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PART ONE Introduction
After studying this chapter,
you will be able to:
Define economics and distinguish between
microeconomics and macroeconomics
Explain the two big questions of economics
Explain the key ideas that define the economic way of
thinking
Explain how economists go about their work as social
scientists and policy advisers
1
Y
ou are studying economics at a time of extraordinary challenge and change.
The United States, Europe, and Japan, the worlds richest nations, are still not
fully recovered from a deep recession in which incomes shrank and millions of
jobs were lost. Brazil, China, India, and Russia, poorer nations with a
combined population that dwarfs our own, are growing rapidly and playing
ever-greater roles in an expanding global economy.
The economic events of the past few years stand as a stark reminder that we
live in a changing and sometimes turbulent world. New businesses are born and
old ones die. New jobs are created and old ones
disappear. Nations, businesses, and individuals must find
ways of coping with economic change.
Your life will be shaped by the challenges that you
face and the opportunities that you create. But to face those challenges and
seize the opportunities they present, you must understand the powerful forces at
play. The economics that youre about to learn will become your most reliable
guide. This chapter gets you started. It describes the questions that economists
try to answer and the ways in which they think as they search for the answers.
WHAT IS ECONOMICS?
1
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CHAPTER 1 What Is Economics?
x Definition of Economics
A fundamental fact dominates our lives: We want
more than we can get. Our inability to get everything
we want is called scarcity. Scarcity is universal. It confronts all living things. Even parrots face scarcity!
Because we cant get everything we want, we must
make choices. You cant afford both a laptop and an
iPhone, so you must choose which one to buy. You
cant spend tonight both studying for your next test
and going to the movies, so again, you must choose
which one to do. Governments cant spend a tax dollar on both national defense and environmental protection, so they must choose how to spend that dollar.
Your choices must somehow be made consistent
with the choices of others. If you choose to buy a laptop, someone else must choose to sell it. Incentives reconcile choices. An incentive is a reward that encourages
an action or a penalty that discourages one. Prices act
as incentives. If the price of a laptop is too high, more
will be offered for sale than people want to buy. And if
the price is too low, fewer will be offered for sale than
people want to buy. But there is a price at which
choices to buy and sell are consistent.
Economics is the social science that studies the
choices that individuals, businesses, governments,
and entire societies make as they cope with scarcity
and the incentives that influence and reconcile those
choices.
Not only do I want a crackerwe all want a cracker!
The New Yorker Collection 1985
Frank Modell from cartoonbank.com. All Rights Reserved.
Think about the things that you want and the
scarcity that you face. You want to live a long and
healthy life. You want to go to a good school, college,
or university. You want to live in a well-equipped,
spacious, and comfortable home. You want the latest
smart phone and a faster Internet connection for
your laptop or iPad. You want some sports and recreational gearperhaps some new running shoes, or a
new bike. And you want more time, much more than
is available, to go to class, do your homework, play
sports and games, read novels, go to the movies, listen
to music, travel, and hang out with your friends.
What you can afford to buy is limited by your
income and by the prices you must pay. And your
time is limited by the fact that your day has 24 hours.
You want some other things that only governments provide. You want to live in a peaceful and
secure world and safe neighborhood and enjoy the
benefits of clean air, lakes, and rivers.
What governments can afford is limited by the
taxes they collect. Taxes lower peoples incomes and
compete with the other things they want to buy.
What everyone can getwhat society can getis
limited by the productive resources available. These
resources are the gifts of nature, human labor and
ingenuity, and all the previously produced tools and
equipment.
The subject has two parts:
Microeconomics
s Macroeconomics
Microeconomics is the study of the choices that individuals and businesses make, the way these choices
interact in markets, and the influence of governments.
Some examples of microeconomic questions are: Why
are people downloading more movies? How would a
tax on e-commerce affect eBay?
Macroeconomics is the study of the performance of
the national economy and the global economy. Some
examples of macroeconomic questions are: Why is
the U.S. unemployment rate so high? Can the
Federal Reserve make our economy expand by cutting interest rates?
s
REVIEW QUIZ
1
2
3
List some examples of the scarcity that you face.
Find examples of scarcity in todays headlines.
Find an illustration of the distinction between
microeconomics and macroeconomics in
todays headlines.
You can work these questions in Study
Plan 1.1 and get instant feedback.
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Two Big Economic Questions
x Two Big Economic
FIGURE 1.1
3
What Three Countries Produce
Questions
Two big questions summarize the scope of economics:
s
s
United States
How do choices end up determining what, how,
and for whom goods and services are produced?
Can the choices that people make in the pursuit of
their own self-interest also promote the broader
social interest?
Brazil
China
What, How, and For Whom?
are the objects that people value
and produce to satisfy human wants. Goods are physical objects such as cell phones and automobiles.
Services are tasks performed for people such as cellphone service and auto-repair service.
0
20
40
60
Percentage of production
Goods and services
What? What we produce varies across countries and
changes over time. In the United States today, agriculture accounts for 1 percent of total production,
manufactured goods for 22 percent, and services
(retail and wholesale trade, health care, and education
are the biggest ones) for 77 percent. In contrast, in
China today, agriculture accounts for 11 percent of
total production, manufactured goods for 49 percent,
and services for 40 percent. Figure 1.1 shows these
numbers and also the percentages for Brazil, which
fall between those for the United States and China.
What determines these patterns of production?
How do choices end up determining the quantities of
cell phones, automobiles, cell-phone service, autorepair service, and the millions of other items that are
produced in the United States and around the world?
How? Goods and services are produced by using pro-
ductive resources that economists call factors of proFactors of production are grouped into four
categories:
duction.
s
s
s
s
Land
Labor
Capital
Entrepreneurship
Land The gifts of nature that we use to produce
goods and services are called land. In economics,
land is what in everyday language we call natural
resources. It includes land in the everyday sense
Agriculture
Manufacturing
80
100
Services
Agriculture and manufacturing is a small percentage of production in rich countries such as the United States and a
large percentage of production in poorer countries such as
China. Most of what is produced in the United States is
services.
Source of data: CIA Factbook 2010, Central Intelligence Agency.
animation
together with minerals, oil, gas, coal, water, air,
forests, and fish.
Our land surface and water resources are renewable and some of our mineral resources can be recycled. But the resources that we use to create energy
are nonrenewablethey can be used only once.
The work time and work effort that people
devote to producing goods and services is called
labor. Labor includes the physical and mental efforts
of all the people who work on farms and construction sites and in factories, shops, and offices.
The quality of labor depends on human capital,
which is the knowledge and skill that people obtain
from education, on-the-job training, and work experience. You are building your own human capital
right now as you work on your economics course,
and your human capital will continue to grow as you
gain work experience.
Human capital expands over time. Today, 87 percent of the adult population of the United States have
completed high school and 29 percent have a college
or university degree. Figure 1.2 shows these measures
of the growth of human capital in the United States
over the past century.
Labor
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CHAPTER 1 What Is Economics?
4
Percentage of adult population
100
For Whom? Who consumes the goods and services
that are produced depends on the incomes that people earn. People with large incomes can buy a wide
range of goods and services. People with small
incomes have fewer options and can afford a smaller
range of goods and services.
People earn their incomes by selling the services of
the factors of production they own:
A Measure of Human
Capital
FIGURE 1.2
Less than 5 years of
elementary school
75
Some high school
s
Completed
high school
50
s
s
s
25
4 years or
more of college
0
1908
Year
1928
1948
1968
1988
2008
In 2008 (the most recent data), 29 percent of the population had 4 years or more of college, up from 2 percent in
1908. A further 58 percent had completed high school, up
from 10 percent in 1908.
Source of data: U.S. Census Bureau, Statistical Abstract of the
United States, 2010.
animation
The tools, instruments, machines, buildings,
and other constructions that businesses use to produce goods and services are called capital.
In everyday language, we talk about money,
stocks, and bonds as being capital. These items are
financial capital. Financial capital plays an important
role in enabling businesses to borrow the funds that
they use to buy physical capital. But because financial
capital is not used to produce goods and services, it is
not a productive resource.
Capital
The human resource that
organizes labor, land, and capital is called entrepreneurship. Entrepreneurs come up with new ideas
about what and how to produce, make business
decisions, and bear the risks that arise from these
decisions.
Entrepreneurship
What determines the quantities of factors of
production that are used to produce goods and
services?
Land earns rent.
Labor earns wages.
Capital earns interest.
Entrepreneurship earns profit.
Which factor of production earns the most
income? The answer is labor. Wages and fringe
benefits are around 70 percent of total income.
Land, capital, and entrepreneurship share the rest.
These percentages have been remarkably constant
over time.
Knowing how income is shared among the factors of production doesnt tell us how it is shared
among individuals. And the distribution of income
among individuals is extremely unequal. You know
of some people who earn very large incomes:
Angelina Jolie earns $10 million per movie; and the
New York Yankees pays Alex Rodriguez $27.5 million a year.
You know of even more people who earn very
