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Chapter 1
Introduction
An Economist’s Theory of Reincarnation: If you’re good, you come back
on a higher level. Cats come back as dogs, dogs come back as horses, and
people—if they’ve been very good like George Washington—come back as
money.
If all the food, clothing, entertainment, and other goods and services
we wanted were freely available, no one would study economics, and
we would not need managers. However, most of the good things in life
are scarce. We cannot have everything we want. Consumers cannot
consume everything but must make choices about what to purchase.
Similarly, managers of firms cannot produce everything and must
make careful choices about what to produce, how much to produce,
and how to produce it. Studying such choices is the main subject
matter of economics. Economics is the study of decision making in
the presence of scarcity.
Managerial economics is the application of economic analysis to
managerial decision making. It focuses on how managers make
economic decisions by allocating the scarce resources at their disposal.
To make good decisions, a manager must understand the behavior of
other decision makers, such as consumers, workers, other managers,
and governments. In this book, we examine decision making by such

1

1

participants in the economy, and we show how managers can use this
understanding to be successful.
Learning Objectives

1. Describe the major business decisions managers face.
2. Explain how economic models are useful in managerial
decision making.
3. Illustrate how a knowledge of economics can help your
career.

1.1 Managerial Decision
Making
A firm’s managers allocate the limited resources available to them to
achieve the firm’s objectives. The objectives vary for different
managers within a firm but each managerial task is constrained by
resource scarcity. At any moment in time, a production manager has to
use the existing factory and a marketing manager has a limited
marketing budget. Such resource limitations can change over time, but
managers always face constraints.
Profit
The main objective of most private-sector firms is to maximize profit,
which is the difference between revenue and cost. Senior managers of
a firm might have other concerns as well, including social
responsibility and personal career objectives. However, the primary
responsibility of senior managers to the owners of the firm is to focus
on the bottom line: maximizing profit.
Managers have a variety of roles in the profit maximization process.
The production manager seeks to minimize the cost of producing a
particular good or service. The market research manager determines
how many units of any particular product can be sold at a given price,
2

which helps to determine how much output to produce and what price
to charge. The research and development (R&D) manager supervises
the development of new products that will be attractive to consumers.
The most senior manager, usually called the chief executive officer
(CEO), coordinates the firm’s managerial functions and sets its overall
strategy.

Trade-Offs
People and firms face trade-offs because they can’t have everything.
Managers must focus on the trade-offs that directly or indirectly affect
profits. Evaluating trade-offs often involves marginal reasoning:
considering the effect of a small change. Key trade-offs include:
How to produce: To produce a given level of output, a firm trades
off inputs, deciding whether to use more of one and less of
another. Car manufacturers choose between metal and plastic for
many parts, which affects the car’s weight, cost, and safety.
What prices to charge: Some firms, such as farms, have little or no
control over the prices at which their goods are sold and must sell
at the price determined in the market. However, many other firms
set their prices. When a manager of such a firm sets the price of a
product, the manager must consider whether raising the price by a
dollar increases the profit margin on each unit sold by enough to
offset the loss from selling fewer units. Consumers, given their
limited budgets, buy fewer units of a product when its price rises.
Thus, ultimately, the manager’s pricing decision is constrained by
the scarcity under which consumers make decisions.
Whether to innovate: One of the major trade-offs facing managers
is whether to maximize profit in the short run or in the long run.
For example, a forward-looking firm may invest substantially in
innovation—designing new products and better production

methods—which lowers profit in the short run, but may raise profit
in the long run.

Other Decision Makers
It is important for managers of a firm to understand how the decisions
made by consumers, workers, managers of other firms, and
governments constrain their firm. Consumers purchase products
subject to their limited budgets. Workers decide on which jobs to take
and how much to work given their scarce time and limits on their
abilities. Rivals may introduce new, superior products or cut the prices
of existing products. Governments around the world may tax,
subsidize, or regulate products.
Interactions between economic decision makers take place primarily in
markets. A market is an exchange mechanism that allows buyers to
trade with sellers. A market may be a town square where people go to
trade food and clothing, or it may be an international
telecommunications network over which people buy and sell financial
securities. When we talk about a single market, we refer to trade in a
single good or group of goods that are closely related, such as soft
drinks, movies, novels, or automobiles. The primary participants in a
market are firms that supply the product and consumers who buy it,
but government policies such as taxes also play an important role in
the operation of markets.

3

Strategy
When competing with a small number of rival firms, senior managers
consider how their firm’s products are positioned relative to those of
its rivals. The firm uses a strategy—a battle plan that specifies the
actions or moves that the firm will make to maximize profit. A strategy
might involve choosing the level of output, the price, or the type of
advertising now and possibly in the future. For example, in setting its
production levels and prices, Pepsi’s managers must consider what
choices Coca-Cola’s managers will make. One tool that is helpful in
understanding and developing such strategies is game theory, which we
use in several chapters.

