been proven. The optimal strategy is to bypass about 37% of the items before choosing the best item to date. The chances of obtaining the best item using this strategy is also 37%! (The optimal proportion and resulting chance are 1/e, where e = 2.71828 is Euler's constant. For a derivation, see M. DeGroot, Optimal Statistical Decisions, McGraw-Hill, 1970.) This is a truly remarkable result. Even if there are one million items, this strategy The Dryden Press

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will select the best of the million 37% of the time. (By contrast, a random selection would provide only a one-in-a-million chance.) Here is one way to see why the sequential method does so well. Suppose one were to observe and bypass half the items. Consider the case that the second-best item appears in the first half of the total number while the best item appears in the second half. This occurs with probability .25 (since there is a .5 chance that each item is in the specified half). In this case, the sequential strategy must stop at the best item. (Make sure you understand why.) Thus, the winning chances are at least .25 regardless of the number of items. By bypassing only 37% of the items and accounting for other ways of winning, one can raise the overall winning chances to 37%.

Discussion Question a. Because tire-related accidents are so rare, they are not going to “pop out on the radar screen” of a safety manager or government regulator.

Unfortunately, Firestone relied on warranty data that indicated that these brands of tires seemed to have no higher rate of failure than the average tire. (What the warranty data didn’t focus on was the few cases of catastrophic failure leading to SUV rollovers. b. Multiple risks made it more difficult to detect the increased risk. Overall, Ford SUVs did not have elevated rollover rates. Overall, Firestone tires did not have greater failure rates. Overall, low tire pressure does not cause significantly higher risk of tire failure. But the combination of particular brands of Firestone (manufactured by particular processes at particular plants) mounted on the Ford Explorer, underinflated and driven at high speeds with heavy loads (in high temperatures) causes much greater rates of tire failure, rollovers, and fatal accidents. c. Both were undeniably contributing factors. Ford argued that its vehicle and recommended tire pressure and loadings were not at fault. Similar size tires (from other manufacturers and even Firestone itself) under similar driving conditions mounted on the Explorer showed no elevated failure risks. For its part, Firestone marshaled evidence that its tires on The Dryden Press

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any other SUV at higher (industry standard) recommended pressures showed no elevated risks. Thus, the combination of Firestone tires mounted on the Ford Explorer was the culprit.

For more information on this subject see: “Firestone Engineers Offer a List of Causes for Faulty Tires,” The New York Times, December 19, 2000, p. C1.

“Study of Ford Explorer’s Design Reveals a Series of Compromises,” The New York Times, December 7, 2000, p. A1.

“Answers still Elusive in Tire Crisis,” The New York Times, September 15, 2000, p. B1.

“Documents Portray Tire Debacle as a Story of Lost Opportunities,” The New York Times, September 11, 2000, p. A1.

“How Firestone Let the Warnings Slide by as Debacle Developed,” The Wall Street Journal, September 9, 2000, p. A1.

“How the Tire Problem Turned into a Crisis for Firestone and Ford,” The Wall Street Journal, August 10, 2000, p. A1.

Bonus Problem An oil wildcatter is considering drilling a site that she judges to be wet with probability .2 and dry with probability .8. Her profit from an oil strike is $1 million, and her loss from a dry hole is -$800,000. a. Before drilling, the wildcatter can pay for a seismic test that will return an outcome of good or bad. In the past, wet sites have tested good 75 percent of the time, and dry sites have tested good 25 percent of the time. What is the test’s EVI? b. For a comparable fee, the wildcatter can find out whether a recently drilled well nearby struck oil (O) or not (N). If the wildcatter’s site were The Dryden Press

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wet, the nearby well also would be wet with certainty. If the site were dry, the nearby well also would be dry with probability .75. What is the EVI in this case? c. Suppose the wildcatter purchases both sources of information. Now what is the EVI? Answer a. For the seismic test, the revised probabilities are: Pr(W|G) = .15/.35 = 3/7, and Pr(W|B) = .05/.65 = 1/13. Even if the test is good, the site isn’t worth drilling; the expected profit is: (3/7)(1,000,000) + (4/7)(-800,000) = -$28,571. Thus, the seismic test has no value. b. If the wildcatter learns the results of the nearby site, the revised probabilities are Pr(W|O) = .2/.4 = .5, and Pr(W|N) = 0/.6 = 0. If the result is O, the wildcatter drills and earns an expected profit of $100,000. If the result is N, he walks away. Because Pr(O) = .4, the overall expected value is (.4)(100,000) = $40,000. c. The accompanying table shows the joint probabilities if both sources of information are available. Note that there are four possible observations.

The top-left entry is Pr(G&O&W). It is computed as Pr(G&O&W) = Pr(G|W)Pr(O|W)Pr(W) = (.75)(1.0)(.2) = .15. The other entries are found in a similar fashion. From the table, we compute the revised probabilities to be Pr(W|G&O) = .75, Pr(W|B&O) = .25, Pr(W|G&N) = 0, and Pr(W|B&N) = 0. The wildcatter should drill only if both indications are favorable (G&O), in which case the expected profit is (.75)(1,000,000) + (.25)(-800,000) = $550,000. With Pr(G&O) = .2, the overall expected profit is (.2)(550,000) = $110,000.

Wet

Site is: Dry

Total

G&O B&O G&N B&N

.15 .05 0 0

.05 .15 .15 .45

.20 .20 .15 .45

Total

.20

.80

1.00

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ANSWERS TO THE SPREADSHEET PROBLEM

(You may download any and all spreadsheets from the John Wiley, Samuelson and Marks Website.)

S1. a. Cell E20 has the value .045, and Cell F20 has the value .003. For instance, we compute Pr(average & 15 of 20) as: Pr(average)*Pr(15 of 20|average) = (.6)(.075) = .045. In turn, the total probability of 15 up years in 20 (Cell H20) is .0835. Thus, the conditional probabilities in row 24 are: Pr(S|15 of 20) = .036/.0835 = .428, Pr(A|15 of 20) = .045/.0835= .536, and Pr(I|15 of 20) = .003/.0835 = .036. b. The last probability shows that this good a performance record is very unlikely (except by pure luck) to have come from an inferior forecaster. Still, it’s over 50 percent likely that the manager is intrinsically an average performer (rather than a superior one). It takes a long and impressive track record to separate the “men from the boys.” The overall expected return in cell J24 (weighting the returns in row 10 by the revised probabilities in row 24 is: (.428)(13) + (.536)(9) + (.035)(5) = 10.57 percent. Thus, strong past performance (15 up years of 20) is indicative – but no guarantee – of future performance. c. Superior performers have only a 4 percent advantage over average performers (cell D9 versus cell E9) making it hard to distinguish the two. Assuming a wider gap or stronger track record would make it easier to distinguish the two groups based on past performance.

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Mini-Case The Science of Baseball The national pastime of baseball has been called a “game of inches.” The umpire calls a pitch a ball instead of a third strike, and the next pitch is hit for a home run. A ball hit just beyond the short stop’s reach becomes a game winner. Baseball is also a game of decisions and statistics. Managers make dozens of moves and decisions during a ball game. General managers put together team rosters (drafting players, making trades) by continually gauging talent, again based on player statistics.

For the last ten years, the Oakland Athletics under General Manager Billy Beane have been the leading proponents of “money ball” – using statistical analysis to build the strongest winning team with a limited total payroll.1 “Old-school thinking judged a prospective ball-player by whether he had the traditional “tools”: the abilities to hit, field, throw, and run throw. Scouts believed they could judge these talents simply by watching a prospect play. This subjective assessment could be backed up by the traditional hitting statistics (batting average, home run, and runs batted in) and pitching statistics (win-loss record and earned run average).

Beane was one of the first to realize that these old school methods were often biased and inaccurate. How good a ballplayer looked on the field was far less important than how many runs he produced (or for a pitcher how many opposing runs he prevented). A new breed of baseball analysts were uncovering much better hitting and pitching statistics to predict winning performance. Oakland’s record between 1999 and 2004 proved the point.

Oakland was the second winningest team during this span (and in the top 10 each year) despite having one of the lowest payrolls (between 25 th and 28th among 30 major league teams). Almost a dozen teams have followed Oakland’s statistical lead. In building a winning team, today, the right statistics (and, of course, money) talk.

Statistics and playing the averages also matter on the field, 162 games a year. Put yourself in the shoes of the manager of the local team. It is the seventh inning of a 3-to-3 ballgame. The opposing team has runners on first and third base due to an infield single and an error. There is one out, and the opposing team’s left-handed “cleanup” hitter is coming to bat.

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Should you allow your starting right-handed pitcher to face the batter, or should you use your ace left-handed relief pitcher?

In pondering this decision, you have no shortage of probabilistic information. Begin with the opposing hitter’s batting average. Let’s say he is a .300 hitter (i.e., has averaged three base hits in every ten times at bat).

This is a fine performance. However, in his last ten games, the player has hit poorly, averaging only .240. But today he already has hit a double against the starting pitcher. However, he is slow of foot and frequently hits into double plays (which your starting pitcher is adept at inducing). Yet, the relief pitcher may be the better bet. The cleanup hitter averages only .255 against left-handers, and the relief pitcher has allowed opposing hitters only a .235 batting average. A telling factor, however, is that the hitter has 11 hits in 24 lifetime attempts against your left-hander.

Our purpose in this example is not to establish the manager’s optimal decision (although second-guessing is fun); rather, it is to make the point that any decision requires categorizing the past data on the basis of the most relevant predictive factors. This example is complicated because for every factor working in one direction, there seems to be another factor working in the other. Nonetheless, the only way to make the best-informed decision is to take all relevant factors into account.

To sum up, from a manager’s or general manager’s point of view, baseball is a game of tendencies and percentages. The difference between a fine .300 hitter and a poor .200 hitter is one extra hit in every ten times at bat. Small as it seems, this difference looms large over a 162-game season.

Earl Weaver, the former manager of the Baltimore Orioles, was a vigorous proponent of baseball by the numbers. In making pitching decisions, he kept tabs on the batting record of each opposing hitter against each of his team’s pitchers. Not everyone (especially his pitchers) agreed with this approach. As Jim Palmer, Baltimore’s Hall-of-Fame pitcher put it, “The only thing Earl Weaver knows about pitching is that as a player he couldn’t hit it.”

1 On building a winning ball team using the “new” statistics, see M. Lewis, Money Ball, (New York, N.Y.: W. W.

Norton & Company, 2003). Bill James was the first to apply a modern statistical approach to baseball.

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CHAPTER FOURTEEN ASYMMETRIC INFORMATION AND ORGANIZATIONAL DESIGN

OBJECTIVES 1.

To show the strategic implications posed by asymmetric information. (pp. 545-549)

2.

To understand the incentive conflicts (including moral hazard) inherent in the relationship between principal and agent. (pp. 550-554)

3.

To identify the factors influencing the nature and breadth of the firm. (pp. 554-557)

4.

To understand how decisions are delegated within organizations and to consider the choice between centralized and decentralized decisions. (pp. 557-562)

5.

To appreciate how firms monitor and reward the performance of workers, individually and in teams. (pp. 562-569)

6.

To understand the conflicts posed by the separation of ownership and control in modern corporations. (pp. 569-576)

TEACHING SUGGESTIONS I. Introduction and Motivation There are many vivid illustrations of asymmetric information. A number of examples appear in the negotiation and bidding settings taken up in Chapters 15 and 16. Here are some examples: John Wiley & Sons

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Example 1. Problem 13, Chapter 15 (slightly modified). Firm A is attempting to acquire Firm T but is uncertain about T’s value. It judges that the firm’s value under current management (call this vT) is in the range of $0 to $10 million, with all values in between equally likely. Whatever the present value of the firm, A estimates that it will be worth 50% more under its own management. (For instance, if vT = $5 million, then vA = $7.5 million.) Firm A will make a price offer to purchase the firm, which T’s management (knowing vT) will accept or reject. On behalf of Firm A, what price would you name?

Example 1 Discussion. This is a version of Akerlof’s classic “lemons” problem. Surprisingly, no mutually beneficial transaction is possible, despite the seller’s 50% value advantage. Asymmetric information is the culprit. As buyer, most students offer a price in the $5 million to $6 million range. They reckon that by offering slightly more than the seller’s expected value ($5 million), they can induce a sale and gain a profit (since A’s overall expected value is $7.5 million). Of course, this reasoning is faulty in that it ignores the implications of asymmetric information. When it receives A’s offer, Firm T knows precisely its value VT and accepts or rejects the offer accordingly.

What’s wrong with an offer of $6 million? Clearly, Firm T will accept the offer only if it knows the firm’s value under current management is less than this price. Thus, if the offer is accepted, the firm’s current value is between $0 and $6 million, or (1/2)($6 million) = $3 million on average. Even with the seller’s 50% value advantage, the seller’s acquisition value is only (1.5)(3) = $4.5 million on average. Because of adverse selection. Firm A tends to acquire low-value firms leaving it with a conditional expected loss of $1.5 million. It’s overall expected profit is: (.6)(-1.5) = -$.9 million (since the offer is accepted 60% of the time. It is easy to check that any price is loss making. The conditional expected acquisition value for price P is: (1.5)(P/2) = .75P. In words, Firm A’s acquisition value is only 75% of the price offered. Adverse selection prevents a profitable acquisition.

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Additional comment. The instructor might ask students whether it would make any difference if the target company (again knowing its value) were to name its buyout price. The answer is no. A naïve analysis might envision high-value firms naming high prices and low-value firms naming lower prices. The idea is that named prices would be calibrated to underlying values. The problem is that asymmetric information prevents targets from credibly signaling their true values. If Firm A were to accept a high price at face value (believing this to signal a high-value firm), a low-value firm would have an obvious incentive to name a high price, as well. Signaling cannot work here; there is no way high-value firms can distinguish themselves from their low-value counterparts.

2. Bidding for an Item of Unknown Value: The Winner’s Curse See Chapter 16 or Chapter 1 of this instructor’s manual for the bidding setting and the analysis.

II. Teaching the “Nuts and Bolts” In using this chapter, the instructor has a choice of options. One approach is to emphasize asymmetric information within market settings. Under this approach, the focus is clearly put on material in the first half of the chapter.

Applications to organizational design might be mentioned briefly or omitted altogether. The second approach focuses on the chapter as a whole.

Asymmetric information, whether in markets or within firms, is a cutting edge topic. Indeed, the eminent microeconomists and game theorists, Paul Milgrom and John Roberts, have written a wonderful text, Economics, Organization, and Management, Prentice Hall, 1992) devoted exclusively to this topic. Time permitting, the instructor can guide management students through a wealth of applications.

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A. Asymmetric Information While the chapter is already stocked with numerous, real-world examples, there are many more applications. Possible examples include: A Benefits Program (p. 546) We recommend posing this problem before the assigned chapter reading where it is discussed. Students offer a range of “reasons” for the policy losses including the zany moral hazard explanation that the generous maternity policy has induced workers to have more babies!

The correct, adverse-selection reason quickly emerges and can be backed up with the two-by-two table in the text. (The appearance of conditional probabilities from the table is a good bridge from the concepts in Chapter 13.)

A Building Contract (p. 550) This is another good application. The example reinforces the important distinction between adverse selection and moral hazard.

Adverse selection occurs when the agent (whose interests are at odds with the principal’s) holds unobservable or hidden information.

Moral hazard occurs when the agent (whose interests are at odds with the principal’s) takes unobservable or hidden actions.

Other Short Examples involving Moral Hazard and Incentives. A host of principal-agent applications fall into this category.

How should a company structure commissions for its direct sales force?

What portion should be paid in the form of a flat guaranteed wage? How much should depend on performance? How should performance be measured? By number of potential customers contacted? By the quantity of sales generated? In the latter case, what if unobservable variables (unrelated to the salesperson’s expertise and effort) influence sales? For instance, some salespeople happen to work in regions, market segments, or for specific John Wiley & Sons

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customers who have high demand for the firm’s product. One partial solution is to base compensation on relative performance. The best performers in a product segment or region earn the highest bonuses.

For many years, the U.S. government has offered low-cost (indeed, highly subsidized) flood and disaster insurance to homeowners in coastal areas.

The intention is to offer affordable insurance against hurricanes and floods that periodically destroy many of these homes. However, the predictable effect of the program is to encourage excessive coastal development.

Homes and structures have been built and rebuilt in the most severely affected, high risk, coastal locations. Economists have called for stricter regulation of coastal development and for an end to subsidized federal programs. Realistic insurance premiums, reflecting the true risks and costs of destruction, would restore incentives for prudent development.

The practice of warranting the health of livestock shows the logical market response to a potential problem of moral hazard. Livestock are prone to disease, and sellers are much better informed about the health of their stock than buyers. To remedy moral hazard, sellers commonly warrant their stock against disease for a stipulated period of time after sale. (This is not a perfect remedy, because the warrantee may reduce the buyer’s incentive to take precautions against disease.)

A Supply Contract. Firm S is about to contract to deliver lumber to Firm B. Firm S estimates that under normal circumstances, it can produce and deliver the lumber at a cost of $100,000. In recent months, however, the firm has been troubled by partial work stoppages. Should such stoppages recur, a portion of the lumber to fulfill the contract would have to be shipped from distant mills, increasing the total cost to $400,000. In the event of a labor strike, all of the order would have to be supplied by other mills, increasing the total cost to $600,000. Management of Firm S believe there is a 80% chance of normal labor conditions, a 10% chance of a partial stoppage, and a 10% chance of a strike. Thus, Firm S’s expected cost of fulfilling the contract is: (.8)(100,000) + (.1)(400,000) + (.1)(600,000) = $180,000.

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Firm B must have the lumber by the first of the month to fulfill a construction job that is expected to bring $480,000 in gross profit. In addition, the firm is about to spend $100,000 in setup costs for the construction job. If Firm B does not receive the lumber on time, it must forfeit the job. In short, timely delivery of the lumber by Firm S spells the difference between $380,000 in net profit for Firm B or a $100,000 loss.

The two firms are considering three different types of contracts: Specific Performance. The seller is required to deliver the lumber on time.

Reliance. A seller who defaults (fails to deliver on time) must pay back any money he has received from the buyer (the price $P) and must compensate for the buyer’s “reliance,” Firm B’s lost $100,000 investment.

Expectation. The defaulting seller must pay the buyer its “expectancy,” the profit expected under the contract. (If it defaults, Firm S would keep the contract price $P but must pay back $480,000 to Firm B.) Question for the class: Which type of contract is most effective in providing the right incentives for Firm S? Answer. This is an interesting principal-agent example dealing with incentives. As will be duly noted in Chapter 16’s discussion of negotiation, the two sides should reach a mutually beneficial contract. After all, Firm S’s expected cost is $180,000 and Firm B’s net profit is $380,000. There is plenty of room for a mutually beneficial price in between. Consider each of the contracts in turn.