small incomes. Servers at McDonalds average
around $7.25 an hour; checkout clerks, cleaners,
and textile and leather workers all earn less than $10
an hour.
You probably know about other persistent differences in incomes. Men, on average, earn more
than women; whites earn more than minorities;
college graduates earn more than high-school
graduates.
We can get a good sense of who consumes
the goods and services produced by looking at
the percentages of total income earned by
different groups of people. The 20 percent of people with the lowest incomes earn about 5 percent
of total income, while the richest 20 percent earn
close to 50 percent of total income. So on average,
people in the richest 20 percent earn more than
10 times the incomes of those in the poorest
20 percent.
Why is the distribution of income so unequal?
Why do women and minorities earn less than white
males?
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Two Big Economic Questions
Economic Instability The years between 1993 and
2007 were a period of remarkable economic stability,
so much so that theyve been called the Great
Moderation. During those years, the U.S. and global
economies were on a roll. Incomes in the United
States increased by 30 percent and incomes in China
tripled. Even the economic shockwaves of 9/11
Economics in Action
A Credit Crunch
Flush with funds and offering record low interest
rates, banks went on a lending spree to home buyers.
Rapidly rising home prices made home owners feel
well off and they were happy to borrow and spend.
Home loans were bundled into securities that were
sold and resold to banks around the world.
In 2006, as interest rates began to rise and the
rate of rise in home prices slowed, borrowers
defaulted on their loans. What started as a trickle
became a flood. As more people defaulted, banks
took losses that totaled billions of dollars by mid2007.
Global credit markets stopped working, and
people began to fear a prolonged slowdown in economic activity. Some even feared the return of the
economic trauma of the Great Depression of the
1930s when more than 20 percent of the U.S. labor
force was unemployed. The Federal Reserve, determined to avoid a catastrophe, started lending on a
very large scale to the troubled banks.
5
brought only a small dip in the strong pace of U.S.
and global economic growth.
But in August 2007, a period of financial stress
began. A bank in France was the first to feel the pain
that soon would grip the entire global financial
system.
Banks take in peoples deposits and get more funds
by borrowing from each other and from other firms.
Banks use these funds to make loans. All the banks
choices to borrow and lend and the choices of people
and businesses to lend to and borrow from banks are
made in self-interest. But does this lending and borrowing serve the social interest? Is there too much borrowing and lending that needs to be reined in, or is there
too little and a need to stimulate more?
When the banks got into trouble, the Federal
Reserve (the Fed) bailed them out with big loans
backed by taxpayer dollars. Did the Feds bailout of
troubled banks serve the social interest? Or might the
Feds rescue action encourage banks to repeat their
dangerous lending in the future?
Banks werent the only recipients of public funds.
General Motors was saved by a government bailout.
GM makes its decisions in its self-interest. The government bailout of GM also served the firms self-interest.
Did the bailout also serve the social interest?
REVIEW QUIZ
1
2
Describe the broad facts about what, how, and
for whom goods and services are produced.
Use headlines from the recent news to illustrate
the potential for conflict between self-interest
and the social interest.
You can work these questions in Study
Plan 1.2 and get instant feedback.
Weve looked at four topics and asked many questions that illustrate the big question: Can choices
made in the pursuit of self-interest also promote the
social interest? Weve asked questions but not
answered them because weve not yet explained the
economic principles needed to do so.
By working through this book, you will discover
the economic principles that help economists figure
out when the social interest is being served, when it is
not, and what might be done when it is not being
served. We will return to each of the unanswered
questions in future chapters.
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CHAPTER 1 What Is Economics?
x The Economic Way
of Thinking
The questions that economics tries to answer tell us
about the scope of economics, but they dont tell us
how economists think and go about seeking answers
to these questions. Youre now going to see how economists go about their work.
Were going to look at six key ideas that define the
economic way of thinking. These ideas are
s A choice is a tradeoff.
s People make rational choices by comparing b enefits and costs.
s Benefit is what you gain from something.
s Cost is what you must give up to get something.
s Most choices are how-much choices made at the
margin.
s Choices respond to incentives.
A Choice Is a Tradeoff
Because we face scarcity, we must make choices.
And when we make a choice, we select from the
available alternatives. For example, you can spend
Saturday night studying for your next economics
test or having fun with your friends, but you cant
do both of these activities at the same time. You
must choose how much time to devote to each.
Whatever choice you make, you could have chosen
something else.
You can think about your choices as tradeoffs. A
tradeoff is an exchangegiving up one thing to get
something else. When you choose how to spend your
Saturday night, you face a tradeoff between studying
and hanging out with your friends.
Making a Rational Choice
Economists view the choices that people make as
rational. A rational choice is one that compares costs
and benefits and achieves the greatest benefit over
cost for the person making the choice.
Only the wants of the person making a choice are
relevant to determine its rationality. For example,
you might like your coffee black and strong but
your friend prefers his milky and sweet. So it is
rational for you to choose espresso and for your
friend to choose cappuccino.
The idea of rational choice provides an answer to
the first question: What goods and services will be
produced and in what quantities? The answer is
those that people rationally choose to buy!
But how do people choose rationally? Why do
more people choose an iPod rather than a Zune?
Why has the U.S. government chosen to build an
interstate highway system and not an interstate
high-speed railroad system? The answers turn on
comparing benefits and costs.
Benefit: What You Gain
The benefit of something is the gain or pleasure that it
brings and is determined by preferencesby what a
person likes and dislikes and the intensity of those feelings. If you get a huge kick out of Guitar Hero, that
video game brings you a large benefit. And if you have
little interest in listening to Yo Yo Ma playing a Vivaldi
cello concerto, that activity brings you a small benefit.
Some benefits are large and easy to identify, such
as the benefit that you get from being in school. A
big piece of that benefit is the goods and services
that you will be able to enjoy with the boost to your
earning power when you graduate. Some benefits
are small, such as the benefit you get from a slice of
pizza.
Economists measure benefit as the most that a
person is willing to give up to get something. You are
willing to give up a lot to be in school. But you
would give up only an iTunes download for a slice
of pizza.
Cost: What You Must Give Up
The opportunity cost of something is the highestvalued alternative that must be given up to get it.
To make the idea of opportunity cost concrete,
think about your opportunity cost of being in school.
It has two components: the things you cant afford to
buy and the things you cant do with your time.
Start with the things you cant afford to buy. Youve
spent all your income on tuition, residence fees, books,
and a laptop. If you werent in school, you would have
spent this money on tickets to ball games and movies
and all the other things that you enjoy. But thats only
the start of your opportunity cost. Youve also given up
the opportunity to get a job. Suppose that the best job
you could get if you werent in school is working at
Citibank as a teller earning $25,000 a year. Another
part of your opportunity cost of being in school is all
the things that you could buy with the extra $25,000
you would have.
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T he Economic Way of Thinking
As you well know, being a student eats up many
hours in class time, doing homework assignments,
preparing for tests, and so on. To do all these school
activities, you must give up many hours of what would
otherwise be leisure time spent with your friends.
So the opportunity cost of being in school is all
the good things that you cant afford and dont have
the spare time to enjoy. You might want to put a
dollar value on that cost or you might just list all
the items that make up the opportunity cost.
The examples of opportunity cost that weve just
considered are all-or-nothing costsyoure either in
school or not in school. Most situations are not like
this one. They involve choosing how much of an
activity to do.
How Much? Choosing at the Margin
You can allocate the next hour between studying and
instant messaging your friends, but the choice is not all
or nothing. You must decide how many minutes to
allocate to each activity. To make this decision, you
compare the benefit of a little bit more study time with
its costyou make your choice at the margin.
The benefit that arises from an increase in an
activity is called marginal benefit. For example, your
marginal benefit from one more night of study before
a test is the boost it gives to your grade. Your marginal benefit doesnt include the grade youre already
achieving without that extra night of work.
The opportunity cost of an increase in an activity is
called marginal cost. For you, the marginal cost of
studying one more night is the cost of not spending
that night on your favorite leisure activity.
To make your decisions, you compare marginal
benefit and marginal cost. If the marginal benefit
from an extra night of study exceeds its marginal cost,
you study the extra night. If the marginal cost exceeds
the marginal benefit, you dont study the extra night.
The central idea of economics is that we can predict the self-interested choices that people make by
looking at the incentives they face. People undertake
those activities for which marginal benefit exceeds
marginal cost; and they reject options for which
marginal cost exceeds marginal benefit.
For example, your economics instructor gives you
a problem set and tells you these problems will be on
the next test. Your marginal benefit from working
these problems is large, so you diligently work them.
In contrast, your math instructor gives you a problem
set on a topic that she says will never be on a test.
You get little marginal benefit from working these
problems, so you decide to skip most of them.
Economists see incentives as the key to reconciling self-interest and social interest. When our
choices are not in the social interest, it is because of