1.2 Economic Models
Economists use economic models to explain how managers and
other decision makers make decisions and to interpret the result-
ing market outcomes. A model is a description of the relation-
ship between two or more variables. Models are used in many
fields. For example, astronomers use models to describe and pre-
dict the movement of comets and meteors, medical researchers
use models to describe and predict the effect of medications on
diseases, and meteorologists use models to predict weather.
Business economists construct models dealing with economic
variables and use such models to describe and predict how a
change in one variable will affect another variable. Such models
are useful to managers in predicting the effects of their decisions
and in understanding the decisions of others. Models allow man-
agers to consider hypothetical situations—to use a what-if analysis
—such as “What would happen if we raised our prices by 10%?” or
“Would profit rise if we phased out one of our product lines?”
Models help managers predict answers to what-if questions and
to use those answers to make good decisions.

Mini-Case
Using an Income Threshold Model in China
According to the income threshold model, people whose
incomes are below a threshold do not buy a particular

consumer durable, while many people whose income ex-
ceeds that threshold buy it.
If this theory is correct, we predict that, as most people’s
incomes rise above the threshold in lower-income coun-
tries, consumer durable purchases will increase from near
zero to large numbers virtually overnight. This prediction
is consistent with evidence from Malaysia, where the in-
come threshold for buying a car is about $4,000.
In China, incomes have risen rapidly and now exceed the
threshold levels for many types of durable goods. In re-
sponse to higher incomes, Chinese car purchases have
taken off.
For example, Li Rifu, a 46-year-old Chinese farmer and
watch repairman, thought that buying a car would im-
prove the odds that his 22- and 24-year-old sons would
find girlfriends, marry, and produce grandchildren. Soon
after Mr. Li purchased his Geely King Kong for the equiva-
lent of $9,000, both sons met girlfriends, and his older son
got married.
Given the rapid increase in Chinese incomes in the past
couple of decades, four-fifths of all new cars sold in China
are bought by first-time customers. An influx of first-time
buyers was responsible for Chinese car sales increasing
by a factor of nearly 18 between 2000 and 2017. In 2005,
China produced fewer than half as many cars as the Unit-
ed States. In 2017, China was by far the largest producer

Simplifying Assumptions
Everything should be made as simple as possible, but not simpler.
—Albert Einstein
A model is a simplification of reality. The objective in building a
model is to include the essential issues, while leaving aside the
many complications that might distract us or disguise those essen-
tial elements. For example, the income threshold model focuses
on only the relationship between income and purchases of
durable goods. Prices, multiple car purchases by a single con-
sumer, and other factors that might affect durable goods purchas-
es are left out of the model. Despite these simplifications, the
model—if correct—gives managers a good general idea of how the
automobile market is likely to evolve in countries such as China.
We have described the income threshold model in words, but we
could have presented it using graphs or mathematics. Represent-
ing economic models using mathematical formulas in spread-
sheets has become very important in managerial decision making.
Regardless of how the model is described, an economic model is a
simplification of reality that contains only its most important fea-
of cars in the world. It produced nearly three times as
many cars as the United States—the second largest pro-
ducer—as well as 39% more than the entire European
Union. One out of every three cars in the world is pro-
duced in China.2

tures. Without simplifications, it is difficult to make predictions
because the real world is too complex to analyze fully.
Economists make many assumptions to simplify their models.
When using the income threshold model to explain car purchas-
ing behavior in China, we assume that factors other than income,
such as the color of cars, do not have an important effect on the
decision to buy cars. Therefore, we ignore the color of cars that
are sold in China in describing the relationship between income
and the number of cars consumers want. If this assumption is cor-
rect, by ignoring color, we make our analysis of the auto market
simpler without losing important details. If we’re wrong and these
ignored issues are important, our predictions may be inaccurate.
Part of the skill in using economic models lies in selecting a mod-
el that is appropriate for the task at hand.

Testing Theories
Blore’s Razor: When given a choice between two theories, take the one
that is funnier.
Economic theory refers to the development and use of a model to
formulate hypotheses, which are proposed explanations for some
phenomenon. A useful theory or hypothesis is one that leads to clear,
testable predictions. A theory that says “If the price of a product rises,
the quantity demanded of that product falls” provides a clear
prediction. A theory that says “Human behavior depends on tastes, and
tastes change randomly at random intervals” is not very useful because
it does not lead to testable predictions.

