CourseBrick Spring2012 Zhou

153
Firms and Markets (COR1-GB.1303.00/0P) Spring 2012 Professor Jidong Zhou

Transcript of CourseBrick Spring2012 Zhou

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Firms and Markets (COR1-GB.1303.00/0P)

Spring 2012

Professor Jidong Zhou

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Table of Contents SYLLABUS AND OUTLINE Syllabus 1 Correspondence between Topics and Textbook 6 Outline and Calendar 8

GROUP PRESENTATIONS Outline of Topics and Directions for Presenting 10

PROBLEM SETS Problem Set 1 (Math Review) 20 Problem Set 2 (Demand, Supply and Market Equilibrium) 21 Problem Set 3 (Pricing) 23 Problem Set 4 (Games) 25 Problem Set 5 (Information) 28

PRACTICE Practice Questions (pre Mid-Term) 31 Practice Questions (post Mid-Term) 36

SUPPLEMENTARY LECTURE NOTES Introduction 39 Calculus Review 42 Demand and Supply: Buyers, Seller and Markets 51 Utility 56 Demand 63 Logarithms 71 Economic Profit and Costs 72 Perfect Competition 78 Pricing 83 Advanced Pricing 88 Market Power 96 Auctions 100 Game Theory 105 Price Competition 115 Competition and Cooperation 124 Commitment, Entry and Exit 133 Imperfect Information 137 Externalities 145 Networks and Standards 148

Firms and Markets Professor Jidong Zhou

Office: KMC 7-72 Telephone: (212) 998-0589

Email: [email protected]

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Syllabus 1

Syllabus

Course Description The goal of this course is to give you some insight into how markets work. The first part of the course starts with the study of decision making by consumers and firms and concludes with a fundamental result in economics: a set of conditions under which markets function efficiently. In the second part of the course, we focus on situations when, for one reason or another, markets don’t work efficiently. We will emphasize the importance of strategic behavior, as modeled by game theory. Microeconomics (as the topic of this course is frequently referred to) is an important component of an MBA program. First, microeconomics focuses on specific dimensions of optimal firm decision making, such as pricing and entry and exit. Second, the formal economics perspective on business plays an important role in other areas of MBA study, such as finance or marketing. Finally, by studying public policy towards market failures, microeconomics highlights important factors conditioning firm strategy. Some of the key concepts we will introduce include economic incentives, marginal analysis, opportunity cost (which costs matter), market efficiency (what does it mean for a market to work), strategic behavior (how to predict and respond to your rivals’ decisions), and asymmetric information (what happens when others know something you do not). Our experience with students in prior years is that much of this is intuitive. But much is not, and our hope is that the combination of theoretical structure and practical examples will be useful in the years to come. It will not make you a success on its own, but it might give you an edge a few times when it matters. Prerequisites You are expected to be comfortable with basic algebra and calculus, including systems of equations, logarithms and NPV calculations, and derivatives.

Firms and Markets Professor Jidong Zhou

Office: KMC 7-72 Telephone: (212) 998-0589

Email: [email protected]

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Syllabus 2

Course Materials

Lecture notes. They review the theory relevant to most classes. In a few pages, they outline and explain the conceptual issues for the day, define terms, give examples, and (where it makes sense) work through numerical problems. They are intended to complement the lectures rather than substitute for them.

Textbook. There is no required textbook for this course. However, if you want to have a reference text, I recommend Michael Baye’s Managerial Economics and Business Strategy (McGraw-Hill, 6th or 5th edition), which is available in the bookstore or online. There is also a study guide to accompany the text. Some students indicate that they find this book helpful.

Slides. I will post the slides on Blackboard after each class, but keep in mind that there is much more to the class than what you see in the slides. I recommend that you take notes during the class as a supplement to the slides.

Additional materials. I will post additional materials on Blackboard, such as some useful materials for group presentation, and other newspaper articles or research papers.

Deliverables and Grades The various “deliverables” in the course are designed to develop different skills:

Class participation. It is important to integrate what you learn and be able to express it effectively. Moreover, there is a great deal of collective insight and experience in the class and we all benefit from sharing it. But the quality of your contributions is more important than the quantity.

Individual problem sets. Problem sets emphasize quantitative applications of the principles and tools developed in class. They are due at the start of class. They will not be graded, but will be marked with a check (and possibly a plus or minus). Most of the problems are quantitative; some require a qualitative answer and for these there may be no definitive right or wrong, it is understanding the issues that is key. You should also note that the problem sets are the best preparation for the exams. Dates and deadlines for all assignments can be found in the detailed course outline.

Group presentation. Groups of about 4 or 5 students will be asked to make a presentation to the class on a topic selected from a list of relevant themes. The goal is to apply economic principles to real-world situations and to hone your communication skills. The content is more qualitative than assignments.

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Syllabus 3

Mid-term exam. Generally three or four problems, similar to the practice mid-term exams that I will distribute in due course.

Final exam. Generally four or five problems, similar to the practice exam that I will distribute toward the end of the class.

Your grade for the course will be based on your contributions to all of these deliverables, weighted as follows:

Group presentation 30% Mid-term exam 30% (only if it helps you!) Final exam 40% (or 70%)

Your performance in terms of class participation and in problem sets will serve as a tiebreaker if you are on the border between two grades. The mid-term only counts if it increases your grade. This means that if you do better in the final than the mid-term, then the mid-term will not count. The reason for doing this is that the course will move fast and I am sensitive to the fact that some students may need some time to familiarize themselves with what economics is about. Ultimately I care about what you learn by the end of the course - the grading scheme is intended to be consistent with that concern. Final grades will follow the School’s guideline for core courses: no more than 35% of the class will receive A or A–. This guideline was instituted in response to student concerns that different sections of a course might be graded by different standards.

Exams and re-grading

Requests for a make-up exam must be made in writing (email) at the earliest instance. Since the mid-term is redemptive, there will be no make-up for the mid-term. You are responsible for checking the midterm exam dates and avoid any conflict with other commitments. During an in-class exam, you are not allowed to consult class notes, books, or any other material. However, you may consult one page of notes (a standard-size sheet of paper written on one side). Questions about grading must be made in writing and no more than a week after the exams are returned.

Honor Code The Stern community believes that honesty and integrity are necessary for rewarding academic and professional experiences. These qualities form the basis for the strong trust among members of the academic community (students, faculty, and administrators) that is essential for excellence in education. The Honor Code requires that each student act with integrity in all academic activities and endeavor to hold his or her peers to the same standard.

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Syllabus 4

In this course, you may discuss assignments with anyone, but any written work submitted for a grade should be your own. On exams, you may bring in and consult one piece of paper with anything on it you like, but your answers should be entirely your own work. Students with disabilities If you have a qualified disability and will require academic accommodation during this course, please contact the Moses Center for Students with Disabilities (CSD, 998-4980) and provide me with a letter from them verifying your registration and outlining the accommodations they recommend. If you will need to take an exam at the CSD, you must submit a completed Exam Accommodations Form to them at least one week prior to the scheduled exam time to be guaranteed accommodation. Getting help I would like each of you to learn and gain as much as you can from this course. If you are stuck, or have any difficulty with the material, don’t hesitate to ask for assistance. Please send me an email ([email protected]), and I try my best to respond promptly. My regular office hours are 4-6pm every Saturday, but if this does not work for you, feel free to email me and set up an alternate time. You can also get help from the teaching assistant, Esther Judelson. You can email her at ([email protected]) with questions, or set up a mutually convenient time to meet. All announcements regarding the course will be made on Blackboard. Besides administrative issues, I may post clarifications on the class material (arising out of our discussion in class or following from a fellow student’s questions). You are responsible for checking Blackboard for announcements on a regular basis (i.e. at least a couple of times a week).

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A preliminary list of topics to be covered: Demand, supply and market equilibrium. Demand and supply. Market forces. Market equilibrium. Shifts in demand and supply. Demand. Utility function. Indifference curve. Budget constraint. Demand function. Consumer surplus. Demand elasticity. Demand estimation. Risk aversion. Economic cost analysis. Opportunity costs. Sunk costs. Marginal costs. Economic costs and cash flows. Perfect competition and market equilibrium. Short run equilibrium. Long run equilibrium. Comparative statics. Welfare analysis: consumer surplus, producer surplus, and economic efficiency. Basic monopoly pricing. Profit maximization. Marginal revenue. Marginal cost. Elasticity rule. Advanced pricing. Price discrimination. Market segmentation. Two-part tariff. Quantity discount. Versioning and bundling. Dynamic pricing. Market power and policy. Economies of scale and economies of scope. Market power. Public policy towards mergers.

Game theory. Strategies and payoffs. Simultaneous-move games and normal-form Games. Sequential-move games and extensive-form games. Dominant and dominated strategies. Best responses. Nash equilibrium. Backward induction. The prisoner’s dilemma, the coordination game and other important games. Price competition. Bertrand competition. How to avoid the “Bertrand trap”: cost leader, cooperative pricing, limiting capacity, product differentiation, price matching. Competition and cooperation. Cooperation in business. Cooperative pricing. Repeated games. Trigger strategies. Cartels. Tacit collusion. Factors that make cooperation easier. Commitment. Credibility. The value of a credible commitment. First mover advantages. Preemption. Product proliferation. Entry and Exit. Asymmetric information. Hidden actions. Moral hazard and the agency problem. Incentive design. Hidden types. Adverse selection and the lemons problem. Screening and signaling. Auctions. Externalities and network effects. Positive and negative externalities. Coase theorem. Network effects. Expectations and critical mass. Strategic compatibility decisions. Two-sided markets

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Where in Baye are the Topics that We Cover in Class?

[Baye 6th and 5th Editions]

Firms and Markets does not follow any of the existing textbooks closely (and that is why we have developed and updates notes to supplement the lectures). However, many have found it useful to have additional supplementary materials and sources for examples and practice questions, though many have found that they can manage the course very well without much reference to textbooks. In addition to differing in coverage, Baye’s presentation is in a somewhat different order and style from ours. This is a guide to the textbook. It is designed to help you find the bits in Baye that are relevant for the topics covered in class. When you read Baye, use the lectures as a guide to what is important. Loosely, corresponding to our topics you will find the relevant material from Baye (5th and 6th Edition) as follows: Supply and Demand: 36-64 (5th Edition) 36-65 (6th Edition) Consumer Demand: 36-44, 74-95, 117-135 (5th Edition) 36-46, 74-95, 117-135 (6th Edition) Economic Costs: 45-52, 177-191 (5th Edition) 46-52, 177-190 (6th Edition) Competitive Markets: 267-280 (5th Edition) 266-279 (6th Edition) Basic Pricing: 236-256 (very good background), 280-296, 397-399, 509-518 (5th Edition) 235-255, 278-294, 397-399, 510-520 (6th Edition) Advanced Pricing: 404-417 (5th Edition) 404-417 (6th Edition)

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Market Power: 280-284, 509-518 (5th Edition) 278-283, 510-520 (6th Edition) Game Theory: 353-365, 378-386 (5th Edition) 353-365, 378-386 (6th Edition) Pricing Games: 315-338 (but particularly 336-338) (5th Edition) 315-338 (but particularly 336-338) (6th Edition) Cooperation: 330-332, 339-340, 365-377 (5th Edition) 330-332, 339-340, 365-377 (6th Edition) Commitment: 378-386, 484-486, 491-494 (5th Edition) 378-386, 485-488, 492-495 (6th Edition) Asymmetric Information: 449-455, 220-228 (5th Edition) 450-456, 219-227 (6th Edition) Auctions: 455-466 (5th Edition) 456-466 (6th Edition) Externalities: 518-526 (5th Edition) 520-528 (6th Edition)

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Firms and Markets (COR1-GB. 1303.00/0P): Outline and Calendar

Date Topic Problem Set Presentation

Feb 11

Introduction. Demand, supply and market equilibrium: demand curve, supply curve, equilibrium Demand I: utility function, indifference curve, budget constraint, demand function, consumer surplus

Feb 18

Demand II: demand elasticity, demand estimation, risk aversion Economic cost analysis: opportunity cost, sunk cost, marginal cost, supply curve

PS#1 (Math Review) due at the start of class

Feb 25

Perfect competition and market equilibrium: short run equilibrium, long run equilibrium, comparative statics, welfare analysis Basic pricing: profit maximization, marginal revenue and marginal cost, elasticity rule

Mar 3 Advanced pricing: price discrimination, market segmentation, two-part tariff, quantity discount, versioning, bundling, dynamic pricing

PS#2 (Demand, Supply, and Market Equilibrium) due at the start of class

Mar 10

Practice midterm exam Market power and policy: economies of scale and economies of scope, market power, public policy towards mergers

PS#3 (Pricing) due at the start of class

Mar 17

No Class – Spring Break

Firms and Markets Professor Jidong Zhou

Office: KMC 7-72 Telephone: (212) 998-0589

Email: [email protected]

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Mar 24

Midterm Exam (in class): same format as the practice midterm (3 or 4 problems, largely quantitative). You may consult one page of notes (a standard-size piece of paper, single sided, with anything on it you like) and a calculator Game theory I: strategies and payoffs, simultaneous-move games, normal-form games, dominant and dominated strategies, best responses, Nash equilibrium

Mar 31

Game theory II: the prisoner’s dilemma and other important games, mixed strategies, sequential-move games, extensive-form games, backward induction Price competition: Bertrand competition, how to avoid the “Bertrand trap”: cost leader, cooperative pricing, product differentiation, limiting capacity, price matching

Apr 7

Competition and cooperation: cooperation in business, cooperative pricing, repeated games, trigger strategies, cartels, tacit collusion

PS#4 (Games) due at the start of class Presentation: Broadway theaters; Google; GE; AT&T

Apr 14

Commitment: credibility, the value of a credible commitment, first mover advantages, preemption, product proliferation, entry and exit

Presentation: Real estate brokerage; Mutual fund; Virgin; Predatory pricing

Apr 21

Asymmetric Information: hidden actions, moral hazard and the agency problem, incentive design, hidden types, adverse selection and the lemon problem, screening and signaling, auctions

Apr 28

Practice final exam Externalities and network effects: positive and negative externalities, Coase theorem, network effects, expectation and critical mass, compatibility decisions, two-sided markets

PS#5 (Information) due at the start of class Presentation: eBay; Health reform; Microfinance

May 5

Final Exam (in class): same format as the practice midterm (4 or 5 problems, largely quantitative). You may consult one page of notes (a standard-size piece of paper, single sided, with anything on it you like) and a calculator

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Group Presentation 10

Group Presentations

Each study group will give a presentation to the class from one of the topics listed below. You should view your presentation as an opportunity to exhibit some creativity, to hone your research and presentation skills, and to attack a real business economics issue.

An ideal presentation should last approximately 10-12 minutes. A time limit of 12 minutes will be enforced ruthlessly! This means that you will not be allowed to keep talking after 12 minutes, leaving 3-5 minutes of questions. You should bear the following points in mind:

Informativeness: How much did we learn from the presentation?

Analysis: Did we gain novel insights into the topic? Were lessons from the course applied effectively? Was evidence used effectively to support the argument?

Style: Was the presentation clear and compelling? Were the slides effective?

Above all, keep your classmates interested. If you use Powerpoint, you should bring your presentation to class on a diskette, CD, or USB pendrive. In addition, bring a hard copy of your slides to class and send me an email with your presentation (before the day of the presentation) so that we have a back up in case any problem occurs. You can learn a great deal from observing and thinking critically about your classmates’ presentations. What worked? What did not? Why? Were the points well argued? How could they be argued better? You will be asked to evaluate each other’s presentations, using the form that appears below. This will encourage you to think critically about the presentations (what did you take away from the presentation?). It will also generate more feedback for the presenters and contribute to the grading process. The grading will be as follows:

Average of classmates’ assessment 50% My assessment 50%

Firms and Markets Professor Jidong Zhou

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Presentation Topics and Sources

Choose your topic from the list below (by the end of February 19th). Topics will be allocated on a first-come, first-served basis. To request a topic, send an email to the teaching assistant, including your first, second, and third choices. Each topic comes with a date (see the course outline) and a series of questions. Feel free to modify some of the questions if you think that the modifications would lead to a more interesting presentation. The material posted on Blackboard is intended to get you started. Further potential sources of information and data include: Bobst Library NYU Virtual Business Library Proquest (newspaper and magazine articles) Lexis-Nexis (news articles, financial filings, legal decisions, etc.) Investext (analyst reports) Global Market Information Database Hoover’s Online (company profiles) ABI/Inform Market Research Monitor DOJ Antitrust FTC FCC EU Competition (1) Price discrimination in Broadway theaters Describe the various ways in which Broadway theatres segment their markets. Would you encourage most Broadway theatres to offer more seat quality and pricing divisions than they currently do? How would you solve the problem of “scalpers”? (Is it a problem?) (2) Google and antitrust The EC and the U.S. Federal Trade Commission are each currently investigating Google for possible antitrust violations. Why is this happening? What are the grounds for the finding of an antitrust violation in this case? What is Google's likely defense?

(3) GE and Honeywell What was the strategic logic for GE to purchase Honeywell? Do you find it compelling? What was the European Commission’s logic in blocking the merger? Do you think it made the right decision? What should Jack Welch have done? (4) AT&T and T-Mobile AT&T and T-Mobile are two of the largest providers of wireless communication services in the United States. In March 2011 AT&T proposed to acquire T-Mobile, but in September 2011 the Department of Justice sued to block this takeover. What were the key concerns of antitrust and regulatory agencies of the U.S. government about this proposed acquisition? What were the key points that AT&T used to defend the acquisition? How did the other two

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major operators Verizon and Sprint respond? In what ways could the acquisition lead to a reduction or enhancement of national economic efficiency? (5) Residential Real Estate Brokerage The standard commission for brokerage services for house sales is 5-6 percent in the United States, and it appears to be resilient in the face of changing demand as well as new technologies and business models. What is the industry’s structure? What is the nature of competition in the industry? What shortcomings of economic efficiency appear to exist, if any, and why? Is the relatively steady commission rate an indication of economic inefficiency? What do you think will happen in the next five to ten years? (6) Product differentiation in the mutual fund industry Give an idea about the number of funds, the dispersion of fees charged to investors, and the financial performance of different funds in the mutual fund industry. What is special about these figures? Do these findings still hold when attention is restricted to apparently more homogenous funds, such as the S&P 500 index funds? What are the possible explanations for these findings? Do you think entry into the industry should be restricted? (7) Virgin and British Airways fuel surcharge In the summer of 2007, British Airways and Virgin were found to be colluding on fuel surcharges. British Airways were fined $546m while, Virgin were not fined at all as part of a relatively recent leniency program for whistleblowers. Discuss the case and more broadly assess the success, impact and design of such leniency programs. (8) Predatory Pricing: Spirit vs. Northwest What is predatory pricing, why is it a concern for antitrust authorities, and how can it be distinguished from competitive behavior? What is distinct about the airline industry? Illustrate the theoretical arguments by describing and analyzing the antitrust battle betweenSpirit and Northwest.

(9) eBay What are the reasons for eBay’s success? How did eBay address the challenges of online trading when traders are anonymous? Why did amazon.com and yahoo.com fail to achieve the same measure of success in online auctions? Do specialized auction sites and direct online selling threaten e-Bay’s dominance? (10) Healthcare reform There is widespread agreement that the healthcare system in the U.S. is excessively costly and that the problems of cost and of excessive utilization are getting worse. What are the causes of these problems? What are some of the solutions that have been suggested?

(11) Microfinance meets the market Give a brief description of credit markets in poor and developing countries, highlighting the role of moral hazard and adverse selection. Describe the evolution of the microfinance industry, highlighting its success and failures and explaining how or why it is better equipped than traditional moneylenders in resolving the usual problems in credit markets. Discuss the future of microfinance and, in particular, whether for-profit models will play a successful role

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in this industry? You may focus entirely on microfinance in poor and developing countries or, if you wish, you may want to focus on the lessons from the microfinance experience that are of relevance to the recent and novel social lending business models that have appeared or have the potential to appear in the US.

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Presentation Tips This guide is designed to remind you of some basic skills to enhance your presentation to the class. It is not concerned about preparation of the content of your presentation, which obviously should be well researched, introduced succinctly, organized logically, with clear transitions and conclusions. You must be audible: When you practice, have a group member listen to you in a large room and have that person alert you if you cannot be heard easily. Make eye contact, or the semblance of it: When you rehearse your presentation, practice scanning the room, even if you are looking just over the heads of the audience, or at people’s eyebrows. Take in the whole room. The norm at Stern tends to be that presenters use PowerPoint slides as their notes. That’s OK as long as you don’t turn your back on the audience. To deal with this potential problem, some people use note cards to keep them facing front, on track, and as a back up in case of technology failure. Do not read your presentation. Reading is the best way to lose your audience. Speak naturally so that you don’t sound as if you have memorized your talk. Many of us speak too fast. If you are one of them, build into your presentation pauses and reminders to speak more slowly. Some people find it helpful to include at selected points in their notes big red marks saying “BREATHE!” or “PAUSE” or “SCAN AUDIENCE” or “SLOW DOWN.” If English is not your first language and you are worried people will have difficulty understanding you, or if you speak with a strong American regionalism, speak more slowly and deliberately distinctly at the beginning of your presentation to allow the audience to get used to your speech patterns. Time yourself. Cut appropriately. Include the crucial information. Save the interesting but non-crucial material for the question and answer period if you have extra time. Remember that less is more: if you add too many details, your audience often loses track of your main points. Plant yourself: Many people have trouble standing still when they give a talk. It helps some people to think of their feet rooted in the ground, as if they could not move. It gives them strength and keeps them literally more grounded. For some people, the choice of shoes is important as well. Since you are presenting in a group format, try to present a united front when you make your presentation. For example, using “we” instead of “I” makes it sound as if you worked together. Showing that you are listening when others talk is good, too. Practice, preferably in front of other people who can give you honest and useful feedback.

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Finally, try to enjoy yourself. [These comments were prepared by Stephanie Nickerson, an NYU teaching consultant who has worked extensively with Stern faculty and students.] A few further and related points arising from presentations in past years that might be helpful, though no doubt to a great extent these comments represent our own peccadilloes and so ought to be treated with more than the usual caveat lector. What is the presentation about? This might sound trivial, but we have sat through numerous presentations (and countless research seminars) where it was such hard work trying to figure out what the point that the speaker was trying to make that no one in the audience bothered. Details are important, arguments can be subtle, but at least the question that you are trying to address or the point of the presentation should be crystal clear. What should the audience take away? People (or maybe we are just speaking for ourselves) have limited concentration spans and abilities to retain information. If there is just one thing that you want them to take away from the presentation, what is it? Make sure you have communicated it. This need not be done as formally as a “takeaway” slide, but at the same time you as a presenter should be clear about what it is that you want your audience to come away with. (This might be a specific recommendation, or set of recommendations, or some other key points—“it depends on x and on y”). Shaping your presentation Allied to the two points above, once you are clear about what the presentation is about and what you want your audience to go away thinking, then this should help to have a clear structure for the presentation. This does not have to involve a formal “roadmap for the presentation” slide —though it could—but you should be clear about the structure of the talk. What to put on the slides Many presentations we have seen have suffered a tendency to put a lot of information on the slides. This has a number of drawbacks for presentation:

Often it results in the presenter reading the slide and keeps them from engaging with the audience;

It also leads to the audience reading the slide and not paying attention or listening to the speaker.

If there are a great number of facts of which you think the audience should be aware, you might consider using handouts (though this is certainly not required for a good grade for presentations in this course). Given these drawbacks, it is perhaps surprising that friends and students who have worked in consulting firms and elsewhere tell us that densely-packed slides with a great deal of text, tables and graphs are far from uncommon. At first blush, this might appear something of a puzzle. However, in many cases slides serve two very different purposes (perhaps unfortunately). First

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and obviously, as presentation aids. Moreover, frequently slides also serve in effect as reports on the projects as a whole (the client often gets no written report but a big slide deck as the sole deliverable). As another way of addressing this issue, you might think of slides (as viewed by your audience) as “valuable real estate”. You don’t want to put too little on a slide (you’re wasting valuable space); but you also don’t want to put too much on a slide (you’ll overload your audience; they won’t absorb everything; and you’ve wasted time, effort, and space). Excessive use of technique Don’t try to impress us with the excessive use of economics tools (e.g., abstract supply and demand charts, or graphs of marginal somethings) unless they directly help you tell your story. Again, your slides are valuable real estate that shouldn’t be wasted! Pitfalls from preparation Having spent a great deal of time and effort researching your topic, there are two common pitfalls:

Overestimating the audience: You may have spent hours trawling through the Internet researching the topic, but few of the audience are likely to have done the same. Try to have some empathy for them.

The sunk cost fallacy in presentation: After learning a great deal of facts and interesting detail, there’s a great temptation to try to communicate all of it. Almost always, though, less is more, and trying to list every fact can get in the way of communicating the main points that you want the audience to take away. The desire to show that you have researched a topic and know a great deal about it may lead you to present a lot of facts. Try instead to show that you have thought about it by using the facts selectively and appropriately! In any case, your knowledge or (lack of it) is likely to be made clear in the way you deal with questions and discussion.

Specific Issues When Presenting an Economic Analysis

Economics is about evaluating the effect of a trade-off. For example, in considering a price reduction a monopolist has to trade-off lost revenue on units that would be sold at the original price versus the extra revenue from any extra units sold due to the rpice decrease. Be very clear about what you think the key economic trade-offs are in what you are presenting. To force yourself to be clear, have a slide called “Key Economic Trade-off” if you can.

Don’t spend too much time on the details of the industry. Don’t be afraid to simplify things.

Relate the facts to the underlying economic trade-off

Use the facts together with an appropriate framework to generate a recommendation on how to resolve the trade-off.

If there are caveats in interpreting you results, better to be upfront about them.

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Summarizing data or analysis in a picture or diagram tends to be more effective than using a whole bunch of dot points

Written by the Stern Economics Department. © Copyright 2012 NYU Stern School of Business.

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(note: “1” means “extremely bad” ----- “7” means “extremely good”; 4 means “average”)

Group:______________________________________

Topic:______________________________________

1. Presentation Format i. Good time management ii. Clarity of presentation iii. Logical structure of presentation

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2. Analysis i. Research: found appropriate background information ii Used data and information selectively and appropriately iii. Used appropriate course concepts in the analysis iv. Effective synthesis of concepts and data/information

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3. Recommendations/Conclusions i. Sound recommendations or conclusions ii. Supported findings with hard evidence iii. Dealt well with questions

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4. Overall Presentation

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Firms and Markets Presentation Evaluation

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Group:_____________________ Topic:_____________________

In one or two sentences what did you understand as “the bottom line” in

the presentation?

Comments:

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Problem Sets 20

Problem Set 1 (Math Review)

(1) Linear equations Solve the following system of linear equations:

x = 10 – 2 y y = x + 4

(2) Quadratic equations

a) Knowing that p>0, determine the solution to the equation: (1+p)2 = 36 b) Solve the equation:

2

125

y

(3) Logarithms

Solve the following equations (log without subscript is “natural logarithm” to the base e): a) log10 x = 4. b) log x = 4 c) log (x) – log(5) = log (0.75) d) log (2y) = 3

(4) Net Present Value

a) Suppose that the annual interest rate is 10%. What is the value of a perpetuity that pays $30 every year from the beginning of next year?

b) Suppose that the annual interest rate is 5%. What is the value of an annuity that pays $100 every year from the beginning of next year?

(5) Derivatives

Compute the derivatives of the following functions: a) 2 y3 + 4 y b) (x + 3) (2 – x)

(6) Derivatives of derivatives Compute the second derivatives of the functions in the previous exercise.

(7) Optimization Find out the maximum of this function: (100-q)×q © 2012 Stern School of Business.

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Problem Sets 21

Problem Set 2 (Demand, Supply, and Market Equilibrium) (1) Demand and Supply basics For each of the following, use a supply and demand diagram to deduce the impact of the event on the stated market in terms of both price and quantity.

(a) Event: Cold freeze in Florida. Market: Orange juice. (b) Event: Digital cameras. Market: Film (c) Event: The FDA announces that aspartame may cause cancer. Market: Saccharin.

[Comment: aspartame and saccharin are low-calorie sweeteners.] (d) Event: An import tariff is imposed on steel. Market: aluminum.

(2) Internet-enabled mobile phones Prices and quantities demanded for an Internet-enabled mobile phone have been observed to be as follows:

P Q $100 600 $105 590 $110 575 $115 550 $120 510

(a) Calculate the approximate elasticity of demand when price is $105. (b) Is the demand elasticity constant at all prices? (c) If the monthly subscription fee for Internet access using the mobile phone falls

from $10 to $2, what would you expect to happen to the quantity of mobile phones demanded at any given price?

(3) Wireless demand. AT&T Wireless estimates that demand for its service has an elasticity of –1.5. In 2001, 18mm customers generated revenues of approximately $ 12.5 billion at an effective price of about 10 cents a minute. If elasticity is constant, what would revenues be at a price of 8 cents? 9 cents? 11 cents? (4) Jared’s restaurant After working for years as a chef, your cousin Jared is thinking about opening his own restaurant and has asked you to help with his financial analysis.

Basic expenses. To open a restaurant, he will have to quit his current job (which pays $46k a year) and invest his savings of $200k (currently earning 6% annually) in equipment. He estimates he will have to spend $4k during the first year to maintain the

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equipment and preserve its market value of $200k. He would not pay rent: his father has gaven him title to a small building, whose current tenant is a shopkeeper. The tenant estimates that she nets $3000 a month from sales, over and above the $2500 a month she pays in rent.

Other expenses. He anticipates spending $50k a year for food, $40k for extra help, and $14k for utilities and other supplies during the first year of operations.

Jared‟s question to you: How much revenue would he have to generate to make his first year more profitable than staying in his current job? 5) Impact of a price ceiling in the instant oatmeal market The demand and supply curves for instant oatmeal are as follows: Qd=10-0.5 Pd where Qd is the quantity of instant oatmeal packets (in million units) demanded when the price consumers pay is Pd. Qs= -2 +Ps , when Ps is greater than or equal to 2 0 , when Ps < 2 where Qs is the quantity of instant oatmeal (in million units) supplied when the price producers receive is Ps. Suppose the Government imposes a price ceiling of $6 in the market for oatmeal.

a) What are the equilibrium price and quantity in the market without a price ceiling? b) What is the size of the shortage in the market with the price ceiling? What is the

producer surplus? c) What is the consumer surplus, assuming the good is purchased by consumers with the

highest willingness to pay? What is the net economic benefit? What is the deadweight loss?

© 2012 Stern School of Business.

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Problem Set 3 (Pricing)

(1) MelCo’s Xamoff The global pharmaceuticals giant, MelCo, has had great success with Xamoff, and over-the-counter medicine that reduces exam-related anxiety. A patent currently protects Xamoff from competition, although rumors persist that similar products are in development. Two years ago, MelCo sold 25 million units for a price of $10 for a package of ten. Last year it raised the price to $11, and sales fell to 22 million units.

a) Estimate the elasticity of demand for this product. b) MelCo is considering a further price increase to $12. Estimate the impact on the

quantity sold. Do you expect revenue to increase or decrease? c) A financial analyst estimates the cost of production at $2 a package. What price

maximizes MelCo‟s profit? d) When the patent expires in 2010, what do you expect to happen to demand? What

about the elasticity?

(2) EasyTax EasyTax markets both a deluxe and a standard version of its software. The deluxe version contains additional features that are likely to appeal to sophisticated users. The marginal costs of producing and distributing the two versions are virtually equal, and equal to zero. The market is equally divided into two types of users, sophisticated and unsophisticated (and assume one user of each type). The maximum willingness to pay for both types of users for the standard and deluxe versions are given in the following table: Standard Deluxe Unsophisticated 20 20 Sophisticated 35 100

a) Assuming that the company producing EasyTax can distinguish between sophisticated and unsophisticated users (because, for instance, the sophisticated users are registered accountants), what are the optimal prices to be charged to each category of users? What is the company‟s profit?

b) Assume now that the company cannot distinguish between the two types of user. What are the optimal prices for the two versions? What is the total profit?