the incentives we face. One of the challenges for
economists is to figure out the incentives that result
in self-interested choices being in the social interest.
Economists emphasize the crucial role that institutions play in influencing the incentives that people
face as they pursue their self-interest. Laws that protect private property and markets that enable voluntary exchange are the fundamental institutions. You
will learn as you progress with your study of economics that where these institutions exist, self-interest can indeed promote the social interest.
REVIEW QUIZ
1
2
3
Choices Respond to Incentives
Economists take human nature as given and view
people as acting in their self-interest. All people
you, other consumers, producers, politicians, and
public servantspursue their self-interest.
Self-interested actions are not necessarily selfish
actions. You might decide to use your resources in
ways that bring pleasure to others as well as to yourself. But a self-interested act gets the most benefit for
you based on your view about benefit.
7
4
5
Explain the idea of a tradeoff and think of three
tradeoffs that you have made today.
Explain what economists mean by rational
choice and think of three choices that youve
made today that are rational.
Explain why opportunity cost is the best forgone alternative and provide examples of some
opportunity costs that you have faced today.
Explain what it means to choose at the margin
and illustrate with three choices at the margin
that you have made today.
Explain why choices respond to incentives and
think of three incentives to which you have
responded today.
You can work these questions in Study
Plan 1.3 and get instant feedback.
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CHAPTER 1 What Is Economics?
x Economics as Social Science and
Policy Tool
Economics is both a social science and a toolkit for
advising on policy decisions.
Economist as Social Scientist
As social scientists, economists seek to discover how
the economic world works. In pursuit of this goal,
like all scientists, economists distinguish between
positive and normative statements.
Positive Statements A positive statement is about
what is. It says what is currently believed about the
way the world operates. A positive statement might
be right or wrong, but we can test it by checking it
against the facts. Our planet is warming because of
the amount of coal that were burning is a positive
statement. We can test whether it is right or wrong.
A central task of economists is to test positive
statements about how the economic world works
and to weed out those that are wrong. Economics
first got off the ground in the late 1700s, so it is a
young science compared with, for example, physics,
and much remains to be discovered.
Normative Statements A normative statement is
about what ought to be. It depends on values and cannot be tested. Policy goals are normative statements.
For example, We ought to cut our use of coal by 50
percent is a normative policy statement. You may
agree or disagree with it, but you cant test it. It
doesnt assert a fact that can be checked.
Unscrambling Cause and Effect Economists are par-
ticularly interested in positive statements about
cause and effect. Are computers getting cheaper
because people are buying them in greater quantities? Or are people buying computers in greater
quantities because they are getting cheaper? Or is
some third factor causing both the price of a computer to fall and the quantity of computers bought
to increase?
To answer such questions, economists create and
test economic models. An economic model is a
description of some aspect of the economic world
that includes only those features that are needed for
the purpose at hand. For example, an economic
model of a cell-phone network might include features such as the prices of calls, the number of cell-
phone users, and the volume of calls. But the model
would ignore cell-phone colors and ringtones.
A model is tested by comparing its predictions with
the facts. But testing an economic model is difficult
because we observe the outcomes of the simultaneous
change of many factors. To cope with this problem,
economists look for natural experiments (situations
in the ordinary course of economic life in which the
one factor of interest is different and other things are
equal or similar); conduct statistical investigations to
find correlations; and perform economic experiments
by putting people in decision-making situations and
varying the influence of one factor at a time to discover how they respond.
Economist as Policy Adviser
Economics is useful. It is a toolkit for advising governments and businesses and for making personal
decisions. Some of the most famous economists work
partly as policy advisers.
For example, Jagdish Bhagwati of Columbia
University has advised governments and international
organizations on trade and economic development
issues.
Christina Romer of the University of California,
Berkeley, is on leave and serving as the chief economic adviser to President Barack Obama and head
of the Presidents Council of Economic Advisers.
All the policy questions on which economists provide advice involve a blend of the positive and the
normative. Economics cant help with the normative
partthe policy goal. But for a given goal, economics provides a method of evaluating alternative solutionscomparing marginal benefits and marginal
costs and finding the solution that makes the best use
of the available resources.
REVIEW QUIZ
1
2
3
4
Distinguish between a positive statement and a
normative statement and provide examples.
What is a model? Can you think of a model
that you might use in your everyday life?
How do economists try to disentangle cause
and effect?
How is economics used as a policy tool?
You can work these questions in Study
Plan 1.4 and get instant feedback.
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Page 9
S ummary
9
SUMMARY
Key Points
The Economic Way of Thinking (pp. 67)
s
Definition of Economics (p. 2)
s
s
s
All economic questions arise from scarcityfrom
the fact that wants exceed the resources available
to satisfy them.
Economics is the social science that studies the
choices that people make as they cope with
scarcity.
The subject divides into microeconomics and
macroeconomics.
s
s
s
s
Every choice is a tradeoffexchanging more of
something for less of something else.
People make rational choices by comparing benefit
and cost.
Costopportunity costis what you must give up
to get something.
Most choices are how much choices made at the
margin by comparing marginal benefit and marginal cost.
Choices respond to incentives.
Working Problem 1 will give you a better understanding
of the definition of economics.
Working Problems 4 and 5 will give you a better understanding of the economic way of thinking.
Two Big Economic Questions (pp. 35)
Economics as Social Science and Policy Tool (p. 8)
s
Two big questions summarize the scope of
economics:
1. How do choices end up determining what,
how, and for whom goods and services are
produced?
2. When do choices made in the pursuit of selfinterest also promote the social interest?
Working Problems 2 and 3 will give you a better understanding of the two big questions of economics.
s
s
s
Economists distinguish between positive statementswhat isand normative statements
what ought to be.
To explain the economic world, economists create
and test economic models.
Economics is a toolkit used to provide advice on
government, business, and personal economic
decisions.
Working Problem 6 will give you a better understanding
of economics as social science and policy tool.
Key Terms
Benefit, 6
Capital, 4
Economic model, 8
Economics, 2
Entrepreneurship, 4
Factors of production, 3
Goods and services, 3
Human capital, 3
Incentive, 2
Interest, 4
Labor, 3
Land, 3
Macroeconomics, 2
Margin, 7
Marginal benefit, 7
Marginal cost, 7
Microeconomics, 2
Opportunity cost, 6
Preferences, 6
Profit, 4
Rational choice, 6
Rent, 4
Scarcity, 2
Tradeoff, 6
Wages, 4
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CHAPTER 1 What Is Economics?
STUDY PLAN PROBLEMS AND APPLICATIONS
You can work Problems 1 to 6 in MyEconLab Chapter 1 Study Plan and get instant feedback.
Definition of Economics (Study Plan1.1)
1. Apple Inc. decides to make iTunes freely available
in unlimited quantities.
a. Does Apples decision change the incentives
that people face?
b. Is Apples decision an example of a microeconomic or a macroeconomic issue?
Two Big Economic Questions (Study Plan1.2)
2. Which of the following pairs does not match?
a. Labor and wages
b. Land and rent
c. Entrepreneurship and profit
d. Capital and profit
3. Explain how the following news headlines concern self-interest and the social interest.
a. Starbucks Expands in China
b. McDonalds Moves into Salads
c. Food Must Be Labeled with Nutrition Data
The Economic Way of Thinking (Study Plan1.3)
4. The night before an economics test, you decide
to go to the movies instead of staying home and
working your MyEconLab Study Plan. You get
50 percent on your test compared with the 70
percent that you normally score.
a. Did you face a tradeoff?
b. What was the opportunity cost of your
evening at the movies?
5. Costs Soar for London Olympics
The regeneration of East London, the site of the
2012 Olympic Games, is set to add extra 1.5
billion to taxpayers bill.
Source: The Times, London, July 6, 2006
Is the cost of regenerating East London an
opportunity cost of hosting the 2012 Olympic
Games? Explain why or why not.
Economics as Social Science and Policy Tool
(Study Plan1.4)
6. Which of the following statements is positive,
which is normative, and which can be tested?
a. The United States should cut its imports.
b. China is the largest trading partner of the
United States.
c. If the price of antiretroviral drugs increases,
HIV/AIDS sufferers will decrease their consumption of the drugs.
ADDITIONAL PROBLEMS AND APPLICATIONS
You can work these problems in MyEconLab if assigned by your instructor.
Definition of Economics
7. Hundreds Line up for 5 p.m. Ticket Giveaway
By noon, hundreds of Eminem fans had lined up
for a chance to score free tickets to the concert.
Source: Detroit Free Press, May 18, 2009
When Eminem gave away tickets, what was free
and what was scarce? Explain your answer.
Two Big Economic Questions
8. How does the creation of a successful movie
influence what, how, and for whom goods and
services are produced?
9. How does a successful movie illustrate self-interested choices that are also in the social interest?
The Economic Way of Thinking
10. Before starring in Iron Man, Robert Downey Jr.
had appeared in 45 movies that grossed an average of $5 million on the opening weekend. In
contrast, Iron Man grossed $102 million.
a. How do you expect the success of Iron Man to
influence the opportunity cost of hiring
Robert Downey Jr.?
b. How have the incentives for a movie producer
to hire Robert Downey Jr. changed?
11. What might be an incentive for you to take a
class in summer school? List some of the benefits
and costs involved in your decision. Would your
choice be rational?
Economics as Social Science and Policy Tool
12. Look at todays Wall Street Journal. What is the
leading economic news story? With which of the
big economic questions does it deal and what
tradeoffs does it discuss or imply?
