A STEP-BY-STEP GUIDE TO THE PRINCIPLES OF MICROECONOMICS (2nd Edition) [2 ed.] 9781945628412

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A Step-by-Step Guide to the PRINCIPLES

OF

MICROECONOMICS Second Edition

NICK HUNTINGTON-KLEIN

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Copyright © 2018 by Kona Publishing & Media Group

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CONTENTS — PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

How Students Can Use the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

How Educators Can Use the Book

CHAPTER I La Lb 1.5

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xiii

ABOUT THE AUTHOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xv

COMPARATIVE ADVANTAGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

l

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Calculate Comparative Advantage . . . . . . . . . . . . . . . . . . . . How to Draw Production Possibilities Frontiers . . . . . . . . . . . . . . . .

1 2 4

I.c.i

How to Draw a Production Possibilities Frontier for One Person. . . . 4

1.c.ii How to Draw a Production Possibilities Frontier for Two People. . . . 7 1.c.iii How to Draw a Production Possibilities Frontier for a Whole Economy.........................................1 0

I.d Le

12 How to Find Consumption With and Without Trade . . . . . . . . . . . . How to Shift a Production Possibilities Frontier ...............1 5 18 Practice Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 2

SUPPLY AND DEMAND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

2a 2!: 2.: 2.0 2.9 2f

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Make a Supply Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Draw a Supply Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Make a Demand Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . How to Draw a Demand Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Aggregate Individual Supply and Demand Curves to Get Market Supply and Demand . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 24 27 29 32

35 iii

iv

CONTENTS

2.9

2.h 2.i EJ 3k

How to Predict Shifts in Supply and Demand . . . . . . . . . . . . . . . . .

37

2.g.i How to Predict Shifts in Supply and Demand: Complements and Substitutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

How to Find Excess Supply (Market Surplus) and Excess Demand (Market Shortage) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

How to Calculate Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . How to Graph Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . How to Find the New Equilibrium when Supply and Demand Curves Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44 46

3.k.i How to Find the New Equilibrium When One Curve Shifts . . . . . . .

47

3.k.ii How to Find the New Equilibrium When Both Curves Shift at Once . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

Practice Problems CHAPTER 3 3.3

3.!)

......................................

47

52

ELASTICITY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Calculate Percentage Change . . . . . . . . . . . . . . . . . . . . . . .

57 58

3.b.i How to Calculate Percentage Change Using the Standard Method. . . 5 9 3.b.ii How to Calculate Percentage Change Using the Midpoint Method . . 60

How to Calculate Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

3.c.i How to Calculate Price Elasticity Using a New Point and an Old Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

3.c.ii How to Calculate Price Elasticity Using a Supply Curve or a Demand Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

3.c.iii How to Calculate Income or Cross-Price Elasticity Using a New Point and an Old Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

3.9

How to Draw Price Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Use Elasticity When the Supply or Demand Shift . . . . . . .

68 71

3.f

How to Determine if Something i s Elastic, Inelastic, or

3.0

CHAPTER 4 Ha Lib

Unit Elastic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Practice Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 75

MARGINAL VALUE AND MARGINAL COST . . . . . . . . . . . . . . . . . . . . .

79

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marginal Cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79 8O

Ll.b.i

80

Ll.b.ii

How to Calculate Marginal Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Derive a Supply Curve from Marginal Cost . . . . . . . . . . . . .

82

CONTENTS

LLCI

LLB LLf

Ll.b.iii

How to Find Marginal Cost on a Supply Curve . . . . . . . . . . . . . . . . .

Ll.b.iv

How to Calculate and Graph Producer Surplus .................8 5

5.3 5.13 5.: 5.1:! 5.9 S.f 5.9

CHAPTER 6

83

Marginal Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

l-l.c.i

How to Calculate Marginal Value . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

Ll.c.ii

How to Derive a Demand Curve from Marginal Value . . . . . . . . . . .

90

L4.1:.iii

How to Find Marginal Value on a Demand Curve...............91

Ll.c.iv

How to Calculate and Graph Consumer Surplus ................9 3

How to Graph Producer Surplus and Consumer Surplus 97 Change When Price Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Determine the Optimal or Efficient Level of an Activity . . . 99 101 Deadweight Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LI.f.i

How to Calculate Deadweight Loss.........................101

l4.f.ii

How to Graph Deadweight Loss ...........................104

Practice Problems CHAPTER 5

V

.....................................

GOVERNMENT POLICY IN COMPETITIVE MARKETS . . . . . . . . . . . . Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Model Price Maximums (Price Ceilings) . . . . . . . . . . . . . How to Model Price Minimums (Price Floors) . . . . . . . . . . . . . . . How to Model Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Calculate Tax Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . How to Model Quotas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Model International Trade . . . . . . . . . . . . . . . . . . . . . . . . . Practice Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

106

Ill 111 112 115 118 122 127 130 134

THE PRODUCTION PROCESS IN COMPETITIVE MARKETS. . . . . . I39

5.13

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Distinguish Fixed and Variable Costs . . . . . . . . . . . . . . . .

6.c

How to Fill Out a Cost, Revenue, and Profit Table

6.1:!

Average Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

147

6.d.i How to Calculate Average Costs . . . . . . . . . . . . . . . . . . . . . . . . . . .

147

6.3

............

139 141 143

5.d.ii How to Graph Average Costs..............................148 6.9 5.f 6.9 5.11

How to Determine the Profit-Maximizing Quantity . . . . . . . . . . . How to Graph a Firm in a Competitive Market . . . . . . . . . . . . . . . How to Calculate Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long-Run Market Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

149 151 152 153

6.h.i How to Predict Entry and Exit.............................153

vi

CONTENTS

6.h.ii How to Model the Market and the Firm Together ..............155 6.h.iii How to Find Long-Run Equilibrium Price and Quantity.........158

CHAPTER 7 7.3 7.13 7.:

5.h.iv How to Graph Long Run Average Total Cost . . . . . . . . . . . . . . . . .

158

Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

162

MONOPOLY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I67

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Distinguish between Market Structures . . . . . . . . . . . . . . The Model of Monopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167 168 170

7.r:.i How to Find Marginal Revenue Using a Demand Curve . . . . . . . .

170

7.c.ii How to Determine the Profit-Maximizing Quantity and Price . . . . 172 7.c.iii How to Calculate Monopoly Profit .........................173 7.C.iv How to Find Deadweight Loss in a Monopoly ................174 7.C.V How to Graph a Monopoly ...............................176 7.t:.vi How to Graph a Natural Monopoly .........................177 7.d

Monopolistic Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

178

7.d.i How to Find Short-Run Equilibrium in Monopolistic Competition ...........................................178 7.d.ii How to Graph Long-Run Equilibrium in Monopolistic Competition ...........................................179

Price Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

180

7.e.i How to Graph Perfect (First-Degree) Price Discrimination ......180

7.e.ii How to Graph Less-than-Perfect (Third-Degree) Price Discrimination .........................................181 7.e.iii How to Calculate Hurdle (Second-Degree) Price Discrimination . . . 182

CHAPTER 8 8.3

Practice Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

185

GAME THEORY AND OLIGOPOLY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

189

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

189

8.13

How to Draw a Game Table (Normal Form) for

8::

Simultaneous Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Find Nash Equilibria in a Game Table . . . . . . . . . . . . . . .

8.0

How to Draw a Game Tree (Extensive Form) for

8.9

8.f

190 193

Sequential Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 How to Solve a Game Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 How to Predict the Effect of Repeated Interaction on G a m e s . . . . 203 Practice Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

CONTENTS

Vii

CHAPTER 9

EXTERNALITIES AND PUBLIC GOODS . . . . . . . . . . . . . . . . . . . . . . . .

2| l

9.3

Glossary and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Graph Extemalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Find the Efficient Outcome under an Extemality . . . . . . . Pigouvian Tax or Subsidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

211 213 214 216

9.d.i How to Calculate the Optimal Pigouvian Tax or Subsidy . . . . . . . .

216

9.13 9.: 9d

9.9

9.f 9.9

9.d.ii How to Graph the Optimal Pigouvian Tax or Subsidy . . . . . . . . . .

218

How to Use the Coase Theorem to Solve an Extemality . . . . . . . . How to Distinguish Types of Goods . . . . . . . . . . . . . . . . . . . . . . . How to Find Efficient and Market Outcomes for Different Types of Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

219 221

9.g.i Public Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

224

9.9.“ Common Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

227

9.g.iii Artificially Scarce Goods/Club Goods. . . . . . . . . . . . . . . . . . . . . . .

228

Practice Problems

.....................................

224

231

ANSWERS T0 ODD-NUMBERED QUESTIONS . . . . . . . . . . . . . . . . .

235

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

275

PREFACE — How Students Can Use the Book Hello, there.

You will find that this book takes a relatively different approach from a regular textbook for Principles of Microeconomics. Most of those books are written with long-form prose explaining economic theory and models. That’s great stuff, and there are a lot of fantastic textbooks out there. However, where many of them fall short is in helping you figure out how to use that theory and those models yourself! That’s too bad. It’s most important to have a good grasp of the concepts, of course, but the technical parts of economics provide some real insight into what’s going on. And if your professor is already explaining those concepts to you in class, your regular textbook can feel a little redundant. So, this book takes a very straightforward approach of what to do and how to do it. I’ve always found it frustrating that it’s so hard to find material that will really walk you through these models, when the models you see in Principles seem almost tailormade to allow that sort of thing! That’s why I wrote this book. S o , what can you do with this book?

I You can use it to learn,

in a no-messing-around manner, about the models you

see in your Principles of Microeconomics course—what the pieces mean and how to work with them.

I You can use it to learn

how to work with those models and solve the kinds of

problems you see in class.

I You can learn why those solutions work conceptually. I hope that you get something out of this material, and good luck in your class!

X

PREFACE

How Educators Can Use the Book This book offers students a step-by-step guide using the models we see most often in Principles of Microeconomics. Having a guide like this available for your students serves a few important functions: I Standard textbooks do their best work when they’re focusing on explaining economic concepts in great detail. The typical format is that they will explain a concept in a few paragraphs of text, and then show a graph or table explaining the model. However, this approach often makes it difficult to understand exactly how the concept relates to the model. In the “Why” columns of this book that accompany every step, I make sure to explain (with the brevity to make reading it a MB > MC choice) exactly how the part of the model relates to the concept, and why we’re doing what we’re doing. There’s no longer a missing link between the economic concept and the model of that concept. When you have students work through these models with this book, paying attention to the “Why” column will improve their understanding of what the model is actually for.

I A s anyone who has taught Principles of Microeconomics knows, there is always a section of the class that has trouble with the technical side. Whether they’re not mathematically prepared, or they are but they’re just not used to the kinds of graphs and equations economists use, some students need a little extra help here. In my graduate school days, I spent plenty of time as a tutor and I saw these students all the time. What I found often helps these students are no-distractions, here’s-the-way-it-works explanations of the models. That’s what this book offers. Making this book available as supplementary material for your students can head off these sorts of problems. I Many of us structure our classes so that we are focusing on explaining the basic economic concepts ourselves in our lectures, through newspaper articles, and in our own notes made available to the class. If you’re already doing a good job explaining the economic intuition that forms the basis of the class, then the standard textbook becomes a little redundant, since that’s also what i t i s

trying to do. You can push this even further, getting rid of the normal textbook entirely, which leaves you more room to demonstrate concepts in your own

PREFACE

xi

way, and provide more readings from the real world. Of course, doing that leaves a gap, since getting technical material to stick in students’ heads without a way to work through it on their own is a little tougher than for concepts. This book, assigned as a primary text, fills that gap. It’s an inexpensive guide that helps students work through the technical side of the material so they can focus on the important concepts in their own way.

ACKNOWLEDGEMENTS — Thanks to Spike, Mom & Dad, Susan & David, my alma maters, and of course the

California State University at Fullerton.

ABOUT THE AUTHOR — Dr. Nick Huntington-Klein is an Assistant Professor of Economics at California State University Fullerton. He holds a PhD in Economics from the University of Washington Seattle, and an undergraduate degree from Reed College. He is the author of numerous journal articles and reports, mostly on the topics of labor and education economics. He was inspired to write this book through his experience teaching Principles of Microeconomics at Fullerton and at Seattle University, as well as through his work tutoring in person and online.

Glossary and Concepts Opportunity Cost is what you have to give up in order to get something. However, this cost is not usually measured in terms of dollars. Instead, it is measured in terms of what you could have had if you’d made a different decision. For example, if you are thinking about whether to spend your evening at the movies or going to a play, the opportunity cost of going to the movies is that you don ’I get to go to the play. Absolute Advantage is when you are better at something than somebody else. If you gave the author of this book and a famous basketball player five minutes to shoot as many baskets as possible, the basketball player would make more baskets. He would have an absolute advantage. Comparative Advantage is when you are better at something relative to other tasks than somebody else. In other words, it is when you have a lower opportunity cost for a particular task than somebody else. If you told the author of this book and a basketball player to spend their time making baskets or running a mile, the basketball player would be better at both. But the basketball player would be much, much better at making baskets, and only somewhat better at running a mile. So, the basketball player would have a comparative advantage in making baskets, and the author would have a comparative advantage in running a mile. Specialization is when people spend most or all of their time doing the things that they have a comparative advantage in.

Autarky is when a person or country produces everything it needs, rather than specializing and trading with others. This term usually refers to countries rather than to individuals.

2

CHAPTER 1

COMPARATIVE ADVANTAGE

Specialize and trade refers to people spending most or all their time doing the one thing they have a comparative advantage in, and trading with others to get all the things they need. An example is if you work at a job you’re good at in order to earn money, and you use that money to buy food, clothes, and shelter, rather than making your own food, clothes, and shelter.

A production possibility frontier (also known as a production possibility curve) describes the different mixes of things you could make given the resources available to you. If you could spend all day writing songs and end up with 5 songs, or instead spend all day packing lunches and end up with 1 0 lunches, then “5 songs, 0 lunches” and “0 songs, 1 0 lunches” would both be on your production possibility frontier.

How to Calculate Comparative Advantage WHAT YOU NEED TO START: Two people or countries, two activities they can do or goods they can make, and information about how much of those activities they can do or how many goods they can make (their capacity to produce those goods). These steps will be stated in terms of people doing activities, but the steps work the same for countries producing goods.

STEP 1 WHAT YOU DO If the problem is stated in terms of capacity (“Sheila can fill out 3 forms in an hour”), then skip this step. If the problem is stated in terms of costs

(“It takes Sheila 20 minutes to fi l l out a form”), then convert

it into capacity by picking a fixed amount of time and calculating how many units the person can make in that time.

Example: If i t takes Sheila 20 minutes to fi l l out a form, and it takes Mark 3 0

minutes, then Sheila can fi l l out 3 forms i n an hour, and Mark can fill out 2 .

WHY

The rest of the steps listed depend on stating everything in terms of capacity.

STEP 2 WHAT YOU DO Draw a table that shows the number of units of each activity A and B each person can do in a fixed period of time (their Capacity).

Example:

WHY

Sheila

Mark

Forms

3/hour

2/hour

Letters

5/hour

3/hour

This table will make clear what each person could produce if they spent all their time on that activity. If Sheila spent her whole hour sending letters, she’d send 5 letters and fill out 0 forms.

STEP 3 WHAT YOU DO For each person, calculate their opportunity cost (0C) for activity A using the formula: _ Capacity 3

Capacity A and for activity 3 using the formula:

OCB= Ca Paci.tYA CapacztyB

Example: For Sheila, .

ocShezla Fomts

:

5

_, 3

.

ocSheila Letters

:

_ 5

For Mark, ocMark‘ Forms

WHY

:

2 ocMark 2 ’ Letters

:

_ 3

Opportunity cost is what you give up in order to get something. If someone spends all their time on task B, they get CapacityB. If you imagine that person giving up all their B to spend all their time on A instead, they get CapacityA. So, the cost of each unit of A (OCA) is

4

CHAPTER 1

COMPARATIVE ADVANTAGE

what they gave up (CapacityB) divided by the number of units of A they got for it (CapacityA).

STEP

Ll

WHAT YOU DO Each person has a comparative advantage in the task for which they have the lowest opportunity cost.

Example:

0C123353 = g and OCMark Forms = 3 . Since g > 3 , Mark has a comparative advantage in Forms.

.

2

2

OCfiggfi = g and OCfljflfis = 3 . Since 5 > %, Sheila has a comparative advantage in Letters. WHY

You have a comparative advantage when you can produce something at the lowest cost, relative to other possible uses of your time. “Cost,

relative to other possible uses of your time” is what opportunity cost measures. So, whoever has the lowest opportunity cost of doing something has a comparative advantage in it. Unless two people have the exact same opportunity costs, each person will always have a comparative advantage in something.

How to Draw Production Possibilities Frontiers 1-9;! How to Draw a Production Possibilities Frontier for One Person WHAT YOU NEED TO START: Two activities the person can do or goods they can make, and information about how much of those activities they can do (their Capacity, see 1.b).

STEP 1 WHAT YOU DO Draw a set of axes. On one axis should be Activity A . On the other axis should be Activity B.

Example: For a PPF describing the amount of Com or Wheat someone can make, you would draw: Corn“

Wheit WHY

A PPF describes the mix of activities you can do. The axes of the PPF should describe how much of each activity you’re doing, and so it should be labeled with the activities.

STEP 2 WHAT YOU DO Label each axis with the person’s capacity. So, if a person can do at most 4 units of Activity A, label the number 4 on the axis for Activity A. Then, draw a straight line connecting those two points on the axis.

Example: If James can make 3 units of Com or 4 units of Wheat, we would label: Cornll

4 VVheEt

6

CHAPTER1

WHY

COMPARATIVE ADVANTAGE

The PPF describes the things you can do. So, if you can do 4 units of Activity A if you spend all your time on it, then “4 units of Activity A and none of any other activity” should be on your PPF, since it’s something you can do, and it takes all your time. That mix—4 of A and O of B—is on the Activity A axis, since you’re doing 0 units of Activity B on the axis. Once you have your axis points, you connect them with a straight line, since for a single person you’re just dividing up your time, and so should be able to trade off doing one activity for another without your opportunity cost changing. The opportunity cost, from 1 b , is the ratio of the capacities, which is also (the negative of) the slope of the line! So, the slope of the line shows you the opportunity cost of producing the good on the x-axis. Since the opportunity cost doesn’t change, the slope doesn’t change, meaning it’s a straight line.

STEP 3 WHAT YOU DO If you have a second person and want to graph their individual production possibility frontier as well, you can put it on the same set of axes by repeating Step 2. B e careful to label the two different lines!

Example: If we also have Andrea, who can make 2 units of Com or 5 of Wheat,

we could graph both James and Andrea at once: Corn“

3

James

Andrea

4

5 Wheat

CHAPTER 1

WHY

COMPARATIVE ADVANTAGE

7

The individual PPFs both naturally should be on graphs with the same activities on the axes, so there’s no reason not to graph them together. Be careful, though—this is not the shared PPF. We are just graphing two individual PPFs together. For a shared PPF, see 1.c.ii.

Laii. How to Draw a Production Possibilities

Frontier for Twe People WHAT YOU NEED TO START: Two activities the person can do or goods they can make, information about how much of those activities they can do (their Capacity, see 1 b ) , and which of them has a comparative advantage in each activity (see 1.b). STEP 1

WHAT YOU DO Draw a set of axes. On one axis should be Activity A. On the other axis should be Activity B.

Example: For a PPF describing the amount of Com or Wheat someone can make, you would draw: CornH

Wheat

WHY

A PPF describes the mix of activities you can do. The axes of the PPF should describe how much of each activity you’re doing, and so it should be labeled with the activities.

8

CHAPTER 1

COMPARATIVE ADVANTAGE

STEP 2 WHAT YOU DO For each activity, determine the amount that would be produced if both people spend all their time on that activity. Label this point on the axis for that activity.

Example: If James can make 3 units of Corn or 4 of Wheat, and Andrea can

make 2 units of Com or 5 of Wheat, and if they spent all their time on Corn, they would make 3 + 2 = 5 units. If they spent all their time on Wheat instead, they would make 4 + 5 = 9 units. Corn“

5?

.— 9 Wheat

WHY

The PPF describes the possible mixes of activities that you can per— form or goods you can make. We know that these two people working together can’t possibly do more of an activity than they would if they spent all their time on it (and so produce zero of the other good). So, if we add up what they’d do while spending all their time on it, then we’d end up with the axis point on the shared PPF.

STEP 3 WHAT YOU DO Determine the kink point. The kink point is where each person is fully specializing in the activity they have a comparative advantage in. For each activity, the amount produced is how much the person with the comparative advantage in that activity would produce by spending all their time on it.

CHAPTER 1

COMPARATIVE ADVANTAGE

9

Connect the dots on the axes to the kink point to complete the shared PPF. The result should “bow out” a little.

Example: Andrea has a comparative advantage in Wheat and can make 5 units of Wheat. James has a comparative advantage in Corn and can make 3 units of Com. S o , at the kink point, there are 5 units of Wheat and

3 units of Com produced. Corn“

m-——--_

Andrea

WHY

9 Wheat

The (negative of the) slope of the PPF represents the opportunity cost of making another unit of the good on the x-axis. And so there must be two different slopes—one representing Andrea’s opportunity cost of Wheat, and one representing J ames’s opportunity cost of Wheat. In order to u s e our most efficient resources first, we have Andrea

produce the first few units of Wheat, since she has the comparative advantage. So, her part of the PPF is furthest to the left (covering the first 5 units of Wheat). Then, only when she is already spending all her time on Wheat (making 5 Wheat) do we switch to having James make Wheat. That’s the point where the slope shifts. And at that point, James is spending all his time on Corn (making 3 Corn).

10

CHAPTER 1

l.l:.iii

COMPARATIVE ADVANTAGE

How to Draw a Production Possibrhties Frontier for a Whole Economy

WHAT YOU NEED TO START: A list of two goods the economy can produce.

STEP 1 WHAT YOU DO Draw a set of axes. On one axis should be Activity A . On the other axis should be Activity B.

Example: For a PPF describing the amount of Com or Wheat an economy can make, you would draw: CornH

Wheat

WHY

A PPF describes the mix of activities you can do. The axes of the PPF should describe how much of each activity you’re doing, and so it should be labeled with the activities.

STEP 2 WHAT YOU DO Draw a curved line that starts out with a shallow slope and gets steeper as you move further to the right (making a shape like a bow pulled back). T h i s i s the PPF.

Example: Corn“

Wheat

WHY

An economy has many different resources available to it. The (negative of the) slope of the PPF represents the opportunity cost of switching one of those resources from being used to make Corn to making Wheat instead. Because all the resources have different opportunity costs, and we want to use the lowest-opportunity cost (shallowest slope) resources first, the slope of the PPF continually gets steeper as you move from left to right.

STEP 3 WHAT YOU DO If you are given the productive capacity of the economy, label the axes with the most the country could produce of each good.

Example: If this economy could produce at most 10,000 units of Com or 8,000 units of Wheat, label: Corn“

10,000

8,000 Wheit

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WHY

COMPARATIVE ADVANTAGE

The axis points represent how much is produced when the economy only makes that good. And so, we can label the axes with the amount we get if we spend all of our resources on that one good, making only that good.

How to Find Consumption With and Without Trade WHAT YOU NEED TO START: Two people or countries, two activities they can do or goods they can make, and information about how much of those activities they can do or

how many goods they can make. You will also need to know who has a comparative advantage in each task (see 1.b).

These steps will be stated in terms of people doing activities, but the steps work the same for countries producing goods. STEP 1 WHAT YOU DO If there is no trade, go to Step 2. If there is specialization and trade, go to Step 3. STEP 2 WHAT YOU DO For each person, determine how many units of good A they are required to produce, GoodA. If the problem says something like “they want an equal number of good A and good B,” then write out the PPF, plug in GoodA = GoodB, and solve for GoodA. Then, go to Step 4 .

Example: If the problem states that Aaron must produce two cans of beans, and Betty must produce two cans of beans, then BeansA‘m’"= 2 and Beans Betty = 2. If the problem states that Aaron must produce an equal number of cans of beans and cans of soup, and Aaron’s PPF is Beans = 6 — ZSoup, then

CHAPTER 1

Beans/WU"

COMPARATIVE ADVANTAGE

13

= 6 — ZBeansAar‘m

3BeansA‘m’” = 6 BeanSAaron

WHY

= 2

The PPF alone won’t tell us which point on the PPF they will choose, so the problem must tell you the amount they choose to produce. If we want to solve for how much they make if they make an equal amount, we can do this by solving the PPF (which describes potential production mixes) alongside GoodA = 000613,

w h i c h describes all

production mixes with the same amount of good A and good B.

STEP 3 WHAT YOU DO Determine how many units of GoodA the two people together must produce of good A. Then, divide the production of good A across the two people. Whoever has a comparative advantage should be the first to work on making good A . If GoodA is bigger than the total number of units that the person with comparative advantage can make, the other person makes the rest.

Example: If the problem states that Aaron and Betty must produce four cans of beans together, then Beans = 4. If Aaron has a comparative advantage in beans, and can make at most 3 cans of beans, then BeansA‘m’" = 3

and BeansBe”y = 4 — 3 = l . WHY

The person with a comparative advantage in a certain task should always be the first person assigned to do that task, since that maximizes productivity. Others should only start working on it once the person with a comparative advantage is already doing as much as he or she can.

S T E P '4

WHAT YOU DO Calculate the fraction of their time each person spends producing good A by dividing the number of units they produce by the total number they could produce if they spent all their time on it.

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GoodA

TimeA =

Capacity A

Example: If Aaron and Betty each produce 2 cans of beans, Aaron could produce at most 4 cans, and Betty could produce at most 3 cans, then TimeBeans

Am”

=

3"”

=

TimeBeans WHY

=

l 2

In order to figure out how much time people will have left to work on other activities, we must first figure out how much of their time they have already spent producing good A.

STEP 5 WHAT YOU DO Multiply the proportion of each person’s time remaining (1 — TimeA) by that person’s maximum capacity to produce good B to find the number of units of good B they will produce. GoodB = ( l — TimeA)CapacilyB

Example: If Betty spends 2/3 of her time making beans, and could make 6 cans of soup if she spent all her time on soup, then the number of cans of soup she makes is SaupBe’W = ( 1 _ § ) 6 = g = 2 WHY

The number of units of a given good someone can make is determined by the amount of time they must spend making it. If you could make X units of something if you spent your whole day on it, but instead you only spend 1/4 of your day on it, you’ll end up making X/4 units.

STEP 6 WHAT YOU DO Add together the amount each person produced of each good to find the total amount of production.

CHAPTER 1

COMPARATIVE ADVANTAGE

15

How to Shift 21 Production Possibilities Frontier WHAT YOU NEED TO START: A production possibilities frontier (see 1.c), usually for a country (1.c.iii), and a description of how that country’s production is changing. STEP 1

WHAT YOU DO Determine if the change being described affects production of only one of the goods on the PPF or both. If it only affects one good, go to Step 2. If it has to do with expanding or contracting the total resources in the economy, then it affects both, and go to Step 3.

Example: On a PPF with the goods Corn and Wheat, “the machinery that harvests Com gets more efficient” would only affect the production of Com, but “bad weather harms agricultural yields for all crops” or “an influx of immigrants expands the labor force” would affect both Corn and Wheat. WHY

The production possibilities frontier describes the possible production mixes in the economy. And so, to figure out the effect of a change, we need to know exactly which parts of production are changing. A change to just the production of Com will have a different effect on total production than a change to the entire agricultural sector.

STEP 2 WHAT YOU DO If the economy has changed to increase the total production of the good (perhaps by making production more efficient), then take the PPF graph and stretch it up (if the good is on the y-axis) or to the right (if the good i s on the x-axis). The axis intercept for the other good

should not move.

If the total production of the good has dropped instead, squash it down or to the left.

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CHAPTER 1

COMPARATIVE ADVANTAGE

Example: If the machinery for harvesting Corn has changed, then the PPF shift can be illustrated as below (the dashed line shows a decrease in production, and the dots show an increase). Corn“

Whegt

WHY

If the productive capacity for only one good has changed, then the maximum production for the other good should not change, since nothing changed about the production of that good! This maximum production is represented by the axis intercept, since this is the most you can produce, spending all your resources making it. So, you can imagine putting a finger on that point and stretching/squashing the rest

of the curve away from it to isolate those production changes for only one good.

STEP 3 WHAT YOU DO If the total amount of resources in the economy has changed, then the entire curve will shift out (if resources have increased) or shift i n (if resources have decreased).

Example: If bad weather harms yields for all crops, the PPF will shift inwards in all directions. If an influx of immigrants expands the labor force, the PPF will shift outwards in all directions as shown in the following illustration. (The dashed line shows a decrease in inputs, and the dots show an increase.)

Wheat

WHY

If the economy gets more total resources, then those resources can be spent on Corn or Wheat. The economy has just become more able to produce overall. So, it will change the total amount of either that you can produce, and both the x-intercept and the y-intercept should be changed.

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PRACTICE Follow-the-Steps Questions To solve, follow directions from one or more of the sections above. 1. In one minute, Sam can type 120 words or read 2 pages. In one minute, Amy can type 80 words or read 4 pages. For each, calculate the opportunity cost of reading one page, and determine who has the comparative advantage in reading pages. 2. Daphne can solve two mysteries per week, or write six news articles. Velma can solve four mysteries per week, or write eight news articles. For each, calculate the opportunity cost of solving one mystery, and determine who has the comparative advantage in solving mysteries. 3.

It takes Ted 20 minutes to wax a car, or 60 minutes to wash one. It takes Tom 1 5

minutes to wax a car, or 3 0 minutes to wash one. What is each man’s opportunity cost of washing a car, and who has the comparative advantage in washing cars? 4. Take Sam and Amy from Question 1. above. Graph their individual production possibility frontiers if they have 10 minutes of time available. 5. Dingo the Clown is planning his six-minute stage act. He is trying to divide his time between jokes and magic tricks. Each joke takes 30 seconds to tell, and each magic trick takes two minutes. Draw Dingo’s production possibilities frontier. (Draw it as a straight line.) 6. Take Sam and Amy from Question 1 above. Graph their shared production possibility frontier if they have 10 minutes of time available. You may find it helpful to do Question 4 first.

7. Belly Steaks is a large restaurant. In an hour, they can produce 300 plates of food or 150 desserts. Tooth Sweets is a bakery. In an hour, they can produce 50 plates of food or 100 desserts. Draw their shared PPF with dessert on the x-axis. Label the x- and y-intercepts and the kink.

CHAPTERl

COMPARATIVEADVANTAGE 19

I n a year, the country of Towlia can produce at most 40,000 30,000

d i s h towels or

bath towels. Draw the PPF for Towlia.

In a day, Jerry can make 15 loaves of bread or 30 jars of jelly. In a day, Lindy can make 30 loaves or 15 jars. If Jerry and Lindy each want 1 0 loaves of bread each day, find how much jelly they produce in total when they’re not specializing and trading, and then how much jelly they produce when they are specializing and trading. 10. Casey spends his time either solving Sudoku puzzles or reading books. Casey’s friend tells him a trick for solving Sudoku puzzles that makes him much faster at them. Draw Casey’s PPF before being told the trick (PPF 1) and after (PPF2). 11. The small nation of Bayo produces cacao (x-axis) and coffee (y-axis). Fall/winter production is PPF 1. Every spring, a bunch of temporary migrants who are great at harvesting cacao, but useless at coffee, move to Bayo (PPF2). Every summer, they are joined by more temporary migrants who are good at everything (PPF3). Draw PPF 1, PPF2, and PPF3 on the same axes.

12. The country of Agasta produces clocks and cows. Then, due to a drought killing much of the grass, it requires more grazing land to raise each cow. Draw the effect on Agasta’s PPF.

Concept Questions A. Every day after class, Mr. Dabble’s third grade class must clean the room. Some kids sweep and some kids put things away. Everyone thinks that sweeping is more fun, and s o he lets the best-behaved kids sweep. I s the classroom likely

being cleaned as fast as possible? Why or why not? Finish the sentence: “When someone can spend their time on X or on Y, the

opportunity cost of X is . . .”

In the shared production possibility frontier depicted in the following illlustration, who has the comparative advantage in brick? How do you know?

20

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Metal

There are three brothers—Justin, Travis, and Griffin. Each of them can write

8 ghost stories in an hour. Or, they can spend their time grooming horses. Justin’s opportunity cost of grooming a horse is 1 / 2 a ghost story. Travis’s opportunity cost is 1 ghost story. Griffin’s opportunity cost is 2 ghost stories. If each of them has an hour of time available, draw each of their individual production possibility frontiers, as well as their shared PPF. Armond and Alvin currently do not specialize and trade. Every day, each of them makes 1 0 shirts and 20 pairs of pants. Then, they decide to specialize and trade with each other. But they find no gains from trade! Together they make 20 shirts and 40 pairs of pants. What must be true about Armond and Alvin?

Why are country-level PPFs typically drawn as curves but individual-level PPFs are drawn as straight lines? The country of Khartem produces chairs and tables. Globally, they happen to have a comparative advantage in tables, and export tables around the world. Then, there’s a boom in interest in tables globally. It has suddenly become the fashion to replace your tables every year, and so demand for tables has gone way up, and the price for tables has as well. How will Khartem’s PPF shift?

Spike spends his time baking cakes and solving puzzles. The following graph describes how much Spike can do in a day:

Cakes

PPF1

PPF2 Puzzles

Which could explain a shift from PPFl to PPF2? . Spike is too busy that day to produce anything. . Spike rented a second oven that day. . Spike lost his handy cake-icing knife. . Spike has a headache that will make puzzles harder to solve. Jared and Shane are great examples of the kind of people who benefit from trade. Jared is great at making jewelry but dislikes jewelry and loves shirts, while Shane is great at making shirts but dislikes shirts and loves jewelry. Write down Jared and Shane’s production capacities such that, without trade, each of them consumes 1 unit of the thing they don’t like and 1 of the thing they do like, and with trade each of them consumes 1 unit of the thing they don’t like and 11 units of the thing they like. (Beware: this is a hard one!)

Glossary and Concepts Supply is the relationship between the price of a good (price, or P) and the number of units that producers want to make and sell of that good (quantity supplied, or Q5). Supply is typically represented either as a supply schedule, which is a table that relates P and Q3, or a supply curve, which is a function relating P to Q5 that can be written algebraically or graphed. Demand is the relationship between the price of a good (price, or P) and the number of units that consumers want to buy of that good (quantity demanded, or QD). Demand is typically represented either as a demand schedule, which is a table that relates P and Q0, or a demand curve, which is a function relating P to Q0 that can be written algebraically or graphed. Inverse supply and inverse demand are supply and demand curves written such that they show price as a function of quantity (for example, P = 1 2 — QD), as opposed to regular supply and demand curves, which show quantity as a function of price (for example, QS = 2 + P). Inverse supply and inverse demand are typically what you would draw on a supply and demand graph. Individual supply and individual demand describe the relationship between the price of a good (P) and either the quantity that an individual firm wants to produce (for individual supply), or the quantity that an individual person wants to consume (for individual demand). These can be contrasted to aggregate supply or aggregate demand (also sometimes called “market supply” and “market demand”), which describe the relationship between the price of a good (P) and either the quantity that

23

24

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SUPPLY AND DEMAND

the entire group of producers wants to produce (for aggregate supply) or the quantity that the entire group of consumers wants to consume (for aggregate demand). Two goods are substitutes if having more of one of them makes consumers want less of the other. For example, we know that butter and margarine are substitutes because if you have a lot of margarine, you don’t need any butter. Two goods are complements if having more of one of them makes consumers want more of the other. For example, we know that pencils and paper are complements because having a bunch of pencils makes it more valuable to get paper to write on! A market surplus (excess supply) or market shortage (excess demand) is when the quantity supplied (Q5) doesn’t match the quantity demanded (QD) because the price is too high, making people want to make more units than want to buy them (Q5 > QD, a market surplus), or because the price is too low, making people want to buy more units than anybody wants to make (QD > Q5, a market shortage). A market equilibrium is when the price is at a level that sets the quantity supplied (Q5) to equal the quantity demanded (QD). This is an equilibrium because at this price, everyone who wants to buy a unit can find one to buy, and everyone who wants to sell a unit is able to find a buyer. S o , nobody needs to change their behavior. A price control is when the government passes a law requiring that a price must be at least as high as a certain level (a price floor or price minimum, a floor on the possible prices, which will lead to a market surplus), or no higher than a certain level (a price ceiling or price maximum, a ceiling on the possible prices, which will lead to a market shortage).

How to Make a Supply Schedule WHAT YOU NEED TO START: Information about how many units will be produced at different price levels. STEP 1

WHAT YOU DO Make a list of all the relevant price levels mentioned. If you are given the marginal cost each producer faces, those marginal costs are the relevant price levels.

CHAPTER2

SUPPLYAND DEMAND

25

Example: If it would cost Shawn $4 to make one unit and Sandy $5 to make one unit, and if it would cost S u l a $ 3 to make one unit and $ 5 to make a

second unit, then the relevant prices are $3, $4, and $5. WHY

A supply schedule gives the relationship between price and quantity supplied, so we need to know the list of prices that we have to think about. Suppliers will be willing to produce a unit if the price is at least enough to cover their costs. S o those suppliers are looking for the price to be equal to, or greater than, their costs.

STEP 2 WHAT YOU DO Make a table with two columns. The first column should have P as a column header, and the second should have Q5. Use the prices from Step 1 to fi l l i n the first column, i n order.

Example: Using the relevant prices from Step 1, we can draw the table:

P

Q5

$3

$4

$5 WHY

The supply schedule is designed to show the quantity supplied at any given price. And so, we need a table that can depict both price and Q5.

STEP 3 WHAT YOU DO Fill in the Q5 column by counting the total number of units that will be produced at each price level. Don’t forget to count all units, not just the new ones produced as the price increases. Q5 should always get bigger as P does.

Then, you have a table that can be read in two ways. You can use the table to ask, “at a given price, how many units will be produced?” or to

26

CHAPTER 2

SUPPLY AND DEMAND

ask, “what does the price need to be to get suppliers to produce a given number of units?”

Example: Using Shawn, Sandy, and Sula from Step 1 , S u l a will make 1 unit at P = $ 3 . At P = $4, Sula will still make her unit, and Shawn will add h i s

for 2 total units. At P = $5, Sula and Shawn will still make their units from before. Sandy will add a third, and Sula will make another unit for a total of Q5 2 4. From this table, we know that if we wanted four units to be produced,

we’d have to offer a price of $5. We also know that if the price were only $3, only one unit would be made.

P

WHY

$3

Q5 1

$4

2

$5

4

The supply schedule tracks the total number of units produced at different prices. So, to fill in the table, it’s necessary to count every unit that will be produced at each price level. This includes units that also would have been produced at lower price levels. A higher price won’t make them stop producing! Suppliers like higher prices. The information that the supply schedule can give us is about the relationship between price and quantity supplied. With the supply schedule, if we’re given either price or quantity supplied, we can find out the other one. This can go in either direction. Knowing the price can help us figure out the quantity supplied at that price, and knowing the quantity supplied can help us find out the price required to reach that quantity supplied.

N

CHAPTER2 SUPPLYAND DEMAND

27

H

How to Draw a Supply Curve WHAT YOU NEED TO START: Either a supply schedule (for Method 1, see 2 b to create the supply schedule), a formula for a supply curve (for Method 2), or nothing at all to draw a generic supply curve (for Method 3).

METHOD] WHAT YOU DO Begin with a supply schedule. Draw a graph with P on the y-axis and Q on the x-axis (you can remember which goes where by remember——————————

ing that “P” has a vertical line in it, and so goes by the vertical axis). Draw each of the points on the supply schedule on the graph. Then, connect them by drawing “stairs.” Draw a vertical line up from each point until you hit the next price point, then a horizontal line right to meet the next point. ———————

Example: For the given supply schedule:

P

$3

Qs 1

$4

2

$5

4

a +-—-----—-

we can draw:

Qua ntity

28

CHAPTER 2

WHY

SUPPLY AND DEMAND

A supply schedule gives the same information as a supply curve does. Both give the number of units that will be produced at each price level. And so, to make a supply curve, all we need to do is draw on the proper points. We connect the points by going up and then right because we don’t add any more quantity until we hit a certain price. And so, at every price between $ 3 and $4, for example, this market will only produce 1 unit. As soon as price hits $4, that’s when we add the second unit.

METHOD 2 WHAT YOU DO If you have a formula for a supply curve, you can simply plot the line described by the formula on a graph with P on the y—axis and Q on the x-axis. Since we have P on the y-axis, be sure that the formula has P as a function of Q5 and not the other way around.

Example: If we are given the supply curve Q5 = (1/2)P — 4, we first solve:

Q5 = (1/2)P — 4 Q5 + 4 = (l/2)P

[Add 4 to each side]

2Q5 + 8 = P

[Multiply each side by 2]

Then, we plot the inverse supply curve P = ZQS + 8, which is a straight line with a y-intercept of 8 and a slope of 2. Pricelk Suppw

Quantity WHY

Supply and demand curves are drawn on graphs that have P on the y-axis and Q on the x-axis. This may seem a little odd, since we think

CHAPTER 2

SUPPLY AND DEMAND

29

of Q5 as being the dependent variable in the supply curve, but they thought a little differently when formalizing the model in the 19th century. And we still do it that way, causing headaches for thousands of Principles students the world over. And so, if we are given a supply curve with Q; as a function of P, rather than the other way around, we have to do a little algebra before graphing the line, just like we would any line.

METHOD 3 WHAT YOU DO If you simply need to draw a supply curve and it doesn’t need to match a particular supply schedule or supply curve formula, all you need to do is draw an upward-sloping line on a graph with P on the y-axis and Q on the x-axis.

Example: Price! Supply

Qua ntity

WHY

For many applications, we just need to draw a generic supply curve, and it doesn’t need to match any specific values or formulas. In this case, the only important thing we need to incorporate is that the supply curve slopes upwards.

How to Make a Demand Schedule WHAT YOU NEED TO START: Information about how many units will be consumed at different price levels.

30

CHAPTER 2

SUPPLY AND DEMAND

STEP 1 WHAT YOU DO Make a list of all the relevant price levels mentioned.

If you are given the marginal value each consumer would get for each unit, those marginal values are relevant price levels.

Example: If Andrew values a unit at $6, Angela values a unit at $7, and Anthony values his first unit at $7 and his second unit at $8, then the relevant price levels are $6, $7, and $8. WHY

A demand schedule gives the relationship between price and quantity demanded, s o we need to know the list of prices that we should think

about.

Consumers will be willing to buy a unit if the price is no higher than the value they set on the good. So, those consumers are looking for the price to be equal to, or l e s s than, their values.

STEP 2 WHAT YOU DO Make a table with two columns. The first column should have P as a column header,

and the second should have QD. Use the prices from

Step 1 to fill in the first column.