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(3) Sal’s satellite company Sal‟s satellite company broadcasts TV to subscribers in LA and NY. Demand functions are QNY=50-(1/3)PNY QLA=80-(2/3)PLA

where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is given by TC=1000+30Q, where Q= QNY + QLA.

a) What are the profit-maximizing prices and quantities for the NY and LA markets? b) As a consequence of a new satellite that the Pentagon developed, subscribers in LA are

now able to get the NY broadcast and vice versa so Sal can charge only a single price. What is the profit-maximizing single price that he should charge?

c) In which situation is Sal better off? In terms of consumers‟ surplus which situation do people in LA prefer and which do people in NY prefer? Why?

d) In the situation with a single price, what are the MRs in each market, at the profit maximizing price? Are they equal? Now consider the situation with different prices for NY and LA. What is the MR in each markets at the profit maximizing prices?

(4) CD pure bundling Suppose a music industry producer just finished producing two compilation CDs of music from the „70s. One disk is pop music, the other disk is disco music. Suppose also that he estimates the market to be evenly segmented into two types of customers. He estimates valuations for each type of customer as follows. Disk 1 Disk 2 Type A 10 2 Type B 9 3 The marginal cost of the disks is zero.

(a) If the producer wants to sell the disks individually, what prices should he set? (b) Can the producer do better with bundling? Explain. (c) Would it be better to mix the content of the disks and obtain two pop/disco disks of

music from the „70s? Suppose now that the estimated evaluations are instead: Disk 1 Disk 2 Type A 10 3 Type B 9 2

(d) Does pure bundling make sense in this case? Explain the difference between the two demand profiles.

© 2012 Stern School of Business.

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Problems 4 (Games)

(1) Simultaneous move game

Use the following game to answer the questions below:

L C R

125 250 100

T 100 300 200

0 500 400

M 250 500 750

-100 300 350

B 0 400 -100

(a) Find each player’s dominant strategy, if it exists

(b) Find the Nash equilibrium (2) Intel and AMD The following normal form game depicts the pricing rivalry between Intel and AMD for their newest top-of-the-line chip. Each company considers five possible price levels: $449, $399, $349, $299 and $249. Monthly profits in million dollars are:

449 399 349 299 249

50 70 55 45 30 449 200 180 150 120 95

35 45 50 40 25 399 230 210 160 130 110

15 25 30 35 20 349 210 190 180 140 120

5 15 20 25 15 299 180 170 150 120 100

-5 10 15 20 10 249 120 110 105 95 90

(a) Find each firm‟s best response to each possible strategy of the other. (b) What is (are) the Nash equilibrium (equilibria) of the game? (c) What combination of strategies generates the highest total profit? Why might the two

firms not be able to come to an agreement on this outcome? (d) What aspects do you think are left out in this game? (This is an open question; please

limit your answer to a paragraph or two.)

AMD

Player 2

Player 1

Intel

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(3) Lowest price guaranteed

Two firms compete in prices. Each firm can set a high price or a low price. Profits as a function of prices are given by the payoff matrix is: Firm 2 Low High Low 70,70 120,0 Firm 1 High 0,120 100,100

(a) Are there dominant strategies? What is the Nash Equilibrium of the game (if any)? Suppose now that each firm offers its customers a “lowest price guarantee:” if firm 2 offers a price lower than firm 1, then firm 1‟s customers are entitled to buy from firm 1 at the same price, even if firm 1 had initially set a high price; and similarly for firm 2‟s customers if firm 1 offers a price lower than firm 2. (Lowest price guarantees are common in many markets, including sporting goods, books, house wares, cellular phones, electronics, luggage and travel accessories, toys, tires, eyewear, prescription drugs, etc.)

(b) How do lowest price guarantees change the game? (c) What is the equilibrium of the new game? What lessons can we learn?

(4) A Bargaining Game

Two players, PI and PII, have to divide 23 M&M's: 12 regular ones (R's) and 11 peanut-coated ones (P's). PI likes both types equally but PII likes only the P's (she will have no use for any R's she gets). Thus, u1(r,p) = r + p and u2(r,p) = p. Moreover, both players' preferences are known to both and the bargaining will be restricted to the allocations of M&M's, e.g., no monetary side payments or other modifications involved.

(a) PI Divides and PII Chooses: PI divides the M&M's into two piles in any way he chooses. Then PII selects one of the piles, leaving the other one to PI. What will be the outcome of this game?

(b) PII Divides and PI Chooses: The same as in Problem 1, but with the order reversed. What will be the outcome?

(5) The Centipede Game There are two players Harry and Sally. They each start with 1 dollar in front of them. They alternate in saying either “Stop” or “Continue”, starting with Harry. When a player says “Continue”, 1 dollar is taken from his / her pile, and 2 dollars are put in the opponent‟s pile. As soon as any player says “Stop”, play is terminated and each player receives the money currently in her pile. Alternatively, play stops if both players reach 100 dollars. Can you predict the equilibrium outcome of this game? To help you think about this problem, the game tree is given below. This is a famous problem in game theory, and because of what the tree looks like, is called the “Centipede game”. As we

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100

100

have done in class, try to think of what your opponent would do, and work backwards. Think of yourself as Harry. Ask yourself at each step what Sally would do. What does that mean for what you should do?

© 2012 Stern School of Business.

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Problem Set 5 (Information)

(1) The Giant Corporation You are a small firm in a market which is dominated by Giant Corp. which has 75% of the market. Your current challenge: to decide whether to expand your capacity. If you don‟t, you expect to earn $2m, as you did last year. Giant will earn $30m. If you do expand, your profits depend on whether Giant responds aggressively by cutting its price or passively by maintaining price at its current level. The estimated possible payoffs if you expand are:

If Giant responds aggressively, you will lose $2m and the giant earns $10m.

If Giant responds passively, your profits increase to $4m and the giant earns $20m. Use a game tree to study the strategic interactions between you and Giant. Should you expand capacity?

(2) 1982 16 K classic pen Mary, a friend of mine at a West Coast business school wants to buy a present for her father‟s birthday. In particular, she knows that he‟s been wanting to get hold of a particular pen for his collection. She know that he‟s particularly keen to get hold of the “1982 16 K classic”. Even though the list price in collector‟s manuals is only $250, Mary is willing to pay $500 for the pen.

My friend has been unable to find the pen at the local dealers and decided to try a new website, www.whatiwanttopay.com. At this site people post descriptions of the items that they would like to buy and how much they are willing to pay for them. Mary is aware that some sellers might try to fool her by sending the “12 K Classic” and it would be hard for her to work out which she‟d received ahead of the birthday. Thus even if she had the opportunity to return it, she would value the “12 K” at only $100. Genuine sellers would meet Mary‟s offer so long as it was at least as high as the list price, whereas as fraudulent sellers would send her the “12 K” version if she posted any price greater than $100.

From speaking to friends, she estimates that out of all potential sellers 25% are genuine sellers and the remainder fraudulent. She determines therefore to post a price of $200(=0.75*100+0.25*500).

(a) She told you about this, and you suggest that she‟d be better off not posting. Why? (b) Suppose that she assessed that 80% of potential sellers are genuine. Should she post to

this site? At what price? (c) Suppose that the proportion of potential sellers who are genuine is x. What is the

smallest value of x at which Mary should post an offer at the site? At what price?

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(3) Pricing as a Signal For a HQ Item (50%) For a LQ Item (50%)

Buy Not

HP 1, 1 0, 0

LP -1, 3 0, 0

This is a game between a seller (S) and a buyer (B). S sells an item which may be of high quality

(HQ) or low quality (LQ). Knowing the quality of the item, S can ask for a high price (HP) or a

low price (LP). B, hearing the price but not knowing the quality, has to decide to buy or not. The

resulting payoffs to S and B, are given above. Overall, there is a 50% probability that the item to

be sold is HQ, and a 50% probability that it is LQ.

(a) Suppose S charges a high price if its item is of high quality but otherwise a low price.

How should B react? Given B‟s reaction, will S stick to its pricing policy? Can price

signal quality in this example? Why?

(b) Now let us modify the above game slightly. Suppose B can discover the item‟s quality

with a probability 70% before she makes her purchase decision (or 70% of the buyers

in the market know the real quality of the item). Can price signal quality now (when the

buyer does not know the quality)?

(4) Natives and tourists

Consider a game between a consumer and firm. The consumer has two strategies, to buy or not. The firm can produce either a low-quality product or a high-quality product. Customers can not tell the quality until after they have bought it. Payoffs are as follows:

Firm

Consumer

Strategy Low-quality High quality

Don‟t Buy 0,0 0,-10

Buy -10,10 1,1

a) Find any dominant and dominated strategies. What is the Nash equilibrium of this

game? Are there any outcomes that would be preferred by both the firm and the consumer?

Buy Not

HP 3, -2 0, 0

LP 1, 0.5 0, 0

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Problem Sets 30

b) Now suppose that there are many potential customers and that consumers buy often. Suppose that the consumer tells the firm, “I‟ll buy your product and continue to buy it if it is of good quality. But if it turns out to be shoddy, I‟ll tell all my friends never to purchase anything from you again.” Under what circumstances would such a statement make a difference?

c) There is a common perception that locals get better service in restaurants than tourists. Discuss briefly in the light of the analysis above.

(5) Vertical relations and vertical integration

Firm D is a supplier of Firm G, a large car manufacturer. For each design cycle, firm D makes an investment of x dollars in design of the new model. Then firms D and G negotiate on a price for G to pay D for its design work. Let V(x) = x0.5 be the value generated by firm D‟s design efforts. In the past, it has always been the case that negotiations led to an equal split of the value at stake, that is, each firm gets 0.5V(x).

a) What is the socially efficient level of investment? b) What is the equilibrium level of investment? c) Explain the difference between a) and b) d) How might the social optimum be achieved?

© 2012 Stern School of Business.

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Practice Questions I

1. Demand for French wine What will be the effect of the following events on the demand for French wine and the quantity consumed? Be sure to distinguish between shifts of the demand curve and movements along the curve. As appropriate, indicate whether you expect the impact will be mostly on price or quantity; and distinguish between the short-run and the long-run impact. Use a graph if necessary.

a) A decrease in the price of French wine. b) A new study linking longevity with moderate amounts of red wine. c) An increase in the price of Californian wine. d) A severe drought in the wine growing regions of France. e) A subsidy to French vineyards.

2. Costs, Elasticity The market for cola flavored soft drink in Peru is for all intents and purposes a monopoly. Inca Kola has an overwhelming market share.

The demand for Inca Kola in Peru for each year is given by

Q = 200 – 4 P.

The Inca Kola has a single plant which it built for 150 million in 1996. Each year it has a loan repayment of 6 million to pay off the loan it took out to finance the plant. The plant itself is fairly specialized and has zero scrap value, but shelving and office equipment is worth 10 million. Each year Inca enters into a bulk electricity contract with Peru Electricity in which they pay 2 million upfront for all the electricity they want. Their marginal cost (which is mostly labor and maintenance) is 2 per unit. (a) At the beginning of each production year, what components of Inca Kola’s fixed costs

are sunk? (b) How does you answer to (a) change if we are in the middle of a production year? (c) Draw a graph of the marginal cost curve. (d) Derive the marginal revenue function for Inca Cola (e) Draw a diagram with Price on the vertical axis and Quantity on the horizontal axis that

shows Inca’s Demand curve, Marginal Revenue curve and Marginal Cost curve. (f) Derive the optimal price and quantity for Inca Cola.

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Practice Questions 32

(g) On the diagram you drew in part (e) indicate the optimal price and quantity (you do not need to have done part (f) to do this.

Remember elasticity? Answer the following:

(h) What is the elasticity of demand when demand is equal to 40? (i) What is the elasticity of demand when demand is equal to 10? (j) Why do we use elasticity measures rather than just the slope of a demand curve to talk

about how quantity responds to price changes? 3. Costs, Demand and Supply Provide responses that are both concise and precise to the following short answer questions. Where appropriate, the use of diagrams is encouraged.

a. Explain how accounting profit and economic profit are different. b. When does a cost become sunk? c. Using a demand and supply framework, and explaining each step in your logic, address

the following: 1. Describe the likely effects of a drop in the cost of employing skilled

craftsmen on the market for fashionable shoes. 2. How might an increase in the cost of car insurance affect the US

market for new cars? 3. Global warming seems likely to increase migration from the south

of the USA to the northern states. It also seems likely to increase the need for insulation in the construction of houses in the northern states. Taking these assertions as given, how would the housing market in North Dakota be affected by global warming?

4. Mayor Bloomberg wants to make all the taxis in New York hybrid

cars by 2010. What effect will this have on the market for used cars in New York?

4. Buttons/badges As election day approaches in the mayoral race, the demand for buttons is hitting unprecedented heights. Three months before election day, your friend John, who currently has a small factory producing badges, is considering expanding production. Previously, this very competitive industry was relatively stable and demand and supply were estimated at:

Demand: PQ 2100

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Supply: PQ 2

(Units are 100,000s of buttons and price in cents.) John estimates that over the past months, monthly demand has risen to a higher level:

PQ 2140 .

He estimates demand will remain at this level until the election, and then fall back down to the old level. John calculates that by buying a new machine for $5,000 he would be able to produce 40,000 more buttons a month at a marginal cost of 30c. (Assume that there are no other additional costs of production.)

a) What was the old price of buttons? How many buttons were being produced at this price?

b) What is the new price of buttons? How many buttons are produced at this price? c) Should John buy the machine? In answering this question, notice that if John went

ahead and bought the machine his additional production would be tiny in comparison with the overall size of the market and would have negligible effect on price. Also, in no more than a couple of sentences mention any drawbacks in this analysis.

5. Water Filters

Assume that the market for water filters in the US has the following yearly demand function: Q=5,000,000-100,000P Suppose that the current price for a filter is $25.

(a) Compute the price elasticity of the demand at the current price. (b) Compute the consumer surplus at the current price.

6. NY Mets pricing Suppose the average demand for tickets at a NY Mets game is given by Q = 120,000 (1 – P/140), where Q is number of tickets and P is price in dollars.

a) Assuming that marginal cost is zero, determine the optimal ticket price. Suppose now the Mets stadium has a capacity of 55,000 seats.

b) What is the optimal price? c) How much should the Mets be willing to pay for a 10,000 seat expansion of their

stadium?

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7. East Village Voice The East Village Voice, a popular newspaper appealing to the young Manhattan population, shows the following P&L statement. Total production costs (including typesetting, printing and overhead) are $24m a year. Average circulation, at the current price of $0.50, is 200,000 (for the purpose of this problem, assume that the newspaper is published 300 times a year). In the past, an experiment was made to increase the price to $0.60; circulation dropped by 30%.

a) Determine the value of the demand elasticity at the current price level. b) Assuming that printing is 25% of total production cost and making any other necessary

assumption, determine the value of marginal cost. c) Determine the value of marginal revenue at the current price level. d) Based on the values obtained in (a), (b), and (c), indicate whether price should be

increased, decreased, or kept constant. e) Determine the optimal price level.

8. NYU Professional school NYU’s professional development school estimates that for the average potential enrollee the demand for courses that they take is given by q=190-15p where q is the number of courses taken and p is the price per course. Suppose that the cost of administering and providing the course is a constant marginal cost of 10 per student.

a) What is the profit maximizing price for a course? b) What is the elasticity at this price? c) Suppose that NYU is considering introducing a fixed registration fee in addition to the

per course charge (i.e., a two-part tariff). Would you recommend such a change in the way that NYU charges its students? Would the price per course change? What fixed fee would you charge?

9. SpokenWord Your software company has just completed the first version of SpokenWord, a voice-activated word processor. As marketing manager, you have to decide on the pricing of the new software. You commissioned a study to determine the potential demand for SpokenWord. From this study, you know that there are essentially two market segments of equal size, professionals (one million) and students (two million). Professionals would be willing to pay up to $400 and students up to $100 for the full version of the software. A substantially scaled-down version of the software would be worth $50 to students and worthless to professionals. It is equally costly to sell any version. In fact, other than the initial development costs, production costs are zero.

(a) What are the optimal prices for each version of the software?

Suppose that, instead of the scaled-down version, the firm sells an intermediate version that is valued at $200 by professionals and $75 by students.

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(b) What are the optimal prices for each version of the software? Is the firm better off by selling the intermediate version instead of the scaled-down version?

10. Equality and night-club pricing – “Barmy Brussels Battles Bars” We read with interest that there is discussion of new legislation being introduced throughout the European Union aims to end differential pricing between males and females, this being viewed as a discriminatory practice. One of the leading firms in the industry, BANCA, the European-wide Bars and Nightclubs Associated, which has considerable market power in this industry, has protested arguing that such legislation would a have severely detrimental effects on the profitability and viability of its business. Moreover, BANCA argues that its customers would suffer through the introduction of such legislation. In no more than a paragraph for each point, discuss

(a) How one might try to assess the extent to which customers might lose or benefit from the current arrangement;

(b) What might account for the current pricing arrangements; and, (c) Whether there are any particular features of this industry which one might take into

consideration. 11. Market shares. The following tables summarize 2001 market shares for investment banking and credit cards (data courtesy Mike Mayo’s March 2002 analyst report on Citigroup for Prudential Financial):

(a) Compute the HHI for each of these markets. (b) What would the DOJ merger guidelines suggest about a merger between Goldman

Sachs and Merrill Lynch? (c) What would the DOJ merger guidelines suggest about a merger between Banc One and

American Express?

© 2012 Stern School of Business.

Investment Banking (Fees)

Goldman Sachs 13.7% Morgan Stanley 11.2% Merrill Lynch 11.0% Citigroup (SSB) 10.4% CSFB 9.5% JP Morgan 6.9% UBS Warburg 4.5% Lehman Brothers 4.4% Deutsche Bank 3.4% Dresdner Kleinwort 3.4%

Credit Cards (Receivables)

Citigroup 18.0% MBNA America 13.5% First USA/Bank One 12.3% American Express 9.3% Discover 8.7% Chase 7.4% Providian 5.9% Capital One 5.8% Bank of America 5.1% Household Bank 2.9%

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Practice Questions II 1. Specialized computer chip You are currently the only producer of a specialized computer chip used in computer animation, but are concerned that your success might attract competitors. You are now considering a major investment in capacity that would reduce your marginal cost below that of any potential rival. The impact of the investment on your strategic position is summarized below:

If you do not make the investment, you expect to make $20m if competitors enter, and $50m if they do not. Your potential competitors, on the other hand, expect to make $10m if they enter, nothing if they do not.

If you do make the investment, you expect to make $10m net of the investment if competitors enter, and $40m (also net) if they do not. Your potential competitors, on the other hand, expect to lose $2m if they enter, nothing if they do not.

Use a “game tree” to study this game and come up with a recommendation on whether to make the investment or not. Comment specifically on this advice from a high-paid consultant: “Investment lowers your payoffs when there is entry and when there is not. It’s a mistake.”

2. Biological MicroProcessor It’s 2016 and the biological microprocessor, for so long a mere promise of science fiction, has finally become a commercial possibility. Intel and archrival AMD ponder the pros and cons of moving ahead with a massive research effort to switch from conventional to biological microprocessors.

Currently, Intel is making an annual profit of $3.2bn, whereas AMD’s profit is $500m. Analysts expect that, if Intel goes alone with the biological program, their profits will drop to $2.8bn, whereas AMD’s will drop to $400m. If however AMD moves alone, then AMD will increase its net profits up to $1.2bn, whereas Intel will drop to $1.8bn. Finally, if both firms initiate their own biological microprocessor programs, then expected profits are $1.6bn for Intel and $100m for AMD.

a) Describe the game played between Intel and AMD if the two firms have to make their decisions simultaneously. Determine the equilibrium of this game.

b) Suppose that Intel has the possibility of credibly committing to a course of action before AMD observes Intel’s choice and makes its own choice. Describe this new game and determine its equilibrium.

c) What is the value of commitment here? 3. Repeated Bertrand Suppose that in an industry there are 3 firms competing in prices. Their marginal cost is the same, constant and equal to 100. The demand is given by Q = 1000 – P.

a) What is the outcome of this game if the market exists just for one period?

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b) Suppose instead that these firms are on this market for the long run, and they play the Bertrand game infinitely many times. At every period there is the same demand, and firms can reset their prices. Suppose that the interest rate is r = 5%. Can cooperation be sustained?

4. On campus corporate presentations: Sympathy for the Devil Many students complain about the high number of corporate presentations taking place both on and off-campus. In this question, we seek to explore this phenomenon.

Suppose that Stern is playing a game with other business schools (to be specific, think of Columbia). Both schools are concerned with ensuring that their students find gainful employment at the end of their courses of study. Specifically, suppose that they assign a value of 100 from doing so. Suppose that if neither or both schools allow corporate presentations, then recruiters are equally likely to hire from either school; however, if only one school allows presentations then its students are likely to be hired with 75% probability, whereas the other school’s students chances of getting hired fall to 25%. Allowing corporate presentations takes time, which could be used for additional classes or recreational activities to which the school assigns a value 10.

a) Describe the elements of this game. What would you expect to be the outcome? b) A limitation of the analysis in (a) is that this game is played out by Stern and Columbia

every year. Suppose that each has an annual interest rate of 5%. It is possible to achieve a better outcome than in a). Explain how and illustrate your argument formally (that is, if you argue for a different equilibrium then prove that this is indeed an equilibrium).

c) Can you think of any factors that might make it difficult to achieve this better outcome? That is, are there any limitations or anything missing from this description of the game?

d) In the remainder of the question, we highlight a different aspect of on-campus presentations. Specifically suppose now that recruiters prefer to speak to full rooms rather than empty ones. If speaking to empty rooms, in a pique of annoyance the recruiter will not hire from the school (more likely they will not return the following year). Suppose moreover that there are ten genuinely interested students, who will come to the presentation and each of whom values the presence of a happy recruiter at 15, but an unhappy one at 0, but for the other 90 students there is an opportunity cost of 1 in coming to the presentation whether the recruiter is happy or not (they would rather spend their time reviewing Firms and Markets). What would be the result? Can the school do anything, which would raise overall welfare?

5. Suits R Us “A new breed of investment firm is capitalising on the boom in litigiousness and taking a piece of the profits. [These firms] underwrite lawsuits in exchange for a share of proceeds.” (Financial Times, Dec 3, 2001.) One example is Suits R Us. Potential plaintiffs come to them with cases. For each one, SRU decides whether or not to take it; if so, it offers a standard percentage rate contract. Given

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Practice Questions 38

SRU’s experience with many previous cases, the firm has a better idea than most plaintiffs of the odds that the case will win in court.

(a) Suppose you have a potential case in hand (in which you would be the plaintiff). What

considerations should you take into account when deciding whether to apply to Suits R Us?

(b) Name two other situations that lead to similar problems.

6. Buffett and GE Paraphrased from the Wall Street Journal (November 13, 2002): GE is apparently trying to sell Employers Re, its huge reinsurance operation. Reinsurers provide insurance to insurers, allowing insurers to spread their risks or cap their potential losses. The top 3 players in this business are Munich Re, Swiss Re, and General Cologne, which is controlled by Warren Buffett’s Berkshire Hathaway. GE CEO Jeffrey Immelt stated that Employers Re was a business he wanted to “reposition for value” – translation: consolidate, sell, shrink or fix. Why? Employers Re was a big money maker after its 1984 acquisition by GE, but has become a trouble spot of late. In October, GE said that Employers Re expects a 2002 loss of $350 million to $450 million, and break-even results in 2003.

Selling the business has proved difficult. A public offering was derailed by a sour IPO market and steep losses in the unit. Observers also cite concerns about the adequacy of the unit’s claims reserves and Employers Re’s own use of reinsurance. A large reason for concern about reserves is mounting asbestos litigation, which is adding billions of dollars to the insurance industry’s already huge exposure. Concerns about reinsurance revolve around Employers’ purchase of “financial reinsurance,” which is known for smoothing earnings as well as spreading risk. Under its typically complex terms, the purchaser often pledges future investment income to the reinsurer selling the coverage. Berkshire’s National Indemnity unit is one of the biggest providers of financial reinsurance.

With Munich Re, Swiss Re, and some other potential bidders in financial distress, Berkshire may emerge as the only bidder. Berkshire would likely wind down much of Employers Re’s operations, using its own claims-handling expertise to try to save money along the way, and squeeze bigger profits out of the parts it keeps. Analysts suggest that Mr. Buffett isn’t likely to do the deal unless it looks like a no-lose situation. Any deal, therefore, is likely to include limitations on how soon Berkshire would pay losses on the policies it acquires or some other sort of cap on payments.

(a) Why might GE want to sell Employers Re, even though in the current market it’s likely to be forced to accept poor terms?

(b) Why might Employers RE be worth more to Buffett than to GE? (c) What problems do you see to completing a deal? What solutions would you

recommend to resolve them? © 2012 Stern School of Business.

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Lecture Notes 39

Introduction to Firms and Markets The goal of this course is to give you some insight into how markets work. The course is structured in two parts. In the first part of the course, we study decision making by consumers and firms. We explore the fundamentals of demand and identify categories of costs that firms must consider when taking critical business decisions like pricing, exit or market entry. We study how supply and demand determines prices in efficient markets. We learn about market power and how the interplay between cost and demand fundamentals determines profit-maximizing decisions for firms. The second part of the course focuses on situations where, for one reason or another, markets don‘t work efficiently. Here, we emphasize the importance of strategic behavior, as modeled by game theory. Strategic interactions between firms in markets can be represented as games and we learn to predict the outcomes of such games and analyze how best firms can respond to their rivals‘ strategies. We discuss the basics of competition (how do firms compete on price?) and cooperation (how do firms collude?), asymmetric information (what happens when sellers know more than buyers?) and market design (auctions). Microeconomics (as the broad topic of this course is often called) is an important component of an MBA program. First, microeconomics focuses on specific dimensions of optimal firm decision making, such as pricing, entry and exit. Second, the formal economics perspective on business plays an important role in other fields of study, such as finance or marketing. Finally, by studying public policy towards market failures, microeconomics highlights important factors conditioning firm strategy. Our experience with students in prior years is that much of what we learn in this course is intuitive. But much is not, and our hope is that the combination of theoretical structure and practical examples will be useful to you in the years to come. It will not make you a success on its own, but it might give you an edge a few times when it matters! Business can be viewed from many perspectives, including those of sociology and psychology. Economists tackle the subject by adopting a formal, explicit analysis of decision-makers that is based upon a number of assumptions. First, we assume that individuals make rational decisions to maximize some objective given a range of feasible choices. For example, firms might maximize profit or consumers might maximize ―utility‖ (a catch-all to include whatever they care about). Secondly, we generally assume that a firm is a single decision-maker with a clear objective. Third, we assume that most economic interactions take place in markets, where buyers and sellers interact through price. All of these assumptions are questionable, and perhaps even wrong, but they bring some clarity to our analysis that we feel is useful. Our task is therefore to determine how individuals define their goals and examine the actions they take to attain those goals, and then analyze the outcomes that result from their actions. We focus on how buyers and sellers interact through markets, how firms adopt strategies to

Firms and Markets Lecture Notes

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Lecture Notes 40

interact with each other, how competitive forces bring resources to their most profitable use, how these same forces can make it difficult to sustain above-average profits, and how governments set rules to limit the power and influence of individual firms. The trick in all of this analysis is to simplify (eliminate nonessential complications) without losing the flavor of the situation being examined. It‘s a delicate balance, and one that makes the subject of this course as much art as science. Markets Markets are incredibly numerous and varied. The New York Stock Exchange is one prominent local market, but so are the farmer‘s market at Union Square and the markets for pharmaceuticals, cable TV programs, and consulting and legal services. Markets can be highly regulated, such as the US aerospace procurement market, or as informal as buyers and sellers haggling over cheap sunglasses on a street corner. Our formal definition of a market is a collection of buyers and sellers who interact in transactions for a product or a set of products. Although we tend to focus on ―a market,‖ in practice it‘s not easy to decide where one market begins and another ends, either geographically or in the range of products. Are Balducci‘s and the Union Square farmers in the same market? It depends on the issue. This is more than a theoretical nicety. The Staples/Office Depot anti-trust case, which effectively ended their proposed 1996 merger, hinged on precisely this issue. Was WalMart part of the same market (in which case the combined firm would have a small market share) or not (in which case the market share in many areas was substantial)? The courts ruled ―not‖, agreeing with the FTC that the merged company would have an unacceptably high market share in many locations. Markets (once we agree on their boundaries) differ along many dimensions: the number of buyers and sellers, the degree of differentiation among products, the transparency of market transactions, and so on. On one end of the spectrum, we consider ―perfectly competitive‖ markets, in which many buyers and sellers of a uniform product make transactions in transparent markets. In a perfectly competitive market the large numbers of buyers and sellers means that no individual firm has any meaningful control (―market power‖) over the price. It‘s an extreme case, but illustrates the impact of competitive forces. Managers abhor such markets, since competition makes it very difficult to make money. Such products are referred to disparagingly as ―commodities,‖ since commodity markets are often good examples (wheat, basic steel, photocopy paper). At another end of the spectrum, markets with one seller are referred to as ―monopolies.‖ Monopolies are said to have market power, generally restricting output and setting prices above what we‘d see under perfect competition. Famous near-monopolies over the years include Standard Oil at the turn of the century, Deutsche Telecomm, and DeBeers (a monopoly distributor of diamonds). While some markets lie at the extremes, the majority are located somewhere in between. We refer to markets with a few sellers as ―oligopolies.‖ These markets are much more common. They‘re also more interesting and challenging to study, since some oligopolies are extremely competitive, while others behave much like monopolies. Hence a central issue for us will be to understand the features of a market that make it more or less competitive.

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Firms The large business firm is one of the distinguishing features of the modern world. For the last century or more, many products have been made and sold by large organizations. The MO course is devoted, in part, to how such large collections of people work. We operate at a more ―macro‖ level, treating each firm as a single object maximizing (say) profits. More on this shortly. Like markets, firms are diverse along many dimensions, including geographical span (think of Coca-Cola versus the Campus Eatery), in span and scope of product offerings (General Electric versus a shoe store), and in degree of vertical integration. Over the course of this class, we will learn about many distinguishing characteristics that lead to differentiation and competition among firms. In focusing on firms, we make an important assumption about firm behavior: firms and managers maximize profits or shareholder value (we think of them as the same thing). Does this make sense? On the face of it, how can the 100,000 employees of Citigroup be thought of as working together to maximize anything? Why would the managers of General Electric work for the good of shareholders? How can the shareholders know whether the managers are doing this or not? Although we own a few shares of many firms through mutual funds, we do not have the time or resources to monitor management‘s actions, other than what we read in the New York Times or Wall Street Journal. And even though Boards of Directors are ostensibly looking out for our interests, they are rarely independent from the CEO and perhaps other top operatives in the company. How, then, might we defend profit maximization? We might argue, first, that Darwinian competition will weed out the firms that don‘t. Or we might argue that managers do this to maximize their own reputations, and that competition leads managers with good reputations to be paid better. Perhaps the most compelling argument is based on capital markets: firms that do not maximize value will be taken over and their management replaced. None of these arguments is watertight, but they give us some hope that the assumption is, at least, a reasonable approximation. It Depends There is an old joke that people love to tell about economists. Harry Truman, the joke goes, once asked for a one-armed economist. His advisors asked: ―Why one arm?‖ ―Because,‖ Truman remarked, ―economists always answer questions with: on the one hand it's this, on the other hand it's that. For once, I'd like to have an economist who will give me one straight answer.‖ We need to tell you now: If you're looking for the one-armed economist, this isn't the course for you. Economics is not a set of answers. It is, instead, a framework for thinking about questions systematically. It will not give you the answer, but it will allow you to ask the right questions. The answer to most questions in this class is, then, ―It depends.‖ After taking the course, you will be able to say what it is they depend on.