13. Provide two microeconomic statements and two
macroeconomic statements. Classify your statements as positive or normative. Explain why.
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A ppendix: Graphs in Economics
Graphs in Economics
Above sea level
After studying this appendix,
you will be able to:
Make and interpret a scatter diagram
Identify linear and nonlinear relationships and
relationships that have a maximum and a
minimum
A graph represents a quantity as a distance on a line.
In Fig. A1.1, a distance on the horizontal line represents temperature, measured in degrees Fahrenheit. A
movement from left to right shows an increase in
temperature. The point 0 represents zero degrees
Fahrenheit. To the right of 0, the temperature is positive. To the left of 0 the temperature is negative (as
indicated by the minus sign). A distance on the vertical line represents height, measured in thousands of
feet. The point 0 represents sea level. Points above 0
represent feet above sea level. Points below 0 represent feet below sea level (indicated by a minus sign).
In Fig. A1.1, the two scale lines are perpendicular
to each other and are called axes. The vertical line is
the y-axis, and the horizontal line is the x-axis. Each
axis has a zero point, which is shared by the two axes
and called the origin.
To make a two-variable graph, we need two pieces
of information: the value of the variable x and the
value of the variable y. For example, off the coast of
Alaska, the temperature is 32 degreesthe value of x.
A fishing boat is located at 0 feet above sea levelthe
value of y. These two bits of information appear as
point A in Fig. A1.1. A climber at the top of Mount
McKinley on a cold day is 20,320 feet above sea level
in a zero-degree gale. These two pieces of information
appear as point B. On a warmer day, a climber might
be at the peak of Mt. McKinley when the temperature
is 32 degrees, at point C.
We can draw two lines, called coordinates, from
point C. One, called the x-coordinate, runs from C to
the vertical axis. This line is called the x-coordinate
0F and
20,320 ft
25
20
B
C
32F and
20,320 ft
15
10
32F and
0 ft
5
60
Below sea level
x Graphing Data
y
Origin
Define and calculate the slope of a line
Graph relationships among more than two
variables
Making a Graph
FIGURE A1.1
Height (thousands of feet)
APPENDIX
11
30
A
0
30
5
Negative
x
60
90
120
Temperature (degrees F)
Positive
10
Graphs have axes that measure quantities as distances.
Here, the horizontal axis (x-axis) measures temperature, and
the vertical axis (y-axis) measures height. Point A represents
a fishing boat at sea level (0 on the y-axis) on a day when
the temperature is 32F. Point B represents a climber at the
top of Mt. McKinley, 20,320 feet above sea level at a
temperature of 0F. Point C represents a climber at the top
of Mt. McKinley, 20,320 feet above sea level at a temperature of 32F.
animation
because its length is the same as the value marked off
on the x-axis. The other, called the y-coordinate, runs
from C to the horizontal axis. This line is called the
y-coordinate because its length is the same as the
value marked off on the y-axis.
We describe a point on a graph by the values of
its x-coordinate and its y-coordinate. For example, at
point C, x is 32 degrees and y is 20,320 feet.
A graph like that in Fig. A1.1 can be made using
any quantitative data on two variables. The graph can
show just a few points, like Fig. A1.1, or many
points. Before we look at graphs with many points,
lets reinforce what youve just learned by looking at
two graphs made with economic data.
Economists measure variables that describe what,
how, and for whom goods and services are produced.
These variables are quantities produced and prices.
Figure A1.2 shows two examples of economic graphs.
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CHAPTER 1 What Is Economics?
FIGURE A1.2
150
Two Graphs of Economic Data
8.3 million
songs at 99
cents per song
99
A
50
0
5
8.3 10
15
Quantity (millions of songs per day)
(a) iTunes downloads: quantity and price
Quantity (millions of albums per day)
12
Price (cents per song)
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1.0
0.8
8.3 million songs
and 0.4 million
albums were
downloaded
0.6
0.4
B
0.2
0
5
8.3 10
15
Quantity (millions of songs per day)
The graph in part (a) tells us that
in January 2010, 8.3 million
songs per day were downloaded
from the iTunes store at a price of
99 cents a song.
The graph in part (b) tells us
that in January 2010, 8.3 million
songs per day and 0.4 million
albums per day were downloaded
from the iTunes store.
(b) iTunes downloads: songs and albums
animation
Figure A1.2(a) is a graph about iTunes song downloads
in January 2010. The x-axis measures the quantity of
songs downloaded per day and the y-axis measures the
price of a song. Point A tells us what the quantity and
price were. You can read this graph as telling you
that in January 2010, 8.3 million songs a day were
downloaded at a price of 99 per song.
Figure A1.2(b) is a graph about iTunes song and
album downloads in January 2010. The x-axis measures the quantity of songs downloaded per day and
the y-axis measures the quantity of albums downloaded per day. Point B tells us what these quantities
were. You can read this graph as telling you that in
January 2010, 8.3 million songs a day and 0.4 million albums were downloaded.
The three graphs that youve just seen tell you
how to make a graph and how to read a data point
on a graph, but they dont improve on the raw data.
Graphs become interesting and revealing when they
contain a number of data points because then you
can visualize the data.
Economists create graphs based on the principles
in Figs. A1.1 and A1.2 to reveal, describe, and visualize the relationships among variables. Were now
going to look at some examples. graphs These are
called scatter diagrams.
Scatter Diagrams
A scatter diagram is a graph that plots the value of one
variable against the value of another variable for a
number of different values of each variable. Such a
graph reveals whether a relationship exists between
two variables and describes their relationship.
The table in Fig. A1.3 shows some data on two
variables: the number of tickets sold at the box office
and the number of DVDs sold for eight of the most
popular movies in 2009.
What is the relationship between these two variables? Does a big box office success generate a large
volume of DVD sales? Or does a box office success
mean that fewer DVDs are sold?
We can answer these questions by making a scatter
diagram. We do so by graphing the data in the table.
In the graph in Fig. A1.3, each point shows the number of box office tickets sold (the x variable) and the
number of DVDs sold (the y variable) of one of the
movies. There are eight movies, so there are eight
points scattered within the graph.
The point labeled A tells us that Star Trek sold 34
million tickets at the box office and 6 million DVDs.
The points in the graph form a pattern, which reveals
that larger box office sales are associated with larger
DVD sales. But the points also tell us that this association is weak. You cant predict DVD sales with any
confidence by knowing only the number of tickets
sold at the box office.
Figure A1.4 shows two scatter diagrams of economic variables. Part (a) shows the relationship
between income and expenditure, on average, during
a ten-year period. Each point represents income and
expenditure in a given year. For example, point A
shows that in 2006, income was $31 thousand and
expenditure was $30 thousand. This graph shows that
as income increases, so does expenditure, and the relationship is a close one.
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A ppendix: Graphs in Economics
13
A Scatter Diagram
Tickets
Movie
DVDs
(millions)
Twilight
38
10
Transformers:
Revenge of the Fallen
54
9
Up
39
DVDs sold (millions)
FIGURE A1.3
11
10
8
9
8
Harry Potter and
the Half-Blood Prince
40
7
Star Trek
34
6
7
A
6
The Hangover
37
6
5
Ice Age:
Dawn of the Dinosaurs
26
5
The Proposal
22
5
0
20
30 34
40
50
60
Box office tickets sold (millions)
The table lists the number of
tickets sold at the box office
and the number of DVDs
sold for eight popular
movies. The scatter diagram
reveals the relationship
between these two variables.
Each point shows the values
of the two variables for a
specific movie. For example,
point A shows the point for
Star Trek, which sold 34 million tickets at the box office
and 6 million DVDs. The pattern formed by the points
shows that there is a tendency for large box office
sales to bring greater DVD
sales. But you couldnt predict how many DVDs a
movie would sell just by
knowing its box office sales.
animation
You can see that a scatter diagram conveys a
wealth of information, and it does so in much less
space than we have used to describe only some of its
features. But you do have to read the graph to
obtain all this information.
Figure A1.4(b) shows a scatter diagram of U.S.
inflation and unemployment during the 2000s. Here,
the points for 2000 to 2008 show no relationship
between the two variables, but the high unemployment
rate of 2009 brought a low inflation rate that year.
Expenditure
(thousands of dollars per year)
35
09
08
06
30
02
25
00
0
07
A
05
04
03
01
31
25
35
40
Income (thousands of dollars per year)
(a) Income and expenditure
animation
Inflation rate (percent per year)
Two Economic Scatter Diagrams
FIGURE A1.4
5
08
06
05
00
07
01 04
03
4
3
2
02
1
0
1
09
2
4
6
8
10
Unemployment rate (percent)
(b) Unemployment and inflation
The scatter diagram in part (a) shows
the relationship between income and
expenditure from 2000 to 2009. Point
A shows that in 2006, income was
$31 (thousand) on the x-axis and
expenditure was $30 (thousand) on
the y-axis. This graph shows that as
income rises, so does expenditure and
the relationship is a close one.
The scatter diagram in part (b)
shows a weak relationship between
unemployment and inflation in the
United States during most of the 2000s.
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CHAPTER 1 What Is Economics?
x Graphs Used in
Breaks in the Axes The graph in Fig. A1.4(a) has
breaks in its axes, as shown by the small gaps. The
breaks indicate that there are jumps from the origin,
0, to the first values recorded.
The breaks are used because the lowest values of
income and expenditure exceed $20,000. If we made
this graph with no breaks in its axes, there would be a
lot of empty space, all the points would be crowded
into the top right corner, and it would be difficult to
see whether a relationship exists between these two
variables. By breaking the axes, we are able to bring
the relationship into view.
Putting a break in one or both axes is like using
a zoom lens to bring the relationship into the center
of the graph and magnify it so that the relationship
fills the graph.
Misleading Graphs Breaks can be used to highlight
a relationship, but they can also be used to misleadto make a graph that lies. The most common
way of making a graph lie is to put a break in the
axis and either to stretch or compress the scale. For
example, suppose that in Fig. A1.4(a), the y-axis
that measures expenditure ran from zero to $35,000
while the x-axis was the same as the one shown. The
graph would now create the impression that despite
a huge increase in income, expenditure had barely