Example: Using the relevant prices from Step 1, we can draw the table:

P

QD

$6

$7

$8 WHY

The demand schedule is designed to show the quantity demanded at any given price. And so, we need a table that can depict both price and Q0.

STEP 3 WHAT YOU DO Fill in the QD column by counting the total number ofanits that will be purchased at each price level. Don’t forget to count all units, not just

CHAPTER 2

SUPPLY AND DEMAND

31

the new ones produced as the price decreases. QD should always get smaller as P gets bigger. Then, you have a table that can be read in two ways. You can use the table to ask, “at a given price, how many units will people want to buy?” or to ask, “what does the price need to be to get consumers to purchase a given number of units?”

Example: Using Aaron, Angela, and Anthony from Step 1, Anthony will buy 1 unit at P = $8. At P = $7, Anthony will still buy his first unit, and will also buy a second unit. Angela will buy a unit as well, for a total of QD = 3 . At P = $ 6 , the three units from before will still be purchased,

and Aaron will buy a unit as well, for a total of QD = 4. From this table, w e know that if we wanted four units to be purchased,

we’d have to offer a price of $6. We also know that if the price were $8, only one unit would be purchased.

WHY

P

Q1)

$6

4

$7

3

$8

1

The demand schedule tracks the total number of units produced at dif— ferent prices. So, to fill in the table, it’s necessary to count up every unit that will be purchased at each price level. This includes units that also would have been purchased at higher price levels. The information that the demand schedule can give us is about the relationship between price and quantity demanded. With the demand schedule, if we’re given either price or quantity demanded, we can find out the other one. This can go in either direction. Knowing the price can help us figure out the quantity demanded at that price, and knowing the quantity demanded can help us find out the price required to reach that quantity demanded.

32

CHAPTER2 SUPPLYAND DEMAND

How to Draw a Demand Curve WHAT YOU NEED TO START: Either a demand schedule (for Method 1 , see 2 . d to create

the demand schedule), a formula for a demand curve (for Method 2), or nothing at all to draw a generic demand curve (for Method 3).

METHOD] WHAT YOU DO Begin with a demand schedule. Draw a graph with P on the y-axis and Q on the x-axis (you can remember which goes where by remembering that “P” has a vertical line in it, and so goes by the vertical axis). Draw each of the points on the demand schedule on the graph. Then,

connect them by drawing “stairs.” Draw a vertical line down from each point until you hit the next price point, then a horizontal line right to meet the next point.

Example: For the given demand schedule:

P

Q1)

$6

4

$7

3

$8

1

w e can draw:

H —______

Q antity C

I I I I I I I 3

h

H

_——--

Denmnd

CHAPTER2 SUPPLYAND DEMAND

WHY

33

A demand schedule gives the same information as a demand curve. Both give the number of units that will be purchased at each price level. And so, to make a demand curve, all we need to do i s draw the

proper points on.

We connect the points by going down and then right because we don’t add any more quantity until we hit a certain price. And so, at every price between $6 and $7, for example, 3 units will be purchased. We

add the fourth unit as soon as the price hits $6.

M ETH UD 2 WHAT YOU DO If you have a formula for a demand curve, you can simply plot the line described by the formula on a graph with P on the y-axis and Q on the x-axis. Since we have P on the y-axis, be sure that the formula has P as a function of Q5 and not the other way around.

Example: If w e are given the demand curve QD = 8 — (1/2)P,

we first solve:

QD = 8 —(1/2)P ( 1 / 2 ) P + QD = 8

[Add ( l / 2 ) P to each side]

(1/2)P = 8 — QD

[Take QD from each side]

P = 1 6 — 2QD

[Multiply each side by 2]

Then, we plot the inverse demand curve P = 1 6 - 2QD, which is a straight line with a y-intercept of 16 and a slope of —2. Price

16

Demand

Qua ntity

34

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WHY

SUPPLY AND DEMAND

Supply and demand curves are drawn on graphs that have P on the y-axis and Q on the x-axis. This may seem a little odd, since we think of QD as being the dependent variable in the demand curve, but they thought a little differently when formalizing the model in the 19th century. And we still do it that way, causing headaches for thousands

of Principles students the world over. And s o , if we are given a demand curve with QD as a function of P, rather than the other way around, we have to do a little algebra before

graphing the line.

METHOD 3 WHAT YOU DO If you simply need to draw a demand curve and it doesn’t have to match a particular demand schedule or demand curve formula, all you need to do is draw a downward-sloping line on a graph with P on the y-axis and Q on the x-axis.

Example: Price“

Demand

Quantity WHY

For many applications, we just need to draw a generic demand curve, and it doesn’t need to match any specific values or formulas. In this case, the only important thing we need to incorporate is that the demand curve slopes downwards (i.e. it follows the “law of demand”).

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SUPPLY AND DEMAND

35

How to Aggregate Individual Supply andDemand Curves to Get Market Supply andDemand WHAT YOU NEED TO START: Two or more supply or demand schedules (Method 1, see 2.b and 2.d to create the schedules), two or more supply or demand curve equations (Method 2), or two or more graphically drawn supply or demand curves (Method 3).

METHOD] WHAT YOU DO Aggregating supply or demand schedules is a process much like creating the schedules in the first place. List every price level that appears on any of the individual supply/demand schedules, and then add up the total quantity produced/purchased.

Example: Given the individual supply schedules: P

Q5 (Nick)

Q5 (Beth)

$4

1

0

$5

2

1

$6

3

2

we add up the quantities to get the aggregate supply schedule:

WHY

P

Q5 (Aggregate)

$4

1+0=1

$5

2+1=3

$6

3+2=5

An aggregate supply or demand schedule simply adds up the quantities produced/purchased by each individual in the market. Since the individual supply or demand schedules already tell us how many units

36

CHAPTER 2

SUPPLY AND DEMAND

each individual wants to produce/purchase, we simply need to add up the units to get the aggregate supply or demand schedule.

M ETH CID 2 WHAT YOU DO Given two or more supply or demand curves, first solve each of them so that they have Q in terms of P, rather than the other way around. Then, add together the individual Q expressions. If you have many producers or consumers with the same supply/ demand curve, you can simply multiply the individual Q expression by the number of producers/consumers. If desired, you can then solve it back to get P in terms of Q.

Example: Given the inverse demand curves P = 1 2 -— Q01 and P = 4 — (l/2)QDZ, we first solve each for QB, getting Q01 = 12 — P and Q02 = 8 — 2P. Then, we add them together, getting QD=QDl+QD2=12—P+8—2P=20—3P

Or, if we have 100 individual (1') firms each with the inverse supply curve P = 2Q5i — 8, we first solve to get Q5,- = 4 + (1/2)P. Then, we add them all together, getting

Q3 2 100(QS,-) = 100(4 + (l/2)P) = 400 + SOP that we could solve back to get P = (QS/SO) — 8. WHY

An aggregate supply or demand curve simply adds together the quantities that each individual producer/consumer produces/purchases. And so, to add together the curves, we get the amount each individual produces/purchases as a function of price, and then add all those quantities together to get aggregate quantity supplied/demanded as a function of price.

METHOD 3 WHAT YOU DO Given two supply or demand curves on a graph, you can add them together to get an aggregate supply or demand curve by adding horizontally. In other words, for any given price, add together the individual quantities to get the aggregate quantity.

Example: PriceH

WHY

51

52

I I

l I

I I

I l

2

3

A

re ate

553mg

I I I I I I I I I I I I : 5 Quantity

An aggregate supply or demand curve simply adds together the quantities that each individual producer/consumer produces/purchases. And so, to add together the curves, we get the amount each individual

produces/purchases as a function of price; then add all those quantities together to get aggregate quantity supplied/demanded as a function of price. Since quantity is on the x-axis, this means that we are adding the curves horizontally, i.e. along the x-axis.

How to Predict Shifts in Supply and Demand WHAT YOU NEED TO START: A description of some change that has happened to a particular market. If the change has to do with a change in the price of a complement or substitute good, see 3.g.i.

STEP I WHAT YOU DO Determine whether the change is likely to affect supply, demand, or both.

A market change will affect supply if it changes the number of units producers will want to make at a given price.

38

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A market change will affect demand if it changes the number of units consumers will want to purchase at a given price.

Example: When a major film is set somewhere interesting, it often makes people more interested in taking vacations there. In the market for tourism in that area, nothing will change about the expense of providing tourism, so supply will not change. But tourism in that area becomes more desirable, so demand will shift.

WHY

Supply and demand give the relationship between price and the quantity supplied/demanded. If something changes about the quantity supplied/demanded at a given price, supply/demand shifts. Careful! Supply and demand describe the underlying costs and benefits of production, not the market outcome. Some things you might expect to shift them, especially the price of the good, don’t. If the good’s price rises (as it might in the film example above), that will increase Q5, but it will NOT shift supply. The supply curve already describes how Q5 responds to price!

STEP 2 WHAT YOU DO Determine whether each of the shifts you found in Step 1 should shift supply or demand left or right. Supply:

If the price of inputs increases (decreases), supply shifts left

(right). If the quality of production technology increases (decreases), supply shifts right (left). If firms are entering (leaving) the market, supply shifts right (left). If firms expect that the good’s future price will rise (fall), supply will shift left (right). Demand:

If incomes rise (fall), demand shifts right (left) for normal

goods. If tastes change in favor of (against) the good, demand shifts right (left). If consumers are joining (leaving) the market, demand shifts right (left). If consumers expect that the good’s future price will rise (fall), demand will shift right (left). See 2.g.i for the influence of the price of complement and substitute goods.

CHAPTER2 SUPPLYAND DEMAND

39

Example: In the film example in Step 1, tastes shift in favor of the good, so demand shifts right from D1 to D2. PriceH

—->

D1

D2

Qua ntity In another example, if there’s a news story in the paper today that makes everyone think housing prices will fall in a few years, expectations of future prices fall, shifting supply right from S ] to 8 2 as they try to sell their stock before prices fall, and shifting demand left from D ] to D2 as people decide to wait to purchase at lower prices. Price“

——)

51

Q

‘—

52

D2

D1

Ojantity

WHY

If the price of the inputs to production (i.e. the price of wood, if you’re making wooden tables) goes up or if the production technology gets worse (i.e. the government bans efficient table—making saws), it becomes more expensive to make the good, so you want to make less of it (supply shifts left).

40

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If new firms/consumers enter the market, there are more firms/consum-

ers around to make/purchase the good, so more quantity will be made/ purchased at a given price (supply shifts right/demand shifts right). If future prices are expected to rise, producers and consumers act to protect themselves. Producers hold onto their current stock so they can sell at high prices later (supply shifts left), and consumers buy now rather than being stuck with high prices later (demand shifts right). If income rises, people have more money to spend, some of which can go to this good (demand shifts right). There are some goods (“inferior goods”) that work the opposite way; see Chapter 3 for these. If tastes turn against a good, fewer people want to buy it (demand shifts left).

.E.‘.-.9.-.i. How to Predict Shifts in Supply and Demand: Complements and Substitutes WHAT YOU NEED TO START: A market of interest, and a change in the price of another, related good.

STEP 1 WHAT YOU DO For the two goods you’re considering (the good in your market of interest, and the good with the changing price), determine whether they are complements or substitutes in consumption. Goods are complements if having one makes you want more of the other (they “go together”). Goods are substitutes if having one makes you want less of the other (they “substitute for each other”).

Example: Burgers and French fries are complements since people tend to like having them together.

CHAPTER2 SUPPLYAND DEMAND

41

A DVD and a Blu-Ray of the same movie are substitutes since having one gives you less use for the other. WHY

The basic reason why the price of complement and substitute goods will affect demand in the market of interest is this: 1. When considering whether you want to buy something, you have to consider the other goods you could spend your money on instead, as well as the other goods you’ll have to buy to go along with what you bought. 2. When the price of those complementary and substitute goods changes, it affects how you value the good of interest, since the price of the stuff you could buy instead has changed, or the price of the stuff that goes along with it has changed.

STEP 2

WHAT YOU DO Demand shifts for the good of interest are based on whether the change in the price of the complement/substitute good has made the good of interest more or less desirable. If the price of a complement increases, demand for the good of interest shifts left. If the price of a complement decreases, demand shifts right. If the price of a substitute increases, demand for the good of interest

shifts right. If the price of a substitute decreases, demand shifts left.

Example: If the price of French fries increases, the price of the burger + fries meal you wanted has effectively gone up, so you don’t want a burger so much anymore. Demand for burgers shifts left. If the price of DVDs increases, your alternatives to buying the BluRay have gotten worse, since they’ve gotten more expensive. This makes the Blu-Ray a better deal than before, relatively. Demand for Blu-Rays shifts to the right.

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SUPPLY AND DEMAND

Predicting the direction that demand shifts follows from a little intuitive story you can tell yourself: I If the price of a complement increases (decreases), it makes the good of interest less (more) interesting, since the other stuff you need to go with it has gone up (down). This shifts demand left (right).

I If the price of a substitute good increases (decreases), it makes the good of interest more (less) interesting, since the alternative available to you has gotten more expensive (cheaper). This shifts demand right (left).

How to Find Excess Supply (Market Surplus) and Excess Demand (Market Shortage) WHAT YOU NEED TO START: A market price P, a supply curve, and a demand curve. Supply and demand schedules also work, but the following steps will use curves.

STEP 1 WHAT YOU DO Plug the market price P into the supply curve to calculate Q5, and then plug the same market price P into the demand curve to calculate QD.

Example: If the current price i s P = 5 , the inverse demand curve i s P = 1 5 — ZQD,

and the inverse supply curve is P = 2 + 3QS, then we can calculate QD using: P = 15 — 2QD 5:15—2QD

[Plug i n P = 5 ]

ZQD + 5 = 15

[Add 2QD to each side]

ZQD = 1 0

[Take 5 from each side]

QD= 5

[Divide each side by 2]

And we can calculate Q3 similarly:

P = 2 + 3QS

WHY

5=2+3Q5

[Plug i n P = 5 ]

3 = 3Q5

[Take 2 from each side]

1 = Q5

[Divide each side by 3]

A market surplus or market shortage is based on the difference between quantity supplied and quantity demanded; surplus and shortage measure how misaligned the two are at a given price! To figure that out, we first need to calculate Q5 and Q0. We can get these by plugging the current price into supply and demand, since the supply and demand curves give us the quantity supplied/demanded at each price.

STEP 2 WHAT YOU DO If Q5 > QD, there are producers out there running around trying to find buyers, but not enough people are willing to buy at the price. This is excess supply, also known as a market surplus. P rI' c e “

I

S

Surp us '3'

____________

: I I I

Q0

I

: I I I

Q;

D

:

Quantity

If QD > Q5, there are consumers running around trying to buy a unit of the good, but they can’t find anyone willing to sell to them at the price. This is excess demand, also known as a market shortage.

Pricelk

p' _ _ _ _ _ _ _ _ _ _ _ _ _

l———| Shortage Il D I

Q5

I Q0

_ Qua ntity

The size of the market surplus, if there is a surplus, is Q5 — QD. Similarly, the size of the shortage, if there is a shortage, is QD — Q5.

Example: Using the price, supply, and demand from Step 1, Q0 > Q5, we have a market shortage. The size of that shortage is QD — Q5 = 5 — 1 = 4 units. WHY

Market surplus and market shortage refer to, respectively, quantity supplied being too high or too low relative to quantity demanded. The size of the surplus or shortage is the distance between these two numbers—how many additional units produced/purchased are needed to cover the gap. It’s important to remember that in economics we use terms like “surplus” and “shortage” a little differently than they are used in everyday life. In particular, in economics, surplus and shortage are pricedependent. If there’s a shortage because not enough people want to produce the good, that’s mainly a problem of the price being too low.

How to Calculate Market

Equilibrium WHAT YOU NEED TO START: A supply curve and a demand curve. Supply and demand schedules also work (look for the single price at which Q5 = Q0), but the following steps will use curves.

STEP 1 WHAT YOU DO Rewrite the supply and demand curves but replace P with P * , and replace both Q5 and QD with Q*.

Example: Given the inverse supply curve P = 3 + 2Q5 and the inverse demand curve P = 18 - QD, we can write: P*=3+2Q*

P * = 18 - Q * WHY

Market equilibrium occurs at the price for which Q5 = QD. Since Q5 and Q0 are equal, we can represent both with one variable, the equilibrium market quantity Q*. And since only the equilibrium market price P * will get us Q*, we can use P * in place of P.

STEP 2 WHAT YOU DO Now you have two equations and two unknown variables ( P * and Q * ) . You can solve this using standard algebra. The common way to do this in the context of supply and demand is to: 1. Start with P * = P * and then substitute supply into the left side, and demand into the right. 2. Solve for Q*. 3. Plug Q * into supply or demand (it doesn’t matter which) to get P*. (If you are not working with inverse supply and demand, i.e. if you have Q5 and QB in terms of P rather than the other way around, you can start with Q * = Q*, solve for P * , and plug back in to get Q*.)

Example: Given the inverse supply and demand curves from Step 1, we can: P* = P*

[Set P * = P * ]

3 + 2 Q * = 18 — Q *

[Plug in supply, demand]

2 Q * = 15 — Q *

[Take 3 from each side]

46

SUPPLY AND DEMAND

CHAPTER 2

3 Q * = 15

[Add Q * to each side]

Q* = 5

[Divide both sides by 3]

P * = 18 — 5 = 13

[Plug Q * into demand]

And so, the equilibrium price and quantity are P * = 13 and Q * = 5. WHY

We’re looking for the price and quantity where supply and demand intersect. In other words, the price at which quantity supplied equals quantity demanded. Once we’ve substituted in Q * to ensure that we’re looking for the spot where the quantities are equal, all we should do is solve the two equations together, like a standard algebra problem, to find the quantity at which that is true.

How to GraphMarket Equilibrium Price“

P* - - - - - - - - -

D

Qfiantity POINTS TO FOLLOW

I The y-axis should be labeled with Price and the x-axis should be labeled with Quantity. I The demand curve should slope downwards and be labeled with D. See 2.e for more on how to draw a demand curve.

I The supply curve should slope upwards and be labeled with S. See 2.c for more on how to draw a supply curve.

CHAPTER 2

SUPPLY AND DEMAND

47

I The market equilibrium occurs where the supply and demand curves intersect (Blue Dot).

I The market equilibrium price occurs at the price where the supply and demand curves intersect. Label this with P * unless you’ve calculated an exact market price (as in 2.i), i n which case label it with the number you found.

I The market equilibrium quantity occurs at the quantity where the supply and demand curves intersect. Label this with Q * unless you’ve calculated an exact mar— ket quantity (as in 2.i), in which case label it with the number you found.

How to Find the New

Equilibrium When Supply and Demand Curves Shift Elsi. How to Find the New Equilibrium When One Curve Shifts WHAT YOU NEED TO START: A set of supply and demand curves, and information about which one of them shifts, and in what direction. (See 2 g and 2.g.i if you have a description of a market change but aren’t sure which curves should be moving, or in what direction.)

STEP 1 WHAT YOU DO Use the table below to figure out how the direction of equilibrium price and quantity will change: Shift

P * will. . .

Q * will . . .

Demand shifts left

Decrease

Decrease

Demand shifts right

Increase

Increase

Supply shifts left

Increase

Decrease

Supply shifts right

Decrease

Increase

48

CHAPTER2 SUPPLYAND DEMAND

To get the exact value of the new P * and Q*, use the steps in 2.i with the new, post-shift supply and demand curves, if you have them.

Example: If the supply for TVs shifts right, the equilibrium price for TVs will decrease, and the equilibrium quantity will increase, relative to what it was before the shift. WHY

Finding the new equilibrium price and quantity just requires us to redo the steps from 2.i for finding the market equilibrium, but using the new, shifted curve along with the old, non—shifted curve ( s o if demand

shifted, for example, using new demand with old supply). Doing this requires knowing the formula for the new supply/demand curve. However, even without knowing the formula, w e can make

a predic-

tion about the direction of the change, since supply slopes up and demand slopes down.

STEP 2 WHAT YOU DO Graph the change by drawing the new, shifted curve. The new market equilibrium is where the new, post-shift supply and demand curves intersect.

Example: If demand shifts right from D ] to D2, we can graph the effect on the market as follows: Price“

P2*

if

_______

P1* " " " "

Dl (11*

02*

D2

Quantity

CHAPTER 2

WHY

SUPPLY AND DEMAND

49

The process of finding an equilibrium point after the market shifts is the same as finding it before the shift—we look for where supply and demand cross. We’re just doing it with shifted supply and demand curves. And so, if we draw some movement i n one of the curves, the new

intersection is the new equilibrium.

akzil How to Find the New Equilibrium When Both Curves Shift at Once WHAT YOU NEED TO START: A set of supply and demand curves, and information on the directions that each of them shifts.

STEP l WHAT YOU DO For each curve, determine using the table below what the effect of that curve ’s shift alone will have on the equilibrium price and quantity. Shift

P * will . . .

Q* will...

Demand shifts left

Decrease

Decrease

Demand shifts right

Increase

Increase

Supply shifts left

Increase

Decrease

Supply shifts right

Decrease

Increase

Example: If the supply for TVs shifts right, that will lead the equilibrium price to decrease, and the equilibrium quantity to increase. And if demand for TVs shifts right at the same time, that will lead the equilibrium price to increase, and the equilibrium quantity to increase. WHY

When two curves shift at once, the total effect on the market equilibrium price and quantity is a mixture of the effect of each individual curve shift. So, we need to start out by finding what effects those individual shifts have.

50

CHAPTER2 SUPPLYAND DEMAND

STEP 2 WHAT YOU DO Combine the effects of the individual shifts. If both effects agree on the effect on price or quantity, then we know what will happen. If the effects disagree, it’s not clear which one will “win out.” In total, we can see the effects of two changes using the following table: Demand

Supply

P * will . . .

Q * will . . .

?

Decrease

Left

Left

Left

Right

Decrease

?

Right

Left

Increase

?

Right

Right

?

Increase

Where “?” indicates that knowing the direction of the shifts alone is not enough to figure out the effect (since the effect of the demand shift and the supply shift oppose each other in that case).

Example: If the supply and demand for TVs both shift right at the same time, both individual changes suggest that the equilibrium quantity will increase, and so equilibrium quantity will increase. But the supply shift suggests equilibrium price will decrease, and the demand shift suggests equilibrium price will increase; and so we won’t know what happens to price without more information about what’s going on. WHY

By combining the individual shifts and their effects on price and quantity, you can determine what will happen after both shifts occur. Unfortunately, we will only be able to pin down the effect on price or quantity, not on both, if all we know is the direction of the supply and demand shifts. If we wanted to fill in those question marks, we could do it in one of two ways: (1) We could use actual formulas for the pre- and post-shift supply and demand curves and calculate the exact equilibria as in 2.i.

CHAPTER 2

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51

(2) Or, we could, roughly, say that whichever side had the “bigger” shift “wins.” So, in the example, if the supply shift was small but the demand shift was big, then equilibrium price probably went up. But, this second method is less exact and requires some subjective judgment of the size of the shifts. You can see it at work if you graph both shifts. Whether price goes up or down in this example depends on how big you draw each shift.

52

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PRACTICE Follow-the-Steps Questions To solve, follow directions from one or more of the sections above. 1. Anne likes to make patio chairs out of wood in her spare time. Her marginal cost of making the first chair i s $ 1 0 , the second chair i s $ 3 0 , and the third chair i s $40.

Draw Anne’s supply schedule for patio chairs, and draw her supply curve.

2. Patch has a demand curve for books that can be described by the function QD = 1.6 — 2P. Draw Patch’s demand schedule at the prices P = 1 , 2 , 3 , and 4 .

Then, draw Patch’s demand curve using the function given (not the schedule). 3.

Kate values her first ice cream cone at $6, her second at $4, and her third at $ 2 .

Mike values his first cone at $4 and his second at $2. Penelope values her first three cones at $6 and her fourth at $0. Draw their aggregate demand schedule at the prices P = $2, $4, and $ 6 . Then, draw a generic example of their demand

curves being aggregated (like in 2.f Method 3). 4. Draw the supply and demand curves for soap on the same set of axes. Label the curves to show that: at a price of P = 4, you will see Q5 = 8 and Q0 = 2, and at a price o f P = 1, you will see Q5 = 2 and QD = 10. 5 . For each of the following scenarios, determine whether supply or demand (or both, or neither) will shift as a result, and what the direction of each shift will be:

a. (Market for cars) Sheet metal gets more expensive. b. (Market for tourism in New Zealand) A major movie is filmed in New Zealand, sparking worldwide interest in vacationing there. c. (Market for books) The printing press is invented, and more people learn how to read. d . (Market for imitation vanilla) People prefer real vanilla to imitation but it’s more expensive. Then, wages go up in every industry but vanilla. e. (Market for pencils) A surprising new law bans pens. People have to use pencils now, and pen factories retrofit to make pencils instead.

CHAPTER2

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53

6. For each of the following, determine whether supply or demand (or both, or neither) will shift, what direction each shift will be, and whether equilibrium quantity and price will rise, fall, stay the same, or change in an unknown direction: a. (Market for used GameBoxes) The new G B 2 video game console is released, making the GameBox obsolete. Everyone wants to get rid of their GameBox and buy a GB2 instead.

b. (Market for leather handbags) A documentary is released detailing abuse in the leather industry, making people feel bad about buying leather. c. (Market for margarine) Due to a cow-based disease, butter supply shifted left, and butter price shot way up. d. (Market for gasoline) The summer months arrive, when people like to go on road trips. Anne (supply given by Question 1) sells her patio chairs to Case, who values his first chair at $60, the second at $ 3 0 , and the third at $ 1 0 . Calculate surplus or

shortage if the price is P = $35, and then find equilibrium price and quantity. Graph the following supply and demand curves, being careful to find and label the y-intercepts, and the x-intercept for demand. Calculate and label the market equilibrium price and quantity. Inverse supply is P = 3 + Q5 and inverse demand is P = 18 — 2QD. Find the market equilibrium price and quantity for each of the following sets of

9999‘?”

supply and demand curves: P=20—QD,P=2+2QS QD=120—2P, Q S = 4 O + 2 P P=77—2QD,P=11+Q5 P=70— 1.5QD,P=20+.5QS P = 1 0 + 2Q?, P = 70 — Q? (Which one is supply and which one is demand?)

10. In the market for olives, inverse demand is P = 30 — 2QD. How much will equilibrium price change if supply shifts from P = 2 + 2Q5 to P = 6 + 2Q5?

54

CHAPTER 2

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Concept Questions A. If someone tried to sell you a dollar for any price above a dollar, you would certainly turn the person down. But at a price of exactly $1, you’d be willing to buy any number of them, since they’re each worth exactly $1 to you. With this in mind, draw your individual demand curve for dollars.

Your Aunt Debby has come to you offering to pay you if you make large signs to advertise her business. The materials for each sign cost $20, and you must spend your own time painting them. Make your own supply schedule, thinking about the value of your own time and the price you’d need to be paid for each sign to make Q5 = l , 2, and 3 signs. Then, graph your supply curve. In the market for milk, the equilibrium price is $3 per gallon. Then, to help the country’s dairy farmers, the government implements a price restriction, requiring the price to be at least $4. How will this shift the supply curve for milk? The market for dish detergent is a competitive market, and the equilibrium price is P * = $2. One day, the CEO of Sally’s Soap gets an idea. She gathers together the thousands of soap producers and gets them to all agree to raise prices to P = $3. a. When the price goes up to P = 3, will there be a shortage, a surplus, or neither? b. Will the price stay at P = 3 long term? Why or why not? The suppliers are better off at P = 3, so why would they not stay there? Consider the market for computers. Over the past fifty years, the equilibrium quantity of computers has gone way up, and the equilibrium price has gone way down. a. For supply and demand, list one thing each that might have shifted them. What direction was each shift? b. Price went way down. Is it likely that the supply shift or the demand shift was “bigger”?

In the market for packets of cookies, demand is P = 45 — 3QD and supply is P = 5 + Q5. Then, a mass hysteria descends upon the nation and everyone simply must have cookies now, shifting demand to P = 90 — 3QD. The change happens

CHAPTER2

SUPPLYAND DEMAND

55

so fast that prices haven’t even updated yet, and it’s still at the pre-hysteria price. How large is the shortage of cookie packets? There’s a new product that’s about to be invented and sold in a competitive mar— ket: the Flooble. A little research reveals that inverse demand for the Flooble is P = 610 — QD. That same research reveals that the marginal cost to produce a Flooble is 10 at a quantity of O, and each Flooble beyond that has a marginal cost of 1 higher than the one before. Calculate the equilibrium price and quantity of Floobles. You’ve probably solved for enough supply and demand equilibria to have a bit of intuition for it at this point. So, design your own set of supply and demand curves such that the equilibrium price and quantity are both positive integers (i.e. n o decimals).

Demand for land in Manhattan in square miles is given by Q0 = 65 — P, where price is measured in billions of dollars. However, there’s a fixed amount of land in Manhattan. In particular, it’s about 23 square miles. There can’t be any more, no matter how much money you offer. Calculate the equilibrium price and quantity of a square mile of Manhattan land. Graph supply and demand, and label the equilibrium. Then, draw a rightward shift in demand. What happens to the equilibrium? Explain why this is different than what we normally get from rightward shifts in demand.

Glossary and Concepts Elasticity is a measure of how quickly and in what direction quantity supplied or quantity demanded changes in response to some change in the market. This could be the response of quantity to a price change (price elasticity of supply for quantity supplied or price elasticity of demand for quantity demanded); the response of quantity demanded to an income change (income elasticity); or something else entirely. Mathematically, elasticity is the percentage change in quantity divided by the percentage change in price (or income, or something else entirely). Supply or demand is inelastic if quantity is changing more slowly, in percentage terms, than price. Supply or demand is elastic if quantity is changing more quickly, in percentage terms, than price. Mathematically, the response is inelastic if the elasticity is between —1and 1 (since the percentage change in quantity is then smaller in absolute value than the percentage change in price); and it is elastic if the elasticity is more negative than —1, or more positive than 1 (since the percentage change in quantity is then bigger in absolute value than the percentage change in price). If elasticity is exactly —1or 1, we call that unit elastic. If elasticity is O, we call that perfectly inelastic. If elasticity is infinity or negative infinity, we call that perfectly elastic.

Point elasticity is a number that represents the elasticity given the current quantity being produced/purchased. Even on the same supply or demand curve, point elasticity will be different depending on the quantity.

Relative elasticity describes the elasticity of the supply or demand curve overall. For price elasticity, the steeper a supply or demand curve is, the more relatively inelastic it is (since quantity doesn’t respond too much to price changes). And the shallower a

57

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supply or demand curve is, the mOre relatively elastic it is (since quantity responds heavily to price changes). A normal good is a good for which demand has a positive income elasticity. That is, the more money people make, the more they want to buy of the good. Most goods are normal goods. An inferior good is a good for which demand has a negative income elasticity. That is, the more money people make, the less they want to buy of the good. Inferior goods tend to be things that people only buy because they can’t afford better versions. For example, as a cash-strapped college student you may eat a lot of instant ramen. But when you graduate and your income goes up, you probably will shift to eating better food. And s o , instant ramen i s an inferior good.

A luxury good is a good with a positive and large (above 1) income elasticity. In other words, your consumption of these goods goes up faster than your income, as your income rises. These are things you largely buy only when you have a lot of money, like fancy watches.

How to Calculate Percentage Change Elasticity requires us to calculate percentage changes. There are two primary approaches to calculating percentage changes that you will see in economics textbooks. The first, which I will call the “Standard method,” you’re probably used to seeing elsewhere. The second, called the “Midpoint method,” is a little harder to cal— culate, but it has the benefit that it still works if the number you’re changing from is 0. It also gives the same answer whether you’re calculating a percentage increase from X to Y, or a percentage decrease from Y to X. Your textbook or professor likely uses only one of these methods. Check which one you want, and see the following two sections for how to calculate percentage changes using that method.

CHAPTERB ELASTICITY

3.b.i

59

How to Calculate Percentage Change Using the Standard Method

WHAT YOU NEED TO START: A number you are changing from and a number you are changing to. We will refer to these as QOLD and QNEW,although the same steps work for price and other non-quantity variables.

STEP 1 WHAT YOU DO Subtract the old from the new to get the change in the variable:

Change = QNEW — QOLD

Example: If QOLD = 1 0

WHY

and

QNEW=16,then

Change

2 16 — 10 = 6.

We are attempting to calculate a percentage change. We can start by figuring out how much changed in the first place.

STEP 2 WHAT YOU DO Divide the change by the old value to get the percentage change: % Chan ge = Chan ge = QNEW _ QOLD

OLD

QOLD

Example: If QOLD = 1 0 and QNEW= 16, then Change = 1 6 — 1 0 = 6 and % Change 2 i = .6 = 60% 10 WHY

Asking “what is the percentage change?” basically asks “how much has it changed relative to where it started?” And so, we calculate the percentage change as how much it changed (QNEw — QOLD) relative to where it started (QOLD).

Note that if Q got smaller; change.

you should get a negative percentage

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.3..-!3.;ii. How to Calculate Percentage Change Using the Midpoint Method WHAT YOU NEED TO START: A number you are changing from and a number you are changing to. We will refer to these as QOLD and QNEW,although the same steps work for price and other non-quantity variables. STEP 1 WHAT YOU DO Subtract the old from the new to get the change in the variable:

Change = QNEW — QOLD

Example: If QOLD = 1 0 and QNEW= 16, then Change = 1 6 — 1 0 = 6 . WHY

We are attempting to calculate a percentage change. We can start by figuring out how much we changed in the first place.

STEP 2 WHAT YOU DO Calculate the midpoint by taking the average of the new and old points:

Midpoint = QNEW ;' Q0“) Example: If QOLD = 10 and QNEW:16, then Midpoint = (16 + 10)/2 = 26/2 = 13. WHY

We want to get the value that is exactly halfway between QNEW and QOLD. You can get this by averaging the numbers, i.e. by adding them both up and dividing by 2.

STEP 3

WHAT YOU DO Divide the change by the midpoint to get the percentage change: % Chan ge = Chan ge 2

Midpomt

QNEW _ QOLD

(QNEW + QOLD) / 2

% Change = 2 QNEW — QOLD NEW + QOLD

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61

Example: If QOLD = 10 and QNEW = 16, then Change = 6, Midpoint = 13, and % Change = WHY

Change _ 6 . ——— z .462 = 46.2% Midpoint 13

Asking “what is the percentage change?” basically asks “how much has it changed relative to its original value?” And so, we calculate the percentage change as how much it changed (QNEW — QOLD) relative to its original value, which we adjust to be the

midpoint for the reasons outlined in 3 b . Note that if Q got smaller, you should get a negative percentage change.

How to Calculate Elasticity 3.c.i

How to Calculate Price Elasticity Using a New Point and an Old Point

WHAT YOU NEED TO START: An old price and quantity, Pow and

quantity,

P NEW and

and QOLD, and a new price

QNEW'

STEP 1 WHAT YOU DO Calculate the percentage change in price ( % Change Price) and the percentage change in quantity ( % Change Quantity) using 3.b.i or 3.b.ii. WHY

The calculation of elasticity is based on relative percentage changes. So, we need to start out by finding the percentage change of price and the percentage change of quantity.

STEP 2 WHAT YOU DO Calculate the elasticity by dividing the percentage change in quantity by the percentage change in price: Elasticity =

% Change Quantity % Change Price

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Note that if you’re working with supply, you should get a positive price elasticity, since quantity and price move in the same direction. But if you’re working with demand, you should get a negative price elasticity. Some textbooks will have you report price elasticity of demand as positive anyway, so check with your textbook.

Example: If you are calculating price elasticity of demand, and quantity increased 60% when price decreased 20%, then Elasticity = £2 = —3 Noting that it’s a negative .2 since it was a 20% decrease. And, if the textbook wants you to report the absolute value of demand elasticity, we take the absolute value here and get Elasticity = 3. WHY

Price elasticity is how fast quantity changes relative to how fast price changes. And so, all we have to do to calculate price elasticity is divide the percentage change in quantity by the percentage change in price. The bigger the result is in absolute value, the more responsive quantity is, i.e. the more elastic!

Think of it like a pair of pants. If the waistband of the pants is elastic, then when you pull on them (change the price), the waist will stretch (quantity will change a lot). But if the waistband is made of something other than elastic, the waist won’t stretch (quantity won’t change much). STEP 3 WHAT YOU DO Determine whether the response is inelastic, elastic, or unit elastic by comparing it to —1and 1.

If the elasticity is between —I and I, then it is inelastic. If the elasticity is equal to 0, we call that perfectly inelastic. If the elasticity is exactly equal to —I o r I, we call that unit elastic. If the elasticity is outside of the range —1 t0 1, then it is elastic. The quantity response is big relative to the price change.

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63

Example: In step 2 we calculated an elasticity of —3 (or 3 if we took the absolute value). This i s outside the range of —1 to 1 , and so this i s an elastic

response.

WHY

The reason we compare the elasticity to the numbers —1. and 1 is because these mark the point where it tips over from “the percentage change in quantity is smaller than the percentage change in price” to

the point where it’s bigger. For example, if we had a 100% increase in price, and quantity supplied increased by 90%, then the quantity change didn’t quite match the price change. Elasticity is .9/1 = .9, which is between —1and 1, and thus is inelastic. But if the quantity supplied increased by 110% instead, then the quantity changed more than price did. Elasticity is 1.1/1 = 1.1, which i s outside of —1 to 1 , and thus i s elastic.

.3..-!-:;ii. How to Calculate Price Elasticity Using a Supply Curve or a Demand Curve WHAT YOU NEED TO START: A supply or demand curve that is linear (i.e. it is of the form P=a+bQ, P=a—bQ, Q=a+bP, orQ=a—bP), andapricePand/oraquantity Q at which to calculate the elasticity. STEP 1 WHAT YOU DO If you only have P or Q, use the supply or demand curve given to calculate the other one, so that you have both.

Example: If we are using the demand curve P = 16 — 2QD and are calculating elasticity at QD = 2, we calculate P by plugging in: P=16—2(2)=12

Or, if we were using the supply curve Q5 = 1 + BF and are calculating elasticity at P = 3, we calculate Q5 by plugging in:

QS=1+3(3)=10

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ELASTICITY

The calculation of elasticity is based on relative percentage changes. And those percentage changes need to know what the original point is that you’re changing from! So, we need to know both the original P and the original Q.

STEP 2 WHAT YOU DO Now that we have the original point, we calculate the slope change in price and quantity using the slope of the supply or demand curve. If you have a supply or demand curve that has Q in terms of P, then the slope change is the coefficient on P (the —b in Q0 = a — bP, using a demand curve).

If you have an inverse supply or demand curve that has P in terms of Q, then the slope change is one divided by the coefficient on Q ( l / b using [9 from P = a + bQS, using a supply curve). For a demand curve, the slope change should be negative. However, some textbooks want you to report a positive demand elasticity anyway. Check which one your textbook wants.

Example: If we were using the demand curve P = 1 6 — ZQD, the slope change would be 1/(—2) = —.5.

Or, if we were using the supply curve Q5 = 1 + 3P, the slope change would be 3. WHY

Elasticity is based on percentage changes. Conveniently, the slope of the supply or demand curve tells us the rate of change immediately, without even needing to have both a before point and an after point.

Writing out elasticity using the standard percentage change method: Elasticity =

% Change Quantity % Change Price

_ (QNEW — cow) / Q0“) (PNEW—POLD

)

/P0LD

(QNEW — QOLD) * (PNEW

_

POLD

)

Pow QOLD

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65

The first term here is just a “rise over run” description of the slope of the supply or demand curve, when we have Q in terms of P. If we’re working with P in terms of Q, we just take the inverse of the slope (l/b), which works out the same. STEP 3

WHAT YOU DO Calculate elasticity using the formula: P Elasticity = slope change * 5

Example: If we use the demand curve P = 1 6 — 2QD and calculate elasticity at QD = 2, then P = 12, slope change 2 1/(—2), and 1 Elasttc1ty

= 7

12 * —2— = — 3

(which then becomes 3 when we take the absolute value). Or, if we were using the supply curve Q5 = 1 + 3P and were calculating elasticity at P = 3, then Q5 = 1.0, slope change 2 3, and Elasticity = 3 * 1 = —9— = . 10 10 WHY

A s noted in the explanation for Step 2, Elasticity =

(QNEW ‘ QOLD) * POLD (PNEW “130140) Qou)

and

(QNEW — QOLD) (PNEW — Pow)

= slope change

In total, we have

Elasticity = slope change *

POLD

OLD All we have to do is plug in!

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STEP '4 WHAT YOU DO Determine whether the response is inelastic, elastic, or unit elastic by comparing it to 1 and —1. If the elasticity is between —1 and I , then it is inelastic. If the elasticity is equal to 0, we call that perfectly inelastic. If the elasticity is exactly equal to —1 or I , we call that unit elastic. If the elasticity is outside of the range —] to 1, then it is elastic. The quantity response is big relative to the price change.

Example: In step 3 we calculated a demand elasticity of —3.This is outside the range of —1 to 1, and so this is an elastic response. We also calculated a supply elasticity of .9. This is between —1 and 1, and so this is an inelastic response. WHY

The reason we compare the elasticity to the numbers —1 and 1 is because these mark the point where it tips over from “the percentage change in quantity is smaller than the percentage change in price” to the point where it’s bigger. For example, if we had a 100% increase in price, and quantity supplied increased by 90%, then the quantity change wouldn’t quite match the price change. Elasticity would be .9/1 = .9, which is between —1 and 1, and thus is inelastic. But if the quantity supplied increased by 110% instead, then the quantity would change more than price. Elasticity would be 1.1/1 = 1 . 1 , which i s outside of —1 to 1 , and thus i s elastic.

3.l:.iii

How to Calculate Income or

Cross-Price Elasticity Using a New Point and an Old Point WHAT YOU NEED TO START: An old quantity QOLD and a new quantity QNEW.You also need an old and a new something else, whether that something else is consumer income, [OLD and INEW,to calculate income elasticity; an old and new price for some

CHAPTER 3

other good,

P’ow

ELASTICITY

67

and P’NEW to calculate cross-price elasticity (the response of one

good’s quantity to the changing price of a different substitute or complement good); or something else! These steps work to calculate the quantity response to a change in anything! The steps will proceed using old and new income, [OLD and INEW, to calculate income elasticity, but all you need to do to get some other kind of elasticity

is to swap out income for something else.

STEP 1 WHAT YOU DO Calculate the percentage change in income ( % Change Income) and the percentage change in quantity ( % Change Quantity) using 3.b.i or 3.b.ii. WHY

The calculation of elasticity is based on relative percentage changes. S o , we need to start out by finding the percentage change of income and the percentage change of quantity.

STEP 2 WHAT YOU DO Calculate the elasticity by dividing the percentage change in quantity by the percentage change in price: Elasticity =

% Change Quantity % Change Income

Example: If quantity demanded increased 3 % when income increased 10%, then Elastici

ty

.03 = — = .3 .10

Note that, unlike with demand elasticity, if we get a negative number here we leave it negative. We don’t take the absolute value. WHY

Income elasticity is how fast quantity changes relative to how fast income changes. And so, all we must do to calculate price elasticity is divide the percentage change in quantity by the percentage change in income.