Under specific performance, delivery is mandatory. If the negotiated price were (say) $280,000, then Firm B’s profit would be 380,000 – 280,000 = $100,000, and Firm S’s expected profit would be $280,000 - $180,000 = $100,000. The combined profit is $200,000.

Under reliance, Firm S would choose to default if there is a partial stoppage or a strike. By defaulting, it must pay back $280,000 + $100,000 = $380,000 John Wiley & Sons

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which is cheaper than delivering at a cost of $400,000 or $600,000. Firm B’s expected profit is (.8)(100,000) = $80,000. (Firm S defaults 20% of the time, forcing Firm B to forfeit the building contract and leaving it with zero profit.) Firm S’s expected profit is: (.8)(280,000 – 100,000) + (.2)(-100,000) = $124,000.

Thus, the combined profit is $204,000.

Under expectation, Firm S would choose to default only if there is a strike.

By defaulting, it must pay back $480,000 (it keeps the $280,000 contract price) which is cheaper than delivering at a cost of $600,000. Firm B receives a guaranteed profit of $100,000. If Firm S defaults (when there is a strike), it must forfeit the construction contract but it is indemnified $480,000 by Firm S. Its profit is: 480,000 – 280,000 – 100,000 = $100,000.

Firm S’s expected profit is: 280,000 – [(.8)(100,000) + (.1)(400,000) + (.1)(480,000)] = $112,000. Thus, the combined profit is $212,000.

Of the three options, the expectation contract is most efficient; it generates the greatest total profits to the parties together. It ensures that delivery is made in the “right” circumstances: under normal work conditions or partial stoppage. The buyer’s benefit from delivery is always $480,000 (the $100,000 setup cost is already sunk). Thus, it is efficient to deliver when the supply cost is $100,000 or $400,000. But, delivery is inefficient when the supply cost is $600,000 (i.e. exceeds the buyer’s $480,000 gain). By penalizing the supplier an amount that reflects the buyer’s gain, the expectation contract gives the supplier exactly the right incentive whether to fulfill or default the contract. (This is akin to taxing the generator of an externality for the harm caused.)

The contract calling for specific performance is inflexible. It requires delivery in all circumstances, even when it is inefficient (during a strike). In this instance, the supplier’s cost ($600,000) exceeds the buyer’s gain ($480,000). Delivery implies a net financial loss of 600,000 – 480,000 = $120,000. With a strike 10% likely, the expected net loss is (.1)(120,000) = $12,000. Thus, specific performance reduces the parties’ total profit John Wiley & Sons

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(relative to the expectation contract) by $12,000 ($200,000 compared to $212,000).

Finally, the reliance contract provides an insufficient delivery incentive. As we saw, Firm S defaults even during a partial work stoppage. (It is cheaper for it to default than to deliver.) But delivery should occur because the buyer’s $480,000 gain exceeds the seller’s $400,000 cost. By not delivering, the parties are forgoing a $80,000 combined profit. With a work stoppage 10% likely, the expected profit forgone is (.1)(80,000) = $8,000. Thus, the reliance contract reduces the parties’ total profit (relative to the expectation contract) by $8,000 ($204,000 compared to $212,000).

B. Organizational Design In teaching this section of the chapter, we suggest starting with the big picture: The essence of the modern firm is the division of information and management responsibilities among a wide group of managers.

Today’s firm is a set of agreements and contracts, both explicit and implicit.

We then go on to describe the boundaries of the firm, the division of decision making responsibilities, and the workings of incentive systems.

Many of the short readings listed on the next page provide real-world applications of these principles. For instance: On dividing responsibilities: The back-of-chapter discussion question highlights different division structures. In turn, the two Honda readings recount how the company changed from a consensus–building decision approach to a centralized approach. (By contrast, the “bread-store” article emphasizes the virtues of decentralized decisions.) An instructor who wants to spend more time on issues of centralization and decentralization might also wish to use the John Wiley & Sons

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Harvard Business School Case, DHL Worldwide Express, 1997 (in the listing of cases). The text (pp. 561-562) contains a capsule summary of this case. The readings section also includes three interesting articles on the benefits and costs of teams.

On incentives: In an effort to minimize costs, many firms have increasingly turned to piecework compensation systems, where compensation is paid according to job outputs. (See the article, “Paid by the Widget and Proud.”) For instance, the instructor might raise the following simple example. Should a typist (word processing worker) be paid a fixed salary? Should he be paid based on hours spent on different jobs? Should he be paid by the number of pages produced? How might pages of ordinary typing be compared to pages of difficulty, technical typing? Should compensation be based on some combination of the above factors?

Incentives are also the subject of the short readings: “Risky Business …”, “Executive Pay”, and the two pay-for-performance readings.

Finally, the article, “Plan to go Public at Goldman, Sachs,” describes the decision by the last major investment firm to abandon the partnership structure in favor of the corporate form that separates the components of ownership and control.

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ADDITIONAL MATERIALS

I. Short Readings J. Vascellaro and S. Morrison, “Google Gears Down for Tougher Times,” The Wall Street Journal, December 3, 2008, pp. A1, A16.

D. Leonhardt, “When Trust in an Expert is Unwise,” The New York Times, November 7, 2007, pp. C1, C9.

E. White, “How a Company Made Everyone a Team Player,” The Wall Street Journal, August 13, 2007, p. B1.

D. Gauthier-Villars, “EADS Considers a Simpler Management Structure,” The Wall Street Journal, July 9, 2007, p. A3.

“The Business of Making Money: Public versus Private Equity,” The Economist, July 7, 2007, pp. 68-70.

J. Lublin, “Ten Ways to Restore Investor Confidence in Compensation,” The Wall Street Journal, April 9, 2007, p. R1.

E. Dash, “Has the Exit Sign ever Looked so Good?” The New York Times, April8, 2007, p. BU6.

M. Karnitschnig, “Too Many Chiefs at Siemens?” The Wall Street Journal, January 20, 2005, p. A12.

J. Madrick, “Where Economists Stand, or Don’t Stand, on the Issue of Corporate Scandals,” The New York Times, October 28, 2004, p. C2.

“Pay for Performance: Running Out of Options,” The Economist, December 11, 2004, p. 10.

R. Lieber, “New Way to Curb Medical Costs: Make Employees Feel the Sting,” The Wall Street Journal, June 23, 2004, p. A1.

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V. Fuhrmans, “Higher Co-Pays Take Toll on Health,” The Wall Street Journal, May 19, 2004, p. D1.

B. Davis, “Finding Lessons of Outsourcing in 4 Historical Tales,” The Wall Street Journal, March 29, 2004, p. A1.

“At Shell, Strategy and Structure Fueled Troubles,” The Wall Street Journal, March 12, 2004, p. A1.

S. Ellison, “Kimberly-Clark is Set to Reorganize,” The New York Times, January 20, 2004, p. A3.

B. Mohl, “Amtrak Satisfaction Guarantee was Doomed from the Outset,” The Boston Globe, November 3, 2002, p. M8.

H. R. Varian, “If there was a New Economy, Why wasn’t There a New Economics?” The New York Times, January 17, 2002, p. C2.

“Wal Around the World,” The Economist, December 8, 2001, p. 55-57.

(This article discusses Wal-Mart’s organizational structure.)

“The Lemon Dilemma,” The Economist, October 13, 2001, p. 72. (George Akerlof, Michael Spence, and Joseph Stiglitz shared the 2001 Nobel Prize in economics for their pioneering work in asymmetric information.)

“Risky Business: A Set Fee for Each Patient Gives Doctors More Control and More of a Financial Stake,” The New York Times, May 30, 1998, p. D1.

“Redesign of Honda’s Management Faces First Test with Unveiling of New Accord,” The Wall Street Journal, September 1, 1993, p. B1.

“Shifting Gears: Just as U.S. Firms Try Japanese Management, Honda is Centralizing,” The Wall Street Journal, April 11, 1991, p. A1.

“Levi’s Factory Workers are Assigned to Teams and Morale Takes a Hit,” The Wall Street Journal, May 20, 1998, p. A1.

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“The Trouble with Teams,” The Economist, January 14, 1995, p. 61.

“Plan to go Public at Goldman, Sachs,” The New York Times, June 15, 1998, p. A1.

“Heinze CEO to Tie Managers’ Pay to Performance to Boost Efficacy,” The Wall Street Journal, June 16, 1998, p. B4.

“Boeing Links Managers’ Stock Options to Five-Year Performance of Shares,” The Wall Street Journal, February 26, 1998, p. B12.

“Paid by the Widget and Proud,” The New York Times, June 16, 1996, p. F1.

“Just Deserts,” The Economist, Jan. 29, 1994, p. 71. (An evaluation of performance pay.)

II. Longer Readings Kevin J. Stiroh, “Playing for Keeps: Pay for Performance in the NBA, Economic Inquiry, vol. 45, 2007, 145-161.

Symposium on Sociology and Economics, Perspectives, Winter 2005, 3-86.

Journal of Economic

B. Hall, “Incentives within Organizations,” Harvard Business School Case (9-904-043), January 9, 2004.

J. G. Riley, “Silver Signals: Twenty-Five Years of Screening and Signalling,” Journal of Economic Literature (2001), 432-478.

P. F. Levy, “The Nut Island Effect: When Good Teams Go Wrong,” Harvard Business Review, March 2001, pp. 5-12.

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E. Brynjolfsson and L. M. Hitt, “Beyond Computation: Information Technology, Organizational Transformation, and Business Performance,” Journal of Economic Perspectives, (2000), 23-48.

E. P. Lazear, “Performance Pay and Productivity,” American Economic Review, December 2000, 1346-1361.

Symposium on the Firm and its Boundaries, Journal of Economic Perspectives, 12, Fall 1998, 73-150. (These are 4 articles by eminent economists.)

A. Shleifer and R. W. Vishny, “A Survey of Corporate Governance,” Journal of Finance (1997), 737-783.

Michael C. Jensen and William H. Meckling, “Theory of the Firm: Managerial Behavior, Agency Costs, and Ownership Structure,” Journal of Financial Economics, 3 (1976), 305-360.

III. Recommended Cases Henderson Global Investors, (UVA-F-1330), Darden Business School, University of Virginia, 2001.

Scope of the Corporation (9-795-139), Harvard Business School, 1995.

DHL Worldwide Express (9-593-011), Harvard Business School, 1997.

Teacher’s Note (5-594-094).

Microsoft in the People’s Republic of China (9-795-115), Harvard Business School, 1995. Teacher’s Note (5-796-072). (Should Microsoft make its own local investments or should it contract out to local software vendors?)

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IV. Quips and Quotes The secret of management is to keep the guys who hate you away from the ones who are undecided. (Baseball manager Casey Stengle) Most organizations can’t hold more than one idea at a time.

In a hierarchy, every employee tends to rise to the level of his incompetence.

(L.J. Peter) Don’t ask the barber whether you need a haircut.

The real objective of a committee is not to make a decision but to avoid it.

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2. a. Commissions can lead to both adverse selection and moral hazard problems. The Sears compensation system may have attracted dishonest employees who saw a chance to make money by defrauding customers. This is the adverse selection problem. Once employed, all employees had the incentive to convince customers that they needed repairs. This is the moral hazard problem. By removing commissions some employees could be expected to quit and others to change their behavior. b. Management of Sears may not have much incentive to monitor its employees and discover the abuses. After all, the employees were generating strong profits for the company and thus there may have been an incentive to turn a blind eye. c. The downside of changing the compensation structure is that employees may have an incentive to shirk. Without the commission, fewer customers mean less work.

4.

First, from the university’s point of view, it is probably relatively inexpensive to offer these educational benefits. (The marginal cost to the system of accommodating additional employee students may be quite low.) Second, the more subtle point is that the university may be able to attract better employees by offering a fringe benefit that only ambitious, highly-motivated workers would value.

6.

The company favors the arrangement because it obtains a guaranteed price. (This price is slightly below the price the underwriter will set for the shares on the market. The difference is the underwriter’s profit.). The company also knows that the underwriter will have a strong incentive to sell the securities. However, there is one obvious John Wiley & Sons

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area of conflict between the two parties. There will be hard bargaining over the guaranteed price. Clearly, the underwriter will argue for a low price in order to be as certain as possible not to be stuck with unsold securities. In addition, the underwriters will need cooperation from the company in order to satisfy disclosure regulations. Typically the price is not set until the morning of the offering.

8.

A seniority system avoids influence costs, that is, the maneuvering, negotiation, and office politics that inevitably occur when one person has the power to dole out perquisites. On the other hand, perquisites could be a way of motivating employees. By using a seniority system the company forgoes these potentially powerful incentives.

10. a. No, the plant manager will report a much lower output, so that his actual output will greatly exceed the understated report, thereby claiming a large bonus payment for himself. b. Under the new bonus schedule, the manager will always strive for maximum output (because the bonus depends positively on actual output) and will also have the incentive to report the plant’s true capacity, QT = 10,000. To confirm this last result, suppose that the manager knows that maximum output is 10,000. If this is his report and his actual output matches the report (Q = Q T = 10,000), then his bonus is .4QT = $4,000. If he were to report a higher target (say Q T = 12,000), his bonus would fall to: (.4)(12,000) + .5(10,000 – 12,000) = $3,800 using the second equation of the bonus payment. Alternatively, if he were to report a lower target (say QT = 8,000), his bonus would fall to: (.4)(8,000) + .3(10,000 – 8,000) = $3,800 using the first equation of the bonus payment. Any overstatement or understatement reduces his bonus; his incentive is to report truthfully.

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Discussion Question a. Paying advertising agencies based on sales results certainly benefits Procter & Gamble and Ford. The new “incentive” contracts are designed so that ad agencies will have a keen incentive to mount the most effective possible ad campaign. Agencies are rewarded (in terms of higher fees) for successful campaigns (as measured by dollar sales). In short, the contract incorporates powerful incentives and a degree of risk sharing.

High performing agencies will also benefit via extra compensation. (A downside is that a product’s sales also depend on varied factors beyond the agency’s control (dulling incentives and increasing agency risk).

For more information, see S. Elliott, “P&G to Tie Agency Compensation to Sales,” The New York Times, September 15, 1999, p. C1, and G. White, “Ford’s Better Idea: Incentives for Agencies,” The Wall Street Journal, September 10, 1998, p. B13. b. The advantage of moving to divisions by product lines is that management (treating each line as a profit center) will be able to make optimal decisions for each line. This encourages standardized production, eliminating overlapping plants, and coordinating worldwide pricing. The product-line organization should eliminate the old internal rivalries between the country units. Besides the significant one-time costs of the reorganization (administrative costs and disruptive shifts in managers’ responsibilities), the main disadvantage is some lack of geographic flexibility. A product manager is unlikely to be as attuned to local economic conditions as the former country manager. After many growing pains with the reorganization, Exide decided to retain separate geographic teams (United States and Europe) for its largest product division, industrial batteries.

For more information, see J. S. Lublin, “Place vs. Product: It’s Tough to Choose a Management Model,” The Wall Street Journal, June 27, 2001, p. A1.

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c. Perry Corporation’s inventive financial transaction allowed it to increase its share holding – shares that it could “vote” in favor of the takeover – at no risk to itself. Though not illegal, Perry’s share maneuver did, indeed, make a travesty of the usual ground rules for corporate decisions – that shareholders are the ones that govern (in the legal sense) the corporation.

Many commentators would argue that the maneuver was certainly unethical. In due course, the rules of corporate government could be altered to close a “loop hole” such as this.

ANSWER TO THE SPREADSHEET PROBLEM (You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. To find the worker’s optimal level of effort, we use the optimizer to maximize the worker’s risk adjusted profit in cell E12 by varying cell D7. We find E* = 15. b. By hand or using the optimizer, we find the worker’s optimal effort levels are 20, 30, 40, and 50 for sharing rates .4, .6, .8, and 1.0 respectively. The higher the worker’s share of the profit he creates, then the greater is his work effort. c. Using the optimizer, we can find the value-maximizing contract by maximizing total profit in cell C17 by varying cells C7 and D7, subject to the constraint that cell E17 is equal to zero. The solution is sharing rate b = .714 and effort E = 35.7. Here, the worker receives a significant profit share giving him a strong work incentive. d. Here, we set the sharing rate in cell C7 equal to zero and simply maximize total profit by varying the worker’s effort in cell D7. The optimal level of effort is E = 50.

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Note to Instructor. The solution in part c can be found by the usual calculus methods. The goal is to maximize: Total profit = Employer’s Profit + Worker’s Risk Adjusted Profit = [(1-b)1000E – W] + [W + b1000E –10E2 – 10,000b2] = 1000E – 10E2 – 10,000b2 The employer sets b and the worker chooses his effort to maximizes his riskadjusted profit. The worker’s first-order condition is 1000b – 20E = 0, or E* = 50b.

(This formula confirms the effort schedule in part b.) Now we can substitute E = 50b into the total profit expression to obtain: Total profit = 50,000b – 25,000b2 – 10,000b2.

Maximizing this expression with respect to b implies the first-order condition: 50,000 – 70,000b = 0, or b* = 5/7 = .714. In turn, E* = 35.7 This confirms the optimizer solution found above.

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CHAPTER FIFTEEN BARGAINING AND NEGOTIATION

OBJECTIVES 1. To identify the economic sources of mutually beneficial agreements -namely, differences in values. (pp. 591-599) 2. To assess the complications posed by multiple-issue negotiations (and to stress the value-maximization principle. (pp. 599-604) 3. To explore issues of negotiation strategy: under perfect information and under imperfect information. (pp. 604-614).

TEACHING SUGGESTIONS I. Introduction and Motivation.

A. Negotiation Examples. Ask students to think about examples of negotiation in business settings and in everyday life. Here is a possible (partial) list: Some Negotiation Examples I. Business.

• Acquiring a Company • Undertaking a Joint Venture • Negotiating with a city government • A labor-management dispute • Settling a dispute out of court.

• Negotiating for resources within a firm • Persuading your boss John Wiley & Sons

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II.

Everyday • Negotiating a Raise • Parents “bargaining” with a four-year old about bed time.

• Bargaining with a used-car dealer • Negotiating a divorce agreement

III. Other • Log rolling in Congress • Formulating an international treaty • Negotiating a multiple-issue procurement contract

II. Teaching the Nuts and Bolts.

Points to Emphasize: A. A basic understanding of negotiation begins with the notion of the zone of agreement. The text chapter uses the example of selling a warehouse.