changed.
To avoid being misled, it is a good idea to get
into the habit of always looking closely at the values
and the labels on the axes of a graph before you start
to interpret it.
Correlation and Causation A scatter diagram that
shows a clear relationship between two variables, such
as Fig. A1.4(a), tells us that the two variables have a
high correlation. When a high correlation is present,
we can predict the value of one variable from the
value of the other variable. But correlation does not
imply causation.
Sometimes a high correlation is a coincidence,
but sometimes it does arise from a causal relationship. It is likely, for example, that rising income
causes rising expenditure (Fig. A1.4a) and that high
unemployment makes for a slack economy in which
prices dont rise quickly, so the inflation rate is low
(Fig. A1.4b).
Youve now seen how we can use graphs in economics to show economic data and to reveal relationships. Next, well learn how economists use
graphs to construct and display economic models.
Economic Models
The graphs used in economics are not always designed
to show real-world data. Often they are used to show
general relationships among the variables in an economic model.
An economic model is a stripped-down, simplified description of an economy or of a component
of an economy such as a business or a household. It
consists of statements about economic behavior
that can be expressed as equations or as curves in a
graph. Economists use models to explore the effects
of different policies or other influences on the
economy in ways that are similar to the use of
model airplanes in wind tunnels and models of the
climate.
You will encounter many different kinds of
graphs in economic models, but there are some
repeating patterns. Once youve learned to recognize
these patterns, you will instantly understand the
meaning of a graph. Here, well look at the different
types of curves that are used in economic models,
and well see some everyday examples of each type of
curve. The patterns to look for in graphs are the four
cases in which
s
Variables move in the same direction.
s
Variables move in opposite directions.
s
Variables have a maximum or a minimum.
s
Variables are unrelated.
Lets look at these four cases.
Variables That Move in the Same Direction
Figure A1.5 shows graphs of the relationships
between two variables that move up and down
together. A relationship between two variables that
move in the same direction is called a positive relationship or a direct relationship. A line that slopes
upward shows such a relationship.
Figure A1.5 shows three types of relationships:
one that has a straight line and two that have curved
lines. All the lines in these three graphs are called
curves. Any line on a graphno matter whether it is
straight or curvedis called a curve.
A relationship shown by a straight line is called
a linear relationship. Figure A1.5(a) shows a linear relationship between the number of miles traveled in
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A ppendix: Graphs in Economics
Positive
linear
relationship
300
A
200
100
0
40
Problems worked (number)
400
Positive (Direct) Relationships
Recovery time (minutes)
Distance covered in 5 hours (miles)
FIGURE A1.5
Positive,
becoming
steeper
30
20
10
20
15
40
60
80
Speed (miles per hour)
(a) Positive linear relationship
0
20
Positive,
becoming
less steep
15
10
5
100
200
300
400
Distance sprinted (yards)
(b) Positive, becoming steeper
Each part shows a positive (direct) relationship between two
variables. That is, as the value of the variable measured on
the x-axis increases, so does the value of the variable measured on the y-axis. Part (a) shows a linear positive
relationshipas the two variables increase together, we
move along a straight line.
0
2
4
6
8
Study time (hours)
(c) Positive, becoming less steep
Part (b) shows a positive relationship such that as the
two variables increase together, we move along a curve that
becomes steeper.
Part (c) shows a positive relationship such that as the
two variables increase together, we move along a curve that
becomes flatter.
animation
5 hours and speed. For example, point A shows that
we will travel 200 miles in 5 hours if our speed is 40
miles an hour. If we double our speed to 80 miles an
hour, we will travel 400 miles in 5 hours.
Figure A1.5(b) shows the relationship between
distance sprinted and recovery time (the time it takes
the heart rate to return to its normal resting rate).
This relationship is an upward-sloping one that
starts out quite flat but then becomes steeper as we
move along the curve away from the origin. The reason this curve becomes steeper is that the additional
recovery time needed from sprinting an additional
100 yards increases. It takes less than 5 minutes to
recover from sprinting 100 yards but more than 10
minutes to recover from 200 yards.
Figure A1.5(c) shows the relationship between
the number of problems worked by a student and
the amount of study time. This relationship is an
upward-sloping one that starts out quite steep and
becomes flatter as we move along the curve away
from the origin. Study time becomes less productive
as the student spends more hours studying and
becomes more tired.
Variables That Move in Opposite Directions
Figure A1.6 shows relationships between things that
move in opposite directions. A relationship between
variables that move in opposite directions is called a
negative relationship or an inverse relationship.
Figure A1.6(a) shows the relationship between
the hours spent playing squash and the hours spent
playing tennis when the total time available is 5
hours. One extra hour spent playing tennis means
one hour less spent playing squash and vice versa.
This relationship is negative and linear.
Figure A1.6(b) shows the relationship between
the cost per mile traveled and the length of a journey.
The longer the journey, the lower is the cost per mile.
But as the journey length increases, even though the
cost per mile decreases, the fall in the cost is smaller
the longer the journey. This feature of the relationship
is shown by the fact that the curve slopes downward,
starting out steep at a short journey length and then
becoming flatter as the journey length increases. This
relationship arises because some of the costs are fixed,
such as auto insurance, and the fixed costs are spread
over a longer journey.
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CHAPTER 1 What Is Economics?
Negative (Inverse) Relationships
5
Negative
linear
relationship
4
3
2
1
0
50
Negative,
becoming
less steep
40
30
20
10
1
2
3
4
5
Time playing tennis (hours)
(a) Negative linear relationship
0
Problems worked (number)
FIGURE A1.6
Travel cost (cents per mile)
16
Time playing squash (hours)
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25
Negative,
becoming
steeper
20
15
10
5
100
200
300 400
500
Journey length (miles)
(b) Negative, becoming less steep
Each part shows a negative (inverse) relationship between
two variables. Part (a) shows a linear negative relationship. The total time spent playing tennis and squash is 5
hours. As the time spent playing tennis increases, the time
spent playing squash decreases, and we move along a
straight line.
0
2
4
8
6
10
Leisure time (hours)
(c) Negative, becoming steeper
Part (b) shows a negative relationship such that as the
journey length increases, the travel cost decreases as we
move along a curve that becomes less steep.
Part (c) shows a negative relationship such that as
leisure time increases, the number of problems worked
decreases as we move along a curve that becomes steeper.
animation
Figure A1.6(c) shows the relationship between
the amount of leisure time and the number of problems worked by a student. Increasing leisure time
produces an increasingly large reduction in the number of problems worked. This relationship is a negative one that starts out with a gentle slope at a small
number of leisure hours and becomes steeper as the
number of leisure hours increases. This relationship is
a different view of the idea shown in Fig. A1.5(c).
Variables That Have a Maximum
or a Minimum
Many relationships in economic models have a maximum or a minimum. For example, firms try to make
the maximum possible profit and to produce at the
lowest possible cost. Figure A1.7 shows relationships
that have a maximum or a minimum.
Figure A1.7(a) shows the relationship between
rainfall and wheat yield. When there is no rainfall,
wheat will not grow, so the yield is zero. As the rainfall
increases up to 10 days a month, the wheat yield
increases. With 10 rainy days each month, the wheat
yield reaches its maximum at 40 bushels an acre (point
A). Rain in excess of 10 days a month starts to lower
the yield of wheat. If every day is rainy, the wheat suffers from a lack of sunshine and the yield decreases to
zero. This relationship is one that starts out sloping
upward, reaches a maximum, and then slopes downward.
Figure A1.7(b) shows the reverse casea relationship that begins sloping downward, falls to a minimum, and then slopes upward. Most economic costs
are like this relationship. An example is the relationship
between the cost per mile and speed for a car trip. At
low speeds, the car is creeping in a traffic snarl-up. The
number of miles per gallon is low, so the cost per mile
is high. At high speeds, the car is traveling faster than
its efficient speed, using a large quantity of gasoline,
and again the number of miles per gallon is low and the
cost per mile is high. At a speed of 55 miles an hour,
the cost per mile is at its minimum (point B). This relationship is one that starts out sloping downward,
reaches a minimum, and then slopes upward.
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A ppendix: Graphs in Economics
Maximum and Minimum Points
Maximum
yield
50
A
40
30
20
Increasing
yield
Gasoline cost (cents per mile)
Wheat yield (bushels per acre)
FIGURE A1.7
15
Decreasing
cost
Increasing
cost
10
Decreasing
yield
Minimum
cost
B
5
10
0
5
10
17
30
15
20
25
Rainfall (days per month)
(a) Relationship with a maximum
0
15
35
55
75
95
Speed (miles per hour)
(b) Relationship with a minimum
Part (a) shows a relationship that has a maximum
point, A. The curve slopes
upward as it rises to its
maximum point, is flat at
its maximum, and then
slopes downward.
Part (b) shows a relationship with a minimum
point, B. The curve slopes
downward as it falls to its
minimum, is flat at its minimum, and then slopes
upward.
animation
Variables That Are Unrelated
There are many situations in which no matter what
happens to the value of one variable, the other variable remains constant. Sometimes we want to show
the independence between two variables in a graph,
and Fig. A1.8 shows two ways of achieving this.
Variables That Are Unrelated
100
75
Unrelated:
y constant
50
25
0
20
40
60
80
Price of bananas (cents per pound)
(a) Unrelated: y constant
animation
Rainfall in California (days per month)
Grade in economics (percent)
FIGURE A1.8
In describing the graphs in Fig. A1.5 through Fig.
A1.7, we have talked about curves that slope upward
or slope downward, and curves that become less steep
or steeper. Lets spend a little time discussing exactly
what we mean by slope and how we measure the slope
of a curve.
20
15
Unrelated:
x constant
10
5
0
1
2
3
4
Output of French wine (billions of gallons)