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Calculus Review In microeconomics, calculus gives you a sharper understanding of (among other things) elasticity and pricing. You can learn microeconomics without calculus, but the logic is invariably less clear. The same is true in some other fields. In finance, for example, calculus is the natural tool for understanding portfolio choice (the minimum variance portfolio) and bond duration (the sensitivity of price to yield). What follows is a short, (relatively) non-technical review of the aspects of calculus needed for the course. Functions In economics, we often use relations between two variables: demand depends on price, cost depends on quantity produced, and so on. We call these relations "functions." Formally, a function f assigns a (single) value y to each possible value of x. We write it this way: y = f(x). In a spreadsheet program, you might imagine setting up a table with a grid of values for x. The function would then be a formula that computes y for each value of x. Perhaps the easiest way to think about a function is to draw it: put x on the horizontal axis and plot the values of y associated with each x on the vertical axis. Some examples are given in Exhibit 1. We'll generally be interested in functions that are "continuous" [they don't have "jumps," as in (b)] and "smooth" [they don't have "kinks," as in (c)]. Exhibit 1: Examples of Functions

Firms and Markets Lecture Notes

y = f(x)

x

(a)

(b)

(c)

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Lecture Notes 43

Slopes and Derivatives The "slope" of a function is a measure of how steep it is: the ratio of the change in y to the change in x. For a straight line, we can find the slope by choosing two points and computing the ratio of the change in y to the change in x. For most functions, though, the slope is different at every point. Take Example (a) in Exhibit 1, for example. The slope is initially positive as the function increases, then turns negative as the function slopes down, then turns positive again at the end. Suppose that f(x) is something like profits that we want to maximize. We are looking at a function like the one below, trying to find the value of x (that we will call x*) where f(x) is the biggest. It might be a whole number, x*=6 or x*=7. It might also be a messy number, like x*=6.2223453443. (Using discrete methods, you can check at 1, 2, 3, 4, …. but not at more messy numbers.) But, if we have an easy way of calculating the slope of the line, we have an easy way of finding x*: it‘s the point at which the slope is equal to zero. (Think of f(x) as being a kind of hill that you are climbing, starting at x=0; the slope goes up for a while, then it is zero once you reach the top of the hill, then it slopes down for a while. Sloping up is a positive slope, sloping down is a negative slope.) y=f(x) x* x What is a slope? It‘s an easy concept for a straight line, since a straight line has a constant slope. On a straight line, start anywhere and then increase x (by any amount). The slope is the amount y goes up, divided by the amount x went up:

y/x =[f(x+x)-f(x)]/x

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Let‘s take an example: y = 3x + 1. And we graph the line: Exhibit 2: y= 3x+1 y y=3x+1 1 2 x For example if you are initially at x=0, then y=1. If you move to x=2, then y=7 at that point.

So the slope is 302

17

x

y. But I could also have chosen two points very close to each

other: For example if you are initially at x=1, then y=4. If you move to x=1.05, then y=4.15 at

that point. So the slope is 3105.1

415.4

x

y, the same slope. Now suppose that you have a

curvy line: for example, y=x2. Then the slope is different at every point. Exhibit 2: y= x2

1 1 x Now, to get a measure of slope that is as accurate as possible, you need to choose two points that are incredibly close together: Let‘s say we want the slope at x=1. Let‘s look at x=1 (where

1

4

7

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Lecture Notes 45

y=1) and x=1.0001 (where y=1.00020001); the rough measure of slope that we get is

0001.210001.1

100020001.1

x

y. The closer you pick the second value of x to 1, the closer you

get to a slope of exactly 2.

The "derivative" dx

dy of a function f(x) gives us its slope at each point x if the function is

continuous and smooth. Formally, we say that the derivative is x

y

as x gets "incredibly

small." We write the derivative as f (x) or dx

dyor

dx

xfd )(. In the latter case, the d's are

intended to be suggestive of small changes, analogous to y/x but with the understanding that we are talking about small changes in x. There are formulae you can just use for the derivatives that we are going to use. If they're new to you, don't try to make sense of them. Take them as facts to be memorized and put to work. (Exhibit 4 tells you how we got the formulae, if you‘re interested. And Exhibit 5 gives you more formulae you can use, in future classes.)

0)10(

dx

d If y=10, that‘s a flat straight line, and the slope is zero.

5)5(

dx

xd If y=5x, when you take the derivative, you just drop the x.

xdx

dx2

2

If y=x2, when you take the derivative, you ―bring the 2 down in front‖.

Notice that this is what we found in Exhibit 3, looking at the curve y=x2: when x=0, the derivative is 2 times 0, which is zero; that is, the line is flat. When x=1, the derivative is 2 times 1, which is 2. So if you have a line that is y= 3x + 1, you take the derivative of each bit in turn, and you get

3)13(

dx

xd, which is what we found in Exhibit 2.

If you have a line that is y=5x2 + 4x + 7, the derivative is 410 xdx

dy.

Examples. Find the derivatives of the following functions [answers in brackets]:

2x + 27 [2]

2x2 + 3x +27 [4x+3]

2x2 + 3x – 14 [4x+3]

(x–2)(2x+7) [4x+3]

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Lecture Notes 46

Technical point. If the function has jumps or kinks, the notion of slope simply doesn't make sense at those points. Take Example (b) in Exhibit 1. What is the slope where the function jumps? We could find the slope just to the left of the jump, or just to the right, but not at the point where it jumps. Similarly, it's not clear what the slope is at the kink in Example (c). We say, in these cases, that the derivative doesn't exist. We'll make sure that most of our functions are continuous and smooth so that this hardly ever happens. Finding the Maximum of a Function Now to our purpose. We'll often want to know the value x that produces the maximum value of a function f(x) for x between (two numbers) a and b. We do this by setting the derivative

f(x) equal to zero and solving for x. Why does this work? You can see in Example (a) of Exhibit 1 that a function is flat (has zero slope) at a maximum. We will use this insight. Example. Find the maximum of this function: Profits (Q) = -Q2 + 9Q – 4, with respect to Q. (What does that mean? That means Profits are a function of Q, and I want to know the slope as Q changes; Q is like the ―x‖ term.)

The derivative is 92)49( 2

QdQ

QQd. So, at the optimal Q*, the derivative is zero,

and so that means -2Q* + 9 = 0, which I solve to get Q*=4.5. Profits are maximized by producing exactly 4½ (say we are measuring quantity in tons, this is four-and-a-half tons). Profits 4.5 Q -4 Try a couple: Find the maximum of

-5x2 + 2x + 11 [f (x) = -10x+2 = 0, x = 5]

function (a) in Exhibit 1 [there are two points with zero slope, but only the first is a maximum]

Profits = - 2Q2 + 5Q + 12

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Lecture Notes 47

Technical aside. Does this always work? If we set the derivative equal to zero, do we always get a maximum? The answer is no. Here are some of the things that can go wrong: (a) The point might be a minimum, rather than a maximum. For example, in Example (a) of

Exhibit 1 the function has both a maximum and a mimimum. Both have derivatives/slopes of zero.

(b) The maximum could be at one of the endpoints, a or b. There's no way to tell without comparing your answer to f(a) and f(b).

(c) There may be more than one "local maximum" (d) The slope might be zero without being either a maximum or a minimum: for example, the

function might increase for a while, flatten out (with slope of zero), then start increasing again. An example is the function f(x) = x3 at the point x=0. [Draw this to make sure you understand the point.]

All of these things can happen in principle, but our job is to make sure they don't happen in this class. (If you want to be extra careful, there are ways to check for each of these problems. One is the co-called second-order condition referred to in our notes.) Maximizing Profit Here's a common application. Suppose a firm faces a demand for its product of q = 10 – 2p (q and p are quantity and price, respectively). The cost of production is 2 per unit. What is the firm's profit? What level of output produces the greatest profit? Answer. Profit is revenue (pq) minus cost (2q). The trick is to first express it in terms of quantity. We need to use the demand curve to eliminate price from revenue: p = (10-q)/2 so pq = [(10-q)/2]q. Profit (expressed as a function of q) is therefore

Profit(q) = [(10–q)/2]q – 2q = 5q – q2/2 – 2q. To find the quantity associated with maximum profit, we set the derivative equal to zero:

Profit(q) = 3 – q = 0, So q = 3. What's the price? Look at the demand curve: if q = 3, then p satisfies 3 = 10–2p, so p = 7/2. [Please check!!] Further Reading There are lots of good calculus books. One good review is

Bernard Zandy, Cliffs Quick Review Calculus, Cliffs Notes, 1993

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Lecture Notes 48

Exhibit 4: Rules for Differentiation

Function f(x) Derivative f(x) Comments

Rules for Combinations of Functions

g(x) + h(x) g(x) + h(x)

ag(x) + bh(x) ag(x) + bh(x) a and b are numbers (constants)

g(x)h(x) g(x)h(x) + g (x)h(x)

g(x)/h(x) [g (x)h(x) – g(x)h(x)]/[h(x)]2

g[h(x)] g[h(x)]h(x) "chain rule"

Rules for Specific Functions

a 0 a is a number

ax + b a a and b are numbers

axn anxn-1 a is a number, n an integer

aebx abebx

a log x a/x a is a number, log means "natural log"

Exhibit 5: Where do the formulae come from? When we talk about the slope of a curvy line at a particular point, what do we mean? The simplest way to think about it is to relate it to the slope of a straight line. At any given point, say x=1, there is a line that is parallel to the curve at just that point; in other words, it has the same slope as the line at that point. (We call that line the tangent.) So when we talk about slope, we mean the slope of the tangent line. y= x2

1 1 x

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Lecture Notes 49

One ―geometry‖ way of getting the tangent line at x=1 is to draw the line between x=1 and another point on the curve, say x=2; then draw the line between x=1 and x=1.5; then, between x=1 and x=1.2, and keep getting closer. The closer you get, the closer you get to the tangent. 1 1 x Now it is easy to find the slope of the line that goes between x0=1 and another point, x1; the

slope is simply 01

01

xx

yy

. So, if your two points are x0=1 (which means y0=1) and x1=1.2

(which means y1=1.22=1.44), then the slope of the line between those two points is

2.212.1

144.1

01

01

xx

yy.

That means that as I choose a point x1 that is closer and closer to x0, I will get a slope that is closer and closer to the slope of my tangent. In math terms:

01

01

at 01

0

limxx

yy

dx

dyxx

x

and we use this to calculate the derivative. So, for example, let‘s take the function y=f(x)= 3x+1. We want to find the derivative of this function at some point x0. It is:

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Lecture Notes 50

3

3lim

1313limlim

01

01

01

01

01

01

at

01

0101

0

xx

xx

xx

xx

xx

yy

dx

dy

xx

xxxx

x

And so we find that the slope is 3, no matter what specific point x0 we were interested in. Let‘s take another example, the function y=f(x)=x2. We want to find the derivative of this function at some point x0. It is:

0

01

01

0101

01

2

0

2

1

01

01

at

2

)(lim

))((lim

)()(limlim

01

01

0101

0

x

xx

xx

xxxx

xx

xx

xx

yy

dx

dy

xx

xx

xxxx

x

(factorizing)

Because x1 gradually becomes x0. So, if I want to know the derivative at point x0=1, I plug that in, and I get 2. Net Present Value (NPV) When the interest rate is r, the net present value of a cash flow X0, X1, X2, … , Xn is

In particular, if n=∞ and X0= X1= … =X, then

Thus,

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Lecture Notes 51

Supply and Demand: Buyers, Sellers, and Markets

There are many situations in which you might want to ask: What is a reasonable price for a product X? You might be an equity analyst trying to value a firm that produces X. Or you could be a consultant trying to evaluate the benefits for a client of entering the market for X. Or you could be a venture capital investor trying to assess the prospects of a startup planning to produce X. A glib answer is to look at the market's current price, but there are times that's not enough. It's not enough, for example, in a market that does not yet exist. And it‘s not enough when you think the current price is likely to change. When production at Canada's Diavik diamond mine comes online in 2003, what is the likely impact on the price of diamonds? What is the impact on airline fares of an increase in the price of jet fuel? The supply and demand diagram is the basic tool of analysis for addressing such questions. In this lecture, we describe the tool and explain how to use it. A critical distinction is the difference between movements along curves and factors that cause one or both of the curves to shift. Unless you've had economics before, this will sound a little mysterious, but it should be less so by the end of class. In future lectures, we go into greater depth on the supply and demand curves themselves. Buyers: Demand You might think of demand as summarizing buyers‘ willingness to buy a product at various price points. As the price decreases, generally more people were willing to buy more units. A ―demand curve‖ represents graphically the relationship between quantity desired and price: the number of units people are willing to buy (―the demand‖) at a given price. By tradition, we graph this relation with price on the vertical axis and quantity on the horizontal access. This can be confusing, but it‘s hard to break a century-old habit among economists. The demand curve is normally downward-sloping, meaning that more people are willing to buy a good if the price is lower. Similarly, if someone is willing to buy a product at one price, he or she is generally willing to buy it at a lower price, as well. The location and shape of the demand curve depend on people‘s tastes. Hence the demand for cod fish is greater in Portugal than it is in Japan, and the demand for rice is greater in Japan than Portugal. The demand for wireless phone service is relatively sensitive to price (the demand curve is flat) but the demand for basic service is not (steep), since people are less willing to forgo basic service to save money for other uses. We often represent the demand curve as a straight line, but that's only a graphical convenience. The quantity of a product people are willing to buy depends, of course, on more than price. It can depend on the prices of other products, the incomes of buyers, the age distribution of the population, and lots of other things. We represent all of these other factors in a ―demand

Firms and Markets Lecture Notes

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Lecture Notes 52

function,‖ in which quantity demanded is a mathematical function of as many of these other variables as we need. (Pay close attention to what‘s coming!) The question is how to picture changes in these variables in a diagram with price and quantity on the axes. We do so by shifting the demand curve up or down when these other variables change. The demand curve gives us the relationship between price and quantity for given values of the other variables. If any of these other variables changes, the demand curve shifts. Now to some examples. Prices of other goods often affect the quantity demanded. For example, if the price of Coke rises, we might expect the quantity of Pepsi demanded to increase at any given price. The demand curve for Pepsi shifts up and to the right. We say that Coke and Pepsi are ―substitutes‖ since an increase in the other's price leads to an increase in demand. If the dependence goes the other way, we call the products ―complements.‖ For example, if the price of gas goes up, we would expect the demand for SUVs to decline. Population and income also affect demand. For example, the demand for undergraduate education is increasing due to a demographic bulge of people of college age. We could represent this as a shift up/right of the demand curve for education. Income also affects demand for many products, with more people willing to buy higher-price goods as income increases. In the UK, for example, the demand for relatively déclassé vacations in Southern Europe has declined as people have become prosperous enough to afford vacations in Florida and the Caribbean. We can represent this as a shift down/left in the demand curve for European vacations. Advertising can also have an impact on demand, by raising the visibility and perceived quality of products. Sellers: Supply The ―supply curve‖ represents the quantity sellers are willing to sell at different prices for given values of other variables. The supply curve is generally upward-sloping since companies will be willing to produce and sell more of a good as prices go up. For example, crude oil producers supply more oil at higher prices, since a higher price makes more wells profitable. Markets differ in how steep the curve is. A high price of electricity has elicited little immediate increase in supply in California (the supply curve is steep, at least in the short run). But if there were a sudden increase in the demand for basic blue jeans, we would expect producers to meet it with little increase in price (supply curve is flat). Like demand, supply is affected by factors other than price and we represent changes in these factors by shifts in the supply curve. One such factor is input prices. If the price of jet fuel rises, we would expect it to increase the price at which airlines are willing to sell tickets (the supply curve shifts up). Technology also affects the supply curve. If improvements in technology reduce costs of production, then we would expect the supply curve to shift down/right. Nature can also play a role. For example, an earthquake that destroys some of the market's capacity would result in a shift left/up in the supply curve. This happened in the semiconductor market after the 1999 earthquake in Taiwan. The number of suppliers also affects supply, with more suppliers tending to mean greater quantity supplied at any given price. Similarly, an investment in a new plant would result in a shift right/down in supply.

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Once again, it is important to distinguish changes in price from changes in other factors. The former is a movement along the supply curve, whereas the latter results in a shift of the whole supply curve. Market Equilibrium The price of a product is the result (in market settings) of the interaction of buyers (demand) and sellers (supply). We refer the point at which the supply and demand curves intersect as ―equilibrium.‖ See Exhibit 1. It‘s an equilibrium in the sense that none of the market participants have an incentive to change their behavior: buyers are buying what they want at that price (the point is on the demand curve) and sellers are selling what they want (it‘s on the supply curve). If the price were higher than the equilibrium price, fewer people would want to buy than sell. The excess of sellers would tend to drive the price down. Conversely, if the price were lower than the equilibrium price, fewer people would be willing to sell than buy. The excess of buyers would cause the price to tend to rise to the equilibrium price. We thus have an answer to one of the questions with which we started: a reasonable price is one at which demand and supply are equal. In practice, we need to know what the supply and demand curves look like, which requires both data and enough expertise and judgment to construct the two curves. But the logic is just what we've described. Creating Surplus Perhaps it‘s not immediately obvious, but trade creates surplus. If trade is voluntary, this has to be true, or people wouldn‘t do it. But we can be more precise in the case illustrated by Exhibit 1. For buyers, the demand curve represents their willingness to pay. The difference between the demand curve and the market price (labeled ―A‖ in the exhibit) is thus surplus to buyers; we call it ―consumer surplus.‖ Similarly, the difference between the price and the supply curve represents surplus to sellers: the difference between the market price and the price at which they‘d be willing to sell (labeled ―B‘‘). We call it ―producer surplus.‖ Total surplus generated by trade is the sum of the areas A and B. Comparative Statics Our other questions concerned changes in market conditions. If the demand or supply curve shifts due to changes in one of the ―other‖ factors discussed above, then a new equilibrium price will be established. The term ―comparative statics‖ is used by economists to describe the exercise of looking at what happens to equilibrium if an exogenous factor changes. We would represent this by shifting the supply or demand curve and noting the change in the equilibrium price and quantity. If you work through an example, you‘ll see that the impact on price depends on the slopes of the supply and demand curves. The effect of a shift in the supply curve depends on the slope of the demand curve. (This sounds a little strange, but it‘s true because the demand curve hasn‘t shifted, so the change in equilibrium is a movement along the demand curve.) If the demand curve is steep, price will react more to a shift in supply than quantity. If the demand

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curve is flat, the impact of a shift in supply will be predominantly on quantity. For shifts in demand, the impact depends on the slope of the supply curve. Thus a key ingredient to any market analysis is an assessment of the slopes of the supply and demand curves: how sensitive the decisions of buyers and sellers are to changes in price. Consider the California electricity market. Supply is virtually fixed, since the capacity of local power plants can‘t be changed much without building new ones. Similarly, the lines to bring in power from other states also have limited capacity. Hence the supply curve is very steep (vertical?) and the impact of an increase in demand (the result of growth of the California economy) is reflected almost entirely in the price. Another example is the September 20, 1999 earthquake in Taiwan, which damaged plants producing a substantial fraction of the world's 64 MB DRAM chips. This can be viewed as a left/up shift in the supply curve (a reduction in supply). The price of the chips increased about 50%, from which we might infer that the demand curve for chips is fairly steep. See Exhibit 2. A third example is copper, whose quantity has increased substantially while price declined slightly over the last century. (This is a general property of primary commodities: their prices have tended to go down, not up, over time.) How is this possible? One explanation is that demand has increased as the world economy has grown, but supply has shifted, too, as new technologies make copper extraction more efficient. In other words, both the supply and demand curves have shifted to the right, with supply shifting slightly faster. Example Vitamin C is a generic vitamin that is produced by many companies: brand names are not very important, entry is easy. A good friend – a world-renowned orthopedic surgeon from New Jersey – tells you that he is about to publish in The New England Journal of Medicine (a highly respected and widely quoted medical journal) a study indicating that daily doses of 500 mg of vitamin C tends to improve the muscle tone and increase the physical stamina of adults, with no adverse side effects. Though a very good doctor, he is woefully ignorant about the basic workings of markets and wants to know what is likely to happen, and why – in the short run and in the long run – to the price of vitamin C, to the quantity sold, to the profits of the producers, and to the number of firms that produce it. Summarize what you would tell him. Answer. One would expect demand to increase as a result of the NEJM article. In the short-run, supply is fixed. So, we will observe a move along the supply curve, with both price and output going up. The extent of the price hike depends on the steepness of the supply curve: the steeper the short-run supply curve is, the greater the price increase. In the long-run, one would expect the supply function to expand, as new producers enter the market and existing producers expand their capacity. Assuming that demand is kept at the same level, this would correspond to a movement along the demand curve, with output going up and price going down. To summarize: We would expect price to go up in the short-run, then back down in the long-run, possibly to almost the same level as the initial level. As to output, we would expect it to go up, with a greater increase in the long-run than in the short run.

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Exhibit 1 Supply and Demand Comment: Price and quantity tend to adjust until buyers (demand) are reconciled with sellers (supply) at ―equilibrium‖ with price p* and quantity Q*. The triangle marked ―A‖ represents consumer surplus, the triangle ―B‖ producer surplus. Exhibit 2 Impact of Taiwan Earthquake on DRAM Market Comment: Earthquake shifts supply left/up, resulting in rise in price and fall in quantity. Note that the impact depends on the shape of the demand curve.

Price

Quantity

Demand

p*

Supply

Q*

Price

Quantity

D

p

S

Q

S′

Q′

p′

“Equilibrium”

E

E′

B

A

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Utility An existing or new business needs to have some idea how a customer might decide whether or not to buy their product. The relevant concept is ―utility‖, or the units of ―happiness‖ that a customer gets from owning the product.1 We think of consumers as wanting lots of ‗stuff‘, but having to make tradeoffs in their budget between different kinds of stuff, and tradeoffs between stuff and investments (such as an MBA). There are different ways to represent these tradeoffs…In class we will concentrate on the most basic way, ―money-metric utility‖. For other applications (especially Finance) you will need slightly more sophisticated concepts of utility. We‘ll start with the more sophisticated notion of utility, because it will be easier to see when you can use money-metric utility, and when it‘s a bad idea. A. Utility and Risk Let‘s suppose that having more stuff actually does make us happy (because we act as though it does, contrary to all psychological evidence), and let‘s say that we can measure that happiness in units called ―utils‖. So, in my case, the first latte of the morning gives me 10 utils, and the fifth latte of the morning might give me just 1 util, or maybe even negative utils. Measuring utility in ―utils‖ allows us to start thinking about risk. Let‘s say that your grandmother gives you a birthday check for $300, and you know exactly what you want to spend the money on; let‘s say you‘ll get 400 utils from the stuff you will buy with the $300. Suppose instead your grandmother had given you a check for twice as much, $600, you would be happier, but probably not twice as happy (because the things you wanted the most urgently, you would have bought with the $300, so the extra $300 gives you less). You might get 800 utils from the stuff you could buy from $600. If she gave you $900, you might get 1000 utils. Your utility from different amounts of money might look like this:

1 This is obviously not a very subtle philosophical concept of happiness…the first economists (Jeremy

Bentham, John Stuart Mill) were reasonably deep philosophers, but it’s been downhill pretty much ever since.

One particular difficulty faced in thinking philosophically about utility is: “how do I make interpersonal

comparisons?” That is, when the government makes a policy (or an individual or company makes a decision)

that affects other people, how do you trade off making one person more happy with another person less

happy? (Amartya Sen is an exception to the recent trend toward shallowness in economists, and his work is

very interesting on this point.)

Firms and Markets Lecture Notes

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Now suppose that you had the misfortune to have an experimental economist for a grandmother, and instead of $600, she decided to give you a gamble: you flip a coin, and she gives you $300 if it‘s heads, and $900 if it‘s tails. In expected value that will give you $600. But in terms of utils, it will give you less than 800 utils:

500u 0.5 = 0.5 (500u) + 0.5 (1000u) = 750u Nature 1000u This is a simple way of expressing risk: we get more utility from having $600 for sure (=800u) than from having a risky gamble that pays $600 in expected value.

money

utils

$300 $600

800u

500u

$900

1000u

$300

$900

0.5

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(The straight line on the graph below is the payoff to different gambles that are a mix of getting $300 and $900; the gamble that gives $300 with probability 0.5 and $900 with probability 0.5 is the middle of the straight line.) B. Utility and Budgets We use utility to think about how a consumer makes tradeoffs within a particular budget. There are several complicating factors:

1. we buy lots of different goods 2. if you buy more of a good, you get less utility from each additional unit: for example,

suppose you are buying more and more pairs of exactly the same kind of shoes (and you are not Imelda Marcos); it‘s useful to have extras, but not as useful as the first pair. This is called ―diminishing marginal utility‖ (aren‘t you glad you now know?).

Let‘s just stick to those two complicating factors, and think of our budget as a fixed amount of money for a given period of time (like a month). Let‘s start with a world where there are just two types of goods to buy, A and B, that come in very small units (such as ounces of Beer). Let‘s say that the total utility I get from consuming a certain amount of A and B is Utility = (Amount of A)0.4(Amount of B)0.4

So consuming 10 units of A and 20 units of B gives me 8.32 utils. We might express different combinations of purchases in a diagram with quantities of product A on the horizontal axis and quantities of product B on the vertical axis. In 3-D it would look something like this, but 3-D is hard to visualize:

money

utils

$300 $600

800u

500u

$900

1000u

750u

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Indifference curves. We want to find a 2-D way to represent our tastes for different combinations. We do this graphically with ―indifference curves‖: lines that represent all the combinations of the two products that we regard as equally good. For example, given the utility function described above, we think of 2 units of product A and 1 of product B as just as good as 1 unit of A and 2 units of B (because both give us 1.32 utils). A line connecting all such points about which we are indifferent (i.e., that we like equally well) is called an indifference curve. The way to think of an indifference curve is like a level curve on a topography map (there is a line on a map showing all the points that are at 100m of altitude; here there is a line showing all the points that give us the same number of utils. Generally, indifference curves are downward-sloping, since we need more of a product to compensate us for less of the other (the ―more is better‖ principle). We also assume they are curved away from the origin, since as we consider combinations with more and more of one product, we need increasing amounts of it to keep us equally satisfied. If we put lots of indifference curves on our graph, we can get a complete description of our tastes. Since ―more is better,‖ indifference curves that are up and to the right (farther from the origin) represent higher levels of satisfaction.

q A

q B

IMore utility

1

1

2

2

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Budgets. The other ingredient in our analysis is what the consumer can afford: the ―budget set.‖ With two products, the budget might be expressed in the equation:

Incomeqpqp BBAA

If we solve for qA we see this is the area below the following downward-sloping line:

B

A

B

A

A qp

p

p

Incomeq

This is a straight line whose position and slope depend on income and prices. If you increase income, for example, the budget line shifts out. If you increase pB, the line twists clockwise (around the vertical intercept, Income/pA). And if you increase pA, the line twists

counterclockwise (around the fixed horizontal intercept, pB

Income).

Demand. Putting together tastes (represented by indifference curves) and possibilities (represented by the budget line) we can find out what our hypothetical consumer should do. With indifference curves and budget line on the same graph, the consumer‘s best choice is the highest indifference curve the budget line touches. The point where they touch gives us the quantities demanded of products A and B. Implicitly, these demands depend on tastes (these are built into the indifference curves). They also depend on income (since a change in income shifts the budget line and therefore leads to a change in demand) and prices (for the same reason).

q A

q B

A p Income

B p Income

Increase in income

Increase in p

B

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We can summarize and abstract from the underlying indifference curves and budget sets by writing down a demand function, qi(pi), denoting the quantity demanded, qi, for a given price of the good, pi, (and supposing that income, the prices of all other goods, and any other relevant factors are not changing). Equivalently, we can write an ―inverse demand function,‖ pi(qi), which denotes what the price must be if the quantity demanded is qi. To summarize, the analysis suggests that the quantity of a product demanded depends on:

The tastes of the individual, expressed by indifference curves.

The price of the product. Generally, the lower the price the higher the demand. Depending on the curvature of the indifference curves, a change in price might have a small or large impact on the number of units demanded.

The price of other products. Decisions are not made in isolation. If we spend less on one product, that necessarily leaves more to spend on others.

Income. At higher levels of income, we can buy more of everything (and generally do). Finance and the Risk-Return tradeoff Why do you care about these utility curves? Good question. Mostly you care if you are going to pursue finance, because one particular type of utility curve figures very prominently in Finance: the risk-return tradeoff. Suppose you are buying $100 of financial assets, and (as we‘ve discussed) you are not too keen on risk. Then when you are buying assets, you are going to trade off return and risk: you will only be interested in a more risky asset if it has a higher return (i.e. if the expected payoff is $115 rather than $110). Your level curves will look like this:

q A

q B

Increasing utility

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Let‘s say that Treasury bills are considered almost zero-risk, and that they pay $103; then I will feel be indifferent between buying T-bills and buying an asset with a higher expected return and higher risk, that lies on this line. This tells me how much I would have to offer this customer, before he would buy my asset rather than buy T-bills.

C. Money-metric utility So that was all very complicated. To keep it simple in class, we will still to ―money metric utility‖: the happiness I get from buying a good is represented in dollars, not utils, and the unhappiness that I feel from parting with my money is represented in dollars, as the price. So if I see a pair of shoes that gives me $200 of utility, and it costs $150, then if I buy it I walk away with $200 – $150 = $50 of utility. What‘s limited about money-metric utility?

- Money metric utility doesn‘t let us express risk, the way we did in part A: obviously, if I get $300 from my grandmother, it gives me $300 of happy, and $600 gives me twice as much happiness. We need utils to express risk.

- Money metric utility lets us talk about budgets in a very limited way: I am sad about the $150 I had to pay for my shoes. Why? Because that‘s $150 of other goods that I won‘t be able to buy. Other goods are all represented in terms of the sadness of giving up dollars in payment. This is OK if we are talking about small items in your budget (for some people, shoes are not a small expenditure category!), but if we want to talk about big expenditures, we want to look at the tradeoffs in more detail.

Expected return on $100

variance = risk

$103

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Demand Any business must have some idea how many people might buy its product at different prices. The relevant concept is the demand curve. Stated differently, the demand curve tells us how much people are willing to pay for a given number of units of a product. Below, we describe properties of demand: how sensitive it is to the product‘s price, to prices of other products, to income, and so on. These concepts are basic tools of business analysis. The Demand Curve Imagine that you had 1000 customers, all with different willingness-to-pay. The first customer is willing to pay $999 for your product, the second is willing to pay $998, the third $997, and so on (until the 999th customer is willing to pay $1 and the thousandth customer only wants the good if it is free). You are charging ―one price for all‖, that is, you cannot charge different customers different prices (later we‘ll explore strategies for doing just that). You can use the above information to figure out how many customers will buy, at different prices: For instance, if you set the price at $999, there will only be one customer. If you set the price at $990, there will be ten customers. The way to represent this information is a demand curve. It tells you exactly how many people will buy, at any price. In the story we told above, each person in our market wanted only one unit, and for a different price, but that is not always the case. Suppose we were selling pizzas: the demand curve would

Price

$674

336 units

Quantity

More formally, we can write down the

formula for this demand curve:

Q = 1000 – P

(Write in the price, and it tells you how many

units people want.)

Firms and Markets Lecture Notes

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be a lot lower, since the maximum price would probably be around $20. Some people want only one pizza, and some people will want several. For now, the only important thing to know is how the total quantity demanded changes as we change the price: If our pizzas get cheaper, some customers will order more (they‘ll be more willing to order an extra one and be sure not to run out of pizza), and some customers will switch from other types of pizza. NOTE: When we come to advanced pricing, we will care about more than just total demand at any given price. We will want to know more details about customers: if different types of customers behave differently; if most customers buy one unit (the car market, for instance), or if most customers would buy different amounts based on the price (cell phone minutes, for instance). Price Elasticity of Demand We presume (based on lots of evidence) that demand for a product – any product! – increases if we lower price. This doesn‘t have to be the case, but it invariably is. The question is how sensitive demand is to price. We measure sensitivity by the ―price elasticity of demand‖:

q

p

p

q

q

p

dp

dq

p

dpq

dq

.