For variety, the instructor might choose a different example: for instance, buying a used car from its owner or a dealer. After formulating hypothetical reservation prices, the instructor can show how different prices imply different divisions of the total profit between the buyer and seller. The point to emphasize here is that mutually beneficial agreements hinge on differences in values. The Check Station vignette concerning the rights to In Search of Excellence is another good example.

B. In multiple-issue negotiations, the principle of value-maximization is crucial. As stated on p. 600: In multiple-issue negotiations, so long as there are differences in the value (importance) parties place on issues, there will be opportunities for mutually beneficial agreements of a quid pro quo nature.

It is often said that negotiation is as much about “value creation” as it is John Wiley & Sons

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about “value claiming.” Clearly, Pareto efficiency is served (i.e. both sides can be made better off) if the “pie” is made as large as possible before it has to be divided. Back-of-the-Chapter Problems 4, 5, 6 and 7 illustrate this principle. A corollary of the value-maximization principle is: Adopt a change in an agreement if and only if the additional benefit to one side (in dollar terms) exceeds the cost to the other.

Under this condition, the new agreement will necessarily have a greater total value than the old agreement (allowing the gainer to compensate the loser for the change).

C. The following two “parables” show how creative thinking can increase total value: a. Two sisters are arguing over who is to have the last orange in the refrigerator. A poor way to “resolve” the dispute is to have it end in a tug of war that reduces the orange to pulp. A better way is simply to slice the orange down the middle. The best solution is to “trade” on differences in the sisters’ preferences. The older sister is about to make a cake for which she only needs the peel; the younger sister is interested in eating the fruit. The simple expedient of peeling the orange accommodates both their needs. b. Two brothers are quarreling in their family room. One wants the window open; the other wants it closed. They argue about how far it should be open: halfway, a crack, more than halfway. There is no solution. Finally, a parent enters the room and asks the first brother why he wants it open. To get some fresh air. Why does the other want it closed? To avoid a draft. One solution: to open the window in the next room, bringing in fresh air without a draft. (Or have the first brother fetch a sweater for the other.)

Both parables show that crafting mutually beneficial agreements requires the parties to examine their intrinsic interests and find ways to increase total value. Agreements are not served by staking out immovable positions.

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ADDITIONAL MATERIALS

I.

Books on Negotiation

R. Fisher and W. Ury, Getting to Yes, Houghton Mifflin, 1992.

T. C. Schelling, The Strategy of Conflict, Harvard University Press, 1990.

H. Raiffa, The Art and Science of Negotiation, Harvard University Press, 1982.

II. Short Readings J. Lublin, “How to Handle the Job Offer You Can’t Afford,” The Wall Street Journal, December 2, 2008, pp. B9, B12.

J. D. Glater, “Study Finds Settling is Better than Going to Trial,” The New York Times, August 8, 2008.

R. Leiber, “Negotiating for a House? Start with ‘Dear Seller ’,” The New York Times, June 2, 2008, pp. B1, B6.

J. Surowiecki, “Striking Out,” The New Yorker, November 19, 2007, p. 42.

Ross Johnson, “Getting a Piece of the DVD Windfall,” The New York Times, December 13, 2004, p. B1.

Joe Lapointe, “NHL Cancels the Rest of Its Season as Labor Talks Fall Apart,” The New York Times, February 17, 2005, p. C1.

Dave Anderson, “A Scoreless Tie After Months of Wasted Words,” The New York Times, February 17, 2005, p. C1.

“Actors on the ‘Simpsons’ Reach a Deal with Fox,” The New York Times, May 1, 2004, p. A23.

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“Asbestos Factions Struggle to Settle Their 30-Year War,” The Wall Street Journal, October 15, 2003, p. A1.

“In a Negotiation Sea, Are you a Carp or a Shark?” New York Times, October 10, 2003, p. BU9.

“In ‘Sopranos’ Staredown, Both Sides Blink,” New York Times, March 17, 2003, p. C1.

“Focus on Recruitment, Pay, and Getting Ahead,” The Wall Street Journal, December 24, 2002, p. B4.

“Knives Drawn for a $15 Billion Family Pie,” The Wall Street Journal, December 11, 2002, p. A1.

M. Murray et al, “GE’s Jack Welch Meets his Match in Divorce Court,” The Wall Street Journal, November 27, 2002, p. A1.

“Latest Word in Luxury is Haggling,” New York Times, October 16, 2002, p.

A24.

“A Letterman Deal with ABC was Just a Signature Away,” New York Times, March 18, 2002, p. C1.

“A Family, a Feud and a Six-Foot Sandwich,” The New York Times, December 18, 2001, p. A1.

J. K. Sebenius, “Six Habits of Merely Effective Negotiators,” Harvard Business Review, April 2001, pp. 87-95.

“Haggling on the Web Interface to Interface,” The New York Times, September 28, 2000, p. E4.

“After 5½ Years, a Labor War Ends at 2 Detroit Papers,” The New York Times, December 19, 2000, p. A20.

M. H. Bazerman and J. R. Gillespie, “Betting on the Future: The Value of Contingent Contracts,” Harvard Business Review, September-October 1999, pp. 155-160.

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“For Dueling Lawyers, Internet is Referee,” The Wall Street Journal, May 12, 1999, p. B1.

“Web Transforms Art of Negotiating Raises,” The Wall Street Journal, September 22, 1998, p. B1.

“A Business Lawsuit Should always be Strictly Business,” The Wall Street Journal, January 16, 1998, p. B1.

“You have to Negotiate for Everything in Life, So Get Good at It,” The Wall Street Journal, January 27, 1998, p. B1.

“Ever Hear the One About the Lawyers and Window Bars?” The Wall Street Journal, March 23, 1994, p. A1 (How a $909 dispute generated $100,000 in legal fees.)

III. Cases The Pacific Sentinel (9-903-133 and 9-903-136) Harvard Business School, 2004.

Jessie Jumpshot (A1, B1, B2, B3) (9-800-388, 9-801-251, 9-801-252, and 9-801-253), Harvard Business School, 2001. (This is a 3-player contract negotiation.

Alphexo Corp. (9-801-418) and Bentonn Corp. 9-801-419), Harvard Business School, 2000.

Atlantis-Biovent Negotiation, (9-801-262 and 9-801-263), Harvard Business School, 2000.

Michael Brown: Negotiating Slots at Foxwoods (A) and (B), (9-899-234 and 9-899-235), Harvard Business School, 1999.

Doyle’s Deal Making Dilemma: Negotiating the Job Search, (9-801-124), Harvard Business School, 1999.

3M: Negotiating Air Pollution Credits, Parts A, B, and C: (9-897-134, 9-897-135, and 9-897-136), Harvard Business School, 1998.

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Discount and Hawkins (9-898-130, 9-898-131), Harvard Business School, 1997. (Negotiation exercise between landlord and tenant.)

Automated Intelligence Corporation (9-898-045), Harvard Business School, 1997.

Precision Controls, Inc. (9-898-046), Harvard Business School, 1997. (This and the previous case describe a merger negotiation.)

Negotiating Corporate Change (9-897-057, 9-897-058, 9-897-059, and 9-897-060), Harvard Business School, 1997.

(This is role-playing exercise with student negotiators.)

The Baseball Strike (9-796-059), Harvard Business School, 1997.

IV. Quips and Quotes Honesty is the best policy. There is much less competition.

You don’t know a woman until you have met her in court. (Norman Mailer) Do not do unto others as you would that they do unto you. Their tastes may not be the same. (George Bernard Shaw) To study the strategy of conflict is to take the view that most conflict situations are essentially bargaining situations. They are situations in which the ability of one participant to gain his ends is dependent to an important degree on the choices or decisions that the other participant will make. The bargaining may be explicit, as when one offers a concession; or it may be tacit. It may involve ordinary haggling in the market place; or it may involve threats of damage, including mutual damage, as in a strike, boycott, or price war, or in extortion. (Thomas Schelling, The Strategy of Conflict) If you don’t go to other men’s funerals, they won’t go to yours.

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When negotiating for money, pay attention to the increments of your opponent’s concessions. When they get progressively smaller, your opponent is reaching his bargaining limit.

The most important thing in acting is honesty. Once you’ve learned to fake that, you’ve got it made. (Sam Goldwyn) I wouldn’t want to belong to any country club that would have me for a member. (Groucho Marx)

V.

Negotiation Exercises

Face-to-face negotiation is an excellent vehicle for engaging students and promoting “learning by doing.” The following exercises are good examples.

To conduct the exercises, the instructor should distribute buyer and seller information sheets and pair the students. An easy way to create pairings is to hand out a “chit” to each student labeled Buyer 1, Buyer 2,... or Seller 1, ... and so on, in random fashion. Then have a roll call asking Buyer 1 and Seller 1 to raise hands and pair off, and so on. If negotiations are conducted in class, tell student pairs to negotiate quietly (and amicably). Also tell students not to be distracted by prices they might hear other pairs discussing.

These are irrelevant since different pairs may have different reservation prices. After completing the exercise, students can hand in data sheets and the instructor can lead a class discussion of what negotiation strategies were used and with what outcomes.

Typical in-class questions: - What kind of negotiation was this? (A distributive bargain; a multi-issue bargain; resolution of a dispute) - What was the alternative to a negotiated agreement?

- How much information did each side have?

- Summarize the course of your partnership’s negotiations. Who made the opening offer? What was it? What was the counter offer? Were concessions fast or slow? Did you “lay your cards on the table” or “play John Wiley & Sons

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things very close to the vest?” What was the final price? How did your experience compare with that of other pairs?

- What bargaining strategies seemed to work well? Is it advantageous to make the opening offer?

- How would things change if one side knew both reservation prices (and the uninformed side didn’t know about the other’s information advantage?)

A. A Negotiation Exercise. This is a purely distributive bargain in which pairs of students (playing the roles of buyer and seller) negotiate the price of a transaction. Each side knows its own reservation price but not the reservation price of the other side. In addition, both sides know that the buyer and seller reservation prices are drawn independently and uniformly from the intervals 150 to 250 and 100 to 200 respectively.

Reservation values can be assigned randomly. A slightly easier option is to use a small number of pre-picked values. The table below suggests five possible values for each side and lists total trading profits.

Buyer Values

111

Seller Values 134 152

239 221 201 178 160

129 110 90 67 49

105 87 67 44 26

87 69 49 26 8

170

189

69 51 31 8 None

50 32 12 None None

Discussion. This type of exercise has been run many times using student subjects. At the risk of some oversimplification, a convenient way to present an overview of typical results is to draw an analogy with the game of chess and speak of strategies in the opening, middle game, and end play.

As is universal in bargaining, students typically begin by making extreme opening offers -- buyer offers in the 130-160 range, seller demands in the 190-220 range. Because they frame the range in which subsequent offers are made, opening offers are an important determinant (in fact the John Wiley & Sons

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most important determinant) of final price. Moreover, opening offer strategy is crucial in the following sense. An opening offer that is too cooperative, i.e. that leaves too little space for the bargaining to follow, almost always destines the bargainer to a meager profit. For example, consider a buyer who offers b1 = 170 when holding value vB = 200. Suppose that the seller counters with s1 = 210 as is typical. Bargaining is now confined to the 170-210 range, and it is a fair bet that the final price will be in the middle of this range, near 190, leaving the buyer a profit of 10. This is considerably less than the buyer should expect to get on average. After all, the average seller value is 150, so the available total profit from an agreement is 50 on average. To have a chance of securing its fair profit share (25), the buyer must stake out enough room (say open with b 1 = 145) for the subsequent “negotiation dance.” The experimental evidence indicates that a bargainer does best by making an extreme opening offer, but not one so extreme as to compromise all credibility. One cannot “win” the negotiation by making the right opening. But one can lose it with an offer that stakes out too little bargaining room.

Like Sherlock Holmes’ dog that didn’t bark in the night, the key observation about the middle game is the absence of stratagems that deliver a clear profit advantage. In principle, a stubborn pattern of slow concessions (conceding more slowly than one’s partner) might be expected to reap profit dividends. The experimental evidence shows that most pairs of bargainers make concessions at roughly the same rate. One side’s slow concessions beget matched slow concessions from the other. (Of course, a small number of subjects make the mistake of a large initial concession, giving away profit to the other side.) Whether slow or fast, if concessions are equally matched, the final agreement (if there is one) can be expected in the neighborhood of the midpoint between the sides’ opening offers. Of course, the farther apart are the opening offers, then the greater are the number of offers and counteroffers it takes to reach agreement.

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In the negotiation exercise, a good prediction for the price of a final agreement is provided by the equation:1 P = .43[(vB + vS)/2] + .38[(b1 + s1)/2] + .19[178].

According to this equation, price is determined as a weighted average of the three bracketed terms. (Note that the weights .43, .38, and, .19 sum to one.)

The first term is the midpoint of the reservation values, an obvious point of attraction for the final price. The second term is the midpoint of the opening offers. As we noted, if concession rates are roughly equal, then the final price will gravitate toward this point (subject, of course to the influence exerted by the bargainers’ reservation prices. The third term represents the influence of the ranges from which reservation prices are drawn. Both sides know that these are drawn from the overlapping ranges 100-200 and 150250. Since the midpoint of the combined range is 175, we would expect this value to act as a center of gravity for final prices.

Since more than half of all agreements were concluded in the last two minutes of the allotted time, one might expect the end play to be important.

The main finding here is that almost all students are willing to make significant last moment concessions rather than fail in reaching an agreement. In fact, the clearest evidence of this behavior is provided by the pairs whose reservation prices precluded agreement. These subjects exchanged offers relentlessly (though fruitlessly), typically conceding within five units of their true reservation prices before giving up or running out of time. As a result of this behavior, pairs were very successful at attaining agreements -- reaching on average 9 of 10 possible agreements accounting for some 96% of the potential bargaining profit.

The cooperative negotiation behavior of subjects produces high marks for efficiency but does not constitute equilibrium behavior. A bargainer could increase his expected profit by departing from average behavior -- by being much more aggressive. This means beginning with an extreme opening offer, making slow concessions in the middle game, and outwaiting 1 The equation was estimated from the experimental data using ordinary least squares regression.

The form of the equation is implied by the hypotheses that (i) the reservation price coefficients are equal and (ii) the offer coefficients are equal. Both of these hypotheses were supported by the data.

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one’s bargaining partner in the last minute. For instance, a smart bargainer knows that a typical, cooperative-minded partner will concede nearly to his true value in the end game. By holding out for a substantial profit and waiting for the partner’s final concessions before time expires, the bargainer can obtain a better price. In fact, a direct way to improve a subject’s profit performance is to tell him a “wrong” reservation price. For instance, consider a buyer whose true value is 200 and earns an average profit from bargaining. If she is told instead that her value is 180, she will bargain more aggressively and earn a significantly greater profit on average. (Profit continues to be computed based on the true value 200.) This is true even though there is a greater chance of missing efficient agreements (for instance, when the seller’s value is above 180). Similarly, a seller will earn greater profit if he is told a tougher (i.e. higher) value than his true one.

In terms of pure self-interest, the key to more profitable bargaining behavior is to act as if one holds a tougher value than is the case. To quote the immortal words of the movie producer Sam Goldwyn, “The most important thing in acting is honesty. Once you’ve learned to fake that, you’ve got it made.” But a move to self-interested behavior on the part of both bargainers inevitably risks missing potentially beneficial agreements.

B. Buying and Selling a Maine House. This provides a slightly different negotiation setting than the first exercise in two respects. First, it provides a real-life setting. Second, an additional issue besides price is open for negotiation -- namely whether the sale should be for all 17 acres of land or for only 14 acres. As in the previous exercise, each bargainer knows his or her own reservation prices but not those of the other side.

According to the information sheet, the buyer’s reservation price is $93,000 if he or she purchases the house and all 17 acres and $78,000 if the deal is for 14 acres. Seller information sheets (see below) come in two different versions. The instructor should distribute version one of the seller information sheet to odd-numbered sellers and version two to evennumbered sellers. According to this version, the seller’s reservation price is $73,000 for a 17-acre sale and $66,000 for a 14-acre sale.

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Part a of the figure below shows the zones of agreement for odd numbered buyers and sellers. Here, a 17-acre sale provides the maximum total profit, which is equal to 93,000 - 73,000 = $20,000. An agreed-upon price of $83,000 would provide each side a profit of $10,000. Part b of the figure below shows the zones of agreement for even numbered buyers and sellers. According to this version, the seller’s value is $73,000 for a 17-acre sale and $50,000 for a 14-acre sale. A 14-acre sale provides the maximum total profit, which is equal to 78,000 - 50,000 = $28,000. An agreed-upon price of $64,000 would provide each side a profit of $14,000.

In the debriefing, the following questions should be addressed: 1. How did you arrive at your given agreement (14 acres or 17 acres)?

You’re your outcome efficient? Did you “lay your cards on the table” or “play things very close to the vest?”

2. Describe the negotiation dance. What was the opening offer? The counter offer? Were concessions fast or slow? What bargaining strategies seemed to work well? Is it an advantage to make the opening offer?

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BUYING AND SELLING A MAINE HOUSE House + 17 acres Buyer's Walk-Away Price: $93,000 Total Profit: $20,000 Seller's Walk-Away Price: $73,000 83

60

70

80

73

90

93

100

(a) House + 14 acres (Odd #) Buyer's Walk-Away Price: $78,000 Total Profit: $12,000 Seller's Walk-Away Price: $66,000 72

60

70

66

78

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(b) House + 14 acres (Even #) Buyer's Walk-Away Price: $78,000 Total Profit: $28,000 Seller's Walk-Away Price: $50,000 64

50

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A Negotiation Exercise Buyer’s Information You will participate in a negotiation exercise involving two parties, a buyer (you) and a potential seller (your bargaining partner). Your job is to try to negotiate the acquisition of the seller’s (unspecified) item at a profitable price. Before beginning negotiations, you will learn your private reservation value (or walk-away price) for the item. This reservation price is a number drawn between 150 and 250 inclusive, with all values in between being equally likely. Your selling partner will also learn his or her reservation price (the least amount acceptable for selling the good). The seller’s value is a number drawn between 100 and 200 inclusive, with all values in between being equally likely. (Note that buyer and seller values are drawn completely independently of one another. Each side knows its own value but not the value of the other.)