(b) Unrelated: x constant
This figure shows how
we can graph two variables
that are unrelated. In part
(a), a students grade in
economics is plotted at
75 percent on the y-axis
regardless of the price of
bananas on the x-axis. The
curve is horizontal.
In part (b), the output
of the vineyards of France
on the x-axis does not vary
with the rainfall in
California on the y-axis.
The curve is vertical.
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CHAPTER 1 What Is Economics?
18
x The Slope of a Relationship
If a large change in the variable measured on
the y-axis ( y) is associated with a small change in
the variable measured on the x-axis ( x), the slope
is large and the curve is steep. If a small change in
the variable measured on the y-axis ( y) is associated with a large change in the variable measured
on the x-axis ( x), the slope is small and the curve
is flat.
We can make the idea of slope clearer by doing
some calculations.
We can measure the influence of one variable on
another by the slope of the relationship. The slope
of a relationship is the change in the value of the
variable measured on the y-axis divided by the
change in the value of the variable measured on the
x-axis. We use the Greek letter (delta) to represent
change in. Thus y means the change in the value
of the variable measured on the y-axis, and x
means the change in the value of the variable measured on the x-axis. Therefore the slope of the relationship is
Slope =
y
x
The Slope of a Straight Line
The slope of a straight line is the same regardless of
where on the line you calculate it. The slope of a
straight line is constant. Lets calculate the slope of
the positive relationship in Fig. A1.9. In part (a),
.
The Slope of a Straight Line
FIGURE A1.9
y
y
8
8
3
Slope =
4
7
3
Slope =
4
7
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
5
6
7
8
x
(a) Positive slope
0
1
2
3
4
5
6
7
8
x
(b) Negative slope
To calculate the slope of a straight line, we divide the change
in the value of the variable measured on the y-axis ( y ) by
the change in the value of the variable measured on the xaxis ( x) as we move along the line.
Part (a) shows the calculation of a positive slope. When
x increases from 2 to 6, x equals 4. That change in x
animation
brings about an increase in y from 3 to 6, so y equals 3.
The slope ( y/ x) equals 3/4.
Part (b) shows the calculation of a negative slope. When
x increases from 2 to 6, x equals 4. That increase in x
brings about a decrease in y from 6 to 3, so y equals 3.
The slope ( y/ x) equals 3/4.
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Page 19
A ppendix: Graphs in Economics
when x increases from 2 to 6, y increases from 3 to
6. The change in x is +4that is, x is 4. The
change in y is +3that is, y is 3. The slope of that
line is
y
x
=
3
.
4
In part (b), when x increases from 2 to 6, y
decreases from 6 to 3. The change in y is minus 3
that is, y is 3. The change in x is plus 4that is,
x is 4. The slope of the curve is
y
x
=
-3
.
4
Notice that the two slopes have the same magnitude (3/4), but the slope of the line in part (a) is positive (+3/+4 = 3/4) while that in part (b) is negative
(3/+4 = 3/4). The slope of a positive relationship is
positive; the slope of a negative relationship is negative.
The Slope of a Curved Line
The slope of a curved line is trickier. The slope of a
curved line is not constant, so the slope depends on
where on the curved line we calculate it. There are
two ways to calculate the slope of a curved line: You
can calculate the slope at a point, or you can calculate
the slope across an arc of the curve. Lets look at the
two alternatives.
Slope at a Point To calculate the slope at a point on
a curve, you need to construct a straight line that has
the same slope as the curve at the point in question.
Figure A1.10 shows how this is done. Suppose you
want to calculate the slope of the curve at point A.
Place a ruler on the graph so that the ruler touches
point A and no other point on the curve, then draw a
straight line along the edge of the ruler. The straight
red line is this line, and it is the tangent to the curve
at point A. If the ruler touches the curve only at
point A, then the slope of the curve at point A must
be the same as the slope of the edge of the ruler. If
the curve and the ruler do not have the same slope,
the line along the edge of the ruler will cut the curve
instead of just touching it.
Now that you have found a straight line with the
same slope as the curve at point A, you can calculate
the slope of the curve at point A by calculating the
slope of the straight line. Along the straight line, as x
19
Slope at a Point
FIGURE A1.10
y
8
7
3
Slope =
4
6
A
5
4
3
2
1
0
1
2
3
4
5
6
7
8
x
To calculate the slope of the curve at point A, draw the red
line that just touches the curve at Athe tangent. The slope
of this straight line is calculated by dividing the change in y
by the change in x along the red line. When x increases from
0 to 4, x equals 4. That change in x is associated with an
increase in y from 2 to 5, so y equals 3. The slope of the
red line is 3/4, so the slope of the curve at point A is 3/4.
animation
increases from 0 to 4 ( x is 4) y increases from 2 to 5
( y is 3). Therefore the slope of the straight line is
y
x
=
3
.
4
So the slope of the curve at point A is 3/4.
Slope Across an Arc An arc of a curve is a piece of a
curve. Fig. A1.11shows the same curve as in Fig.
A1.10, but instead of calculating the slope at point A,
we are now going to calculate the slope across the arc
from point B to point C. You can see that the slope of
the curve at point B is greater than at point C. When
we calculate the slope across an arc, we are calculating
the average slope between two points. As we move
along the arc from B to C, x increases from 3 to 5
and y increases from 4.0 to 5.5. The change in x is 2
( x is 2), and the change in y is 1.5 ( y is 1.5).
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CHAPTER 1 What Is Economics?
20
x Graphing Relationships Among
Slope Across an Arc
FIGURE A1.11
More Than Two Variables
y
8.0
7.0
3
Slope = 1.5 =
2
6.0
4
C
5.5
A
5.0
= 1.5
B
4.0
3.0
2.0
1.0
0
1
2
3
4
5
6
7
8
x
To calculate the average slope of the curve along the arc
BC, draw a straight line from point B to point C. The slope
of the line BC is calculated by dividing the change in y by
the change in x. In moving from B to C, the increase in x is
2 ( x equals 2) and the change in y is 1.5 ( y equals 1.5).
The slope of the line BC is 1.5 divided by 2, or 3/4. So the
slope of the curve across the arc BC is 3/4.
We have seen that we can graph the relationship
between two variables as a point formed by the xand y-coordinates in a two-dimensional graph. You
might be thinking that although a two-dimensional
graph is informative, most of the things in which
you are likely to be interested involve relationships
among many variables, not just two. For example,
the amount of ice cream consumed depends on the
price of ice cream and the temperature. If ice cream
is expensive and the temperature is low, people eat
much less ice cream than when ice cream is inexpensive and the temperature is high. For any given
price of ice cream, the quantity consumed varies
with the temperature; and for any given temperature, the quantity of ice cream consumed varies with
its price.
Figure A1.12 shows a relationship among three
variables. The table shows the number of gallons of
ice cream consumed each day at two different temperatures and at a number of different prices of ice
cream. How can we graph these numbers?
To graph a relationship that involves more than
two variables, we use the ceteris paribus assumption.
Ceteris Paribus
animation
(often shortened to cet par) means if
all other relevant things remain the same. To isolate
the relationship of interest in a laboratory experiment, a scientist holds everything constant except for
the variable whose effect is being studied. Economists
use the same method to graph a relationship that has
more than two variables.
Figure A1.12 shows an example. There, you can
see what happens to the quantity of ice cream consumed when the price of ice cream varies but the
temperature is held constant.
The curve labeled 70F shows the relationship
between ice cream consumption and the price of ice
cream if the temperature remains at 70F. The numbers used to plot that curve are those in the first two
columns of the table. For example, if the temperature is 70F, 10 gallons are consumed when the
price is $2.75 a scoop and 18 gallons are consumed
when the price is $2.25 a scoop.
The curve labeled 90F shows the relationship
between ice cream consumption and the price of
ice cream if the temperature remains at 90F. The
Ceteris paribus
Therefore the slope is
y
x
=
1.5
3
=.
2
4
So the slope of the curve across the arc BC is 3/4.
This calculation gives us the slope of the curve
between points B and C. The actual slope calculated
is the slope of the straight line from B to C. This
slope approximates the average slope of the curve
along the arc BC. In this particular example, the
slope across the arc BC is identical to the slope of the
curve at point A, but the calculation of the slope of a
curve does not always work out so neatly. You might
have fun constructing some more examples and a few
counter examples.
You now know how to make and interpret a
graph. So far, weve limited our attention to graphs of
two variables. Were now going to learn how to graph
more than two variables.
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A ppendix: Graphs in Economics
Graphing a Relationship Among Three Variables
Ice cream consumption
(gallons per day)
Price
Price (dollars per scoop)
FIGURE A1.12
21
3.75
(dollars per scoop)
70F
90F
2.00
25
50
2.25
18
36
2.50
13
26
2.75
10
20
2.75
3.00
7
14
2.50
3.25
5
10
3.50
3
6
3.50
When temperature
rises, curve shifts
rightward
3.25
3.00
2.25
90F
70F
2.00
0
Ice cream consumption depends on its price and the temperature. The table tells us how many gallons of ice cream are
consumed each day at different prices and two different
temperatures. For example, if the price is $2.75 a scoop
and the temperature is 70F, 10 gallons of ice cream are
consumed.
To graph a relationship among three variables, the
value of one variable is held constant. The graph shows the
relationship between price and consumption when tempera-
10
20
40
60
Ice cream consumption (gallons per day)
ture is held constant. One curve holds temperature at 70F
and the other holds it at 90F.
A change in the price of ice cream brings a movement
along one of the curvesalong the blue curve at 70F and
along the red curve at 90F.
When the temperature rises from 70F to 90F, the
curve that shows the relationship between consumption
and price shifts rightward from the blue curve to the red
curve.
animation
numbers used to plot that curve are those in the
first and third columns of the table. For example, if
the temperature is 90F, 20 gallons are consumed
when the price is $2.75 a scoop and 36 gallons are
consumed when the price is $2.25 a scoop.
When the price of ice cream changes but the temperature is constant, you can think of what happens in
the graph as a movement along one of the curves. At
70F there is a movement along the blue curve and at
90F there is a movement along the red curve.
When Other Things Change