In words, the price elasticity is the ratio between the percentage change in quantity and the percentage change in price for a small change in price. Note that elasticity is not the same

thing as slope, although slope is an input to it; see above, where the slope is dp

dq. One of the

Price

$10.50

290 units

Quantity

This is the demand curve for pizzas from

our shop, for a given week. The demand

curve might be something like

Q = 500 – 20P

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Lecture Notes 65

advantages of elasticity over slope is that it does not depend on units of measurement and thus is more easily compared across products. [Technical point: A useful variant of this formula uses logarithms. You might recall that

pd

qd

p

dpq

dq

log

log .

(This is basic calculus; the equation is valid for any base logarithm, including natural log, sometimes written ln.) If we do our usual approximation, replacing d‘s with Δ‘s, we have

p

q

pd

qd

p

dpq

dq

log

log

log

log

.

The approximation is exact if the elasticity is constant along the demand curve. In this case, the demand function is

log q = a + b log p and the elasticity is ε = b. Given two sets of price and demand combinations for a given product, (p1,q1) and (p2,q2), we can recover the elasticity from

1

2

1

2

log

log

log

log

log

log

p

pq

q

p

q

pd

qd

.

since log x – log y = y

xlog . For more on logarithms, see the appendix.]

Note that elasticities are generally negative, since demand declines with price. The question is how negative. We say that products in which – ε > 1 are ―elastic,‖ meaning the quantity demanded is sensitive to price. The higher |ε| is, the more sensitive to price. Conversely, if |ε| is small, we say that demand is ―inelastic,‖ meaning that demand is relatively insensitive to price. Note that the elasticity is defined at a point: it generally differs from one point to another along a demand curve. This property of demand depends on tastes (about which there is no argument!), but we can nevertheless get some insight through examples. Demand for personal computers is elastic, with the result that the demand for PCs has expanded dramatically as the price has fallen. Demands for gas and energy are relatively inelastic, at least in the short run, since there is little

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people can do easily to alter the amount they use. Consider the demand for gasoline as an example to highlight an important point about elasticities over time. If gasoline increased from $1.50 per gallon to $3 per gallon overnight, most people who commuted by car would still fill their tanks in the morning and drive to work. In the short run, they would not be willing or able to find a substitute means to avoiding the higher gasoline prices. Thus, as we said above, gasoline would be inelastic in the short term. However, if a news report revealed that the government was planning to levy a 100% tax on gasoline for the next 3 years, consumers‘ behavior would undoubtedly change. In the next day or week they would probably still drive their cars, but in the longer term their demand for gas could change for many reasons. They might buy more fuel-efficient cars, carpool, or take the bus or train to work, or work from home. As a result, the quantity of gasoline demanded at the new price would decrease. This illustrates a general feature of elasticities: demand tends to be more elastic in the long run than in the short run. Another useful point is the difference between the elasticity of demand for a product category (personal digital assistants, say) and specific products in that category (Handspring‘s Visor Deluxe). Generally the demand for a specific product is more elastic than the demand for the category as a whole. Why? Because when the price of a specific product rises, people are willing to buy fewer units. Some of this reduction leads to purchases of other products in the same category (a Palm IV), and part to a reduction in the category as a whole. Only the latter shows up in the elasticity of the category as a whole, so it‘s typically less elastic. Elasticity and Revenue From a firm‘s perspective, the elasticity of demand is a critical piece of information, since it determines the change in revenue that results from a given change in price. Recall that revenue is simply price times quantity demanded. It is easy to see that by increasing a product‘s price by 15%, each unit sold will yield more money. But if overall demand for the product drops as a result of the price increase, the positive effects of higher per unit prices will be offset by a decline in the number of units demanded. Which effect is larger? Formally, the percentage change in revenue induced by a (small) change in price is

p

dp

p

dp

q

p

dp

dq

p

dp

q

dq

p

dp

pq

pqd)1(

)(

That is, the percent change in revenue following a price change is (1 + elasticity) x (% change in price). Since ε < 0, the direct effect of the price change (the ―1‖) and the indirect effect of demand (the ―ε‖) are opposite. If demand is elastic (ε < –1), the demand effect is larger and an increase in price reduces revenue. This is a basic point, but one that some have missed: that to increase revenue in markets with elastic demand, you need to lower price, not raise it.

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Cross-Price Elasticity We have seen that demand for a product depends not only on its own price, but on prices of other goods. When there are lots of other products it‘s easy to lose sight of this, but it‘s always there. Some examples are obvious. The demand for ski boots depends on the demand for skis: if skis get more expensive, we might expect people to buy fewer boots, too. And as we saw above, the demand for commuter rail tickets may be influenced by the price of gasoline. We summarize the sensitivity of demand to the price of another product with the ―cross price elasticity‖:

Cross-price elasticity =

2

2

1

1

p

dpq

dq

.

That is, the ratio of the percent change in demand for product 1 to the percent change in the price for product 2. The essential distinction here is between substitutes and complements. If the cross-price elasticity is positive, we say that the products are ―substitutes.‖ Hence Coke and Pepsi are substitutes: If Coke gets more expensive, we‘d expect some people (but not all) to switch to Pepsi. Similarly, gas and commuter rail tickets are substitutes, since an increase in the price of gas would lead some people to switch from car to train travel. Conversely, if the cross-price elasticity is negative, we say the products are ―complements.‖ The language of business is filled with competitive metaphors for which substitutes seem appropriate (Coke v. Pepsi). But there are lots of examples of complements, in which a price reduction for one product increases demand for others. Skis and boots are one example. Others include: Windows OS and Intel microprocessors, beer and pretzels, gas and cars. Income Elasticity Changes in income also affect demand. Higher income generally means greater demand for all products, but some products benefit more than others. We define the ―income elasticity‖ of a

product by Income elasticity =

y

dyq

dq

.

i.e., percent change in demand induced by one percent change in income (denoted by y). Economists have names for products with different income elasticities. ―Inferior goods‖ have negative income elasticities. Although inferior goods aren‘t all that common, it‘s fun to try to think of examples. Spam comes to mind, on the assumption that anyone with enough money would buy something else. (You can see the source of the term.) ―Normal goods‖ have positive income elasticities. Within normal goods, those with elasticities between zero and one are referred to as necessities, and those with elasticities greater than one as luxuries. Can you explain why?

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Measuring Demand In an ideal world, firms would know the demands for their products. In practice, it‘s not easy. One reason is that it‘s hard to get reliable market data: how much was bought by whom and at what price? Another is that it‘s inherently difficult to tease out the effect of price from the effect of other variables, especially when the latter might be changing at the same time as price (or, even worse, when they are not known to us). Another approach – one that is increasingly common – is to do experiments in markets. Thus catalog companies sometimes send out catalogs to different customers in which some of the prices are different. These experiments run the risk of alienating customers (what if you find out you got the high price?), but you can see the value to the firm of knowing the demand for its products. Numerical Examples Example 1. Demand for a product is estimated to be

Price Quantity Revenue

10 6.31 63.10

11 5.63 61.90

12 5.07 60.84

13 4.61 59.87

14 4.21 58.99

15 3.88 58.18

What is the elasticity of demand at price 10? We approximate it by the ―change formula,‖

ε (Δq/Δp)(p/q) = [(5.63-6.31)/(11-10)](10/6.31) = –1.08. This is approximate, since we‘re using discrete changes. (In fact, the numbers were generated by the demand curve, log q = log 100 – 1.2 log p, which has an elasticity of –1.2.) We could get a better approximation by using a finer price grid. Example 2. Village microbrew raised its price from $10 to $12 a case (wholesale). Shipment quantities at the two prices were

Price Quantity

10 10,500

12 8,100

What is the elasticity of demand? We can approximate it by the ―change formula,‖

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Lecture Notes 69

ε 77.1

12

100,81210

100,8500,10

p

qp

q

.

This is approximate, since we‘re using discrete changes. If we assume that the elasticity of demand is constant then could get an exact solution by using the log formula:

ε = 423.1)12log()10log(

)8100log()10500log(

log

log

p

q.

Did revenue rise or fall? Since ε < -1, the increase in prices led to an overall fall in revenue. (If you want to make sure then calculate the revenues before and after the price change). If the elasticity is constant, what is the demand at $9? If the elasticity is constant then the log formula calculates the elasticity exactly and in addition we know that:

423.1

9

10log

500,10log

9 q

where q9 is the demand when the price is $9 per case, so (after a little bit of algebra).

199,129

10log423.1)500,10log(exp9

q

Example 3. Suppose the demand for ―product 1‖ is given by the demand curve,

q1 = a – b1 p1 + b2 p2,

which you‘ll note also depends on the price of product 2. The price elasticity is

ε = (dq1/dp1) (p1/q1) = – b1 (p1/q1). Note the demand is elastic for high values of (p1/q1) and inelastic for low values. ―The‖ cross-elasticity is

(dq1/dp2) (p2/q1) = b2 (p2/q1). Suppose a=500, b1=10, b2=5, and p1=p2=50. Then q1=250, the elasticity is –2, and the cross-elasticity is 1. The positive sign of the cross-elasticity means the products are substitutes. Consumer surplus is the area under the demand curve but above the price. Since demand is linear, this is a triangle. With the same numbers, the consumer surplus is 250 x (75–50)/2=31,250.

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Example 4. The table below gives the ―own‖ and cross-price elasticities for selected automobile models.

Model 323 Cavalier Accord Taurus Century BMW

Mazda 323 -6.4 0.6 0.2 0.1 0.0 0.0

Cavalier 0.0 -6.4 0.2 0.1 0.1 0.0

Accord 0.0 0.1 -4.8 0.1 0.0 0.0

Taurus 0.0 0.1 0.2 -4.2 0.0 0.0

Century 0.0 0.1 0.2 0.1 -6.8 0.0

BMW 735i 0.0 0.0 0.0 0.0 0.0 -3.5

(Source: BLP, 1990 data.) Why are the ―own‖ elasticities so high? Answer: These are models for which many substitute models are available. Thus, even if the demand for cars is not very elastic, the demand for a particular model is.

Are the Accord and Taurus complements or substitutes? Answer: The cross-price elasticity of the Accord with respect to the price of the Taurus is given by 0.1, a positive value. The two models are therefore substitutes. In fact, no two models in this sample are complements. What are the Taurus‘s closest competitors? Answer: Looking at the Taurus row, we see that the cross-price elasticity is highest for the Accord. In other words, a 1% change in the price of the Accord would have a greater impact than a 1% change in the price of any other model (other than the Taurus). If GM lowers the price of its Chevy Cavalier, does it ―cannibalize‖ its Buick Century? Answer: The cross price elasticity of the Century with respect to the price of the Cavalier is negligible. Therefore, a decrease in the price of the Cavalier will reduce the demand for the Century by only a tiny amount. Why is the direct elasticity for the Mazda not lower than the elasticity for more expensive models (as the rule of thumb would suggest)? Answer: As suggested by the qualitative analysis of demand elasticity, luxuries tend to have higher elasticity than non-luxuries. However, another rule of thumb to keep in mind is that the elasticity for a particular product is always higher than the elasticity for the group of products it belongs to. As it happens, there are many more compact car models than there are luxury car models. Therefore, even though the elasticity for luxury cars is higher than the elasticity for compact cars, the elasticity for a particular luxury model may not be much greater than the elasticity for a particular compact. Suppose Honda sold 300,000 Accords in 2001. In 2002, the price of the Accord decreased by 2%, whereas the price of the Taurus decreased by 3%. What is the likely change in Accord sales? Answer: The percent change in demand is approximately given by (-2%)*(-4.8) + (-3%)*(0.1) = 9.3%. We would expect an increase in Accord sales of approximately 9.3%, or .093*300,000 = 27,900 units.

Response to change in price of:

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Appendix: Logarithms Why logarithms? They just turn out to be useful in lots of places: elasticities, compound interest, growth rates, and so on. What are logarithms? The natural logarithm of a number x comes from the power of a number e, which is approximately equal to 2.718. If x = ey, then y is the logarithm of x. We write

y = log x. There are logarithms based on powers of other numbers (any positive number, not just e). We‘ll stick with e. In Excel, the natural logarithm of x is written ―ln(x)‖. Suppose, instead, you know the logarithm y of x. How do you find x? From the definition, x = ey. In Excel, this is written ―exp(y)‖. How do they work? The most useful properties of logarithms are

log (xy) = log x + log y

y

xlog = log x – log y

log (xy) = y log x. In addition, the derivative of the natural log of x is the inverse of x:

xdx

xd 1log .

Can you give us an example? We showed how to compute elasticities earlier. Another application is compound growth. GDP per capita in Korea was $1000 in 1960, $6000 in 1990. (These are rough estimates, measured in 1990 US$ – i.e., corrected for inflation). What was the average annual growth rate? We‘re looking for a number ―g‖ satisfying

6000 = (1+g)30 1000 How do we find g? One way is to use logarithms. Note that

log 000,1

000,6 = 30 log (1+g)

Since log 6 = 1.792, log (1+g) = 30

792.1 = 0.0597, and 1+g = exp(0.0597) = 1.062. The growth

rate was 6.2% a year, which is extraordinarily high. Similar calculations show up in present value calculations.

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Economic Profit and Costs Suppose you need to decide whether to start up a plant or shut it down, whether to eliminate a product line, whether to produce at capacity or below. The answers to these questions depend on costs. But which costs matter? Cash flow measures of cost exclude some costs that matter (―opportunity costs‖) and include others that do not (―sunk costs‖). We refer to the costs that matter as ―economic costs,‖ where ―economic‖ in this context means ―the ones that matter for the purposes of decision making.‖ More formally, let‘s say you are making a decision, and you only have two choices—call them A and B. Using a decision tree is a way to think about the tradeoffs clearly: A Revenues(A) – Expenditure(A) You B Revenues(B) – Expenditure(B) In making the choice between A and B, you care only about the difference between those two payoffs. This leads to our definition of Economic profit:

Economic profit of choosing A instead of B = top line minus bottom line

= [Total balance after choosing A] – [Total balance after choosing B]

You can think of your total balance as ―how much money you‘d have in bank or in investments at the end of the year‖. Notice that the first thing that drops out of the comparison (we didn‘t even bother to write it down) is the amount you made on other projects during the year, and any other money you have in the bank. Those amounts will cancel out when we take the difference. That leads to two key points:

1. Sunk costs do not matter (i.e. sunk costs are not a part of “economic” costs).

Sunk costs are costs that you have already incurred, and can never retrieve. Let‘s suppose for instance that you spend $500,000 on advertising a new product line earlier this (accounting year); that amount is ―sunk‖—you cannot get the money back from the advertising firm, even if you discontinue the product line.2 Another category of sunk costs (sometimes called ―fixed costs‖) are costs that you have not yet incurred, but that you can‘t avoid paying: your payroll for the upcoming month, for example (if none of your employees are on flexible contracts).

2 If you spend $500,000 on an asset (a building, a piece of equipment), and you can only re-sell it for $80,000,

then $420,000 of that expense is sunk.

Firms and Markets Lecture Notes

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You are trying to decide whether to discontinue the product line or to keep it going. The economic profit of that decision will not depend on the sunk costs: keep Revenues(keep) – Cost(keep) – 500,000 You discontinue 0 – 500,000 When we look at the difference between these two payoffs, the 500,000 will cancel out. Say the British Government was trying to decide whether to continue rail service between two cities or instead to change to bus service. The revenues gained by both choices are 120. The costs of the rail company are 30 for interest on bonds used to finance the rails, 50 to lease trains, and 50 for labor (or labour, since we‘re talking about the UK). The costs of running the bus service are 60 to lease the buses and 50 for labor. At first glance the government is losing 10 on the Rail Company and would make a profit on the bus company, so it would make sense to switch to buses. The fact is that the British Government is not going to default on the rail bonds, so the interest has to be paid regardless of which option is chosen. The interest cost is a sunk cost, then, and the rail company is not only profitable in an economic sense, but more profitable than the bus company. That is, economic profit = 120 – (30 + 50 + 50 – 30) = 20 for the rail company, and economic profit = 120 – (60 + 50) = 10 for the bus company. This may not seem to make sense, but it does in an economic sense since you would have to pay the cost of the interest anyway. If you could default on the railway bonds, it would be a different story and it would be worthwhile to do so and change to buses. Further examples:

You have spent $15 on a ticket to a football game. Come Sunday, it is raining cats and dogs and there is no way for you to sell the ticket. You should make your decision on how much you value watching the game versus how much you hate the rain. The price of the ticket should not come into the equation since it is a sunk cost. Regardless of the option chosen you will have spent $15 on the ticket.

A company has built a dam. There was a huge initial investment in the dam that comes out to 5 per unit of energy when amortized over the life of the dam. The operating costs of the dam add 5 to the unit energy cost so that the total cost of power from the dam is 10. Once the dam is completed, a new source of energy is discovered so that the price of energy falls to 7. Should the dam continue to operate since it will be losing 3 on every unit of electricity generated? The answer is that the dam should continue operating as long as the price is expected to average over 5 in the short to medium term (that is, it might make sense for the dam to absorb short term losses if there is a cost for shutting it down and reopening it). The cost of building the dam does not come into the equation since it cannot be recovered if the dam stops producing electricity. Thus it makes economic sense to continue to operate the dam as long as the operating costs are covered.

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Say you have purchased a laptop computer for $2,000. A week later a new, improved model is introduced for $1000 that is 3x as fast as your laptop. The company offers to sell you the new computer for $400 if you trade in your old laptop. This seems to be paying $2,400 for a computer that costs $1000; should you do it? In order to decide whether to take the trade in, you need to place a value on the extra speed of the new laptop. You then need to ignore the $2,000 as a sunk cost. The only thing important to you is if the extra speed is worth $400 or more to you, in which case you should trade the laptop in.

Airbus is a jointly owned consortium that makes commercial aircraft. The four European governments that own the consortium invested huge sums in subsidies to develop the company as a competitor to U.S. aircraft manufacturers. Currently the company is profitable, but it would have to be enormously more profitable in order to recoup the amount spent on subsidies. If there had been loans made instead of subsidies, the company would not be profitable. What should the governments of the countries do if there had been loans to pay off instead of subsidies? Provided that they are not willing to default, the company should continue to produce aircraft even if loan payments made the company permanently unprofitable. This is true provided there is enough cash to stay solvent (but it would make sense for the governments to inject more cash or to assume the loans anyway). As long as Airbus is covering its operating costs, it should ignore the sunk costs of the hypothetical loans and keep churning out aircraft.

Haas (the business school at Berkeley) installed ―swing Macs‖ in their classrooms for academic purposes due to the fact that they could run both Macintosh and IBM software. They proved unable to run this software well, however, and this became an impediment to learning as well as an embarrassment to the staff. A proposal was brought up in a meeting to replace these machines (which cost $5,000) with $1,000, functional PCs. A faculty member said that this would be fiscally irresponsible since the school had spent so much on the swing Macs in the first place. The economics faculty at this point chimed in that it made no sense not to replace the Macs since they were a sunk cost.

2. Opportunity costs matter According to this decision tree, choices A and B are mutually exclusive. (If they are not exclusive, then the tree should have a third branch, entitled ―A+B‖.) That means that one cost of choosing A is that you cannot choose B—you give up on the opportunity to do B. This is called an opportunity cost. Calculating economic profit using a decision tree means that you take opportunity cost into account. Let‘s say that Stern has space in another building off of Washington Square which it could use to run an extra section of Langone, or it could rent the building out for office spaace Run extra section Stern Rent space out

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Economic profit of running an extra section = [Total balance after running extra section] – [Total balance after renting space] The profits from renting the space appear as a ―cost‖ when we think of the economic profit of running an extra section, because they are subtracted at the end. Why? Stern only wants to run an extra section if that branch has a higher payoff, that is, if the economic profit of running it is positive. Otherwise, Stern should rent the space out. *** Note on opportunity costs *** Beware of double-counting!! If you are not using a decision tree, but just using the intuition derived from the trees, you just go ahead and subtract them at the end of your profit calculation. But if you are using a decision tree, don‘t subtract them along one branch of the decision tree!! The decision tree is already calculating opportunity costs for you… Examples of Opportunity Costs An example of opportunity costs is going to the movies. Say you are considering going to the cinema on a Friday night and a ticket costs $10. If your alternative to going to the cinema is to sit at home and do nothing, then there are no opportunity costs (presuming doing nothing holds no value to you). Thus the economic cost of going to the movies is $10. Let us say, however, that you have a part time job and you have been offered a four-hour shift delivering pizza for $10 an hour. Assuming that you do not mind the pizza delivery job (that is, not delivering pizza does not have a value for you on that particular Friday), then the opportunity costs of going to the movie is the money you are foregoing by not working (i.e. $40). Consequently the economic costs of going to the movie in the second case would be $50. Note that you may have the opportunity to baby-sit for those same four hours for $8, but we use the $10 for the pizza delivery job since that is the best alternative use of your time. Another example of opportunity costs is in the use of Carnegie Hall. Say you are managing the facility and the agent of a concert pianist comes to you and suggests holding a recital. You expect that the net revenue for the recital would be 100. The alternative to holding the concert would be holding a rock concert, which would net 150. The impresario may try to convince you that you would be gaining 100 from this recital, but actually you would be losing 50 (net economic revenue of –50) since you need to add in the opportunity costs to get to the economic costs. Say you had total revenues of 900 and expenses of 800 for the recital. In that case you would calculate the net economic revenue as 900 – (800 [actual expenditures] – 150 [opportunity costs]). Alternatively you can make decisions by comparing the net benefits (i.e. 150 is better than 100). A third example would be using a part of an NYU building to house short-term visitors such as executive education students. Say that this use brought in 80 in room fees but required 30 in cleaning and other expenses. The next best use of the space is to lease it out for office space at 60. You can look at this in the same two ways as before. In net benefit terms the 80 – 30 would lead to a benefit of 50, which is less than 60. The right decision would be to rent out the space for offices. Similarly the net economic revenue of the student housing is 80

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[revenues] – (30 [cleaning, etc.] + 60 [opportunity costs]) = -10. This is less than zero, and thus should be rejected as an option. Thus, either way you look at it, renting out offices is the way to go. It would be different if there were other benefits to having housing for executive education students that were not being considered. All these examples illustrate a common feature of opportunity costs: it‘s not easy to quantify them. We have to put a value on an alternative use, and such values inherently involve some judgment. Perhaps that‘s why financial statements tend to leave them out. Economic Profits and Cash Flows Economic profits are used to make decisions. They tell you whether choice A or B generates higher profits and how much higher those profits will be. They do not replace accounting measures, since it is quite possible to have the amortization of sunk costs bankrupt the firm even though it makes economic sense to keep the firm producing. Similarly, often cash flows are not useful for making economic decisions. The costs of choice A are defined only in relation to the choice B that it is being compared to. You can look at the costs and benefits in different ways, but they give the same answer. Further differences between accounting and economic profits: Economics ignores the past if you cannot do anything about it, but cash flow statements look backwards. Opportunity costs are not reflected in cash flows, but they do affect decisions (if they‘re made correctly). Conversely sunk costs involve cash flows, but don‘t affect economic profits: They don‘t matter. Economic profits are not the same as cash flows. Examples Example 1 (health club). If you own a health club that makes $3,800 in revenue, should you stay open? The following is the cost structure of the health club: Actual expenses of $2,500 for labor and $2,000 for lease payments. The lease is unbreakable and bankruptcy is not possible. There is a possibility to sublet the space, however, for $1,200 a month. Thus the $2,000 lease payment is a sunk cost, and the $1,200 is the opportunity costs for keeping the health club open. Answer. With this cost structure, one is losing $700 a month on an accounting basis. On an economic basis, however, the decision tree is: 3,800 - 2,500 - 2,000 You 1,200 - 2,000 - 2,000

stay

open

close & lease

close & do

nothing

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(―Do nothing‖ is an option people often forget! In this case it‘s obviously worse, so we ignore it.) Economic profits of staying open relative to the next best option (leasing) are $3,800 - $2,500 - $1,200 (opportunity cost) = $100 a month. In this case it makes sense to keep the health club open. What if bankruptcy were an option? In that case, the obligation to pay the lease goes away when you declare bankruptcy, so you may not have to pay it. 3,800 - 2,500 - 2,000 You 1,200 - 2,000 0 Now, economic profits of staying open relative to the next best option (declaring bankruptcy) are $3,800 - $2,500 - $2,000 = - $700 a month. In this case it makes sense to close and declare bankruptcy (if there are no other businesses that are affected by bankruptcy—that would require a more complicated tree!). Example 2 (Redsyke quarry, real example from UK). There was an expansion of the M6 motorway that required the extension of a quarry, including an 8-hectare plot used for grazing. The quarry offered the farmer approximately 3x the market value of the land. The farmer‘s lawyer suggested that the farmer ask for compensation for foregone earnings based on the value from the cows and sheep that would be displaced. What would you give as testimony if you were called as an expert witness (your testimony could vary depending on which side you were supporting)? Answer. The question is what the opportunity cost is to the farmer. If the farmer could rent adjacent land, then 3x market value seems high. Otherwise the profit on cows and sheep is a legitimate opportunity cost. Note: the farmer lost.

Why all this effort to belabor what may seem obvious? The history of business is filled with huge mistakes from an incomplete understanding of the nature of costs. Opportunity costs involve no payment of money and are therefore easy to overlook. Large sunk costs often come with political supporters, whose reputation hinges on the success or failure of the project. But from a purely economic point of view, there‘s nothing you can do about them: they‘re gone.

stay

open

close &

lease close &

declare

bankruptcy

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Perfect Competition When talking about pricing, we consider the monopoly benchmark. What happens when, instead of monopoly, we are at the opposite extreme—a competitive environment? In particular, how are prices determined in such markets? How can we assess the impact of a given exogenous event on market prices? We have thought about the demand and supply before but having a better understanding now of the underlying individual consumer decisions that feed into demand and the underlying individual firm decisions that contribute to supply, we can understand that classic diagram, the circumstances under which it is appropriate, and its implications. Further, the competition benchmark will allow us to establish an important result, namely that perfectly competitive markets are efficient (in a sense to be specified). This provides a rationale for anti-trust policy and promotion of competition, a topic that will appear frequently in the rest of the course. Perfect Competition The ―perfectly competitive‖ industry, an industry with no barriers to competition, is a useful benchmark. It is also a reasonable approximation to many important industries, including many sectors of agriculture, some sectors of labor markets and reasonably heavily traded financial securities. Consider the competitive forces in this situation:

Atomistic firms. Many firms, all small relative to the market and unable to affect the market price through their actions. Moreover, the minimum efficient scale is small relative to the size of the market.

Homogeneous product. Competitors produce exactly the same product (and therefore compete head to head on price, the only remaining variable).

Perfect information about price and quality. Everyone knows it‘s the same.

Free entry and access to technology. Imitation is possible: others can enter the business if it‘s profitable with (eventually) the same costs as incumbents.

Under these conditions, which we term ―perfect competition,‖ we‘d expect intense competition. How reasonable is this? More so in some industries than in others. There are industries where differences in profit rates across companies can last for decades. Although the source of these differences remains somewhat of a mystery, they appear to be related to industry characteristics, scale economies, market share, and research and development intensity. Related work suggests that one of the more persistent sources of high performance is ―organizational capital,‖ the processes that underlies the organization of the firm. Thus

Firms and Markets Lecture Notes

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Toyota‘s production system has proven very hard to imitate. Similarly, existing airlines have found it difficult to reproduce the low-cost, high-value delivery system used by Southwest (although new entrants seem to find it easier). This perfect competition benchmark is useful not only in itself, but also as a comparison to consider violations of these conditions. With one or few firms, we have a monopoly or an oligopoly (which leads to complex strategic interactions that we‘ll study later in the course). With differentiated products, we moderate the impact of competition (a recurring theme) and open up the issue of product positioning. With imperfect information, we create the possibility of branding (a brand often being a signal of quality). With entry and access to technology, we raise the issues of scale economies, patent protection and intellectual property, entry preemption, and network effects (which we discuss later). Stated differently: if a firm has a sustainable competitive advantage, it must lie in a violation of one of these conditions. Firm supply and market supply in competitive markets Let‘s look more closely at a market or industry under conditions of perfect competition. First, each firm faces effectively a flat (―infinitely elastic‖) demand curve: it can sell all it wants at the market price and can sell nothing at any higher price. Why? Because each firm is small relative to the whole market and has no impact on market price. People sometime refer to the market as ―atomistic,‖ since each firm is small like an atom. In these circumstances a firm‘s total revenue is TR(q) = pq, hence the firm‘s marginal revenue is p. The usual profit-maximizing condition that marginal cost equals marginal revenue simplifies to

MC(q) = p. Thus under these conditions, each firm‘s supply decision is governed by its marginal cost curve. It supplies the quantity at which price equals marginal cost. Each firm‘s supply curve gives the quantity that the firm would want to supply at a given price. Specifically, firm i would want to supply qi such that MC(qi) = p. If we put all firms together, we sum their supply at each price to come up with the industry supply curve. Specifically, if we add up each firm‘s value of qi, then we obtain the industry supply curve S(p) = q1+…+qn. Consider the specific example of an industry with three firms, each with constant marginal cost. Firm 1 has a capacity of 200 at MC = 5. Firm 2 has a capacity of 100 at MC = 8. Firm 3 has a capacity of 100 at MC = 10. If the three firms are competitive (this is a question we‘ll want to come back to), what is the industry supply curve? How much does each firm produce? The hard part is finding the industry supply curve is getting reliable cost data. Once we have cost data (or at least estimates), we basically graph the demand and supply curves and find the point where they cross. The supply curve is flat at p = 5 for 200 units, then jumps up to p = 8 for 100 units, and up to p = 10 for another 100 units.