Your final profit depends on your reservation price and the price you negotiate. For the sake of example, suppose you draw the value 210. If negotiations end with an agreement at price P, your profit is simply 210 - P. Obviously, the lower the price you negotiate the greater your profit. If you and your partner fail to reach an agreement, you both earn zero profits.

Negotiation Ground Rules. You and your partner will have 10 minutes to negotiate an agreement. Negotiations are conducted by offers and counteroffers. You may accept the other side’s offer at any time and this ends the negotiations. Either side can make the first price offer. The main bargaining ground rules are: 1) You may not reveal your reservation price to the other side. However, you and your partner are free to discuss and argue about agreement terms.

Besides exchanging offers, you may also make general statements such as, “I can’t go higher” or “I can’t afford to pay that price.”

2) Offers must alternate between the players. A bargainer’s offer cannot get any worse (buyer offers cannot fall nor seller demands rise over time). The bargainer is free to repeat his previous offer, i.e. make no concession.

On the data form that follows, please record the offers as they are made. Indicate whether an agreement was reached and at what price.

Finally, compute your profit (if any) from the negotiation.

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A Negotiation Exercise Seller’s Information You will participate in a negotiation exercise involving two parties, a seller (you) and a potential buyer (your bargaining partner). Your job is to try to negotiate the sale of an (unspecified) item to the buyer at a profitable price. Before beginning negotiations, you will learn your private reservation value (or walk-away price) for the item. This reservation price is a number drawn between 100 and 200 inclusive, with all values in between being equally likely. Your buying partner will also learn his or her reservation price (the greatest amount he or she is willing to pay for the item). The buyer’s value is a number drawn between 150 and 250 inclusive, with all values in between being equally likely. (Note that buyer and seller values are drawn completely independently of one another. Each side knows its own value but not the value of the other.)

Your final profit depends on your reservation price and the price you negotiate. For the sake of example, suppose you draw the value 140. If negotiations end with an agreement at price P, your profit is simply P - 140.

Obviously, the higher the price you negotiate the greater your profit. If you and your partner fail to reach an agreement, you both earn zero profits.

Negotiation Ground Rules. You and your partner will have 10 minutes to negotiate an agreement. Negotiations are conducted by offers and counteroffers. You may accept the other side’s offer at any time and this ends the negotiations. Either side can make the first price offer. The main bargaining ground rules are: 1) You may not reveal your reservation price to the other side. However, you and your partner are free to discuss and argue about agreement terms.

Besides exchanging offers, you may also make general statements such as, “I can’t go higher” or “I can’t afford to pay that price.”

2) Offers must alternate between the players. A bargainer’s offer cannot get any worse (buyer offers cannot fall nor seller demands rise over time). The bargainer is free to repeat his previous offer, i.e. make no concession.

On the data form that follows, please record the offers as they are made. Indicate whether an agreement was reached and at what price.

Finally, compute your profit (if any) from the negotiation.

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A Negotiation Exercise Data Form On the data form, please record the sequence of offers as they are made. Either side may make the opening offer. Please circle the first offer made. Upon completing negotiations fill in the outcome (the final price if there is an agreement). If there is no agreement, record a “D” for disagreement. Also record your profit from any agreement.

Name: ____________________

Role: ________

Partner’s Name: ___________________ My Reservation Price: ____ Sequence of Offers Buyer

Seller

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

Outcome of the Negotiations: _______ (Final Price or D)

My Final Profit: ______.

Extra Question: What is your best guess as to your partner’s profit? _____ John Wiley & Sons

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Buying a Maine House

After reading these instructions, you will participate in a negotiation exercise involving two parties, a buyer (you) and a potential seller (a bargaining partner to be assigned). The description of the bargaining setting and information about your role as buyer are outlined below.

You and your spouse are in your late thirties and live outside New York City. For the last five years, you have been renting a cottage near a lake in an isolated and unspoiled part of Maine. Recently, you were contacted by the owner of a nearby summer house who has decided to sell the cottage and a considerable parcel of land surrounding it. Since the owner’s spouse died two years ago, the house has been unused and unattended. You and your spouse went to college with the owner’s son and remember the house from a visit three summers ago. You were both taken with the cottage, so taken that you asked to be called if it ever were put up for sale. A week ago over the phone, you and the owner agreed to meet at the house, tomorrow (Memorial Day weekend) to explore the terms of a possible sale. As yet neither side has even mentioned a price; both sides prefer to discuss and negotiate in person. You remember the owner (whose age you guess is near 65) as something of a “Yankee Trader” and probably a good negotiator. You also acquired negotiating experience in your former job as a purchasing agent.

The rambling “cottage” sits on a bluff overlooking a river and gorge.

The house is in the Cape Cod style but is equal to the size of two Capes.

The first floor has kitchen, bathroom, storage room, small dining room and an impressive, 40-foot living/family room with a fine view of the river below. The second floor has three normal bedrooms and one “dormitory size” bedroom over the living room, with no bathroom. A good euphemism for the cottage is “rustic”; the carpentry, appointments, kitchen appliances, plumbing and electrical systems all date from forty-five years ago. There are two first floor fireplaces, one on the second floor, but no central heat.

The cottage is located six miles from the nearest (small) town, and the final turnoff consists of two miles of unpaved road. (There is one, poor quality, year-round house at the junction of the dirt road and highway.) Besides the house, there are 17 acres of surrounding land, wooded except for two acres of lawn around the house. The lawn and former flower gardens have been untended for two years.

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Over the phone, you and the owner agreed to be prepared to discuss two sale options: (1) sale of the house and all 17 acres, or (2) sale of the house and 14 acres allowing the owner to retain 3 acres (separated by a small knoll from the house). The owner explained that keeping a small part of the land in the family as a link to the beloved spot would be appealing.

Prior to the negotiations, you have done two important bits of homework. First, you have explored with your spouse the maximum amount of money that you are willing to pay for the house. You prize the site, the view, and the cottage’s wonderful downstairs rooms. On the other hand, the kitchen and upstairs bedrooms (and adding a bathroom) mean considerable trouble and expense. You are also thinking about converting it to all-year use, since you are avid skiers and there is terrific skiing nearby. Accounting for these expenses, you come to the conclusion (after long thought) that your walk-away price for the house and all 17 acres is $93,000. You will never pay more than this price. Of course, you hope to pay a price below this level (and as small a price as possible). Acquisition of only 14 aces is obviously less desirable than getting all 17. After hard thought, you figure that giving up the 3 acres reduces your value for the house and property by $15,000.

That is, you would be willing to pay at most only $78,000 for the house and 14 acres.

Second, you have tried to imagine the kind of price the owner might demand for the house and land. To your mind, the house, because of its condition and isolation, will be very difficult to sell locally. You also realize that the owner’s personality and circumstances will probably have as much influence on an acceptable selling price as the quality of the house itself.

You know very little and would like to know much more about the owner.

On a note pad, you have listed the following, possibly pertinent facts: (1) The owner seems to be in the middle-income bracket and may need the sale income for later retirement. (2) None of the owner’s three children are interested in retaining the house. (3) Question: how much is retaining the 3 acres worth to the owner? All in all, your best guess concerning the owner’s minimum acceptable price (the least he would be willing to accept) for the house and 17 acres is that it ranges between $60,000 and $100,000, all values in between equally likely.

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You will have 15 minutes to negotiate possible sale terms with your bargaining partner representing the owner. Negotiations are conducted by offers and counteroffers. You may accept the other side’s offer at any time and this ends the negotiations. Either side can make the first price offer.

The main bargaining ground rules are: 1) You may not show this information sheet to your partner. In particular, it is not permitted to show the other side your walk-away price.

However, you and your partner are free to discuss and argue about agreement terms. Besides exchanging offers, you may also make general statements such as, “I can’t go higher” or “I can’t afford to pay that price.”

2) Offers must alternate between the players. A bargainer’s offer cannot get any worse (buyer offers cannot fall nor seller demands rise over time). The bargainer is free to repeat his previous offer, i.e. make no concession.

Your final profit from any agreement is the difference between your reservation price and the price you pay. Example: if you purchase the house and 14 acres for $66,000, your profit is 78,000 - 66,000 = $12,000.

(Remember, you are not allowed to pay more than your walk-away price!)

If no agreement is reached, your profit is zero.

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Selling a Maine House

After reading these instructions, you will participate in a negotiation exercise involving two parties, a seller (you) and a potential buyer (your bargaining partner sitting next to you). The description of the bargaining setting and information about your role as seller are outlined below.

In recent months you have thought about and finally decided to sell your summer house, a rambling isolated “cottage” on a bluff overlooking a river and gorge in Maine. You live in a Boston suburb, are sixty-five (in good health) and widowed since your spouse died two years ago. Though you have owned the house for twenty-four years and vacationed there weekends and for three weeks each summer, you have not been there for two years. Your three grown children agree with you that it is time to sell.

Though they have some sentimental attachments, no child wishes to retain the house. At your time of life, you could also use the sale proceeds for retirement.

The shingled cottage is in the Cape Cod-style but is equal to the size of two Capes. The first floor has kitchen, bathroom, storage room, small dining room, and an impressive, 40-foot living/family room with a fine view of the river below. The second floor has three normal bedrooms and one “dormitory size” bedroom over the living room, with no bathroom. A good euphemism for the cottage is “rustic”; the carpentry, appointments, kitchen appliances, plumbing and electrical systems all date from forty-five years ago. There are two first floor fireplaces, one on the second floor, but no central heat. The cottage is located six miles from the nearest (small) town, and the final turnoff consists of 1.5 miles of unpaved road. There is one, poor quality, year-round house at the junction of the dirt road and highway.

Besides the house, you own 17 acres of surrounding land, wooded except for two acres of lawn around the house. The lawn and former flower gardens have been untended for two years.

Two weeks ago, you telephoned the Wilsons, a New York couple, who are interested in buying the house. Three years ago, the couple visited the cottage as a guest of your son (who went to college with them). At the time, the wife had seemed very taken with the cottage and had taken a full tour of it and the grounds. In passing, she asked that you let them know if you ever decided to sell the house because they would be interested in John Wiley & Sons

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buying. From your recent conversation, they still seem to be seriously interested. Tomorrow (Memorial Day weekend), you and they are meeting at the house to explore the terms of a possible sale. As yet neither side has even mentioned a price; both sides prefer to discuss and negotiate in person.

You are aware that the husband has had extensive negotiating experience in his former job as an industrial purchaser. You pride yourself on being an experienced “Yankee Trader” and are comfortable negotiating.

Over the phone, you and the Wilsons agreed to be prepared to discuss two sale options: (1) sale of the house and all 17 acres, or (2) sale of the house and 14 acres allowing you to retain 3 acres (separated by a small knoll from the house). Psychologically, the second option is appealing. You wouldn’t sever all immediate connection with your beloved vacation spot, and the land might be passed on to a child or grandchild after your death.

Prior to the negotiations, you have done two important bits of homework. First, you have explored with the local real estate agent (an old Maine friend) the prospects of selling the house locally. Though he predicts a good year for sales in this part of Maine, his expert opinion is that the cottage, because of its condition and isolation, will be difficult to sell. If he were to list it, he thinks that the house and surrounding land intact could be sold (sometime during the upcoming season, possibly late) for a price in the $75,000 to $80,000 range. Excluding the neighboring three-acre section from the sale, he says, would drastically reduce the attractiveness of the house, resulting in a significantly lower price. Based on this conversation, you have decided to adopt $73,000 as your walk-away (or minimally acceptable) price for a complete land and house sale. (This figure accounts for the deduction of a 6% broker’s fee.) That is, you will never sell the house and all 17 acres for a price below $73,000. Of course, you hope to get as high a price as possible -- one in excess of this amount. You figure that retaining the 3 acres has a value of $7,000 to you. That is, you would be willing to sell the house and 14 acres (retaining 3 acres) for as little as $66,000.

Second, you have tried to imagine how much the Wilsons might be willing to pay for the house and land. You realize that this may depend as much on the Wilsons themselves as on the quality of the house. You know very little and would like to know much more about the couple. On a note pad, you have listed the following, possibly pertinent facts: (1) They have three children and rented a cottage on a nearby lake for the past five summers. (2) The couple appears to be wealthy; he has a good job, she John Wiley & Sons

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works part-time. New Yorkers earn a great deal. But do they also spend a great deal? (3) Question: What makes the house attractive to the couple: the fireplaces? The view? Winter skiing nearby? Your best guess concerning the Wilsons’ monetary value (the most they are willing to pay) for the house and 17 acres is that it ranges between $60,000 and $100,000, with all values in between equally likely.

You will have 15 minutes to negotiate possible sale terms with your bargaining partner representing the Wilsons. Negotiations are conducted by offers and counteroffers. You may accept the other side’s offer at any time and this ends the negotiations. Either side can make the first price offer.

The main bargaining ground rules are: 1) You may not show this information sheet (particularly, your walkaway price) to your partner. However, you and your partner are free to discuss and argue about agreement terms. You may make broad statements such as, “I can’t go any lower” or “I can’t afford to accept that price.”

2) Offers must alternate between the players. At his turn, a bargainer’s offer cannot get any worse (buyer offers cannot fall nor seller demands rise over time). However, the bargainer is free to repeat his or her previous offer (i.e. make no concession).

Your profit from any agreement is the difference between the price you receive and your walk-away price. Example: if you sell the house and 14 acres for $77,000, your profit is 77,000 - 66,000 = $11,000. (Remember, you can’t settle for less than your walk-away price!) If you fail to reach an agreement, your profit is zero.

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Selling a Maine House

After reading these instructions, you will participate in a negotiation exercise involving two parties, a seller (you) and a potential buyer (your bargaining partner sitting next to you). The description of the bargaining setting and information about your role as seller are outlined below.

In recent months you have thought about and finally decided to sell your summer house, a rambling isolated “cottage” on a bluff overlooking a river and gorge in Maine. You live in a Boston suburb, are sixty-five (in good health) and widowed since your spouse died two years ago. Though you have owned the house for twenty-four years and vacationed there weekends and for three weeks each summer, you have not been there for two years. Your three grown children agree with you that it is time to sell.

Though they have some sentimental attachments, no child wishes to retain the house. At your time of life, you could also use the sale proceeds for retirement.

The shingled cottage is in the Cape Cod-style but is equal to the size of two Capes. The first floor has kitchen, bathroom, storage room, small dining room, and an impressive, 40-foot living/family room with a fine view of the river below. The second floor has three normal bedrooms and one “dormitory size” bedroom over the living room, with no bathroom. A good euphemism for the cottage is “rustic”; the carpentry, appointments, kitchen appliances, plumbing and electrical systems all date from forty-five years ago. There are two first floor fireplaces, one on the second floor, but no central heat. The cottage is located six miles from the nearest (small) town, and the final turnoff consists of 1.5 miles of unpaved road. There is one, poor quality, year-round house at the junction of the dirt road and highway.

Besides the house, you own 17 acres of surrounding land, wooded except for two acres of lawn around the house. The lawn and former flower gardens have been untended for two years.

Two weeks ago, you telephoned the Wilsons, a New York couple, who are interested in buying the house. Three years ago, the couple visited the cottage as a guest of your son (who went to college with them). At the time, the wife had seemed very taken with the cottage and had taken a full tour of it and the grounds. In passing, she asked that you let them know if you ever decided to sell the house because they would be interested in John Wiley & Sons

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buying. From your recent conversation, they still seem to be seriously interested. Tomorrow (Memorial Day weekend), you and they are meeting at the house to explore the terms of a possible sale. As yet neither side has even mentioned a price; both sides prefer to discuss and negotiate in person.

You are aware that the husband has had extensive negotiating experience in his former job as an industrial purchaser. You pride yourself on being an experienced “Yankee Trader” and are comfortable negotiating.

Over the phone, you and the Wilsons agreed to be prepared to discuss two sale options: (1) sale of the house and all 17 acres, or (2) sale of the house and 14 acres allowing you to retain 3 acres (separated by a small knoll from the house). Psychologically, the second option is appealing. You wouldn’t sever all immediate connection with your beloved vacation spot, and the land might be passed on to a child or grandchild after your death.

Prior to the negotiations, you have done two important bits of homework. First, you have explored with the local real estate agent (an old Maine friend) the prospects of selling the house locally. Though he predicts a good year for sales in this part of Maine, his expert opinion is that the cottage, because of its condition and isolation, will be difficult to sell. If he were to list it, he thinks that the house and surrounding land intact could be sold (sometime during the upcoming season, possibly late) for a price in the $75,000 to $80,000 range. Excluding the neighboring three-acre section from the sale, he says, would drastically reduce the attractiveness of the house, resulting in a significantly lower price. Based on this conversation, you have decided to adopt $73,000 as your walk-away (or minimally acceptable) price for a complete land and house sale. (This figure accounts for the deduction of a 6% broker’s fee.) That is, you will never sell the house and all 17 acres for a price below $73,000. Of course, you hope to get as high a price as possible -- one in excess of this amount. You figure that retaining the 3 acres has a value of $23,000 to you. That is, you would be willing to sell the house and 14 acres (retaining 3 acres) for as little as $50,000.

Second, you have tried to imagine how much the Wilsons might be willing to pay for the house and land. You realize that this may depend as much on the Wilsons themselves as on the quality of the house. You know very little and would like to know much more about the couple. On a note pad, you have listed the following, possibly pertinent facts: (1) They have three children and rented a cottage on a nearby lake for the past five summers. (2) The couple appears to be wealthy; he has a good job, she John Wiley & Sons

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works part-time. New Yorkers earn a great deal. But do they also spend a great deal? (3) Question: What makes the house attractive to the couple: the fireplaces? The view? Winter skiing nearby? Your best guess concerning the Wilsons’ monetary value (the most they are willing to pay) for the house and 17 acres is that it ranges between $60,000 and $100,000, with all values in between equally likely.

You will have 15 minutes to negotiate possible sale terms with your bargaining partner representing the Wilsons. Negotiations are conducted by offers and counteroffers. You may accept the other side’s offer at any time and this ends the negotiations. Either side can make the first price offer.

The main bargaining ground rules are: 1) You may not show this information sheet (particularly, your walkaway price) to your partner. However, you and your partner are free to discuss and argue about agreement terms. You may make broad statements such as, “I can’t go any lower” or “I can’t afford to accept that price.”

2) Offers must alternate between the players. At his turn, a bargainer’s offer cannot get any worse (buyer offers cannot fall nor seller demands rise over time). However, the bargainer is free to repeat his or her previous offer (i.e. make no concession).

Your profit from any agreement is the difference between the price you receive and your walk-away price. Example: if you sell the house and 14 acres for $67,000, your profit is 67,000 - 50,000 = $17,000. (Remember, you can’t settle for less than your walk-away price!) If you fail to reach an agreement, your profit is zero.