The bigger the result is in absolute value, the more responsive quantity is, i.e. a higher income elasticity!

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STEP 3 WHAT YOU DO Characterize the response. For income elasticity: I Negative income elasticity indicates an inferior good. I Positive income elasticity indicates a normal good. I Income elasticity above 1 indicates a luxury good. For cross-price elasticity: I Negative cross—price elasticity indicates that the goods are complements. I Positive cross-price elasticity indicates that the goods are substitutes.

Example: In Step 2, we calculated an income elasticity of .3. This is positive but below 1, so this is a normal good and not a luxury good. WHY

For income elasticity, a negative value indicates an inferior good because that means that the more money you make, the more you choose to buy things other than this good. And a value above 1 indicates luxury; since you buy the good basically only when you have lots of money with which to afford it. For cross-price elasticity, a negative value indicates complements since an increase in the other price reduces consumption of that good, and so you want less of the complement good. And a positive value indicates substitutes since an increase in the other price reduces consumption of that other good, so you buy this good instead.

How to Draw Price Elasticity STEP 1 WHAT YOU DO For supply and/or demand, determine whether the response of quantity to price should be relatively elastic or relatively inelastic.

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69

Example: Because it would take people a long time to change their driving hab— its, the demand for gasoline is relatively inelastic. But since there are stores of gas ready to be released if prices go up, the supply of gasoline is relatively elastic. WHY

When drawing supply and/or demand, elasticity will show up largely through relative elasticity. Relative elasticity is a general description of how elastic the response is overall, rather than how elastic it is at a single point.

STEP 2 WHAT YOU DO Draw supply and/or demand. The more relatively inelastic the curve is, the steeper its slope should be. The more relatively elastic the curve is, the shallower its slope should be.

Example: In the market for gasoline, demand is relatively inelastic, and supply is relatively elastic, and so we draw demand with a steep slope and supply with a shallow slope. Price“

Quan tity

WHY

A steeper slope indicates that the response is more inelastic because very large changes in price (vertical movement) are required to get a relatively small change in quantity (horizontal movement).

Similarly, a shallow slope indicates a more elastic response because very small changes in price (vertical movement) can get you a pretty big change in quantity (horizontal movement).

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STEP 3 WHAT YOU DO If supply or demand is perfectly inelastic, draw it as a perfectly vertical line straight up and down. Something is only perfectly inelastic if the quantity is always the same, and doesn’t respond to price at all. If supply or demand is perfectly elastic, draw it as a perfectly horizontal line. Supply is only perfectly elastic if an infinite number will be produced at a certain price, but if the price drops at all, zero will be produced. Demand is only perfectly elastic if an infinite number will be demanded at a certain price, but if the price rises at all, zero will be demanded.

Example: The demand for dollar bills is perfectly elastic. People will buy any number of them at a price of $1, but they will buy zero of them if you try to sell at a higher price. So, we can draw demand for dollar bills as: Price“

Quantity

The supply for the authentic Mona Lisa is perfectly inelastic. Only one of them exists, and more can’t be produced no matter how high the price goes. So, we can draw the supply for Mona Lisas as: Price“

5

1

QJantity

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WHY

ELASTICITY

71

Perfect inelasticity and perfect elasticity are just taking the concept of elasticity and inelasticity to their logical extreme.

Perfect

inelasticity is when the quantity doesn’t respond to price at all. Perfect inelasticity is rare for demand curves, since at high enough prices, nobody has the money to buy the good, and so quantity demanded necessarily must drop. But there are certainly supply curves that are perfectly inelastic. Anything that only exists in a completely fixed quantity, like the Mona Lisa, is generally thought to have a perfectly inelastic supply curve. Perfect elasticity is when supply or demand is based on a very specific price point.

How to Use Elasticity When the Supply or Demand Shift WHAT YOU NEED TO START: A shift in supply or demand (see 2 g and 2.g.i to predict the direction of the shift), and whether the curve not shifting is relatively elastic or relatively inelastic.

STEP 1 WHAT YOU DO Whichever curve is shifting, use 2.k to determine whether equilibrium price goes up or down, and whether equilibrium quantity goes up or down.

Example: In the market for mattresses, if supply shifts to the right because of the price of springs dropping, then we would expect equilibrium price to drop and equilibrium quantity to increase. WHY

When a curve shifts, we are interested in how equilibrium price and quantity change. Although elasticity will affect the relative size of those changes, the old steps from Chapter 2 will still hold for the direction of the changes!

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STEP 2 WHAT YOU DO If the curve that didn’t shift is relatively elastic, then the quantity change from Step 1 is going to be larger than it would have been if the curve that didn’t shift were relatively inelastic; and the price change from Step 1 is going to be smaller than it would have been if the curve that didn’t shift were relatively inelastic.

Example: If we shift the supply curve for mattresses to the right, we get a bigger quantity change and a smaller price change by drawing demand as relatively elastic Price‘

P1 P2

01 02

Qu:a ntity

than we do if we instead draw demand as relatively inelastic, keeping the supply shift and the original equilibrium the same: Price!

P1 P2 I I I I I

. I 01 02

_ Quantity

CHAPTERB ELASTICITY

WHY

73

When supply or demand shift, basically, “something’s gotta give.” We know that the equilibrium price and quantity are going to change. Also, we know that the change will occur by moving along the curve that didn’t shift. However, if the curve that’s not shifting is inelastic, it doesn’t like to change the quantity it produces/purchases very much, and so the thing that “gives” is going to have to be the price. Thus, the price will change a lot relative to the quantity. And if the curve that’s not shifting is elastic, then it wants to keep the price more or less the same, and instead the thing that “gives” is the quantity. So, you get a larger quantity response relative to the price change.

How to Determine if Something is Elastic, Inelastic, or Unit Elastic WHAT YOU NEED TO START: A point elasticity (see 3 . c ) .

STEP 1 WHAT YOU DO If the elasticity is exactly —1 or 1, then it is unit elastic. WHY

By definition, something is unit elastic if its elasticity is exactly 1 or —1(1 being “a unit”). This is the elasticity at which quantity and price are changing at the exact same percentage rate.

STEP 2 WHAT YOU DO If the elasticity is between —1 and 1, then it is inelastic. WHY

Elasticity is the percentage change in price divided by the percentage change in quantity. If this is between —1 and 1, that means that the quan— tity change was smaller (in absolute value) than the price change. So,

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quantity changed more slowly than price. This describes an inelastic response. STEP 3 WHAT YOU DO If the elasticity is lower than —1 or higher than 1, then it is elastic. Elasticity is the percentage change in price divided by the percentage change in quantity. If this is outside of the range —1 to 1, that means that the quantity change was larger (in absolute value) than the price change. So, quantity changed faster than price. This describes an elastic response. Elastic

‘

”

Inelastic

|

I

-1

0

I

l

Elastic

Y

WHY

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ELASTICITY 75

PRACTICE Follow-the-Steps Questions To solve, follow directions 1.

Choose

from one or more of the sections above.

either the standard method

or the midpoint method. Then, calculate the

percentage change from A to B in each of the following cases:

woe???

FromQA=4to QB=6 From PA = 10 to PB = 20 From QA = 9 to Q 3 : 15 From PA = 15 to PB = 9 From QA = 102 to QB = 100 FromPA=4toPB=1

2. The price of a photo frame just jumped from P = 4 to P = 6. Calculate the elastic— ity of demand for each of the following people: {DP-9.0"?”

Niall went from QD = 6 to Q0 = 4.

John went from QD = 12 to QD = 6. Daron went from QD = 40 to Q0 = 30. Helen went from QD = 3 to Q0 = 1. Jean went from QQ = 5 to QD = 3.

3. The market for rubber bands was in equilibrium at P * = 12 and Q * = 36. Then, the government put a price restriction into place, pushing the price up to P = 18. As a result, quantity supplied became Q5 = 4 8 and quantity demanded became QD = 12.

a. Calculate the elasticity of supply. Is supply elastic or inelastic? b. Calculate the elasticity of demand. Is demand elastic or inelastic? 4. Calculate the price elasticity of demand for each of these demand curves at QD = 4 and again at QD = 8: a. P = 40 — 2QD b. P = 24 — QD c. P = 10 — QD

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d. P = 25 — 3QD e. P=120—10QD f. Is there a pattern about whether demand is more elastic at QD = 4 or QD = 8 ? 5. Frank’s consumption of coffee just increased from 1 cup per day to 3. You then learn the cause for this change, which is one of the reasons listed in a—e below. For a—b, calculate Frank’s income elasticity of demand for coffee and determine whether coffee i s an inferior, normal, or luxury good; and for c—e, calculate

Frank’s cross-price elasticity of demand between coffee and whichever other good is mentioned, and determine if they’re complements or substitutes. a. Income goes from $16k to $20k annually.

Income goes from $6k to $24k annually. The price of tea went from $4 per cup to $6.

The price of soda went from $2 per cup to $4. The price of a jug of cream went from $5 to $1.

The graph below depicts five different demand curves all going through the same point. Label them D1 through D5, with D1 as the perfectly elastic curve, and getting more inelastic from there. Price“

Qua ntity

You work in the glass bauble industry, where the equilibrium price and quantity are currently P * = 1 and Q * = 1 0 . You know that, soon, due to a glass short-

age, supply will be shifting to the left. Your market research division scrambles to figure out whether demand is relatively elastic or relatively inelastic. Would you expect a bigger price increase if you found out that demand was elastic or inelastic?

Concept Questions A. Provide an intuitive explanation for why goods with very close substitutes have a more elastic demand.

When w e are using a good’s elasticity to label it in some way (elastic, inelastic, luxury, normal, inferior), we are often comparing the elasticity to the number 1 (or —1). What’s so special about 1? Why is it important whether an elasticity is greater or less than 1 (or —I) specifically? You observe the market for bananas at two different times. At time X , the

demand curve is P = 24 — QD. At time Y, the demand curve is P = 44 — 2QD. At both times, the equilibrium price and quantity are P * = 4 and Q * = 20. The thing that changed demand between the two times is the new appearance of dananas on the market, an exotic substitute for bananas. Keeping in mind elasticity in the two periods, which of X and Y was before dananas, and which was after? As time goes on, it becomes easier to substitute between different goods. With this in mind, draw three demand curves with three different slopes. Label them

“most short term” to “most long term.” The government is considering imposing a tax on some good. They will charge a tax of 1 per unit sold. For now, let’s just assume that this tax will raise the price that consumers pay for the good by exactly 1. They are trying to figure out whether to levy this tax on the market for soda or the market for cigarettes. In both markets, equilibrium price is P * = 5 and equilibrium quantity is Q * = 1000, but demand is a lot more elastic for soda than it is for cigarettes. a. Should the government tax soda or cigarettes if its goal is to raise as much money as possible? b. Should the government tax soda or cigarettes if its goal is to lower consumption as much as possible? (It might do this if it thinks people shouldn’t be consuming these things.) Using the inverse supply curve P = 2 + 3QS: a. Calculate price elasticity of supply at P = 8. Show work. b. Solve the inverse supply curve to get the supply curve, with Q5 in terms of P. c. Calculate price elasticity of supply at P = 8 using the curve you got in b. You should get the same answer as in part a. Show work.

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G. At the current market equilibrium, in which inverse supply is P = 4QS — 1, the elasticity of supply is 3/4. Calculate the market equilibrium price and quantity. In the market for farm-grown food, improvements in technology have led the supply curve to shift to the right. This has lowered the equilibrium price of food by 10%.

a. Will this shift lead the total amount spent on food (equilibrium price times quantity) to rise or fall if demand is elastic? b. Will this shift lead the total amount spent on food (equilibrium price times quantity) to rise or fall if demand is inelastic? [H1NT2 If demand is elastic/inelastic, then the percentage change in price is smaller/larger than the percentage change in quantity] Cross-price elasticity can be represented on a graph of a demand curve by show— ing a shift in the demand curve in response to a price change for the other good.

The price of hand soap is $4 per bottle. The price of hand sanitizer is $2 per bottle, and at this price 28 sanitizer units are demanded. The cross—price elasticity describing how the quantity demanded of hand sanitizer responds to the price of hand soap is .5. a. Does this cross-price elasticity indicate substitutes or complements? b. Draw the demand curve for hand sanitizer and label the price and Q0 at P = 2. c. Draw how the demand curve shifts when the price of hand soap rises by 50%. Label the new quantity. [HINT2 Use the formula in 3.c.iii Step 2, and plug in the elasticity, the percentage price change, and the old quantity. Then, solve for the new quantity]

Glossary and Concepts Marginal

value is the additional value that someone gets as a result of getting one more unit of the good. So, for example, if you would get $15 worth of enjoyment out of having 8 apples, and you’d get $18 worth of enjoyment out of having 9 apples, then the ninth apple has a marginal value of $18 — $15 = $3. Marginal cost is the additional cost that someone must pay as a result of producing one more unit of the good. For example, if the total cost (including opportunity cost)

of making 4 tables is $100, and the total cost of making 5 tables is $130, then the fifth table has a marginal cost of $130 — $100 = $30. Willingness to pay (or reservation price for consumers) is the most that a consumer would be willing to pay for something. This is related to its marginal value. If the marginal value of the ninth apple you buy is equivalent to $3, then you’d be willing to buy that apple for any price up to $3. So, $ 3 is the most you’d be willing to pay. If someone tried to charge you a higher price, you’d say no, and hold out until the price dropped below this reservation price of $3. Willingness to accept (or reservation price for producers) is the least that a producer would be willing to accept to make a unit of the good. This is related to marginal cost. If the marginal cost of the fifth table you build is $30, then you’d be willing to sell that table for any price of $30 or above. So, $30 is the least you’d be willing to accept. If someone offered you a lower price, you’d say no and hold out until the

price rose above this reservation price of $30. Consumer surplus is the difference between a consumer’s willingness to pay/ marginal value and what the person actually had to pay, the price of the good. So, if

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you value your ninth apple at $3, but you only had to pay $ 1 for the apple, then you

got a consumer surplus of $3 — $1 = $2 for that purchase. You can add up the consumer surplus from each individual purchase to get consumer surplus for the whole market. On a supply and demand graph, the whole market’s consumer surplus is the area below the demand curve and above the price. Producer surplus is the difference between a producer’s willingness to accept/ marginal cost and what the person actually got paid, the price of the good. So, if the marginal cost of the fifth table i s $ 3 0 , but it sold for $ 7 0 , then the producer got a pro-

ducer surplus of $70 — $30 = $40 for making the table. You can add up the producer surplus from each individual sale to get producer surplus for the whole market. On a supply and demand graph, the whole market’s producer surplus is the area above the supply curve and below the price.

Total surplus (or economic surplus) is the sum of consumer and producer surplus. A market is efficient if total surplus is as large as possible. Deadweight loss is the difference between the amount of total surplus there actually is, and the amount of total surplus would be if the market were efficient (i.e. if total surplus were as large as possible). In other words, deadweight loss is the amount of surplus that the market is not producing, but that it could produce.

Marginal Cost 3-9.1 How to Calculate Marginal Cost WHAT YOU NEED TO START: The total cost of producing different quantities of a good (for example, “it costs $500 to produce 3 units of the good, or $600 to produce 4 units”).

STEP 1 WHAT YOU DO Make a table. In one column, list each quantity of the good. In the other, list the total cost of producing that many units.

Example: If i t costs B i g Boxes $0 to make n o boxes, $ 5 to make one box, $ 1 1 to

make 2 boxes, and $ 1 9 to make 3 boxes, then we draw the table:

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Quantity

Total Cost

0

$0

1

$5

2

$11

3

$19

81

The marginal cost is the additional total cost that you get by increasing the number of units by one. So, in order to calculate the marginal cost, we start out by figuring the total cost required to produce each number of units.

STEP 2 WHAT YOU DO Calculate marginal cost by taking total cost and subtracting the total cost on the row above. Note that the marginal cost will be blank for the top row, since there’s no row above to marginally improve on.

Example: Using the table from Step 1, we calculate the marginal cost of the first box as $5 — $0 = $5, the second box as $11 — $5 = $6, and the third box

as $19 — $1.1= $8.

WHY

Quantity

Total Cost

Marginal Cost

0

$0

1

$5

$5 - $0 = $5

2

$11

$11 — $5 = $6

3

$19

$19—$11=$8

The idea of “marginal” cost is that it asks how much additional cost is added when you add one more unit (i.e., how much cost is added at the margin). And so, to calculate marginal cost, we just need to ask “how much cost was added by this unit?”

So, for example, if 2 units cost $1 1 to make, and 3 units costs $19, then that third unit added $ 8 i n costs.

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3.9.1! How to Derive a Supply Curve from Marginal Cost WHAT YOU NEED TO START: A table of quantities and their associated marginal costs. Use 4.b.i to create this table if you have quantities and total costs. STEP 1

WHAT YOU DO Write out a table associating each quantity with a marginal cost.

Example: Marginal Cost

If B1g Boxes margmal cost for the first box 18 $5, the marginal cost for the second box is $6, and the marginal

Quantity 0 1

$5

cost for the third box is $8.

2

$6

We would draw the table shown on the right.

3

$8

STEP 2 WHAT YOU DO Relabel the columns of the table. Replace “Quantity” with “Quantity Supplied,” and replace “Marginal Cost” with “Price.” The result is a supply schedule. See 2.c Method 1 on how to turn a supply schedule into a supply curve, or 2.f if you have multiple producers whose supply schedules you need to combine to get market supply.

Example: Starting with the table in Step 1, w e relabel to get: Quantity Supplied

Price

0

1

$5

2

$6

3

$8

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A producer is only willing to sell something if it sells for at least as much as it cost to make it. So, if the price is $6, for example, the producer will sell every unit that costs $6 or less to make. Since the first and second unit both cost $6 or less, Big Boxes will be willing to make both of them. And so Big Boxes’ supply schedule has its quantity supplied increasing from 1 to 2 at a price of exactly $6. At a price of $5.99, the second unit isn’t worth it.

Ella-iii. How to Find Marginal Cost on a Supply Curve WHAT YOU NEED TO START: A supply schedule (Method 1), a graph of a supply curve (Method 2), or an equation for a supply curve (Method 3).

METHOD] WHAT YOU DO Using a supply schedule, the marginal cost of a particular unit of the good is the price associated with that quantity.

Example: In the supply schedule below, the marginal cost of the second unit of the good is $6, and the marginal cost of the third unit of the good is $8. Quantity Supplied

Price

0

WHY

1

$5

2

$6

3

$8

A producer is willing to sell a unit of the good if the price received from selling it is at least as much as the cost of producing it.

So, someone will be willing to sell that unit as soon as the price rises high enough to hit their marginal cost. This means that the price on a

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supply curve for a quantity X is the same as the marginal cost of the Xth unit produced. METHOD 2 WHAT YOU DO Using a supply curve, find the price associated with a given quantity. The marginal cost of that unit of the good is that price.

Example: In the supply curve below, the marginal cost of the second unit of the good is $6, and the marginal cost of the third unit of the good is $8. Price“

Quantity WHY

A producer is willing to sell a unit of the good if the price received from selling it is at least as much as the cost of producing it. S o , someone will be willing to sell that unit as soon as the price rises

high enough to hit their marginal cost. This means that the price on a supply curve for a quantity X is the same as the marginal cost of the Xth unit produced. METHOD 3 WHAT YOU DO Using an equation for a supply curve, plug in a given quantity for Q3 and calculate P. The resulting P is the marginal cost for the quantity you plugged in.

Example: Using the inverse supply curve P = 4 + Q5, we can calculate the marginal cost for the second unit of the good by plugging in Q5 = 2.

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85

P = 4 + (2) = 6 And so, the marginal cost of the second unit is 6. WHY

A producer is willing to sell a unit of the good if the price received from selling it is at least as much as the cost of producing it. So, someone will be willing to sell that unit as soon as the price rises high enough to hit their marginal cost. This means that the price on a supply curve for a quantity X is the same as the marginal cost of the Xth unit produced.

3.19:1! How to Calculate and Graph Producer Surplus WHAT YOU NEED TO START: You need a price. To use Method 1, you also need a table of quantities and their associated marginal costs. Use 4.b.i to create this table if you have quantities and total costs, or use 4.b.ii backwards to create this table if you have a supply schedule. To use Method 2, you need a linear supply curve (supply is linear ifithas thefoe=a+bPorP=a+bQ).

METHOD] WHAT YOU DO Using a table of quantities and marginal costs, calculate the producer surplus created by each unit by subtracting marginal cost from the price. Then, get total producer surplus by adding up the producer surplus created by each unit. Producer surplus can then be graphed by first graphing the associated supply curve. (See 4.b.ii to get a supply schedule, and 3.c Method 1. for graphing a supply curve from a supply schedule.) Then, draw a horizontal line at the price, and shade in the area underneath price and above supply.

Example: Using the table of quantities and marginal values that follow and a price of $ 6 . 5 , we know that the first two units will be produced, since

the $6.5 exceeds the marginal cost of producing those units. The producer surplus from the first unit is then $6.5 — $5 = $1.5, and from the

second unit it is $6.5 — $6 = $ 5 .

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Quantity _ Supplied

_

Producer Surplus

1

$5

$1..5

2

$6

$5

3

$8

Price

O

Total producer surplus is then $1.5 + $ 5 = $2. This producer surplus can then be graphed by creating the associated supply curve, and shading the area below price and above supply.

Producer

Surplus I I I I 1

WHY

¥ r

2

3

Quan tity

Producer surplus is the difference between what you’d be willing to make something for and what you actually did get paid. So, if you can make something for $ 5 but you got paid $6.5 for it, you just got

$6.5 — $5 = $1.5 in producer surplus. We can calculate this value for each unit of the good produced, and

add them up to get the total producer surplus.

Remember to only include the units actually produced. At a price of $ 6 . 5 , the third u n i t i s not produced here, so it’s not included i n the

producer surplus calculation.

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87

METHOD 2 WHAT YOU DO First, plug Q5 = 0 into the supply curve. The resulting P is the y intercept of the inverse supply curve. Second, plug price into supply to get the produced quantity Q;. The producer surplus is then: PS = ( P — y intercept) * QE / 2

Example: Using the inverse supply curve P = 4 + QD, we can calculate the producer surplus at a price of P = 7 by first plugging Q5 = 0 to get the y intercept:

P=4+(O)=4 Then, we get the produced quantity by plugging in P = 7: P

=

4

+

Q5

7 = 4 + Q;

[Plug in]

3 = Q5

[Take 4]

Consumer surplus is then: PS=(7—4)*3/2

=3*3/2=4.5

This producer surplus can then be graphed by creating the associated supply curve, and shading the area below price and above supply. PriceM Supply

Producer

Surplus

Price

QJantity

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Producer is surplus the difference between what you’d be willing to make something for and what you actually did get paid. So, if you can make something for $ 5 but you got paid $6.5 for it, you just got

$6.5 — $5 = $1.5 in producer surplus. The amount you’d be willing to make something for is represented by the price on the supply curve. And so, producer surplus is the entire area underneath price and above the supply curve. With a straight-line supply curve, this area is a triangle (as shown above). The area for a triangle is height * base / 2. The height of the triangle is the distance between the price (7 here) and the y-intercept of the supply curve (4). So, we get (price — y intercept) in the equation. The base of the triangle is the horizontal line going from the y-axis (an

x-value of O) to the quantity produced, Q; So, we get (Q; — O), or just Q; in the equation as well. Don’t forget to divide by 2!

Marginal Value Ll.l:.i

How to Calculate Marginal Value

WHAT YOU NEED TO START: The value that a consumer places on having different quantities of a good (for example, “Mark puts a value of 10 on having two oranges, and puts

a value of 12 on having three oranges”).

STEP 1 WHAT YOU DO Make a table. In one column, list each quantity of the good. In the other, list the total value placed on having that many units. The total value is sometimes expressed in terms of dollars.

Example: If Mark puts a value of $0 on having no oranges, $7 on having an orange, $10 on having two oranges, and $12 on having three oranges, we would write the table:

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Quantity

Total Value

0

$0

1

$7

2

$1.0

3

$12

89

The marginal value is the additional total value that you get by increasing the number of units by one. So, in order to calculate the marginal value, we start by figuring out the total value placed on each number of units.

STEP 2 WHAT YOU DO Calculate marginal value by taking total value and subtracting the total value on the row above. Note that the marginal value will be blank for the top row, since there’s no row above to marginally improve on.

Example: Using the table from Step 1, we calculate the marginal value of the

first orange as $7 — $0 = $7, the second orange as $10 — $7 = $3, and the third orange as $12 — $10 = $2.

WHY

Quantity

Total Value

Marginal Value

0

$0

1

$7

$7 — $0 = $7

2

$10

$10 — $7 = $3

3

$12

$12—$10=$2

The idea of “marginal” value is that it asks how much additional value is added when you add one more unit (i.e. how much value is added at the margin). And so, to calculate marginal value, we just need to ask, “how much value was added by this unit?”

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So, for example, if two units bring us $7 in value, and three units bring u s $ 1 0 in value, then that third unit added $ 3 value for u s , making u s

$ 3 richer.

flail How to Derive a Demand Curve

from Marginal Value WHAT YOU NEED TO START: A table of quantities and their associated marginal values,

expressed in terms of dollars. Use 4.c.i to create this table if you have quantities and total values.

STEP 1 WHAT YOU DO Write out a table associating each quantity with a marginal value.

Example: If Mark’s marginal value for the first orange is $7, the marginal value for the second orange is $3, and the marginal value for the third orange is $2, we would draw the table as follows: Quantity

Marginal Value

0

1

$7

2

$3

3

$2

STEP 2 WHAT YOU DO Relabel the columns of the table. Replace “Quantity” with “Quantity Demanded,” and replace “Marginal Value” with “Price.”

The result is a demand schedule. See 2.e Method 1 on how to turn a demand schedule into a demand curve, or 2.f if you have multiple consumers whose demand schedules you need to combine to get market demand.

Example: Starting with the table in Step 1, we relabel to get: Quantity Demanded

Price

0

WHY

1

$7

2

$3

3

$2

A consumer is only willing to buy something if it brings them at least as much value as they had to pay for it. So, if the price is $3, for example, consumers will buy every unit that they value at $3 or more. Since the first and second unit both bring at least $3 of marginal (additional) value, Mark will be willing to buy both of them. And so, Mark’s demand schedule has his quantity demanded increasing from 1 to 2 at a price of exactly $3. At a price of $3.01, the second unit isn’t worth it.

3.2.!!! How to Find Marginal Value on a Demand Curve WHAT YOU NEED TO START: A demand schedule (Method 1), a graph of a demand curve

(Method 2), or an equation for a demand curve (Method 3).

METHUDl WHAT YOU DO Using a demand schedule, the marginal value of a particular unit of the good is the price associated with that quantity.

Example: In the demand schedule that follows, the marginal value of the second unit of the good is $7.5, and the marginal value of the third unit of the good is $5.

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Quantity Demanded

Price

0

WHY

1

$10

2

$7.5

3

$5

A consumer is willing to buy a unit of the good if the marginal value they receive from purchasing it is at least as much as the price they must pay.

So, someone will be willing to buy that unit as soon as the price drops low enough to hit their marginal value. This means that the price on a demand curve for a quantity X is the same as the marginal value of the Xth unit purchased. METHOD 2 WHAT YOU DO Using a demand curve, find the price associated with a given quantity. The marginal value of that unit of the good is that price.

Example: In the demand curve below, the marginal value of the second unit of the good is $7.5, and the marginal value of the third unit of the good is $5. Price“

10 7.5

5

Demand

Quantity WHY

A consumer is willing to buy a unit of the good if the marginal value they receive from purchasing it is at least as much as the price they must pay.

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93

So, someone will be willing to buy that unit as soon as the price drops low enough to hit their marginal value. This means that the price on a demand curve for a quantity X is the same as the marginal value of the Xth unit purchased. M ETH U D 3

WHAT YOU DO Using an equation for a demand curve, plug in a given quantity for Q0 and calculate P. The resulting P is the marginal value for the quantity you plugged in.

Example: Using the inverse demand curve P = 1 2 . 5 — 2 . 5 QD, we can calculate

the marginal value for the second unit of the good by plugging in QD=23

P = 1 2 . 5 — 2.5(2) = 12.5 — 5 = 7.5 And so, the marginal value of the second unit is 7.5. WHY

A consumer is willing to buy a unit of the good if the marginal value they receive from purchasing it is at least as much as the price they must pay. So, someone will be willing to buy that unit as soon as the price drops low enough to hit their marginal value. This means that the price on a demand curve for a quantity X is the same as the marginal value of the Xth unit purchased.

H:.C.-.i.V. How to Calculate and Graph Consumer Surplus WHAT YOU NEED TO START: You need a price. To use Method 1., you also need a table

of quantities and their associated marginal values, expressed in terms of dollars. Use 4.c.i to create this table if you have quantities and total values, or use 4.c.ii backwards to create this table if you have a demand schedule. To use Method 2 , you need a linear

demand curve (demand is linear if it has the form Q = a — bP or P = a — bQ).

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METHOD] WHAT YOU DO Using a table of quantities and marginal values, calculate the consumer surplus created by each unit by subtracting price from the marginal value. Then, get total consumer surplus by adding up the consumer surplus created by each unit. Consumer surplus can then be graphed by first graphing the associated demand curve (see 4.c.ii to get a demand schedule, and 2.e Method 1 for graphing a demand curve from a demand schedule). Then, draw a horizontal line at the price, and shade in the area underneath demand and above the price.

Example: Using the table of quantities and marginal values below and a price of $2.5,

we know that the first two units will be purchased, since the

marginal value for those units exceeds $2.5. The consumer surplus from the first unit is then $7 — $2.5 = $4.5, and from the second unit it

is $3 — $2.5 = $.5. Qua ntit y

Ma rgin al Value

Con sum er Surplus

O

1

$7

$4.5

2

$3

$5

3

$2

Total consumer surplus is then $4.5 + $ 5 = $5. This consumer surplus can then be graphed by creating the associated demand curve, and shading the area below demand and above price.

Consumer

Surplus Price I I I

WHY

| | |

I

I

1

2

l I I I

¥ 7

3 Quantity

Consumer surplus is the difference between what you’d be willing to pay and what you actually did pay. So, if you value something at $7 but only had to pay $2.5 for it, you just got a consumer surplus of

$7 — $2.5 = $4.5. We can calculate this value for each unit of the good purchased, and add them up to get the total consumer surplus.

Remember to only include the units actually purchased. At a price of $2.5, the third unit is not purchased here, so it’s not included in the consumer surplus calculation.

METHOD 2 WHAT YOU DO First, plug Q0 2 0 into the demand curve. The resulting P is the y intercept of the inverse demand curve. Second, plug price into demand to get the purchased Q3. The consumer surplus is then:

CS = (y intercept — P) * Q*D / 2 Example: Using the inverse demand curve P = 25 — SQD, we can calculate the consumer surplus at a price of P = 5 by first plugging in Q0 = O to get the y intercept: P=25—5(0)=25

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Then, we get the purchased quantity by plugging in P = 5: P = 25 — 5QD

5 = 25 — 5QD

[Plug in]

5QD = 20

[Add 5QD and take 5]

QD = 4

[Divide by 5]

Consumer surplus is then CS=(25—5)*4/2

=20*4/2=40

This consumer surplus can then be graphed by creating the associated demand curve, and shading the area below demand and above price.

Price

Demand

QJantity WHY

Consumer surplus is the difference between what you’d be willing to pay and what you actually did pay. So, if you value something at $7 but only had to pay $5 for it, you just got a consumer surplus of

$7 — $5 = $2. In a demand curve, the amount you’re willing to pay is represented by the price on the demand curve. And so, consumer surplus is the entire area underneath demand and above the price. With a straight-line demand curve, this area i s a triangle (as shown at

left). The area for a triangle is height * base / 2. The height of the triangle is the distance between the price (5 here) and the y-intercept of the demand curve (25). So, we get (y intercept — price) in the equation. The base of the triangle is the horizontal line going from the y-axis (an

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97

x-value of O) to the quantity purchased, Q23. So, we get (Q23 — O), or just 0

Q23, in the equation as well. Don’t forget to divide by 2!

How to Graph Producer Surplus and Consumer Surplus Change When Price Changes PRODUCER SURPLUS WHAT YOU DO Comparing producer surplus at a lower price and a higher price can be graphed, in both cases, by shading in producer surplus as the area below each price and above supply. Producer surplus will be larger at the higher price for two reasons: (1) It brings new producers into the market, and they earn producer surplus (gold region), and (2) producers already in the market get paid more for their products (red region). Additional PS at n h Price

Supply High Price Low Price

Quantity WHY

In a supply curve, the amount you’d be willing to make something for is represented by the price on the supply curve. And so, producer surplus, which is the difference between what you got paid and what you would have been willing to take, is the entire area underneath price and above the supply curve.

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When the price increases, the region between price and supply will be larger. Part of this is because the price increases on the units that would have been sold anyway, increasing producer surplus for those units. The other part is that the higher price makes it worthwhile to produce more units, and so producer surplus is generated for those

sales as well. When price decreases, producer surplus gets smaller for these same reasons, i n reverse.

CONSUMER SURPLUS WHAT YOU DO A comparison of consumer surplus at a lower price and a higher price can be graphed by, in both cases, shading in consumer surplus as the area below demand and above price. Consumer surplus will be larger at the lower price for two reasons: (1) It brings new consumers into the market, and they get consumer surplus from their purchases (gold region); and (2) consumers already

in the market get a better deal (red region).

,

A A,

Low Price

Additional CS at Low Price

Quantity WHY

In a demand curve, the amount you’d be willing to pay for something is represented by the price on the demand curve. And so, consumer surplus, which is the difference between what you would be willing to pay and what you did pay, is the entire area underneath demand and above the price. When the price decreases, the region between demand and price will be larger. Part of this is because the price decreases on the units that

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99

would have been bought anyway, increasing consumer surplus for those units. The other part is that the lower price makes it worthwhile to produce more units, and so consumer surplus is generated for those sales as well. When price increases, consumer sUrplus gets smaller for these same reasons, in reverse.

How to Determine the Optimal or Efficient Level of an Activity WHAT YOU NEED TO START: Some measure of the marginal value/marginal benefit and marginal cost of an activity. That activity may be just about anything, including producing a good. Note that the price in a demand curve is a measure of marginal value, and the price in a supply curve is a measure of marginal cost. STEP 1 WHAT YOU DO Find the amount of the activity for which marginal value equals marginal cost.

Example: In the market for pens, the price in the supply curve for pens, P = 2 + 3QS, represents the marginal costs of production; and the price in the demand curve for pens, P = 1.8 — QD, represents the marginal value of consumption. And s o , we solve

MC = M V 2 + 3 Q = 18 — Q

[Substitute in]

4Q = 16

[Add Q and take 2]

Q = 4

[Divide by 4]

For another example, if a slice of pizza costs $3, then the marginal cost of a slice of pizza to you is $3. If you place a marginal value of $10 on your first slice of pizza, $ 5 on your second slice, $ 3 on your third slice, and $1 on your fourth, then marginal cost equals marginal value for the third slice of pizza ( Q = 3 ) .

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The concept of efficiency and optimal choice has to do with marginal costs and marginal values. Specifically, we know that we can’t get any better off than we already are if MC = M V. How do we know that? Imagine that MC > M V. If that’s true, then the last unit you added cost more than it got you. So, you shouldn’t get that unit in the first place! How about if M V > M C ? In that case, the next unit you could add would bring more value than it costs. So, you should add another unit instead of staying how you are. And so, as long as MC ISN’T equal to M V, you could be improving things. Once MC = M V, that’s as good as it gets. This is what we sometimes call the “Golden Rule” of economics.

STEP 2 WHAT YOU DO If the marginal costs and marginal values in Step 1 refer to the costs and values faced by an individual person or firm, we say that the quantity we got in Step 1 is the optimal quantity that maximizes that individual’s well-being or profit. If the marginal costs and marginal values in Step 1 refer to all the costs and values faced

by society, then we say that the quantity we got in

Step 1 is the efificient quantity that maximizes the value that this activity can produce for the economy.

Example: In the pens example in Step 1, the supply and demand curves represent all the costs and benefits to society for producing pens. So, Q = 4 is the efficient quantity that maximizes the benefits that the pen market can bring to society.

In the pizza example in Step 1, we are concerned only with your costs and benefits. S o we know that Q = 3 is the amount of pizza that makes you best off (your optimal amount). If the costs and benefits of pizza

you considered also happen to be the only costs and benefits of pizza relevant to anyone, then this optimal quantity will also be efi‘icient. WHY

For the reasons outlined in Step 1, setting MC = M V will select the optimal quantity, which will maximize the benefits relative to the costs.

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101

When those benefits and costs refer to all the benefits and costs borne by society, we call an optimal quantity the “efficient” quantity. This is the quantity that maximizes the benefits relative to the costs for society. While not all efficient outcomes are desirable (for example, sometimes the efficient outcome is highly unequal), all the most desirable outcomes are efficient. If you have an inefficient outcome, you could make everyone better off by making it more efficient.

Deadweight Loss Hi! How to Calculate Deadweight Loss WHAT YOU NEED TO START: Some measure of the marginal value/marginal benefit and marginal cost of an activity. That activity may be just about anything, including producing a good. Note that the price in a demand curve is a measure of marginal value, and the price in a supply curve is a measure of marginal cost. STEP 1 WHAT YOU DO Find the efficient amount of that activity (see 4e) and call that Q*.

Find the amount of the activity that is actually being done, and call that QA. If the quantities differ because of a government policy, you can find QA using one of the sections in 4.g. The outcome i s inefficient, and there will be some deadweight loss, if Q*

>

QA

01' i f Q *


QA or QA > Q*.

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PRACTICE Follow-the-Steps Questions To solve, follow directions from one or more of the sections

above.

1. Susan makes pizzas in a small cart that she pushes around town. But she runs out of space in that cart pretty quickly, so her costs ramp up fast. Her total cost for making zero pizzas is $0, one pizza is $10, two pizzas is $25, and three pizzas is $45. Calculate her marginal costs and draw her supply curve. 2. Dean likes to attend rock shows and also likes to spend time at home watching TV. He receives $0 i n total value from 0 rock shows, $ 1 0 0 from one rock show, $ 1 7 5 from two rock shows, and $ 1 8 5 from three. Calculate his marginal values

and draw his demand curve.

3. Consider Susan from Question 1.. The going sale price for a pizza is $17. a. Draw Susan’s supply curve with the producer surplus shaded in b. Calculate her producer surplus.

4. Using the set of supply and demand curves below, draw a marginal cost and marginal value table at the quantities of 6, 7, and 8. Price“

14 - - - - - - - - - - - \1 -—-t--—

m

————

___-_|-___

11 —---

D

3

(10a ntity

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107

In the market for razors, the demand curve is given by P = 44 — 2QD. If the going price of razors is 20, then calculate the consumer surplus in the market for razors. Rudy is one consumer in this market. He only buys one razor and places a marginal value of 22 on it. Calculate Rudy’s consumer surplus. In the market for water bottles, market demand i s P = 90 — 3QD. Two of the consumers i n this market are Leslie, who values a water bottle at 3 0 , and Steve,

who values a water bottle at 15. The price of water bottles is at first 20, and then drops to 10. Graph consumer surplus before and after the change, and draw lines on the graph that represent the consumer surplus gained by Leslie and by Steve. A pair of sunglasses will typically cost Krista $100, but she has two coupons (which must be used on different pairs): one for $60 off and another for $20 off. The first pair she buys will bring her $200 of value, the second will bring her

$150, the third $100, and the fourth $50. a. Calculate the efficient number of sunglasses that Krista should purchase. b. If, for some reason, Krista were forced to purchase exactly one pair of sunglasses, what would the deadweight loss be? In the market for boxes of cereal, a tax has been levied. This means that the

consumers will pay the above—equilibrium price of P 1 and will buy QT units, and producers will receive P2 and will sell QT units. QT is less than the efficient quantity, and P1 > P2. Graph this market and shade in and label consumer surplus, producer surplus, and deadweight loss. In the cereal market described i n Question 8 , inverse demand i s given by

P = 30 — 2QD and inverse supply is given by P = Q5. If QT = 8, then calculate P1, P 2 , and deadweight loss. 10. In the market for apples, inverse demand is P = 80 — 3QD and inverse supply is P = 20 + Q5. However, due to a quota on the production of apples, the actual number of apples produced is 20. Graph this market, labeling all relevant values, and shade deadweight loss.

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Concept Questions A. In the market for health care, the price P is set by outside forces rather than being negotiated between consumers and producers. Consumers as a whole have a shared marginal value curve M V, which is a function of Q. Producers have a shared marginal cost curve MC, which is a function of Q. a . For some given P, what should consumers do to maximize consumer surplus? b. For some given P, what should producers do to maximize producer surplus? c. What would it mean for the market for health care to be efficient? d . How could those outside forces set P to make the market efficient? In the market for wallets, which is competitive and made up of many thousands of wallet makers, the inverse supply curve is P = 5 + 2Q5. Graph this supply curve. Then, consider Ari, Barry,

and Carrie. Each makes only one wallet. It costs Ari

$ 1 3 to make her wallet; Barry’s costs are $ 2 1 , and Carrie’s

costs are $ 3 3 . Label

the three points on the supply curve that represent Ari, Barry, and Carrie. Give an intuitive explanation of what deadweight loss is. Your explanation should probably refer to some sort of surplus as well as the “efficient quantity” and the “actual quantity.” A well-known economic puzzle is the “water and diamonds paradox.” Water, vital to life, is cheap. But diamonds, mostly useless, are expensive. Consider a marginal value function for water of M V = 120 — QW, and assume that the consumption of water is QW = 110 units, with a marginal value function for diamonds of M V = 40 — 2QD, and assume that the consumption of diamonds is QD = 3 units. Explain how this resolves the paradox.

Consider the demand curve on the right. Calculate the total value (not the marginal value!) produced by this good at the quantities of Q = 1,

Q=3,andQ=5.

Price“ 21

18

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1

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109

F. You are considering how many hours per day to spend at work. Every hour you spend at work, you get paid a wage of $60. However, this is also an hour you must spend away from your family. Your marginal value of the first hour you spent with your family every day (i.e. what you lose if you change from 23 hours of work per day to 24) is $240. The marginal value of the second hour you spend with your family (what you lose if you change from 22 hours of work to 23) is $230, the marginal value of the third hour you spend with your family is $220, and so on. a. Describe what the marginal cost and marginal benefit of working are. b. Calculate how many hours you should work. c. Explain why we can think of a marginal value (what you get from spending time with your family) as a marginal cost (cost of working). You will want to use the term “opportunity cost.” G . Deadweight loss typically ends up taking the shape of a triangle. But in which of the following cases would it take the shape of a rectangle?

a. M V slopes up and MC slopes down. b. MC and M V are both constant (flat lines), but at a certain quantity, you don’t want any more and M V becomes zero. c. M V slopes down and MC is constant. d. A tax is levied on a good as a lump sum rather than on a per-unit basis. e. It never will, this is impossible.