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Market Equilibrium Whether considering long run or short run outcomes, the price of a product is the result (in market settings) of the interaction between buyers (demand) and sellers (supply). We refer to the point at which the supply and demand curves intersect as ―equilibrium.‖ as we have discussed in the earlier note on supply and demand. Short-run and long-run equilibrium We define the short-run as the period when the number of firms is fixed, whereas, in the long run, we also consider the possibility of entry and exit. Consider an industry with a given number of firms (short run) and an aggregate supply curve as described above. The intersection of supply and demand determines the equilibrium price. Depending on the number of firms in the market, this may result in a short-run equilibrium in which price is above average cost (meaning firms are making above-normal profits), below (firms are losing money), or equal. But firms are doing their best, given their prior choice to enter the market. The next stage of competition concerns the decisions of these firms, plus potential entrants, to stay, enter, or leave the industry. Suppose price is greater than average cost for all firms in the industry. Then we would expect incumbent firms to expand their capacity and new firms to enter. As a result, the market supply curve shifts to the right, driving down the price. This may take some time, but the ultimate effect is to drive firm profits down to zero (by which we mean normal levels). Conversely, if price is below average cost, then some firms will leave the industry, the supply curve will shift to the left, and firms will eventually attain a normal level of profit. Specifically, let‘s think about how this might work in a competitive industry in which all firms have the same cost structure. The market price might allow firms to make money or not, depending on the relation between p = MC and AC. If market price p is below average cost AC, then the firm is not making enough to cover its fixed costs. When it gets a chance, it might choose to leave the industry. This would tend to reduce supply and increase the market price. Conversely, if at the market price p is above average cost AC, then the firm is making money and would likely choose to stay. If other potential entrants face similar costs, they might choose to enter, too. This would tend to increase supply and reduce the market price. Eventually, we‘d expect this process of entry and exit to drive profits and losses out of industries and leave firms with p = MC = AC. At this point, note that the industry is operating at minimum cost. It is important and interesting to highlight that if firms have different cost structures then in a long run competitive equilibrium (with many price-taking who are small relative to the overall market), the marginal firm will be one for which p = MC = AC, however some firms lucky enough to have cost advantages will be earning rents. To earn such rents these factors need to be impossible or hard to replicate. For example, for many minerals mining is a commodity industry but some mines are lucky enough to find seams located near the surface while others

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incur greater costs of extraction. The marginal mine will be earning no profit, but some mines may be earning profits, which are termed rents on their superior location. The challenge for managers is to create or develop products, practices or skills on which they can earn such rents. Let us go back to the example above. Suppose market demand is Q = 540 – 20 p. At p = 10, demand is Q = 540 – 200 = 340. Then Firm 1 produces q = 200, Firm 2 q = 100, and Firm 3 produces q = 40. Since the supply curve is such that price equals 10 for any output level between 300 and 400, we confirm that equilibrium is given by p = 10 and Q = 340. Is this equilibrium a long-run equilibrium? If the technology available to potential entrants is like firm 3‘s, then the answer is yes: an additional entrant would not be able to make positive profits. Notice that, in this equilibrium, while firm 3 earns zero profit (it is the marginal firm), both firms 1 and 2 earn positive profits (rents from a superior cost function). Other interesting questions we may ask with this framework: If demand falls to D(p) = 400 – 20p, what happens to the profits of Firm 1? (They fall, since the price falls.) What happens to the profits of Firms 1 and 2 if Firm 3 reduces its MC to 8? (They both fall.) The Fundamental Theorem and The Invisible Hand Why do economists (and sometimes even policy makers) wax lyrical about markets? One reason (and there are other perhaps more compelling ones) is that competitive markets are efficient, meaning that in a competitive market the equilibrium level of output and prices are such that they lead to the largest level of total surplus. To economists this is a sufficiently important and striking result that it has won the (somewhat grandiose) designation ―The Fundamental Theorem‖. Adam Smith‘s famous ―invisible hand‖ refers to the role that prices play in achieving a good allocation of resources in the economy. Though buyers and sellers may have disparate and conflicting preferences and capabilities, the price and market mechanism ensures that consumers who value goods most receive them, and those firms for whom it is cheapest to produce the goods produce them. Moreover, in the equilibrium of a perfectly competitive market there are no remaining consumers whose willingness to buy one additional unit is greater than what it would cost any firm in the economy to produce it. That is, all trades such that willingness to pay is higher than marginal cost take place. This no doubt is a good thing; however, a couple of observations are worth highlighting. First, the Fundamental Theorem is a statement about efficiency rather than equity, that is, if concerns the size of total surplus, not its distribution. In particular, note that in calculating total surplus we value consumer and producer surplus equally. We presumably attach value to profits because they are eventually returned to shareholders of the firm. However, in as much as shareholders tend to be wealthier as a group than consumers, some would argue that firms‘ profits ought not to be weighted as much as consumer benefits. Institutional arrangements or regulations that, for example, raised consumer surplus by the equivalent of $20 million and decreased firms‘ profits by $25 million may be judged to improve welfare even as a cost of $5 million in terms of total surplus.

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Another important caveat is that the Fundamental Theorem applies to competitive markets, which, as outlined at the beginning of this note, correspond to some fairly strong assumptions. Where producers or consumers are large enough to affect market prices, products are differentiated, there is less than perfect information about price and quality or entry into the industry is restricted, then the Fundamental Theorem does not necessarily hold. Further, an important result—the ―Theory of the Second Best‖—suggests that if there are some frictions in a market (if some of the assumptions for the Fundamental Theorem fail), then reducing others may well reduce welfare. Relaxing the assumptions of an idealized competitive market and thinking through their implications will keep us busy through the rest of this course. Another important assumption that arises in the context of the Fundamental Theorem is an implicit assumption that a consumer‘s enjoyment of a good does not depend on other people‘s consumption—technically speaking, the assumption that there are no externalities. We shall return to consider relaxing this assumption in our discussion of networks. Summary

In a competitive market—a useful benchmark and approximation—firms are atomistic and act as price takers, competitors produce a homogeneous product about which there is perfect information, and there is free entry into the industry and access to technology.

For a competitive firm (one that cannot directly influence price), the (short-run) supply curve is the MC curve. Short-run here means that firms have already committed to pay whatever fixed costs are required to enter the industry.

For a competitive industry, the short-run supply curve is the sum of the supply curves of the individual producers.

In the short run, the price is the intersection of demand and the short-run industry supply. In the long run, firms enter profitable industries and exit unprofitable ones. The interesting result is that price is governed by the minimum average cost.

In a competitive industry (and under the strong requisite assumptions) the Fundamental Theorem applies: Efficiency obtains in the sense that the total of producer and consumer surplus is maximized.

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Pricing Most firms have some control over the price they set. Although they may have competitors, they can charge a higher or lower price, and generate less or more demand as a result. The question is how high to set the price. A high price generates more revenue per unit, but fewer units are sold. A low price generates less revenue per unit, but more units are sold. Which is best? It depends … on the elasticity of demand and marginal cost. Pricing: intuition To see this most clearly, consider a monopoly: an industry with a single producer. You can set your price however you like, but you sell only what the market demands at each price. You can either price low and sell a lot, or price high and sell a little. The key insight is that for a monopolist to sell an additional unit, it must lower the price on that unit but also on all other units it sells. Thus the overall benefits are less than the price it gets for the extra unit. Consider an example. Suppose you sell 80 CDs for $15.10, and to sell 81 you must reduce the price to $15. Is the marginal revenue $15? No! Your revenue rises from 1208 (=15.10x80) to 1215 (=15x81), an increase of only $7. This is less than the $15 price, because we had to reduce the price on the first 80 CDs by 10 cents (leading to 0.10x80=$8, the difference). Thus the marginal revenue of an extra unit is less than the sales price. Now how much should we produce? We produce until the extra benefit of an additional unit is balanced by the extra cost: when marginal revenue equals marginal cost, or simply MR = MC. As we will see, for a competitive, price taking firm, the demand curve is flat, and thus marginal revenue is equal to price. It follows that profit maximization implies p = MC. Since MR is less than price, and marginal cost is level or increasing, this results in less output under monopoly. Another way to see this is to recall that competitive firms are ―price takers:‖ they are too small to affect the market price through their own actions. A competitive firm can‘t raise its price above the industry price, because it would then lose all its customers to competitors. Generally, a monopoly will set a higher price, and sell fewer units, than competitive firms in the same industry. The same analysis applies to any firm that has some control over price. In markets with differentiated products, for example, each firm might be considered a monopolist for its own version of the product (although the existence of close substitutes will affect its demand curve). Pricing: calculus We can see the same thing mathematically. If the inverse demand curve (price as a function of quantity) is p = D(q), then revenue (expressed as a function of output, q) is

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R(q) = pq = D(q)q.

Marginal revenue (the extra revenue from an additional unit) is

MR(q) = dq

qdR )( = D(q) + D′(q)q = p + D′(q)q < p,

where D′(q) denotes derivative of D with respect to q. The last step follows from our standard assumption that demand declines with output (hence D′<0). The optimal output level can be found by maximizing profit,

Profit(q) = R(q) – C(q), which we do by setting the derivative equal to zero and then verifying that we have a maximum. The derivative equated to zero leads to

dq

qd )(Profit = MR(q) – MC(q) = 0,

or simply MR(q) = MC(q). In words, the profit maximizing output level is such that marginal revenue equals marginal cost. Technical Aside: To check that we have a maximum, we look at the second derivative:

2

2 )(Profit

dq

qd= MR′(q) – MC′(q).

If this is negative, MR = MC gives us a max. It‘s sufficient that MC increase with q (MC′ > 0) and MR decrease with q (MR′ < 0). For most of the problems we‘ll consider, we‘ll assume MR′ < 0 and MC′ ≥ 0, which is enough to cover us without ruling out constant MC. Elasticity rules The math is useful for some people because it is clear and concise. It is also useful for demonstrating an interesting relationship between seller margin and elasticity. Define the

margin as m = p

MCp . For a monopolist, the margin is generally positive. But how large is

it? The answer is m =

1 , where ε is the price elasticity of demand (and is negative). It

implies

11p = MC.

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We will refer to both as versions of ―the elasticity rule‖. Note that the margin depends on how sensitive demand is to price. If it is very sensitive (|ε| large), then the margin is small. Even for a monopolist it is hard to squeeze out a large margin, because customers will simply decline to buy the product. But if the elasticity is small, the margin can be quite large. (There is a limit of one, for reasons related to the fine points above). Where did this rule come from? Recall that

MR = p + D′(q)q = MC.

Then , p

qqD

p

MCp)('

.

Except for the minus sign, the expression on the right hand side is just the inverse of the elasticity of demand. Examples. Local telephone service is a must for most people, so demand is inelastic (|ε| small). An unfettered monopolist would presumably choose a high markup and price. The classic role of telecomm regulation, therefore, is to keep the local operator from exploiting its position. Similarly, demand for prescription drugs is inelastic, both because they‘re necessities (how often have you said: ―Sorry, that drug‘s too expensive, I‘d rather be sick?‖) and because in most cases the customer isn‘t paying anyway. Conversely, a competitive firm might be regarded as one facing an infinitely elastic demand curve (horizontal), which produces a markup of zero. Thus the key issue for a monopoly is how elastic its demand is. If it is very elastic, the cost of monopoly is low. Numerical examples Example 1. Consider a monopoly facing linear demand and constant marginal cost. Demand is q = a – bp, with a=12 and b=2. Costs are C(q)=cq, with c=1, so MC=c=1. What is the optimal price for the monopolist?

Answer. The inverse demand curve (we need to solve for p) is b

qap

.

Then profits are

cqqb

qb

acqq

b

qacqpqq

21

)(Profit .

To maximize, we differentiate with respect to q and set the result equal to zero, implying MR=MC:

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cqbb

a

2.

Optimal output is therefore 2

cbaq

, substituting in a=12, b=2 and c=1 yields that the

optimal output it 5, price is 5.32

b

bca

b

qap , and profit is 12.5.

As for the elasticity rule: At the optimal price, the elasticity is

5

7

5

5.32

q

pb

q

p

dp

dq .

Thus the markup is

1

7

5

5.3

5.2

p

MCpm , as promised.

If c increases by 1, then substituting in a=12, b=2 and c=2 yields that the optimal output is 4, the optimal price is 4 and profit is 8. Example 2. Consider a similar problem with a log-linear demand curve. This kind of demand curve is uglier mathematically, but is convenient because it has constant elasticity of demand. In practice, it‘s generally a much better approximation than the linear demand curves we often use as examples. Let‘s say that the inverse demand is

log p = + log q, or

p = q.

(Why ―inverse‖? Because we solved for p, rather than q.) The elasticity of demand is =1/. If marginal cost is a constant c, then profit is

Profit(q) = pq – cq = q+1 – cq.

To find the optimal quantity:

0)1()(Profit

cqdq

qd .

If you recall that q = p, this turns into

cp )1

1(

,

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which is equivalent to the elasticity rule. Example 3. A firm sells one million units at a price of $100 each. The firm's marginal cost is constant at $40, and its average cost (at the output level of one million units) is $90. The firm estimates that its elasticity of demand is constant at –2. Should the firm raise price, lower price, or leave price unchanged? Optimal pricing implies m

=

1 , where m=

p

MCp is the margin. In this problem, we have

100

40100

p

MCpm

or 0.6, which is greater than 5.02

11

. This tells us that the price/cost margin is too

high, so a lower price (for practice you can check that it would be $80) would be optimal. Note that the margin depends on MC, not AC.

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Advanced Pricing Consider a situation faced by a stylized biotech firm:

―Ken, it‘s brilliant science, but I just don‘t see how we can make any money from it.‖ CEO Allison Schreter of biotech startup BioStern is discussing strategy with CFO Charles Miller and Research Director Ken Goldman. ―It will cost at least $20m to complete the research and get regulatory approval. If we charge $10/dose to meet the US market, we can't expect to recoup more than $15m. But at that price no one outside the US can afford it. If we charge a lower price, we can attract the overseas markets, but our overall profit picture is even worse.‖ Ken is crestfallen. Two years ago, he left a tenured research position at NYU to pursue an idea. Whatever its commercial merits, he felt his team was doing pathbreaking science, and he hoped that commercial success would make further breakthroughs possible. Charles, meanwhile, was doodling on his Palm V, apparently oblivious to the discussion. Suddenly he stood up. ―I have an idea,‖ he said. ―What if we charge a high price in the US, where people can afford it, and a lower price elsewhere? If we do it right, we might be able to make enough money to cover our development costs and keep the firm going for another five to ten years.‖ Allison wondered. If Charles was right, there was hope. But she needed to base her decision on more than hope.

We won't be quitting our jobs any time soon to write screenplays. But you get the picture: there may be situations in which you can increase profits by charging different prices in different markets, or more in general using a pricing strategy that may be more sophisticated than just posting one price. We refer to any scheme that induce different customers to pay different prices as “price discrimination.” In practice, price discrimination is connected to a number of related decisions, including product versioning and bundling. Price Discrimination Our analysis to date has been based on uniform pricing: a firm charges the same price for a homogeneous good to all buyers. But it is not hard to think of examples of non-uniform pricing or price discrimination:

Student, child, and senior discounts. Kids, for example, pay less at New York movie theaters, although they use the same size seat as anyone else.

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Airfares. Business customers pay far more for seats, and in return get more room (large seats), better service, and greater flexibility (the tickets can be purchased late and changed with no additional cost).

Site licenses for software. A classic example of a volume discount. No doubt you can think of other examples yourself. Roughly speaking, firms can generally increase revenue and profit by ―extracting‖ some of the consumer surplus. The extreme case is to charge each customer exactly his/her willingness to pay, thereby extracting all of the consumer surplus. The hard part is doing it. There are two basic questions a firm must address in considering whether price discrimination makes sense. The first is whether it can distinguish between markets. If you cannot tell the customers who are willing to pay more from those who are not, you are in trouble. The second is whether you can keep the low-price customers from reselling to the high-price customers. Take the biotech example. The answer to the first question is that we distinguish between customers by where they live. Presumably you can do this reasonably well. The second is more difficult. What if (say) the Brazilians buy at a low price, but some unethical intermediaries manage to buy in bulk and resell in the US? In finance, we call this arbitrage and think of it as a good thing. Here it may be either good or bad from a social perspective (―it depends‖), but it clearly puts a dent into the producer's US profits, and might even make the drug unprofitable. Or take airfares. Here the airlines let the customers distinguish themselves. When a family goes on vacation, it may be sensitive to price and willing to book in advance. But a management consultant or investment banker often travels on short notice and is less sensitive to price, the cost of the plane ticket being small relative to the value of the trip. So airlines have learned that differentiating tickets on how long in advance they are booked is a good way to segment the market. Like other things in this course, it's as much art as science. What follows is a catalog of approaches. Two-Part Tariffs One way sellers can extract a consumer‘s surplus is by setting a two-part tariff. Suppose that each consumer has a known downward-sloping demand curve. By setting the price corresponding to MR = MC, the seller would be leaving money on the table (a positive surplus that is captured by the consumer and a potential surplus that is neither captured by the seller nor the buyer). Suppose however that the seller sets a two-part tariff: a fixed fee and a variable fee. Suppose moreover that (a) the variable fee is equal to marginal cost; (b) the fixed fee is equal to consumer surplus given that price is equal to marginal cost. With this two-part tariff, it is easy to see that the seller would be extracting all of the buyer's surplus.

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Discrimination Among Groups Firms usually cannot ask every consumer her willingness to pay, but they can segment their consumers into various groups with differing elasticities and demand curves. For example, some mail order companies send out retail catalogues to various U.S. markets. These catalogues are identical with one important exception: prices. A New York City consumer would receive a catalogue with prices of, say, 10% higher than that for a consumer in Des Moines. In addition to geographical segmentation, firms can offer special rates to certain segments (students, senior citizens, etc.). In this way, they can capture more consumer surplus by better targeting various consumers‘ willingness to pay. Geographic differentiation is particularly common across countries, where international borders and local regulations help to reduce arbitrage. Thus similar cars and electronic appliances (TVs and stereos) still sell for significantly different prices in the countries of the European ―single market.‖ Self-Selection Schemes Firms often do not have the required information to know your willingness to pay, and thus are unable to capture your surplus. Yet firms in many industries are adept at inducing consumers to reveal that information about themselves. For example, airlines measure differing consumers‘ elasticities in several ways. If you need a ticket for a business trip, you are likely to be willing to pay a lot for it: you are less price elastic; you need to take the trip and you need to take it now. Other consumers who are very price sensitive may book their flights far in advance so they can ―shop around‖ many rates. In any event, the amount of time you wait to book a flight reveals important information about your elasticity. Likewise, firms can offer a product line with various attributes across products to discriminate between consumers who will choose their selection based on their particular demand and elasticity. PalmOne, for example, offers a full line of handheld devices. The PalmOne Tungsten handheld costs $450 whereas cheaper versions of the handheld with fewer features and less aesthetic quality cost under $100. By giving consumers this choice, they will reveal their willingness to pay by their choice of product. If PalmOne only had offered one version, say priced at $250 with a medium amount of features, they would have lost sales margin from some high-end consumers and sales from some low-end consumers. When setting different prices for different versions of a product (―versioning‖), the seller must be careful not to set prices so that the high-end consumers prefer to buy the low-end product. That would defeat the whole purpose of versioning. Coupons are another well-known strategy. Some customers will take the time to lug 50 coupons to the checkout counter while other, more inelastic customers will rush to the check-out without caring about paying the full price.

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Another strategy is discrimination over time. The idea is that the high valuation customers are less patient, so you can start with a high price and reduce it once the impatient have bought it. Many information goods work this way (computer software, books). Bundling and non-linear pricing (e.g., quantity discounts) are also examples of customers revealing themselves. Bundling Bundling is the practice of selling two or more goods together. A supermarket sells apples in cases rather than individually, a car manufacturer sells cars with several optional add-ons such as A/C and stereo, a theater selling subscriptions for an entire season of shows, are all examples of bundling. Bundling can be ―pure‖ or ―mixed‖. A seller does ―pure bundling‖ when the only way his products are sold is as a bundle. In other words, the customers do not have the choice to buy the goods individually. Examples of pure bundling are most of the double CDs on the market. ―Mixed bundling‖ is the practice of selling the goods separately but also to give the customers to buy the bundle at a discount. For instance, theater tickets could be bought separately, but buyers usually have the choice to buy a subscription at a price that is lower than the sum of the individual prices of the tickets. Typically, bundling is a useful practice if the seller faces a demand that is heterogeneous in tastes – what is called “negative correlation of demand” – i.e., the customers that like one good the best are the ones that dislike the other good the most. Example: Double CDs. Consider the situation in which a rock band just recorded 20 new songs. These 20 songs can fill two CDs. The composition of the fist CD is slightly more metal-oriented, while the second CD contains a easy-listening ballad. The typical buyers, who are the fans of the band, can be divided evenly into two groups of about 50,000 individuals each, the metal-oriented (type A) and the romantic (type B), and their willingness to pay are the following:

CD1 CD2 Type A 10 9 Type B 9 10

Let us assume MC=0. If the CDs are sold individually, the optimal prices are P1=P2=9, and the profit is going to be $1.8M0. However, if the CDs are sold together, the optimal price for the bundle is $19, and the profit is going to be $1.9M. Notice that the increase in profit is due to the fact that the demand displays negative correlation.

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Suppose now that CD2 contains a song that becomes very popular with a segment of people that are not the usual band fans. They are 1M people. Then, for instance, suppose that the demand is given by

CD1 CD2 Type A 10 9 Type B 9 10 Type C 0 10

Type C customers does not value CD1 at all and as a result they will not buy the bundle at the $19 price. On the other hand, by decreasing the price of the bundle we loose surplus with the other customers. In these situations, in which it is optimal to ―prune‖ some purchase out, a mixed bundling strategy can help. Suppose now that we sell the CDs at $10 each and the bundle for $18.99. At these prices, types A and B will keep on buying the bundle (as they get 1c of surplus rather than 0 if they just buy their preferred disk), and type C will buy only CD2. The total profit is almost $19M+$10M=$29M. Numerical Examples Example 1. You own a pizzeria that produces at a marginal cost of $6 per pizza and operates as a local monopoly in a small college town. At lunchtime only students come into the restaurant, whereas in the evening while students are studying (or doing whatever it is that students do in the evening) faculty come in. You calculate that students have an elasticity of demand for pizzas of –4 and that faculty has an elasticity of demand of –2. What are optimal prices? Suppose both faculty and students come throughout the day. What challenges do you face to maintain the same revenue as before? Answer: It will be profitable to charge one price pL for the lunch menu and a different price pD for dinner. To determine exactly what these prices should be recall the elasticity rule for a monopolist, which implies that you should charge

6)2

11(

Dp

and

6)4

11(

Lp .

Solving these equations, we get pL=$8 and pD=$12. If both faculty and students come throughout the day, this scheme would not work: faculty would pay the lower price at lunch and you would lose the students‘ custom at dinner. What alternatives are possible?

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Example 2. Biotech startup BioGar has developed Xamoff, an over-the-counter medicine that reduces exam-related anxiety. A patent currently protects Xamoff from competition. BioGar is now thinking of entering the European market but wonders if it should charge the same price in the two markets. They estimate that the demand curves have the form qi = ai – bi pi. In the US (market i=1), the parameters are a1=12 and b1=2. In the EU (market i=2), the parameters are a2=4 and b2=1. The marginal (and average) cost per unit is c=1. All of these units are millions. How much could BioGar gain by charging different prices in the two markets? Answer. Consider first the problem of setting one uniform price. Total demand at price p1=p2=p is Q = q1 + q2 = (a1+a2) – (b1+b2) p = A – B p. (The idea is to save ourselves some writing by defining A=a1+a2 and B=b1+b2.) To find profit as a function of output Q, we solve for price p=(A-Q)/B and substitute:

Profit(Q) = pQ – cQ = cQQB

QB

AcQQ

B

QA

21.

To maximize, we differentiate with respect to Q and equate to zero, which yields

Q = 5.62

cBA

.

Price is

p= 17.3

B

QA.

Finally, quantities are q1=5.67 and q2=0.83, and Profit=14.08. Now find the best prices in the two markets separately. The presumption is that we can avoid ―parallel‖ imports from Europe (which we guess is the cheap location) back to the U.S. Mathematically, this is two separate monopoly problems, but we‘ll do them simultaneously. Profit is in this case depends on both quantities, but otherwise we follow similar logic:

Profit(q1,q2) = )( 212

2

221

1

11 qqcqb

qaq

b

qa

.

This time we differentiate with respect to q1 and q2 (one at a time) and set each derivative equal to zero. The result is

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52

111

cbaq and 5.1

2

222

cbaq .

The prices are now p1=3.5 and p2=2.5, and Profit=14.75. We conclude that, by setting different prices in Europe and in the U.S., profits increase from 14.08 to 14.75, an increase of about 4.76%. For your own enlightenment: Verify that the elasticity rule applies to each market. Show, too, that total consumer surplus falls when we charge different prices. Example 3. We had the ―baby Mac,‖ then the iMac; it‘s now time for the ―baby iMac.‖ As head of marketing of Apple Computer, you decided you could do better than the current situation. Last year, the company sold 1 million iMacs for $1,500 each. This is the most you can get from the market segment that currently buys the iMac. According to a marketing study, there is a second market segment of 2 million people willing to pay up to $500 for a stripped-down version of the iMac. Your market researchers also tell you that (i) the first segment would be willing to pay up to $800 for the stripped down version, (ii) the second segment would not be willing to pay more than $600 even for the full-fledged version of the iMac. Finally, your production people tell you that it costs $300 to produce an iMac, be it the standard version or the stripped-down version. What is your optimal pricing policy? Answer. A first possible strategy (benchmark) is to only sell the full version and charge $1,500. This would lead to selling 1million units, for a total profit of (1500-300) x 1m = $1.2b. A second possible strategy would be to hit each segment by charging $500 for the stripped-down version and $1500 for the full version. But would this work? No: high-end consumers get zero value from buying the full version (it‘s priced at exactly their value), but 800-500=$300 from the stripped-down version. Thus they would buy the stripped-down version. An alternative strategy is to charge $1,200 for the full version (think of it as slightly less than $1,200) and $500 for the stripped-down version. This will lead high-end users to pay $1,200 and low-end users to pay $500. Total profit is now (500-300)x2m + (1200-300)x1m = $1.3b, an improvement over the current solution. Example 4. Monthly individual demand for hours at the NPNG (no pain no gain) gym is Q=10 – P, where P is price per hour. Marginal cost is zero. Find the optimal price and quantity under standard pricing. What is the profit per customer? Suppose the gym charges monthly passes. What is the optimal price of a monthly pass? How much do customers pay per hour? What is the profit per customer? Answer. The standard monopoly pricing problem implies an optimal price of P=5 and output Q=5, for a profit per customer of 25 (note that this is variable profit and does not take into account any fixed cost that might be incurred).

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Suppose now that the gym can charge a monthly fee. Following the logic of two-part tariffs, it should charge an hourly fee equal to the marginal cost, P = 0, in which case demand will be 10; and a fixed fee equal to the consumer surplus at this price, that is,

502

10*10F .

In this case, profit per customer is 50, a clear improvement over simple pricing. Public Policy Price discrimination is not per se illegal. But it raises issues if used in a way that restricts competition. It also raises political issues (think of AIDS drugs). Perhaps for that reason, many price discriminations schemes are disguised, either through bundling or versioning or more complex means. See how long it takes you to figure out the Met‘s ticket pricing scheme!

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Market Power

Previously, we have discussed competitive markets and how they generate efficient outcomes. We highlighted that the Fundamental Theorem rests on some key assumptions. In this chapter, we relax the assumption that firms have no market power. What is market power? How (and why) do governments tend to set rules limiting anti-competitive behavior? These are some of the central themes we will address. Industry Structure Industries vary widely in range of products (broad or narrow), geographic scope (cement is harder to transport long distances than CDs), cost structure (how does the minimum efficient scale compare to the size of the market?), number of firms (presumably related to costs), and intensity of competition (vaguely related to the number of firms). Exhibit 1 describes several mostly-US industries in broad terms. In addition to a name, each industry comes with an SIC code (―standard industrial classification‖), which can be used to identify it. Most are ―4-digit‖ codes, which define industries with a modest amount of detail. Even so, many of the industries listed cover a wide range of products. Telecommunications, for example, covers local service, long distance, wireless, and a variety of specialist providers. If we wanted to understand the industry in any depth, we‘d want to look at finer categories. These industries differ in a number of respects. One is how ―concentrated‖ they are: how dominant the largest firms are in terms of their market shares. The ―4-firm share‖ (sometimes called the 4-firm concentration ratio) is the market share of the largest 4 firms (these market shares are computed from revenue). They range from 1.8% for legal services (there are lots of law firms, and even the largest isn‘t very big relative to the market overall) to 84.8% for aircraft manufacture (where, to be honest, a national number is less meaningful than a global one). Another measure of concentration is the ―Herfindahl-Hirschman Index‖ (HHI), which is widely used by regulators to guide decisions on mergers. The HHI is computed by

HHI = (s1)2 + (s2)

2 + (s3)2 + … + (sn)

2, the sum of the squared market shares (expressed as percentages) of the firms in the industry. If this sounds somewhat esoteric, note that a monopoly would have HHI=10,000 [=1002], an industry with many small firms would have HHI close to zero, and an industry with 4 equal-size firms would have HHI=2500 [=252+252+252+252] (approximately what we see for motor vehicles).

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An alternative route to measuring market power—one that we have considered in the notes on pricing—is the margin (the premium above marginal costs that the firm is charging). However, margins may be difficult to determine without accurate cost data. Moreover, if products are bundled or firms use other advanced pricing schemes it may be difficult to determine the relevant price margins. Thus, in practice margins are used less frequently than market shares. Concentration measures are relatively crude. Depending on the industry, one might want to see finer product categories and/or regional differences (for airlines, for example, concentration is considerably greater at individual airports). While concentration measures don‘t tell us exactly how intense the competition is, they‘re a good start. Generally, we‘d expect to see intense competition if there are many firms, no competition if there is one firm, and something in between if there are a few firms. We have looked in some detail at the two polar cases (competition and monopoly) and plan to turn to the more complex issue of how a small number of firms (an ―oligopoly‖) might interact. Monopoly A firm that is large enough to influence price will generally restrict output and raise price. That‘s good for the firm, in the sense that the monopoly position is profitable. But is it good for society as a whole? The economic basis for competition policy goes back to Adam Smith‘s ―invisible hand.‖ We expect the forces of competition to allocate resources where they are most valuable, thus increasing the welfare of consumers. A monopoly, however, restricts output, raises price, and attracts fewer resources to the industry than one would get under competitive conditions. In a sense, not enough resources are allocated to the industry. Theoretically, we might note that the sum of consumer surplus and producer surplus (profit) is lower under monopoly. The difference is termed the ―deadweight loss‖ of monopoly. All this could change if there are economies of scale. In this case, costs would be higher with competition. The question, then, is whether the cost advantage of monopoly exceeds its markup. Government Policy Firms and industries range from government-owned and operated (Post Office) to regulated (telecommunications, local utilities, pharmaceuticals, financial services), to unregulated but subject to laws on fraud, anti-trust, and so on. As economist Andreu Mas-Colell once said: ―The invisible hand of the free market apparently needs a lot of help.‖ That‘s true even in the US, the bastion of free markets. Competition policy. Most countries have laws enforcing competition: outlawing price agreements among competitors, restricting mergers that substantially increase market concentration, and limiting the behavior of monopolies and near-monopolies.

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Most countries outlaw price fixing (when two or more firms get together to agree on price and carve up the market). In effect, price fixers agree to act collectively as a monopoly (the term is ―cartel‖). The DeBeers diamond cartel is a good example. Many countries also limit mergers that they feel would reduce competition in one or more markets. In the US, the Department of Justice has guidelines based on the HHI. As a rule of thumb, mergers that lead to an HHI of 1000 or less ordinarily lead to no further scrutiny; those that raise the HHI by 100 or more and produce a post-merger HHI between 1000 and 1800 raise significant questions; and those that raise the HHI by 50 or more and produce a post-merger HHI above 1800 raise significant concern. All of this is contingent on the definition of the market (geographic, range of products). Monopolies themselves are not illegal, although monopolies generally have an obligation not to exploit their monopoly advantage to enter other markets. That was an issue in the Microsoft case: whether Microsoft had used its monopoly position in operating systems to extend its reach to the browser market. International issues have become increasingly important, the ill-fated GE/Honeywell deal being a recent example. In this case, a merger of two U.S. firms was blocked by the EU‘s Competition Commission on the grounds that it would reduce competition in some European markets (specifically, aircraft engines). Regulation of monopolies. Typically, industries in which the minimum efficient scale leaves room for only a single producer are regulated. The basic theory of regulation is to force a price equal to what we‘d see under competition. Experience tells us, though, that poorly implemented regulation can be as bad as unfettered monopoly. Governments continue to experiment with new approaches. Essential facilities. A critical issue in monopoly regulation is what to regulate. For years, governments regulated telecommunications in their entirety. But more recently, governments have loosened restrictions on long distance service, which is increasingly competitive. Local service, however, is generally regulated by states. The argument is that the local connection is a natural monopoly (it‘s expensive to build more than one) and should be regulated, but long distance is not. Similar arguments have been applied to electricity.