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A Maine House Data Form On the data form, please record the sequence of offers as they are made. Upon completing negotiations fill in the sale terms (how much land was sold and at what price). If there is no agreement, record a “D” for disagreement. Also compute your final profit.

Name: ______________________

Role: ________ #: ___

Partner’s Name: _____________________ Fill in the appropriate blank: Disagreement: ____ OR Agreement to sell House & 17 acres at a price of ______ thousand dollars.

OR Agreement to sell House & 14 acres at a price of ______ thousand dollars.

My Profit: _____ Record of Offers: House & 17 acres (Please circle the first offer made.)

Seller ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ Buyer ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ Record of Offers: House & 14 acres (Please circle the first offer made.)

Seller ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ Buyer ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ (You should fill out both records assuming offers for both 17 acres and 14 acres are made.)

Extra question: What is your best guess about your partner’s profit? _____ John Wiley & Sons

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2. a. When the firm’s profits are booming, management is vulnerable to a costly strike by labor. Labor’s bargaining power is strengthened. b. Again, labor is in a strong position when it has ample reserves in its strike fund. c. With high unemployment, labor has more to lose from a prolonged strike. Management’s bargaining power is strengthened.

4. a. No. Zero percent defects is very costly for firm S who will insist on an accordingly high price. b. The value-maximizing agreement calls for 4 percent defects. Here the players’ total trading gain is: Vb - Cs = 72 - 37 = 35.

6. a. As a general rule, an outcome on an issue should be adopted if and only if doing so increases the value of the contract to the parties together. The table below summarizes these impacts (in $ millions).

The UMW’s values, originally expressed in wage equivalents, have been converted into total dollars (in millions).

Right-to-Strike Open up Job Impact of Both Clauses

UMW +30 -20

Producers -50 +60

Parties Together -20 +40

+10

+l0

+20

Introducing the right-to-strike clause has a negative (-$20 million) impact on the parties together. Since it reduces total value, it should

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not be introduced. Opening non-mine jobs increases total value (management’s gain exceeds labor’s loss) and therefore should he introduced. Thus, only the second clause should be part of an efficient contract. Of course, with the introduction of the second clause, the UMW will insist upon a wage concession from the producers. Any wage concession worth between $20 million and $40 million will generate a mutually beneficial improvement in the contract terms. b. Now it is impossible to introduce a single clause, since a compensating wage change is ruled out. Besides the status quo, the only other option is to introduce both clauses. Is this mutually beneficial? The table shows that each side gains $10 million, so the answer is yes.

Introducing both clauses is an example of negotiation quid pro quo.

However, notice that the total profit of the parties is now only $20 million (less than the $40 million of part a). Both parties would be better off if wages were unfrozen allowing adoption of the job clause alone (along with appropriate wage compensation).

8. a. A’s expected value for company is (.5)(50) + (.5)(20) = $35 million.

T’s expected value for company is (.8)(40) + (.2)(30) = $38 million.

Thus, there is no zone of agreement, making a 100% cash transaction impossible. b. A 100% stock transaction (at the right terms) works because it allows A to pay a 50% depreciated price in the event of liability. Effectively, A pays a contingent price. For instance, suppose A pays a price of $44 million in stock (based on the current stock price). Therefore, A’s expected payment is (.5)(44) + (.5)(22) = $33 million which is less than its $35 million value. In turn, T’s expected receipt is (.8)(44) + (.2)(22) = $39.6 million which is more than its $38 million value. The stock deal is mutually beneficial.

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c. A buyback provision makes perfect sense because if T is liable, the firm will be worth more under T’s management ($30 million) than under A’s ($20 million). The buyback is mutually beneficial.

Including such a provision (at a mutually beneficial price) upfront in the terms of the acquisition increases both sides’ values.

10.

If firm A claims 55%, its expected profit is (.9)($110,000) = $99,000.

If it claims 60%, its expected profit is (.85)($120,000) = $102,000. If it claims 65%, its expected share is (.8)($130,000) = $104,000. Thus, a 65% claim is optimal.

12.

Firm X should conclude an agreement with Firm C which offers the lowest cost and use its alternative options to get the best terms possible. Thus, Firm C should be approached first, with B (the next lower cost firm) reserved as the next stop. To solve the problem, we work backwards beginning with the last “stop”, Firm A. Here, the players’ walk-away prices (i.e. costs) are 10 and 8, so the equal profit price is 9. Thus, at the next to last stop (Firm B) both negotiators know that X’s walk-away price is 9 (what it can get from A).

Splitting the difference between 9 and 7 (B’s cost) means a negotiated price of 8. In turn, this becomes X’s walk-away price in its negotiations with C. Thus, X and C will reach an immediate agreement at a price of (8+5)/2 = 6.5. Note that if X bargained with C without other alternatives, the equal-profit price would be (10+5)/2 = 7.5. Thus, X benefits from the presence of other competitors even though it does not actually contract with them. It is easy to check that any other order of negotiation leads to a worse price for X.

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Discussion Question Negotiation and litigation can be thought of as opposite ends of the dispute resolution spectrum, with mediation and arbitration in between.

Negotiation is private, voluntary, informal, and (usually) low cost. The disputants themselves craft the terms of any ultimate agreement.

Litigation is public, imposed, formal, and costly. Via an adversarial process governed by strict rules and influenced by legal precedents, judge or jury determines the ultimate resolution of the case.

Under mediation, a third-party is assigned to help the disputants reach their own agreement. The mediator can play many roles: Setting the negotiation agenda and ground rules Creating a constructive atmosphere for compromise Gathering information about the goals and interests of each side Suggesting tradeoffs and mutually beneficial agreements Instilling a note of realism in the demands of the parties.

However, the mediator cannot impose an agreement or bind the parties to one. If mediation fails, the parties can pursue arbitration or litigation.

Under binding arbitration, the disputants present their cases to a third-party who imposes the final outcome. The arbitrator (usually an expert in the area of dispute) judges the case and offers a reasoned decision. Unlike litigation, the arbitration proceeding is private, informal, expeditious (hearings usually last a few days and written verdicts are rendered in a few weeks), low cost, and not bound by legal precedent. An arbitrator can decide the dispute on narrow grounds or can use considerable discretion in crafting the final outcome.

In short, mediation is a close cousin of negotiation, while arbitration is meant to be a much more flexible form of adjudication.

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ANSWERS TO THE SPREADSHEET PROBLEM (You may download any and all spreadsheets from the John Wiley, Samuelson and Marks Website.)

S1. a. and b. To find one end of the zone of agreement, we use the optimizer to maximize Company B’s profit in cell L13 by changing the dummy variables (cells C7, C9, C12, C13, C14, I7, and I9) and the payment in cell H13, subject to Company U’s profit in cell K13 being equal to zero. In addition, the sum of the first four dummies (computed in Cell K8) and the sum of the last three dummies (computed in Cell C16) must be equal to one. Finally, all dummy variables must be non-negative. From the optimizer’s solution, we find that Company B’s maximum profit is attained by a low-quality, full-warranty, 5-year contract with U paying B 77 million pounds.

At the other end of the zone of agreement, Company U’s maximum profit calls for the same contract terms but a payment of only 6 million pounds. In this case, U’s profit is $142 million (equivalent to 71 million pounds). c. We see that the low-quality, full-warranty, 5-year contract is efficient. The efficient frontier is found by varying the size of the U’s payment to B.

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A

B

C

D

E

F

G

H

I

J

K

L

M

1 2

A BRITISH-US CONTRACT

3 4 5

Warranty Quality

6 7

High

0

Full

Partial

Co U Co B

Co U Co B

238

180

68

42

0

8 9

Sum 1

Low

1

178

24

92

18

0

10 11

Delivery

Co U Co B

U's Payment to B

12

2 Years

0

18

10

(pounds)

13

3 Years

0

0

0

77

14 15

5 Years

1

-24

-28

16

Sum

1

Co U's Co B's Profit Profit 0

71

.

17

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CHAPTER SIXTEEN AUCTIONS AND COMPETITIVE BIDDING

OBJECTIVES 1. To demonstrate the potential advantages of auctions compared to posted prices, on the one hand, and to unconstrained negotiation, on the other, and to show how auctions can enhance revenue. (pp. 625-629) 2. To analyze bidder strategies under various auction mechanisms including English auctions, Dutch auctions and sealed-bid auctions. (pp. 629-639) 3. To examine the phenomenon of the winner’s curse and how it affects the bidding process. (pp. 639-641) 4. To analyze the auction process from the auctioning party’s perspective and to determine which types of auctions produce the best terms for the auctioning party. (pp. 641-647) 5. To discuss competitive procurements. (pp. 647-648)

TEACHING SUGGESTIONS I. Introduction and Motivation A. Guinea Pig Question Bidding for an Item of Unknown Value. Tell the class that you will conduct a sealed-bid auction for a valuable item. The high bidder will pay his bid and win the item. The item is a jar of pennies. Actually its easier to fill a glass pickle jar with colored plastic Christmas ornaments John Wiley & Sons

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(little pinwheels about penny size) to spare the bother of dealing with pennies. Fill the jar with a predetermined number of trinkets. (For instance, set the number at 463 by using two packs of 250 trinkets minus 17.) Tell the class that the winning bidder will receive the value of the jar where each trinket is redeemable for a penny. Thus, though the students don’t know it the jar is worth $4.63. A buyer with a winning bid of $3.50 would make a profit of $1.13. If the winning bid were $6.00, the “winner” would lose $1.37.

Ask each student to write down 4 items: 1) an estimate of the value of the jar (i.e. the number of trinkets translated into dollars); 2) a sealed bid for the jar; and 3) upper and lower bounds constructed to form a 90% confidence interval around the true value. (Remind students what a confidence interval is.)

B. Guinea Pig Question, Discussed Bidding for an Item of Unknown Value. This example introduces complications posed by uncertainty. Each bidder is uncertain about the value of the jar and also about the level of competitors’ bids. Before revealing the true value of the jar, ask a number of students to reveal their estimates. Students will be surprised by the wide dispersion of estimates.

Ask the class what the distribution might look like if it were plotted. A number of students are sure to suggest a bell-shaped normal curve. By shows of hands, find roughly the median of the class estimates and sketch a normal curve with this mean. Then ask students how they bid. Compare bids to estimates to emphasize the logic of placing bids below estimates.

Note that the optimal degree of shading involves a tradeoff between the chance of winning and the profit from winning. (Finding an optimal solution is a complex problem.) Superimpose the bid distribution next to the estimate distribution. Your graph should resemble Figure 16.2, p. 640.

Now is the time to suggest the possibility of the winner’s curse by raising two hypotheses. First, suppose estimates are unbiased, i.e. centered around the true value of the item. (This seems reasonable.) Second,

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suppose that estimates and bids are quite disperse. (Also reasonable.) These two points imply that the highest bids (the shaded tail in Figure 16.2) are above the true value of the item. On average, the winning bidder loses money on the acquisition. At this point, you may ask some of the high bidders in the class, whether this argument worries them. (Do they still want to play for real or only for fun?) Find the highest bid. Then, reveal the value of the item. With 20 or more students in the class, nine times out of ten, the winning bidder will fall prey to the winner’s curse, i.e. pay more than the item’s value. The only exceptions occur if the class estimates are biased well below the true number of trinkets. (To avoid this problem, try the trinkets in different shaped jars, and see that the jar is 75% or more full.)

Having made the main point, you can raise some other questions. What factors increase the likelihood and magnitude of the winner’s curse? As discussed on pp. 640-641, the winner’s curse increases with the degree of uncertainty and the number of bidders. Does the winner’s curse happen in real life? Yes, bidding for off-shore oil leases, competitive tender-offers, and free-agent bidding for athletes are just three examples. How well did you (the student) gauge your degree of uncertainty? Most individuals are overconfident of their estimation abilities. Ask students if the true estimate fell between their lower and upper bounds. Typically, less than half the students answer in the affirmative by a show of hands. By construction, the intervals should bracket the true value 90 percent of the time. In short, students are surprised that their knowledge is so uncertain.

II. Teaching the “Nuts and Bolts” This chapter contains a good deal of advanced material. Accordingly, the instructor has a number of decisions concerning teaching strategy.

A. In our view, the most important points include: 1. Optimal sealed-bids against a BCB distribution; 2. The winner’s curse; 3. The benefits of auctions.

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B. A number of advanced topics can be omitted without loss of continuity: 1. Equilibrium bidding strategies; and 2. Revenue Equivalence Teaching Hint: The formulas and intuition for equilibrium bidding strat-egies in the uniform case are greatly simplified if the lower bound is taken to be zero, L = 0. For instance, suppose values are uniformly distributed between 0 and 100. It follows that: E(vmax) = [n/(n+1)]100, E(v2nd) = [(n-1)/(n+1)]100, bi = [(n-1)/n]vi E(bmax) = [(n-1)/n]E(vmax) = [(n-1)/n][n/(n+1)]100 = [(n-1)/(n+1)]100.

This is a direct confirmation of revenue equivalence: E(bmax) = E(v2nd). \ C. Recommended Problems Problems 3, 4, 5, 10, and 11.

D. Exercise: Bidding for Film Exhibition Rights In this exercise, student teams representing movie chains bid for the right to show actual feature films. (The accompanying student information sheets provide full details.) For instance, suppose a student team wins the right to show a blockbuster film for a four-week run by placing a high bid of $6,000 per week. If the actual gross revenues for the run turn out to be $10,000, $8,000, $5,000, and $4,000, its overall profit would be 27,000 - 24,000 = $3,000.

The great virtue of this exercise is that bidding is for real films and profits are based on actual theater revenues (as reported each week by the trade publication Variety). To conduct the exercise, the instructor should

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carry out the following steps. (The illustration is for a class of 25 students.

Larger classes would mean more teams and more films up for bid.)

1. Divide the class into 5 teams.

2. Select 8 films that are about to open nationwide. Consult Variety.com or other entertainment websites or publications for about-to-open or recently opened films.

3. Have teams bid for these films in class. Use the conventional English auction (higher and higher bids) for the first 5 films. Use sealed bid auctions for the final 3 films. (No team can acquire more than two films.

Some teams will acquire one or no films.)

4. For each of the next four weeks, look up the revenue for each film in Variety.com or other websites. To compute weekly revenue per theater, divide the total “Gross” by the number of screens. Report the teams’ cumulative profits. Students usually take a strong interest in how they are doing.

Optional tasks: 5. Update the information on page 3 of the handout. (That information is drawn from December 2007 and early 2008.)

6. Provide movie reviews or other information on the films up for bid.

Remarks.

1. Based on past history, an average top-25 film in weeks 1 to 4 of release can expect to earn typical weekly grosses of $6,000, $4,500, $3,000, and $2,000.

A block-buster could earn grosses twice as large, a box-office bust grosses half as large. Weekly revenues also depend on the time of year (see the chart on page 3 of the handout) and the breadth of the release. Frequently, “art” films or foreign films have a narrow release

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(less than 100 theaters nationwide) and can earn $10,000 or more per theater.

(To get some benchmarks for potential film values, the astute student should compute gross revenues per screen for the films reported on page 3 of the handout. To arrive at a final value estimate for a particular film up for bid, the student can then adjust these benchmarks based on any of a variety of subjective factors.

2. The winner’s curse is definitely present in this exercise. Dreaming of blockbusters (and forgetting that weekly revenues decline as weeks go by) leads many student teams to overbid for films. (Remember, each team submits a fixed bid to apply for all 4 weeks, even though weekly revenues typically fall over time.) Though there is a wide variance, the typical team makes a zero profit on average. (This is worse than if a team were to win no films, in which case its total profit for the 4 weeks would be $4,000; see page 2 of the handout.) Some 40% of all teams end up making losses.

Earning a final profit of $10,000 or more is a strong performance accomplished by only about one team in four.

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Bidding for Film Exhibition Rights

Many of the motion pictures released by major film companies are distributed via blind bidding. Theater owners bid for the exhibition rights to a film without having seen it (often in advance of the film’s completion). The merits of this practice are hotly disputed by theater owners and distributors alike. Theater owners contend that under the system they frequently overpay for movies that are flops and that they shoulder a disproportionate share of the risk inherent in film rentals. For their part, movie companies insist that blind bidding is necessary. Big budget blockbusters will be produced, they insist, only if solid play dates in prime time (summer, Christmas, and Easter) can be assured. Advertising campaigns (especially television) must be planned as much as a year in advance. They add that theater owners should bear some share of film risk.

About 25 states have passed laws banning blind bidding. Exhibitors in these states bid for films after regional screenings -- a process which delays film openings two to three weeks behind states that do not prohibit blind bidding.

The Bidding Competition Members of the class will be divided into teams and bid to obtain the exhibition rights to a number of films. Each team represents a theater chain seeking to acquire the rights for up to two films. The major film companies that distribute the films have specified a “standard” contract with the following provisions: 1. The film will be shown for a minimum play period of four weeks. This period begins following the film’s nationwide release date.

2. The EXHIBITOR will guarantee the DISTRIBUTOR a weekly payment of $ _______.

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Bidding In all, 8 films are up for bid. The first five films (A-E) will be sold in order by English auction. The last three films (F-H) will be sold by successive sealed bid auction.

If a chain fails to acquire a film to play in its theaters, its fall-back option is to play a previously released film (in which case it earns $500 a week in net revenues).

Calculation of Payoffs A chain’s return from film exhibitions is calculated according to its average gross revenue per theater during the four week run. For example, if a particular film were playing in five theaters and earned a total revenue of $24,000 in a given week, then the average gross revenue per theater is $4,800.

Therefore, the chain receives net revenue equal to $4,800 minus its bid. (For example, if its bid were $3,200, the chain’s net revenue on the film would be $1,600.) Each chain seeks to maximize its total net revenues over the fourweek movie run. At the end of the competition, your team’s total net revenue payoff will be converted into a grade equivalent.

Pre-Bid Information Prior to bidding, each team should review its packet of materials. These describe the films up for bid (including reviews by critics) and provide historical statistics on film rentals. In class, your team will bid for the films.

At that time, you should indicate on the data sheet your best estimate of each film’s weekly gross revenues and your bid (if any) for the film. Describe briefly the method (if any) used to arrive at your estimates and bids.