Glossary and Concepts A market is efficient if total surplus is as large as possible. Deadweight loss is the difference between the amount of total surplus there actually is, and the amount of total surplus would be if the market were efficient (i.e. if total surplus were as large as possible). In other words, deadweight loss is the amount of surplus that the market is not producing but that it could produce. Price controls limit how a market can operate by setting restrictions on what prices producers are allowed to set. One common form of this is a price minimum (price floor), which is the lowest price you’re allowed to charge. (If you try to lower it further, you “hit your feet on the floor”) These are commonly put in place to try to help producers. Another common form is a price maximum (price ceiling), which is the highest price you’re allowed to charge. (If you try to raise it higher, you “hit your head on the ceiling”) These are commonly put in place to try to help consumers.

Excise taxes are taxes that are levied on the sale of particular goods. So, for example, there might be a $1 tax on the sale of each gallon of milk. In principles of economics courses, we tend to focus on taxes where a fixed amount is charged for the sale of each unit (i.e. a $1 tax per gallon sold) rather than as a percentage of the sale price (i.e. 3 0 % of the sale price of the milk) because it’s basically the same idea, but the

math is easier.

Tax incidence is the burden that falls on producers and consumers, respectively, when a tax is placed on a good. For example, consider a good that would have an equilib—

rium price of $5 without a tax. If the government collects a $1 tax on each unit of 111

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that good, there will have to be $1 difference between what consumers pay and what producers receive after tax. If consumers now pay $6 and producers receive $5, then the tax is basically only hurting the consumers, and the tax incidence falls entirely on the consumers. But if the consumers now pay $5.25 and the producers receive $4.25, then the pain i s shared, and the tax incidence i s $ 5 . 2 5 — $5 = $ . 2 5 for consumers and

$5 — $4.25 = $.75 for producers. Quotas or limited licensing systems directly limit the number of units of a good that can be sold in a market. For example, in New York City there are a fixed number of taxi licenses available. Since you can’t drive a taxi legally without a license, this acts as a direct limit on the amount of taxi services that can be sold in the city.

How to Model Price Maximums

(Price Ceilings) WHAT YOU NEED TO START: A supply curve, a demand curve, and a price ceiling 1—) (a maximum allowable price). Nobody is allowed to sell at a price higher than the price ceiling.

STEP 1 WHAT YOU DO Check whether the price ceiling 1—9 binds (actually constrains the market, like a pair of handcuffs would bind your hands together and keep them from moving freely). Do this by calculating the equilibrium market price (see 2.i), ignoring the price ceiling, to get P * and Q*. If P * < I), then the ceiling doesn’t do anything. Skip the rest of the steps, and treat the market like there’s no ceiling at all. If P * > 5 , then the ceiling prevents you from reaching the equilibrium price, and so binds.

Example: In the market for wood, inverse demand is P = 25 — 2QD and inverse supply is P = 1 + 2Q5. Using the standard 2.i method, w e find P * = 1 3 and Q * = 6.

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If there’s a price ceiling of E = 11, then P * > 1—9, and the ceiling makes the equilibrium price illegal. S o the ceiling does in fact bind the market. WHY

A price ceiling won’t do anything if people don’t want to set prices that high anyway. If the government passes a law saying, “the price is

not allowed to be above $5,” but the price is only $3 anyway, then that law doesn’t do anything and we can ignore it in our analysis. And so, this step just serves to check whether or not the law is actually going to have any effect at all.

STEP 2 WHAT YOU DO Calculate the quantity supplied and the quantity demanded by plugging 1—) into supply and demand. You will find QD > Q5. There will be a shortage of the good of QD — Q5 units.

Example: In the market for wood, inverse demand is P = 25 — 2QD and inverse supply is P = 1 + 2QS. If there’s a price ceiling of f) = 11, then: 11 = 1 + 2QS

[Plug in to supply]

1 0 = 2QS

[Take 1 from each]

5 = Q3

[Divide by 2]

11 = 25 — 2QD

[Plug in to demand]

2QD = 14

[Add 2QD and take 11]

Q0 = 7

[Divide by 2]

Shortage = Q0 — Q5

Shortage = 7 — 5 = 2 WHY

Since the price is “too low” relative to the equilibrium market price, it’s going to be the suppliers who are the first to say “this isn’t worth it! I’m not willing to make as many as you want! I need to be paid more!” So, you’re going to find QD > Q5.

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When quantity demanded outstrips quantity supplied, you have a shortage. There are people out there running around trying to buy the thing at the going price, but they can’t all find a unit to buy!

STEP 3 WHAT YOU DO The actual amount produced, QA, is Q5 from Step 2. Use this, along with Q * from Step 1, to calculate deadweight loss using 4.f.i.

Example: Using the supply, demand, and price ceiling from Steps 1 and 2, we plug QA = 5 into supply to get MCA = 11, and into demand to get M VA = 15. Then, deadweight loss is:

DWL = (MVA —MCA)*(Q*—QA)/2 DWL=(15—11)*(6—5)/2=4*1/2=2 STEP

LI

WHAT YOU DO Graph the effects of the price ceiling by drawing the supply S and demand D curves as usual. Then draw in the price ceiling 5 below the equilibrium price. Using Q5 as the actual quantity sold, graph deadweight loss DWL as the triangle between S and D from Q5 to Q*, consumer surplus as the area between D and f9 up to Q5, and producer surplus as the area between E and S up to Q5.

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(1S 0* _

I I I I

\D _

I

WHY

r

D

Quantity

Having a binding price ceiling in effect is basically the same as the market operating normally but at a non-equilibrium price. And so, the

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115

same rules as always apply for finding DWL, PS, CS, and Shortage on a supply and demand graph. Refer back to 4 . f for DWL, to 4.b.iv for PS, to 4.c.iv for CS, and to 2 . h

for Shortage.

It’s all coming together!

How to Model Price Minimums

(Price Floors) WHAT YOU NEED TO START: A supply curve, a demand curve, and a price ceiling E (a minimum allowable price). Nobody is allowed to sell at a price lower than the price floon

STEP I WHAT YOU DO Check whether the price floor p binds (actually constrains the market, like a pair of handcuffs would b—ind your hands together and keep them from moving freely). Do this by calculating the equilibrium market price (see 2.i), ignoring the price floor, to get P * and Q*. If P * > p, then the floor doesn’t do anything. Skip the rest of the steps, and treat the market like there’s no floor at all. If P * < p, then the floor actually prevents you from reaching the equilibrium price, and so binds.

Example: In the market for wood, inverse demand is P = 25 — 2QD and inverse supply is P = 1 + 2QS. Using the standard 2.i method, we find P * = 1.3 and Q * = 6.

If there’s a price floor of p = 17, then P * < p, and the floor makes the equilibrium price illegal. S o the ceiling does in fact bind the market. WHY

A price floor won’t do anything if people don’t want to set prices very low anyway. If the government passes a law saying, “the price is not

allowed to be below $5,” but the price is $7 anyway, then that law doesn’t do anything and we can ignore it in our analysis.

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And so, this step just serves to check whether or not the law is actually going to have any effect at all.

STEP 2 WHAT YOU DO Calculate the quantity supplied and quantity demanded by plugging p into supply and demand. You will find QD < Q5. There will be a market surplus of the good of Q 5 — QD u n i t s .

Example: In the market for wood, inverse demand is P = 25 — 2QD and inverse supply is P = 1 + 2QS. If there’s a price floor of p = 17, then: 17 = l + 2QS

[Plug in to supply]

16 = 2QS

[Take 1 from each]

8 = Q5

[Divide by 2]

1 7 = 25 — 2 Q D

[Plug i n to demand]

2QD = 8

[Add 2QD and take 1 1]

Q0 2 4

[Divide by 2]

Surplus = Q5 — QD

Surplus = 8 — 4 = 4 WHY

Since the price is “too high” relative to the equilibrium market price, it’s going to be the consumers who are the first to say “this isn’t worth it! I’m not willing to buy as many as you want to sell! The price needs to come down!” And so, you’re going to find Q5 > QD.

When quantity supplied outstrips quantity demanded, you have a surplus or market surplus (not to be confused with consumer surplus, producer surplus, or total surplus). There are people out there running around trying to sell the thing at the going price, but they can’t all find a person to buy their stuff!

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STEP 3 WHAT YOU DO The actual amount produced, QA, is QD from Step 2. Use this, along with Q * from Step 1, to calculate deadweight loss using 4.f.i.

Example: Using the supply, demand, and price ceiling from Steps 1 and 2, we plug QA = 4 into supply to get MCA = 9, and into demand to get M VA 2 17. Then, deadweight loss is: DM=*(Q*—QA)/2

DWL:(17—9)*(6—4)/2=8*2/2=8

STEP

l-|

WHAT YOU DO Graph the effects of the price floor by drawing the supply S and demand D curves as usual. Then draw in the price floor p above the equilibrium price. Using QD as the actual quantity sold, graph deadweight loss DWL as the triangle between S and D from QD to Q*, consumer surplus as the area between D and p up to QD, and producer surplus as the area between E and S up to Q0.—

I I

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Q0 WHY

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Qua ntity

Having a binding price floor in effect is basically the same as the mar— ket operating normally but at a non-equilibrium price. And so, the same rules as always apply for finding DWL, PS, CS, and Surplus on a supply and demand graph. Refer back to 4.f for DWL, to 4.b.iv for PS, to 4.c.iv for CS, and to 2 . h

for Surplus. It’s all coming together!

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How to Model Taxes WHAT YOU NEED TO START: A supply curve, a demand curve, and a per-unit tax T in which the government collects a tax of T for each unit sold. Supply and demand should both be inverse supply and demand. That is, they should be P as a function of Q rather than the other way around. If they’re Q as a function of P instead, solve

them for P first. STEP 1

WHAT YOU DO Add the tax T to the inverse supply curve. So, if your original supply curve was P = a + bQS, you now have P = a + bQS + T.

Example: In the market for mugs, the inverse supply curve is P = 3 + 2QS. But there i s a u n i t tax of T = 3 . And so, we move on to Step 2 with

P=3+2QS+3,orP=6+2QS. WHY

A unit tax means that, between the consumers paying for a good and the producers receiving the money, the government takes a certain amount T We can think of this in two ways: (1) the marginal cost of production has risen by T, since “pay some money to the government” is now a cost of production, or (2) we need to account for a gap (or “wedge”) of Tbetween the price that consumers pay and the price that producers rece1ve.

In either case, we can account for this by taking the supply curve and adding T to it.

STEP 2 WHAT YOU DO Use the modified supply curve from Step 1 with the normal demand curve to find the quantity sold under the tax, QT, and the price paid by consumers, PD.

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Example: In the market for mugs, the inverse supply curve is P = 3 + 2QS and the inverse demand curve is P = 21 — QD. There is a unit tax of T : 3.

WHY

6 + 2QT = 21 — QT

[Use modified supply]

3QT = 15

[Add QT and take 6]

5 = QT

[Divide by 3]

PD = 21 — QT = 16

[Plug into demand]

The supply curve modification we made in Step 1 accounted for the effect of the tax on the market, which either increases marginal cost or drives a “wedge” between supply and demand, depending on how you look at it. With the modification i n place, the market operates as normal, s o we

use the standard approach as in 2.i.

STEP 3 WHAT YOU DO Calculate the price actually received by producers, PS, by either plugging QT into the unmodified supply curve, or as P5 = PD — I You should get the same result either way.

Example: Using the same example as above, we first try plugging QT into unmodified supply:

PS =3+2QS =3+2(5)=13 And then try the alternate method of subtracting the tax from the price the consumer pays:

PS=PD—T=16—3=13 WHY

The price the producer actually receives for the good sold is whatever is left over from what the consumer paid, after the government took its share. Unmodified supply represents supply without the tax, and so it gives us what’s “left over.” We can also just simply subtract the amount of the tax from what’s paid.

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LI

WHAT YOU DO The amount of revenue the government collects from the tax is T multiplied by QT.

Example: Using the same example as above, the government collects:

Revenue=T*QT =3*5215 WHY

The government collects T in tax for each unit sold, and QT units are actually sold, so the government collects a total of Ttimes QT in revenue from the tax.

STEP 5 WHAT YOU DO The actual amount produced, QA, is Q T from Step 2 . The marginal value of the last unit produced is PD from Step 2. The marginal cost is PS from Step 3. Calculate Q * using unmodified supply and demand, and calculate deadweight loss, DWL, using 4.f.i.

Example: Using the same example as above,

DWL=(MVA _ M C A ) * ( Q * — Q A ) / 2

DWL=(PD—PS)*(Q*—QT)/2 DWL=(16—13)*(6—5)/2=3*]./2=1.5 STEP 6 WHAT YOU DO Graph the effects of the tax by drawing the supply S and demand D curves as usual. Then, find QT in one of two ways. Either shift S straight up (up, not right) by T and find QT where D and modified S meet, or take a vertical line of length T and just sort of “wedge it in” between S and D until it “sticks.” Finally, using QT as the actual quantity sold, graph deadweight loss DWL as the triangle between S and D from QT to Q*, consumer surplus as the area between D and PD up to QT, and producer surplus as

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121

the area between P5 and S up to QT. Government revenue is the area between PD and P5 up to QT. Modified

Q WHY

D -x-

5

Quantity

We can graph a tax one of two ways, each of which gives the exact same QT, PD, P5, PS, CS, DWL, and Government Revenue.

The first, which is the top graph on the left, has us shifting supply straight up to represent the increase in the cost of bringing something to market (since you must pay a tax!). The quantity at which the modified S intersects with D is the exact same quantity you get if you simply look for the quantity at which the difference between S and D is the exact size of the tax, T. In other words, it’s the same as if you take

a “wedge” as large as the tax and just shove it in there until it can’t go any further! As a final note, keep in mind that at no point have we discussed whether the tax in question is being levied on the consumers or on the

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producers. That’s because it doesn’t matter! An additional cost of T has been introduced into the market. That cost will be shared the same way no matter who is writing the check to the government. The way that T is borne by consumers and producers, or “tax incidence,” can be calculated in S e .

How to Calculate Tax Incidence WHAT YOU NEED: A supply and demand curve, and a tax on each unit of the good sold (start with Step 1); a tax on each unit of the good sold, the with-tax price it’s currently sold at, and the original equilibrium price (start with Step 3); OR just the elasticity of supply and the elasticity of demand (start with Step 5).

STEP I WHAT YOU DO Forget the tax and calculate the equilibrium price using the standard method (see 2.i or 2.j).

Example: If demand is P = 18 — ZQD and supply is P = 3 + Q5, then we calculate equilibrium price as:

18—2Q*=3+Q*

WHY

15 = 3Q*

[Take 3 and add 2Q*]

5 = Q*

[Divide by 3]

P*=3+Q*

[TakeSorD]

P*=3+5=8

[Plugin]

Tax incidence is defined relative to what producers and consumers would have had without the tax. S o first, we need to find out the price

that would be paid (by consumers) and received (by producers) without a tax in place.

STEP 2 WHAT YOU DO Add the tax to the supply curve, so if the tax is T per unit, and the supply curve is P = a + bQS, we end up with P = a + bQS + T. Then,

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re-solve for price. The price you’ll end up with, called PD, is the price that consumers pay. The price that producers receive, P5, is P5 = PD — T, since producers receive whatever’s left over after the government takes out taxes.

Example: If inverse demand is P = 18 — 2QD, supply is P = 3 + Q5, and there’s a T : 3 tax per unit, we calculate the price consumers pay as:

18—2Q*=3+Q*+3 12 =

3Q>n
l
AC, then A C is increasing. Imagine taking the average height (AC) of a room full of people. If you add a new person to the room (MC), then the average height (AC) will decrease (slope down) i f that person i s shorter than average (MC < AC)

and the average height (AC) will increase (slope up) if that person is taller than average (MC > AC). The same logic goes for AVC. I AVC should always be below AC. They should be relatively far apart for low values of Q, and should get closer and closer together for high values of Q. - Why: A C = AFC + AVC. Since AFC is always positive, AVC will always be below AC. However, since AFC gets smaller and smaller for high values of Q, between A C and AVC also gets smaller and smaller, and they

the difference

grow together.

How to Determine the . Profit-Maximizing Quantity WHAT YOU NEED TO START: The price that a competitive firm can sell their goods at, P, and the marginal cost MC for that firm. The marginal cost can be either a function (Method 1 ) or a table (Method 2).

METHOD] WHAT YOU DO If you have a function for MC, then set P = MC and solve for Q. This is the profit-maximizing quantity Q*.

Example: I f M C = 2 + 3 Q a n d P = 11, then P = MC

WHY

11 = 2 + 3Q

[Plug in]

9 = 3Q

[Take 2]

3 = (2*

[Divide by 3]

Firms in general can maximize their profits by setting MR (marginal revenue) equal to MC. This works because if MR > MC, you can earn more profit by increasing quantity, and if MR < MC, you can earn

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more profit by decreasing quantity (see 4.e for more information). So, you want MR = MC. In a competitive market, MR and P are the same thing. So, you want P = MC.

M ETH DD 2 WHAT YOU DO If you have a table of marginal costs, then first look for a quantity at which P = MC. That is the profit maximizing quantity.

If there is no quantity at which P = MC, then choose the highest quantity at which P > MC. That is the profit-maximizing quantity.

Example: Consider the below costs table.

Q 1 2

MC 10 20

3

30

If P = 20, then P = MC at a quantity of Q = 2, and Q = 2 maximizes profit.

If P = 15, then P = MC isn’t true for any quantity. But Q = 1 is the highest quantity for which P > MC, so that’s the profit-maximizing quantity. WHY

When considering the profit-maximizing quantity with a costs table, you can always ask the marginal-minded question “would I make more if I made one more unit?” Starting from a quantity of 0 , every time w e produce another unit, you add on P i n revenues, and l o s e MC i n c o s t s . And s o , i f P > MC

for the next unit, you should go ahead and produce it! Therefore, you forge ahead, producing the units as long as P > MC, and then stopping when the next unit has P < MC. For that unit, if you did make it, it would cost you MC, but you’d only get paid P, which is less! Clearly not a great idea.

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151

How to Graph 21 Firm in a Competitive Market

Priced

MC

AC

I I

I I

0*

:

Quantity

NOTES TO FOLLOW I Costs should be graphed as they are in 6.d.ii. AFC and AVC are left off this graph for clarity, but they can be included just as they are in 6.d.ii.

I Demand D should be completely flat. “Demand” and “price” P are interchangeable. Sometimes you will see this line labeled as P or MR instead. - Why: A competitive firm is a price taker and has no control over the price. And so, no matter how much quantity they produce, they always face the exact same price. That means that the price is completely unresponsive to the firm’s quantity, which gives you a flat demand curve.

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I The optimal quantity Q * and the optimal price occur where D intersects with MC (Red Dot). I Average cost occurs where Q M intersects with AC (Blue Dot). Note that this is not (usually) the point where MC intersects with AC. I Profit is a box. The horizontal side of the box goes from the y-axis to Q*. The vertical side of the box goes from price to average cost. I If P > Average cost (as on the left graph), then the profit box represents positive profits. If P < Average cost (as on the right graph), then the profit box represents negative profits (a loss). If P = Average cost, then profit is zero.

How to Calculate Profit WHAT YOU NEED TO START: The Total Revenue TR (price times quantity) at a given quantity, and the Total Cost TC at that quantity (Method 1); or the quantity Q, price P, and Average Total Cost AC at that quantity (Method 2). METHOD l WHAT YOU DO If you have, or can calculate, TR and TC, then profit i s

Profit = TR — TC

Example: I f P = 100, Q =10, and TC is T C : 50 + 2Q, then TR = PQ = 100(10) = 1000

TC = 5 0 + 2(10) 2 70 Profit = TR — TC = 1000 — 70 = 930 WHY

Profit is whatever revenue is left over after you cover your costs (including opportunity costs, which are also a part of TC).

METHOD 2

WHAT YOU DO If you have Q, P, and AC, you can calculate profit as Profit

= Q * (P - AC)

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153

Example: If P = 100, Q = 10, and AC is AC = (SO/Q) + 2, then AC=(50/10)+2=5+2=7 Profit=Q*(P—AC)=10(100—7)=93O We could also have been able to tell immediately that profit would be positive since P>AC 100>7

WHY

This approach to calculating profit breaks profit down into the average profit earned on each unit sold (P — AC) times the number of units sold (Q). This method of calculating profit i s useful because it has an obvi-

ous graphical interpretation. In the profit box on a competitive—firm graph (see 61), Q is the width, P — AC is the height, and Q * (P — AC) is the area. This version is also useful since you can see at a glance if profit is positive (P > AC), zero (P = AC), or negative (P < AC) without having to calculate profit directly.

Long-Run Market Behavior EFL! How to Predict Entry and Exit WHAT YOU NEED TO START: To predict entry and exit in the long run, you’ll need a firm’s profit (see 6 .g). If you want to predict entry and exit in the short run, you’ll also need a firm’s Average Variable Cost AVC (see 6.d.ii).

STEP I WHAT YOU DO Calculate the profit the marginal firm makes in the market. If profit is positive, then there will be entry in the long run, eventually shifting the supply curve to the right. If profit is negative, then there will be exit in the long run, eventually shifting the supply curve to the left. If profit is

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zero, then there will be n o entry and exit, and we say the market i s i n

long-run equilibrium. Another way to calculate this is: if P > AC, then there will be entry (since profit will be positive). If P 2 AC, then there will be no entry or exit (since profit i s 0 ) . And if P < AC, then there will be exit (since

profit will be negative).

Example: In the competitive market for raw coffee, the price of a bag of coffee is P = 10, the total cost of production for the marginal firm is TC = 20 + Q2, and the marginal cost is 2 Q . Using 6.e, we find that Q = 5, and using 6.g we calculate that profit is 5. Since profit is positive, we predict that other firms will start to enter the raw coffee mar-

ket, which will shift supply right and bring down the price. WHY

Firms want to chase profits. And so, each firm will join the industry in which it can make the most profit at any given time! Since profit as we’ve calculated it includes opportunity costs, then a positive profit doesn’t just mean you’re making money. It means you’re making more money in that industry than you could make elsewhere. And so, other firms will also see a benefit to joining your industry, where they’ll make more than they would elsewhere! This will be entry into the market. Similarly, if your profits are negative, you’d do better elsewhere, and you’ll leave the market.

STEP 2 WHAT YOU DO In Step 1, you determined whether there would be entry or exit in the long run. However, it’s also possible that a firm will shut down right away (in the short run) if things are really bad. If P < AVC, then there will be short-run exit. This i s also known as the

“shutdown point.”

Example: Use TC = 20 + Q2 and MC = 2Q above, but this time P = 4. Then, Q = 2 and profit is —16, which is a loss. Using 6 b and 6.d.i we find

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AVC = Q, so AVC = 2 . S o even though P < A C and the firm i s making

a loss, P > AVC and the firm will shut down only in the long run, but it will stay open in the short run. In other words, they lose money (—16), but they’d lose more (—20) if they decided to shut down and produce Q=O. WHY

In the short run, the firm is already committed to paying the fixed costs. But firms can’t just shut down and get a profit of 0 . They’re going to have a loss equal to their fixed costs, since they can’t avoid those. The fixed costs are “sunk costs” at that point, so you shouldn’t consider them in your decision to shut down. Therefore, while any firm making a loss will shut down in the long run, a firm will only shut down i n the short run if i t i s making a l o s s

even if you don’t count the fixed costs as losses. This will be true if P < AVC, since AVC doesn’t count the fixed costs (like how P < AC indicates a loss if you do count the fixed costs).

How to Model the Market and

the Firm Together Price‘-

Price

S

P*

AC D

Quantity

(1*

FIGURE1 : Making Profit in a Competitive Market

Quantity

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Pricey

Price

MC

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/

/ AC D.

p*22:222221122222122222222

AC

. I I l

D

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Q*

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FIGURE 2: Supply Shifts Right Because of Market Entry

Price"

5 PriceH

MC

AC

AC D

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P* r - - - - - - - - - - - - - - - - - - - - - - - - - -

l l

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FIGURE 3: Losing Money in a Competitive Market

Price“

5' S Price“

MC

p* _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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FIGURE 4: Supply Shifts Left Because of Market Exit

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Price“

THE PRODUCTION PROCESS IN COMPETITIVE MARKETS

5

PriceH

P* ___________________________

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MC

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AC

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FIGURE 5: Long-Run Equilibrium at Zero Profit and Minimized Cost

NOTES TO FOLLOW Draw a supply and demand curve as normal on the left. On the right, draw a competitive market fi r m ’ s costs as normal (see 6.f).

Find the equilibrium market price where S and D cross on the left. Follow this point over to the right to create the D that the individual firm sees. The individual firm’s quantity Q * is determined by where D intersects with MC, and their profit is a box with a width Q * and a height P — AC. Note that the individual firm’s Q * is only how much they make. The entire market quantity adds up each firm’s quantity. If profit is positive (P > AC, as in Figure 1), then there will be market entry in the long run, shifting S to the right and dropping the equilibrium market price, thus reducing profit (as in Figure 2). Given enough time, price will drop all the way down to P = AC (as in Figure 5 ) where the market entry stops, since profit is 0. If profit is negative (P < AC, as in the third figure), then there will be market exit in the long run, shifting S to the left and raising the equilibrium market price, reducing losses (as Figure 4). Given enough time, price will rise all the way to P = A C (as in Figure 5 ) where the market entry stops, since profit is O.

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an!!! How to Find Long-Run Equilibrium Price and Quantity WHAT YOU NEED TO START: Functions for an individual firm’s Marginal Cost MC and Average Total Cost AC, or a graph of an individual firm’s costs, perhaps next to a graph of supply and demand in the market (skip to Step 4).

STEP I WHAT YOU DO If you have a function for MC and a function for AC, set MC = AC and solve for Q*. Plug Q * into P = MC to get market price P * . Q * is the quantity that each individual firm makes. Example: If MC = 2 Q and A C 2 (4/Q) + Q, then

MC = AC 2 Q = (4/Q) + Q

[Plug in]

Q = (4/Q)

[Take Q]

Q2 = 4

[Multiply by Q]

Q* = 2

[Take the square root]

P = MC P * = 2(2) = 4

[Plug in]

Therefore, i n t h i s market, the long-run equilibrium price i s P * = 4 , and

each firm makes Q * = 2 units. WHY

In the long run, firms in competitive markets make zero profit. A firm makes zero profit when P = AC. Further, we know that the firm wants to set P = MC. So, we plug that in and realize that for profits to be 0, we need MC = AC, the spot on the graph where MC and AC intersect. By setting MC = AC, we can find the quantity and price (using P = MC) at which profits are 0, and thus the quantity and price for the firm in the long run.

STEP 2 WHAT YOU DO If you want to know the number of firms in the market in the long run, you can: (1) use P * with the demand curve to find the market quantity Q * * in the long run, and (2) divide Q** by the amount each firm makes, Q * , to get the number of firms i n the market.

Example: Using the example from Step 1, if the demand curve is QD = 16 — P, then QD= 1 6 — (4) = 12 in the long run. So, Q * * = 12. Each firm makes Q * = 2 units, so there must be Q * * / Q * = 12/2 = 6 firms in the market in the long run. WHY

We already know the number of units each firm is making when it is making zero profits, Q*, and we know the market equilibrium price P*. As always, we can get the number of units demanded by plugging price into demand. Since the market is in equilibrium, we know that this will give us the equilibrium market quantity. Then we just divide the responsibility for producing that quantity equally across all the firms.

STEP 3 WHAT YOU DO If you want to know the market quantity in the long run, and are told the number of firms and that all firms are identical, then simply multiply Q * by the number of firms to get the market quantity.

Example: Using the example from Step 1, if we are told that there are 6 firms in the long run, then we know that the long-run quantity is 6 Q * = 12. WHY

If all firms are identical, then they’ll be producing the same quantity. And since we know how much each of them produces, all we need to

do to get the total production is add up what each individual firm is making. S T E P '-l

WHAT YOU DO See 6.h.ii Figure 5 for a graph that shows a competitive market and firm in long-run equilibrium. This graph is easiest to draw if you work

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from right to left. Draw the cost graph and find P * where MC intersects with AC. Then follow that price left to the supply and demand graph. Draw D, and then draw S so that it intersects S at P * . WHY

The zero-profit point determines the price in the long-run equilibrium. And so, we can start our long-run graph by finding that price where MC and AC intersect. In the long run, 5 will have shifted left and right until it intersects D at exactly that price, so we have them intersect at that price.

Ian-ix How to Graph Long-Run Average Total Cost Price“

SRAC1

SRAC3 LRAC

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taraa'rtg gopstant, saver“ ° 2 urns 0 Scale

Scale

Quantity NOTES TO FOLLOW

I Long-run Average Total Cost (LRAC) is a “U” shape, kind of like a pie tin or frying pan (although other types of U shapes without the big flat bottom are possible, depending on context). In the area where it slopes down, the firm receives increas— ing returns to scale (“economies of scale”). In the area where it i s flat, the firm

receives constant returns to scale. In the area where it slopes up, the firm receives decreasing returns to scale (“diseconomies of scale”). - Why: When a firm is just starting out and is small (left side of LRAC, with low output), it’s likely that there’s not enough opportunity to specialize. It’s not big enough, for example, to hire an accountant, s o the owner does her own taxes.

Therefore, increasing in size allows for more specialization and becoming much

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161

more efficient (increasing returns to scale). As the size gets bigger, the firm manages to get as much specialization as it needs, and while it can continue to grow without issue, it no longer gets the huge gains to expansion it once had (constant returns to scale). As it gets bigger still, eventually it will become so big that it’s hard to manage. There are coordination problems making sure the many, many people working in the company are on the same page. And so, growing further gets more and more expensive (decreasing returns to scale). - Also: The reason why LRAC is differently shaped is because, in the long run, fixed costs are not fixed any more (so if you want to expand, for example, you can move to a bigger building rather than be bursting at the seams in the one on which you’re still under lease). This flexibility makes it easier to expand, and so longrun costs aren’t as sensitive to quantity produced as short—run costs are. Imagine being told that you had to double production in ten years—no problem! But if you had to double production tomorrow, you’d be scrambling to hire more people and machinery. It would be really expensive!

I Within the LRAC, fit the short-run average cost SRAC curves. Each curve intersects with LRAC at its minimum, since in the long run you produce at the minimum of the SRAC curve (the zero-profit point), so the minimum of each SRAC curve should

be on the LRAC curve. AC curves further to the right represent higher levels of production. For example, for a shirt-printing company, SRAC] might represent the company working out of the founder’s garage, SRACZ might represent them once they’ve opened a small factory, and SRAC3 might represent them with an enormous

factory and multiple warehouses.

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PRACTICE Follow-the-Steps Questions To solve, follow directions

from one or more of the sections above.

1. In each of the following descriptions, describe the firm’s fixed costs and variable costs. a. A bookmaker has a lot of large printing presses in a warehouse she rents, and she buys paper and pays workers to make the books. b. Gerald makes handcrafted

wooden chairs. He buys the wood and screws, and

he had to take several expensive classes teaching him how to make the chairs safely. c. A taxi driver pays every day to rent the taxi from the taxi company, and then he pays for gas and spends his own time picking up fares. 2. Andy is a TV producer figuring the price of producing a certain number of episodes of his TV show. If Q = 0, TC = 10 (all costs are in millions of dollars). If Q = 1 , T C = 1 2 . I f Q = 2, T C = 1 5 . I f Q = 3, T C : 19. Fill out a table ofAndy’s costs, with columns for: Q, TC, F C, VC, AC, AVC, AFC, and MC.

3. Using the total cost function TC = 36 + Q2: a. Calculate the function for A C by dividing TC by Q. b. Calculate the function for AC by calculating AFC and AVC and adding them together. c. Calculate the value o f A C at Q = 4, Q = 8, and Q = 12.

4. Draw a graph with MC, AC, AVC, and AFC curves. Draw them such that the firm shuts down in the long run at any price below 10, and shuts down immediately at any price below 8. Label these prices.

5. Consider a firm for which MC = 4Q, TC = 1.2 + 2Q2, and the market price is P * = 12. Calculate the profit-maximizing quantity and the firm’s profit. Then make a graph with demand, MC, and AC, labeling the price, quantity, and profit.

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163

Sandals are produced in a competitive market, and the market price is P = 50. One sandal producer has MC = lOQ and AC = (25/Q) + 5Q. Calculate the firm’s profit-maximizing quantity and their profit. The market for bowls is competitive. Inverse demand is P = 22 — 2QD and inverse supply is P = 2 + 2Q5. Each firm’s marginal cost is MC = 6 Q and average cost is AC = (24/Q) + 3Q. a. Calculate the quantity each firm produces. b. Calculate the profit each firm makes. c. What will happen to the supply curve next? Draw a graph of an individual competitive firm’s MC, AC, and AVC curves. Label the price at which the firm makes zero profit. Then, label the price region at which the firm makes a profit, the price region at which the firm makes a loss but won’t shut down right away, and the price region at which the firm shuts down immediately. Draw two graphs. On the right, draw a graph of an individual firm’s MC and AC. On the left, draw a supply and demand curve with an equilibrium price such that the individual firm makes a profit. Then, show how these graphs change as the market approaches the long run.

10. Draw a long-run average total cost curve with four short-run average cost curves nested inside of it. Label the four average cost curves SRAC], SRACZ, SRAC3, and SRAC4, where the higher numbers indicate average cost curves for larger productions. Also, draw a star next to each SRAC curve with increasing returns to scale, a square next to each SRAC curve with constant returns to scale, and a circle next to each SRAC curve with decreasing returns to scale.

Concept Questions A. Marginal revenue MR and marginal cost MC are the additional revenue and cost (respectively) added when the amount produced increases by one. With that in mind, add and fi l l i n MR and MC columns for the table that follows. (Assume

that each unit 0—99 has the same MC, and s o does each unit 100—199, and s o o n . )

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Q

TR

TC

0 100 200

0 1000 2000

500 1000 2000

300

3000

4000

In the market for potted plants, which is competitive, each firm has a marginal cost of MC = 4 Q . There are 500 identical firms.

a. Calculate the market quantity supplied Q5 at P = 16, P = 20, and P = 24. b. Write out the market supply curve for this market as an equation. Consider the market for potted plants from Question B. a. Calculate the long-run price. b. If inverse demand is P = 162 — ZQD, calculate the number of firms that will be in the market in the long run. Consider a firm with a constant marginal cost. For example, MC = 8. For a firm like this, we would get a total cost function that looks like TC = 36 + 8Q. Thinking carefully about where these curves come from (they’ll look different than in the standard graphl), draw a graph of this firm’s costs, including MC, AC, AFC, and AVC. For each of the following, determine whether the firm has increasing,

decreasing

constant, or

returns to scale. (HINT: Look at the Glossary and Concepts section.)

a. Total costs went from $200 to $400 and quantity increased from 40 to 80. b. Total costs went from $1000 to $1200 and quantity increased from 50 to 70.

c. Total costs went from $300 to $500 and quantity increased from 100 to 150. We say that a firm will shut down in the long run if P < AC, but that the firm will shut down immediately only if P < AVC. Explain why we use AC for the long run shutdown decision, but AVC for the immediate shutdown decision. We have two main ways of calculating profit: Profit = TR — TC and Profit = Q * (P — AC). Show mathematically that these will always give the same answer. [HINT2 Start by thinking about how you can factor Q out of TR and TC.]

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165

Diane runs a factory that makes coffee mugs. In the factory, she employs a lot of part-time workers she can hire or fire as she needs. She also has a bunch of huge mug-making machines that take a lot of time to install, and she hires some highly-skilled workers who have special knowledge about how to run the machine. Last year she made 1 million mugs. But this year her designs unexpectedly got very popular and she will need to make 2 million mugs. Referring to “short run average cost” and “long run average cost,” describe the things she can change now to increase production, and what things she can change in the long run, as well as how the costs of production will change in the long run as a result. Consider the competitive market for leather handbags. In the hope that people will not treat the lives of leather cows lightly, the government has implemented a price floor on the bags. They cannot be sold for less than $200. Price“

/S

R\

D Qo

QTJantity

Given this market, draw to the right of this graph a graph of an individual handbag supplier. Draw it so the firm makes a profit.

Glossary and Concepts Pricing power refers to the ability of a firm to set its own price. Competitive firms have no pricing power, since if they attempt to set their price above market price, nobody will buy their goods. Firms with pricing power can choose to set a higher price and sell fewer units, or set a lower price and sell more units.

Barrier to entry is something that keeps new firms from entering the market. There are also barriers to exit, which keep unprofitable firms from leaving the market. Examples of barriers to entry are high startup costs, laws that require you to get a license to operate, patent laws, or when one firm controls an important input to production (like how one diamond company might own all the world’s diamond mines). Barriers to entry are necessary to keep monopolies or oligopolies from becoming competitive markets. Monopoly is a market in which there is only one firm operating.

Oligopoly is a market in which there are a few firms operating—more than one, but still a small enough number that firms have pricing power. Monopolistic competition is a market in which there is no barrier to entry and there are many producers competing, but where each firm has a differentiated product. This gives the firms a small amount of pricing power. A natural monopoly is an industry in which average total costs are always decreasing over the range of possible quantities that might be produced (remember from 6.c—6.e that ATC usually decreases until it intersects with MC, then increases). In

these industries, a monopoly can produce at a lower cost than a competitive market can, since the entire output can be made by one firm, reaching the lowest possible ATC.

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MONOPOLY

Product differentiation is when different firms sell slightly different versions of the same product. For example, two different brands of mint toothpaste may be similar, but taste different, or you might like the packaging on one a bit better, and so you wouldn’t consider them exact substitutes. Marginal

revenue is the additional revenue a firm makes by selling one additional

unit of their good. In a competitive market, marginal revenue is just equal to the price, but with pricing power, a firm must lower their price a bit to sell one more unit. Because they must lower their price on all the units they sell, the marginal revenue ends up being a little lower than the price. Price discrimination

is when a single firm sells the same good (or extremely similar

goods) at difi‘erent prices to diflerent people. An example is when a movie theater charges seniors less for the same movie ticket than it charges adults. Note that this does not apply to very different goods (a chocolate company selling very good chocolate and very bad chocolate at two different prices is not price discrimination) or different companies (product differentiation is not an example of price discrimination). I In Perfect (First-degree) price discrimination, each person is charged their exact marginal value. I In Hurdle or bulk-buying (Second-degree) price discrimination, a discount is offered for buying a larger amount (like when you see an offer for “buy two get one free” or when you pay a membership fee to buy bulk goods). I In Less-than-perfect

or group (Third-degree) price discrimination, people or

firms are charged different prices based on the group they belong to (like the seniors and adults in the movie ticket example, or when a coupon is offered that only some people will bother redeeming).

How to Distinguish between Market Structures WHAT YOU NEED TO START: A description of a market.

STEP 1 WHAT YOU DO Determine how many producers are in the market.

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169

If there’s one producer taking up all or nearly all the market, it’s a monopoly. Go to Step 2. If there are several producers taking up all or nearly all the market, it’s an oligopoly. Go to Step 3. If there are many producers, it’s a competitive market. Go to Step 4. WHY

One of the primary distinguishing characteristics of how a market acts is how competitive it is. A primary way we can measure competitiveness is by the number of active firms. The more firms there are, the more you must compete!

STEP 2

WHAT YOU DO Think about whether it is likely that startup costs in this market are extremely high, or marginal costs are extremely low. If they are, the market is likely to be a natural monopoly, where average total costs are always declining. If not, then the market is likely just a regular monopoly.

Example: The costs of building sewer systems are extremely high (high startup costs), but once built the cost of using them is very low (low marginal cost). So, the market for sewer systems is a natural monopoly. But this is not likely to be true in the market for high-end branded laptops, where marginal costs are significant. So, the market for highend branded laptops, if there is only one firm, is a monopoly but not a natural monopoly. WHY

A natural monopoly is an industry in which nearly all the costs of running the business are in setting it up in the first place. This is common for infrastructure projects like sewer or electricity systems. When this happens, the average total cost is always declining, and the market will “naturally” produce at the lowest cost if it’s a monopoly.

STEP 3 WHAT YOU DO If there i s a small number of firms, but more than one, you have an oligopoly.

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As a note, some textbooks will define markets as oligopolies only if the products are not differentiated (i.e. each firm sells the exact same product). Markets with few firms and differentiated products (i.e. each firm makes products that are a little different, or there are strong brands) can also be thought of as oligopolies. However, if your textbook defines oligopoly as only applying to non-differentiated goods, and you are looking at a market with differentiated goods, you may want to think of it as monopolistic competition instead.

STEP '4 WHAT YOU DO Think about whether the goods in the market are differentiated. If the products are differentiated (each firm makes a slightly different version, and consumers have their own preferences for one type over another), then you have monopolistic competition. If not, and each firm sells identical goods, then you have perfect competition. WHY

The thing that makes monopolistic competition “monopolistic” is the fact that while each firm does face competitive pressure, it also has a

little bit of market power because its good is not the same as that of its competitors.

The Model of Monopoly 2:9}. How to Find Marginal Revenue Using a Demand Curve WHAT YOU NEED TO START: An inverse demand curve ( a demand curve with P as a func—

tion of QD). If you instead have a table of costs and want to find marginal revenue that way, look at 6.c Step 2.

STEP 1 WHAT YOU DO Check that the inverse demand curve you are given is linear. In other words, whether it looks like: P=a—bQD

Example: P = 1 2 — QD is linear.

P = 12 — Q12) is not linear. WHY

The process in Step 2 that lets you find marginal revenue (MR) using the inverse demand curve only works if the inverse demand curve is linear.

STEP 2

WHAT YOU DO If the inverse demand curve i s linear, double the slope on QD to get the monopolist’s marginal revenue (MR).

Example: If the inverse demand curve is P = 1 2 — QD then marginal revenue is MR 2 12 — 2 Q . WHY

MR is defined as “the additional amount of revenue you get by producing one more unit of the good.” When the demand curve is linear, the function that describes this additional revenue happens to look like the inverse demand curve with a doubled slope. This can be proven using calculus (as in Step 3).

STEP 3 WHAT YOU DO If the inverse demand curve is not linear, you will have to use calculus. Plug demand into total revenue (TR). Take the derivative with respect to Q0 to get a monopolist’s MR.

Example: If inverse demand is P = 1 2 — Q12) then total revenue is:

TR = PQ = (12 - Q2)Q and marginal revenue is:

_ aTR

MR — —

aQ1)

WHY

=12—3Q2

MR is defined as “the additional amount of revenue you get by produc— ing one more unit of the good.” So, the derivative of TR with respect

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to Q, which is the amount by which TR increases when Q increases, gives you MR.