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Exhibit 1. Properties of Selected Industries

Industry SIC Code 4-Firm Share HHI Region Source (Date)

Electric power 2211 14.3 US Commerce (97)

Pharmaceuticals 3254 32.2 446 US Commerce (97)

Computers 3341 37.0 465 US Commerce (97)

Semiconductors 334413 52.5 1080 US Commerce (97)

Motor vehicles 3361 82.4 2506 US Commerce (97)

Aircraft 3364 84.8 1637 US Commerce (97)

Air transportation 4811 25.5 US Commerce (97)

Motion pictures 5121 32.5 US Commerce (97)

Sound recording 5122 53.1 US Commerce (97)

Telecommunications 5133 42.3 US Commerce (97)

Commercial banking 52211 17.3 US Commerce (97)

Securities brokerage 52312 37.7 US Commerce (97)

Wholesale banking 716 World Roy Smith (98)

Legal services 5411 1.8 US Commerce (97)

General hospitals 6221 73.5 US Commerce (97)

Performing arts cos. 7111 8.5 US Commerce (97)

Sources. US Department of Commerce web site, Roy Smith.

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Auctions Many business transactions are now handled with auctions, rather than through conventional markets in which sellers post prices and buyers decide whether – and how many – to buy. Common examples include fine art, electro-magnetic spectrum rights, US treasury securities, many equity markets, some IPOs, privatizations of state-owned companies, wine, eBay, and on-campus interviews. You get the idea. These are all sales, but there are many auctions by buyers, too: government contracts to buy goods and services, for example. Why auctions? Our usual market story is that sellers get together with lots of buyers, and after enough transactions they figure out a reasonable price: an ―equilibrium.‖ But in most of the examples we just mentioned, the assets are unique; we don‘t have the luxury of experience to establish a reasonable price. Once a Vermeer painting or 3G spectrum rights are sold, they‘re gone. If you price such a product/asset low, you get less revenue than you could. If you price it high, you get no takers (and no revenue). The solution is to run an auction, and let buyers reveal what they think it‘s worth. But what kind of auction? A conventional English auction? A Dutch auction in which the price falls until someone bids? A sealed-bid auction? Over the last few decades, there have been enormous advances in our understanding of auctions and comparable advances in their range of use. We‘ll try to give you some sense of both. The theory of auctions has taken great strides in recent years, and builds on the theory of mechanism design (the topic for which Hurwicz, Maskin and Myerson won the 2007 Nobel prize in economics). The broad field of mechanism design (as the name might suggest!) looks at designing a system of rules and regulations in a way that achieves good outcomes and takes into account that those involved will change their behavior as the rules change. In the context of auctions, the auctioneer can choose the type of auction that is run and will wish to consider the impact on the revenues raised and (for example if the auctioneer is the government) the efficiency of the outcome (does the person who gets the good value it most, is the contractor who gets the job the one who can conduct it most efficiently etc.) Auction design has hit the headlines, in its use to sell public assets. Historically, and still in some countries and some sectors public assets were sold through ―beauty contests‖ in which firms submitted long-detailed proposals and a committee of officials would choose which they liked best. However, in part following the theoretical work, auctions are being increasingly used and with some success. Sales of radio spectrum (necessary to run a mobile phone operation) throughout Europe and the US have raised hundreds of billions of dollars, and seemed to raise much more revenue than the previous system of beauty contests. The telecom auction in Britain alone raised $35 billion!

Firms and Markets Lecture Notes

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Common Auction Mechanisms The most common auction types are:

The (ascending) ―English auction,‖ in which buyers make increasingly higher bids until only one bidder remains. The highest bidder buys the object at the highest bid. This is how auctions for antiques in auction houses (Sotheby‘s or Christie‘s) are conducted

The (descending) ―Dutch auction,‖ which works the other way around: starting with a very high bid, the price is reduced until someone is willing to bid. The first and only bidder buys the object at the bid price. Flowers are sold in this way in the Netherlands and this can be a particularly fast way to run an aucion.

―Sealed bid‖ auctions, in which potential buyers submit ―sealed,‖ or secret, bids for an object. The highest bid buys the object for the bid price. If you think about this, you might realize that the sealed bid and Dutch auctions are equivalent, in the sense that bidders do not have any information about other bids and the highest bid wins.

o A variant is the ―Vickrey auction,‖ in which buyers submit sealed bids. The

highest bidder wins, but must pay only the second highest price. There are lots of variations on these basic designs, but this is a good start. The obvious question is which of these auctions works best. For example, if you‘re the seller, which auction generates the most revenue? The answer is the usual: it depends. We‘ll be fairly concrete what it depends on before we‘re done. How Bidders Value the Object Probably the most important ingredient in an auction is the values placed on the object by potential buyers. We‘ll assume that the seller does not know the values placed on the object by potential buyers; if she did, she could simply charge a price equal to (or just below) the highest valuation. We‘ll also assume that buyers do not know each others‘ valuations. They do know their own valuation: we say that it is private information, since the knowledge is their own. However, to progress we need to make some assumptions about what the auction designer and bidders believe about what the distribution of values that other bidders might be. In trying to figure out what price to bid on in a Dutch auction, for example, a bidder will clearly bid differently if he expects rival bidders to have say a 90% chance of having a valuation of $10 and a 10% chance of a valuation of $12 than if he expects rival bidders to have an equal likelihood of any valuation between $5 and $8. Key for the design and performance of auctions therefore would appear to be what is known about bidders‘ valuations. The way theorists think about this is to assume that we know the distribution from which their values are drawn. (This is like much of statistics: we use a pdf to summarize the extent of our uncertainty.)

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As well as taking great care in what bidders know about each other‘s valuations. Theorists (and practitioners!) must be careful to distinguish between private values and interdependent values. Bidding with “Private Values” If I buy a picture solely to put on my wall to enjoy, then the benefit that I get from that does not depend on others‘ valuations. We call this a ―private values‖ case and here, bidding strategies are relatively simple. For example, suppose that Luis wants to sell his apartment and the only potential buyers and John and Heski. To see how they should bid under different auction formats, we need to be more specific about the value of the object being auctioned. We‘ll start off by assuming that for each of Heski and John their valuation for the apartment is equally likely to take any value between 0 and $1 million. Consider first the English auction: Heski and John should each keep bidding until the going price reaches their valuation, after which they should keep quiet. The winner will therefore pay the loser’s valuation. Since the loser‘s valuation is equally likely to be anything less than the winner‘s valuation, on average the winner ends up paying half his valuation. It is now easy to see that the English auction raises as much as the Vickery auction. Suppose Heski and John submit their true valuations as their bids in the Vickery auction then Luis sells his house to the highest bidder at a price equal to the second highest bid: with the same average payoff as the English auction. Note that we must of course ask whether they would want to submit their valuations as bids. It is easy to see that they do. No matter what John does, Heski wold like to bid his valuation. If John bids lower than Heski‘s valuation, then by bidding his valuation Heski can guarantee winning without affecting the price. If John bids higher than Heski‘s valuation then Heski doesn‘t want to win! and so might as well bid his valuation. Bidding strategies for the first price auction, or the Dutch auction are a little more subtle. In such auctions, you won‘t want to bid your true valuation, since if you win then you pay your bid and so you have pay your full valuation and don‘t gain anything by winning, and so a bidder shades their bid down below their valuation; however the more you shade your bid, the lower the probability of winning. Trading off the probability of winning against the gain from winning turns out to follow a similar analysis to the margin-volume trade-off for a price-setting monopolist, though we leave the analysis for another day… Bidding with “Interdependent Values” When agents have private values they learn nothing in the course of the auction. However there are cases where the agents have ―interdependent values‖ that is where if Heski has a higher valuation then John is also likely to have a higher valuation. For example, suppose that instead of buying a house to live in, Heski and John were both looking to buy as an investment

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(rather than to live there). They might have different knowledge of the market (leading to different estimates). If John naively bids his full valuation in the Vickery auction, for example, then on winning the auction he will usually be disappointed. Why? Because his winning the auction suggests that Heski had a lower valuation, which suggests that Heski had relatively bad news about the state of the market and that John‘s estimate was an over-estimate. This phenomenon is called the ―winner‘s curse‖ and has been widely discussed in the context of oil tracts. For all oil drilling companies, the key determinant in valuing a tract is the amount of oil to be found there. Different bidders‘ estimates are likely to rely on differing geological surveys – some are likely to be more optimistic and some more pessimistic. If you win then it is likely that you had a relatively optimistic survey and so bidders should shade down their bids to take into account this effect. Since an English auction allows bidders to gain some information about other bidders valuations in the course of the auction, it allows bidders to realize when other bidders are optimistic and so will typically raise greater revenues than a Dutch or sealed bid auction. Practical Considerations Beyond the considerations addressed above there are a number of further practical considerations to be considered:

In general we might think about the costs of making a bid. Do bidders have to devote resources to prepare business plans etc ahead of bidding? Are bidders forced to disclose valuable commercial information?

In general, a key determinant of revenue for an auctioneer is the number of bidders (an auction with only one bidder, regardless of the format is unlikely to raise much revenue---this sounds obvious but there are examples of telecom auctions when there were no more bidders than objects being sold). Encouraging bidder participation is therefore critical.

How long does the auction take to run? This is a particular issue for perishable goods and affects the design of fish markets in Tokyo and flower markets in Amsterdam?

In the Vickrey auction you need to trust the auctioneer, who has an incentive to change your bid, or make claims about others‘ bids that can be hard to verify.

An English auction can make it easier for bidders to collude in their bids (it is easier for those colluding to verify that the others are sticking to their agreements).

Is the winners‘ curse a problem? Botton line: This gives you the idea that posting prices is only one way to sell.

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Further Reading This is a topic about which experts have real knowledge: they simply know more about how auctions work than the rest of us. If you‘re interested, a number of interesting sources are easily availabe:

Paul Klemperer has a free and excellent online book Auctions: Theory and Practice at http://www.paulklemperer.org/index.htm. reading the whole book might be for those only very interested, but the introductory chapter is an excellent introduction.

John McMillan, ―Selling Spectrum Rights,‖ Journal of Economic Perspectives, Summer 1994, 145-62.

Paul Milgrom, ―Auctions and bidding,‖ Journal of Economic Perspectives, Summer 1989, pages 3-22.

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Game Theory: Introduction to Strategy With perfect competition and monopoly, the interactions between firms are minimal to nonexistent. In a perfectly competitive market, the impact of competitors is summarized entirely by the market price. In a monopoly, there are no competitors to worry about. In markets with a small number of firms, however, the interactions can be substantially more complex. If I cut prices, will my competitors cut them, too? If I enter a new market, will others follow? If I introduce a new flavor of ice cream, will my competitors imitate or look for other niches in the ice cream market? This note is an introduction to the formal analysis of interactions among a small number of players: what we call ―game theory‖. We‘ll do this in settings that are very. For example, there will typically be only two ―players.‖ Why? Because it‘s helpful to reduce distractions, even if that makes the situations less realistic. Of course, the challenge is to recognize strategic situations in practice, where they often come in heavy disguise. A Strategic Situation Suppose you own a software business. You only have one competitor. You can decide to launch a new software package this year or not to launch one. You don‘t know whether your rival has decided to launch her own new software package. However, you are pretty certain what will happen in the following four scenarios. ―If I launch and my rival launches, we both lose money. If I launch and she doesn‘t, only I make money. If she launches and I don‘t, only she makes money. And if neither of us launch, we both lose money – but less than if we both launch.‖ You wish you knew what your rival was going to do, but you don‘t. So how do you proceed? You might say to yourself: ―If she thinks that I am going to launch, she won‘t.‖ But then you think: ―If she thinks I think she will launch and thus I don‘t, she will launch and I will not make money.‖ But that seems too simple. So after pondering a bit more you think: ―If she thinks that I think that she thinks that I think she will launch, she might think I will actually launch and so she won‘t.‖ And so on, and so on. Pretty soon you‘re totally confused and have no idea what to do. How do we break out of this logical conundrum? How do we reason strategically when confronting uncertainty and risky decisions in a competitive setting? How do we predict what our competitors will do given what we will do when our decisions are based on what our competitors do (and vice versa)? We‘ll see.

Firms and Markets Lecture Notes

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As we work through some formal games and learn how to use game matrices and trees, we‘ll come across a few general ideas that underlie strategic behavior. Among them:

Understand your competitor.

Timing matters.

Information matters, too.

Some games are better to play than others.

Some games have win-win solutions and some don‘t. These platitudes will become more than that in a few weeks. Two Ways to Represent Games Formal games have a number of ingredients: a list of players, rules that govern how they play, a set of possible ―strategies‖ (moves) for each player in every possible situation, and the payoffs (benefits) to each player for every possible combination of strategies. We‘ll focus here on relatively simple games, in which two players make one move each from a short lists of choices. A key part of the ―rules‖ is the order of moves. In a so-called ―normal-form game,‖ the players choose their moves at the same time without knowledge of the other‘s move. We represent such games in a matrix (table) (sometimes we will refer to these games as ―matrix games‖). In a so-called ―extensive-form game,‖ players choose and make their moves sequentially, one after the other. (Think of chess.) We represent these games with game trees (sometimes we refer to them as ―tree games‖). Let‘s talk about normal-form games first. An example might be:

L R

20 10 T 15 5

5 15 B 10 20

In this game, Player 1 and Player 2 choose moves at the same time. Player 1 chooses between top (T) and bottom (B). Player 2 chooses between left (L) and right (R). The numbers in the matrix tell us the benefits to the two players of each combination of strategies (moves), with Player 1‘s benefits in the lower left corner of the relevant box and Player 2‘s in the upper right corner. For example, if Player 1 chooses T and Player 2 chooses R, the benefit to Player 1 is 5 (in whatever units seem appropriate to Player 1) and the benefit to Player 2 is 10.

Player 2

Player 1

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Extensive-form games have similar elements. A sample game tree might be:

Here, the boxes tell you who moves when and the branches illustrate the possible choices at each point. Thus Player 1 moves first, choosing (again) between T and B. Once Player 1 has moved, Player 2 chooses either R or L. In this case, the two ―2‖ boxes show you that Player 2‘s choice might depend on the choice made by Player 1. The payoffs at the end tell you the benefits to the two players for every combination of strategies, with payoffs to Player 1 listed first. A point to keep in mind: Even though these two games look similar (same players, same choices of strategies, same payoffs), they‘re different games. Why? Because the order of moves is different. We‘ll see shortly that this can make a difference to the outcome. Outcomes to Games The next step is to consider reasonable outcomes of games. What would we expect Player 1 to do? Player 2? What is the outcome of the game and the payoffs received by each player? As an illustration, let us consider the following normal-form game:

L C R

T

5 6 7

9 8 1

M

3 5 6

1 2 0

B

7 6 8

2 3 4

1

2

2

(15,20)

(5,10)

(10,5)

(20,15)

T

H

B

L

H

R

L

R

L

S

H

Player 1

Player 2

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Dominant and dominated strategies. In some games, there are moves that are good in all situations, in the sense that their payoff is greater for every strategy chosen by the other player. Such strategies are ―dominant.‖ Conclusion: play them. In the above game, Player 2‘s R is a dominant strategy: it‘s better than both L and C for any choice of Player 1. In some other games, you may find that one strategy has lower payoffs than another strategy for every move by the other player. We say that such strategies are ―dominated‖ (by the other strategy). In the game above, Player 1‘s M is dominated by T (and by B, too!): Regardless of Player 2‘s choice, T is better than M (and so is B). Clearly you‘d never play a dominated strategy. The converse need not be true: just because you wouldn‘t play a strategy doesn‘t mean it‘s dominated. We conclude: do not play dominated strategies. We can cross them out and proceed without them. One important note, taking the above game as an example: If Player 2 expects Player 1 to choose B, you might think that Player 2 is better off by choosing L: even though Player 2‘s payoff is lower than by choosing R, Player 1‘s payoff is lower in the (B,L) combination than in (B,R). However, each player‘s goal is to maximize his payoff, not to minimize the other player‘s payoff or maximize the payoff difference. True, in some real-world applications the rival‘s payoff matters. For example, if the rival firm‘s profit is sufficiently low then the rival firm may decide to exit, leaving me as a (more profitable) monopolist. If that were the case, then we should include this additional benefit as part of my payoff. In other words, the payoffs in the matrix already reflect all of the above considerations. Best responses. In many games, the best strategy choice depends on the other player‘s strategy. We call the best choice for each move by the other player the ―best response.‖ If there‘s a dominant strategy, it‘s the best response for every move by the other player. In this case, Player 2‘s best response is to play R always. We mark those payoffs in bold. How about Player 1? If Player 2 chooses L, the best response is T. If Player 2 chooses C, the best response is also T. And if Player 2 chooses R, the best response is B. Nash equilibrium. We consider a ―reasonable outcome‖ in a game to be a combination of strategies in which each player chooses its best response. Such a combination is called a ―Nash equilibrium.‖ In the preceding example, (B,R) is a Nash equilibrium. At a Nash equilibrium, neither player has an incentive to change its strategy unilaterally. Summary:

Don‘t play dominated strategies.

Do play dominant strategies.

In general: Each player chooses best response to every choice of the other player.

Equilibrium: Each player makes the best response to the others‘ possible move. An outcome in which each player chooses his best response is called a Nash equilibrium.

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Historical note. Early pioneers in game theory include the brilliant mathematician John von Neumann (Theory of Games and Economic Behavior, 1944, with co-author Oscar Morgenstern) and John Nash. Nash is a particularly intriguing case. After doing path-breaking work in the early 1950s, schizophrenia kept him out of circulation until he recovered in the 1980s. He received the Nobel Prize in economics in 1994. There‘s a terrific book about him, Sylvia Nasar‘s A Beautiful Mind (there‘s also a fairly inaccurate movie of the same name). Examples The most famous example of a game is the ―prisoner‘s dilemma.‖ A business version is this: Firm A and Firm B both have to set output levels. They cannot discuss their choice of output levels, because that‘s illegal. Each would like total supply to be low (to generate a high price) but sell a lot itself. You can see the conflict. An example might look like:

High Low

High

10 5

10 20

Low

20 15

5 15

You can see the incentive to get together to divide the market: both firms do well if they agree to limit supply (Low, Low). But you can also see the incentive to produce more: once (say) Firm B chooses Low, the best thing A can do is produce High. Let‘s examine this formally as a game. The problem is that High and High are dominant strategies. The only Nash equilibrium is therefore for both firms to produce a lot (High,High), which drives down price and profit. This shows why cartels are so attractive to firms: they could both make more if they were allowed to collude. It also shows why – in the absence of a binding agreement – cartels tend to fall apart. The Prisoner‘s Dilemma is striking in showing how a bad outcome (for the firms) might be an equilibrium. But not all games work this way. You might try slapping down some numbers and see where they lead. Some games have win-win possibilities. Consider below the game we looked at earlier, with some local color added.

What‘s going on here? Richie and Dave are friends and would like to do something together. Richie prefers the Opera and Dave prefers the Knicks, but it‘s more important to each of them to do something together than to get their first choice. Let‘s assume that they can‘t do the obvious thing and simply agree on what to do: Each must make his choice without knowing what the other will do. What‘s the Nash equilibrium? In this case, there are two Nash equilibria, (O,O) and (K,K). The difficult part is how to choose among them, and game theory has little to say about that.

Firm B

Firm A

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Knicks Opera

20 10 Knicks 15 5

5 15 Opera 10 20

Many students find this confusing, so let‘s take a closer look. A common question is: If we‘re moving simultaneously, how do we know which Nash equilibrium to play? And if we don‘t know which one, couldn‘t we end up at a non-equilibrium square? (Yes!) A defense of the Nash equilibrium outcome might be that neither player would want to change its strategy unilaterally. Or we might decide that the concept of Nash equilibrium is simply not enough in this case to tell us what the outcome of this game should be. Whatever its complexities, the situation turns up in the business world routinely. One example is standards for new products. Two companies might have a preferred technical standard, but in some cases they‘re each better off if the other chooses the same standard. That is, each firm would prefer to use the competitor‘s standard than choose different standards and confuse the market. Things like industry associations are sometimes used as ways to accomplish this. (Technical agreements between competitors are not per se illegal.) Timing Matters The same game can be used to illustrate the impact of timing on the outcome. Suppose Richie gets to move first: he chooses, and calls Dave to tell him where to meet. Dave then decides whether to meet him or choose the other event. The game tree looks like this:

How do you find the outcome for a game like this? Answer: you start at the end. When it‘s Dave‘s turn to move, Richie has already chosen. If Richie chose K, then the best thing Dave can do is choose K (20 is greater than 10). If Richie chose O, then Dave chooses O, too (15 is

Dave

Richie

R

D

D

(15,20)

(5,10)

(10,5)

(20,15)

K

T

H

O

B

K

O

K

O

S

H

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greater than 5). Richie now takes Dave‘s choices into account in choosing his own strategy. He knows that he‘ll get 15 if he chooses K and 20 if he chooses O, so he chooses O. The equilibrium: (O,O). You can see how important the timing of moves is here. If both move at the same time, it‘s not clear which Nash equilibrium occurs. If Richie moves first, they go to the Opera. If Dave were to move first, they‘d go to the Knicks. You might say that Dave has a first-mover advantage in this game. The point, however, is not that going first is good (sometimes it is, sometimes it isn‘t), but that timing has an impact on the outcome. Additional examples Example 1. The tables below represent a series of two-player games which illustrate the rivalry between Time magazine and Newsweek. Each magazine's strategy consists of choosing a cover story: ―Impeachment‖ or ―Financial crisis‖ are the two choices. (Time‘s strategy is in row, Newsweek‘s in column. In each cell, the first value is Time‘s payoff, the second Newsweek‘s payoff.)

Impeachment Financial crisis

Impeachment 35,35 70,30 Financial crisis 30,70 15,15

(i) Time and Newsweek are evenly matched

Impeachment Financial crisis

Impeachment 42,28 70,30 Financial crisis 30,70 18,12

(ii) Time is more popular than Newsweek

Impeachment Financial crisis

Impeachment 42,28 70,50 Financial crisis 50,70 30,20

(iii) Some readers will buy both magazines

The first version of the game corresponds to the case when the game is symmetric (Time and Newsweek are equally well positioned). As the payoffs suggest, ―Impeachment'‖ is a better story but payoffs are lower when both magazines choose the same story. The second version of the game corresponds to the assumption that Time is a more popular magazine (Time's payoff is greater then Newsweek's when both magazines cover the same story). The third version of the game is the case when the magazines are sufficiently different that some readers will buy both magazines even if they cover the same story. For each of the three versions of the game,

(a) Determine whether the game can be solved by dominant strategies; (b) Determine all Nash equilibria;

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(c) Indicate clearly which assumptions regarding rationality are required in order to reach the solutions in (a) and (b).

Answer. In (i), Impeachment is a dominant strategy for both players. It follows that (Impeachment, Impeachment) is the unique Nash equilibrium. All we need to assume to reach this conclusion is that players are rational and know their own payoffs. In (ii), Impeachment is a dominant strategy for Time, but not for Newsweek. Given that Time chooses Impeachment, Financial Crisis is the optimal choice for Newsweek. It follows that (Impeachment, Financial Crisis) is the unique Nash equilibrium. This solution assumes that Time is rational and knows its payoffs; and Newsweek is rational, knows the payoffs for both players, and believes Time is a rational player. In (iii), there are no dominant strategies. There are two Nash equilibria (in pure strategies): (Impeachment, Financial Crisis) and (Financial Crisis, Impeachment). In this context, the concept of Nash equilibrium presupposes that players know the payoffs of both players; moreover, it is common knowledge (I expect that you expect that I expect...) that the particular equilibrium will be played. Example 2. Consider the situation where Ericsson and Nokia compete in the market for 4G handsets. Each firm contemplates setting one of two possible price levels: $100 or $90. Production cost is the same for both firms: $40 per handset. Market demand as a function of the prices set by each firm is given by the following matrix (notice that this is not the payoff matrix; each firm‘s payoff is profit, not output).

100 90

800 1100 100 700 400

700 900 90 800 600

Suppose firms choose prices simultaneously. Describe the game and solve it. Answer. Based on the values provided, we can compute profits for each price combination. For example, if Ericsson sets a price of 100 and Nokia a price of 100 too, then Ericsson gets a demand of 700k and total profit $42m = (100 – 40) 700k. Doing the same for all price combinations we obtain the following profit matrix (in $m per quarter):

100 90

48 55 100 42 24

42 45 90 40 30

Ericsson

Nokia

Ericsson

Nokia

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Nokia has a dominant strategy: to price at $90. Knowing that Ericsson should price at $90 too, though it is not a dominant strategy. The Nash equilibrium of this game is therefore (90,90), leading to profits of (30,45) for Ericsson and Nokia, respectively. Notice that both Ericsson and Nokia are worse off than they would be by pricing at $100. This game has a similar outcome as the prisoner‘s dilemma. Example 2 (continued). Suppose that Nokia has a limited capacity of 800k units per quarter. How would the analysis change? Answer. The constraint binds in the case when Nokia sets a price of $90. In this case, Nokia‘s sales are now 800k, not the values previously reported. Everything else remains the same. The new payoff matrix is:

100 90

48 40 100 42 24

42 40 90 40 30

It is now a dominant strategy for Nokia to price at $100. Knowing that Ericsson should price at $100 too. The new equilibrium is therefore given by (100,100), leading to profits (42,48) for Ericsson and Nokia, respectively. This example shows that one firm‘s capacity constraint can soften price competition and benefit all firms in the market. Example 2 (continued further). Suppose you work for Ericsson. Your CIO is unsure whether Nokia is capacity constrained or not. How much would you value this piece of information? Answer. This information would have no value (as far as this game is concerned). In fact, regardless of whether Nokia is or is not capacity constrained, Ericsson‘s dominant strategy is to price at $90. Information only has value if it would lead me to change my course of action and improve my prospects. Other Issues In the coming weeks, we‘ll look at additional strategic issues. Among them:

Sources of leverage. When firms interact repeatedly, either over time or across markets, this gives them additional leverage over each other. Sometimes that can be used to moderate the impact of Prisoner-Dilemma-like situations. Example: American Airlines and United compete on the NY-Chicago route. If American reduces fares on this route to gain market share, United might not only meet the lower fare, but also retaliate by reducing its fare on the Chicago-Dallas route, which is important to American. This makes fare-cutting less attractive to both players.

Ericsson

Nokia

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Information. When one player knows something the other doesn‘t (or knows it earlier), that can affect the game, too. Example: You‘re a new entrant to the PC market and buyers do not yet know the quality of your products. How do you convince them that your products are good?

Reputation. This is essentially a combination of the first two. There are times when a firm‘s actions have an impact not only on the current situation, but also on customers‘ and competitors‘ interpretations of your future actions. An example is branding: A company with a strong brand and products will be less willing (presumably) to sell shoddy products under the same brand. (Can you see why?) Or: Intel suing AMD sends the message that Intel will aggressively defend its property (and maybe more).

Choose the right game. Some games lead to bad outcomes and you should avoid them if you can. Example: The ―Browser Wars‖ drove the price of web browsers to zero. Could Netscape and Microsoft have played a different game with a better outcome?

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Price Competition We‘ve acquired some tools to analyze games in which players are taking a short-run perspective, that is, they are trying to do as well as possible in the game today, without thinking about the long-run implications. The relevant concept is Nash equilibrium: players settle into playing a best response to what the other players are doing. We‘ll start by looking at differentiated products, which are markets in which consumers perceive a difference between different brands: a button-down white men‘s shirt from Ralph Lauren is not the same as a button-down white men‘s shirt from The Gap, though each may be preferred by different customers. Then we‘ll look at goods that are identical from the point of view of the customer, such as gas or sugar or flour; these are sometimes called ―commodity‖ businesses. We‘ll see how serious the short-term price competition perspective can be, in that environment. A. Differentiated Price Competition Let‘s think of Time and Newsweek, and imagine that every week they are choosing their price for the week, not knowing what the other magazine has chosen: that‘s a simultaneous game. Here prices are the strategic variable, so we will think of all payoffs in terms of price, and actions in terms of prices (i.e. not in terms of quantities!). Time and Newsweek are looking for the stable point, or Nash equilibrium, of this game. That involves figuring out the best responses for each player to what the other player does. For instance, Newsweek will have to ask the following question: ―Suppose I had ESP, and I knew that Time was going to charge $3.00 this coming week, how much would I want to charge?‖ Then it will have to ask ―Suppose I had ESP and I knew that Time was going to charge $3.10 this coming week, how much would I want to charge?‖ and so on, for all possible prices that Time might want to charge. What Newsweek will come up with is what‘s called a ―Best response curve‖ (or ‗reaction function‘), that indicates what price Newsweek would want to charge, based on Time‘s price:.

Firms and Markets Lecture Notes

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Why is it upward sloping? It‘s probably easiest to think in terms of a price cut: Suppose both newspapers are priced at $4, and Time decides to cut price to $3.50. Newsweek will probably want to cut its price, too, to stay competitive, but maybe not all the way to $3.50. Newsweek might price at $3.88, for instance. Why doesn‘t Newsweek match Time‘s price cut penny for penny? Imagine a market of readers: some are very loyal to Newsweek, some prefer Newsweek, some slightly prefer Newsweek, some don‘t care, and some prefer Time. Quite a few of the loyal customers will still buy Newsweek even if Time is a little cheaper. Newsweek wants to compete with Time for the ―less loyal‖ customers, but it doesn‘t want to lose so much revenue on loyal customers. So it does not cut price quite as much as Time. In the extreme, if Time were to cut its price to zero, Newsweek‘s best response would not be to cut its price to zero: after all, it has a positive marginal cost. Probably it would keep the price a little above its MC, and still have a few loyal customers. Meanwhile, Time performs the same calculation: ―Suppose I knew that Newsweek would charge ___, what would my best response be?‖ This gives a best response curve for Time. (In this case we‘ve drawn them as identical, but if Time and Newsweek has different costs or readers of different loyalty, the curves would be different.)

Newsweek’s

Price

$3.00

$4.00

Time’s

price

Newsweek’s best response curve

$4.00

Time’s Price

$3.00

$4.00

Newsweek’s

price

Time’s best response curve

$4.00

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Now, in order to graph both curves on the same picture, we are going to flip the ―Time‘s best response‖ graph around, by flipping the axes: Now we can draw both curves on the same graph, and find the point that is a best response for both players: If Newsweek knew that Time would charge $4.00 this week, Newsweek would want to charge $4.00; and if Time knew that Newsweek would charge $4.00 this week, Time would want to charge $4.00. So that is the Nash equilibrium, or stable point. (Notice that both charging $5.00 is not an equilibrium: if Time were going to charge $5.00, Newsweek would want to charge $4.25.) We expect that prices would settle down here, once they had competed for a few weeks. One thing to note, though, is that the prices are lower than if a monopolist owned both Time AND Newsweek, and were setting the price for each: the monopolist might choose a price of

$3.00 $4.00

Time’s price

Time’s best response curve

$4.00

Newsweek’s

price

Newsweek’s

Price

$3.00

$4.00

Time’s

price

Newsweek’s best response curve

$4.00

Time’s best

response

curve

$3.00

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$5.50 per magazine, for example. This isn‘t something you can see from the graph, so we will give a mathematical example. Math example: This is purely for nerds who find it easier to follow once you’ve seen the math! Ignore this example if it is not

helpful. You are not expected to know this math.

Suppose we have the demand for Time and Newsweek:

qT = 5 – pT + 0.5pN

qN = 5 – pN + 0.5pT

and we have A and B’s marginal cost: MCA = $1, and MCB = $1

How do we find T’s best response curve?

Question Time needs to ask: What price should T charge, to maximise her profits, if she knows that

Newsweek will charge a price pN? (In maths, we now treat pN as a number that we know, like $3.00 or $4.00,

even though we write it in algebra.)

Max ProfitsT = pTqT - MCqT = (pT - 1)qT

This is differentiated Price competition put everything in terms of price

ProfitsT = (pT - 1)qT = (pT - 1) (5 – pT + 0.5pN)

= 5pT – pT2 + 0.5pN pT - 5 + pT – 0.5pN

= 6pT – pT2 + 0.5pN pT - 5 – 0.5pN

Remember, profits are maximised at the point where marginal profits are zero (or, equivalently, where MR =

MC)

maximise taking pN as a known constant number: find the derivative with respect to pT, and find the best

response pT* at which it’s zero (the top of the hill).