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Box Office Gross Revenues Selected Holiday Films 2007

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14

American Gangster (11/2) Revenue Screens 56.4 3054 31.4 3059 18.8 3110 10.9 2799 5.6 2699 3.5 2132 1.62 1215 0.59 459 0.52 307 0.35 327 0.25 282 0.18 213 0.14 172 No Longer Playing

Bee Movie (11/2) Revenue Screens

Lions for Lambs (11/9) Revenue

46.2 3928 33.3 3944 20.5 3984 13.1 3507 5.2 3150 3.2 2707 1.1 1609 0.9 539 1.2 475 0.44 407 0.37 338 0.37 296 0.24 265 0.18 246 Still Playing

8.7 3.9 1.5 0.55 0.20 0.055 0.017 0.004 0.003 No Longer Playing

Rank 1 2 5 10 15 20 30 40 50

Film Title Hanna Montana The Eye Juno There will be Blood Alvin & Chipmunks I am Legend Enchanted 4 Months, 3 Weeks …

Deep Sea 3D

.

Top Grossing Films Week of 2/1 - 2/7/08 Weeks in Release 1 1 9 6 8 8 11 2 101

Screens 2215 2216 1527 825 350 116 32 12 7

Atonement (12/7) Revenue Screens 1.1 32 2.7 117 4.3 306 6.0 310 6.8 583 6.2 950 6.8 1291 5.2 1400 3.9 1367 Still Playing I am Legend (12/1) Revenue Screens 103.3 3606 63.8 3620 45.3 3636 19.8 3648 10.5 3353 6.9 2525 2.8 1405 1.3 777 Still Playing

Revenue

Screens

42.9 14.9 9.1 6.3 3.3 1.30 0.44 0.17 0.056

683 2436 2475 1507 1958 777 282 17 10

105 113 108 104

Sept.

Oct. Nov. Dec.

Average Film Revenues

By Month @ Jan .

Feb. March April

101 92 88 99

May June July Aug.

Revenue = Gross Box Office Revenues in $ millions @ Annual Average is Indexed to Equal 100

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91 83 102 114

Week 1 2 3 4 5 6 7 8 9

Week 1 2 3 4 5 6 7 8

Questions for Class Discussion 1. As a consultant for a major theater chain, your task is to predict the box office gross revenues (per screen) for a given film in a given city, week by week.

Describe how you would set about making this kind of forecast. Which factors listed below might be relevant?

• Category and Characteristics of Film • City-Specific Audience Characteristics • Number of Weeks Since Initial Release • Number of Theaters Showing Film in City • Time of Year • Other Factors (such as?)

Which factors can be expressed quantitatively? Which qualitatively?

Accounting for these factors, what degree of error remains in your forecast?

2. How would your forecasting model help in evaluating the following statement? “The practice of blind bidding places undue risk on theater owners.”

3. How are competing buyers’ reservation prices for films determined? Is this an instance of a common, unknown value, or private personal values, or something in between?

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Bidding for Films Data Sheet Theater Chain __________ Team Members ______________________ ______________________ ______________________ ______________________ Average Weekly Film Gross (Your Estimate)

Your Bid*

Film A Film B Film C Film D Film E Film F Film G Film H Estimate of Weekly Gross Receipt:_________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ ___________________________________________________ Bidding Strategy:_____________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ ___________________________________________________ John Wiley & Sons

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ADDITIONAL MATERIALS

I. Short Readings S. Stellin, “In Florida, New Condos on the Block,” The New York Times, November 28, 2008, pp. D1, D6.

J. Lahart, “Economists Look at Ways to Structure Auctions,” The Wall Street Journal, September 25, 2008, p. D1.

S. Rubenstein, “Hospitals put Patients’ Debt up for Auction,” The Wall Street Journal, June 3, 2008, pp. D1, D6.

A. Gregor, “Auctions are Aiding Sales in a Weakened Market,” The New York Times, June 25, 2008, p. C7.

Daniel Grant, “Secrets of the Auction Houses,” The Wall Street Journal, October 31, 2007, p. D9.

Joe Nocera, “Open and Fair: Why Wall Street Hates Auctions,” The Wall Street Journal, March 18, 2006, pp. B1, B12.

Robin Sidel, “Google IPO Tests Theories on Auctions,” The Wall Street Journal, June 7, 2004, p. C1.

Varian, H. R., “Picasso Portrait from his Rose Period Sets Record for a Painting Sold at Auction,” The New York Times, May 6, 2004, p. A28.

Joe Flint, “Air Ball?” The Wall Street Journal, March 15, 2004, p. R10.

“Do I Hear $2 million?” The New York Times, November 14, 2003, p. D1.

“Vancouver Wins 2010 Games, but did NBC Overbid?” The Wall Street Journal, July 3, 2003, p. B1.

“NBC Extends Olympic Run with a Record $2 Billion Bid,” The New York Times, June 7, 2003, p. A1.

“In the Secret World of Airplane Deals, One Battle Up Close,” The Wall Street Journal, March 10, 2003, p. A1.

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“Tales of Manipulation and Design Flaws from the Crypt of Auction History,” The New York Times, August 1, 2002, p. C2.

“Auctions Old and New: Truck Space, Pigs, and Plastics,” The New York Times, September 20, 2000, p. 16.

“Dog-Fight Over a Must-Win Contract,” The New York Times, August 15, 2000, p. BU1.

“The Heyday of the Auction,” The Economist, July 24, 1999, p. 67.

“Revenge of the Nerds,” The Economist, July 23, 1994, p. 70.

(Government auctioneers take the advice of game theorists.)

“States’ Bidding War over Mercedes Plant Made for Costly Chase,” The Wall Street Journal, Nov. 24, 1993, p. A1.

“Without Competing Bids New York Pays the Price,” The New York Times, February 19, 1991, p. A1.

Milton Friedman, “How to Sell Government Securities,” The Wall Street Journal, August 28, 1991, Op Ed Page.

II. Longer Readings P. Milgrom, “Putting Auction Theory to Work,” Cambridge University Press, 2004.

P. Bajari and A. Hortacsu, “Economic Insights from Internet Auctions,” Journal of Economic Literature, 42, 2004, 457-486.

O. Ashenfelter and K. Graddy, “Auctions and the Price of Art,” Journal of Economic Literature, 41, 2003, 763-787.

G. Hohner. et al, “Combinatorial and Quantity-Discount Procurement Auctions Benefit Mars Inc. and its Suppliers,” Interfaces, January-February 2003, 23-35.

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P. Klemperer, “What Really Matters in Auction Design,” Journal of Economic Perspectives, 16, Winter 2002, 169-190.

W. Samuelson, “Auctions in Theory and Practice,” Chapter 10 in K. Chatterjee and W. Samuelson (Eds.) Game Theory and Business Applications. Boston, Mass.: Kluwer Academic Publishers, 2001.

Symposium on the Spectrum Auctions, Journal of Economics and Management Strategy 6, 1997, 431-675.

R. P. McAfee and J. McMillan. “Analyzing the Airwaves Auctions.” Journal of Economic Perspectives, Spring 1996, 159-176.

J. H. Kagel, “Auctions: A Survey of Experimental Research.” in J. H. Kagel and A. E. Roth (Eds.), The Handbook of Experimental Economics, Princeton NJ: Princeton University Press, 1995.

S. Bikhchandani and C. Huang, “The Economics of Treasury Security Auctions,” Journal of Economic Perspectives, Summer 1993, 117-134.

Symposium on Auctions, Journal of Economic Perspectives, Summer 1989, 3-50.

R. Forsythe, R.M. Isaac, and T.R. Palfrey, “Theories and Tests of ‘Blind Bidding in Sealed-bid Auctions,” The RAND Journal of Economics, Summer 1989, 214-238.

R. H. Thaler, “The Winner’s Curse,” Journal of Economic Perspectives, Winter 1988, 191-202.

III. Cases EBay, Inc. (B) (9-703-499) Harvard Business School, 2003.

Olympian Competition: Bidding for Olympic Television Rights (IB50) Stanford Business School, 2003.

Travelexis.com (9-703-059, 9-703-060, 9-703-061) Harvard Business School, 2003.

(This competitive bidding exercise involves 3 separate roles and handouts.)

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Bidding for Antamina. (9-297-054), Harvard Business School, 1997.

Teaching Note (5-298-102).

Pricing and Market Making on the Internet (9-500-065), Harvard Business School, 2000.

Fabtek (A) (9-592-095) and Fabtek (B) (9-592-096), Harvard Business School, 1992. Teaching Note (5-593-006).

FairMarkets Inc.: Where Buyers and Sellers Connect. (9-399-006), Harvard Business School, 1998.

The Great Engine War (Abridged) (#629.3), JFK School of Government. (This case describes the competition between General Electric and Pratt and Whitney for $17 billion of fighter engine sales to the US Air Force.)

IV. Quips and Quotes Everything is worth what it’s purchaser will pay for it.

A cynic is someone who knows the price of everything and the value of nothing. (Oscar Wilde)

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2.

Winning 9 of 10 contracts is not necessarily a sign of good bidding performance. The main implication of winning this many contracts is that your bids are too low! You should probably raise your margins significantly even though this means winning somewhat fewer contracts.

The scarcity of available consultants to service these contracts is an additional reason for raising prices (and cutting back the number of contracts). In any case, your bid should include a provision for an opportunity cost -- embodied by the lost profit that would have been earned if the needed consultants were free to work on other contracts.

4. a. The renter matches if his value exceeds the outsider’s bid, if v2 > b. b. The outsider’s expected profit is: [v1 - b][(b - 200)/60]. Therefore, her optimal bid is: b = (.5)(200) + .5v1. Holding v1 = $240 thousand, the outsider should bid $220 thousand, and so on. c. The seller’s expected price is: E[b] = (.5)(200) + (.5)E[v1] = 100 + (.5)(230) = $215 thousand.

This is less than the expected revenue from either the English or sealedbid auctions: E[P] = (2/3)(200) + (1/3)(260) = $220 thousand.

6. a. The bidder might be a much more efficient (i.e. low cost) producer. A more likely explanation is that the winner (though no more efficient) is overly optimistic about the actual cost of the job. In this case, the firm risks falling prey to the winner’s curse, i.e. finding that its actual costs exceed its bid price.

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b. The low bid is not all good news for the government. If its contract losses are too large, the firm may default on the contract, leaving the government in the lurch. Or the firm may simply lack the management capabilities to complete the contract satisfactorily. In this sense, a procurement is different from an auction sale. In the former, the parties have a continuing relationship until the work outlined in the contract is performed and completed. In the latter, the relationship ends with the sale. To guard against these ongoing contract risks, the government’s selection procedure should scrutinize contractors’ capabilities and cost estimates, in addition to their price bids. Incentive contracts allowing for cost sharing are also recom-mended.

8. a. As more bidders enter the auction, the problem of the winner’s curse becomes more pronounced. Thus, with more bidders it may be desirable to lower one’s bid to account for the winner’s curse. b. Adding one more bidder may cause the original bidders to lower their bids (thus lowering the high bid among the original bidders) yet the new winning buyer may still outbid the original high bid. On average, the winning bid will be higher with more bidders in spite of corrections for the winner’s curse.

10. a. With 100 percent of production costs covered by the government, Firm J will submit the lower profit bid and be selected. The selection process is inefficient; Firm J has the greater total cost (110 > 102). b. With a fixed-price contract, Firm K will submit the lower bid (based on a lower total cost) and be selected. Because of the risk it bears, however, a risk averse Firm K will incorporate a risk premium into its bid.

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c. Firm J’s expected profit is T + .25(100 - 105). To clear its required $5 million in profit, the Firm submits T = $6.25 million. Firm K’s expected profit is T + .25(100 - 95). It bids T = $5.75 million (to gain its required $7 million profit) and wins the contract. By allowing some cost sharing under an incentive contract, the government succeeds in identifying the low-cost supplier.

Discussion Question a. Many bidders can be expected to have downward sloping demand curves; they may wish to guarantee the purchase of a certain amount of securities (even at low interest rates) while accepting additional securities only if paid higher rates. They can reflect these preferences by making multiple bids for different amounts at different interest rates. As in any sealed-bid auction, each bidder should determine the minimum interest rate he or she is willing to accept and then markup the actual bid above this amount. b. The government should select the lowest interest rate bids first and then accept additional bids in ascending order until its desired quantity of bills is sold. This way its gets the lowest interests rate on the bills. c. In a uniform price auction, buyers should make bids equal to their true reservation values. Here, it does not pay to mark up one’s interest rate bid above one’s value. This cannot improve one’s final terms (since all successful bids are filled at the same interest rate), but it does risk being excluded (since only the lowest interest rate bids are filled). The revenue comparison between the traditional auction (in part a) and the common-price auction is much like that between the sealed-bid auction and English auction. If revenue equivalence holds, the Treasury will get the same average interest rate in either type of auction.

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ANSWER TO SPREADSHEET PROBLEM

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1. a. and b. To find the firm’s optimal bid markup, use your spreadsheet’s optimizer to maximize the expected profit in cell G7 by varying the markup in cell E7. The optimal markup is 50.05. c. If the BCB distribution has a mean of 40 (instead of 60), the optimal markup becomes 38.8. In turn, if the BCB distribution has a mean of 80, the optimal markup is 63.0.

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CHAPTER SEVENTEEN LINEAR PROGRAMMING

OBJECTIVES 1. To become familiar with the types of problems that linear programming can solve. (pp. 660-662) 2. To formulate LP problems. (pp. 662-671, 679-690) 3. To solve LP problems using graphs. (pp. 664-671) 4. To relate LP to marginal analysis through the concept of shadow prices. (pp. 671-679) 5. To interpret the output from LP computer algorithms. (pp. 683689)

TEACHING SUGGESTIONS I. Introduction and Motivation The purpose of this chapter is not to make students into experts at solving linear programming problems. Rather it is to teach them (1) to recognize when a problem is amenable to solution through linear programming, (2) to be able to formulate such problems as linear programs and (3) to be able to interpret the output of computer algorithms that solve linear programs. Of course, all of this implies that the student must have an intuitive feel for how linear programs are solved. Besides understanding the meaning of the optimal solution the student should also understand the meaning of shadow prices.

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II. Teaching the “Nuts and Bolts” The chapter is quite straightforward and therefore our comments are brief. One pedagogical issue is how much time to spend on graphical analysis. The easiest examples using graphical analysis involve putting the decision variables on the axes such as in our PC example.

Of course, this requires having exactly two decision variables. Still it provides all of the intuition necessary. From here it is possible to proceed to a discussion of more complex problems for which graphical solutions are not possible. In other words, you may want to skip the sections entitled “Production For Maximum Output” and “Production For Minimum Cost” (pp. 679-682) and go straight to “Computer Solutions.” Although these two examples provide a graphical analysis for cases where there are only two constraints but more than two decision variables, they add nothing to the explanation of larger problems (and they may require an inordinate amount of class time to explain.) In courses where time is at a premium they can be dropped. They are included because these standard applications of graphical analysis are taught in many courses.

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ADDITIONAL MATERIALS

I. Suggested Readings R. Fourer, “Linear Programming: 2007 Software Survey, OR/MS Today, June 2007, pp. 42-51.

V. Postrel, “Operation Everything,” The Boston Globe, June 27, 2004, p. D1.

S. Begley, “Did you Hear the One about the Salesman who Traveled Better?” The Wall Street Journal, April 23, 2004, p. B2.

L.J. LeBlanc et al, “Nu-kote’s Spreadsheet Linear-Programming Models for Optimizing Transportation,” Interfaces, 34, March-April 2004, 139-146.

J. L. Higle and S. W. Wallace, “Sensitivity Analysis and Uncertainty in Linear Programming,” Interfaces, July-August 2003, pp. 53-60.

S. Bollapragada et al, “NBC’s Optimization Systems Increase Revenues and Productivity,” Interfaces, January-February 2002, pp.

47-60.

G. Brown et al, “The Kellogg Company Optimizes Production, Inventory, and Distribution,” Interfaces, 31, November-December 2001, 1-15.

T. A. Grossman, “Reversing Tradition: Nonlinear Optimization Deserves More Emphasis, OR/MS Today, August 2001, pp. 22-25 E. H. Kaplan, “Allocating HIV Resources,” OR/MS Today, February 2001, pp. 26-29 E. W. Schuster and S. J. Allen, “Raw Material Management at Welch’s, Inc,” Interfaces, September-October 1998, pp. 13-24.

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R. A. Bosch, “Big Mac Attack,” OR/MS Today, October 1993. (This article formulates a linear program for optimizing fast-food meals at McDonalds.)

D. Klingman et al, “The Successful Deployment of Management Science Throughout Citgo Petroleum Corporation,” Interfaces, January-February 1987, pp. 4-25.

Kimes, S.E. and J.A. Fitzsimmons, “Selecting Profitable Sites at LaQuinta Motor Inns,” Interfaces, Mar.-April. 1990, pp. 12-20.

II. Cases Timeshare Exchange Fair (A and B), (UVA-QA-0709), Darden Business School, University of Virginia, 2007.

Australian Motors Ltd. (OIT23), Stanford University, 1998.

(Available from Harvard Business School Publishing.)

MacPherson Refrigeration Ltd. (93D021), Richard Ivey School of Business, 1997. (Available from Harvard Business School Publishing.)

Chase Shipping (9-196-098), Harvard Business School, 1995.

Buckeye Power and Light Company, (UVA-QA-0326), Darden Business School, University of Virginia, 1991.

III. Quips and Quotes Has anything witty ever been said about linear programming?

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ANSWERS TO EVEN-NUMBERED PROBLEMS

2. a. This maximization problem cannot be solved since the feasible region is unbounded above (x and y can be made indefinitely large). b. This is not an LP problem since the objective function (xy) is nonlinear. c. This is an LP problem. The solution is x = 1.5, y = .5. d. This maximization problem has no solution since the inequalities are contradictory. There is no feasible region. e. The second inequality (though it looks strange) can be rearranged to fit the LP requirements. x/(x + y)  7 can be rewritten x  .7(x + y) or .3x - .7y  0. The LP solution is y = 2, x = 0.

4.

Let the initial resource constraints be: 1A + 2B  X 2A + 2B  Y and assume that both are binding in the optimal solution. The innovation means that producing A units requires fewer units of good X. Thus, the new constraint might be: .5A + 2B  X The original solution is A = Y - X. The new solution is: A = (Y - X)/1.5 The output of A has fallen!