The temperature is held constant along each of the
curves in Fig. A1.12, but in reality the temperature
changes. When that event occurs, you can think of
what happens in the graph as a shift of the curve.
When the temperature rises from 70F to 90F, the
curve that shows the relationship between ice cream
consumption and the price of ice cream shifts rightward from the blue curve to the red curve.
You will encounter these ideas of movements
along and shifts of curves at many points in your
study of economics. Think carefully about what
youve just learned and make up some examples (with
assumed numbers) about other relationships.
With what you have learned about graphs, you can
move forward with your study of economics. There are
no graphs in this book that are more complicated than
those that have been explained in this appendix.
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CHAPTER 1 What Is Economics?
22
MATHEMATICAL NOTE
Equations of Straight Lines
If a straight line in a graph describes the relationship
between two variables, we call it a linear relationship.
Figure 1 shows the linear relationship between a persons
expenditure and income. This person spends $100 a
week (by borrowing or spending previous savings)
when income is zero. Out of each dollar earned, this
person spends 50 cents (and saves 50 cents).
All linear relationships are described by the same
general equation. We call the quantity that is measured
on the horizontal axis (or x-axis) x, and we call the
quantity that is measured on the vertical axis (or y-axis)
y. In the case of Fig. 1, x is income and y is expenditure.
straight line hits the y-axis at a value equal to a.
Figure 1 illustrates the y-axis intercept.
For positive values of x, the value of y exceeds a.
The constant b tells us by how much y increases
above a as x increases. The constant b is the slope of
the line.
Slope of Line
As we explain in the chapter, the slope of a relationship is the change in the value of y divided by the
change in the value of x. We use the Greek letter
(delta) to represent change in. So y means the
change in the value of the variable measured on the
y-axis, and x means the change in the value of the
variable measured on the x-axis. Therefore the slope
of the relationship is
Slope =
A Linear Equation
y
a
bx.
Expenditure (dollars per week)
In this equation, a and b are fixed numbers and
they are called constants. The values of x and y vary, so
these numbers are called variables. Because the equation describes a straight line, the equation is called a
linear equation.
The equation tells us that when the value of x is
zero, the value of y is a. We call the constant a the
y-axis intercept. The reason is that on the graph the
400
y = a + bx
Value of y
Slope = b
300
200
x
To see why the slope is b, suppose that initially
the value of x is x1, or $200 in Fig. 2. The corresponding value of y is y1, also $200 in Fig. 2. The equation of the line tells us that
y1
a
bx 1.
(1)
Now the value of x increases by x to x 1 + x
(or $400 in Fig. 2). And the value of y increases by
y to y 1 + y (or $300 in Fig. 2).
The equation of the line now tells us that
y1
Expenditure (dollars per week)
The equation that describes a straight-line relationship between x and y is
y
y
a
b(x 1
x).
400
300
200
y1
100
0
y-axis
intercept = a
100
200
Value of x
100
x1
300
400
500
Income (dollars per week)
Figure 1 Linear relationship
0
100
200
300
400
500
Income (dollars per week)
Figure 2 Calculating slope
(2)
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M athematical Note
To calculate the slope of the line, subtract equation
(1) from equation (2) to obtain
y
bx
(3)
and now divide equation (3) by x to obtain
y/ x
relationships have a slope that is positive. In the
equation of the line, the constant b is positive. In this
example, the y-axis intercept, a, is 100. The slope b
equals y/ x, which in Fig. 2 is 100/200 or 0.5. The
equation of the line is
y
b.
100
Position of Line
The y-axis intercept determines the position of the
line on the graph. Figure 3 illustrates the relationship
between the y-axis intercept and the position of the
line. In this graph, the y-axis measures saving and the
x-axis measures income.
When the y-axis intercept, a, is positive, the line
hits the y-axis at a positive value of yas the blue line
does. Its y-axis intercept is 100. When the y-axis intercept, a, is zero, the line hits the y-axis at the origin
as the purple line does. Its y-axis intercept is 0. When
the y-axis intercept, a, is negative, the line hits the
y-axis at a negative value of yas the red line does. Its
y-axis intercept is 100.
As the equations of the three lines show, the value
of the y-axis intercept does not influence the slope of
the line. All three lines have a slope equal to 0.5.
Figure 4 shows a negative relationshipthe two variables x and y move in the opposite direction. All negative relationships have a slope that is negative. In the
equation of the line, the constant b is negative. In the
example in Fig. 4, the y-axis intercept, a, is 30. The
slope, b, equals y/ x, which is 20/2 or 10. The
equation of the line is
y
30
Positive Relationships
Figure 1 shows a positive relationshipthe two variables x and y move in the same direction. All positive
( 10)x
or
y
30
10x.
Example
A straight line has a y-axis intercept of 50 and a slope
of 2. What is the equation of this line?
The equation of a straight line is
y
Saving (dollars per week)
0.5x.
Negative Relationships
So the slope of the line is b.
a
bx
where a is the y-axis intercept and b is the slope.
So the equation is
y 50 2x.
y
300
Positive y-axis
intercept, a = 100
y = 100 + 0.5x
200
y = 0.5x
100
40
Positive y-axis
intercept, a = 30
y = 100 + 0.5x
30
Slope, b = 10
20
0
100
200
100
200
300 400 500 600
Income (dollars per week)
10
Negative y-axis
intercept, a = 100
y = 30 10x
0
Figure 3 The y-axis intercept
23
1
2
Figure 4 Negative relationship
x
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24
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Page 24
CHAPTER 1 What Is Economics?
REVIEW QUIZ
1
2
3
4
5
6
Explain how we read the three graphs in Figs
A1.1 and A1.2.
Explain what scatter diagrams show and why
we use them.
Explain how we read the three scatter diagrams in Figs A1.3 and A1.4.
Draw a graph to show the relationship between
two variables that move in the same direction.
Draw a graph to show the relationship between
two variables that move in opposite directions.
Draw a graph to show the relationship between
two variables that have a maximum and a minimum.
7
8
9
10
11
Which of the relationships in Questions 4 and
5 is a positive relationship and which is a negative relationship?
What are the two ways of calculating the slope
of a curved line?
How do we graph a relationship among more
than two variables?
Explain what change will bring a movement
along a curve.
Explain what change will bring a shift of a
curve.
You can work these questions in Study
Plan 1.A and get instant feedback.
SUMMARY
Key Points
The Slope of a Relationship (pp. 1820)
s
Graphing Data (pp. 1114)
s
s
s
A graph is made by plotting the values of two variables x and y at a point that corresponds to their
values measured along the x-axis and the y-axis.
A scatter diagram is a graph that plots the values of
two variables for a number of different values of
each.
A scatter diagram shows the relationship between
the two variables. It shows whether they are positively related, negatively related, or unrelated.
Graphs Used in Economic Models (pp. 1417)
s
s
Graphs are used to show relationships among variables in economic models.
Relationships can be positive (an upward-sloping
curve), negative (a downward-sloping curve), positive and then negative (have a maximum point),
negative and then positive (have a minimum point),
or unrelated (a horizontal or vertical curve).
s
s
The slope of a relationship is calculated as the
change in the value of the variable measured on
the y-axis divided by the change in the value of the
variable measured on the x-axisthat is, y/ x.
A straight line has a constant slope.
A curved line has a varying slope. To calculate the
slope of a curved line, we calculate the slope at a
point or across an arc.
Graphing Relationships Among More Than Two
Variables (pp. 2021)
s
s
s
s
To graph a relationship among more than two
variables, we hold constant the values of all the
variables except two.
We then plot the value of one of the variables
against the value of another.
A cet par change in the value of a variable on an
axis of a graph brings a movement along the curve.
A change in the value of a variable held constant
along the curve brings a shift of the curve.
Key Terms
Ceteris paribus, 20
Direct relationship, 14
Inverse relationship, 15
Linear relationship, 14
Negative relationship, 15
Positive relationship, 14
Scatter diagram, 12
Slope, 18
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Page 25
S tudy Plan Problems and Applications
25
STUDY PLAN PROBLEMS AND APPLICATIONS
You can work Problems 1 to 11 in MyEconLab Chapter 1A Study Plan and get instant feedback.
Use the following spreadsheet to work Problems 1 to
3. The spreadsheet provides data on the U.S. economy: Column A is the year, column B is the inflation
rate, column C is the interest rate, column D is the
growth rate, and column E is the unemployment rate.
7. Calculate the slope of the following relationship.
y
10
8
A
B
C
D
E
1
1999
2.2
4.6
4.8
4.2
2
2000
3.4
5.8
4.1
4.0
3
2001
2.8
3.4
1.1
4.7
4
2002
1.6
1.6
1.8
5.8
5
2003
2.3
1.0
2.5
6.0
6
2004
2.7
1.4
3.6
5.5
7
2005
3.4
3.2
3.1
5.1
8
2006
3.2
4.7
2.7
4.6
9
2007
2.8
4.4
2.1
4.6
10
2008
3.8
1.4
0.4
2009
0.4
0.2
2.4
9.3
4
2
0
4.0
1. Draw a scatter diagram of the inflation rate and
the interest rate. Describe the relationship.
2. Draw a scatter diagram of the growth rate and
the unemployment rate. Describe the relationship.
3. Draw a scatter diagram of the interest rate and
the unemployment rate. Describe the relationship.
Use the following news clip to work Problems 4 to 6.
Clash of the Titans Tops Box Office With Sales of
$61.2 Million:
Theaters
Movie
Revenue
( dollars
(number)
per theater)
Clash of the Titans
3,777
16,213
Tyler Perrys Why Did I
2,155
13,591
Get Married
How To Train Your Dragon 4,060
7,145
The Last Song
2,673
5,989
Source: Bloomberg.com, April 5, 2010
4. Draw a graph of the relationship between the revenue per theater on the y-axis and the number of
theaters on the x-axis. Describe the relationship.
5. Calculate the slope of the relationship between
4,060 and 2,673 theaters.
6. Calculate the slope of the relationship between
2,155 and 4,060 theaters.
8.0
12.0
x
Use the following relationship to work Problems
8 and 9.
5.8
11
6
y
10.0
8.0
A
6.0
4.0
B
1.5
2
0
4
6
8
10
x
8. Calculate the slope of the relationship at point A
and at point B.
9. Calculate the slope across the arc AB.
Use the following table to work Problems 10 and 11.
The table gives the price of a balloon ride, the temperature, and the number of rides a day.
Balloon rides
(number per day)
Price
(dollars per ride)
50F
70F
90F
5
32
40
50
10
27
32
40
15
18
27
32
10. Draw a graph to show the relationship between
the price and the number of rides, when the temperature is 70F. Describe this relationship.
11. What happens in the graph in Problem 10 if the
temperature rises to 90F?
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Page 26