How to Determine the ProfitMaxirnizing Quantity and Price WHAT YOU NEED TO START: A marginal cost (MC) function and a marginal revenue (MR) function. See 7.c.i if you do not know MR.

STEP 1 WHAT YOU DO Set marginal cost (MC) equal to marginal revenue (MR).

Solve this equation for Q. This is the profit-maximizing Q. Let’s call it QM.

Example: If MR = 1 2 — 2 Q and MC = 3 + Q, then the profit-maximizing quantity

can be found by: MR 2 MC

WHY

12 — 2 Q = 3 + Q

[Substitute in]

9 — 2Q = Q

[Take 3 from each side]

9 = 3Q

[Add 2 Q to each side]

3 = QM

[Divide each side by 3 ]

Profit i s maximized when MR = MC. If, instead, MR > MC, then pro-

ducing more will increase your profit, since producing more will add MR to your profit, and take away only MC. If, instead, MR < MC, then producing less will increase your profit, since producing less will add MC to your profit, and take away only MR. So, profit is not maximized if MR > MC or if MR < MC, and it will instead be maximized if you choose the Q that sets MR = MC.

STEP 2 WHAT YOU DO Plug the profit-maximizing quantity into the demand curve to find the profit-maximizing price. Let’s call it PM.

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Example: If the profit-maximizing quantity is QM = 3, and inverse demand is P = 1 2 — QD, then the profit-maximizing price is PM = 1 2 — 3 = 9. WHY

The demand curve determines the relationship between price and quantity demanded. So, if you want to know the price people are will— ing to pay for your profit-maximizing quantity, you “ask the demand curve” the price at which they would like to buy that quantity.

7.4.2!!! How to Calculate Monopoly Profit WHAT YOU NEED TO START: Profit-maximizing price PM and quantity QM. See 7.c.ii if you do not know these. You also need a total cost function TC (for Method 1), an aver-

age cost function A C (for Method 2 ) , or a fixed/constant marginal cost (for Method 3 ) .

METHOD 1 WHAT YOU DO Plug QM into the total cost function TC to get TC. Calculate profit as: PFOfitZTR—Tc=PMQM—TC

Example: If PM = 9, QM = 3, and TC = 3Q + (Q2/2), then 2 TC: 3(3)+%=

13.5

Profit = 9 *3— 13.5 =13.5 WHY

Profit is the money you earn minus your costs (which include opportunity costs). The money you earn is equal to the total revenue, which is the number of units you sell times the price you sell each unit at, or PMQM.Subtract your total costs from your total revenue to get profit.

METHOD 2

WHAT YOU DO Plug QM into the average cost function AC to get AC. Calculate profit as:

Profit= QM(PM — AC)

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Example: If PM =15, QM = 5, and AC = 3 + (Q/Z), then 3 AC=3+E=45 Profit = 3 *(9—4.5) = 3 * 4 . 5 = 13.5 WHY

The average profit made on each unit of the good sold is the amount you sell it for (PM) minus the average amount you spent to make it (AC). So, average profit per unit is PM — AC. If you multiply the average profit per unit by the number of units sold (QM), you get total profits.

M ETHUD 3 WHAT YOU DO Take the fixed/constant marginal cost c (“each unit costs the monopolist c to make”) and calculate profit as: C) Profit = QM(PM —

Example: If PM = 10, QM = 4, and each unit costs 6 to make, then

Profit=4*(10—6)=4*4=l6 WHY

The profit made on each unit of the good sold is the amount you sell it for (PM) minus what you spent to make it (c). So, profit per unit is PM — c. If you multiply the profit per unit by the number of units sold (QM), you get total profits.

2.9-}! How to Find Deadweight Loss in a Monopoly WHAT YOU NEED TO START: A linear marginal cost (MC) function and a linear inverse

demand curve (it has the form P = a — bQ). You also need the profit—maximizing price PM and quantity QM. See 7.c.ii if you do not know PM and QM.

STEP l WHAT YOU DO Set P = MC, and then plug in inverse demand for P. Solve this equation for Q. This is the efficient level of quantity. Let’s call this Q*.

Example: If inverse demand is P = 12 — QD and MC 2 3 + Q, then P = MC

WHY

12 —Q = 3 + Q

[Substitute i n ]

9 —Q = Q

[Take 3 from each side]

9 = 2Q

[Add Q to each side]

4.5 = Q *

[Divide each side by 2]

The outcome is efficient if the marginal value of the last unit purchased equals the marginal cost of production. The marginal value is the price that consumers are willing to pay, based on the demand curve. S o , the efficient outcome occurs when P = MC.

STEP 2 WHAT YOU DO Plug the profit-maximizing quantity QM (not Q * ) into MC to get the marginal cost of the last unit sold, MC M .

Example: IfMC=5

+Qand

Q M = 3 , then

MCM=5+Q=5+3=8 WHY

Deadweight loss is based on the surplus you didn’t get because the monopolist sold less than society would like. So, we are calculating surplus. Part of calculating surplus is calculating costs.

STEP 3 WHAT YOU DO Calculate deadweight loss as: DWL = (PM —MCM)*(Q*—QM)/2 WHY

Deadweight loss is the area between demand and marginal cost (height PM - MCM ) and between the efficient and monopoly quantities (base

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Q * — QM). When demand and MC are linear, this area is a triangle, so you use the height * base/ 2 formula for the area of a triangle.

2.9x How to Graph 21 Monopoly

Qua ntity POINTS TO FOLLOW

I Quantity should be on the x-axis, and Price should be on the y-axis. Sometimes the y-axis is marked with Cost instead of Price, which works the same. I The marginal cost curve MC should slope upwards. Depending on preference, the MC curve may be drawn as a straight line, or in more of a “J” shape (as it is above).

I The average cost curve AC has a “U” shape. It goes down and then back up again. I The MC curve and the AC curve should intersect at the minimum point of the AC curve (the bottom point of the “U”). - Why: This i s a natural result of the fact that if MC < AC, then A C i s declining, and

if MC > AC, then AC is increasing. Imagine taking the average height (AC) of a room full of people. If you add a new person to the room (MC), then the average height (AC) will decrease i f that person i s shorter than average (MC < AC)

and the average height (AC) will increase if that person is taller than average (MC > AC). I The demand curve D should slope downwards.

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The marginal revenue curve MR should also slope downwards. It should have a steeper slope than D, and always be lower than D. The profit-maximizing quantity QM occurs where MC intersects with MR (Red Dot).

The profit-maximizing price PM occurs where QM intersects with D (Green Dot). Average cost occurs where QM intersects with A C (Blue Dot). Note that this is not the point where MC intersects with AC. Profit is a box. The horizontal side of the box goes from the y-axis to QM. The verti— cal side of the box goes from PM to average cost.

If PM > Average cost, then the profit box represents positive profits. If PM < Average cost, then the profit box represents negative profits (a loss). Deadweight loss (DWL) is the area above the MC curve and below the D curve, between QM and the point where D intersects with MC. - Why: This area represents lost economic surplus that results from the fact that the monopolist prefers selling an inefficiently low number of units so as to increase the price. So, it goes above MC and below D (since this area represents the economic surplus of selling units) and between QM and where D intersects with MC (since QM is the number of units produced, but the efficient number to produce would be where D intersects with MC).

.7.-..C.-.V.i. How to Graph a Natural Monopoly

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POINTS TO FOLLOW The marginal cost curve MC should be flat or slope downwards. Typically, it is drawn flat. The average cost curve A C is always above MC and always sloping downwards. They never intersect. As it gets closer to MC, the curve gets flatter. - Why: The definition of a natural monopoly is that it is a monopoly in which average costs are always declining (at least in the range of quantities that are being produced). As such, costs are minimized by having only one firm produce the good. Because monopoly behavior reduces costs, this is a “natural” monopoly. The demand curve D should slope downwards. The marginal revenue curve MR should also slope downwards. It should have a steeper slope than D, and always be lower than D. The profit-maximizing quantity QM occurs where MC intersects with MR (Red D ot).

The profit-maximizing price PM occurs where QM intersects with D (Green Dot). Average cost occurs where QM intersects with AC (Blue Dot). Profit is a box. The horizontal side of the box goes from the y-axis to QM. The vertical side of the box goes from PM to average cost.

Deadweight loss (DWL) is the area above the MC curve and below the D curve, between QM and the point where D intersects with MC.

Monopolistic Competition 2.9-}. How to Find Short-Run Equilibrium in Monopolistic Competition The steps to finding a short-run equilibrium in monopolistic competition are identical to the steps to finding the equilibrium in monopoly. See 7.c.i—7.c.v.

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If you are given a demand function that is a function of what the other producers do (or how many of them there are), plug in the appropriate values before going to see 7.c.i. For example, if the inverse demand curve is P = 60 — QD — F, where QD is the firm’s production and F is the number of other firms, and there are 18 other firms, then the inverse demand function is P = 60 — QD — 18 = 42 — QD. Other versions of this may require you to plug in other firms’ quantities produced or their average price.

2:11:11 How to Graph Long-Run Equilibrium in Monopolistic Competition Price“

MC

AC

MR

QM

Quantity

POINTS TO FOLLOW I MC should be upward sloping. A C should have a “U” shape, and should intersect with MC at the minimum of AC. I D should be downward sloping and should intersect with the A C curve at exactly one point (it should be tangent to the A C curve).

I MR should be downward sloping, should be lower than D, and should slope down more quickly than D. It should intersect MC directly below the point where D intersects AC. - Why: In the long run, firms enter the market (shifting the demand curve D that the individual firm observes to the left) until there’s zero profit left for the marginal

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firm. That’s when we are in long-run equilibrium. For there to be zero profit, it must be the case that, at the profit—maximizing quantity (where MR = MC), the firm makes zero profit (P = AC). S o , w e must draw it so that MC intersects MR at

the same quantity that D intersects AC.

The profit-maximizing quantity Q occurs where MC intersects with MR (Red Dot). The profit-maximizing price PM occurs where QM intersects with D (Green Dot). Profit should appear nowhere, since it’s 0 . Deadweight loss (DWL)

i s the area above the MC curve and below the D curve,

between Q and the point where D intersects with MC.

Price Discrimination 1.9;! How to Graph Perfect (First-Degree) Price Discrimination

(1*

Quantity

POINTS TO FOLLOW

I MC can slope upwards or be flat. Here it is drawn to slope upwards. I Demand curve D should slope downwards. I MR i s the same curve as D.

- Why: In perfect (first-degree) price discrimination, each consumer is charged their own price. If you want to sell another unit, you don’t have to lower everyone

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else’s price to do it. So, the marginal revenue is just the price you sell the next unit at, which is given by the demand curve. The demand curve and the MR curve are the same. I The quantity produced, Q*, is the efficient quantity, found where demand crosses with MC (Red Dot); in other words, where P = MC, like we want from an efficient quantity. I The entire surplus of the market is the area between the D curve and the MC curve. This surplus is entirely producer surplus. There is no deadweight loss or consumer surplus. - Why: If the seller can charge each person a different price, they can just charge the consumer the most the consumer is willing to pay. If the seller does that, the entire surplus of the transaction goes to the seller, since the consumer doesn’t value the good any more than they paid for it. And since the seller gets the entire surplus, they will want to make that surplus as big as possible, and will choose to eliminate deadweight loss.

Lei! How to Graph Less-than-Perfect (Third-Degree) Price Discrimination

POINTS TO FOLLOW

I Third-degree price discrimination entails charging different prices to different groups of people. There are several ways to model this. One way is to simply solve it as multiple standard monopoly problems (for example, solving 7.c.i—7.c.v for

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women using the “female demand curve,” and then again for men using the “male demand curve”). This particular graph does not show how the optimal prices are selected, but i t does show profit, consumer surplus, and deadweight l o s s are

found given the prices chosen, assuming that prices are charged based on marginal value (M V)—that is, high M V consumers pay high prices, low M V consumers pay low prices. I MC can be flat or upward sloping, but typically it is flat for simplicity. I D should be downward sloping.

I Mark the different prices charged, here P1 , P2, P3. I The quantity purchased at a price of P1 is Q ] , where P ] intersects with D. The quantity purchased at a price of P2 is Q2 — Q ] , with Q2 coming from where P2 intersects with D, and so on. - Why: Each person is only allowed to purchase at the price closest to their marginal value. S o Q2 — Q ] is sold at a price of P2 since in total Q2 will be sold at that price or above, but Q 1 of that is sold at the higher price P I . I Deadweight loss (DWL) is the area to the right of the total quantity sold (the actual quantity), to the left of the point where MC intersects with D (the efficient quantity), and between D and MC. This area represents surplus-creating sales that are not made. If the lowest price is equal to MC, then there is no DWL.

I Consumer surplus (CS) is all the areas below demand and above the price that that part of the demand curve pays. I Profit/producer surplus is the area below the price that that part of the demand curve pays and above MC.

Z-e-Jii. How to Calculate Hurdle (Second-Degree) Price Discrimination WHAT YOU NEED TO START: A marginal cost MC and an individual demand curve for each consumer. This example will assume each consumer i s identical, and that mar-

ginal cost is constant/fiat, as you are unlikely to see more complex versions of this model in a Principles course.

STEP 1

WHAT YOU DO Solve MC and demand together to find the efficient quantity to sell to each consumer.

Example: If MC = 1 0 and each consumer has the individual inverse demand curve P = 24 — 2QD, then the firm will sell each consumer a quantity: P 2 MC

WHY

24 — 2QD = 1 0

[Substitute in]

14 — 2QD = 0

[Take 1 0 from each side]

14 = 2 Q

[Add 2 Q to each side]

7 = Q*

[Divide each side by 2]

With a two-part tariff, the firm will be able to extract the entire surplus,

and so it wants to make that surplus as big as possible. It does this by selecting the efficient quantity, which occurs when P = MC, where P is set by demand. So, we solve demand and MC together.

STEP 2 WHAT YOU DO Calculate the consumer surplus (CS) each consumer would receive if sold the efficient quantity at a price of P = MC. If the inverse demand function is a straight line (i.e. is of the form P = a — bQD), then CS can be calculated using the formula:

CS= (MvO — MC)Q* / 2 where M V0 is the marginal value of the good at a quantity of O, or the y-intercept of the demand curve.

Example: If MC = 1 0 , Q * = 7 , and each consumer has the individual inverse

demand P = 24 — 2QD, then M V0 = 24 — 2(0) = 24 and each consumer gets:

CS = (24— 10)7 / 2 CS=(l4)7/2=49

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The firm will know how much it can charge the consumer based on how much consumer surplus they get. Once it knows that, it knows how much it can squeeze that consumer!

STEP 3 WHAT YOU DO The firm will then charge a price of P = MC for each unit, but it will charge a tariff equal to the consumer’s CS for the right to shop. It will earn a profit equal to each consumer’s CS multiplied by the number of consumers.

Example: consumers, MC = 1 0 and each consumer would get CS = 49 at P = 1 0 without a tariff, then the firm will charge 49 for the right to shop, and will earn a profit of 49 * 1000 = 49,000.

If there are

WHY

The firm wants to take the entire consumer surplus for itself, and so it will charge an entry fee equal to the consumer surplus that would have been created without the fee. Consumers are just barely willing to shop with the firm. Since the firm makes no profit on the sale of each unit (because MC is flat and equal to P), the firm makes all its profit from the tariff/entry fee.

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185

PRACTICE Follow-the-Steps Questions To solve, follow directions

from one or more of the sections above.

1. Billboards are provided in a market run by a monopoly, ClarityStream. The demand for billboards is P = 1600 — 20QD.

a. Calculate the function for ClarityStream’s marginal revenue. b. Calculate marginal

revenue at Q = 10, 20, 30, and 40.

0. Calculate profit-maximizing quantity if MC = l.000. Satellite radio is provided by a monopoly. The marginal cost for providing satellite radios is MC = 10 + (Q/ 10). The demand function for satellite radios is P = 10,000 — 5.5QD. Calculate the profit-maximizing price and quantity that the monopoly will choose. The demand function for musical tonal bells is P = 5 2 — QD. Musical tonal bells are produced by a monopoly Philly Bells (nobody else has ever managed to make them quite as good). The total cost of producing bells is TC = 48 + 4 Q + Q2, which means that marginal cost is MC = 4 + 2Q. Calculate the optimal price, quantity, and profit. Consider the market monopolized by Philly Bells in Question 3. Calculate the deadweight loss generated by the monopoly, relative to efficient production. Consider the market for solar panels, which are produced by a monopoly. The marginal cost of producing solar panels is MC = 40 + 2Q, and the demand function for solar panels is P = 440 — Q0. The total cost curve is: TC = 30,000 + 40Q + Q2 Calculate the optimal quantity and price as well as the profit, and then graph and label MC, AC, P, Q, and profit.

Draw a graph of a natural monopoly such that the profit-maximizing quantity is QM = 500. Then, show on the graph what AC would be if the firm instead produced QM = 250. Finally, describe how the comparison of these two quantities

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shows that the market is more efficiently handled by one firm than by multiple firms. Consider the market for hamburgers, which is a market in monopolistic competition. In this market, one of the producers is Barry’s Burgers. The current demand function for each firm in the market is P = 40 — Q0. The marginal cost of producing burgers is MC = 10 + Q and the average cost is AC = 1 0 + (Q/2). a. Calculate Barry’s Burgers’ short-run optimal price, quantity, and profit. b. What will happen to the demand curve for Barry’s Burgers next? c. What is Barry’s Burgers’ profit in the long run? Consider the market for online advertising, which is run by a monopolist who has enough information on consumers that it can engage in perfect (first-degree) price discrimination. If demand for online advertising is P = 60 — 2QD and the marginal cost of producing advertising is MC = .5 Q, then calculate the consumer surplus and producer surplus in the market for online advertising. Movie theaters charge two different prices for tickets—one for seniors and one for everyone else. If seniors have lower marginal valuations than everyone else, and the price for seniors is still higher than the efficient level, graph MC (as a horizontal line), D, PS, CS, and DWL in this market.

Concept Questions A. Consider the following demand schedule. Using this demand schedule, calculate marginal revenue for each quantity Q = 2 to 4. P

Q1)

100

l

90

2

8O

3

7O

4

B. If you ask the average person why companies raise prices, they’ll tell you it’s to make more profit. But when economists study monopolies, we say that the profit-maximizing price is not the highest price they could set. Give an intuitive

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187

explanation (without referring to MR or MC) about why monopolies only raise prices to a given level, and don’t raise them any further. Use the relationship between (1) how a firm chooses its profit-maximizing quantity, (2) how a firm chooses its profit—maximizing price, and (3) where marginal revenue comes from, to explain intuitively why P > MC at the profit-maximizing point for a monopoly. Which of the following is a market with a barrier to entry? Select all that apply. a. To put off competition, SodaSoap has bought up the entire production capacity of every soap-pump-making factory for the next five years. b. Decades ago, Gary developed an extremely popular cartoon character, and he still holds the copyright.

c. In the market for chocolate, each chocolate company has its own secret recipe. (1. In the early days of aviation, there only existed one firm that had figured out the correct engineering to make a plane fly. Draw a graph of a monopoly firm, including MC, AC, D, MR, and the profitmaximizing QM and PM, as well as the profit and deadweight loss. Then, show

how a price ceiling (a maximum price that cannot be exceeded) can improve efificiency in the market. Consider the market for airplane bays. Because there are huge startup costs for airports, generally they are thought of as being a natural monopoly. But if the market grows big enough, it can lose this distinction. Consider care— fully the notes in 7.c.vi. If the total and marginal costs for airplane docks are TC = 1,000,000

+ Q 2 and MC 2 2 Q , i s this market a natural monopoly if we think

that the market will never ever get bigger than Q = 100? Q = 500? Q = 2000? For each of the following, is it best described as a monopoly, an oligOpoly, monopolistic competition, or perfect competition? a. [Market for coffee] There are many different brands of cafes, but each produces a cup of coffee that isn’t quite the same as all the others. b. [Market for diamonds] One company owns all the mines that are the only source for diamonds in the world. c. [Market for chicken] A few companies have bought up many chicken farms, each making more or less the same quality of chickens. The firms own a huge chunk of the market.

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H. In the short run, we figure out what a firm will do in a monopoly or a monopolistic competition in the same way. However, in the long run, we say that profits go away in a monopolistic competition, but the profits stick around in a monopoly. Explain why this is. Consider a market for a supermarket with a member’s fee. You can’t enter the market without paying the fee. Each consumer’s demand function for the market’s products is P = 80 — ZQD, and the marginal cost of production is MC = 16. Calculate the fee the supermarket will charge to shop there to maximize profits, the price the market will charge per unit, and the number of units each customer will purchase.

Glossary and Concepts Oligopoly is a market in which there are a few firms operating. There is more than one, but still a small enough number that firms have pricing power. A game is a way of describing a strategic interaction in which your payoff depends not only on what you do, but also on what others do. A game consists of (1) players who play the game, (2) a list of possible actions they can choose, and (3) a set of payoffs for each player that depends on the actions of all the players, not just their own. A simultaneous game is a game in which each player chooses what to do without knowing what the other players have chosen. For example, rock/paper/scissors is a simultaneous game since you have to choose whether to play rock, paper, or scissors without knowing what the other person has chosen. A game table (or normal form) is usually used to depict simultaneous games. These tables show one player’s options on the rows of the table, the other player’s options on the columns of the table, and the payoffs in the cells of the table. A sequential game is a game in which at least one of the choices made in the game is made after finding out what the other player has chosen. For example, chess is a sequential game, since you see what move the opponent has made before choosing your own move.

A game tree (or extensive form) is usually used to depict sequential games. These are branching trees that split every time a player makes a decision. The payouts for each set of outcomes are shown at the end (“leaves”) of the tree.

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A best response is the strategy you play that gives you the best payout possible given what the other person is doing. For example, in rock/paper/scissors, since paper beats rock and scissors beats paper, paper is the best response to rock, and scissors is the best response to paper.

A Nash equilibrium is a solution to a game in which all players are playing best responses at the same time. So, what I’m doing is the best response to what you’re doing, and what you’re doing is the best response to what I’m doing. When this happens, no player will want to change strategies. Backwards induction is a method for solving a sequential game in which you figure out how players would react in the final choices of the game, and work backwards from there. A prisoner’s dilemma is a game in which players can either c00perate with, or betray, each other. Both players prefer the outcome where they both cooperate to the outcome where they both betray, but their individual incentives tell them to betray. The Nash equilibrium of a prisoner’s dilemma is for both players to betray each other, even though everyone would be better off if they both cooperated. One example of a prisoner’s dilemma is firms in an oligopoly setting high prices (cooperating), or setting low prices and taking over the market (betraying). A dominant strategy is a strategy that is always your best response, no matter what the other person does.

Repeated interaction refers to the idea that players can play a non-Nash equilibrium outcome if they interact with each other repeatedly, since it gives each player an opportunity to punish the other one for not cooperating. This is one way to get a better outcome in a prisoner’s dilemma.

How to Draw a Game Table

(Normal Form) for Simultaneous Games WHAT YOU NEED TO START: Two people, two or more actions they can each take, and the payoffs that they get for each combination of actions.

STEP 1 WHAT YOU DO First, decide which player will be on the left (so their actions will be on the rows of the table) and which player will be on the top (so their actions will be on the columns) of the table. Generally, if the players’ names have a natural order (“Player A and Player B” or “Player 1 and Player 2”), the first name will go on the left.

Example: In a game played by PlayerA and Player B, PlayerA will go on the left and Player B will go on top. WHY

We are drawing a game table here, so we need to decide where on the table each player goes! Who goes where exactly is arbitrary, as the table would work just as well if you put Player A on top and Player B on the left.

STEP 2 WHAT YOU DO Draw a table with one row for each action the player on the left can take, and one column for each action the player on the top can make. Fill in the actions that can be taken in the row and column headings.

Example: If Player A on the left can play Up, Middle, or Down, and Player B on top can play Left or Right, then we draw the table: Player B Left

Right

Up

Player A

Middle Down

WHY

The point of a game table is that we can look at the outcome of each combination of choices. By putting each action Player A can take on its own row, and putting each action Player B can take on its own column,

each cell then can show the result of combining those two actions.

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STEP 3 WHAT YOU DO Fill in each cell with the payouts according to the actions in that row and column. The payouts can be written to explicitly say who gets what payout (“PlayerA gets 5, Player B gets 2”), or they can just write the numbers (“5, 2”). If only the numbers are included, the first number is the payout for the player on the left. You may also see payouts written by drawing a diagonal line across the cell, putting the left player’s payout in the bottom-left comer, and the top player’s payout in the top-right comer.

Example: Player A playing Up and Player B playing Left gets A a payout of 4 and B a payout of 14; Up and Right gets 6 and 10; Middle and Left gets 6 and 6 ; Middle and Right gets 8 and 12; and Down gets 7 and 5 no matter what B does. Therefore, the game table is: Player B Left

Player A

Right

14)

10)

Up

(4,

Middle

(6, 6)

(8, 12)

Down

(7, 5)

' » (7, 5)

(6,

or, equivalently

Player B Left

6

10 ,

Middle

6 8

12

Down

5

Up

Player A

Right

, 14

7

5

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193

The payouts for each combination of activities go into the cell that is produced by combining the row action with the column action. So, if Player A going Up and Player B going Right leads to a payout of 6 for A and a payout of 1 0 for B, then (6, 10) should go in the cell in the Up row and the Right column.

How to Find Nash Equilibria in a Game Table WHAT YOU NEED TO START: A game table (normal form) depicting a simultaneous game. See 8.b for how to draw the table if you only have a description of the game in words.

STEP 1 WHAT YOU DO Start with one of the options that the player on the left has. Then, put yourself in the shoes of the player on the top. Think “if I knew for certain that my opponent would choose this strategy, how would I want to respond?” Finally, circle or highlight the payout that represents this best response.

Example: For the game table below, we start considering the Up action for Player A . If Player A plays Up, Player B could either play Left and get 14, or play Right and get 10. Since 14 is better than 10, we circle or highlight the 14. Player B Left

Player A

Up

(4, 14)

(6, 10) '

Middle

(6, 6)

(8, 12)

I ' (7, 5)

' I (7, 5)

Down WHY

Right

A Nash equilibrium occurs when each player is playing a best response to whatever the other person is doing, at the same time as everyone

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else is playing a best response to what they’re doing. When this happens, no player will want to change what they’re doing (that’s what makes it an equilibrium). So, to find the Nash equilibrium, where everyone is playing a best response, we need to find out what those best responses are. We start off here with Player B’s best response to the Up strategy.

STEP 2 WHAT YOU DO Repeat Step 1 for the other actions that the player on the left could choose.

Note that there might be more than one best response—if the player on top has two or more actions that all give the same payout, and that’s the best payout, all those actions are best responses!

Example: For the game table below, in response to Middle, Player B can go Left and get 6 or Right and get 1 2 ( l 2 is better, highlight it). In response to Down, Player B gets 5 no matter what, and so both Left and Right are equally “best” responses. We highlight both Ss. Player B

Player A

Left

Right

Up

(4, 14)

(6, 10)

Middle

(6, 6)

Down WHY

(7, 5)

(8, 12) A,

(7, 5)

We do this for the same reason as in Step 1. When it comes to the response to Down, Player B doesn’t really care which strategy he or she plays! Each option is equally good, and they’re both in the group of responses you’d call “best” responses. So, we highlight them both.

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STEP 3 WHAT YOU DO Repeat Step 1, but reverse the roles. Now, for each strategy that the player on top could play, select and highlight the best response of the player on the left.

Example: For the below game table, in response to Left, Player A could play Up and get 4, Middle and get 6, or Down and get 7. Since 7 is better than 6 or 4, we highlight the 7 . Similarly, we highlight the 8 in response to Right. Player B

Player A

WHY

Left

Right

Up

(4, 14)

(6, 10)

Middle

(6, 6)

(8, 12)

Down

(7, 5)

(7, 5) .

We do this for the same reason as in Step 1.

Remember that this time we’re interested in Player A picking the action that is the best response for them. The key here is that A doesn’t really care what B gets—A isn’t vindictive. So, in response to Right, for example, A will pick Middle rather than Down, even though A gets “more” than B with ( 7 , 5 ) , and “less” than B with ( 8 , 1 2 ) . But A

doesn’t care. All A cares about is 8 > 7.

STEP ‘4 WHAT YOU DO Any cell in which both payouts are highlighted is a Nash equilibrium outcome. The strategies that lead you to that cell are a Nash equilibrium.

Keep in mind that you may end up with more than one Nash equilibrium. You may even end up with zero Nash equilibria for some games!

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Example: For the game table below, both payouts are highlighted in the “Down, Left” cell and the “Middle, Right” cell. And so, we have found two

Nash equilibria: (1.) Down, Left and (2) Middle, Right. Player B

Left

Up Player A

WHY

Right

. (4,-14)

(6, 10)

Middle

(6, 6)

(8, 12)

Down

(7, 5)

(7, '5)

Since we were circling only best responses in Steps 1—3, any cell in which both payoffs are highlighted is a cell in which both players are playing best responses at the same time. That’s the definition of a Nash

equilibrium! As an aside, the result that we could end up with zero Nash equilibria will turn out to not be quite true once you begin learning about “mixed strategies.” But as interesting as those are, they’re not something you’ll likely to have to worry about in your Principles class.

How to Draw a Game Tree (Extensive Form) for Sequential Games WHAT YOU NEED TO START: A description of a sequential game, including the payouts for each combination of actions.

STEP 1 WHAT YOU DO First, list all the decisions that must be made in the game, including what leads

options are.

to that decision,

who makes the decision,

and what the

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Example: Let’s consider a negotiation game where Jill and Bob are splitting $1. First, Jill can propose a 50/50 split or a 75/25 split in her favor. Second, Bob can either accept the proposed split or reject it. Finally, if Bob rejects a 75/25 split, Jill can choose to force Bob to accept a 10/90 split in his favor, or can choose that nobody gets anything. The decisions in this game are:

1 . Jill can choose a 50/50 split or a 75/25 split. 2. If Jill chooses a 50/50 split, then Bob can choose to accept or reject. 3. If Jill chooses a 75/25 split, then Bob can choose to accept or reject.

4. If Jill chooses 75/25 and Bob chooses to reject, Jill can choose 10/90 split or nothing. WHY

The key to drawing a game tree correctly is to make sure that you have correctly ordered and constructed each decision. Each choice made depends on the choices that came before it, even if the options are the same. For example, Bob choosing to accept or reject after a 50/50 split is a different choice than Bob choosing to accept or reject after a 75/25 split, and so we need to model both decisions separately. We also need to be careful to keep track of the order of the decisions to draw the game tree correctly.

STEP 2 WHAT YOU DO Starting from the first decision made, draw a “node” (a dot or circle) and label the node with the name of the person making the decision. Draw “branches” (lines) from that node, one for each available option,

and label them.

Your tree can run from left to right, or from top to bottom, as shown in the following example.

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Example: For the game described in Step 1, the first decision is made by Jill deciding whether to offer a 50/50 split or a 75/25 split. So, we draw a node and label it Jill, and then draw two branches, labeling them

“50/50 split” and “75/25 split.”

WHY

In a game tree, w e are trying to draw a branching path that describes the course that the game could take. Each decision point is a “node” that branches out based on the available actions that could be taken (the different ways the game could play out).

STEP 3 WHAT YOU DO At the end of each branch, if that branch ends the game, label the payouts that would result from the game taking that path.

Example: For the game described in Step 1, if Jill offers 50/50, it leads to Bob deciding between accepting and rejecting, so we draw a node for Bob with an “accept” branch, which ends the game with a payout of (.50, .50) and a “reject” branch, which ends the game with a payout of (0, 0 ) . The rest of the tree can also be drawn i n this manner.

Jill

Reject

Accept

Reject

ACCEDt

(0,0) (.50,.50)

WHY

1090 sp It

Nothing

(.10,.90)

(0,0)

We continue drawing the tree in the same way as Step 2, describing the different paths the game could take. When we get to a path that ends the game (for example, when Bob chooses to reject the 50/50 split), we tally up the payouts for each player. Payouts are often written as two numbers, with the first payout referring to the payout for the player who went first. So, if Jill offered 75/25, for example, and Bob accepted, the payout would be (.75, .25).

How to Solve a Game Tree WHAT YOU NEED TO START: A sequential game described using a game tree (extensive form). See 8.d for how to draw the game tree if it is not already drawn.

STEP l WHAT YOU DO You are going to start with the end of the game and work backwards. Select a decision for which each option leads to a known payout. Determine who is making that decision, and have them choose the option that leads to their highest payout. Then, circle the option they chose, and write in the payout it leads to next to their name on the node.

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Example: For the game tree below, we can start with Jill’s decision to force a 10/90 split or offer nothing after Bob rejects a 75/25 split. This is Jill’s decision, and she prefers a payout of .10 to 0, so she chooses to offer the 10/90 split. We circle “10/90 split” and write the resulting payout, ( . 1 0 , .90), next to the decision node. Jill

(0,0) (50,.50)

WHY

( 10,

90)

(75,25)

90 10. 5 0 It

Nothing

(.10,. 90)

(0,0)

Backwards induction is a process of solving game trees. The idea here is that each player is trying to predict how the other players will respond to their actions.

If we start from the beginning of the game, Jill will think “Should I offer a 50/50 split or a 75/25 split? It depends on how I think Bob will respond.” She can’t make her decision until she knows how Bob will respond. So, we have to look to the end of the game to predict responses, so we know what decisions are made at the top of the tree. Formally, this will give us what’s called a subgame-perfect

Nash

equilibrium. There are other ways to solve game trees that give “non— subgame-perfect” solutions, but generally you will not see those in a Principles course. So, we just refer to these solutions as Nash equilibria for short.

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STEP 2 WHAT YOU DO Repeat Step 1 until you’ve determined which option will be chosen at every node. As you determine more nodes, you can “move up the tree,” since you’ll now know what payouts each option leads to.

Example: Since in Step 1 we determined that Jill would choose “10/90 split” over “reject” if given the chance, giving a payout of (.10, .90), we can figure out what Bob will do if offered a 75/25 split. Bob knows that he can accept the split and get a payout of .25, or reject it and get .90. He

prefers .90 to .25, and so will choose to reject. We then circle “reject” and write ( . 1 0 , .90) next to B o b ’ s decision node. Jill

(0,0)

WHY

Jill (.10,.90) (.75,.25)

(50,50) 1 0 .90 5 0 It

Nothing

(.10,.90)

(0,0)

Having solved later decisions in the game tree allows the players to predict what will happen if they do reach that part of the tree. Therefore, they can now make their decisions with full knowledge of the consequences.

STEP 3 WHAT YOU DO Once every decision is determined at each node, the “Nash equilibrium outcome” is the payout that the players get because of playing out the game as it has been solved. The set of “Nash equilibrium strategies” is

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the full list of choices the players make, even if they never actually get a chance to play them out.

Example: From Step 2 , we know that if Bob i s offered the 75/25 split, he’ll

Reject, then Jill will offer the 10/90 split. We also know that if Jill offers the 50/50 split, Bob will Accept. S o , if Jill offers 7 5 / 2 5 , she’ll end up with . 1 0 , and if she offers 50/50, she’ll end up with . 5 0 . Since . 5 0 i s better than . 1 0 , Jill will offer a 50/50 split, which Bob will

accept. The Nash equilibrium outcome is (.50, .50). The full set of Nash equilibrium strategies i s “Jill offers 50/50, Bob accepts 50/50,

Bob rejects 75/25, Jill offers 10/90 if Bob rejects 75/25.”

(0,0)

(50,50)

10 _90

J'II (I.10 .90) (.75,.25 ) Nothing

5 0 It

(.10,.90)

WHY

(0,0)

This process leads to the Nash equilibrium because it ensures that nobody wants to change what they’re doing, given that they know how people will respond to their choices. Everyone is playing best responses. The set of Nash equilibrium strategies must include the actions that aren’t taken (like how in this Nash equilibrium Bob plans to reject 75/25, but never actually gets a chance to) because we need that information to be sure that the players are playing their best responses. If

we didn’t specify that Bob would reject 75/25, then Jill might want to offer 75/25 thinking that he’d accept it! And that would be wrong.

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How to Predict the Effect of Repeated Interaction on Games WHAT YOU NEED: A simultaneous or sequential game, their equilibria (see S c and S e to solve for equilibria), and an outcome that one or both players would like to achieve but is not the equilibrium. For example, in the prisoner’s dilemma, both players prefer the outcome where both cooperate to the equilibrium outcome where both betray.

STEP 1 WHAT YOU DO First, determine if either player can make a credible

threat or prom-

ise to get to the desired outcome. In other words, if a player said, “I promise that I will do action X,” would the other player have reason to believe them, or would they suspect they were lying? If the players can credibly promise to play the desired outcome, they can reach the desired outcome without needing any repeated interac— tion. If they can’t, go to Step 2.

Example: In the game table below, “Up, Left,” and “Down, Right” are both Nash

equilibria. If Player A says, “I am going to play Up,” then Player B will believe this credible promise, since the best response to Up is Left; and if Player B plays Left, Player A will have no reason not to play Up, which is what he or she promised to do. Player B

Right

Left Player A

u

p Down

_

(2, 2) w (0, 0) 7 » . (0, 0)

’

(1, 1)

However, in the game tree below, if Player B says, “if you offer a 50/50 split, I’m going to reject it, so you’d better offer 25/75 instead!” that would be a non-credible threat. If Player A does offer a 50/50

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split, it’s now in Player B’s interest to go back on their threat and take .50 over 0. So, Player A has no reason to believe what Player B says.

(0,0)

WHY

(.50,.50)

(0,0)

(.25,.75)

In game theory, we assume that people are perfectly rational strategizers (in other words, good game-players). Even if they make a promise or a threat to do something, they’re going to break that promise or threat if it offers them a strategic advantage to do so. Even in the game tree example on the left, it’s not actually in Player B’s interest to follow through on their promise if it comes down to it! Imagine you’re Player B and Player A did offer you a 50/50 split. At this point, it’s too late for your threat to make them change their mind and switch to offering 25/75 instead. So, you may as well forget about the possibility of getting a payout of .75. Your choice is only between .50 and 0 . Since .50 is better than 0, you swallow your pride and accept the offer, failing to follow through on your threat. Player A knows you will act this way, and so doesn’t believe your non-credible threat.

STEP 2 WHAT YOU DO If the desired outcome can only be reached using non-credible promises, the players can reach it anyway if they repeatedly interact with each other. They can turn non-credible promises into credible promises if they will face some punishment for breaking their word. Some examples of these approaches are (1) tit for tat, in which each player cooperates this time if their opponent cooperated last time;

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205

and (2) trigger, in which each player cooperates until their opponent betrays them once, then punishes them by not cooperating for a certain period (if they never ever cooperate again, that’s called a grim trigger). Both encourage cooperation because each player knows that they will be punished if they fail to cooperate.

Example: Consider the price-setting oligopoly game below, which is an example of a prisoner’s dilemma. The payouts are profits in billions of dollars. The Nash equilibrium is (low price, low price). But if these two firms repeatedly set prices, they can each plan to set high prices; and if the other firm suddenly sets low prices, they can punish them with a “price war” by setting their own prices low for some period. Firm B

FirmA Q WHY

High Price

Low Price

High Price

($2b, $2b)

($Ob, $3b)

Low Price

($3b, $Ob)

($1b, $1b)

By setting up a strategy in which each player can punish the other player’s betrayal by implementing their own betrayal, players can enforce any outcome. This allows players to reach better-payoff outcomes even if they’re not the Nash equilibrium, like in the prisoner’s dilemma game. In the context of oligopolies, this applies most directly to price-setting. If you have lower prices than a competitor, you’re going to grab a big chunk of the market. But if you both have low prices, you share the market but sell for a low price, which nobody likes! High prices can be maintained because the firms interact repeatedly with each other, and nobody wants to lower their prices to steal the market because it will start a price war, which is when the other firms retaliate against a price drop by lowering their own pi'ices, ending up in that undesirable (low price, low price) Nash equilibrium.

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PRACTICE Follow-the-Steps Questions To solve, follow directions

from one or more of the sections above.

1. Draw the game table for a game played between two competing oligopolies, Tape Source and Place for Tape. Each must decide whether to invest in R&D. Any innovation will be easily copied and shared by both. So, if neither invests, then each makes

a profit of $40 million. If either o r both invests, each makes a

profit of $60 million, but each firm that invests spends $10 million doing so and so only makes $50 million. 2. Solve for Nash equilibria in the game below in which Fahad and Jacques will decide whether to drive on the left or the right side of the street.

Jacques Left Left

Right

1 0 0 for F

0 for F

1 0 0 for J

O for J

Ri ht

0 for F

1 0 0 for F

g

o for J

100 for J

Fahad

3. Consider the game table you drew in Question 1. Solve for the Nash equilibria in this game. 4. Find the Nash equilibria in the game below in which two oligopoly firms are deciding whether to produce a lot or a little. The more produced overall, the lower the price will be. But each firm wants to sell as many units as possible.

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GAME THEORY AND OLIGOPOLY

Firm

B

Lot

Lot

Firm A

Little

207

Little

$10m for A

$30m for A

$10m for B

$5m for B

5 f A or $30m for B

$

$ m

20

m

f

or

A

$20m for B

5. Consider a game between theater companies Shakes and Bardtron. Each decides which actor to offer the part of Hamlet. If they both approach the same actor, they’ll fight, scaring the actor away and getting 0. If they ask different actors, they get who they ask. There are three actors: John, Mark, and Steve. John is the best; you get 5 if you get John. Mark and Steve are okay. You get 2 if you get one of them. Draw the table and find the Nash equilibria.

6. Consider a game in which Chad has a five-dollar bill that he can keep to himself or give to Raven. If he gives the bill to Raven, then it triples in value to be worth $15. Raven then decides whether to give back $10 to Chad, or give back nothing and keep the entire $15. Draw this game tree. 7 . Use backwards induction to find the Nash equilibrium in the game tree below: New Competitor Enter

hAarket AAarket Leader Raise Pnce

[Dorrt

.

[Dot

Raise . Prlce

Essa £232.? %$1%an)g$8%a) 8. Use backwards induction to find the Nash equilibrium in the game in Question 6.

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Consider a game in which a Market Leader first decides whether to Lobby for a new law making it more difficult to compete in their market. Then, a New Entrant decides whether to Enter the Market, Stay Out, or Enter a Different Market. The Market Leader makes $60m if the New Entrant enters their market, and $ 1 0 0 m

otherwise. The New Entrant makes $80m for Entering Different Market, and $0 for Staying Out. If they Enter the Market, they make $60m if the leader Lobbied, and $100m otherwise. Draw this game tree and find the Nash equilibrium.

10. Consider the game table: Firm B

Hi h Price Firm

A

g

Low Price

Lot

Little

$10m for A

$2m for A

$10m forB

$15m forB '

$15m for A

$5m for A

$2m for B

$5m for B

'

a. Find the Nash equilibrium. b. Explain what the firms will do if they play this game repeatedly, and why.