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6. a. Let x and y be the numbers of tires produced via processes 1 and 2 respectively. The LP formulation is: Maximize

 = 4x + 6y

subject to

x + y  10 (capital) 4x + 2y  32 (labor) 2x + 4y  32 (raw materials)

After graphing the feasible region and comparing slopes, we find the first and third constraints to be binding. Solving the two equations, x + y = 10 and 2x + 4y = 32, we have that x = 4, y = 6, and  = $52. b. Since the labor constraint is not binding, labor's shadow price is zero. If we increase the supply of raw materials to 33, the new solution becomes x = 3.5, y = 6.5, and  = $53. Thus, the shadow price of materials is /M = (53-52)/(33-32) = $1.

8.

Let T and M be the numbers of TV and magazine ads respectively. The LP formulation is: Minimize

Cost = 120,000T + 40,000M

subject to

10,000T + 5,000M



600,000 (total)

5,000T + 1,000M



150,000

(prime)

250T + 500M



30,000

(sweepstakes)

Note that this is a minimization problem involving “greater to or equal” constraints. After graphing the feasible region and comparing slopes, we find the first and second constraints to be binding. Thus, the solution is M = 100, T = 10, and the producer's minimum advertising cost is $5,200,000.

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Discussion Question a. Counseling (preventing .2 new HIV cases per enrollee) is more effective than needle exchange (preventing .1 new case per enrollee). However, needle exchange (.1 case prevented per $500 spent) is more cost effective than counseling (.2 cases prevented per $1,500 spent). Thus, it is not immediately clear which program is more deserving of funding. b. The LP formulation is Maximize .2C + .1N subject to C + N  1,000 1,500C + 500N  450,000 Graphing the two constraints shows that the former is never binding (it lies entirely outside the latter.) Thus, the optimal use of the $450,000 budget is to allocate all funds to needle exchange (the more cost-effective program), treating 900 persons and preventing 90 HIV cases. c. Now the sole binding constraint is: C + N  250. All 250 atrisk individuals should be enrolled in the counseling program, thereby preventing 50 HIV cases. d. Now, the LP formulation is Maximize .2C + .1N subject to C + N  500 1,500C + 500N  450,000 The optimal corner has both constraints binding, implying the allocation, C = 200 and N = 300. Total HIV cases prevented come to: (.2)(200) + (.1)(300) = 70.

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ANSWERS TO SPREADSHEET PROBLEMS

(You may download any and all spreadsheets from the John Wiley Samuelson and Marks Website.)

S1 a. The LP formulation is: minimize Cost = 14x1 + 26x2 + 30x3 + 24x4 + 10x5 + 12x6 subject to: x1 + x2 + x3  8,000 x4 + x5 + x6  10,000 x1 + x4  5,000 x2 + x5  7,000 x3 + x6  6,000 and all variables non-negative. b. Using the spreadsheet optimizer, we minimize the total transport cost in cell H6 by changing cells C13, D13, E13, C14, D14, and E14 subject to cells C21, D21, E21, I13, and I15 all being greater or equal to zero. The optimal solution is: x1 = 5,000 x2 = 3,000 x3 = 0 x4 = 0, x5 = 4,000 x6 = 6,000. c. Using the optimizer, we find the shadow price associated with shipments to New York to be 28. The explanation for the shadow price is as follows. The extra unit shipped to New York is produced in Tennessee (shipping cost = 12). With Tennessee at full capacity, a unit formerly produced in Tennessee and bound for New Orleans now must be produced in Oregon (extra shipping cost is 26 – 10 = 16). Thus, the total additional cost (or shadow price) is 12 + 16 = 28.

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A

B

C

D

1 2

E

F

G

H

I

J

Factory

Unused

Shadow

A SHIPPING PROBLEM

3

Transport

4

Costs

Los Angeles

New Orleans

New York

Cost

Oregon

14

26

30

260,000

Tennesee

24

10

12

Ports

Minimum

5 6 7

Factories

8 9 10

Units Shipped

11 12

Ports Los Angeles

New Orleans

New York

Total

Capacity

Capacity

Price

Oregon

5,000

3,000

0

8,000

9,000

1,000

0

15 16

Tennesee

0

4,000

6,000

10,000

10,000

0

16

17 18

Total

5,000

7,000

6,000

19 20

Requirements

5,000

7,000

6,000

21 22

Extra Exports

0

0

0

23

Shadow Price

14

26

28

13 14

Factories

S2 a.

The LP formulation is: maximize  = 60x1 + 70x2 + 48x3 + 52x4 + 48x5 + 60x6 subject to:

.5x1 + 2x2 + 2x4 + x5  400 2x1 + 2.5x2 + 1.5x3 + .5x5  580 1.5x2 + 4x3 + .5x5  890

x1 + .5x3+ 1x4 + .5x5 + 2.5x6  525 x1 + 2x2 + x3+ x4 + x5 + 2x6  650 .5x1 + 2x2 + .5x3+ 2x4 + 1.5x5 + 2x6  620 b. From the spreadsheet optimizer, the optimal solution is: x1 = 120, x2 = 0, x3 = 220, x4 = 160, x5 = 20, and x6 = 50.

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Bonus Spreadsheet Problem A refinery processes two types of crude oil, heavy (H) and light (L), into its final product, fuel oil (F). Two different production processes (which can be used singly or simultaneously) are available.

Process 1: 1 unit of H and 2 units of L to yield 2 units of F at a cost of $1.00.

Process 2: 1 unit of H and 1 unit of L to yield 1.5 units of F at a cost of $.70.

The refinery must determine its production plan for the summer cycle (May-October) and the winter cycle (NovemberApril). It has contracts to purchase 100 units of H and 150 units of L in each cycle and to deliver 125 units of F in the summer and 170 units of F in the winter. (The company is free to sell more than these contract amounts.) The summer unit fuel price is $1.00, and the winter price is expected to be $1.20. Finally, the refinery’s goal is to maximize profit. a. Formulate the refinery’s problem as two separate linear programs − one for the summer cycle and one for the winter cycle. Explain (in a sentence or two) why this is possible. Solve using a spreadsheet. (Hint: The appropriate decision variables for the problems are the levels of the two processes used in production during the two cycles. Denote these variables by s1, s2, w1, and w2.) b. Now suppose the refinery has facilities to store crude oil over the course of the year, but it cannot store the final product, fuel oil. Any excess crude that is not processed incurs a $.05 per unit charge for storage between cycles. The refinery only considers storing “summer” crude for winter production (and not vice versa). Formulate a single linear program by which the firm can maximize annual profit. Solve using a spreadsheet. (Hint: Introduce the additional decision variables IH and IL denoting the amounts of crude held in inventory between summer and winter.

With these two new variables, modify and integrate the twin LP’s in part a into a single LP. How do the inventory variables affect the constraints pertaining to crude supplies in summer and winter?) c. How does the refinery benefit from inventory holding, and why does it benefit? (A general, qualitative answer will suffice.)

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S3 a. If the firm uses processes 1 and 2 at levels s1 and s2 in the summer its profit is:  = [($1.00)(2) - $1.00]s1 + [($1.00)(1.5) - $.70]s2 = 1s1 + .8s2.

Thus, the LP formulation for the summer is: Maximize  = s1 + .8s2, subject to 1s1 + 1s2  100 (heavy crude), 2s1 + 1s2  150 (light crude) 2s1 + 1.5s2  125.

In turn, If the firm uses the processes at levels w 1 and w2 in the winter, its profit is:  = [($1.20)(2) - $1.00]w1 + [($1.20)(1.5) - $.70]w2 = 1.40w1 + 1.10w2.

Thus, the LP formulation for the winter is: Maximize  = 1.40w1 + 1.10w2, subject to 1w1 + 1w2  100 (heavy crude) 2w1 + 1w2  150 (light crude) 2w1 + 1.5w2  170.

The LP problems are modeled on the spreadsheet below. To solve the summer problem, one maximizes profit in cell G15 by varying the process levels in cells C6 and E6, subject to cells I7, I8, and I11 all being greater or equal to zero. The solution is: s1 = s2 = 50, and  = 90. The corresponding solution for the winter cycle is: w1 = w2 = 50, and  = 125. b. The new formulation is: John Wiley & Sons

17-11

Maximize s1 + .8s2 + 1.40w1 + 1.10w2 - .05IH - .05IL, subject to

s1 + s2 + IH = 100, 2s1 + 1s2 + IL = 150, 2s1 + 1.5s2  125, w1 + w2  100 + IH, 2w1 + w2  150 + IL, 2w1 + 1.5w2  170.

and all variables non-negative.

Here IH and IL are the inventories of heavy and light crude oil carried over from summer (when not all crude is processed) to winter (when fuel oil prices are most profitable). Of course, all decision variables must be nonnegative. The spreadsheet below already allows for inventories. (In the part a solution, the inventories were simply set to zero to maintain separation between the summer and winter problems.) Using the optimizer, we maximize total profit in cell J28, by changing cells C6, E6, C19, E19, subject to I7, I8, I11, I20, I21, and I24 all being greater or equal to zero. The solution is: s1 = 62.5, s2 = 0, IH = 37.5, IL = 25, w1 = 37.5, w2 = 100, and T = 221.875.

Note that the firm barely meets its fuel oil delivery obligations in the summer and stores crude for more profitable sales in the winter. As one can easily confirm, the same solution applies for a range of inventory costs: $.10 per unit, $.05 per unit or $0 per unit. (Of course, total profit increases as inventory costs decline.)

John Wiley & Sons

17-12

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

B

C

D

E

F

G

H

I

J

Inputs Used 62.5 125

Available Inputs 100 150

Summer Inventory 37.5 25

Cost of Inventory 0.05 0.05

Summer Level H L

Process 1 62.5 1 2

F

2

Revenue Cost Profit

1.00

Process 2 0 1 1

Output 125

1.5 1.00

125 62.5 62.5

0.70

Winter Process 1 37.5 1 2

Process 2 100 1 1

F

2

1.5

Revenue Cost Profit

1.00

Level H L

Min Output Extra 125 0

Inputs Used

Available Inputs

Winter Inventory

137.5 175

137.5 175

0 0

Output 225

1.20

270 107.5 162.5

0.70

John Wiley & Sons

17-13

Min Output Extra 170 55

Profit/Yr 221.875

OVERVIEW This file contains completed spreadsheets for all problems (chapters 2-11 and 13-17).

The file also contains spreadsheet regressions for text examples in chapters 4 and 17.

For convenience, the spreadsheet cells are color coded. Cells in black font are lables or fixed numbers. Cells in blue font are decision variables to be adjusted in finding optimal solutions. Cells in dark green font are linked by formula to other cells. Finally, the cell in red indicates the objective to be optimized (usually maximum profit or minimum cost).

For each spreadsheet, we have already filled in the parameters for one solver menu.

For instance, in the microchip sheet (see next tab), invoking Tools then Solver brings up the menu in which cell F7 is to be maximized by changing cell B7. If a problem involves multiple optimizations, the completed menu for the first such solution is given.

To find additional solutions, simply change cell references and constraints in the menu.

If you have any doubt about how the spreadsheet is constructed, be sure to look at the formulas behind any cells that seem to be unclear. Clicking on a cell displays its formula in the bar (found just above the alphabetical column labels). Or clicking F2 (as if to edit the formula) displays the formula in the cell itself.

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14

B

C

D

E

F

G

THE OPTIMAL OUTPUT OF SPARE PARTS

Quantity

Price

Revenue

Cost

Profit

20

760

15,200

24,200

-9,000

MR

MC

Mprofit

720

220

500 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14

B

C

D

E

F

AN OPTIMAL ADVERTISING BUDGET

Advertising

Revenue

Cost

Profit

8.000

10.00

8.000

2.000

MR

MC

Mprofit

0.625

1.000

-0.375 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14

B

C

D

E

F

G

THE OPTIMAL OUTPUT OF MICROCHIPS

Quantity

Price

Revenue

Cost

Profit

2.0

130

260

176

84

MR

MC

Mprofit

90

38

52 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13

B

C

D

E

F

G

THE OPTIMAL PRICE FOR SPARE PARTS

Price

Quantity

Revenue

Cost

Profit

780

10

7,800

22,050

-14,250

Elasticity

MC

(P-MC)/P

-1/EP

-39.000

210

0.7308

0.0256 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

B

C

D

E

Planes Seats/Plane Cost/Plane Total Seats

2 200 20,000 400

Business

Non-Bus.

Total

Number of Seats

200

200

400

One-way Fare

440

330

----

Revenue MR

88,000 340

66,000 280

154,000

MC

100

Total Cost

40,000

Total Profit

114,000

DUAL AIRFARES

F

G

H

.

A 1 2 3 4 5 6

B

C

D

E

F

G

H

J

K

SS 6,858.8 4,847.2 11,706.0

MS 6,858.8 346.2

F 19.81

Coefficients Stand Error 478.55 88.039 -1.633 0.367

t Stat 5.436 -4.451

Price 250 265

C Price 250 250

Income 104.0 101.5

SUMMARY OUTPUT

7 8 9 10 11 12

37.8 83.3 111.7 137.5 109.5 96.8

265 240 230 225 225 220

240 240 240 260 250 240

103.0 105.0 100.0 96.5 93.3 95.0

Regression Statistics Multiple R 0.765 R Square 0.586 Adjust R Square 0.556 Standard Error 18.607 Observations .

16

13 14

59.5 83.2

230 235

240 250

97.0 99.0

ANOVA

15 16 17 18 19

90.5 105.5 75.7 91.6 112.7

245 240 250 240 240

250 240 220 230 250

102.5 105.0 108.5 108.5 108.0

20 21 22

102.2

235

240

109.0

Q = 478.6 - 1.63P R2 = .586

Regression Residual Total

Intercept Price

df 1 14 15

M

N

Signif F 0.00055

P-value Lower 95% Upper 95% 0.00009 0.00055 -2.419 -0.846 .

Q = 28.84 - 2.12P + 1.03P* + 3.09Y R2 = .776

SUMMARY OUTPUT

28 29 30 31 32 33

Regression Statistics Multiple R 0.881 R Square 0.776 Adjust R Square 0.721 Standard Error 14.766 Observations .

16

34 35

ANOVA

36 37 38 39 40

Regression Residual Total

SS 9,089.6 2,616.4 11,706.0

MS 3,029.9 218.0

41 42 43 44 45

Coefficients Stand Error Intercept 28.84 174.67 Price -2.124 0.340 Competitor's Price 1.035 0.467 Income 3.089 0.999

t Stat 0.165 -6.238 2.218 3.093

46

L

ESTIMATING DEMAND FOR AIR TRAVEL

Seats 64.8 33.6

23 24 25 26 27

I

df 3 12 15

F 13.90

Signif F 0.0003

P-value Lower 95% Upper 95% 0.872 0.00004 -2.865 -1.382 0.04664 0.018 2.051 0.00931 0.913 5.266 .

PREDICTING TOY SALES Sales 133 135 140 181 141 170 172 186 143 148 150 194 154 156 158 196 153 161 193 204 158 169 171 209 172 207 209 214 183 212 184 219 185 190 222 227 199 228 230 229

Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

W 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0

S 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0

U 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0

F 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjust R Square Standard Error Observations ANOVA Regression Residual Total

Intercept Time

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjust R Square Standard Error Observations ANOVA Regression Residual Total

Intercept Time W S U F

UMMARY OUTPUT

Regression Statistics 0.800 0.640 0.631 17.744 40

df 1 38 39

SS 21278.0 11964.4 33242.4

Coefficients Stand Error 141.165 5.718 1.998 0.243

MS 21278.02 314.85

F

Signif F 67.58 ##########

t Stat P-value Lower 95% Upper 95% 24.688 5.2993E-25 129.59 152.74 8.221 5.8601E-10 1.506 2.490

MMARY OUTPUT

Regression Statistics 0.92891204 0.86287758 0.81863501 11.4121176 40

df 5 35 40

SS 28684.1 4558.3 33242.4

MS 5736.8 130.2

Coefficients Stand Error 0 #N/A 1.89 0.16 126.24 4.68 139.85 4.78 143.26 4.89 164.38 5.00

t Stat #N/A 12.02 26.96 29.23 29.30 32.90

F

Significance F 44.05 6.6992E-14

P-value Lower 95% Upper 95% #N/A #N/A #N/A 5.6091E-14 1.57 2.21 5.3219E-25 116.7 135.7 3.5216E-26 130.1 149.6 3.2383E-26 133.3 153.2 6.4684E-28 154.2 174.5

Four Years Sales: OLS Fit FITTED EQUATION S = 95 + 5.5Y SUMMARY OUTPUT Year 1 2 3 4 5

Sales 100 110 105 120 ?

Predicted 100.5 106 111.5 117 122.5

Regression Statistics Multiple R 0.832 R Square 0.691 Adj R Square 0.537 Stand Error 5.81 Number 4 ANOVA Regression Residual Total

Intercept Year

df 1 2 3

SS 151.25 67.5 218.75

MS 151.25 33.75

F 4.481

Significance

Coeffs 95.0 5.5

Stand Error 7.12 2.60

t Stat 13.35 2.12

P-value 0.006 0.168

Lower 95% Upper 95%

0.168

64.39 -5.68

125.61 16.68

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

B

C

D

E

AUTO DEMAND REGRESSION Year 1990 1991 1992 1993 1994

Sales 2.00 1.86 1.94 1.90 1.90

Price 10.0 10.4 10.0 11.0 12.0

Income 100 95 97 100 105

F

G

H

I

J

K

L

M

SUMMARY OUTPUT Regression Statistics Multiple R 1 R Square 1 Adjust R Square 1 Standard Error 8.177E-15 Observations 5 ANOVA df Regression Residual Total

Intercept Price Income

2 2 4

SS 0.0112 1.337E-28 0.0112

MS F Signif F 0.0056 8.376E+25 1.194E-26 6.686E-29

Coefficients Stand Error t Stat P-value Lower 95% Upper 95% 1 1.19923E-13 8.33869E+12 1.43815E-26 1 1 -0.1 7.84708E-15 -1.27436E+13 6.15767E-27 -0.1 -0.1 0.02 1.75098E-15 1.14222E+13 7.6648E-27 0.02 0.02

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

B

C

D

E

F

WATER TABLE REGRESSION Water Table 17.6 19.2 14.8 18.1 13.2 15.1 20.0 14.6 13.9 13.5

Year 1 2 3 4 5 6 7 8 9 10

H

I

SUMMARY OUTPUT

Rainfall 36 52 34 44 26 48 56 45 39 42

W = 18.25 - .41Y -1.616

G

Regression Statistics Multiple R 0.496 R Square 0.246 Adjust R Square 0.152 Standard Error 2.295 Observations 10 ANOVA

R2 = .246

W = 9.69 - .51Y + .216R R2 = .82 -3.815 4.75

Regression Residual Total

df 1 8 9

Intercept Year

Coefficients 18.247 -0.408

Regression Statistics Multiple R 0.906379948 R Square 0.82152461 Adjust R Square 0.770531641 Standard Error 1.19405335 Observations 10 ANOVA Regression Residual Total

df 2 7 9

Intercept Year Rainfall

Coefficients 9.694 -0.508 0.216

A 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

B

C

D

E

F

G

H

I

A 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123

B

C

D

E

F

G

H

I

A 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

B

C

D

E

SUMMARY OUTPUT

F

G

H

I

J 1 2 3 4 5 6 7 8 9 10 11 12 SS 13 13.766 14 42.154 15 55.92 16 17 Stand Error 18 1.568 19 0.253 20 21 22 23 24 25 26 27 28 29 30 31 SS 32 45.940 33 9.980 34 55.92 35 36 Stand Error 37 1.977 38 0.133 39 0.045 40 41

K

L

MS 13.766 5.269

F 2.613

t Stat 11.636 -1.616

M

N

O

Signif F 0.145

P-value Lower 95% Upper 95% 0.000003 14.631 21.863 0.145 -0.991 0.174 .