Marginal Profits = d(ProfitsT)/dpT = 6 – 2pT + 0.5pN

to find pT* that sets marginal profits equal to zero: 6 – 2pT* + 0.5pN = 0

pT* = 3 + 0.25 pN

That’s T’s best response curve.

Doing the same maximisation for Newsweek gives N’s best response curve.

pN* = 3 + 0.25 pT

As before, we solve by finding the Nash equilibrium: pT* and pN* are a Nash equilibrium if

T wants to charge pT* if N is charging pN*

N wants to charge pN* if T is charging pT*

When both T and N are at a best response, we’re at the Nash equilibrium solve the two together:

pT* = 3 + 0.25pN*

AND pN* = 3 + 0.25pT*

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And then solve the two together:

pT* = 3 + 0.25 pN* = 3 + 0.25(3 + 0.25 pT*)

= 3.75 + 0.0625 pT*

0.9375 pT* = 3.75

pT* = 3/(0.75) = 4

pN* = 3 + 0.25 pT* = 3 + 0.25(4) = 4

We said that these are lower prices than a monopolist would charge. A monopolist would choose pT and pN to

maximize the sum of profits:

Monopolist: Max pN, pT { pTqT - MCqT + pNqN - MCqN }

= {(pT - 1) (5 – pT + 0.5pN) + (pN - 1) (5 – pN + 0.5pT)}

Usual approach: Take the derivative of profits with respect pT and set equal to zero:

6 – 2pT + 0.5pN + 0.5pN – 0.5 = 0

pT = 2.75 + 0.5pN

Take the derivative of profits with respect pN and set equal to zero:

0.5pT – pN + 6 – 2pN + 0.5pT = 0

pN = 2.75 + 0.5pT

Solving these two equations together (as above) gives pN = pT = $5.50

So prices are higher under a monopoly that owns both magazines.

B. Price Competition in Identical Goods What happens if a small number of firms compete on price, that is, they produce identical products and try to attract business by pricing below the competition? In some situations, the result can be that price is driven down to marginal cost and no one makes any money. This is particularly painful in industries with high fixed costs: marginal cost is well below average cost and firms pricing at marginal cost lose money. A good example is airlines, where price competition in the 1990s resulted in pretty much everyone but Southwest losing money. The point of this session is that the price-cutting game is a prisoner‘s dilemma: it‘s a bad outcome, but the outcome is inherent in the game. The outcome is sometime referred to as the Bertrand trap, named after the 19th-century French economist Joseph Bertrand. The lesson to you should be: price competition is hazardous. Or as they say in the business world: avoid ―commodity‖ businesses. The Price-Cutting Game Consider an industry with two firms producing a single homogeneous product. Suppose each has the same cost structure. We‘ll show that each has an incentive to reduce its price below the

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other‘s as long as price is above marginal cost. The result: progressive price-cutting reduces the price to marginal cost. Let‘s look at this a little more formally. Suppose marginal cost is a constant c and demand for the product is D(p). If one firm has a lower price than the other, it gets the whole market, D(p). If they charge the same price, they each get half the market, D(p)/2. (This is arbitrary, but since it‘s not an essential part of the story we want to keep it simple.) Now let‘s look at the incentive to cut price. If each firm is charging the same price, then they split the market. If the price is above marginal cost, then both firms make a profit. But what if one firm charges one penny less? Its profit per unit falls (just a little, since the price cut was one penny), but because it gets the whole market its profits go up. (Profit should almost double.) Therefore it has a clear incentive to reduce price. The picture changes only when price falls to marginal cost. At this point, further reductions in price are unprofitable. We illustrate this graphically in Exhibit 1, where for each firm we graph the optimal price for one firm given the price charged by the other. We call the lines showing these optimal choices ―reaction curves.‖ They‘re analogous to best responses in matrix games. In fact, the only difference is that price is a continuous variable, not discrete, so it‘s easier to describe strategy graphically rather than in a table or matrix. The optimal strategy for each firm, then, is to reduce price below the other, unless price equals marginal cost. (Also, if the other firm were pricing above monopoly price, then my optimal price would be monopoly price. In fact, I would be a de facto monopolist, since my rival‘s high price effectively places it out of the market.) Since each firm is trying to undercut the other, we end up with price equal to marginal cost. In game theory terms, this is a Nash equilibrium, the intersection of the reaction curves of the two firms (Exhibit 1). In economic terms, we have reproduced the competitive solution (price equal to marginal cost) with only two firms. It‘s a remarkable result and an important business lesson: you can have intense competition even with a small number of firms. Escaping the Trap We‘ll spend some time exploring ways to escape the ―Bertrand trap‖ of competitive price-cutting, but it‘s worth a quick look now. Here‘s a partial list:

Buy your competitor. This has clear anti-trust problems, but you can see the incentive for firms to do so. Alternatively, one firm might decide to exit (since it‘s not making any money) leaving the other with a monopoly.

Collude on price. Also illegal. But what if you and your competitor simply come to understand that price competition hurts you both? Are there legal ways of interacting that avoid the hazards of price competition? More on this soon.

Develop a cost advantage. Suppose you (as Firm 1) have a cost advantage over your competitor (Firm 2). Then the game plays out like this: you reduce your price to just

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below your competitor‘s cost. At that point Firm 2 drops out and you get the whole market. Your profit is determined by the difference in your costs. See Exhibit 2. This is yet another example of the value of low cost.

Differentiate your product. Generally, products are not homogeneous: buyers perceive differences between them that moderate the tendency for the low price to take the whole market. In such cases, the pressures of price competition are less severe, but they are generally there.

Examples Airlines. Some observers think that airlines increased capacity too much in the 1990s, buying new planes and expanding into new markets. With fewer planes, they would have less ability to expand output and drive prices down. Telecommunications. In hindsight, too much capacity was added in the late 1990s, much of it fueled by cheap venture capital. The result (this is a high-fixed-cost, low-marginal-cost business) was a sharp drop in prices. WorldCom and Global Crossing are just two of the casualties. Movie theaters. In the 1990s, capacity expanded dramatically with no obvious market reason. The result is that prices fell and margins paid to producers rose. Manufacturing. A few years ago, a senior exec from a New Jersey-based company spoke at the annual meeting of the Asian Business Society. At the time, many firms were discussing the possibility of buying Asian companies in or near bankruptcy. In his view, excess capacity in his industry had led to overly aggressive price-cutting. He mentioned trying to buy three Asian manufacturing facilities, with the idea of using one and closing the other two to reduce capacity in the industry. Numerical examples of competition in IDENTICAL goods Example 1. You are the sole domestic producer of the generic antidepressant Sensitrum. Your marginal cost is $2 per dose. Demand is given by Q = 400 – 50 p (Q in millions of doses, p in $). There is a second producer in India whose marginal cost is INR 145 (including transportation cost to the US). Firms set prices simultaneously. (a) What is your equilibrium profit at the current exchange rate of INR 48 / US$? (b) An advertising and retailing campaign costing $80m is expected to increase demand by

40%. Should your firm go ahead with it? (c) One macroeconomics expert tells you that ―it is likely that the rupee will appreciate in the

near future.‖ How would this influence your decision? Answer. (a) First we must determine the Indian firm‘s marginal cost in US$. This is given by 145/48 =

$3.021. In order to determine the price equilibrium, notice that we are in the situation of homogenous product with different marginal costs. As we saw before, the equilibrium

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consists in the lower cost firm, the domestic firm, to set a price just under foreign firm‘s marginal cost and get the whole domestic market. The domestic firm‘s profit is (400 – 50 x 3.021) (3.021 – 2) = 248.95 x 1.021 = $254m.

(b) The advertising campaign would increase profits by 40% x 254 = $101.6. This is more than cost ($80m), so do it.

(c) The possibility of the rupee appreciating only makes things better: it raises your competitors cost. Let e be the spot exchange rate expressed as rupees per dollar. An appreciation of the rupee means e goes down. This implies that the Indian firm‘s marginal cost in US$, 145/e, goes up. Since your competitor‘s costs are higher, you can charge more, your profits are higher, and the benefits of the advertising campaign are higher.

Example 2. You are currently the sole seller of ByeByeCold, a revolutionary drug that almost instantly eliminates cold symptoms. Although the production cost is only $.10 per dose, you sell ByeByeCold for $1.39 per dose, for a total profit of $900m a year. You are currently considering licensing ByeByeCold to a second producer. One of your managers suggested, since the firm would be sharing the market with a competitor, it would be appropriate to charge a flat fee that covers half the current profits plus a generous margin; the value of $700m was suggested. An alternative proposal would be to set a royalty fee of $.50 per dose. What is your opinion? Answer. If you license ByeByeCold for a flat fee, you will be competing with another firm selling the same product and with a similar marginal cost. Except for the possibility of collusion, this would imply approximately zero profits for both firms. It follows that half the current profits would not be sufficient to compensate for the profit loss from licensing. In fact, there exists no licensing contract that would be profitable for both parties. Why do firms ever license, then? One possibility is that the second firm is more efficient in production so that there are gains from bringing it on board. Also, there may be reasons why production by a second firm increases the size of the market. If these were true, then it is possible that a profitable licensing arrangement can be made.

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Exhibit 1 Reaction Curves in Price Game Comment: Each firm undercuts the other‘s price, until price hits its marginal cost. Exhibit 2 Reaction Curves in Price Game When Firm 1 Has Lower Cost Comment: This time, the low cost firm reduces price to just below the other‘s cost, which is enough to drive it out of the market.

p1

p2

45° MC2 Firm 2’s

reaction

curve

MC1

p1* = MC2-ε

p1

p2

45° MC2

Firm 2’s

reaction

curve

MC1 p1* = c

Firm 1’s

reaction

curve

p2* = c

Firm 1’s

reaction

curve

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Competition and Cooperation The language of business is frequently based on the language of competition, or even war. In fact, business has elements that are competitive, and other elements that are cooperative; elements that are zero-sum, and others that are positive-sum; elements focused on creating value, others focused on distributing value. Without the cooperative elements, the competitive ones wouldn‘t be worth the effort. This note is devoted to restoring the balance. We will look at situations in which firms are as much allies as adversaries and explore ways in which they might develop their common interests. Examples include:

Microsoft and Windows. Since both depend on the health of the PC market, they have a clear common interest (which is not to say that their interests are the same).

Management and labor. Other things constant, a firm makes more money if its labor costs are lower. But strikes and disagreement between management and labor can shrink the pie and potentially leave both worse off. Surely one of the reasons Southwest is more efficient than US Airways or United is that they do not have a history of labor-management strife.

International trade. The logic of trade, which has been understood by specialists (if no one else) for almost two centuries, is that both countries benefit. Voluntary trade creates value that benefits both sides.

Stern students. There is a narrow sense in which one student‘s success comes at the expense of another‘s: not everyone can get the highest grade. But there is a more important sense in which students have a common interest: you learn from each other, share insights and contacts, and the success of your fellow students increases the reputation value of a Stern degree.

Such combinations of cooperation and competition were dubbed ―co-opetition‖ by Novell‘s founder, Ray Noorda. The message is not that you should be nice in business (although courtesy remains a virtue, even in the 21st-century business world), but that you should understand (i) when you and others have similar interests and (ii) how to take advantage of them.

Firms and Markets Lecture Notes

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Common Interests Some decisions concern the creation of value, others how to divide it up: making the pie and fighting over its pieces. Let‘s start by stressing the ―creating value‖ part of business relationships. Consider the relation between a firm and its suppliers. On the one hand (the economist in us speaking!), a firm does better if it gets a low price on its inputs. On the other, the firm and supplier both benefit if the final product does well. Take two airlines, American and Delta. In one sense, they are in direct (and often quite cutthroat) competition for market share, landing slots, and gates. Yet these firms also complement each other. How? They both buy planes from Boeing. These planes are expensive for Boeing to design and produce. If only Delta purchased planes from Boeing, it might not be enough to allow Boeing to invest in improved design features. Moreover, aircraft manufacture benefits from a steep learning curve: the more Boeing produces, the cheaper they can sell them. So if American buys more, there is a clear indirect benefit to Delta. There is a similar logic for a firm and its employees. Suppose you are the representative of a labor union, and I am an executive of a corporation. We are engaged in negotiations over the next contract. We realize we do not have identical interests. I think that you want an unreasonable wage hike and excessive vacation time; you think I am an indifferent manager who wants to deny you any added benefits or share in the firm‘s success. I think any gain you receive will be at my expense. You think that any denial of your demands results in a win for me. This is a distributive, zero-sum mindset where we each think there is no way to win without the other side losing. But picture a somewhat different scenario. Suppose I (the executive) believe that profits will be way up in the next five years thanks to efficiency gains in the firm‘s productive capital, and thus its labor. As a result, I am willing to give quite a bit on wages to reflect these productivity gains. Nevertheless, I am adamant in opposing any additional vacation benefits, which raise cost without increasing productivity. Similarly, suppose you (the labor rep) are flexible over vacation time, but adamant about wage increases. Suddenly, there is a clear win-win possibility. You and the manager can cooperate on those issues on which you agree. A more subtle example brings us back to the Bertrand trap of price-cutting: if we are direct competitors, can we avoid the destructive temptation to undercut each other‘s prices? Clearly we both gain if we understand that cooperation on price benefits each of us. In this case, there‘s a legal issue, too, since getting together to fix the price violates antitrust law in the US and many other countries. But if we understand our common interest, perhaps we could approach the same outcome without explicit agreement.

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More Examples

Sony and Electronic Arts. Sony needs good games to sell its Playstation machines, and EA needs machines to sell its games. Nintendo recognized the common interest and has produced both from the start.

Intel and AMD. Right now, Intel is the standard for PC chips. But it wasn‘t that long ago that Intel was trying to carve out a niche for itself. Its major customer in the early 1980s was IBM and its fledgling PC, and IBM was concerned about sourcing from a single supplier. To convince IBM to buy their product, they licensed the technology to IBM, AMD, and several other manufacturers. In this case, Intel realized it had a common interest with AMD and others to persuade IBM that the supply of chips was competitive, so it supported them through licensing. Once Intel had a lock on the market, of course, the common interest evaporated.

GE and Westinghouse in the 1950s and 60s. A classic case, first, of price-fixing, and later of clever cooperation that was ultimately judged to be illegal (but still clever!).

National Basketball Association. There are at least two layers of common interest here. First, the league needs credible competition to succeed. It‘s simply not optimal (most believe) for a small number of big-market teams to win all the time. Among other things, the primary source of revenue is television fees, which are paid to the league, not to individual franchises. Second, owners and players have a common interest in the success of the league. How do we align all these interests? It‘s a complex situation, but the salary cap is an attempt to both even the playing field across teams and guarantee that owners and players share in the overall success of the league (they are guaranteed a minimum percentage of revenues). Anyone who follows the sport knows this is grossly simplified, but the fact remains: it‘s critical in a sport to balance the interests of teams, the league, and the players.

Cooperation as a Nash Equilibrium Let‘s continue with the price-cutting game we studied earlier. How might firms learn to avoid behavior that is mutually destructive? One answer—the one we will spend our time on—is that when firms interact repeatedly over time, they might be able to avoid the short-run temptation to cut prices or otherwise act in their narrow self-interest. If two firms compete not only today, but tomorrow and the next day and so on, this gives each of them leverage over the other. If one cuts prices too low today, the other can instigate a price war to punish it tomorrow. Take OPEC as an example to see how this might work. Oil-exporting countries meet periodically to restrict output, setting output quotas for each country. Say in country X the quota is 100,000 barrels per day. What if the country actually produced 120,000 to generate additional revenue? After all, no judicial body enforces the cartel agreement. If others stick to the agreement, this will keep the price high and increase the benefits of producing more. In

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the language of game theory, country X has an incentive to ―cheat‖ on its agreement with OPEC to limit supply. If others cheat (after all, they have the same incentives), output increases and the price falls, foiling the cartel‘s efforts. So what stabilizes a cartel? In fact, they tend not to be that stable. But when they work, there are other sources of leverage at stake. One is that OPEC members play this game over and over. If a country cheats in one round, then the cartel can retaliate against in the future by cutting its quota or flooding the market with oil to drive prices down (Saudi Arabia is in a good position to do this), i.e., it could launch a price war. There is a further difficulty with OPEC, which is that members may not know exactly what the others are producing. We will return to this later. The general point is this: when firms interact repeatedly, the possibility of ―retaliation‖ or ―punishment‖ for non-cooperation can support cooperation as a Nash equilibrium. One example is the price-cutting: it may be less attractive to undercut your rival if such behavior triggers a price war. Related issues:

Distressed firms. If a firm is worried that it may not survive to tomorrow, future punishment no longer works as a deterrent. Thus we frequently see distressed firms starting price wars. This has been a particular problem with airlines, many of which have been in and out of bankruptcy throughout the 1990s.

Multi-market contact. Some firms compete in more than one market. This gives them each more leverage over the other. If they behave uncooperatively in one market, you can ―punish‖ them in another. A good example is airlines. A study showed that when airlines compete on multiple routes, they are less likely to compete aggressively on price. The media industry is filled with examples of multi-market contact, which presumably gives them leverage over each other.

Information. Generally it is harder to punish non-cooperative behavior if you do not observe it. This is one reason antitrust authorities worry about transparency: it allows firms to cooperate more effectively. It has been a major source of debate on B2B e-commerce, since it puts a great deal of information into one or more competitor‘s hands, which might be used to enforce cooperation.

Legal Issues Some kinds of cooperation are illegal (price-fixing, for example), others are legal (for example, most industry standards groups), and others lie somewhere in between.

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Numerical Examples Example 1. Repeated pricing game. Suppose that demand in an industry is given by Q = 100 – p and there are two firms producing, each with MC = 20.

(a) Determine monopoly price and profits. (b) Determine the NPV of future monopoly profits, assuming interest rate r. (c) Determine threshold value r below which cooperation (cartel pricing) is an equilibrium.

Answer (a) We begin by writing the inverse demand function for the industry p = 100 – Q. Then the problem for a monopolist with MC=20 is to maximize profits. Taking the derivative to maximize profits (or equivalently setting MR=MC) yields Q = 40, p = 60 and total profits of 1600. (Check that you can obtain these values.) (b) The NPV of future monopoly profits is

rrrr

1600...

)1(

1600

)1(

1600

1

160032

(c) Therefore by sticking to cartel pricing each firm would earn 2

1600 in the current

period and future profits of r

1600

2

1 in future profits.

If instead a firm chooses to break the cartel agreement, then by undercutting the other firm slightly it would obtain the entire monopoly profits of 1600 (or extremely close to this value) but would trigger a future price war in which profits would fall down to zero (recall notes on the hazards of price competition). Thus the cartel is sustainable so long as the value of sticking

to the cartel agreement r2

1600

2

1600 is greater than the value that can be obtained by

deviating from the agreement, which is 1600 (+0 in all future periods). Thus the condition that allows cooperation to be sustained as an equilibrium is:

16002

1600

2

1600

r,

which is equivalent to r < 1. NOTE: This might seem like a non-binding constraint (r < 100%). However, we must recall we (implicitly) made the assumptions that there are only two firms, that they are identical, that there is no product differentiation (punishment profits = 0), that prices are perfectly observable, and so forth. Example 2. Secret price cuts (challenging example). Consider the same set up as in Example 1 and the particular case when r = .3. Suppose, however, that each firm cannot observe the rival‘s price (ready-mixed concrete might be an example). All that a firm can observe is its own price and its own demand. This creates a

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difficult inference problem, since zero demand can result from two causes: (a) rival underpricing and (b) low market demand. Low market demand occurs with probability 20%, independent from period to period. Suppose firms revert to marginal cost pricing whenever they receive zero demand. Show these strategies are a Nash equilibrium. Is this the best equilibrium? If not, what is a better alternative? Answer. As before, monopoly profits in a given period are 1600 (when demand is not low). Assuming that firms remain at monopoly price while demand is high, the NPV of future monopoly profits is now given by

25605.

1280

3.1

8.1

1

3.1

16008....

)3.1(

16008.

)3.1(

16008.

3.1

16008.

3

3

2

2

If the firm undercuts the rival‘s price today, it gets an expected profit of (.8) 1600 = 1280 today, and zero thereafter. The no-deviation constraint is thus

19202

2560

2

1600)8(.1280 ,

which is clearly satisfied. Or to put it another way. We check for Nash equilibrium by seeing that for a combination of strategies, no firm want to deviate. Well, here, what does the firm get by sticking to the strategy? With a 20% probability demand is low – in which case it earns nothing today (since there is no demand) and given that firms revert to marginal cost pricing following a low demand realization, the firm will get nothing in the future. With 80% probability demand is normal and the firm earns half the monopoly profits 1600/2=800. Further in the next period, it has the chance to earn money, again by sticking to its strategy then with 20% probability there is low demand and it earns nothing this period or for evermore, but with 80% probability earns half the monopoly profits and continues on potentially earn more profits in the future. The NPV of sticking to the strategy can thus be written down as: 0.2*0+0.8*(800+1/1.3*(0.2*0+0.8*(800+1/1.3*(0.2*0.+0.8*(800+1/1.3*(0.2*0.+0.8*(… which we can re-write more simply as 0.8*800+0.8/1.3*800+0.8^2/(1.3)^2*800+….=1920 Instead if the firm deviates and undercuts then it gets 0 with 20% probability and with 80% probability the full monopoly profits today and nothing for evermore, that is it earns an average of 1280.

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Since 1920>1280, the firm has no reason to deviate. It is indeed playing a best response (and since the game is symmetric) so is the other firm. If both firms are playing strategies that are best responses to each other, then this is a Nash equilibrium. There is one important difference with respect to the previous example. The equilibrium strategies call for reversion to marginal cost pricing whenever a firm observes zero demand. In the previous example, this never actually takes place, since both firms anticipate a price cut will lead to an indefinite price war. By contrast, in the present example zero demand may simply result from low market demand. Since the firms have no way to tell what causes low demand, they will revert to a price war when in fact there is no culprit to punish. You might think firms would be better off by not starting a price war, since they know that, in equilibrium, zero demand is caused by market conditions, not by defection. However, if a firm expects its rival will not start a price war then it has an incentive to defect, so that can‘t be an equilibrium. Although the above strategies form an equilibrium, there may be better equilibria. At some point, market demand will be low and firms will plunge into an indefinite price war. This seems a little too much, especially in light of the fact that the no-deviation constraint has a lot of ―slack‖ (1280 < 1920). So, instead of an indefinite price war, suppose that, whenever a firm observes zero demand, a finite price war starts. Given the slack in the no-deviation constraint, it must be possible to have finite price wars and still avoid the temptation of price cutting. Example 3: Tit-for-tat in Iran-Iraq game. Consider the following game in which Iraq and Iran must determine how much to produce.

2 4

42 44 2 46 26

22 24 4 52 32

Suppose this game is infinitely repeated and that the interest rate is 50%. Suppose moreover that players start with Q1 = 2 at t = 1, then Qt = rival‘s Qt-1 (tit-for-tat) thereafter. Show that these strategies form a Nash equilibrium. (Hint: consider a one-time deviation from equilibrium.) Answer. If Iran and Iraq play the equilibrium strategies, then Iran will get

1385.

4646...

)5.1(

46

)5.1(

46

5.1

4646

32

Iraq’s output

Iran’s Output

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This follows, since its strategy starts by choosing 2 and so does Iraq, then since Iraq in the second period does what Iran did in the first, and Iraq does what Iran did in the first, both again choose 2, and so for the third period etc. Suppose Iran deviates in the first period by producing high output and sticks to tit-for-tat thereafter. Then at t = 2, Iraq will choose high (tit-for-tat), whereas Iran will be choosing low output. At t = 3, the situation is reversed: Iraq chooses low output and Iraq high output. Given this sequence of play, Iran anticipates an NPV of

8.1242.316.93

25.1

25.2

5.1

26

25.1

25.252

)5.1(

11

1

5.1

26

)5.1(

11

152

...)5.1(

26

5.1

26...

)5.1(

5252...

)5.1(

52

5.1

2652

22

322

which is less than 138. For Iraq, the equilibrium NPV is

1265.

4242...

)5.1(

42

)5.1(

42

5.1

4242

32

If Iraq deviates in the first period and then proceeds to play tit-for-tat, it expects an NPV of

6.1054.262.7925.1

25.2

5.1

22

25.1

25.244...

)5.1(

44

5.1

2244

2

which is less than 126. We might try other deviation strategies, but it will still be the case that the best a player can do against tit-for-tat is to play tit-for-tat as well. In other words, tit-for-tat by both players constitutes a Nash equilibrium. Is tit-for-tat the only equilibrium? Suppose that Iran chooses low output during the first 10 periods, high output thereafter. Is tit-for-tat Iraq‘s best response to Iran‘s strategy? Would Iran‘s strategy and Iraq‘s best response for a Nash equilibrium?

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Example 4. Finitely repeated game. Let us continue with the Iran-Iraq game, assuming now that it is repeated for 10 periods. What is the (natural) Nash equilibrium of this game? Answer. The best way to approach finitely repeated games is to think of them as a big game tree. As we saw before, the way to solve these games is to start from the end and move backwards. So, let us consider the very last period. Since there is no future to worry about, players treat this as a one-shot game. Since this is a prisoner‘s dilemma, we know what the equilibrium is: both players choose high output. Consider now the period before last. Since players anticipate that, no matter what, they will choose high output in the very last period, they treat the second-to-last period also as a one-shot game. It follows that both choose high output. And so forth. We conclude that the only equilibrium is to choose high output in every period. (Technical note for aficionados: generally speaking, extensive-form games, including finitely repeated games, may have more equilibria then the ones we find by solving the game backwards. The additional equilibria, while satisfying the requirements for a Nash equilibrium, are however not reasonable in the sense that they implicitly assume players ―promise‖ to play future actions that, when the time comes do take them, are not in their best interest. We will return to this in the chapter on commitment.)

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Commitment, Entry and Exit One of the key areas of strategic decision-making relates to entry and exit in competitive markets. A good example is the competition between Boeing and Airbus in widebody aircraft. When they each decide whether or not to enter a given market segment, they realize that they‘d each be better off if its rival decided not to enter. So who enters? As in other situations of strategic behavior, firms facing entry and exit decisions must attempt to see this ―game‖ through the eyes of their rivals and reason backwards to decide on an optimal strategy. In some cases there is a clear first mover advantage, in others not. Either way, timing is critical. Commitment One aspect of timing is commitment: the ability to commit to a decision before your rival has acted. For example, suppose Boeing could persuade Airbus that it was entering a given market segment. If Airbus believed this, it might choose not to enter. We will see that in many cases, a firm that makes a credible, irrevocable commitment to entering can increase its expected profits by convincing rivals to stay out. We would say that commitment is valuable. Commitment consists of reducing your options, since the idea is to lock into a decision now. Why would that be valuable? Aren‘t options good? To see why, consider an example (this is becoming a cliché, and may not even be true, but it makes a good story). When in the 16th century Spanish conquistador Hernán Cortés arrived in the ―New World‖ (what is now Latin America), he faced long odds. With only a small army backing him, he intended to conquer and colonize a large population of unknown, potentially hostile indigenous people. Upon his arrival in Mexico, he made the seemingly insensible move of burning his entire flotilla of ships (except for one), ensuring that the local people observed this act. Why burn the ships? After all, he was essentially destroying his escape strategy. He was also destroying assets that could prove valuable from a military point of view. Was Cortés insane or what? Cortés probably was crazy to some extent. (If you are ever in Mexico City, go see Diego Rivera‘s murals in the Mexican government headquarters where he unflatteringly portrays Cortés as a hideous-looking, shriveled-up pasty-white demon.) Nevertheless, Cortés‘s ship-burning was not crazy; it was most probably a calculated, rational move. He was demonstrating his unwavering commitment to colonizing the New World. By burning his ships in plain view, he was saying in a matter of words ―we are here to stay; and we will either conquer you or die trying to do it.‖ This commitment was credible because he was destroying his ability to undertake any other course of action besides staying and fighting. Note that commitments must be credible in order to work. If Hernán Costés decided to signal his commitment by sending the Mexican natives a message stating ―we will fight,‖ this would not have much effect. After all, we know that talk is cheap. Similarly, any firm can make a

Firms and Markets Lecture Notes

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public statement of its intentions; but only by acting on these commitments in an observable and credible way that is hard or expensive to retract can it ensure its commitment has an enduring effect. Preemption Why does DR build stores just two blocks away from each other in Manhattan? Aren‘t the stores stealing each other‘s market share? Firms can create barriers to entry by increasing their capacity or product line in the hopes that they will capture demand that otherwise could be appropriated by a potential entrant. We can say more formally that a preemption strategy by a firm is one that makes entry by a new firm unprofitable. This is different from an unrestricted monopoly strategy because, as the Duane Reade example suggests, it may intentionally sacrifice profitability in exchange for controlling the market. Predation Another related dimension is predation: If you can‘t keep ‘em out, drive ‘em out. Predatory pricing has a long and infamous history in the United States, ranging from Standard Oil to railroad companies to AT&T‘s longstanding clench of the telephony market. Predation occurs when a firm prices its products below cost to force others out of the market or preventing their entry. You may wonder why a firm would ever wish to price below cost and lose money. In a static world, this would make no sense, but in a dynamic setting, predatory pricing can be an effective deterrent. There remains, however, a range of opinions about whether it should be a serious concern for competition policy. At one extreme there is the so-called Chicago school. According to the Chicago school, predatory strategies cannot be profitable; if a firm prices low, then this must be considered a competitive, not anti-competitive, strategy. There are however several explanations of why below cost might be a successful predatory strategy:

Asymmetric information. If firms know more about their costs than do the public and rival firms, they are able to exploit this fact by pricing low to convince rivals they are very efficient and not worth competing against.

Reputation-building. It can be rational to establish a reputation for irrationality. If firms signal that they are willing to act irrationally from an economic standpoint to dominate a market (after all, pricing below cost is not a rational economic decision, at least not in the short run) they may create a reputation that scares firms off from competing with it.

Learning curves and network effects. Firms can reduce cost as output rises through learning effects and other means. Anticipating these effects, firms may price below cost in the present to stave off rival entry. Once they attain their cost reductions, later they can return to profitability—especially if they have driven rivals out of the market.

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Deep pockets. If a firm has more cash than its rivals, pricing below cost leads to a war of attrition where the winner is the firm with deeper pockets. (Although we list this in the fourth place, it is likely the most common reason why predatory pricing works.)

The above discussion notwithstanding, we should add that predation is not always so clear-cut. (Look at the testimony of the Microsoft trial if you need convincing!) Moreover, it is important to note that pricing below cost is not the only way for a firm to behave in a predatory fashion. Firms can also enlist predatory strategies such as capturing demand through product design (eg, MS Windows) and through striking exclusive contracts with other members of the value chain that put them at an advantage with respect to the competition. Why is predation illegal and ―bad‖ for consumers if it leads to lower prices? Recall our earlier discussions of monopoly firms. Once predatory firms drive other firms out of the market, they can increase prices and act without regard to competitive dynamics that ensure competition and choice for consumers. Examples Example 1. The word is out: a revolutionary discovery by a faculty member at NYU's Courant Institute for Mathematical Sciences will finally allow the practical implementation of parallel processing in personal computers. As holder of the patent, NYU has licensed the technology to two firms, to assure PC manufacturers of two sources of supply. One firm, located in the US, has already moved ahead with engineering plans for building a production facility. The question is whether to go for a plant of size 1, 2, or 3. The second firm is located in Brazil. It will also have to decide whether to build a plant of size 1, 2, or 3. However, it is a bit late with respect to the US firm, and won‘t be able to move ahead before next year. When it does so, it will know what plant size the US firm has opted for. You have been hired as a consultant to the US firm. Your analysis shows that the profits from various combinations of plant sizes are:

1 2 3

3.9 5.8 5.7

1 3.9 2.9 1.9

2.9 3.8 2.7

2 5.8 3.8 1.8

1.9 1.8 -0.3

3 5.7 2.7 -0.3

Question: As a consultant for the US firm, what size factory do you recommend? Answer: As indicated, the US firm chooses output this year, whereas the Brazilian firm only chooses output next year. We thus consider an extensive-form game, with the US moving

Brazilian firm

US firm

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first. Suppose US chooses 1; then Brazil chooses 2 (which has the highest payoff) and the US payoff is 2.9. Similarly, if US chooses 2, Brazil chooses 2 and the US payoff is 3.8. And if US chooses 3, Brazil chooses 1 and the US payoff is 5.7. The last (3) generates the highest payoff, so the US should build a plant of size 3. Question: When you meet with the Executive Committee of the US firm, one executive remarks: ―There's no need for haste. The Brazilians will not build a factory until next year, so why don‘t we wait and build our factory next year as well?‖ How would you reply? Answer: The situation described above gives the US a large advantage: by choosing/moving first, it can force Brazil to choose a low output level. If the US firm waits, then it will either be choosing output at the same time as the Brazilian firm or after the Brazilian firm. If the two firms choose capacities at the same time, the Nash equilibrium is (2,2) and the US firm has a payoff of 3.8, substantially less than 5.7.