Concept Questions A. Consider the method for finding Nash equilibria detailed in 8.c. Explain why this method works for finding Nash equilibria. How do we know that a Nash equilibrium found by this method will be guaranteed to be an actual Nash? B. Consider the following version of a game in which each player simultaneously chooses either Heads or Tails. If they choose difi‘erently, both get 0 . If they both choose Heads, both get 2. If they both choose Tails, both get 1. a. Draw the game table and find all Nash equilibria. b. Is “both players play Tails” a Nash equilibrium? Explain why it can be a Nash even though both players would prefer “both players play Heads.”

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209

C . Find the Nash equilibrium on the table below. Market Leader (M)

Enter

Lot

Little

$80m for E

' $Om for E ,

$80m for M

$Om for M

$0m for E $99m for M

$0m for E $40m for M

Entrant (E) Don’t

D. Draw your own game table. Specifically, draw one in which following the steps in 8.c will produce no Nash equilibria! [HINTz Rock—Paper—Scissors is an example of a game like this.] E. You are playing a prisoner’s dilemma, in which you can Cooperate or Betray your partner. You’re both better off if you both Cooperate, but each player’s best response is to Betray. Before making your simultaneous plays, you both agree to Cooperate. Explain whether this is likely to lead to both of you Cooperating. F. Consider a game between Firm A and Firm B. First, Firm A chooses whether to invest. Then, Firm B chooses to advertise A Lot or A Little. The payoffs are (4 for A , 4 for B ) for strategies (Invest, A Lot), ( 1 for A, 5 for B ) for (Invest,

A Little), (2 for A, 2 for B) for (Not, A Lot), and (3 for A, 1 for B) for (Not, A Little). a. Draw the game tree and solve it. b. If Firm A could offer to reverse the order the decisions are made in, would it want to?

c. Would Firm B want to reverse the order? G . Consider a game in which an Entrant first chooses to Enter or Not Enter. If it does Not Enter, then the Market Leader is a monopolist, and the Entrant gets 0 . If it does Enter, then it pays a fixed cost of 100 and colludes with the Market Leader to set the monopoly price. The Entrant gets 1/4 of the market if MC = O for both firms and inverse demand is P = 44 — QD. a. Calculate each firm’s profits if the Entrant Enters, and if it does Not Enter. b. What will the Entrant do in Nash equilibrium?

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H. Consider the “tipping game” in which you (Y) are at a restaurant. The server (S) first either provides Good service or Bad, and then you either Tip or Stiff (don’t tip). The payoffs are (4 for S , l for Y) for (Bad, Tip), ( 3 for S, 3 for Y) for (Good, Tip), ( 2 for S , 2 for Y) for (Bad, Stiff), and ( 1 for S , 4 for Y) for (Good, Stiff).

a. Draw the game tree and find the Nash equilibrium. b. Would you expect people to tip more at restaurants where they’re regulars, or strangers? c. Why do you think people tip at restaurants they’re never going back to? It’s clearly behavior we observe. Have we just designed this particular game in a way that doesn’t represent reality, or can game theory not explain this behavior at all? There’s not a single right answer here.

Glossary and Concepts A good has an externality if the production and consumption of that good have effects on people other than the ones producing and consuming it. A positive externality has a positive effect on others. An example is gardening supplies, which lead to pretty gardens that people get to enjoy looking at even if they aren’t consumers of gardening supplies themselves. Goods with positive externalities are underproduced by the market. That is, because the good creates all these benefits that go to people who aren’t making the decision about how much to produce, the efficient level of the good is higher than the equilibrium market quantity. A negative externality has a negative effect on others; for example, any good that creates pollution as a part of its production, which harms people living near the factory even if they’re not producers or consumers of the good. Goods with negative externalities are overproduced by the market. That is, because the good creates all these costs that go to people who aren’t making the decision about how much to produce, the efficient level of the good is lower than the equilibrium market quantity. A Pigouvian tax is a tax designed with the intent to get the market to produce the efficient level of a good. The tax is applied to goods with negative externalities, for which the market makes more than the efficient amount, and so you want to decrease quantity. If a good has a positive externality, then you would use a Pigouvian subsidy instead to increase quantity up to the efficient level. The Coase theorem suggests a way for private individuals to solve externalities. If the efficient quantity of a good with an externality isn’t already being produced, then everyone involved can work out a deal where the efficient quantity gets produced in

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exchange for payment. For example, say your neighbor burns garbage fires in his backyard and values the ability to do so at $100 per fire. But you value not having the

fire at $120. Since $120 > $100, it’s more efficient not to have the fire. If you have the legal right to stop him from having fires, you stop him. And if he has the right to have fires, you just pay him $100 to stop (which you’re willing to do since $100 is less than the $120 you value for not having fires at all) and he agrees. The Coase theorem only works if everyone affected can negotiate freely and easily, and if the property rights are well defined (i.e. it’s clear whether you have the right to make him stop, or he has the right to make fires).

A good is rival if someone using it keeps others from using it. For example, if you buy a slice of pizza and eat it, someone else can’t eat that same slice, since you already ate it. So, pizza is rival, since it gets “used up” when you use it. But using the light from a streetlight to see doesn’t keep someone else from using that same light, so streetlights are non-rival.

A good is excludable if you can stop people who didn’t pay for it from using it. For example, if you make a pizza, you can refuse to give someone a slice unless they pay you. So, pizza is excludable. But if you build a streetlight, it’s pretty hard to force people to pay you in exchange for seeing the light. Freeloaders walking by will use your light without paying! So, streetlights are non-excludable. Public goods are goods that are non-rival and non-excludable. So, providing a public good offers benefits that don’t get “used up,” and you can’t force people to pay to use them. If someone builds a public good, there’s an incentive to free ride—use the public good (which you can do because it’s non-rival) without paying (because it’s non-excludable). As a result, public goods are underproduced in a competitive market and are frequently provided by the government. Examples of public goods include streetlights (as above) and national defense (the military stops everyone in the country from being invaded, and there’s no way to just let the one person who didn’t pay for the military to get invaded).

Common goods are goods that are rival but non-excludable. So, they get used up when they’re used, but you can’t stop people from using them. As a result, everyone rushes to use the common good right away before it gets used up, and it runs out. An example of a common good is the stock of fish in the ocean when there are no fishing laws, since overfishing will make it run out, and without the laws you can’t stop people from using it.

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Artificially scarce goods (also known as club goods) are goods that are non-rival but excludable. So, letting someone use the good doesn’t really cost anything, since it doesn’t get used up. But you can stop people from using it unless they pay. And so, makers of artificially scarce goods can charge prices above the marginal cost. An example of an artificially scarce good is online downloads. Giving someone a download doesn’t really mean there are “fewer downloads left” so nothing is getting used up. But companies can keep people who don’t pay from getting them. These are sometimes also called club goods because one common way to sell them is to sell memberships in a “club.” Then, everyone in the club can use as much as they like for no additional cost. An example of a “club” like this is most premium music streaming services, where you pay one price for your account, and then can use as much as you like for free.

How to Graph Externalities MSC

Pricell

Pricell

Negative [Externality S

Eggitiven erna ' y S=MSC

I

E

MSB

I I

D=MSB

I

QMARKETQEFFICIENT Quantity

QEFFICIENTQMARKET

Qlla ntity

NOTES TO FOLLOW

I Supply S and demand D are drawn as normal. The market equilibrium QMARKETis the quantity at which they cross. I If there are positive

externalities, then draw the Marginal Social Benefit (MSB)

above D (as in the figure o n the left). If there are no positive externalities,

then

MSB is the same as D (as in the figure on the right).

- Why: Marginal social benefit is the marginal benefit of consumption to all of society. That includes benefits produced through extemalities as well as benefits

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to consumers. S o MSB will always be at least as high as D, since it includes the same private benefits that D does. The difference between MSB and D is the amount of the positive externality. I If there are negative

externalities,

then draw the Marginal Social Cost (MSC)

above 5 (as in the figure on the right). If there are no negative externalities, then MSC is the same as S (as in the figure on the left). - Why: Marginal social cost is the marginal cost of production to all of society. That includes costs produced through extemalities as well as costs to producers. S o MSC will always be at least as high as S, since it includes the same private costs that S does. The difference between MSC and S is the amount of the negative externality.

I If there are both positive and negative extemalities for the same good, draw MSB above D and draw MSC above S (not pictured). I The efficient/optimal quantity QEFFICIENT is the quantity at which MSB and MSC cross. Remember, if there are only positive extemalities, then MSC i s the same as

S, and if there are only negative extemalities, then MSB is the same as D.

How to Find the Efficient

Outcome under an Externality WHAT YOU NEED TO START: A function for supply S and demand D and information about the extemality being produced. If you are already given functions for Marginal Social Cost (MSC) and Marginal Social Benefit (MSB), then skip to Step 2.

STEP 1 WHAT YOU DO Take the inverse supply curve (P as a function of Q). Replace P with MSC, and add on the cost of the negative externality. If there’s no negative extemality, don’t add anything. Take the inverse demand curve (P as a function of Q). Replace P with MSB, and add the benefit of the positive externality. If there’s no positive extemality, don’t add anything.

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215

Example: In the market for electricity, inverse supply is P = 3 + 2QS and inverse

demand is P = 20 — QD. There is a negative externality, imposing a cost of 2 for each unit produced, and no positive extemality. And so MSC=3+2Q+2=5+2Q MSB=20—Q WHY

Marginal social costs and benefits are just the private costs and benefits (as represented by the supply and demand curves) plus any externality imposed on others. And so, to get MSC, we simply take the supply curve and add the external cost. Similarly, to get MSB, we take the demand curve and add the external benefit.

STEP 2 WHAT YOU DO Set MSC equal to MSB and solve for Q. This is the efficient outcome, QEFFICIENT’

Example: If MSC = 5 + 2 Q and MSB = 20 — Q, then: MSC = MSB

WHY

5+2Q=20—Q

[Plug in]

3 Q = 15

[Take 5 and add Q]

QEFFICIENT = 3

WWW? by 3 ]

An outcome is efficient if the total benefit minus the total cost is maximized. This will happen when marginal cost equals marginal benefit. In the context of extemalities, the same idea apples! We just need to be sure to incorporate everyone ’3 costs and benefits. S o , we u s e MSC

and MSB, and when they’re equal we have efficiency.

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Pigouvian Tax or Subsidy 9:92! How to Calculate the Optimal Pigouvian Tax or Subsidy WHAT YOU NEED TO START: A function for supply S and for demand D, and the efficient quantity QEFFICIENT.See 9.c if you do not have QEFFICIENT. Or, if there is a constant negative extemality of $X per unit, and no positive extemality, then a tax of $X per unit will lead to the efficient quantity. Similarly, if there is a constant positive extemality of $Y per unit, and no negative extemality, then a subsidy of $Y per unit will lead to the efficient quantity. In these cases, we know exactly what the external costs and benefits are. Since they’re always the same, we

can simply apply those costs or benefits directly to producers and consumers, making them “intemalize” the external costs/benefits.

STEP 1 WHAT YOU DO Just like you would normally do when calculating a tax (as in 5.d), add the tax per unit T into the inverse supply curve.

Example: In the market for electricity, inverse supply is P = 3 + 2QS. And so, we create the modified supply curve P = 3 + 2QS + T. WHY

Our approach here is going to be this: instead of putting in a known amount of tax and solving for the new quantity (as we would in 5.d), we’re going to put in a known quantity and solve for an unknown tax. So, we start by adding in that unknown tax.

STEP 2 WHAT YOU DO Set the modified supply curve equal to demand, and plug in the efficient quantity QEFFICIENT. Then, solve for T

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217

If T is positive, then it’s a Pigouvian tax. If T is negative, that means that it’s a Pigouvian subsidy (which is equivalent to a negative tax) equal to the absolute value of T.

Example: If demand in the market for electricity is P = 20 — Q0 and the efficient quantity (from 9.c) is QEFHCIENT = 3, then we set:

3+2Q+T=20—Q 3 Q + T : 17

[Take 3 and add Q]

3(3) + T : 1 7

[Plug in]

T: 8

[Take 9]

And so the optimal Pigouvian tax is T = 8. This tax will lead to the efficient quantity. If w e had instead found a negative number, like T = —3 for example,

then a subsidy of 3 would lead to the efficient quantity. WHY

We know that, with a tax imposed, producers and consumers will go about business as normal, but with the tax acting as an additional cost (i.e. they “internalize the cost”). So, we can solve supply and demand together, with the tax included, just like normal. However, we know what we want the quantity to be! We want it to be QEFFICIENT. And so, what we want is to find the Tthat makes the withtax equilibrium quantity be QEFFICIENT. To find that, we just force the quantity to be QEFFICIENT! Plug in QEFFICIENT as the quantity, and then solve for the T that makes the

equation true.

A shortcut you can take here is to notice that the optimal tax will always be the marginal cost to everyone except the producers at QEFFICIENT. Similarly, the optimal subsidy will always be the marginal benefit to everyone except the consumers at QEFFIUENT.

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218

39:11How to Graph the Optimal Pigouvian Tax or Subsidy MSC

Priceyl

s with

Tax

Price“ Subsidy

IWSC S I

i

:

:

[MSB

I

:

:

I :

D =_MSB

QEFHOENTQMARKET Quantity

I

I I l

D with

SUbSldy

D >

QMARKETQEFFICIENT Quantity

NOTES TO FOLLOW Graph supply S, demand D, marginal social cost MSC, marginal social cost MSC, the market quantity QMARKET,and the efficient quantity QEFFICIENT as normal (see 9.b).

If the market overproduces the good (Q EFFICHENT < QMARKET), then add a tax. Shift the supply curve up until it intersects with demand at QEFFICIENT (Red dot). Note that this isn ’t necessarily the same as making supply match MSC exactly (although that might end up being what happens).For example, in the figure on the left above, S and MSC have different slopes, and when you shift S straight up with the tax, it retains its old slope. If the market underproduces the good (QEFFICIENT > QMARKET), then add a subsidy. Shift the demand curve up until i t intersects with supply at QEFFICIENT (Red dot). Note that this isn’t necessarily the same as making demand match MSB exactly (although that might end up being what happens). For example, in the figure on the right above, because there’s both a positive and negative extemality, D doesn’t shift quite as high as MSB in order to get S and D to cross at QEFFICIENT.

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How to Use the Coase Theorem

to Solve an Externality WHAT YOU NEED TO START: A situation in which the Coase theorem applies, and information about the value each person places on the extemality-causing activity happening or not. (Everyone involved can negotiate with each other without cost, and property rights are clearly defined.) The steps below will detail how to solve an extemality using the Coase theorem specifically for a situation that involves only two people, and an activity that either

happens or doesn ’1‘ (rather than something that could happen more or less). The same principles apply to more complex scenarios, but it gets tricky pretty quickly, and you don’t often see those sorts of scenarios in Principles courses.

STEP 1 WHAT YOU DO First, determine whether it’s more efficient for the activity to happen or not. Calculate the value that would be generated if it does happen, and then calculate the value that would be generated if it doesn’t. Whichever one generates the higher value is the efficient option.

Example: Jerry puts a value of $200 on letting his dog roam free outside. But the dog always chews up the vegetables in Adrian’s garden. Adrian puts a value of $150 on the dog not being allowed to roam free (and thus not chewing the veggies).

If the dog roams free, it generates $200 of value. If the dog doesn’t roam free, it generates $150 of value. Since $200 > $150, it’s more efficient for the dog to roam free. WHY

The Coase theorem is one way of solving extemalities. And what we mean by a “solved” extemality is that the efficient outcome is reached. And so, for everyone involved to negotiate to reach the efficient outcome, they first need to figure out what that efficient outcome is!

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The efficient outcome is simply whatever generates the most surplus. Whichever outcome happening leads to the highest value being generated (relative to any costs) will create the most surplus, and thus be the efficient option. STEP 2 WHAT YOU DO Determine who has the legal right to determine what happens.

If the person who prefers the efficient outcome has the legal right to get their way, then we’re done! The efficient outcome happens and negotiations end.

If the person who prefers the inefficient outcome has the legal right, then go to Step 3.

Example: Continuing from Step 1, if Jerry has a right to let his dog do whatever he wants, then negotiation ends without any money changing hands, and Jerry’s dog continues to roam free. However, if Adrian has a right to a dog-free veggie growing environment, then negotiations start in Step 3. WHY

If the person who prefers the efficient outcome has the legal right, then there’s really nothing to negotiate. Adrian could try to offer Jerry money to stop his dog, but Adrian isn’t willing to pay more than $ 1 5 0 , and Jerry w o u ld rather let h i s dog roam free than accept

anything lower than $200. Adrian simply doesn’t care enough to change Jerry’s mind. STEP 3 WHAT YOU DO The person who prefers the efficient outcome, but doesn’t have the legal right, will pay the person with the legal right in exchange for permission to carry out the efficient outcome.

They will offer to pay exactly as much as the person with the legal right values their legal right.

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Example: If Adrian has a right to a dog-free veggie growing environment, he

values that right at $150, since he’s $150 happier with his un-gnawed veggies than without. However, Jerry will offer to pay Adrian $150 in exchange for Adrian giving Jerry permission to let his dog roam free, and Adrian will accept. Jerry’s dog will roam free, which is the effi— cient result.

WHY

Since we determined the efficient outcome in Step 1 by asking who values their outcome the most, and since the legal right in Step 3 belongs to the person who values the inefficient outcome, by defini-

tion, the person with the legal right values their outcome less than the person without the legal right does. And so, there are potential gains from trade to be made! Jerry, who values his outcome at $200, is perfectly happy to offer $150 to Adrian for the right to let his dog roam free. Adrian will accept since he only values his veggies at $150 anyway. And so, no matter who has the legal right, we end up with the same efficient outcome.

How to Distinguish Types of Goods STEP 1

WHAT YOU DO First, determine whether the consumption of the good in question is rival or non-rival.

Consumption of the good is rival if someone using it means that there is less left over for someone else. It gets “used up” when someone uses it.

Note that some goods can be rival sometimes and non-rival at other times.

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Example: Art museums are usually non-rival, since someone walking around looking at the art doesn’t make it any more difficult for other people to do so. However, if the museum starts to get crowded, then i t becomes rival,

because the crowded room means that adding another person might actually make it harder for other people to use the museum. WHY

Whether consumption is rival is an important way of categorizing goods. This is because rival and non-rival goods consumption work in very different ways. With rival goods, you must make a new unit every time someone wants to consume more. With non-rival goods, you can make one unit that can be used repeatedly by a whole lot of people!

These are fundamentally different things. Are you producing one per person, or one per everyone? STEP 2 WHAT YOU DO Second, determine whether the good in question is excludable or non-excludable.

The good is excladable if you can stop people from using it if they haven’t paid.

Example: A huge fireworks display in the sky is non-excludable because you can’t stop people from watching it just because they haven’t bought a ticket. You can’t “turn off the show” for just the people who didn’t buy tickets.

On the other hand, a tiny fireworks display on the grass in your backyard is excladable. If you want to stop someone seeing it, you can plausibly keep them from coming into your backyard.

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Whether a good is excludable will have serious implications on how that good is produced and how the market for it works. It’s difficult to create functioning markets around goods that are non— excludable, since it’s hard to recoup your costs of production. If you make the good available, nobody really has any reason to pay you for your hard work, since you can’t stop them from consuming it without paying.

STEP 3 WHAT YOU DO Then, determine the type of good using the below table: Rival

Non-Rival Artificially

Excludable

Private Goods

Scarce Goods/ Club Goods

Non-Excludable

Common Goods

Public Goods

Example: Private goods are rival and excludable, the kinds of goods we’ve focused on in every chapter outside of this one. They include goods commonly sold i n markets like coffee mugs, books, cars, and shelves.

Artificially scarce/club goods are excludable but non-rival. They include goods like museums when they’re not crowded and digital downloads.

Common goods are rival but not excludable. They include many types of natural resources like fi s h or forests, when there aren’t mechanisms

in place to make them excludable.

Public goods are non-rival and non-excludable. They include many goods typically provided by governments or collectives, like national defense and streetlights. WHY

The table above is simply based on the definitions of public, private, common, and artificially scarce goods.

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If you’re having trouble trying to figure out whether a particular good i s rival/non-rival or excludable/non-excludable,

i t sometimes helps to

work backwards a bit. Look at the kinds of outcomes you get for that good (see 9.g.i—9.g.iii for help) and then see if you can back out the type of good it is. Let’s take traffic as an example. “Non-toll highways” are a kind of good. But what kind of good? It seems clear that highways are nonexcludable, at least if there aren’t any toll stations. But are they rival? We can think about the outcome. We often get traffic jams on highways. That indicates a rush to over-consume the good. That’s something that happens with common goods! And thinking about it, if the highway is near—jammed, then adding more cars certainly makes it harder for others to use it. S o at least sometimes, highways are common goods and thus rival in consumption.

How to Find Efficient and Market Outcomes for Different

Types of Goods 9.9;! Public Goods WHAT YOU NEED TO START: Information on the marginal cost MC of providing the public good, and the marginal benefit MB received by each person who benefits from the public good being around (or the willingness to pay, which is the same thing as the MB).

STEP 1 WHAT YOU DO First, add up each person’s individual MB to get the total MB of the public good being produced. Let’s call this the marginal social benefit, MSB. If you have graphical representations of MB, then add them up vertically:

Price“

3+4=7

MSB

Quantity

Or, if you have functions that give you MB, then just add up all the M33. If MBl = 1 0 — Q and M32 = 20 — 2Q, then:

MSB=10—Q+20—2Q=30—3Q Then, find the quantity for which MC = MSB (or, if there i s no such

quantity, the highest quantity for which MSB > MC). This is the effi— cient level of the public good, QEFHCIENT.

Example: Kyung and Harrison are roommates.

The marginal benefit they receive

from each piece of art hung on the shared wall of their apartment,

measured in dollars, is:

MBKYUNG MBHARRISON

Q 1

$20

$15

2

$10

$12

3

$5

$10

And so, to get MSB, we add together their individual MBs: Q

M BKYUNG

M BHARRISON

M 53

1

$20

$15

$35

2

$10

$12

$22

3

$5

$10

$15

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If the marginal cost of a piece of art is $15, then the efficient quantity of art to purchase is QEFFIGENT = 3, since at that quantity, MC 2 M58. WHY

Because public goods are non-rival, the same unit purchased can be used by everyone. And so, if we want to know the real marginal benefit of adding another unit, we have to add up everyone ’5 marginal benefit, since they all get to use it.

And once we know the real, total marginal benefit, we find the optimal quantity the same way w e always do (the same way w e started doing all the way back in 4 e ) and set marginal cost equal to marginal benefit

Also, sanity check—is the art really a public good? Kyung looking at it d o es n ’t leave less art for Harrison to look at, so it’s non-rival

(checkl). And if it’s in the common room, Kyung can’t force Harrison to pay to look at it, so it’s non-excludable (double check!) and we have a public good.

STEP 2 WHAT YOU DO Second, forget the adding-up you did in Step 1. Instead, ask if each unit is worth purchasing for any one person. A unit of the public good will be purchased only if there is a single person for which their individual MB is higher than the price.

The quantity that is purchased by individuals in this way is the amount that would be produced in an open market, i.e. QMARKET. You should

find QMARKET < QEFFICIENT-

Example: Continuing with the example from Step 1, if the cost of each piece of art is $15, then the first painting will be purchased, since Kyung values it at more than $15. However, Kyung values a second painting at only $10, and Harrison values a second painting at only $12, s o nobody will bother buying the second painting, and only one will be purchased. Then QMARKET = 1 < QEFFICIENT = 3

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227

In an open or competitive market, each person will make purchasing decisions only based on their own costs and benefits.

That applies to public goods too, if you’re trying to provide them in a standard market. And so, units of the public good will only be purchased if they are worth the individual ’5 money. This of course means that the purchasing decisions are being made without thinking about the benefit the good provides to others. Public goods aren’t far off from just being goods with huge positive externalities. And so, we’d expect a market to under-provide them (i.e.

Q MARKET < Q EFFICIENT)-

Elsi! Common Goods It is not common to see a Principles—level problem in which you are asked to calculate the efficient level of a common good. However, when you do, it is often framed as being about the same as a negative externality problem, where the externality is the cost imposed on other users of the good, rather than on people who aren’t consumers or producers at all. So, 9.c will address problems like these.

Example: Consider a crowded highway. Without traffic, it takes 1 0 minutes to drive to downtown on the highway, or 20 minutes to take the back roads. When the highway is crowded with 1 0 cars, the highway becomes a common good, and each additional car (starting with the tenth) slows down each other car by 1 minute.

On the individual level, if Q 2 1 0 other cars are currently taking the highway, then the marginal cost of adding yourself to the highway is

10 + (Q — 10), since it takes 10 + (Q — 10) minutes to take the highway, and the marginal benefit of adding yourself is 20, since you don’t have to take the 20-minute back roads. The market quantity is reached by finding the number of cars there must be on the highway for the next car to decide not to take it.

MC=MB 10+(Q—10)220 so And so, QMARKET = 20. The twenty-first car will just take the back roads. But what is the marginal social cost of MSC? Well, if you add yourself to the road when there are already 1 0 cars on it, you add on one minute of travel time for each other car, so the extemality i s a cost of Q .

Therefore, MSC = 1 0 + ( Q — 10) + Q, and

MSC=MB 10+(Q—10)+Q=20

2Q=20

Q=10 And 30 QEFFICIENT = 1 0

9.9;!!! Artificially Scarce Goods/Club Goods WHAT YOU NEED TO START: The demand function (or, equivalently, the marginal benefit function MB) for the good.

STEP 1 WHAT YOU DO Set MB = O and solve for Q to get the efficient quantity of the good, QEFFICIENT-

Example: If demand for digital music downloads is P = 100 — Q, then we also know that the marginal benefit from digital music downloads is MB = 100 — Q. And so, we solve

MB = MC 100 — Q = 0

[Plug in]

100 = QEFFICIENT

[Add Q]

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229

Also note that the price that achieves this efficient quantity is P = 0 . Since marginal cost is always 0, the efficient price is P 2 MC = 0 . WHY

An artificially scarce good is non—rival. Allowing another person to use the good is costless. And so, the marginal cost is MC = 0. Specifically, this is the marginal cost of allowing another person to access the good, not the cost of production itself. And so QEFFIGENT is really the number of people allowed access, not the number of units created. Then, as always, we get the efficient quantity from MB = MC. We just plug MC = 0 into that!

STEP 2 WHAT YOU DO The market quantity of the good is based on the price that the firm in charge of the artificially scarce good decides to charge. If the firm acts like a monopoly, see 7.c.ii (the standard monopoly profit maximization problem) to get the monopoly price and quantity, which will then be the market quantity QMARKET.

Or, you might just be given a price P . In that case, plug P into the demand function to find the market quantity QMARKET. You should find

that QMARKET < QEFFICIENT-

Example: Using the example from Step 1, if the firm decides to set a price of P = 5 0 (which also happens to be the price you’ll get if you use the steps in 7.c.ii), then we can find quantity by P = 100 —Q

[Demand curve]

5 0 = 100 — Q

[Plug in]

QMARKET :

WHY

50

[Take

5 0 and

add

Q]

If the firm actually charged the efficient price of P = 0 , it would go out of business, and quantity produced would be 0 ! That price simply would not cover the actual costs of producing the artificially scarce good in the first place. In the music streaming example, if music streaming were actually free, then musicians couldn’t get paid.

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And so, the firm will end up charging a positive price. This means that it will be down to demand exactly how much will be produced at that above-marginal-cost price. STEP 3 WHAT YOU DO In the case of a firm that controls access to many artificially scarce goods at once, such as a music streaming company with access to many songs, they may charge a single “club entry fee” that gives access to all their artificially scarce goods at once. The market quantity for these sorts of companies follows the same logic as in Step 2,

but the math is more difficult than you are likely to see in a Principles course.

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PRACTICE

231

'

Follow-the-Steps Questions To solve, follow directions from one or more of the sections above. 1. The production of a certain kind of hot sauce puts spicy capsaicin molecules in the air, which can cause eye pain and damage to people who live near the factory. Inverse demand and supply for this hot sauce are P = 30 — Q0 and P = 2QS, but each bottle of sauce causes 3 units of damage to others. Graph D, S, MSC, MSB, market quantity, and efficient quantity. Gardeners produce a positive extemality, since people walking by the garden can enjoy the view. If inverse supply and demand for gardeners are P = 800 — 2QD and P = 200 + 2QS, but the marginal social benefit of a gardener is MSB = 1200 — 2Q: a. Calculate the efficient quantity of gardeners. b. Calculate the number of gardeners that would be produced in a competitive market. c. Are your answers to a and b consistent with having a positive extemality? How do you know? Consider the market from Question 1.

a. Could this extemality problem be solved with: ( l ) a Pigouvian tax, (2) a Pigouvian subsidy, or (3) neither? b. If you selected (1) or (2) in part a, solve for the optimal Pigouvian policy.

Vaccinating for contagious diseases provides a positive extemality, since it reduces the chance that someone else will get sick. If inverse demand and supply are P = 300 — 2QD and P = 30 + Q5, but each vaccine provides 30 value to other people, then calculate the market and efficient quantities, and the optimal Pigouvian subsidy.

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Because of the trash that they tend to produce, soda cans provide a negative externality. Inverse demand and supply are P = 40 — Q0 and P = 1 0 + 2QS. Demand and marginal social benefit are the same, but MSC = 15 + 4Q. a. Graph D, S, MSC, and MSB, noting that S and MSC have different slopes. b. Solve for the market and efficient quantities, and the optimal Pigouvian tax. c. Graph the effect of the Pigouvian tax. Steve and Darryl live together. Steve plays his music way too loud in the momings, waking up Darryl. Steve values the ability to play his music loudly at $50 per day, and Darryl values sleeping in at $70 per day. If Steve has the right to play loud music, explain what would happen if Steve and Darryl bargained as in the Coase theorem. For each of the following goods, determine if they are public, private, common,

or artificially scarce (club) goods: a . Lighthouses b. Online newspapers c. A shared serve-yourself platter of dinner rolls at a family meal d . Sweaters Streetlights are a public good. Dave receives a marginal benefit of MB = 1 0 — Q from each streetlight, and Gary receives a marginal benefit of MB 2 20 — 2Q. The marginal cost of a streetlight is MC = 6. Calculate the market and efficient quantities of streetlights. Andy and Amy are fishing in the same pond this year and next year. There are 20 fish in the pond now, and every fish left un-caught after this year will turn into 1.5 fish next year. Assume that, at the end of next year, they will catch any remaining fish and split them evenly. Assume a fish this year is worth exactly as much as a fish next year. In fish, what is the marginal private benefit of catching one fish this year? What is the marginal private cost of catching one fish this year? What is the marginal social cost of catching one fish this year? How many fish will be caught this year? What is the efficient number of fish to catch this year?

Concept Questions A. When calculating an optimal Pigouvian tax, you set marginal social cost of production equal to marginal social benefit. What assumption does this make about the benefits provided by the government revenue from the tax? Describe some of the difficulties that would go into implementing an optimal Pigouvian tax. Be sure to discuss both the difficulties of implementing the tax as well as the difficulties of solving for the optimal tax in real life. The production of safety signs produces both positive and negative extemalities, because they provide useful information to everyone, but also the paint can sometimes leak into the environment. And so, while inverse demand and supply are P = 60 — 2QD and P = 1 0 + 3QS, we have MSB = 80 -— Q and MSC = 20 + 4QS. Calculate the market and efficient quantities, and the optimal Pigouvian tax or subsidy. Then, graph this market, showing the supply curve without and with the tax in place (noting when slopes are different). Give three examples of actual taxes or subsidies designed mostly to increase/ decrease use rather than collect revenues. You may want to use the intemet to do some research on this. If you’re having trouble, you might get started looking for taxes referred to as “sin taxes.” Diane routinely annoys her neighbor James because she doesn’t mow her lawn. James values her having a mowed lawn at $5 per day, and Diane values not hav—

ing to mow her lawn at $8 per day. a. If Diane has the right to do what she likes with her lawn, explain what would happen if Diane and James bargained as in the Coase theorem. b. Solve part a again, but this time James has the right to force Diane to mow her lawn (perhaps they live under a homeowner’s association).

Consider once again Question 9 in the Follow—the-Steps Questions section. However, this time, Amy owns the pond, and James pays Amy for each fish he catches. a. How many fish will be caught this year? b. Intuitively, why would Amy owning the pond make a difference as to whether the outcome is efficient or not?

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G. Explain intuitively why a per-unit subsidy (like a Pigouvian subsidy) wouldn’t be a great way of producing the optimal amount of a public good.

Consider two different types of goods—one is a public good. The other is a private good with a huge positive extemality—so huge that marginal private benefit is very, very tiny relative to marginal social benefit. What is the difference between these two goods? Two factories, A and B, produce 1 0 units of pollution each per year. The marginal cost of reducing pollution is MCA = QA for firm A and MC = 4 + QB for firm B. The social marginal benefit of reducing pollution is MSB = 6, but the private marginal benefit is O. a. If the government imposed a tax of 6 for each unit of pollution, what would QA and QB be? b. If the government imposed a quota and said, “Each factory must reduce pollution by X units,” where X is the average of what you found for QA and QB in part a, would this be more or less efficient than the tax? You oversee the government and are trying to decide what to do about the public good of streetlights. You are trying to decide whether to have the government provide streetlights directly (public provision), or whether to have the govemment subsidize streetlight makers (subsidy). Give two reasons in favor of public provision, and two in favor of subsidy.

ANSWERS TO ODD-NUMBERED QUESTIONS —

Chapter 1 Follow-the-Steps Questions 1. Following 1 b , we can create a capacity table: Sam

Amy

Words Typed

120/minute

80/minute

Pages Read

2/minute

4/minute

12 OCEZgLS = To = 60 Words

ocg‘a’gs = ¥ = 20 Words Amy’s opportunity cost of reading a page is lower (20 words instead of 60), so she has the comparative advantage in reading a page.

3. Following 1.b, we first need to convert these into capacities. Using an hour as a benchmark (it doesn’t matter what we choose, the opportunity cost will remain the same), we get the following capacity table: Ted

Tom

Cars Waxed

3/hour

4/hour

Cars Washed

1/hour

2/hour

235

236

ANSWERS TO ODD—NUMBERED QUESTIONS

3

OCVYfiih = l = 3 Waxes

0cm,

4

= 2 = 2 Waxes

Tom’s opportunity cost of washing a car is lower ( 2 instead of 3), so he has a comparative advantage in washing cars.

5 . Doing a little math, we determine that Dingo can tell at most 1 2 jokes (6 minutes times two jokes per minute) or do 3 magic tricks (6/2). We can choose to put magic tricks on the x-axis. And so, the y-intercept of the PPF should be 12 jokes, and the x-intercept should be 3 magic tricks. Jokes

12

3

Trick?

7. Following 1.c.ii, w e first determine the x- and y-intercept values. If both spent all their time making plates of food, they’d make 300 + 5 0 = 350 plates, so the y-intercept is 350. If they spent all their time on dessert instead, they’d make 150 + 100 = 250 desserts, so the x-intercept is 250. Next, we can calculate the opportunity cost of making dessert for each:

_ 300

ocgzfifg’m _ —— = 2 Plates offood 150 5 1 OCSZfiZH = fi

= 2 Plates offood

And so, Tooth Sweets, unsurprisingly, has the comparative advantage in dessert. And so the kink comes when Tooth Sweets spends all its time on dessert (making

ANSWERS TO ODD—NUMBERED QUESTIONS

237

100 desserts) and Belly Steaks spends all of its time on plates of food (making 300 plates of food). The kink i s at ( 1 0 0 , 300). Plates

350 300

100

250

Desserts

9. Following 1.d, first, w e can find out how much jelly they’ll make independently. If Jerry makes 1 0 loaves of bread, this takes (10/15) = 2/3 of his time. This leaves 1 — (2/3) = (1/3) of his time for jelly. In this amount of time, he can make (1/3)30 = 1 0 jars of jelly. Similarly, if Lindy makes 1 0 loaves of bread, this takes ( 1 0 / 3 0 ) = ( 1 / 3 ) of her time. This leaves 1 — (2/3) = (2/3) of her time for jelly. In

that amount of time, she can make (2/3)15 = 1 0 jars of jelly. So, in total, they make 1 0 + 10 = 20jars ofjelly. To specialize and trade, we first need to figure out who has a comparative advan— tage in bread

acme, = g = 2 Jars ofjelly Loaves

.—— 3 O= —

l 2

Jarso

f]

'ell y

Because Lindy has a comparative advantage in loaves, we’ll have her make all 20 loaves of bread (since each of them needs 10). This takes (20/30) = 2/3 of her time, leaving 1 — (2/3) = 1/3 of her time for jelly. In that amount of time she can make (1/3)15 = 5 jars of jelly. Jerry can spend all his time on jelly, and he makes 30 jars. So, in total, they made 5 + 30 = 35 jars of jelly, a lot more than the 20 they got without trade.

238 ll.

ANSWERS TO ODD—NUMBERED QUESTIONS

Here we follow 1.e. Moving from PPF] to PPF2, we should see an increase in production capacity for just cacao, since the new workers aren’t good at producing coffee. This will stretch the PPF to the right, just like in Step 2 of 1.e, except this time we’re stretching to the right instead of up, since cacao is on the x-axis. Then, moving from PPF2 to PPF3, we get more production capacity for both cacao and coffee, since the new workers are good at both. This will expand the

PPF out in all directions, just like in Step 3 of l.e. Coffee‘ *

I -—>]

PPF1PPF2 PEFB Cacao

Concept Questions A. It’s unlikely that the classroom is cleaned as fast as possible. The whole idea of comparative advantage suggests that, to use resources most efficiently (and thus minimize the time it takes to clean the room), we should put the students with a comparative advantage in sweeping on the task of sweeping, and similarly for putting things away. Mr. Dabble has instead put the best—behaved students on

sweeping duty. These may or may not be the students with a comparative advantage in sweeping, but it seems unlikely that behavior and sweeping skills line up very cleanly. So, he’s not using comparative advantage to assign tasks and isn’t being as efficient as possible. In this graph, Emily has a comparative advantage in brick. The (negative of the) slope represents the opportunity cost of the good on the x-axis, metal. Emily’s slope is steeper than Carlye’s, so metal is more expensive for her to make than it is for Carlye. This also means that brick is cheaper for Emily to make than it is for Carlye. So, Emily has a comparative advantage in brick. Another way to think about it is this: If you were currently making all metal and no brick (on the

ANSWERS TO ODD—NUMBERED QUESTIONS

239

x-intercept of the PPF), and you wanted to start making brick, you can see that you’d give Emily that task, moving along her part of the PPF. That’s because she has the comparative advantage.

E. For there to be no gains from trade, it must be the case that nobody has a comparative advantage. This can only happen if Armond and Alvin have the same opportunity costs. Then, nobody has a specialty in which they can specialize! G. Khartem’s PPF will not shift at all! A PPF describes a country’s productive capacity, and the changing price of tables might make them want to produce more tables, but it won’t change the number of tables they can produce. This would shift them to a point on the same PPF where they make more tables and fewer chairs, but won’t shift the PPF itself (not until they invest in some things that will make table production more efficient!) I. We can work a little backwards with this one. First, we know they must have a comparative advantage in the thing they dislike, or they’d just have 11 units of the thing they like even without trade. Further, we know that with trade, there should be 1.2 units produced of each good (11 going to the person who likes it, and 1 going to the person who doesn’t). And so, we can already see that each person should be able to produce 12 units of the thing they dislike, so when there’s specialization, they can make the appropriate amount. Next, we can think about what happens without trade. We know they’re capable of making 12 units of the thing they dislike, but they only make 1 unit. That means that it takes 1 1/12ths of their time to produce that 1 unit of the thing they like. And so, if they spent all their time making the thing they like, they could make 12/11ths of a unit of it. And so, Jared has the capacity to make 12 units of jewelry and 12/11ths of a shirt, and Shane has the capacity to make 1 2 shirts, or 12/1.1ths of a unit of jewelry.

Chapter 2 Follow-the-Steps Questions 1. Following 2.b: Anne’s marginal cost of the first chair is $10, so she’ll make Q; = 1 chair at a price of $10. Similarly, she’ll make Q5 = 2 chairs at a price of $30, and Q5 = 3 chairs at a price of $40. So, her supply schedule is:

ANSWERS TO ODD-NUMBERED QUESTIONS

P

Q5

10

1

3O

2

40

3

H

240

Price“

_-_

Then, following 2.c Method 1, we graph the points from the supply schedule and connect them by going straight up and then over.

Supply

4o -----30F-

w

N

10--

Qua ntity

3. Following 2.d, we can first generate their individual demand schedules by thinking about the quantities they want to buy at each price. Then, with 2.f we can aggregate those demands by adding them together.

P

QKATE

QMIKE

QPENELOPE

QAGGREGATE

2

3

2

3

3+ 2 + 3 = 8

4

2

1

3

2 + 1 + 3= 6

6

1

O

3

1+ O+ 3= 4

Then, we draw a graph containing three individual downward-sloping demand curves, and add them horizontally to get a shallower-sloped aggregate demand curve, like s o :

Aggregate

Price“

H————————

emand

Qfia ntity

5. Following 2.g: a.

An increase in the price of sheet metal, which is an input to the production of cars, will raise the marginal cost of making a car and thus shift supply to the left.

If more people want to vacation in New Zealand because of the movie, that constitutes a rightward shift in demand. . The printing press greatly reduces the marginal cost of producing books, shifting the supply curve to the right. At the same time, the increased literacy rate increases the number of people who might be interested in buying a book, shifting demand to the right as well. As incomes go up, people will shift away from the good that they don’t like but only buy because it’s cheaper (imitation vanilla) and towards the good they’d rather buy instead (real vanilla). This will lead to a leftward shift i n

demand for imitation vanilla. Since people must use pencils now, this will shift demand for pencils to the right. At the same time, a bunch of new pencil factories are opening as the pen factories get retrofitted, shifting supply to the right as well. 7. Following 2.d w e can make the demand schedule for Case as:

P

Q0

60

1

3O

2

10

3

242

ANSWERS TO ODD-NUMBERED QUESTIONS

Then, following 2 . h , if P = $ 3 5 , Case will only want to buy QD = 1 chair, since

60 > 35 > 30. Next, we can look back up to Question 1 to see that Anne will want to make Q5 = 2 chairs, since 30 < 35 < 4 0 . And s o , the difference between these

twoisQS-QDz2—1 =1. Finally, following 2.i, we can find the market equilibrium by looking for the price at which the quantities match (or the quantity at which the prices match). Here, at a price of P = 3 0 , we have QD = Q5 = 2 , and s o the market equilibrium

price is 3 0 and the quantity is 2. 9.