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Second Generation Indian Immigrants inThe Interpreter of MaladiesBy: Jhumpa Lahiri Summaries: A Temporary Matter: This story revolves around a young Indian married couple that lives in the United States, and realizes that their marriage is not as happy

NYU - SAGC - 101

Jagannadharao Buddhavarapu South Asian Cultures Midterm 5. When Queen Elizabeth founded the East India Company in the 1600's, her intention was not to gain government and regulatory control of over a billion people. With India's array religions and cultur

NYU - SAGC - 101

Jag Buddhavarapu Final Exam 4. After Independence in 1947, the worldwide expectation was that India would struggle greatly in its newborn stages, as it no longer had the established British Rule to guide its economy and monitor its foreign relationships.

NYU - SAGC - 101

The Mogul Empire Left with the Lodis Great Lodhi leader was known as the Sultan Ibrahim Lodhi, last great sultan from delhi Timur was making way across Central Asia towards india Early 1500's Establishes base camp in Peshawar The northwest frontier provin

NYU - SAGC - 101

1492 Columbus sails to America Italy Galileo figures out earth is round Cristoph Columb wants to find the sea route to india Marco Polo traveled land route and described it as wealthy and prosperous precious metals, stones, silver, gold goes to Ferdinand

NYU - SAGC - 101

1530's onward Henry 8th forces people to convert to anglo dissolution of the monasteries 1533 forces monks to become protestants burns abbeys declares catholic church dead in England high renassiance people are ruled by their religion at this time expec

NYU - SAGC - 101

1666 fire in London fleetstreet onwards bakery on pudding lane near Bank of England and London stock exchange not a single person dies gets rid of the plague (rats escaped fire) needed new architect to rebuild Christopher Wren(pupil of Jones) Inigo Jones

NYU - SAGC - 101

Buddhavarapu 1 Jag Buddhavarapu "Indira Priyadarshini Nehru" India is a country that is rapidly developing and become westernized, as immense skyscrapers are taking the place of slums, and German cars are being substituted for auto rickshaws. Though cultu

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter1The Life, Times, andCareer of the ProfessionalSalesperson1-2C

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 1 AppendixThe Golden Rule of SellingA1-2The Golden Rule of Perso

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter2Relationship Marketing:Where Personal SellingFits2-2Chapter2

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.3ChapterChapter3Ethics FirstThenCustomer Relationships3-2Chapter33

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter4The Psychology of Selling:Why People Buy4-2Chapter44-3The T

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter5Communication forRelationship Building: Its NotAll Talk5-2Cha

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter6Sales Knowledge:Customers, Products,Technologies6-2Chapter6

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 6 Appendix Sales Arithmeticand PricingA6-2Types of PricesList

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter7Prospecting TheLifeblood of Selling7-2Chapter77-3The Tree o

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.8ChapterChapter8Planning the Sales Call Isa Must8-2Chapter88-3The

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter9Carefully Select WhichSales PresentationMethod to Use9-2Chapt

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter10Begin Your PresentationStrategically10-2Chapter1010-3The T

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter11Elements of a Great SalesPresentation11-2Chapter1111-3The

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter12Welcome Your ProspectsObjections12-2Chapter1212-3The Tree

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter13Closing Begins the Relationship13-2Chapter1313-3The Tree of

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter14Service and Follow-up forCustomer Retention14-2Chapter1414-

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter15Time, Territory, and SelfManagement: Keys toSuccess15-2Chapte

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter16Planning, Staffing, andTraining SuccessfulSalespeople16-2Cha

American Public University - MKT - 4461

FUNDAMENTALS OF SELLINGCustomers For Life Through Service12th EditionCharles M. FutrellMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter17Motivation, Compensation,Leadership, and Evaluation ofSalespeo

Rutgers - CS - 642

Rutgers - CS - 642

Homework 1Combinatorics I (Fall 2012)Rutgers UniversitySwastik KoppartyDue Date: September 24, 2012.1. Let (an ) be a sequence of complex numbers. Show that an is a linear-recurrent sequencen=0if and only if there exist 1 , . . . , k C and polynomi

Rutgers - CS - 642

Homework 2Combinatorics I (Fall 2012)Rutgers UniversitySwastik KoppartyDue Date: October 22, 2012.1. Let be a nite set, with | = q . For a sequence s, let |s| denote its length.Let s1 , s2 , . . . , sk be (nonempty) sequences composed of elements fr

Rutgers - CS - 642

Homework 3Combinatorics I (Fall 2012)Rutgers UniversitySwastik KoppartyDue Date: November 19, 2012.1. Generalize the Erdos-Rado argument from class to show the following relationship between2-color k -uniform hypergraph Ramsey numbers and 2-color k

Rutgers - CS - 642

Homework 4Combinatorics I (Fall 2012)Rutgers UniversitySwastik KoppartyDue Date: December 5, 2012.1. Let be a nite set of cardinality q . Formulate and prove a version of the Sauer-Shelahlemma for subsets of n (The original Sauer-Shelah lemma deals

Rutgers - CS - 642

Rutgers - CS - 640:491

MATH 642:491Fall, 2012Problems on 2-way counting and inclusion-exclusion1. A frog hops on the number line from 0 to n. If he is on position i, then he can eitherhop to i + 1 or to i + 2. Let Fn be the number of ways he can get from 0 to n. Showthat Fn

Rutgers - CS - 640:491

MATH 642:491Fall, 2012Problems1. Let a, b, c be real numbers in (0, 1). Suppose a + b + c = 2. Show thatabc 8.(1 a)(1 b)(1 c)2. Let A1 , . . . , An be a regular n-gon which is inscribed in a circle of radius 1.Show thatn|A1 Aj | = n.j =2(Hint:

Rutgers - CS - 640:491

MATH 642:491Fall, 2012Problems on Analysis and Geometry1. Suppose f : R R is a continuous function such that for every a, b, iff a+b . Show that f (x) = x + for some , .2f (a)+f (b)2=If we drop the condition that f is continous, does the same conc

Rutgers - CS - 640:491

MATH 642:491Fall, 2012Problems1. How many 0s does 400! end with?2. Find the smallest positive integer having exactly 100 positive divisors.3. You have a 7 gallon jug and a 10 gallon hat (both the jug and the hat have no markings).You have access to a

Rutgers - CS - 640:491

Linear Diophantine EquationsA Diophantine equation is an equation which is to be solved over the integers.A linear Diophantine equation of the formhas solutions if and onlyif. There is a similar result for linear Diophantine equations in morethan 2

Rutgers - CS - 640:491

MATH 642:491Fall, 2012Problems in elementary number theory(1) Prove that any two successive Fibonacci numbers are relatively prime.(Two integers are relatively prime if they have no common factor otherthan 1).(2) Show that the tens digit of any power

Rutgers - CS - 640:491

MATH 642:491Fall, 2012The Pigeon-Hole Principle(Note: The book has solutions to some of these problemsdont read them!)1. Let A be a subset of integers of size n. Prove that there is a nonempty subset of Awhose sum is divisible by n.2. Given 19 distin

Rutgers - CS - 640:491

MATH 642:491Fall, 2012Problems on polynomials1. Suppose P (X ) C[X ] is such that for every x R, P (x) R. Show that all thecoecients of P (X ) are real numbers.2. Let P (X ) = X r + a1 X r1 + . . . + ar1 X + ar be a polynomial with complex coecientss

Rutgers - CS - 640:491

MATH 642:491Fall, 2012Problems on power series1. Use the technique of generating functions to solve the recurrence relation a0 = 1, a1 =0, a2 = 5 and for n > 3,an = 4an1 5an2 + 2an3 .2. Prove that the value of the nth derivative of x3 /(x2 1) at x =

Missouri (Mizzou) - ECON - 1014

Prelab 10 CS1050 Fall 2012Prepare yourself for C structures before lab 10 assignment. Some prelab functions will be usedin the main lab. Implement following structure and functionstypedef struct cfw_int id;float gpa; data;data student[10]; (Array i

Georgia Tech - PSYCH - 2210

Social Psychology 2210Final Study GuideChapter 9: Group ProcessesGroup Three or more people who interact and are interdependent in the sense that their needs and goals causethem to influence each other.Social roles Shared expectations in a group abou

UNC - COMM - 063

Hayley MikkelsonHuman Rights NarrativeSecond ChanceIt was the typical Sunday morning for college students. My friend and I had stayed uplate the night before and we both woke up groggy, yet thinking about the loads of homework westill had to do. Whil

UNC - COMM - 063

Hayley MikkelsonComm 063Paper 3Hey Pearl Harbor; the painful stab comes every time.Stretching the corners of your eyes, you imitate mine.The teasing and taunts have etched themselves onto my heart,my mind, my tongue, suffer; the tiny box holding thi