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Imperfect Information Many business situations are plagued by information difficulties, in which one party to a transaction has better information than the other. (Think of the phrase: ―Trust me on this.‖) We refer to these situations as having ―asymmetric information.‖ Inevitably, the party with superior information is tempted to exploit its advantage. And even if it doesn‘t, the other party may think it will. And the uninformed part has some leverage, too: the possibility of walking away from a deal may offer it some advantage. The result is one of the most interesting and challenging aspects of business. Consider these examples:

An employer wants his sales team to work hard but cannot observe whether or not they are working hard. What steps can he take to ensure that they work hard?

Health insurance company faces pricing dilemma. A low price leads to small margins. But a high price runs the risk of attracting only high-risk patients. What should it do? We refer to its problem as ―adverse selection,‖ since the high-risk patients are more likely to ―select‖ the plan. The problem is that the health of a patient may be known better by the patient than the insurance provider.

Large firm would like to spin off subsidiary. Potential buyers ask: Is this a strategic move (the firm wants to concentrate on other businesses) or an attempt to unload what it knows to be an unprofitable business?

Price as signal of quality. New firm enters market for luxury luggage. It would like to reduce price to gain market share, but worries that this might be interpreted by customers as a sign of low quality.

Information can be a serious friction to doing business and to prevent markets from working efficiently. We will first explore some of the ramifications of asymmetric information in stylized settings where the issues are clear, even if unrealistic. We later return to reality and discuss ways in which information problems might be ameliorated. Games with Imperfect Information Games with imperfect information are games where one player has better information than the other (in particular following some hidden action). We begin by considering an agency model, where a principal (employer, board of directors, regulator etc), who would like to induce some kind of good behavior from an agent, cannot directly observe the agent‘s actions. In this case, known as ―moral hazard,‖ (hidden action) the agent has better information only with respect to the action that he takes and that the principal

Firms and Markets Lecture Notes

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does not observe. The key in games of moral hazard is that even though the principal might not observe the agent‘s actions, she might be able to observe outcomes that are related to actions (e.g. output, an observable, is a function of effort, an unobservable). Then the principal might want to set up a reward system based on observables—though she should beware about what kind of behavior this encourages. A different kind of information problem arises if we suppose that before the game even starts one of the players is relatively well informed (hidden information). We can find many examples of such asymmetric information in day-to-day life. When people apply for health insurance they often know more about their health status and history than the insurer. Manufacturers of products often know more about the quality of their product than do consumers. Firms presumably know more about their assets than potential buyers. In a legal setting, defendants often know more than plaintiffs. And in Edgar Allen Poe‘s ―Telltale Heart,‖ the guilt-ridden criminal knows about his crime while the investigators do not. (And, if he had kept his cool, he would have probably remained a free, yet disturbed, man.) We can consider two polar cases of asymmetric information. First, we can consider a game where the relatively less-informed player moves first. In this case, ―adverse selection‖ becomes a risk for that first mover. Consider, for example, the case of litigation for medical malpractice. Before the trial proceeds to the discovery stage, it seems reasonable to assume the defendant has better information than the plaintiff. If the plaintiff makes the defendant an offer for an out-of-court settlement, he should take into account that such offer will be accepted if and only if liability is likely to be greater than the proposed settlement—the exact situation in which the plaintiff would want the offer not to be accepted. Second, we could consider a game in which the informed player moves first. In this case, the first move may tell the other player something about the first player‘s information, and so the first player will take this into account. If a firm knows the quality of its product, could a buyer infer quality from the seller‘s price? Typically the move by the first player contains information that the second player can use to make a better decision. The first player knows this, of course, and uses it to guide its choice. The takeaway point on hidden information: the uninformed player must guess how the informed player will act react. Who is likely to take up this kind of insurance? When the informed player moves first, the move conveys information: if this is really such a good deal, why is it being offered to me? The trick is to convey the right information.

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Agency problems There are numerous examples where an agent takes actions that cannot be observed by a principal. The actions chosen by this agent will be determined by the incentives that he faces and so the principal might try to structure transactions so that these incentives lead to the behavior that she prefers. The most obvious example and (in the light of the Enron debacle) perhaps most notorious is pay for performance; however, similar issues are at play in numerous other examples. For instance, if an insurance company sells a factory owner insurance against fire it will wonder whether the factory owner (now that she has insurance) will do all that she can to prevent the outbreak of a fire; or, if a commercial bank decides to lend money to an entrepreneur, it will wonder whether the entrepreneur will be prudent or gamble the funds hoping for a big win and spectacular IPO. In many applications where explicit incentives are used, an important consideration is that the incentive scheme might subject the agent to considerable risk. For example, performance pay leads to higher variance in pay than fixed compensation. If, moreover, the agent is more risk-averse than the principal (e.g., worker and corporation), then we have a trade-off: efficient risk sharing suggests shielding the agent from risk but unless some risk is imposed on the agent there is no motivation. Another widely discussed and prominent issue is a concern about misaligned incentives, or, as Steven Kerr nicely put it, ―the folly of rewarding A, while hoping for B.‖ In his beautiful paper, he mentions numerous examples, to which we add the perhaps apocryphal one from the planning days in the Soviet Union: A particular nail factory was subject to an annual production quota of 1 ton of nails. It fulfilled this requirement by spending a week manufacturing a single 1 ton nail! In short, incentives work but expect to get exactly what you pay for. We now turn to consider problems of asymmetric information where one of the players is relatively well-informed even before the game starts. Selling “Lemons” Suppose that the problem is one of hidden information and that the uninformed player moves first; what considerations will guide her strategy? The classic example is the sale of a used car. It made more sense in the 1970s than it does now that car quality is uniformly higher. But the idea is that when you buy a used car from an individual, you probably know less about the quality of the car than the seller. You move first in the sense that you don‘t observe any informative moves by the seller before you make an offer. The risk is that you might buy a ―lemon‖ (meaning a low-quality car). Consider a concrete example. The buyer makes an offer and the seller decides whether or not to take it. Suppose that you, a potential buyer of a used car, know from reading Consumer Reports that 50% turn out to be lemons. You decide that a lemon is worth zero and a non-lemon is worth $1,500. You might then set your reservation price (the most you are willing to

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pay) at $750 based on the 50% probability of buying a dud [750 = (.5x0) + (.5x1500)]. Anything more, and you‘d prefer to walk away. What about the seller? Let us say a seller would be unwilling to part with a non-lemon for less than $1,000, the fair market value based on the blue-book value of the car, etc. Now we have a problem. Given your lack of information about whether you will get a lemon or not, you are willing to pay less for the model than the reservation asking price of legitimate sellers. This means that anyone willing to sell you a car for your price is probably selling you a lemon! It only gets worse. Fearing that you will get a lemon at $750, you change your reservation price downward because you think the likelihood of getting a worthless lemon is now 90%. Thus, the new bid is $150 [=(.9x0) +(.1x1500)]. Now who on earth would sell you a car that, worth $1,000 without defects, sells for only a fraction of this price? Only people selling lemons. As this downward spiral continues, both buyers and legitimate sellers drop out of the market until the market vanishes. This happens because buyers do not have the information they need to make risk-free offers based on fair market values. It‘s a classic example of bad products driving out the good: if it‘s impossible to demonstrate quality directly, no one would be willing to produce and sell high-quality products at the price buyers (who don‘t know quality) will pay. Viewed from the perspective of game theory, we ask ourselves the basic question: Why is the seller willing to part with the product? If we fear that it‘s because he knows that it‘s of low quality, we decide not to buy and the market collapses. We would say (formally) that the only Nash equilibrium is when no transactions take place. This extreme outcome is the result of the parameters we started with, but more generally the difference in information will lead some mutually beneficial transactions not to take place. Asymmetric information is a barrier to beneficial economic transactions. The takeaway point is that the absence of good verifiable information makes it difficult to conclude transactions that are valuable to both sides. If only the owner of the non-lemon car could convey that information to the buyer in a convincing way. In practice, there are many institutions that play that role: warranties, legal systems, third-party ratings (Moody‘s and S&P, Consumer Reports, Zagat Guides), the seller‘s reputation, free trials, and so on. Protecting the integrity of these systems is often in the interest of sellers. For example, financial service firms in the US have been the beneficiaries, by and large, of SEC regulation designed to protect buyers. “Signaling” Quality The other application of asymmetric information we can consider is when the informed party moves first. In this case, the informed player must understand that her action will convey (―signal‖) information to the less-informed party. For example, price is considered an important signaling mechanism. If you choose to bring a bottle of wine to a friend‘s house for dinner and know very little about wine, you might buy a $20 bottle of wine instead of the $7.99 special. (Of course, beer is always good.) As a non-expert, you may not know how the two taste, but clearly the more expensive one seems a safer bet. The vintner in this case is signaling information that she possesses and you don‘t about her wine‘s quality. Similar things can occur

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with other products: stereos, consultants, surgeons, investment banking services. The key is that the seller has demonstrably better information about the product than the buyer. That‘s one of the hazards about using a low price to gain market share: it might convey to buyers that the product is low quality. To understand this type of game better, suppose that there is one seller of stereos and many buyers. The seller sets one price and buyers decide whether to buy. Only the seller knows the true quality of the stereo‘s many components. In some theoretical examples, we would find that only a high-quality producer would charge a high price: If a stereo producer used high quality parts, and those parts cost more, she should set a higher price. If she is using low quality parts, which cost less, he should set a lower price. How can we explain that, in equilibrium, price reflects quality? First, a high-quality product would not be profitable at a lower price because its parts cost more; these costs must be recovered via a higher price. But why would a low-quality producer not want to (falsely) signal high quality setting a higher price? In many cases this will limit your market: fewer consumers are willing to spend more for high-priced stereos to feel more secure about quality (or not everyone has enough income to do so). Thus, by pricing your cheaper goods at a higher rate, you would lose the larger market of people looking for more affordable equipment. Based on what we know about revenue (price times quantity) we can see that we may very well lose more in quantity by selling high than we gain from the higher price. In addition, as people found out in the long run that your stereos were not worth their higher price, you would lose your market to the higher-quality competition. In short, there are games in which the equilibrium is for the high-quality product to sell at a higher price than the low-quality product, which allows uninformed buyers to infer quality from price. This works if the signal has a cost (if it‘s free, the low-quality producer will follow suit) and the cost of that signal is lower for high-quality producers. (In this case, higher production costs imply lower costs of signaling high quality with high price.) In practice, other factors play a role, too: the reputation/brand of the seller, warranties (which are presumably more costly to the producer of the low-quality product), reviews by consumer product firms and other buyers, and so on. Historical Note The 2001 Nobel Prize went to three economists who were instrumental in developing the theory of economic behavior in situations of asymmetric information. George Akerlof is responsible for the lemons model. Mike Spence developed the signaling model. In his example, students used education to signal ability. We prefer to think of education having value in its own right, but we suspect you can see his point. Joe Stiglitz applied the theory to capital markets; in particular, to an entrepreneur trying to finance a new venture.

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Examples Example 1. Sale of business. Suppose a firm owns a business unit that it wants to sell. Potential buyers know that the seller values the unit at either $100m, $110m, $120, … $190m, each value equally likely. The seller knows the precise value, but the buyer only knows the distribution. The buyer expects to gain from synergies with its existing businesses, so that its value is equal to seller‘s value plus $10m (there are gains from trade.) The buyer must make take-it-or-leave-it offer at some price p. How much should the buyer offer? Answer. We can write down a table, which summarizes, for each offer that the buyer makes the probability that the offer gets accepted, the expected value (to the buyer) conditional on having the offer accepted and the overall expected profit from any given offer:

Offer Probability of Acceptance Expected value (to buyer) if accepted

Expected profit

100 10% 110 1.0

110 20% 115 1.0

120 30% 120 0

130 40% 125 -2.0

140 50% 130 -5.0

150 60% 135 -9.0

160 70% 140 -14.0

170 80% 140 -20.0

180 90% 150 -27.0

190 100% 155 -35.0

The seller should offer either $100m or $110m. Discussion. Suppose the buyer offers p = 100 (in $m). Then, in most cases offer is rejected. Specifically, 90% of the times the offer is rejected. Offering more would imply a higher probability of sale, but the expected value of the unit would increase by less than the price paid. The intuition for this result is the force of adverse selection: the seller will only sell the unit if its value is relatively low. Example 2. You work for Pepsi. The company has just signed a major star endorsement. You must decide how much to spend on your Summer ad campaign: $1m (―Lo‖) or $2m (―Hi‖). Net profits (in $m) depend on how much you and Coke spend – and on whether or not Coke has signed a major star:

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High Low

Hi 3 2

0 1

Lo 4 5

1 2

Coke‘s decision of whether to sign a major star has already been taken, but you do not know what the decision was. Your CIO tells you that there is a 70% chance they did. You also know that Coke will have a chance to react to your decision of how much to spend. Should you go for a $1m or a $2m campaign? Answer. This is an extensive-form game with incomplete information. Let us solve it backwards and include ―Nature‖ as a player. If Coke did sign a star, then it will choose $2m if and only if Pepsi chooses $2m. If Coke did not sign a star, then it will choose $1m regardless of what Pepsi chooses. Now, moving backwards: If Pepsi chooses $1m, then Coke will choose $1m. Pepsi‘s expected payoff is 70% 2 + 30% 3 = $2.3m. If Pepsi chooses $2m, then Coke will choose $2m with probability 70%, $1m with probability 30%. Pepsi‘s expected payoff is 70% 0 + 30% 6 = $1.8m. Pepsi should therefore choose $1m.

(Additional question: What considerations are we leaving out of the analysis?)

High Low

Hi 0 1

4 6

Lo 2 3

2 3

P

Coke’s advertising Coke’s advertising

(a) Coke signed a major star (b) Coke didn’t sign a major star

no star (30%) star (70%)

2 1 2 1 2 1 2 1

1 2

no star (30%) star

70% 0 +

+ 30% 6 = 1.8 70% 2 +

+ 30% 3 = 2.3

2

5

1

4

3

3

2

2

1

2

0

3

6

1

4

0

Pepsi’s

Advert.

C C C C

N N

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Additional examples of asymmetric information Health insurance. Many policies exclude ―preexisting conditions.‖ Why? Other policies offer better rates to groups. Why? Life insurance. Most policies require a physical. Why? Downsizing. Firm must reduce payroll by 10%. But if it offers a standard package to all of its employees, the best employees are the most likely to take it. Again, adverse selection. How might it reduce its payroll without losing its most productive employees? For example, Merrill Lynch announced such a plan in October of 2001. The plan allowed employees to apply for a severance package, but the company could decide which applications to accept. Why do you think they structured the plan this way? Ethnic business ties. Some businesses involve important judgments about quality. The diamond business, for example. We sometimes see that such businesses are dominated by members of a single ethnic group. Why do you think this is? American Express‘s spinoff of Shearson. In 1993, American Express sold Shearson to Primerica (now part of Citigroup). In the March 9 Wall Street Journal: ―Among the sticking points in acquiring Shearson‘s brokerage operations would be the firm's litigation costs. More than most brokerage firms, Shearson has been socked with big legal claims by investors who say they were mistreated, though the firm has made strides in cleaning up its backlog of investor cases. In 1992‘s fourth quarter alone, Shearson took reserves of $90 million before taxes for ‗additional legal provisions.‘‖ When the deal was completed, Primerica bought most of Shearson‘s assets but left the legal liabilities with American Express. Why do you think the deal was structured this way? Was it fair to American Express?

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Externalities Do you normally order salad but go for the lobster when splitting the bill? This might not seem like a key strategic issue or one of crucial economic importance, but the same logic that drives diners to spend more when splitting the bill underlies numerous applications from traffic to pollution abatements and large multi-divisional firms.3 Externalities Underlying the diner‘s dilemma is the fact that, when splitting a bill, some of the costs of a more expensive menu choice are borne by the other diners. The latter find themselves in the unenviable position of suffering the consequences of someone else‘s actions without the ability to do much about it. Formally, when a person‘s utility or a firm‘s profits depends on the actions of someone else, we say that the latter exerts an externality on the former. Examples abound; perhaps more common are negative externalities where the action of one party imposes costs on another party (when I smoke, people around me suffer) but there are plenty of examples of positive externalities when the action of one party benefits another party (when I plant flowers in my yard, everyone who passes by benefits). Externalities are prominent in organizations. In a large multi-division organization, for example, division managers and heads are often rewarded only for the performance of their own divisions, and so might not take into account the impact of their actions on the firm as a whole. Even at a smaller scale, giving strong individual incentives to salesman can lead them to go after each other‘s sales and to ignore the negative externalities imposed on other salesmen and the organization as whole. Public Goods An extreme case of an externality is what economists call a public good, where consumption by one party in no way hinders consumption by another party. This sounds obscure, but consider examples such as clear air, parks and national defense. The public good has the possibility of exclusion if we can control the parties that can enjoy the good. For example, we can restrict access to parks but it is hard to stop residents of some area from enjoying clean air, if clean air is provided.

3 Regarding the restaurant problem, a recent study found that on average diners spend close to 40% more

when splitting the bill. See Gneezy, U., E. Haruvy, and H. Yafe. “The inefficiency of splitting the bill: A

lesson in institution design” The Economic Journal, April 4004, 114, 265-280.

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Given that many people can enjoy a public good simultaneously (indeed by definition infinitely many people can enjoy the good) providing a public good is therefore an activity with considerable positive externalities associated with it—a cure for a disease or a piece of music which can bring pleasure to many. An important policy challenge is to ensure the provision of such public goods. Externalities and Market Failure When externalities are present, the price of a good need not reflect its true social value, and so firms may produce too much or too little. It follows that the equilibrium market outcome is inefficient. Recall that an important assumption in our discussion of market efficiency (The Fundamental Theorem) is that one person‘s consumption decision does not affect the utility of any other agent and it is precisely this assumption that fails when externalities are present. Overcoming Market Failures Market failure in the presence of externalities provides a clear rationale for government intervention or other market non-market mechanisms: Social norms. Even in the case of the diner‘s dilemma and splitting the bill, frequently we don‘t order the Beluga caviar, Dom Perignon Champagne or whatever the most expensive item on the menu happens to be. Why not? Often going out to restaurants is a repeated game: we tend to go out with the same groups of friends or colleagues, and so a norm of behavior (with a consequent threat of punishment) can arise. Similarly, my front garden, if well tended, generates positive externalities for my neighbors as do theirs for me. If each of us maximizes his own private utility, each of us might spend less on our front gardens than is socially optimal, but it might be that we fall into some convention or arrangement whereby if I let my garden go to seed then my neighbors will exert social pressure on me to do something about it. Explicit Regulation and Intervention. Everyone in New York knows (though they may have different views about it) how Mayor Bloomberg (and increasingly many others) chose to deal with the externality imposed by smokers on those around them: to ban smoking. Though possibly (probably?) a measure that improves social welfare, notice that such explicit regulation does not fully maximize social welfare. Suppose that some fabulously wealthy person came to town and really, really wanted to light up in a small bar, to the point where he was willing to pay $1m to each person in the bar. It is far from clear that we are maximizing social welfare by stopping him from doing so. If there were some way, however, of cheaply instituting and enforcing property rights over the air in the bar, then the situation might be improved. For the air in the bar, there probably is not a market, but in other applications there might be, which leads us to the next measure. Property Rights and The Coase Theorem. A final method for dealing with externalities involves the establishment of clear and unambiguous ―property rights.‖ Consider the case of a steel plant dumping waste in the river. Society might decide that (a) downstream parties have a property right to clean water, or (b) that the plant has the right to dispose of its waste as it sees fit.

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Property rights can be established in either way. But once those rights have been clearly established (and so long as they are properly enforced), individuals can bargain over how they exercise these rights. If downstream parties have the right to clean water, then the steel plant can pay them in order to get permission to pollute. Alternatively, if the plant has the property rights, then downstream parties can compensate the steel plant to restrict its pollution. The Coase Theorem, named after its originator, Ronald Coase, deals with this situation. It asserts that, so long as all parties have full information, bargaining is costless, and there are well-defined property rights, then the outcome is efficient regardless of how property rights are assigned. Essentially this is a market solution: clearly establish property rights and then let the ―market‖ bargaining determine the outcome. Though in some contexts the underlying assumptions for the Coase Theorem might seem a little too strong, in others contexts they are quite reasonable. In fact, the Coase approach has been much discussed recently, for example, in the context of transferable emissions permits or licenses to pollute. Example. Common facility. Different divisions within a firm frequently compete for a common resource. Suppose that divisions 1 and 2 of a given firm share a common facility F. Let yi be the service level used by division i (i=1,2). Division i‘s gross benefit in terms of improved divisional earnings is given by yi – 0.25 yi

2 – 0.1 (y1 +y2). a) What are the equilibrium levels of yi if the various divisions act separately? b) What are the optimal levels of yi from an overall firm point of view? c) Explain the difference between the results in a) and b). d) How can equilibrium and optimality be reconciled?

Answer. a) Each division maximizes yi – 0.25 yi

2 – 0.1 (y1 +y2). Let us consider division 1. Since it cannot control the other division, the optimal solution corresponds to maximizing y1 – 0.25 y1

2 – 0.1 y1 = 0.9 y1 – 0.25 y1

2. The solution is y1 = 1.8. By symmetry, the same is true for the other division, so y2 = 1.8. b) The firm maximizes total benefit, that is y1 – 0.25 y1

2 – 0.1 (y1 +y2) + y2 – 0.25 y2 2 – 0.1 (y1

+y2) = 0.8 (y1 + y2) – 0.25 (y1 2 + y2

2). Maximizing with respect to y1 we get y1 = 1.6. c) The equilibrium value is greater than the optimal value. The reason is that there is a negative externality: when division 1 uses the facility more intensely, it does not take into account that this costs division 2 lower divisional earnings. In other words, part of division 1‘s gain is not a gain for a firm as a whole. d) One possibility is to create a system of transfer pricing whereby each division pays for the use of the common facility F. If the fee is set at .1 (the cost imposed on the other facility), then the equilibrium solution will be optimal.

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Networks and Standards Almost all of us use PCs that run Microsoft Windows. Do we simply have the same taste, or is something deeper going on? 20 years ago, Betamax was a technologically superior format to VHS. Yet we now all use VHS (which has improved markedly in the meantime). 150 years ago, hundreds of phone companies existed. But since they weren‘t interconnected, the AT&T ―Bell System‖ eventually took over almost the entire market as a government supported and regulated monopoly. The rationale behind all of these stories is what we term ―network effects.‖ The value of the product to customers depends not only on its quality but on the number of other people using the same product. There is, in essence, a network of users, and the size of the network plays a large part in its creating value. Thus we all use Windows-based PCs because they support the same programs and allow us to share files easily. Similarly, VHS won because once it got a large enough market share (another story), there was no reason for video stores to stock tapes in a second format. AT&T won for a similar reason: once it got a critical mass of customers, it attracted others who wanted to communicate with them. Markets with network effects have a number of unusual features. First, there‘s a tendency for the winner to claim all or most of the market, since buyers want not only a good product, but a product compatible with similar products used by others. Second, such markets are frequently subject to battles over standards, since a firm that is able to establish its own product as the standard is often in a strong competitive situation. Third, the best product need not win. An accident that gives a product a critical mass of users (an installed base) has a strong competitive position, regardless of the quality of its product. Fourth, monopoly may be the natural outcome of competition. How should antitrust authorities respond to such market power? In short, it changes the nature of competition in fundamental ways. Network Effects Suppose I were to tell you that I had here, in my overcoat, a brand new Panasonic cordless phone with all the bells and whistles on it, and that I would sell this telephone to you for $1. Not a bad deal, right? It‘s even cheaper than a subway fare. Now suppose you knew the following information. The year is 1789, and even though I am selling the phone to you in real terms (i.e., the phone costs the 1789 equivalent of $1 dollar today), you would probably not buy it. Why? Because no one else had telephones in 1789! What would the value of owning a telephone be if you couldn‘t call anyone? Now let‘s jump ahead to the early 20th century. Thanks to our friendly monopolist AT&T, more and more people are connected to the telephone network across the US. Now you may be able to call a very small percentage of your family members or business associates. All of a sudden the phone that was worthless to you in 1789 begins to look better. Now suppose I tell you that we have traveled back to the future and we are in 2001. You can call just about

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anyone you know in the world on the phone – not just a handful of people. This same piece of electronic equipment, which hasn‘t changed one bit since I offered it to you 200 years ago, is worth a lot more. Why? The answer is network effects. Network effects arise when each consumer‘s valuation of a certain product increases with the addition of other consumers who use the product. We can extrapolate the telephone example above to many other daily applications like email and fax machines. We call such examples direct network effects because, as we show above, it is obvious how these products‘ utility increases as other people also demand them. Still another example of direct network externalities is given by software. For example, consider Microsoft Word. On one level, your valuation for this product relates to the features and functionality it provides you (for example, the spell-checker if you are a terrible typist). But in addition, suppose you insisted on using an old, DOS-based Word program that no one else uses anymore. It may be great for you if you are used to it and love it, but what if you need to email someone a document (and vice versa)? What if you need to print on a printing network that does not recognize your software? What if you are working on a group project and splitting up a paper assignment? Because millions of us use Microsoft Word together and are able to interconnect through this shared application, the value of the program increases with each additional MS Word user to the extent that we can all communicate easily and efficiently. We also can observe indirect network effects arising from many products. One example is given by ATM machines. My banking with Chase has nothing to do (directly) with your value of using Chase directly, but the fact that we all are using Chase makes the firm more likely to build ATMs all over the city – which provides us all with increased utility. We can probably guess at this point that the value of a network good depends on the number of consumers who demand it. This point is not lost on firms, who realize that they must achieve a so-called critical mass of users in order to reap the benefits of network effects. What are these benefits? Firms like Microsoft and Chase create added inelasticity for their products, keeping consumers from switching to other products and attracting new consumers thanks to the ―bandwagon‖ effect of demanding something that everyone around you also has. Critical Mass The logic of critical mass is as follows. Because the demand for network products increases with the expectation that there will be additional users whose presence increases the network‘s value (called an externality because you, as the additional consumer, do not capture this added value that you create), the demand curve takes on an unusual humped shape instead of the normal downward sloping line. For this reason, as price declines, a snowball effect may take place as many, many additional consumers suddenly demand the product. At this point in the demand curve we say that the installed base (the number of customers comprising the network) has attained critical mass. We can see why firms want to attain critical mass for their network products, but this is not always easy. One confounding factor can be that of excess inertia—that is, the prevention of

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critical mass from being attained by some ―stickiness‖ to a rival product or an unwillingness to adopt a new network product. A good example of this is DVD players. While firms are gradually lowering the price of DVD players as their marginal cost declines, DVDs have been slow to ―explode‖ in the marketplace. Why? Because many consumers are unwilling to substitute DVDs for their VCR players and the scores of tapes that would need to be replaced. Even though everyone may find that they prefer DVD players to VRC players once they switched, this leap is not easy for sellers to induce. Thus, sellers often take recourse against excess inertia by introducing new network standards that are ―backwards compatible‖ (that is, they can be integrated with existing network goods) or by pricing at an extremely low level to offset consumers‘ switching costs. Standards Wars In the late 1970s, VHS and Betamax hit the scene around the same time with different, incompatible, VCR formats. When VCRs started to be used for viewing movies (in the 1980s), video stores typically offered both types of cassettes to consumers. While it is agreed that Betamax was a better technology, we know today that VHS all but eclipsed the Betamax standard. What happened from Betamax‘s point of view? Some bad decision making in terms of pricing and vendor relationships and some lucky factors for VHS led to more network adoption of the inferior VHS product; eventually as the market was ―tipped‖ in the favor of VHS its installed base soared relative to that of Betamax. And once consumers were ―stuck‖ on the VHS standard, there was no looking back Betamax was left in the dust. This example underscores the point that in standards wars between network products, usually one standard eventually captures the entire market due to network effects. The other standard generally is abandoned, or is relegated to a small niche of users that generate lower network externalities (as in the case of the Mac OS). Related to this, we can see that the best standard is not always the winning standard. Thus, firms must behave strategically to capture the bandwagon of consumer behavior with respect to network products whether or not their product is superior. Why? Because once they lose the ability to harness network effects, consumer demand snowballs in favor of another standard for the reasons discussed above. It is further important to note that not all outcomes in standards wars are controllable by firms, even if they are acting strategically. While it is easy to cast hindsight onto many standards wars over the years and point to why one product is victorious over another, the actual escalation of network demand is determined by a conspiracy of smaller events—some controllable by the firm, some not. Sometimes economists use the expression ―path dependence‖ to denote this determinism by ―small historical events‖ that irrevocably shape the future. An additional strategic dimension of network products and standards wars is that of the compatibility question. Why did IBM allow rival firms to ―clone‖ its PCs? And why did Apple refuse to integrate its computing platform with IBM-compatible PCs? Firms with standards must weigh the potential costs and benefits of making their products compatible with competing products. On the positive side, allowing your products to be used with a wider number of applications, even though you are competing with those applications, creates additional demand for your products that would otherwise not exist. IBM, from above, figured that if it allowed for the number of IBM-compatible PCs to explode, its own

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computers—at the center of the standard—would be more demanded and other computing standards (i.e., Apple) would suffer. But on the downside, compatibility also creates risks. If you make your software compatible with that of a rival firm with superior software, you may find your installed base migrating to their products over time. There is no clear answer to whether compatibility or incompatibility is better for a firm; it depends on the particular industry, the size of the firm, consumer behavior, and of course the competitive landscape. We can generalize a bit by saying that if product market competition is intense, then incompatibility is a superior strategy. Conversely, if competition for an eventual standard is intense—in other words, if there are two competing standards vying for critical mass and only one will survive—compatibility may be the better option. Example Two firms, Firm 1 and Firm 2, have heavily invested in a new type of high-density versatile disk. This new disk will be able to contain the information corresponding to about twelve two-hour movies. The technology comes with a computer device that allows for reading and writing the new disks at high speed. Each firm has come up with its own design, A and B. Although each design performs approximately the same functions, the designs are not compatible. The firms must now decide which design to market. The payoffs from such decision can be summarized in the following table.

A B

u w A u+v w

w u+v B w u

Question: What values would you expect u, v and w to take? Why. Answer: If network effects are very significant, it is likely that w is a small number, probably close to zero. If the firms continue to support different, incompatible standards, then it is likely that the market will be very confused and shy away from investing in high-density DVDs (we always have the good old DVDs that we have now). We would also expect u and v to be positive numbers. The idea is that firms gain from supporting the same design (u>0), especially if that is the design they invested on initially (v>0). Question: What are the Nash equilibria of this game? Answer: Suppose that w<0, say w=0 and that u,v>0. Then there are two Nash equilibria, (A,A) and (B,B). Open question: What examples can you think of where a game like this was played? What aspects of your example are not depicted in this game? © 2012 NYU Stern School of Business.

Firm 2

Firm 1