In each case, we will follow 2.i.

a. 2 0 — Q = 2 + 2 Q — > 1 8 = 3 Q — > 6 = Q * — > P * = 2 0 — Q * = 2 0 — 6 = 1 4 b. 1 2 0 — 2 P = 4 0 + 2 P — > 8 0 = 4 P — — > 2 0 = P * — > Q * = 1 2 0 — 2 P * = 1 2 0 — 2 ( 2 0 ) =80 c. 7 7 — 2 Q = 1 1 + Q — > 6 6 = 3 Q — - > 2 2 = Q * — > P * = 1 1 + Q * = 1 1 + 2 2 = 3 3 d. 70—1.5Q=20+.5Q——>50=2Q—->25=Q*—>P*=20+.5Q*=20+.5(25) =32.5 e. First, we know that P = 1 0 + 2Q? is supply because it slopes upwards, and P = 70 — Q? is demand because it slopes downwards. Then, 1 0 + 2 Q = 70 — Q —>3Q=60—>Q*=20—> P * = 7 0 — Q * = 7 0 — 2 0 = 5 0 .

Concept Questions A. As described, at any price above P = $1, the quantity demanded will be 0 . But at a price of $1 exactly, the quantity demanded might as well be infinite. This describes a demand curve that is completely flat at a price of P = $1 and extends infinitely to the right. Price“

Demand

Quantity

ANSWERS TO ODD—NUMBERED QUESTIONS

243

C . Here we have the price of milk changing. However, this will not lead the supply curve for milk to shift at all. The supply curve already tells us how quantity supplied will respond to price. And we just have a price change, so nothing about the supply curve needs to change to tell us how quantity supplied will respond—the good ol’ supply curve we started with will do that! Instead, we will shift along the exact same supply curve. So, quantity supplied will change, but supply will not.

E. Changes in the market for computers: a. The production cost for computers went way down. Because of technological improvement, we can make computers using far fewer materials than we used to. This shifts supply to the right. The demand for computers went way up. As more people become computer literate, more people want computers. This shifts demand to the right. b. A rightward shift in supply increases quantity but decreases price. A rightward shift in demand increases price and quantity. Since prices went down overall, it looks like the supply shift, which decreases price, “won out” and was a bigger shift. G . The supply curve being described has P = 1 0 when Q; = 0. Further, w e know that it increases by l for every additional unit, and so the marginal cost of pro— duction must be 1 0 + lQS. So, supply is P = 1 0 + Q5. We can then combine this with demand to get: 610 — Q * = 1 0 + Q * —-> 600 = 2 Q * —> 300 = Q * —> P * 2 1 0 + Q * = 1 0 + 3 0 0 = 310. I. If there are a fixed 23 square miles of land in Manhattan, then supply is Q5 2 23. We solve this with demand: 65 — P * = 23 ——> 42 = P * —> Q * = 65 — P * = 65 —42 = 23. We can then graph this out. First, we solve for the inverse demand, which w e can

graph: QD = 65 — P ——> P = 65 — QD that has a y-intercept of 65. Then, note that supply will be perfectly vertical at 23, since no matter how high the price goes, they can’t provide any more land.

244

ANSWERS T0 ODD—NUMBERED QUESTIONS

Price1k

S

65

42 D1

23

D2

Quantity

We can then draw a shift from D1 rightwards to D2, bringing us to the new equilibrium at the blue dot. Note that this equilibrium is at a higher price, but the same quantity. This is strange, since usually a rightward shift in demand increases quantity. But since quantity here is completely fixed, that can’t really

happen! So, w e just get a price increase.

Chapter 3 Follow-the-Steps Questions 1. Following 3.b.i for the Standard Method:

hog-99‘s»

( 6 — 4)/4 = 2/4 = 1 / 2 ( 5 0 % increase) (20 — 1 0 ) / 1 0 = 1 0 / 1 0 = 1 ( 1 0 0 % increase)

(15 — 9)/9 = 6/9 = 2/3 (approximately 66% increase) (9 — 15)/15 = —6/15 = —2/5 (40% decrease) (100 — 102)/102 = —2/102 = —l/51 (approximately 2 % decrease) ( 1 — 4)/4 = —3/4 ( 7 5 % decrease)

Following 3.b.ii for the Midpoint Method: a . Midpoint i s (4 + 6)/2 = 5 , then (6 — 4)/5 = 2/5 (40% increase)

b. Midpoint is (10 + 20)/2 = 15, then (20 — 10)/15 = 10/15 = 2/3 (approximately 66% increase) c . Midpoint i s ( 9 + 1 5 ) / 2 = 1 2 , then ( 1 5 — 9 ) / 1 2 = 6/ 1 2 = 1 / 2 ( 5 0 % increase) (1. Midpoint i s ( 1 5 + 9)/2 = 1 2 , then ( 9 — 1 5 ) / l 2 = —6/12 2 —1/2 ( 5 0 % decrease) e . Midpoint i s ( 1 0 2 + 100)/2 = 1 0 1 , then ( 1 0 0 - 1 0 2 ) / 1 0 1 = —2/101 (approxi—

mately 2 % decrease) f. Midpoint is ( l + 4)/2 = 2.5, then (1 — 4)/2.5 = —3/2.5= —6/5 (120% decrease)

ANSWERS TO ODD-NUMBERED QUESTIONS

245

3. Following 3.b.i for the Standard Method: The percentage price change was (18 — 12)/12 = 6/12 = 1/2 (50% increase). a.

For supply, the quantity change was from 36 to 48, and so the percentage quantity change was (48 — 36)/36 = 12/36 = 1/3. Elasticity is the percentage change in quantity divided by the percentage change in price, or (1/3)/(1/2) = 2/3. Following 3.f, this i s within the bounds of -—1and 1 , and so this i s

inelastic supply. For demand, the quantity change was from 36 to 12, and so the percent— age quantity change was (12 — 36)/36 = —24/36 = —2/3. Elasticity is the per— centage change in quantity divided by the percentage change in price, or (—2/3)/(1/2) = —4/3. Following 3.f, this is outside the bounds of ——1 and 1, so this is elastic demand. Following 3.b.ii for the Midpoint Method: The percentage change in price was: Midpoint = (12 + 18)/2 = 15, and then ( 18 — 12)/1.5= 6/15 = 2/5 (40% increase). a.

For supply, the quantity change was from 36 to 48, the midpoint of which is (36 + 48)/2 = 42. The percentage change in quantity is then (48 — 36)/42 = 1.2/42 = 2/7. Elasticity is the percentage change in quantity divided by the percentage change in price, or (2/7)/(2/5) = 5/7. Following 3.f, this is within the bounds of —1 and 1, and so this is inelastic supply. For demand, the quantity change was from 36 to 12, the midpoint of which is (36 + 12)/2 = 24. The percentage change in quantity is then (12 — 36)/24 = —24/24 = —1. Elasticity is the percentage change in quantity divided by the percentage change in price, or —1/(2/5) = —5/2. Following 3.f, this is outside the bounds of —1and 1 , s o this i s elastic demand.

5 . Following 3.b.i for the Standard Method:

The percentage change in the consumption of coffee was ( 3 — 1)/1 = 2. a.

The percentage change in income was (20 — 16)/16 = 4/ 1 6 = 1/4. Following 3.c.iii, the income elasticity i s then 2/(1/4) = 8 . This i s above 1 , and s o in this

case coffee is a luxury good. . The percentage change in income was (24 — 6)/6 = 18/6 2 3. Following 3.c.iii, the income elasticity i s then 2/3. This i s above 0 but below 1 , s o i n this case

coffee is a normal good.

246

ANSWERS TO ODD—NUMBERED QUESTIONS

The percentage change in the price of tea was (6 - 4)/4 = 2/4 = 1/2. Following 3.c.iii, the cross-price elasticity of demand is 2/(1/2) = 4. This is positive, and s o coffee and tea are substitutes. d. The percentage change in the price of soda was (4 — 2)/4 = 2/2 = 1. Following 3.c.iii, the cross-price elasticity of demand is then 2/1 = 1. This is positive, C.

and so coffee and soda are substitutes. The percentage change in the price of cream was (1 — 5)/5 = —4/5. Following 3.c.iii, the cross-price elasticity of demand i s then 2/(—4/5) = —lO/4 = —5/2.

This is negative, and so coffee and cream are complements. Following 3.b.ii for the Midpoint Method: The percentage change in the consumption of coffee was: Midpoint = (1 + 3)/2 = 2 , and then ( 3 —1)/2 = 2/2 = 1 . a.

The percentage change in income was: Midpoint = (20 + 16)/2 = 18, and then (20 — 16)/18 = 4/18 = 2/9. Following 3.c.iii, the income elasticity is then 1/(2/9) = 9/2. This is above 1, and so in this case coffee is a luxury good. The percentage change in income was: Midpoint = (24 + 6)/2 = 15, and then (24 — 6)/15 = 18/15 = 6/5. Following 3.c.iii, the income elasticity is then l/(6/5) = 5/6. This i s above 0 but below 1 , s o i n this case coffee i s a normal

good. . The percentage change in the price of tea was: Midpoint = (4 + 6)/2 = 5, and then (6 — 4)/5 = 2/5. Following 3.c.iii, the cross-price elasticity of demand is l/(2/5) = 5/2. This is positive, and so coffee and tea are substitutes. The percentage change in the price of soda was: Midpoint = (2 + 4)/2 = 3, and then (4 — 2)/3 = 2/3. Following 3.c.iii, the cross-price elasticity of demand is then 1/(2/3) = 3/2. T h i s i s positive, and s o coffee and soda are substitutes.

The percentage change in the price of cream was: Midpoint = (1 + 5)/2 = 3, and then (1 — 5)/3 = —4/3. Following 3.c.iii, the cross-price elasticity of demand i s then 1/(—4/3) = —3/4. T h i s i s negative, and so coffee and cream are

complements. Following 3.e, since supply is the one shifting, we’re largely interested in the elasticity of demand. And, true to form, we would expect a bigger price change if demand is inelastic than if it were elastic (see the graphs in 3.e Step 2). Intuitively, if demand is relatively inelastic, they don’t want to change the quantity

ANSWERS TO ODD—NUMBERED QUESTIONS

247

they purchase. And so, even though there’s a glass shortage, everyone wants just as many baubles as before, and they’ll pay through the nose if they have to! But if demand is more elastic, they’re more willing to change the quantity they purchase, and so price doesn’t have to change so much to reach the new equilibrium (since quantity is doing some changing too).

Concept Questions A. Goods with more substitutes are more elastic because, in the case of a price change, it is easier for the consumers to respond by shifting to/away from other goods. In the extreme, you can think about a good with a perfect substitute— maybe two different brands of the same item when you don’t care about brands. If one raises its price even slightly, you’ll shift entirely to the other, making your response very elastic.

We should expect that the demand curve exhibiting more elasticity is the demand curve from after the introduction, since the addition of new substitutes should increase elasticity. Following 3.c.ii, the elasticity with P = 24 — QD at P * = 4 and Q * = 20 i s (4/20)

(l/—l) = —l/5 (or 1/5 if you take the absolute value), and the elasticity with P = 44 — 2 Q D i s (4/20)(1/—2) = —l/ 1 0 (or 1 / 1 0 ) . 1 / 5 i s larger in absolute value than 1 / 1 0 , and so demand i s more elastic at P = 24 — QD (also note that, with

a steeper slope, P = 44 — 2QD should be more inelastic than P = 24 — QD at the same point). Therefore, Time X must be the period after the introduction of dananas, and Time Y i s the period before.

We should keep in mind here how demand will respond to an increase in price. The more elastic demand is, the more quantity will drop when the price increases. a. If the goal is to raise as much money as possible with a $1 tax per unit sold, you want quantity to drop as little as possible, so there are still plenty of units being sold for you to tax. So, the government should tax cigarettes (more inelastic) if it wants to raise as much money as possible. b. If the goal is to reduce consumption as much as possible, you want the more elastic good, soda, to be taxed, since a good with elastic demand will respond

to a price increase by more sharply reducing consumption.

248

ANSWERS TO ODD-NUMBERED QUESTIONS

G . We know that the supply curve is P = 4QS —— 1, and thus supply elasticity is (l/4)(P/QS). We know that elasticity at the market equilibrium is 3/4, and so we have

3/4=(1/4)(P*/Q*) 3=P*/Q* Then, we know that the market equilibrium must be on the supply curve, so we can substitute in the inverse supply and solve for Q * and then for P *: 3=(4Q*-1)/Q*

3Q*=4Q*—1 1=Q* P*=4Q*—1=3 I. Here we are looking at the relationship between hand soap and hand sanitizer. a. Following 3.c.iii, a positive cross—price elasticity indicates that they are substitutes, which makes sense for hand soap and hand sanitizer.

b. As established, on this demand curve, at a price of $2, the quantity demanded is 28, so we label that point. Price l

D1

28

New Q

D2

QLiantity

c. We add to the above graph a shift in demand. Since the price of hand soap rose, we should see a rightward shift in demand for the substitute of hand sanitizer (you want more hand sanitizer now that you’re not buying as much

ANSWERS TO ODD—NUMBERED QUESTIONS

249

of the more expensive hand soap). But what’s the new quantity that we label? (This is left generic in the graph since you get two different answers depending on which percentage increase method you use.) We have a cross-price elasticity of .5, and we saw a 50% increase in the price of hand soap. As always, Elasticity =

% Change Quantity % Change Price

We substitute in what w e know:

.5

_ % Change Quantity .5

.25 = % Change Quantity And so, the new quantity should be whatever we get after a 25% increase. The old quantity was 28, so we need a 25% increase from that. If we’re using the standard method for calculating percentage increase, this is

.25 = (Ne

— 28) / 28

7 = Ne

— 28

35 = Ne

And so, we would label the new quantity as 35. Using the midpoint method, we have

.25= (Ne

— 28) / ((Ne + 28) / 2)

(Ne + 28) / 8 = Ne Ne+28

— 28

= 8*Ne—28*8

9 * 28 = 7 * Ne 36 = Ne And so we would label the new quantity as 36.

_—————-

250

ANSWERS TO ODD—NUMBERED QUESTIONS

Chapter 4 Follow-the-Steps Questions 1. Following 4.b, we can calculate the marginal cost by subtracting each total cost from the total cost above. We start with a table of total costs and then fill in marginal cost: TC

MC

0

$0

1

$10

$10—$O=$10

2

$25

$25—$10=$15

3

$45

$45 — $25 = $20

Then, we can graph the supply curve by plotting out the Q and MC points on the table above, and connecting the dots following the steps in 2.c. PriceM

Supply 20 ------

I I I I I I I I I I I I I

15 10

I

2

3

Quantity

3. Following 4.b.iv Method 1, we can shade in her producer surplus by taking the supply curve from question 1 and drawing a horizontal line at the price. Therefore, producer surplus is the area below price and above supply.

w _..__._.________

N

H

—-—--

1.3.1:!

(103 ntity

Then, we can calculate producer surplus by subtracting marginal cost from the price for each unit sold, since producer surplus is the amount received above and beyond what the producer had to pay to produce the good. Two units are sold here (since the marginal cost of the second unit is only $15, making it worth— while to produce at a price of $ 1 7 , but the third unit i s not, at a marginal cost of

$20 > $17). The first unit has a marginal cost of 10, creating a producer surplus of $17 — $10 = $7, and the second has a marginal cost of $16, creating a producer

surplus of $17 — $15 = $2. The total producer surplus is then $7 + $2 = $9. Following 4.c.iv Method 2, we first want to get the y-intercept of the demand curve, which is P = 44 — 2(0) = 44. Second, we want to get the quantity demanded, which comes from 20 = 44 — 2QD —> Q0 2 11. Then, consumer surplus is

(y intercept — P) * QD/2 = (44 — 20) * 11/2 2 132 Rudy, however, only buys one razor. His consumer surplus is 22 — 20 = 2. Following 4.e: We can start by constructing Krista’s table of marginal costs and benefits. Her first pair of sunglasses costs $40, the second $80, and the rest $100. We pair that with the marginal values:

Q 1

MV $200

MC $40

2 3 4

$150 $100 $50

$80 $100 $100

252

ANSWERS T0 ODD-NUMBERED QUESTIONS

. The efficient level of sunglass-purchasing to engage in is where M V 2 MC, which occurs at 3 pairs of sunglasses, where 100 = 100. . How about deadweight loss? If forced to buy only 1 pair of sunglasses instead of 3, we can calculate the deadweight loss generated by each pair not pur— chased that should have been. The second pair adds $150 —— $80 = $70 in

deadweight loss, and the second generates $100 - $100 = $0 in deadweight loss, for a total deadweight l o s s of $ 7 0 .

First, we need to calculate P 1 and P2 using our standard supply-and-demand tools. We plug in the quantity of 8 to get the price consumers pay, P1 = 30 — 2(8) = 14, and the price producers receive, P 2 = 8.

Then, following 4.b.iii and 4.c.iii, we know that the marginal value at a quantity of 8 is 14 and the marginal cost at a quantity of 8 is 8. Then, we can get the efficient quantity in the usual Chapter 3 way by solving supply and demand together: 30 — 2 Q = Q ——> 30 = 3 Q —> 10 = Q*. Finally, following 4.f.i, we can calculate deadweight loss as (14 — 8) * (10 — 8)/2

= 6 * 2/2 = 6.

Concept Questions A. In this market, we’re thinking about three things: the best choice for consumers, the best choice for producers, and the socially efficient best choice for society (where society cares about both consumers and producers equally).

a. As always, consumers will make themselves best off by setting MC = M V. Since they’re the ones paying for health care, their MC is the price P. Therefore, consumers will maximize consumer surplus by choosing the quantity such that P = M V. . Similarly to part a, producers want to set MC 2 M V. Their marginal value is what they get by selling another unit, or P. And so, they maximize producer surplus by choosing the quantity such that MC = P. . Health care is efficient if the total surplus (consumer plus producer surplus) i s maximized.

. We can maximize this surplus by thinking about the problem from society’s point of view. Since society cares about the costs and benefits generated for everyone, the consumer’s M V is the relevant M V, and the producer’s

ANSWERS TO ODD—NUMBERED QUESTIONS

253

MC is the relevant MC. And as always, we get the best quantity by setting M V : MC. S o , the efficient price i s the one that makes consumers and produc—

ers both choose the quantity for which M V = MC. And since consumers set P = MV and producers set MC = P, we want M V = MC = P. C . Deadweight loss is the total amount of surplus that could have been generated but was not. Total surplus is maximized under the efficient quantity (by definition, that’s what the efficient quantity is). If we are not at the efficient quantity, there will be less surplus. The difference between the surplus w e would get at the efficient quantity and the surplus we get at the actual quantity is deadweight loss. E. First, we know that the price on the demand curve represents the marginal value of that unit. The total value produced is the area below the demand curve covering the quantity that has been purchased. So, for example, the total value produced at Q = 1 is shown by

D

QJantity This is a combination of a triangle above the marginal value and below the demand curve, which is the same triangle we get by calculating consumer surplus where P = M V, plus a rectangle below the marginal value. Following 4.c.iv, the consumer-surplus—style triangles at Q = 1 , 3 , and 5 are (21 — l 8 ) * 1 / 2 = 1.5,

(21 — 12) * 3/2 = 9 * 3/2 = 13.5, and (21 — 6) * 5/2 = 1 5 * 5/2 = 37.5, respectively. The rectangular areas are just marginal value times the quantity, or 18 * 1 = 18, 1 2 * 3 = 3 6 , and 6 * 5 = 3 0 . In total, then the total surplus at Q = 1 i s 1 . 5 + 1 8

= 19.5, at Q = 3 is 13.5 + 36 = 49.5, and at Q = 5 is 37.5 + 30 = 67.5.

254

ANSWERS TO ODD—NUMBERED QUESTIONS

G. What we are looking for here is a situation in which deadweight loss would take the shape of a rectangle. For this to be the case, the amount of surplus lost for each unit not produced that should be should be constant (so that you can have a shape with a constant height, which a rectangle does).

The surplus lost per unit is based on the difference between M V and MC (as shown in 4.f.i). This can’t be constant if M V and MC have different slopes, as they do in options a and c. And option (1 doesn’t really describe a deadweight loss—causing scenario, since the quantity is determined based on marginal costs and benefits; and since a lump sum tax wouldn’t change those, there’s no reason to believe the quantity wouldn’t just be the efficient quantity. S o , i s it c or e ? Let’s think about c . We have two constant (fiat) lines, and at a

certain quantity, M V drops down to 0. That must be the efficient quantity, since past that point, M V < MC and so you’ve gotten all the surplus you can. And, up to that point, the surplus from each unit i s constant, since M V — MC i s constant. Therefore, if the quantity i s for some reason below the efficient level,

the deadweight loss is a rectangle, as pictured below. PriceH

MC MV alliantity

Chapter 5 Follow-the-Steps Questions 1. All following 5 b :

a. The equilibrium price and quantity can be found by ignoring the price restriction. So, we solve supply with demand: 400 — 2 Q = 100 + Q —> 300 = 3 Q —> 100 = Q * —> P * = 100 + Q * = 100 + 100 = 200. The restriction sets the price

ANSWERS TO ODD—NUMBERED QUESTIONS

255

to 150, which is below the equilibrium price of 200. As a result, this restriction basically acts as a price ceiling, by not allowing the price to rise up to the equilibrium price. . When the price is too low, as it is here, it’s going to be the suppliers who are the ones who say, “no more!” before the consumers do. So, the suppliers here are setting the quantity, since at this low price, suppliers won’t be interested in making as many as people will want to buy. Therefore, we can get the quantity by plugging the new price into the supply curve. So, 150 = 100 + QS —> 5 0 = Q5. 50 units will be sold.

. Since the price is too low, we already know there will be a shortage. We can figure out exactly how much by calculating QD: 150 = 400 — 2QD —> 2QD = 250 ——> QD = 125. The shortage is then the difference between quantity supplied and quantity demanded, or Shortage = Q0 — Q5 = 125 — 5 0 = 75. . We can then calculate the deadweight loss using the standard method from 5.b Step 3. We know Q * = 100, QA = 50, and MCA = 150. We can calculate M VA by plugging QA into demand: M VA 2 400 — 2(50) = 300. Then,

DWL = ( 3 0 0 — 1 5 0 ) * ( 1 0 0 — 5 0 ) / 2 = 150 * 5 0 / 2 = 3750 Following 5.d, we can calculate the actual quantity by adding the tax to the supply curve and solving. So, we get an adjusted supply of P = 6 + Q5 + 3 and solve 36 — 2 Q = 6 + Q + 3 —> 27 = 3 Q —> 9 = Q*. We get price paid by plugging this quantity into demand: PD = 36 — 2(9) 2 18. And we get price received by plugging the quantity into unadjusted supply: P5 = 6 + 9 = 15. We can then graph the market as in 5.d. Here we graph it with a supply curve shift, but using a “tax wedge” works just as well. Modified S

I I

I 9

(1*

c 06a ntity

256

ANSWERS TO ODD—NUMBERED QUESTIONS

5. Following 5.e: In Question 3, we found that PD 2 18, P5 = 15. a. We can find tax incidence by comparing these to the equilibrium price, which we find by resolving supply and demand together ignoring the tax: 1 0 : 1 6 . So, 36—2Q=6+Q—>30=3Q—> 10=Q*—>P*=6+Q*=6+ tax incidence for consumers i s (PD — P * ) / T = ( 1 8 — 1 6 ) / 3 = 2/3.And for pro-

ducers it’s ( P * — PS)/T= (16 —15)/3 = 1/3. b. 2/3 > 1/3, so consumers pay a larger share. c. We first need to find demand and supply elasticities at the equilibrium point. The slope on the demand curve is —2, and s o demand elasticity should be (1/(—2)) * ( 1 6 / 1 0 ) = —.8. The slope o n the supply curve i s l , and s o supply elasticity should be ( 1 /1 ) * ( 1 6 / 1 0 ) = 1 . 6 . Then, w e should get:

IncidenceCONSUMERS = ES / (ES + |ED|) = 1.6 / (1.6+ .8) = 2/3 InCidencePRODUCERS

=

IED'

/ (ES

+ ‘EDD

=

.8 / (1.6

+.8):1/3

which does indeed match our answer from part b. 7. Following 5.f, we can calculate all the important aspects of this quota. a. We first want to check if this quota binds. The equilibrium quantity we can get as normal: 36— Q : 2 + Q —> 3 4 : 2 Q —> 17 = Q*. The quota of 1 0 is less than this, so it does indeed keep us from equilibrium. Then, we can get PD by plugging the quantity into demand: PD = 36 — 10 = 26, and PS by plugging the quantity into supply: P5 = 2 + 1 0 = 12. The quota rent is the difference between these two multiplied by the quantity, or (26— 12) * 1 0 : 14 * 1 0 : 140. b. The quota rent goes to whoever has the access to the market. In this case, it’s the shipping people. They’re going to charge very high shipping charges to SallyAnne makers and collect the quota rent. 9.

To figure out how the market for cashews will work with trade, w e first need

to figure out how it would look without trade. We can get the autarky (without trade) price by solving regularly: 2O — Q = 4 + Q ——> 16 = 2 Q —> 8 = Q * —> P * = 4 + Q * = 4 + 8 = 1 2 . S o , without trade, the price would be 1 2 . S i n c e the world

price is 16, Nigeria will want to export cashews to the world, where they command a higher price than in Nigeria. So, the world price is above the autarky

ANSWERS TO ODD-NUMBERED QUESTIONS

257

equilibrium price, and we graph accordingly, labeling QD where the world price intersects with demand and Q5 where world price intersects with supply.

I I I

I

Q0

:

Qs

Quantity

Concept Questions A. First off, we can calculate the original pre-subsidy equilibrium quantity, since we’ll need it later for the deadweight loss. We solve as normal:

50—2Q=lO+2Q—>40=4Q_)10=Q* Then, as instructed, w e can treat the subsidy as a negative tax. S o , w e adjust the

supply curve to get P = 1 0 + 2 Q + T, and then T : —8, so we have P = 1 0 + 2 Q — 8 . Then w e solve with demand: 5 0 — 2 Q = 1 0 + 2 Q — 8 —> 48 = 4 Q —> 1 2 = QA. We plug this into demand to get PD: PD 2 5 0 — 2(12) = 26, and into unadjusted supply to get P5: P5 = 1 0 + 2(12) = 34. Note that, unlike with a tax, P5 > PD, since the consumers pay a certain price and then the government chips in some more to get to P5.

Then, we can use the same deadweight loss formula as with taxes: Deadweight loss 2 (PD — PS) * ( Q * — QA)/2 = (26 — 34) * (10 —12)/2 = (—8) * (—2)/2 = 8. C . Price controls like price ceilings create their effect by keeping the price below the equilibrium level and not allowing it to adjust. Therefore, anything that doesn’t let the price adjust up properly will have the same effect. We can see this happening in the situations in a and c. Retailers won’t raise prices to the new equilibrium in part a, and in part c the price can’t adjust to the proper level either. That’s because the price either must stay as it is, which isn’t properly adjusting, or it will rise by a whole $.25, which isn’t adjusting properly either!

258

ANSWERS TO ODD—NUMBERED QUESTIONS

Part b isn’t like a price ceiling because there’s nothing stopping the adjustment; it just hasn’t happened yet. And part (1 is not like a price ceiling because it’s a tax—it’s like a tax! If demand or supply shift further, the price can still change, unlike what happens with a price ceiling or floor, and the government collects revenue from the market. In reference to 5 . d and 5.f, some differences are:

I With a tax, the government collects revenue from the tax. With a quota, the people who get their hands on the licenses collect the quota rent.

I With a tax, if demand or supply shift to the right, the quantity can increase, but with a quota it can’t. First, w e can calculate the market outcome with and without free trade. Without

trade, we solve as usual: 40 — Q = 1 0 + Q ——> 30 = 2 Q —> 15 = Q * —> P * = 1 0 + 15 = 25. This is above the world price, and so with trade they would import. The price would be PW = 15. Q0 comes from demand: 15 = 40 — QD —> QD = 25. And Q3 comes from supply: 15 = 1 0 + Q5 ——> Q5 = 5.

a. We can calculate the change in CS by calculating CS before and after. The y-intercept of the demand curve is 40, and so CS without trade is (40 — 25) *15/2 = 15 * 15/2 2 112.5. After trade opens, consumer surplus is (40 — 15) * 25/2 = 25 * 25/2 = 312.5. S o the change is 312.5 — 112.5 = 200. b. We do the same for PS. The y-intercept for supply is 10. Without trade, PS is (25 — 10) * 15/2 = 1 5 * 15/2 = 112.5. With trade, PS is (15 — 10) * 5/2 = 5 * 5/2 = 1 2 . 5 . S o , the change i s 1 2 . 5 —112.5 = —100.

c. Total surplus is CS + PS. CS goes up by 200 when free trade is implemented, and PS only goes down by 100, not enough to cancel out the gain. Total TS then goes up by 200 — 100 = 100, a win for total surplus! So, the government should allow free trade. d. The producers would be happy if they were paid 100 to make up for what they lost.

ANSWERS TO ODD—NUMBERED QUESTIONS

259

Chapter 6 Follow-the-Steps Questions 1. Following 6.b Method 1, we can think of the fixed costs as being the costs that are necessarily paid no matter how many units are created. You can’t stop paying them, at least not immediately! And variable costs are the costs that you must pay more of if you want to expand production. a.

Here, the cost of the printing presses (either newly purchased, or by paying the opportunity cost of not selling them) and the warehouse rent must be paid the same no matter how many books are made, so these are the fixed costs. The paper and labor costs are variable. Gerald paid for the classes regardless of how many chairs he ended up making. Can’t get that money back! The cost of the classes is a fixed cost. The cost of the wood and screws is variable. The cost of renting the taxi is paid no matter how many fares are picked up. However, the opportunity cost of the driver’s time, and the price of gas, are

variable. 3. Here we follow 6.c, using the average cost formulas. a.

Here we can simply divide TC by Q, as indicated. AC = TC/Q = (36 + Q2)/Q = (36/Q) + Q. This time, we want to calculate this by first getting FC = 36 and then getting AFC by dividing it by Q: AFC = 36/Q. Then, we do the same by getting

VC= Q2, and get AVC= Q2/Q = Q. Finally, we add them together: AC 2 AFC + A V C = (36/Q) + Q. . Now, we can plug the given values of Q into ATC to get the values. At Q =

4,AC=(36/4)+4=8+4=12.AtQ=8,AC=(36/8)+8=4+8=12.At Q=12,AC=(36/12)+12=3+12:15. 5.

Following 6 . e , we first set P = MC —> 1 2 = 4 Q —> 3 = Q * . Then, w e can calculate A C as A C = TC/Q = ( 1 2 / Q ) + 2 Q = ( 1 2 / 3 ) + 2 ( 3 ) = 4 + 6 = 1 0 . Finally, using 6 . g ,

we can calculate profit as Profit = Q * (P —AC) = 3 * (12 — 10) = 3 * 2 = 6.

260

ANSWERS TO ODD—NUMBERED QUESTIONS Then, following 6.f, we can graph demand, MC, AC, and profit as:

(1*

3

Qiantity

7. To figure out the individual firm decisions, we first need to solve for the market price, which we do as normal: 22 — 2 Q = 2 + 2 Q —> 20 = 4 Q —> 5 = Q * ——> P * = 2 + 2(5) = 12. a. Now that we have market price, following 6.e we can get profit-maximizing quantity by setting P = MC —> 1 2 = 6 Q ——> 2 = Q . So, each firm makes 2 units. b. Following 6.g, we can get profit by first plugging the quantity into AC. A C = (24/2) + 3(2) = 1 2 + 6 = 1 8 . Then, profit i s Profit

= Q * (P — AC)

= 2 * (12 — 18) = 2 * (—6) =—12. So, it’s a loss of 12. c. Since each firm is making a loss, firms will start dropping out and the supply curve will, as a result, shift left.

9. This graph is exactly 6.h Figure 2.

Concept Questions A . Since we want to get the marginal revenue and marginal cost of each one unit, we need to take the increase i n total revenue and total cost, and then divide it by

the increase in Q. This will give an increase-per—unit, which is what we want!

Q

TR

TC

0

0

500

100 200

1000 2000

1000 2000

300

3000

4000

MR

(1000—0)/100=

MC 10

(1000—500)/100=5

10

10

10

20

ANSWERS T0 ODD-NUMBERED QUESTIONS

261

C . Long-run behavior in the potted plant market. a. Following 6.h.iii, we can get the long-run price by finding the zero—profit price where MC = A C —> 4 Q = ( 1 8 / Q ) + 2 Q ——> 2 Q = ( 1 8 / Q ) —> 2 Q 2 = 1 8 ——> Q2

= 9 —> Q : 3 —> P=MC=4(3) = 12. The long-run price is 12.

b. Since the long—run price is 12, we can get the equilibrium long—run quantity by plugging this price into demand: 1 2 = 162 — 2QD —> 2QD = 150 —-> QD = 75. To find out how many firms there are in the long run, we need to fig— ure out how many units each firm makes, which we get from P = MC ——> 12 = 4 Q —> 3 = Q. So, there are 7 5 units made total, and each firm makes 3 units, so the number of firms required to get to those 75 units is 75/3 2 25. There are 25 firms in the long run.

E. Remember that we have increasing returns to scale if average costs decrease as quantity rises; constant returns to scale if average costs are constant as quantity rises; and decreasing returns to scale if average costs increase as quantity rises. a. Average costs went from 200/40 = 5 to 400/80 = 5, and so we have constant returns to scale.

b. Average costs went from 1000/50 = 20 to 1200/70 increasing returns to scale. 0. Average costs went from 300/100

2:

17.1, and so we have

2 3 to 500/150 z 3.3 and so we have

decreasing returns to scale. G . We can get from one expression of profit to the other by remembering some equalities from the chapter: TR = P * Q and AC = TC/Q. We can manipulate this second equality, in particular, to get TC = AC * Q. Then, w e have Profit = TR — TC 2 P * Q —AC * Q = Q * ( P —AC), which i s what

we were looking for! The last step comes from regular algebra, factoring the Q out of the P * Q and the AC * Q.

I. This graph is largely the same one we see in 6.h Figure 1. The only difference here is that the price (and thus the individual demand curve) isn’t coming from the standard market equilibrium where supply meets demand, but instead from the price floor.

ANSWERS TO ODD—NUMBERED QUESTIONS

"°/

262

Pricel‘

\

Price

I I I I I I é)

Ofuantity

Q

Quantity

Chapter 7 Follow-the-Steps Questions 1. Getting marginal revenue for ClarityStream:

a. Following 7.c.i, we can get marginal revenue by taking demand and doubling the slope on the quantity. Demand is P = 1600 — 20QD, and so marginal revenue is MR = 1600 — 4OQ. b. We can get marginal revenue at these quantities by simply plugging in quantity. Q = 1 0 —> MR

21600

21600

— 40(10) = 1200.Q = 20 —> MR = 1 6 0 0 — 40(20) = 800. —40(30) 2 400. Q = 80 —> MR = 1 6 0 0 — 40(40) = 0.

Q = 5 0 —> MR c. Following 7.c.ii, we can find optimal quantity by setting MR 2 MC ——> 1600 —40Q= 1000 ——> 6 0 0 = 4 0 Q ——> 15 = Q. First, following 7.c.i, we get marginal revenue from doubling the slope on Q in the demand curve: MR = 5 2 — 2Q. Then, following 7.c.ii, we can get the optimal price and quantity by setting MR 2 MC —> 5 2 — 2 Q = 4 + 2 Q —> 4 8 = 4 Q —> 12 = QM. We plug this into demand to get price: PM = 5 2 — 12 = 40. Next, we can get average cost by dividing TC by Q: AC = TC/Q = (48 + 4 Q + Q2)/Q = (48/Q) + 4 + Q. At the optimal quantity, AC = (48/12) + 4 + 1 2 = 4 + 4 + 1 2 = 20. Finally, profit is Profit: Q * (P —AC) = 1 2 * (40 — 20) = 12 * 20 = 240.

First, as always, following 7.c.i, we get marginal revenue by doubling the slope on Q in demand: MR 2 440 — 2Q. Then, following 7.c.ii, we can get optimal quantity from MR 2 MC —> 440 — 2 Q = 40 + 2 Q —> 400 = 4 Q —> 100 = QM.Then, we plug this quantity into demand to get optimal price: PM = 440 — 100 = 340.

ANSWERS TO ODD-NUMBERED QUESTIONS

263

We can get average cost from AC = TC/Q = (30,000 + 40Q + Q2)/Q = (30,000/Q) + 40 + Q. We plug in quantity to get AC = (30,000/ 100) + 40 + 100 = 440. Finally, profit is Profit = Q * ( P — AC) = 100 * (340 — 440) = 100 * (—100) = —10,000. Next, as we graph the market according to 7.c.v, it’s important to keep in mind that this firm, despite being a monopoly, is making a loss. So, we need to draw it such that MR = MC at a quantity where P < AC.

QM

Qua ntity

Short and long-run equilibrium in monopolistic competition: a. Following 7.d.i, we approach the short-run optimal price and quantity just as if it were a normal monopoly. So, we double the slope on quantity in demand to get MR 2 40 -— 2 Q . We then get optimal quantity from MR = MC —> 40 — 2 Q : 1 0 + Q — > 3 0 = 3 Q — > 1 0 = Q M — > P M = 4 0 — 1 0 : 3 0 . Then, average cost is AC = 1 0 + (10/2) = 15. Finally, profit is Profit 2 Q * (P —AC) = 1 0 * 2150. (30— 15) = 1 0 * 15 b. Following 7.d.ii, since each burger firm is making profits, and this is monopolistic competition, other firms will enter the market. Because this intensifies competition in the market, consumers will want fewer units of each type of burger at a given price, shifting demand for Barry’s Burgers to the left. 0. In the long run, firms will continue to enter the market until there are no more profits to be made. S o in the long run, profits are 0, as in 7.d.ii.

The graph we want here follows 7.e.ii closely, except that we only have P ] and P2, and no P3, since there are only two prices being set here. And so, we have:

264

ANSWERS TO ODD-NUMBERED QUESTIONS

MC

1 l

.

(11

02

r

o

Quantity

Concept Questions A. We can get marginal revenue from this demand schedule by first calculating total revenue (by multiplying P by Q0) and then getting marginal revenue by subtracting each total revenue above.

P

QD

TR

100

1

100*1=100

90

2

90*2=180

180—100=80

80

3

80*3=240

240—180=6o

70

4

70 >r< 4 = 280

280 — 240= 40

MR

We can start by noting that a monopoly is going to choose its profit-maximizing quantity by setting MR = MC. Then, it chooses profit-maximizing price by plugging that profit-maximizing quantity into the demand function. We know that, for any given quantity, P > MR, since to sell an additional unit, the firm must lower price a little bit. And so, P i s added to the revenue since you sell an addi-

tional unit at P, but that additional revenue is defrayed because you had to lower price for everyone else, so P > MR. And since MR = MC at this quantity, we have P>MR=MC, orP>MC.

The basic graph we need to draw is the exact same as in 7.c.v. Then, to show that a price ceiling can improve efficiency, we can set the price ceiling at the price where demand crosses MC. This is the efficient price (since P = MC, we have efficiency at this point). This enforced lower price encourages the monopolist to

ANSWERS TO ODD—NUMBERED QUESTIONS

265

produce the efficient quantity. It no longer must lower prices on everyone else to sell more units, which is the typical reason the monopolist doesn’t lower prices, because it can’t have higher prices on those people anyway! There’s no DWL at this price and quantity, since the efficient quantity is being produced.

QMQ* Quantity Following 7.b: a.

Here we have a lot of producers, and so we’re not dealing with monopoly or oligopoly. There’s no barrier to entry either. So, is this perfect or monopolistic competition? Since each cafe’ makes a slightly different cup of coffee that consumers wouldn’t consider to be perfect substitutes, this is monopolistic competition, not perfect competition. Here, one company owns the entire set of inputs to diamond production (the diamonds themselves). Nobody else can compete because they can’t get any diamonds to sell. Therefore, this is a monopoly. Here we have a small number of firms, each of which is making basically the same product. This small number of firms controls nearly all the market. And so, this is an oligopoly.

Here we can largely follow 7.e.iii. First, we want to calculate the consumer surplus generated at the efficient quantity. We can get efficient quantity from P = M C — > 8 0 — 2 Q = 1 6 — > 6 4 = 2 Q -—>32=Q* ——>P*= 16. Consumersur— plus can be calculated in the standard way, noting that the y-intercept is 80: CS 2 (80 — 16) * 32/2 = 64 * 32/2 = 3 2 * 3 2 = 1024. So, we know that the firm can charge 1024 for the right to shop at the market as long as it charges P = 1 6 for its products. This price and entry fee maximize the surplus generated by the store, and then uses the entry fee to soak up the consumer surplus created so the market can have it all instead.

266

ANSWERS T0 ODD—NUMBERED QUESTIONS

Chapter 8 Follow-the-Steps Questions 1. We can follow 8 b to draw this game table. We have two players here: Tape Source and Place for Tape. Each of them has two options: Invest or Don’t Invest. And so, we know that there will be two rows, one labeled Invest and one labeled

Don’t Invest, and the same for columns. Within each of the cells we’ll end up with, we have four outcomes. If both sides select D o n ’ t Invest, then every-

one makes $40 million each. If both sides select Invest, then everyone makes

$60 — $10 = $50 million each. And if one side selects Invest while the other selects D o n ’ t Invest, the D o n ’ t Invest side makes $60 million, while the Invest

side makes $60 — $10 = $50 million. Place for Tape D o n ’ t Invest

Invest

$40m for Tape

$60m for Tape

Source

Source

Tape

$40m for Place for Tape

$50m for Place for Tape

Source

$50m for Tape

$50m for Tape

Source

Source

D o n ’ t Invest

Invest

$60m for Place

$ 5 0 m for Place

for Tape

for Tape

Following 8.c, we can find the Nash equilibria for the game table from Question 1 by highlighting the best responses. First, we say “If Tape Source played Don’t Invest, Place for Tape would want to Invest (since $50m > $40m)” and highlight the “$50m for Place for Tape” payoff on the Don’t Invest row. Similarly, we highlight “$60m for Place for Tape” on the Invest row. Then we switch it up, saying “If Place for Tape played Don’t Invest, Tape Source would want to Invest (since $50m > $40m)” and highlight “50m for Tape Source” on the Don’t Invest column. And similarly, highlight “$60m for Tape Source” on the Invest column.