MS 22.970 1.426

t Stat 4.905 -3.815 4.750

F 16.11

Signif F 0.0024

P-value Lower 95% Upper 95% 0.0017 5.020 14.368 0.0066 -0.823 -0.193 0.0021 0.108 0.323

J 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

K

L

M

N

O

J 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123

K

L

M

N

O

J 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

K

L

M

N

O

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

B

C

D

E

F

G

H

I

J

K

L

M

SS 11335.3 715.0 12050.3

MS 11335.3 71.5

F Signif F 158.54 0.0000002

N

SOFT DRINK REGRESSION Month Quantity 1 98 2 80 3 95 4 123 5 163 6 168 7 82 8 68 9 96 10 77 11 130 12 125

Price 0.45 0.50 0.45 0.40 0.35 0.35 0.50 0.55 0.45 0.50 0.40 0.40

Log(Q) Log(P) 4.585 -0.799 4.382 -0.693 4.554 -0.799 4.812 -0.916 5.094 -1.050 5.124 -1.050 4.407 -0.693 4.220 -0.598 4.564 -0.799 4.344 -0.693 4.868 -0.916 4.828 -0.916

SUMMARY OUTPUT Regression Statistics Multiple R 0.970 R Square 0.941 Adjusted R Square 0.935 Standard Error 8.456 Observations 12 ANOVA df Regression Residual Total

1 10 11

Intercept Price

Coefficients Stand Error 332.5 17.9 -506.6 40.2

t Stat P-value Lower 95% Upper 95% 18.5 0.00000000 292.5 372.5 -12.6 0.0000002 -596.3 -417.0

SUMMARY OUTPUT Regression Statistics Multiple R 0.9959653 R Square 0.9919469 Adjusted R Square 0.9911416 Standard Error 0.0277731 Observations 12 ANOVA df

SS 0.9501 0.0077 0.9578

Regression Residual Total

1 10 11

Intercept Log(P)

Coefficients Stand Error 2.97 0.048 -2.02 0.058

MS 0.9501 0.0008

t Stat 61.53 -35.10

F Signif F 1231.76 8.36E-12

P-value Lower 95% Upper 95% 3.13E-14 2.867 3.083 8.36E-12 -2.153 -1.896

O

A 42

B

C

D

E

F

G

H

I

J

K

L

M

N

O .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

B

C

D

E

F

G

H

DOES ADVERTISING DRIVE SALES?

Sales 120 115 97 118 88 63 82 80 95 106 105 136 122 112 116 104 137 114 104 122 108 94 98 104

Advertising Sales-1 39 36 120 38 115 39 97 23 118 22 88 40 63 42 82 36 80 49 95 66 106 65 105 51 136 56 122 60 112 51 116 55 104 47 137 50 114 47 104 32 122 41 108 45 94 34 98

Adv-1

SUMMARY OUTPUT

39 36 38 39 23 22 40 42 36 49 66 65 51 56 60 51 55 47 50 47 32 41 45

Regression Statistics Multiple R R Square Adjust R Square Standard Error Observations ANOVA Regression Residual Total

Intercept Advertising

SUMMARY OUTPUT

.

Regression Statistics Multiple R R Square Adjust R Square Standard Error Observations ANOVA Regression Residual Total

A 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

B

C

D

E

F

G

H Intercept Sales -1

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total

Intercept Advertising -1

I J 1 2 3 4 SUMMARY 5OUTPUT 6 Regression 7 Statistics 8 0.609 9 0.371 10 0.343 11 13.987 12 24 13 14 15 df SS 16 1 2541.1 17 22 4304.2 18 23 6845.3 19 20 Coefficients Stand Error 21 65.256 11.616 22 0.915 0.254 23 24 25 SUMMARY26 OUTPUT 27 Regression 28 Statistics 29 0.487 30 0.237 31 0.201 32 15.529 33 23 34 35 36 df SS 37 1 1571.9 38 21 5064.0 39 22 6635.9 40 41 Coefficients Stand Error

K

L

MS 2541.1 195.6

F 12.988

t Stat 5.618 3.604

MS 1571.9 241.1

t Stat

M

N

Signif F 0.00158

P-value Lower 95% Upper 95% 1.197E-05 4.117E+01 8.935E+01 1.577E-03 3.886E-01 1.442E+00

F 6.519

P-value

Signific F 0.0185

Lower 95%

Upper 95%

O

I J K 42 54.45 20.15 2.70 43 0.479 0.19 2.55 44 45 SUMMARY46 OUTPUT 47 Regression 48 Statistics 49 0.750356211 50 0.563034443 51 0.54222656 52 11.75071515 53 23 54 55 56 df SS MS 57 1 3736.24761 3736.247607 58 21 2899.66544 138.0793065 59 22 6635.91304 60 61 Coefficients Standard Error t Stat 62 54.57740611 10.038698 5.436701672 63 1.130795786 0.21738554 5.201798515

L 0.013 0.019

M 12.556 0.089

N 96.346 0.870

O

F Significance F 27.0587078 3.7275E-05

P-value Lower 95% Upper 95%Lower 95.0% 2.1536E-05 33.7007872 75.454025 33.70079 3.7275E-05 0.67871773 1.58287385 0.678718

P 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Q

P 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61Upper 95.0% 62 75.45403 63 1.582874

Q

BEST FIT FOR A TIME SERIES Sales 103.2 105.7 111.3 113.8 116.9 121.8 125 132.4 137.1 140.9 142.7 149.3 154.4 158.1 164.8 172 181.3

Quarter Ln(sales) 1 4.636669 2 4.660605 3 4.712229 4 4.734443 5 4.761319 6 4.80238 7 4.828314 8 4.885828 9 4.920711 10 4.94805 11 4.960745 12 5.005958 13 5.039547 14 5.063228 15 5.104733 16 5.147494 17 5.200153

SUMMARY OUTPUT

Sales

Regression Statistics Multiple R 0.994 R Square 0.988 Adjust R Square 0.987 Standard Error 2.675 Observations 17 ANOVA df Regression Residual Total

Intercept Quarter

1 15 16

SS 8920.8 107.4 9028.2

Coefficients Stand Error 95.016 1.357 4.676 0.132

SUMMARY OUTPUT

MS 8920.8 7.158

F Signif F 1246.3 7.4714E-16

t Stat P-value Lower 95% Upper 95% 70.0 2.759E-20 92.12 97.91 35.3 7.471E-16 4.39 4.96

LN(Sales)

Regression Statistics Multiple R 0.998 R Square 0.997 Adjust R Square 0.996 Standard Error 0.011 Observations 17 ANOVA df Regression Residual Total

Intercept Quarter

SS MS F Signif F 1 0.47804625 0.478046 4306.9245 7.2516E-20 15 0.001664922 0.000111 16 0.479711172

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 4.599 0.0053 860.41 1.279E-36 4.59 4.61 0.03423 0.0005 65.63 7.252E-20 0.033 0.035 .

OPTIMAL LABOR PLAN

Labor 200

MCL 20

Output 150

Price 40

MRP 20

MPL 0.5

MR 40

Profit 2000

A 1 2 3 4 5 6 7 8 9 10 11 12 13

B

C

D

E

F

G

H

I

Output Price

136.0 10.0

MR Revenue

10.0 1360.0

Cost Ave Cost

1200.0 8.8

Profit

160.0

J

OPTIMAL INPUTS

Labor MPL

20.0 1.600

Capital MPK

50.0 1.000

MRPL MCL

16.0 10.0

MRPK MCK

10.0 20.0

.

A 1 2 3 4 5 6 7 8 9 10 11 12 13

B

C

D

E

F

G

H

I

Output Price

72 10.00

MR Revenue

10.00 720

Cost Ave Cost

288 4.00

Profit

432.0

J

OPTIMAL PRODUCTION

Labor MPL

4.00 9.00

Capital MPK

9.00 4.00

MRPL MCL

90.00 36.00

MRPK MCK

40.00 16.00

.

A 1 2 3 4 5 6 7 8 9 10 11 12 13

B

C

D

E

F

G

H

I

Output Price

36 8.50

MR Revenue

8.00 306

Cost Ave Cost

180 5.00

Profit

126

J

OPTIMAL PRODUCTION

Labor MPL

1.00 18.00

Capital MPK

9.00 2.00

MRPL MCL

144.00 36.00

MRPK MCK

16.00 16.00

.

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

B

C

D

E

F

G

0

Extra < Output

45

< Price Gap

H

WORLDWIDE CHIP DECISIONS Set Sales & Output Quantities (000's)

Sales

Home

Abroad

Total

10

10

20

Output

10

10

20

Price

290

245

Revenues MR

2,900 280

2,450 240

5,350 ---

Costs MC

1,200 120

550 60

1,750 ---

Profit

1,700

1,900

3,600 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

B

C

D

E

F

G

D-S

Tot Profit

8

552

H

Equilibrium in a Perfectly Competitive Market The Industry Supply Demand

Price

# Firms

10

24

192

QF

MC

The Typical Firm Cost AC P - MC

8

12

57

200

7.13

-2

Firm Profit 23

SR: (1) D - S = 0 and (2) P = MC; Adjust: P & QF LR: (1) and (2) and (3) P = AC; Adjust: P & QF & #Firms .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B

C

D

E

F

G

Efficiency of Perfect Competition Quantity

32

Price

96

Benefit P = MB

4,096 96

Con Surplus

1,024

Revenue MR

3,072 32

B-C CS + Pft

1,504 1,504

Profit

480

Cost MC

2,592 72 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

B

C

D

E

F

MR

Tot Profit

6.00

500

G

Monopolist controls the Market

Output

The Industry Plants Price

100

20

11

QF

The Typical Production Unit MC Cost AC

5.0

6.00

30

6.00

Short Run: Maximize total profit : Adjust: QF Long Run: Maximize total profit : Adjust: QF & # Firms .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B

C

D

E

F

G

Inefficiency of Monopoly Quantity

24

Price

112

Benefit MB

3,264 112

Con Surplus

576

B-C CS + Pft

1,916 1,916

Profit

1,340

Revenue MR Cost MC

2,688 64 1,348 64

.

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

B

C

D

E

F

G

H

I

J

Dominant Firm Price Leadership

Price 10.5

Market Demand # S. Firms Qs 8

Qd

58

190

Dominant Firm Qd - Qs Cost Profit 132

730.0

q

MC

Cost

Small Firms AC P - MC Firm Profit

7.25

10.5

48.5625

6.698

0

656

27.5625

Small Firms' supply is determined by P = MC. Large Firm maximizes profit based on net demand. .

A 1 2 3 4 5 6 7

B

C

D

E

F

G

Price

Revenue

Cost

Profit

13.54

135.36

100

35.36

H

OPTIMAL ADVERTISING Output Advertising 10

50

.

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B

C

D

E

F

G

H

I

J

K

USED CAR DEALERS Average Auto Inventory of the Other Three Dealers My Inventory 175 200 225 250 275 300 325 175 200 225 250 275 300 325 350

280.0 320.0 360.0 400.0 440.0 443.6 443.5 440.0

280.0 320.0 332.7 341.2 345.7 346.7 344.3 338.9

238.8 251.4 260.0 264.9 266.3 264.6 260.0 252.7

185.4 193.7 198.5 200.0 198.5 194.3 187.4 178.2

140.0 144.4 145.7 144.2 140.0 133.3 124.3 113.2

100.9 101.8 100.0 95.7 88.9 80.0 69.0 56.0

67.0 64.7 60.0 53.1 44.0 32.9 20.0 5.3 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14

B

C

D

E

F

G

H

I

J

K

Mkt I 30

Mkt II 18

B's Split A's Payoff

L

ALLOCATING A SALES FORCE

A's Split

2

B's Split 1

0

3

27

22.5

30

2

33

29

36

A's Split

1

28

27

39

7.000

0

18

13.5

25.8

6.00

23.86813

.

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

B

C

D

E

F

G

H

COPING WITH AN EXTERNALITY Market Demand P = 500 - 10Q

LMC = LAC 150

MCext 100

Quantity

Tax

Clean Up (u)

Price

10

0

0

400

Con Surp

Net Profit

Govt Rev

External Cost

Total Benefit

500

2,500

0

1,000

2,000

Gross Profit

tax/clup cost

tax - MCu

2,500

0

0 .

EVALUATING FUND MANAGERS Possible Annual Returns (%) 25 or -15 Fund Manager Types Superior Average Inferior Prob(Up) 0.7 0.6 0.5 Exp Return 13 9 5 Likelihood Track Record Superior Average Years Ups 20 15 0.179 0.075 Joint Prob Track Record Superior Average Years Ups 20 15 0.036 0.045

Inferior 0.015 Total Inferior 0.003

Prior Prob

0.2

0.6

0.2

Revised Prob

0.428

0.536

0.035

0.0835 Exp Return 1.000

10.57

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

B

C

D

E

F

AN OPTIMAL INCENTIVE CONTRACT Fixed Wage (W)

Profit Share (b)

Worker's Effort

Expected Gross Profit

10,000

0.30

30.00

30,000

Expected Compensation

Worker's Risk Premium

Worker's Disutility

Risk-adjusted Profit

19,000

900

9,000

9,100

Employer's Profit

Total Profit

Worker's Marginal Profit

11,000

20,100

-300 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

B

C

D

E

F

G

H

I

J

K

L

M

A BRITISH-AMERICAN CONTRACT

High

Warranty Full Partial Co U Co B Co U Co B 1 238 68 180 42 0

Low

0

Quality

178

24

Delivery Co U Co B 2 Years 1 18 10 3 Years 0 0 0 5 Years 0 -24 -18 Sum

92

18

Sum 1

0

U's Payment to B Co U's Co B's (Pounds) Profit Profit 110 36 32

1 .

A

B

C

D

E

F

G

H

1 2

OPTIMAL STRATEGY WHEN BCB

3

IS NORMALLY DISTRIBUTED

4 5

Mean = 60

6

St Dev = 30

Markup Pr(win) E(Profit)

7

20

0.9088

18.176

8

40

0.7475

29.900

9

60

0.5000

30.000

10

80

0.2525

20.199

11 12

.

A

B

C

D

E

F

G

H

I

J

K

1 2

POLICE STAFFING

3 4 5

8AM-12 12-4PM

4-8PM

8PM-12 12-4AM

4-8AM

1.25

1.375

1.25

6 7

Shift Costs

1

1.125

1.5

8 9

Total Cost 1,150

# of Officers

150

175

75

325

175

0

# per 8-hour shift

150

325

250

400

500

175

Officers required

150

100

250

400

500

175

Extra Officers

0

225

0

0

0

0

Shadow Price

1.0

0

1.125

0.125

1.25

0.25

10 11 12 13 14 15 16 17 18

.

A

B

C

D

E

F

G

H

I

J

K

L

1 2

SCHOOL BUSSING PROBLEM

3 4

Distances

5 6

Total

North

East

West

South

Kid Miles 1,792

7

School 1

2.0

3.0

1.4

3.2

8

School 2

3.2

2.4

2.0

2.0

9

School 3

3.6

1.4

3.0

2.2

10 11

Students

12 13

Total in

Capacity

Extra

Shadow

North

East

West

South

School

of School

Spaces

Prices

14

School 1

240

0

120

0

360

360

0

0.8

15

School 2

0

0

280

120

400

400

0

0.2

16

School 3

0

120

0

80

200

260

60

0

17 18

Total Kids Bussed

240

120

400

200

19

Students in District

240

120

400

200

20

Difference

0

0

0

0

21

Shadow Prices

2.8

1.4

2.2

2.2

22

.

A

B

C

D

E

F

G

H

I

Munis

Junk

Portfolio

0

0.375

1

J

K

L

M

N

1 2

AN OPTIMAL PORTFOLIO

3 4

T-Bills

T-Bonds Corp Bonds

5 6

Proportions

0.260

0.365

0

7 8

Shadow Returns

4

6

4.4

5.6

8

6.23

Ratings

5

5

3.5

3

1

3.5

Requirement

Gap

Price

>

3.5

0

0.708

>

1.5

1

0

<

2.5

0

0.555

9 10 11 12 13 14 15

Maturities

0.4

4

3.2

2

2.5

2.5 .

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

B

C

D

E

F

G

H

I

J

K

L

A SHIPPING PROBLEM Transportation Costs

Ports Los Angeles New Orleans

New York

Minimum Cost 260,000

Oregon

14

26

30

Tennesee

24

10

12

Factories

Units Shipped

Ports Los Angeles New Orleans

New York

Total

Factory Unused Shadow Capacity Capacity Price

Oregon

5,000

3,000

0

8,000

9,000

1,000

0

Tennesee

0

4,000

6,000

10,000

10,000

0

16

Total

5,000

7,000

6,000

Requirements

5,000

7,000

6,000

Extra Exports

0

0

0

Shadow Price

14

26

28

Factories

.

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

B

C

D

E

F

G

H

I

J

1

2

Products 3 4

5

6

Total Profit

Quantity

120

0

220

160

20

50

Profit

60

70

48

52

48

60

K

L

M

N

INPUT-OUTPUT

30,040

Inputs Used Aluminum Steel Inputs Plastic Rubber Glass Chrome

0.5 2 0 1 1 0.5

2 2.5 1.5 0 2 2

0 1.5 4 0.5 1 0.5

2 0 0 1 1 2

1 0.5 0.5 0.5 1 1.5

0 0 0 2.5 2 2

400 580 890 525 620 620

Inputs Extra Available Inputs 400 580 890 525 650 620

0 0 0 0 30 0 .