ANSWERS TO ODD—NUMBERED QUESTIONS

267

Place for Tape

Don’t Invest Don’t Invest

Tape

Source

I

nvest

Invest

$40m for Tape Source

$60m for Tape Source

$40m for Place for Tape

$50m for Place for Tape

$50m for Tape Source

$50m for Tape Source

$60m for Place for Tape

$50m for Place for Tape

Finally, we note that both payouts are highlighted in the “Tape Source Invests, Place for Tape Doesn’t Invest” and “Tape Source Doesn’t Invest, Place for Tape Invests” cells. These are our two Nash equilibria. Following 8 b , we can draw the game table. Keep in mind there are three actions here: offer to John, offer to Mark, and offer to Steve. S o , there should

be three columns and three rows. When drawing payoffs, remember that if they both approach the same actor, and they both get 0 . Then, when highlighting best responses, note that if the other company approaches Mark or Steve, your best bet is to approach John (since 5 > 2 and 5 > 0). But if the other company approaches John, your best bet is to approach Mark or Steve (since 2 > 0). And so, we have four Nash equilibria: Shakes gets John and Bardtron gets Mark, Shakes gets John and Bardtron gets Steve, Shakes gets Mark and Bardtron gets John, and Shakes gets Steve and Bardtron gets John.

Bardtron John

Mark

Ste ve

OforS

5forS

5forS

OforB

2forB

2forB

2forS

OforS

2forS

5forB

OforB

2forB

2forS

2forS

OforS

5forB

2forB

OforB

John

Shakes

Mark

Steve

268

ANSWERS TO ODD—NUMBERED QUESTIONS

7. Following 8 . e w e work backwards. First, w e ask what the Market Leader will do if the New Competitor Enters the Market. Then, they have a choice between

Raising Price ($60m) and not raising the price ($40m). $60m > $40m, so they i will raise the price. Next, we consider what they will do if the New Competitor Stays Out. Then, it’s $100m > $80m, and so they’ll Raise Price in that situation as well. Now, the New Competitor knows that the price will get raised no matter what they do, so their choice is between Enter Market to get $60m or Stay Out for $0. $60m > $Om, so they Enter the Market. The Nash equilibrium strategies are “New Competitor Enters the Market and Market Leader Raises Price.” New Competitor Enter

hAarket hAarket Leader Raise Price/

Don't

Don't Raise Price,

gssom tiger" tars...) a: Following 8.d, we can draw this game tree by noting that the Market Leader moves first and has two options—Lobby or Don’t—and the New Entrant has three options—Enter Market, Stay Out, or Enter Different Market. Once we put i n the payoffs, we follow 8 . e to note that if the Market Leader Lobbied, then Enter Different Market i s the best call, and if the Market Leader d i d n ’ t Lobby,

then Enter Market is the best call. So, if the Market Leader Lobbies, they make $lOOm. And if they don’t, they make $60m. So, in Nash Equilibrium, the Market Leader Lobbies, and the New Entrant Enters a Different Market. Market Leader

New Entrant

(S60m, $100m)

Different

$810005“ gain tier $100.25“ alarm 96%“

ANSWERS TO ODD—NUMBERED QUESTIONS

269

Concept Questions A. To recap, this method tells us the following: (1) For each strategy Player 1 could play, find the best response Player 2 could have to that strategy and highlight Player 2’s payoff; (2) for each strategy Player 2 could play, find the best response Player 1 could have to that strategy and highlight Player 1’s payoff; and (3) find any mix of strategies in which both sides have highlighted their payoffs. These are Nash equilibria. We know this approach works because of the definition of the Nash equilibrium. A Nash equilibrium is a set of strategies in which each player is playing a best response at the same time as everyone else. Steps (1) and (2) above identify those best responses. Then, in Step (3), we identify which combinations of strategies there are in which each strategy is a best response to the other at the same time. This is, by definition, a Nash equilibrium.

C . For the most part, w e can follow the standard steps for getting a Nash equilibrium in this game. However, there is a minor twist in that the Entrant has two best responses to the Market Leader choosing a Low Price, since the Entrant gets $0 that way no matter what. But we can still follow our steps with no issue!

We just highlight both best responses (they’re both the best! Can’t do better than $Om when the Market Leader picks Low Price), and still find a Nash equilibrium where both payoffs are highlighted, when the Entrant Enters and the Market Leader sets a High Price. Market Leader ( M )

High Price Enter

Entrant (E)

Low Price

$80m for E

$Om for E

$80m for M

$Om for M

$Om for E

$Om for E

$99m for M

$40m for M

Don’t

E. This is unlikely to lead to you both Cooperating, because this agreement is a non-credible promise (see 8.f). Even though both of you agreed to Cooperate, and you’re both better off if both of you do Cooperate, as soon as it comes time to make the decision, there’s no reason not to go back on your word and Betray

127C! ANSWERS TO ODD—NUMBERED QUESTIONS instead. If they stuck to their word, you’re better off Betraying than Cooperating, and if they broke their promise, you’re also better off Betraying than Cooperating. So, you’ll both break your promise and Betray. G . Just like with any sequential game, we work backwards. a. In this step, we figure out what the profits will be for each of the Entrant’s options, so the Entrant knows the consequences of the decision. We calculate this as a standard monopoly model. First, we get MR = 44 — 2 Q , then MR=MC—>44—2Q=O—>44=2Q —>22=QM—>PM=44—(22)=22. Since MC i s constant, profits are then Profit:

Q * (P — MC) 2 Q * P = 22 * 22

= 4 8 4 . And so, if the Entrant does Not Enter, i t gets 0 and the Market Leader

gets 484. If the Entrant Enters, then it gets 1/4 of the market (the overall profit stays the same since the two collude perfectly to get monopoly price) and so has a profit of 484/4 = 121, and the Market Leader gets 3 * (484/4) = 363. However, the Entrant also must pay that fixed cost, so the Entrant really gets 121 — 100 = 21. b. The 21 the Entrant gets for Entering is better than the 0 it gets for Not Entering, so it will Enter.

Chapter 9 Follow-the-Steps Questions 1. Following 9.b, we note that there is a negative extemality here but no positive extemality, s o w e should see MSC above S, but D 2 M53.

Further, since each

bottle causes a constant 3 units of damage, the slope of S should be the same as the slope of MS C. This is very like the graph we see on the right at the end of 9 b .

Price‘l

MSC

D = MSB

QEFFICIENT QMARKEI'

Qfiantity

ANSWERS TO ODD—NUMBERED QUESTIONS

271

3. We can follow 9.d.i in our thinking here. a. We have a negative extemality, and we’re dealing with a private good, so a Pigouvian tax seems like a perfect fit! We just need to take that graph we drew in Question 1 and shift supply until we get the quantity we want. b. We can follow 9 c in calculating the efficient and market quantities. Market quantity comes from 30 — Q = 2 Q —-> 30 = 3 Q ——> 1 0 = QMARKET. And efficient quantity comes from MSB = MSC ——> 30 — Q = 3 + 2 Q —> 27 = 3 Q ——> 9 = QEFFICIENT. Now that we know the efficient quantity (9), we can choose a tax that will get the competitive market to produce that quantity. We add a tax T t o the supply curve, and then plug in the quantity we want. 30 — Q = T + 2 Q —-> 30 — 9 = T + 2(9) —> 3 = T. And so, a Pigouvian tax of T : 3 will produce the efficient quantity of 9. We also could have just recognized that the damage per unit is a constant 3, so the optimal tax will be T : 3. 5 . We can follow 9.b for part a here, 9.d.i for part b, and finally 9.d.ii for part c. The graph below shows how the graph should look after including the Pigouvian tax as well. You’ll note that this graph is exactly the same as the graph on the left from 9.d.ii. Price“

MSC

s with Tax 3X

. QEFFICIENT QMARKET

D = MSB QLIantity

For part b, we can calculate the optimal tax using 9.d.i. First, we calculate the efficient quantity by noting D = MSB and then setting MSB = MSC —> 40 — Q = 15 + 4 Q —> 25 = 5 Q —> 5 = QEFHCIENT. Then, we can add a tax to supply, plug in the efficient quantity, and solve for T. 40 — Q = 10 + 2 Q + T —> 40 — 5 = 10 + 2(5)+T—>35=20+T—>

15=T.

272

ANSWERS TO ODD—NUMBERED QUESTIONS

7. Following 9.f, we can think about whether these goods are rival and/or excludable. a.

The light provided by lighthouses is certainly not rival—using some light to see doesn’t make that light any less illuminating for someone else steering a ship! It’s not excludable either—if you’re lighting up some coastline, you can’t stop some ships from seeing the light just because they refused to pay. This is thus a public good. Online newspapers are nonrival—someone reading an article doesn’t really “use up” the article in any meaningful way (negligible bandwidth costs aside). But they are excludable, and in fact many newspapers are hidden behind paywalls. So, this is an artificially scarce/club good.

. The dish in the middle of the table is rival—if you reach in and take some rolls, those rolls are no longer there for someone else to eat. But they’re not excludable. If they’re within reach of everyone and everyone is free to take some, then you can’t stop someone. And so, this is a common good. Sweaters are the exact kind of good we’ve been discussing in the other chapters of this book! A sweater is rival—outside of some unfortunate circumstances you can’t have two people wearing the same sweater. And it’s excludable—you can just withhold a sweater from someone who doesn’t pay for it. So, sweaters are private goods. 9. We can follow the spirit of 9.g.ii here, although this question is a bit simpler. If you catch one fish, you’ve caught one fish, s o the marginal benefit is one fish. If you catch one fish, then you have removed 1 5 fish from next year’s pond. Since that 1.5 fish would have been caught (because they’re emptying the pond) and shared evenly, the private marginal cost is 1.5/2 = .75 fish next year. . The social marginal cost will include the costs levied on everyone. That fish would have been 1.5 fish next year, so the social marginal cost is 1.5 fish next year . The number of fish that will be caught is based on private costs and benefits. Private benefit is 1 and private cost is .75. l > .75, so they’ll catch all 20 fish this year. The efficient number of fish to catch is based on the social costs and benefits. The social benefit is just the private benefit of 1 fish, and the social cost is 1.5 fish. 1 < 1.5, so they should catch 0 fish this year.

a.

Concept Questions A. This approach doesn’t consider the usage of the tax revenue at all, and indeed a Pigouvian tax is intended to make sure that the optimal amount of a given good i s produced, not that overall societal welfare i s maximized. And s o , implicitly, the Pigouvian tax i s completely neutral on the effect of the tax, effectively

assuming that the tax revenue will not be used to provide any benefits or costs to society.

C . We can calculate the market quantity in the usual way: 60 —- 2 Q = 1 0 + 3 Q —> 5 0 = 5 Q —-> 10 = QMARKET. And, similarly, we can get the efficient quantity from MSB = MSC —> 80 — Q = 20 + 4Q —> 60 = 5 Q —-> 12 = QEFFICIENT.So, the efficient quantity is 12, and we need a tax or subsidy that will get us a quantity of 12. Therefore, we add the tax T into the supply curve and then plug in Q = 12 toget60—2Q=10+3Q+T—>60—2(12)=10+3(12)+T—>36=10+36+ T —> T = —10. This means the optimal Pigouvian tax is —10, which is a negative number, so what we really have is a Pigouvian subsidy of 10. We can then graph in the usual way, shifting D up to represent the subsidy, and keeping track of Q EFnCIENT > QMARKET, and the fact that the slopes are all different. Then D with subsidy should intersect S at the efficient quantity, and have the same slope as D. Price“ MSC

10 12

Quantity

E. First, we need to figure out what the efficient outcome here is. James values having a mowed lawn at only $5, but Diane values not having to mow the lawn

highly—at $8. That trumps James’ $5, and so the efficient outcome here is for Diane to not end up with a mowed lawn.

274

ANSWERS TO ODD-NUMBERED QUESTIONS

a . Therefore, if Diane has the right to d o what she wants, the lawn will remain

unmowed, and no money will change hands. James will only be willing to pay her $ 5 to change her mind, and she won’t do it for less than $8. b. But if James has the legal right, Diane will realize she’s about to have to mow her lawn, and will offer James $5 per day in exchange for him not exercising his right. He’ll take it, since he only values the mowed lawn at $5 anyway, and her lawn will remain unmowed. Public goods are, by nature, non-rival and non-excludable. If provided in a competitive market (even a subsidized market), people will only buy units of the public good if it’s in their own self-interest. However, that self-interest leaves out the benefit provided to a lot of other people. And so, to provide the efficient quantity, the subsidy would need to be large enough to cover the marginal benefit provided to everyone else who benefits. That’s a big subsidy! Therefore, this approach isn’t going to be all that effective.

We’re looking here at taxes versus quotas as ways of dealing with pollution. a. Here, the government charges a fee of 6 per unit of pollution produced. And so, for each factory, the marginal benefit of reducing pollution by one unit is not having to pay that tax. And the marginal cost is as listed. And so, firm A s e t s M C A = 6 — > Q A = 6 , a n d fi r m B setsMCB=6—>4+QB=6——>QB=2. b. The government is forcing reduction now by the average of 6 and 2 units, which is 4 units per factory. We can immediately see that this is going to be less efficient than the tax, because it forces firm B to reduce pollution by 2 more units than before when it would be cheaper to have firm A do that reduction instead. We can also prove this mathematically. The benefit to society is the same in each situation (since pollution is reduced by 8 units in each case) so w e can just look at how costly the policy is. Simplifying a bit and considering each unit discretely (we can also do this by calculating the area of a triangle, but it’s a bit trickier), the cost to society of reducing pollution at firm A from the tax is l + 2 + 3 + 4 + 5 + 6 = 21, and the cost for reducing pollution at firm B i s (4 + l ) + (4 + 2) = l l , for a total cost of 2 1 + 11 = 3 2 . But under the quota, the cost to reduce pollution at firm A i s l + 2 + 3 + 4 = 1 0 , and the cost for reducing pollution at firm B i s (4 + l ) + (4 + 2) +

(4 + 3 ) + (4 + 4 ) = 2 6 , for a total cost of 1 0 + 26 = 3 6 . And s o , it’s more costly

to use the quota to achieve the same reduction.

INDEX

A

market quantity for, 229—230

absolute advantage, 1

M S B in relation to, 228—229

AC. See average cost accept. See willingness to accept activities capacity for, 3

autarky defined, 1

actually quantity, 104, 105, 108, 134

market equilibrium in relation to, 130—131 price compared to PW, 131 AV. See average cost AVC. See average variable cost

additional value, 8 9

average cost (AC), 143—144, 1 4 6 . See

efficient level of, 99—101 OC calculation for, 3—4

AFC. See average fixed cost aggregate demand curves, 35—37 defined, 23—24

schedule, 35—36

aggregate supply

also average fixed cost; average variable cost; long—run average total cost; short-run average cost calculating, 147—148 defined,139

curves, 35—37

graphing for, 148—149

defined, 23—24

MC i n relation to, 148—149,

schedule, 35—36

agriculture comparative advantage example from, 7—9

158—160, 176—177 practice problems on, 1 6 2 , 1 6 3 , 1 6 4

profit in relation to, 151—152 average fixed cost (AFC), 1 4 3 , 1 4 6

PPF example from, 10—12

calculating, 147

weather impacting, 1 5 , 1 6

defined,l39

artificially scarce goods defined,213 efficient outcome for, 228—230

as excludable and non-rival, 223

graphing for, 148—149 practice problems on, 162, 164 average variable cost (AVC), 1 4 3 ,

145—146

275

INDEX

276

average variable cost (AVC) (continued)

calculating, 147 defined,139

graphing for, 148—149 practice problems on, 162, 163, 164

extemality solved using, 219—221 practice problems on, 2 3 2 , 2 3 3

common goods defined, 2 1 2

market quantity for, 227—228 M S C in relation to, 2 2 8

B backwards induction defined,190

practice problems on, 207 for solving game trees, 199—202 barrier to entry defined,167

practice problems on, 187 barrier to exit, 1 6 7

benefits, 100—101. See also marginal social benefit best response defined,190

Nash equilibrium in relation to, 193—196 practice problems on, 209 as strategy, 193-196 binding market with price ceiling, 1 12—113, 114 market with price floor, 1 1 5 , 1 1 7

market with quotas, 127 branching path, 198—199 buy. See willingness to buy

as rival and non-excludable, 223, 224 comparative advantage agriculture example of, 7—9 calculating, 2—4 defined,1

kink point of, 8—9

DC in relation to, 18 in PPF, 1 3 practice problems on, 1 8 , 1 9 , 20

competition. See competitive market; monopolistic competition competitive market, 156 graphing firm in, 151—152 long-run equilibrium for, 158—160 practice problems on, 231 profit i n , 1 5 4 , 1 5 5

profit-maximizing quantity for, 149—150 zero-profit i n , 1 5 7 , 1 5 8 , 1 6 0

complements for cross—price elasticity, 6 8 defined,24

practice problems o n , 7 6 , 7 8

C capacity calculating, 3—4 costs conversion into, 2

club goods. See artificially scarce goods Coase theorem defined,211—212

supply and demand impacted by, 40—42 constant returns to scale defined,140—141 practice problems on, 1 6 3 , 1 6 4

consumer surplus calculating and graphing for, 93—97

INDEX

defined, 79—80

277

demand curve for, 95—96, 98—99

old and new points for calculating, 66-68

hurdle price discrimination in

practice problems o n , 7 6 , 7 8

relation to, 183—184 MV i n relation to, 93—94

practice problems o n , 1 0 7 , 1 0 8 ,

1 3 4 , 1 3 5 , 1 3 6 , 1 3 7 , 186 price changes graphed with, 98—99

deadweight loss (DWL) calculating, 101—104 defined,80

for quotas, 129—130

efficient quantity in relation to,

total of, 94, 9 5

102—103, 175—176 graphing for, 104—105 market surplus impacting, 175

willingness to pay in relation to, 95, 96 consumers. See also consumer surplus producers in relation to, 1 18—122 tax incidence i n relation to,

1 11—112 taxes compared to producers, 122—126 consumption practice problems o n , 7 6 , 7 7 , 1 0 8

rival and non-rival goods, 221—224 with or without trade, 12—14

costs. See also average cost; average fixed cost; average variable cost; fixed c o s t ; long-run average total c o s t ; marginal cost; marginal social cost;

MC and MV i n relation to, 101—105

in monopoly, 174—176 practice problems on, 1 0 7 , 1 0 8 ,

109,134,136,185,186 for price ceiling, 114-115 for price floor, 117 for quotas, 129—130 for taxes, 120—121

total surplus in relation to, 102—103, 111 decreasing returns to scale defined, 1 4 1

practice problems on, 163, 164 demand. See also demand curve; demand schedule; demand

benefits relative to, 100—101

shifts; inverse demand; quantity demanded complements and substitutes impacting, 40—42

capacity converted from, 2

defined,23

filling out tables for, 143—146

income impacting, 38—40 market surplus and shortage in

opportunity cost; short-run average c o s t ; total cost; variable

cost

profit in relation to, 173—174 of units, 24—26

cross-price elasticity complements and substitutes for, 6 8

relation to, 42—44

perfect elasticity and inelasticity for, 70—71

INDEX

practice problems, 52—53, 54—55

demand (continued)

practice problems on, 5 2 predicting shifts in, 37—42 relative elasticity and inelasticity

predicting, 37—42 dominant strategy, 190 drawing of demand curve, 32—34

for, 124—126

of game table for simultaneous

demand curve

aggregate, 35—37 for consumer surplus, 95—96, 98—99

games, 190—193

defined,23

of game tree for sequential games, 196—199

drawing of, 32—34

PPF for economy, 10—12

inverse, 3 6 , 45

PPF for one person, 4—7

for market equilibrium, 44—47 market equilibrium with shifting, 47—51 for market surplus and shortage, 42—44

PPF for two people, 7—9

of price elasticity, 68—71 of supply curve, 27—29 DWL. See deadweight loss

for MR , 170—172

E

from MV, 90—91

economic surplus, 80. See also total surplus economy

M V on, 91—93 practice problems o n , 5 2 , 5 3 , 5 4 ,

76, 106, 107, 108, 163, 186 price elasticity calculated with, 63—66 slope change for, 64—65 for taxes, 120—121 demand schedule

aggregate, 35—36 defined,23 for demand curve, 32—34

making of, 29—31 for MV, 90—91

practice problems on, 52, 186 demand shifts

elasticity used with, 71—73 for equilibrium price, 47—51 , 71—73

for equilibrium quantity, 47—51 , 71—73

PPF for, 10—12 PPF shift for, 15—17

efficiency. See also efficient level; efficient outcome; efficient

quantity of market, 8 0 , 1 1 1 practice problems on, 1 0 7 , 1 0 8 ,

185—186, 187, 232, 234 efficient level of activities, 99—101 practice problems on, 186 of public good, 225 efficient outcome, 101 for artificially scarce goods, 228—230 with Coase theorem, 219—221

for common goods, 227—228

INDEX defined,215

for price ceiling, 1 12—11 3

for extemality, 214—215, 219—221

for price floor, 1 1 5 , 1 1 6

practice problems on, 233 for public goods, 224—227 efficient quantity artificially scarce goods in relation to, 228—230 benefits with, 100—101

DWL in relation to, 102—103,

175—176 with hurdle price discrimination, 183 optimal quantity in relation to, 100—101, 226 Pigouvian tax and subsidy in relation to, 216—21 7

practice problems on, 107, 108, 231, 232, 233 elasticity, 6 2 . See also cross-price elasticity; income elasticity;

price elasticity; relative elasticity; unit elasticity defined,57

for quotas, 1 2 7

shifting supply and demand curves for, 47—51, 71—73 for taxes, 1 2 2

equilibrium quantity graphing, 46—47 long run, 158—160 practice problems on, 5 3 , 5 4 , 5 5 ,

77, 78, 134 for quotas, 1 2 7

shifting supply and demand curves for, 47—51 , 71—73

excise taxes, 1 1 1

excludability defined,212

for goods, 222—224 exporting goods, 131—133 extemality. See also negative extemality; positive extemality Coase theorem used for solving, 219—221

determination of, 73—74

defined,2ll

practice problems o n , 7 5 , 7 6 , 7 7 ,

efficient outcome for, 214—215,

78, 134

219—221 graphing for, 213—214 inverse supply and demand for,

response, 66, 7 5

for supply and demand, 5 7 supply and demand shifts using, 71—73 for tax incidence compared to inelasticity, 124—126 equilibrium price graphing, 46—47 long-run, 158—160 practice problems on, 5 3 , 5 4 , 5 5 ,

77, 78, 134, 163

279

214—21 5 F

F C. See fixed cost firm

calculating profit for, 153—155 competitive market graphing of, 151—152 modeling for market and, 155—157

280

INDEX

firm (continued)

defined,189

modeling market entry and exit for, 156, 157 specialization for, 160—161 first-degree price discrimination. See perfect price discrimination

practice problems on, 207, 208 predicting effects of repeated

fixed cost (FC), 145—146. See also

average fixed cost defined,139

practice problems on, 162 TC i n relation to, 1 4 2

VC compared to, 141—143 free ride, 2 1 2

G game table defined,189

drawing for simultaneous games, 190—193 Nash equilibrium i n , 193—196

outcomes for, 1 9 1

payouts, 192—193 practice problems o n , 206, 2 0 8 , 209

interactions with, 203—205

tit for tat w i t h , 204

trigger for, 205 goods, 6 8 . See also artificially scarce

goods; common goods; exporting goods; importing goods; price of goods; private goods; public goods excludable and non-excludable,

222—224 practice problems on, 232, 234 rival and non-rival consumption of, 221—224 types of, 58, 212—213, 221—230 government revenue practice problems on, 134 taxes as, 120—122

graphing. See also modeling for AC, 148—149 for consumer surplus, 93—97

game tree backwards induction for solving, 199—202 branching path for, 198—199 defined,189 drawing for sequential games, 196—199

for consumer surplus with price changes, 98—99

nodes for, 197—198, 199—201

discrimination, 181—1 8 2

payouts for, 198—200, 201 practice problems on, 207, 209, 2 1 0

threats impacting, 203—204 games. See also game table; game tree;

sequential games; simultaneous games

for DWL,

104—105

for extemality, 213—214 firm in competitive market, 151—152 for less-than-perfect price long-run equilibrium for monopolistic competition, 179—180 for LRAC, 160—161 for market equilibrium, 46—47

for monopoly, 176—177

INDEX

for natural monopoly, 177—178 for perfect price discrimination, 180—181 for Pigouvian subsidy, 218 for Pigouvian tax, 218 practice problems on, 107, 108, 134, 135, 162, 163, 165, 185—186, 187, 233 for producer surplus, 85—88 for producer surplus with price changes, 97—98

short-run equilibrium for monopolistic competition, 178—179

281

practice problems on, 5 4 individual supply defined,23

market supply from aggregating, 35—37 inelasticity, 62. See also perfect inelasticity; relative inelasticity determination, 73—74 practice problems on, 7 5 , 7 8 response, 66, 74

for supply and demand, 5 7 for tax incidence compared to elasticity, 124—126 inferior good defined,58

H

for income elasticity, 6 8

hurdle price discrimination calculating, 182—184 consumer surplus i n relation to,

183—184 defined,168

efficient quantity with, 183

infinite number, 7 0

international trade importing and exporting goods for, 1 3 1—133 modeling for, 130—133 inverse demand curve, 3 6 , 45

I

curve for M R , 1 7 1

importing goods, 131—133

defined, 2 3

income, 38—40

for extemality, 214—215

income elasticity, 5 7 old and new points for calculating, 66—68

practice problems o n , 5 3 , 1 0 7 , 1 3 4 ,

practice problems on, 7 6

increasing returns to scale defined,140

practice problems on, 1 6 3 , 1 6 4

individual demand

135, 136, 137, 163, 164, 209, 231, 232, 233 for price ceiling, 112—11 3 for price floor, 115—].1 6 for taxes, 118—119

inverse supply curve, 2 8 , 3 6 , 4 5

defined, 2 3

curve for M C , 84—85

market demand from aggregating, 35—37

defined,23

for extemality, 214—215

282

INDEX

inverse supply (continued) practice problems o n , 7 7 , 7 8 , 1 0 7 ,

marginal cost (MC), 1 4 3 , 145—146. See

also marginal social cost

134, 1 3 5 , 1 3 6 , 1 3 7 , 1 6 3 , 231, 232, 233 for price ceiling, 112—11 3 for price floor, 115—11 6

158—160, 176—177 calculating, 80—81

for taxes, 118—1 1 9

DWL i n relation to, 101—105

AC i n relation to, 148—149,

defined,79,139

inverse supply curve for, 84—85

K

MR i n relation to, 149—150

kink point of comparative advantage, 8—9 practice problems on, 18

MV equaling, 99—100 practice problems on, 106, 108, 109, 162, 163, 164, 185, 186, 234 on supply curve, 83—85 supply curve derived from, 82—83 TC in relation to, 80—81 as VC, 141 willingness to sell in relation to, 83—84, 85

L less-than-perfect price discrimination defined,168

graphing for, 181—182 limited licensing systems, 1 l 2 long-run average total cost (LRAC)

graphing for, 160—161 practice problems on, 163, 165 long-run equilibrium monopolistic competition graphing of, 179—180 price and quantity, 158—160 long-run market behavior market entry and exit for, 153—155 practice problems on, 164, 188 short-run market behavior compared to, 1 4 0

marginal revenue (MR), 1 4 3 , 1 4 4

defined,l68 demand curve for, 170—172

MC i n relation to, 149—150

practice problems on, 163—164, 185, 186, 187 marginal social benefit (MSB) artificially scarce goods in relation to, 228—229 common goods in relation to, 227—228 efficient outcome i n relation to,

LRAC. See long-run average total cost luxury good, 58, 6 8

214—215 positive extemality impacting, 213—214

M

practice problems on, 2 3 1 , 2 3 2 , 234

marginal benefit. See marginal social benefit

public goods in relation to, 224—227

INDEX

marginal social cost (MSC)

common goods in relation to, 228 efficient outcome i n relation to,

214—215 negative extemality impacting, 213—214 practice problems on, 232, 233 marginal value (MV), 30 calculating, 88—90 consumer surplus in relation to, 93—94

162, 163, 185—186, 187, 188, 208 price ceiling binding, 112—]13, 114 price control for, 1 11 price floor binding, 115, 117 price taker in, 151 quotas binding, 127 structure distinction, 168—170

supply and demand, 35—37 world, 130—133 market entry

defined,79

defined, 1 4 0

on demand curve, 91—93 demand curve derived from, 90—91

for long-run market behavior, 153—155

DWL i n relation to, 101—105

for modeling of firm, 1 5 6 , 1 5 7

MC equaling, 99—100 practice problems on, 1 0 6 , 1 0 8 , 1 0 9

for producer surplus, 85 total value in relation to , 88—89

willingness to buy in relation to, 91, 92—93 market. See also competitive market; long—run market behavior; market entry; market equilibrium; market exit;

market quantity; market shortage; market surplus; short-run market behavior behavior, 153—155

efficiency of, 80, 111 graphing firm in competitive, 151—152 imperfection, 102 modeling for firm and, 155—157 as monopoly, 169 as oligopoly, 169—170 practice problems o n , 1 0 7 , 1 0 8 ,

283

market equilibrium. See also equilibrium price; equilibrium quantity; long-run equilibrium; short-run equilibrium autarky in relation to, 130—131 calculating, 44—46 defined,24

graphing, 46—47 practice problems on, 53, 5 4 quantity and price, 47—51 shifting supply and demand curves for, 47—51 supply and demand curves for, 44—47 market exit defined, 1 4 0 for long-run market behavior,

153—155 for modeling of firm, 1 5 6 , 1 5 7

market quantity for artificially scarce goods, 229—230

284

INDEX

perfect competition in relation

market quantity (continued) for common goods, 227—228

to, 1 7 0

practice problems on, 186, 187, 188 product differentiation in relation

practice problems on, 2 3 1 , 2 3 2 ,

233 market shortage defined,24

practice problems on, 53, 134 price ceiling in relation to, 113—114, 115 supply and demand in relation to, 42—44 market surplus

to, 1 7 0

monopoly. See also natural monopoly calculating profit for, 173—174 defined,167

DWL in, 174—176 graphing for, 176—177 market as, 169

defined, 24

DWL impacted by, 175 practice problems on, 53, 134 price floor in relation to, 1 1 6 supply and demand in relation to, 42—44 MC. See marginal cost midpoint method percentage change calculated with, 58, 60—61 practice problems on, 7 5 modeling for international trade, 130—133 for market and firm, 155—157

modeling of, 170—178 M R for, 170—172

practice problems on, 1 8 5 , 1 8 7 ,

188, 209 profit-maximizing quantity and price for, 172—173 MR. See marginal revenue MSB. See marginal social benefit MSC. See marginal social cost MV. See marginal value

N Nash equilibrium defined,190

of monopoly, 170—178

i n game table, 193—196

for price maximums, 1 12—11 5

outcomes, 201—202

for price minimums, 115—] l 7 for quotas, 127—130

practice problems on, 206—207, 208, 209, 210

for taxes, 1 18—122

with repeated interactions, 203, 205

monopolistic competition defined,167 graphing long-run equilibrium for, 179—180 graphing short-run equilibrium for, 178—179

strategy, 201 —202 natural monopoly defined,167,178

graphing for, 177—178 market as, 1 6 9

practice problems on, 187

INDEX

negative extemality defined,211

MSC impacted by, 213—214 practice problems on, 232, 233 nodes, 197—198, 199—201

non-excludability defined, 2 1 2

for goods, 222—224 non-rival defined, 2 1 2

goods consumption, 221—224 normal good, 5 8 , 6 8

0 OC. See opportunity cost oligopoly defined, 167, 189 market as, 169—170

practice problems on, 1.87, 206 price war in relation to, 205 opportunity cost (0C) calculating, 3—4

comparative advantage in relation to, 18 defined, 1

in PPF, 6, 9, 'l 1 practice problems o n , 1 8 , 1 9 ,

20, 109 optimal price, 152 practice problems on, 185, 186 for third-degree price discrimination, 182 optimal profit, 185, 186 optimal quantity, 105, 152 efficient quantity in relation to, 100—101, 226 practice problems on, 1 8 5 , 1 8 6

285

outcomes. See also efficient outcome for game table, 191 with Nash equilibrium, 201—202 promises impacting desired, 203—204

p pay. See willingness to pay payouts

best response impacting, 193—196 for game table, 192—193 for game tree, 198—200, 2 0 1

PD. See price paid percentage change midpoint method calculating, 5 8, 60—61 practice problems on, 7 5 in price and quantity for elasticity, 57, 61—63, 67 standard method calculating, 58, 5 9 perfect competition monopolistic competition in relation to, 1 7 0

practice problems on, 187 perfect elasticity, 5 7 practice problems on, 7 6 for supply and demand, 70—71 perfect inelasticity, 5 7 , 6 2 , 66, 70—71

perfect price discrimination defined, 1 6 8

graphing for, 180—181 practice problems on, 186 Pigou’vian subsidy, 21 1. calculating, 216—217 graphing for, 218 practice problems o n , 2 3 1 , 2 3 3 , 234

286

INDEX

Pigouvian tax calculating, 216—217 defined,211

graphing for, 218 practice problems on, 2 3 1 , 2 3 2 , 2 3 3

point elasticity, 5 7 positive externality defined,211

M S B impacted by, 213—214 practice problems on, 2 3 1 , 2 3 3 , 234

PPF. See production possibility frontier price, 143—144. See also hurdle price discrimination; less—than-

perfect price discrimination; perfect price discrimination; price ceiling; price control; price elasticity; price floor; price maximum; price minimum; price of goods; price paid; price received; profit—maximizing price

price control defined,24 for market, 1 1 1

price discrimination, 168. See also hurdle price discrimination; less-than-perfect price discrimination; perfect price discrimination price elasticity drawing of, 68—71 old and new points for calculating, 61—63 percentage change in calculating, 57, 61—63, 67 supply and demand curves for calculating, 63—66 price floor, 24 b in d ing market with, 1 1 5 , 1 1 7 DWL for, 1 1 7

practice problems on, 186—187

equilibrium price for, 115, 116 inverse supply and demand for, 115—116

profit-maximizing quantity in

market binded with, 1 1 5 , 1 1 7

relation to, 149—150 as PW, 130—133, 1 3 5

third-degree price discrimination for charging, 181—182 price ceiling, 24 binding market with, 112—113, 114 DWL for, 114—1 1 5

equilibrium price for, 1 12—11 3 market binded with, 112—113, 1.14

market shortage in relation to, 113—114, 115 practice problems on, 1 3 4 , 1 3 6 ,

137, 187 Q5 and QD for, 113—114

market surplus in relation to, 116 practice problems on, 1 3 4 , 1 3 7 , 1 6 5

Q5 and Q0 for, 116—117 price maximum, 24. See also price

ceiling defined,111

modeling for, 112—115 price minimum, 24. See also price floor defined,111

modeling for, 115—117 price of goods, 23. See also world price complements and substitutes impacting, 40—42 QD in relation to, 30—31 , 32—34

INDEX 287 QS i n relation to, 24—26

supply impacted by, 38—40 price paid (PD) practice problems o n , 1 3 4 , 1 3 5 , 1 3 6

P5 i n relation to, 118—130

price received (PS)

PD in relation to, 118—130 practice problems on, 1 3 4 , 1 3 5 , 1 3 6

price taker defined,139—l40 i n market, 1 5 1

price war, 205 price-setting, 205 pricing power, 167 prisoner’s dilemma, 203 defined,190

practice problems on, 209 as price-setting oligopoly game, 205 private goods practice problems on, 234 as rival and excludable, 223

producer surplus calculating and graphing for, 85—88

product differentiation defined,168 monopolistic competition in relation to, 170 production license, 128 production possibility frontier (PPF) comparative advantage in, 1 3 for consumption, 12—14 defined,2

drawing for economy, 10—12 drawing for one person, 4—7 drawing for two people, 7—9 DC in, 6, 9, 11 practice problems o n , 1 8 , 1 9 , 20—21

shifting of, 15—17 weather impacting, 15, 16 profit. See also optimal profit; profit—maximizing price; profit—maximizing quantity; zero-profit AC i n relation to, 151—152

calculating, 152—153 calculating, for firm, 153—155

defined,80

i n competitive market, 1 5 4 , 1 5 5

practice problems o n , 1 0 6 , 1 0 7 ,

defined,139

108, 134, 135, 136, 137, 186 price changes graphed with, 97—98

filling out tables for, 143—146 monopoly calculating, 173—174

for quotas, 129—130

practice problems on, 1 6 4 , 1 6 5 ,

willingness to accept in relation to, 86, 8 8 producers. See also producer surplus consumers i n relation to, 118—122

consumers taxes compared to, 122—126 production license for, 128 tax incidence in relation to, 111—112

185, 186, 188, 209 profit-maximizing price for monopoly, 172—173 for natural monopoly, 177—178 practice problems on, 185, 187 profit-maximizing quantity for competitive market, 149—150 defined,140

for monopoly, 172—173

288

INDEX

profit-maximizing quantity (continued) for natural monopoly, 177—178

practice problems o n , 1 6 2 , 1 6 3 ,

185, 187 price in relation to, 149—150

quota rent, 129—130, 1 3 5

quotas consumer and producer surplus for, 129—130 defined,112

specialization for, 160—] 6 1

promises, 203—204 P5. See price received public goods defined, 2 1 2

efficient outcome for, 224—227 as non-rival and non-excludable,

223 practice problems on, 234 PW. See world price

0 QD. See quantity demanded Q5. See quantity supplied quantity. See actually quantity; efficient quantity; equilibrium quantity; market quantity; optimal quantity; profit-maximizing quantity; quantity demanded; quantity supplied quantity demanded (QB), 2 3

for international trade, 131—1 3 3

for price ceiling, 1 13—114 for price floor, 116—117 price of goods in relation to, 30—31,

32—34 quantity supplied (Q5), 2 3 for international trade, 1 31—133

practice problems on, 164 for price ceiling, 1 13—114 for price floor, 1 16—117 price of goods in relation to, 24-26

modeling for, 127—130 practice problems on, 135

R relative elasticity defined, 57—58

practice problems on, 7 6 relative inelasticity compared to, 68—69, 71—73 for supply and demand, 124—126 relative inelasticity practice problems on, 7 6 relative elasticity compared to, 68—69, 71—73 for supply and demand, 124—126 repeated interaction defined,190

with games, 203—205 Nash equilibrium with, 2 0 3 , 205

reservation price, 7 9 response. See also best response elastic, 66, 7 5 inelastic, 66, 74

revenue. See also marginal revenue; total revenue filling out tables for, 143—146 government, 120—122, 1 3 4

practice problems on, 233 rival defined, 2 1 2 goods consumption, 2 2 1 - 2 2 4

INDEX

S schedule. See demand schedule; supply schedule second-degree price discrimination. See hurdle price discrimination sell. See willingness to sell sequential games defined,189

game tree drawing for, 196—199 short-run average cost (SRAC) LRAC i n relation to, 160—16 1

practice problems on, 163, 165 short-run equilibrium, 178—179 short-run market behavior long-run market behavior compared to,14O practice problems on, 1 8 6 , 1 8 8

shutdown

practice problems on, 7 5 strategy best response as, 1 9 0 , 193—196 dominant, 1 9 0

Nash equilibrium as, 201—202 subgame-perfect Nash equilibrium, 200 subsidy, 135. See also Pi gouvian subsidy substitutes for cross-price elasticity, 6 8 defined,24 practice problems on, 7 6 , 7 8

supply and demand impacted by, 40—42 supply. See also inverse supply; quantity supplied; supply curve; supply schedule; supply shifts complements and substitutes impacting, 40—42

defined,140

defined,23

practice problems on, 1 6 4

market surplus and shortage in

simultaneous games defined, 189 game table drawing for, 190—193 slope change practice problems on, 109 for supply and demand curves, 64—65 specialization defined, 1 for firm, 160—161

specialize and trade defined, 2

practice problems on, 19 SRAC. See short-run average cost standard method percentage change calculated with, 58, 5 9

289

relation to, 42—44

as perfect elasticity and inelasticity, 70—71, predicting shifts in, 37—42 price of goods impacting, 38—40 relative elasticity for, 124—126 relative inelasticity for, 124—126 supply curve aggregate, 35—37 defined, 23 drawing of, 27—29 inverse, 2 8 , 3 6 , 45

for market equilibrium, 44—47

market equilibrium with shifting, 47—51 for market surplus and shortage, 42—44

290

INDEX

106, 108, 163, 164, 233

DWL for, 120—121 equilibrium price for, 122 inverse supply and demand for, 1 18—119 modeling for, 118—122

price elasticity calculated with,

practice problems on, 1 3 4 , 1 3 5 ,

supply curve (continued) from MC, 82—83 MC o n , 83—85 practice problems on, 5 2 , 5 3 , 5 4 ,

63—66 for producer surplus, 97—98 slope change for, 64—65 for taxes, 120—121, 122—123

supply schedule, 2 3 aggregate, 35—36 making of, 24—26 from MC, 82—83 practice problems on, 52, 54 for supply curve, 27—29 supply shifts elasticity used with, 71—73 for equilibrium quantity and price, 47—51, 71—73

136, 234 supply and demand curve for, 120—]21 TC. See total cost third-degree price discrimination. See less-than-perfect price discrimination threats, 203—204

tit for tat, 204 total cost (TC), 1 4 1 , 143—146. See also

long-run average total cost AC i n relation to, 147—148

defined,139 FC i n relation to, 1 4 2

practice problems o n , 52—53, 54—55

MC in relation to, 80—81

predicting, 37—42

practice problems on, 1 0 6 , 1 6 2 ,

surplus. See consumer surplus; market

surplus; producer surplus; total surplus

163—164 TR in relation to, 1 5 2 VC i n relation to, 1 4 2

total revenue (TR), 143~144

T

defined,139

tax incidence calculating, 122—126

defined, 111—112 elasticity compared to inelasticity for, 124—126

practice problems on, 136 taxes. See also excise taxes; Pigouvian tax; tax incidence

consumers compared to producers with, 122—126

practice problems o n , 1 6 4

TC i n relation to, 1 5 2

total surplus defined,80 DWL i n relation to, 102—103, 1 1 1

total value, 88—89 TR. See total revenue

trade. See also international trade consumption with or without, 12—14

I N D EX

,21, 134,

291

defined, 7 9

producer surplus i n relation to, 86, 88

willingness to buy, 9 1 , 92—93

_//‘ .4"

.‘

,ity, 62, 66 nned,57

willingness to pay. See also willingness to buy consumer surplus in relation to, 95, 96 defined,79

determination, 73—74

perfect price discrimination in

units, 23, 24—26. See also quantity supplied

relation to, 180—181

willingness to sell, 79

V

MC i n relation to, 83—84, 8 5

value, 88—89. See also additional value;

perfect price discrimination in

marginal value variable cost (VC), 145—146. See also average variable cost

relation to, 180—181

FC compared to, 141—143

world market, 130—133 world price (PW) autarky price compared to, 131 practice problems on, 135

practice problems on, 1 6 2

world market in relation to,

defined,139

TC i n relation to, 1 4 2

130—133

W weather, 1 5 , 1 6

Z

willingness to accept. See also willingness to sell

zero Nash equilibria, 195—196 zero—profit, 1 5 7 , 1 5 8 , 1 6 0