Economists test theories by checking whether the theory’s predictions
are correct. If a prediction does not come true, they might reject the
theory—or at least reduce their confidence in the theory. Economists
use a model until it is refuted by evidence or until a better model is
developed for a particular use.
A good model makes sharp, clear predictions that are consistent with
reality. Some very simple models make sharp or precise predictions
that are incorrect. Some more realistic and therefore more complex
models make ambiguous predictions, allowing for any possible

outcome, so they are untestable. Neither incorrect models nor
untestable models are helpful. The skill in model building lies in
developing a model that is simple enough to make clear predictions
but realistic enough to be accurate. Any model is only an
approximation of reality. A good model is one that is a close enough
approximation to be useful.
Although economists agree on the methods they use to develop and
apply testable models, they often disagree on the specific content of
those models. One model might present a logically consistent
argument that prices will go up next quarter. Another, using a different
but equally logical theory, may contend that prices will fall next
quarter. If the economists are reasonable, they will agree that pure
logic alone cannot resolve their dispute. Indeed, they will agree that
they’ll have to use empirical evidence—facts about the real world—to
find out which prediction is correct. One goal of this book is to teach
managers how to think like economists so that they can build, apply,
and test economic models to deal with important managerial
problems.
6

Positive and Normative
Statements
Economic analysis sometimes leads to predictions that seem
undesirable or cynical. For instance, an economist doing market
research for a producer of soft drinks might predict that “if we double
the amount of sugar in this soft drink we will significantly increase
sales to children.” An economist making such a statement is not
seeking to undermine the health of children by inducing them to
consume excessive amounts of sugar. The economist is only making a
scientific prediction about the relationship between cause and effect:
More sugar in soft drinks is appealing to children.
Such a scientific prediction is known as a positive statement : a
testable hypothesis about matters of fact such as cause-and-effect
relationships. Positive does not mean that we are certain about the
truth of our statement; It indicates only that we can test the truth of the
statement.
An economist may test the hypothesis that the quantity of soft drinks
demanded decreases as the price increases. Some may conclude from
that study that “The government should tax soft drinks so that people
will not consume so much sugar.” Such a statement is a value
judgment. It may be based on the view that people should be protected
from their own unwise choices, so the government should intervene.


This judgment is not a scientific prediction. It is a normative
statement : a belief about whether something is good or bad. A
normative statement cannot be tested because a value judgment
cannot be refuted by evidence. A normative statement concerns what
somebody believes should happen; a positive statement concerns what
is or what will happen. Normative statements are sometimes called
prescriptive statements because they prescribe a course of action, while
positive statements are sometimes called descriptive statements
because they describe reality. Although a normative conclusion can be
drawn without first conducting a positive analysis, a policy debate will
be better informed if a positive analysis is conducted first.
Good economists and managers emphasize positive analysis. This
emphasis has implications for what we study and even for our use of
language. For example, many economists stress that they study
people’s wants rather than their needs. Although people need certain
minimum levels of food, shelter, and clothing to survive, most people
in developed economies have enough money to buy goods well in
excess of the minimum levels necessary to maintain life. Consequently,
in wealthy countries, calling something a “need” is often a value
judgment. You almost certainly have been told by someone that “you
need a college education.” That person was probably making a value
judgment—“you should go to college”—rather than a scientific
prediction that you will suffer terrible economic deprivation if you do
not go to college. We can’t test such value judgments, but we can test a
(positive) hypothesis such as “Graduating from college or university
increases lifetime income.”

3

New Theories
One of the strengths of economics is that it is continually evolving, for
two reasons. First, economists—like physicists, biologists, and other
scientists—are always trying to improve their understanding of the
world around them.
For example, traditional managerial textbooks presented theories
based on the assumption that decision makers always optimize: They
do the best they can with their limited resources. While we cover these
traditional theories, we also present another recently developed
approach referred to as behavioral economics, which is the study of how
psychological biases and cognitive limits can prevent managers and
others from optimizing.
Second, economic theory evolves out of necessity. Unlike physical and
biological scientists, economists and managers also have to develop
new ways to think about disruptive innovations. Although most
innovations are incremental, some are sufficiently disruptive to
dramatically change the way an industry is structured—or even to
create new industries and destroy old ones.
The internet is an example of a disruptive innovation. Internet-based
online retailing has displaced much traditional brick-and-mortar
retailing, online payment systems have largely replaced cash and
4
7

checks, and online media, especially social media, have changed the
way most people acquire and transmit information.
To analyze the economic effects of the internet and other disruptive
innovations, economists have extended established theories and
developed new ones. For example, the internet has given rise to many
services that allow two groups of users to interact—such as auction
services, dating sites, job matching services, and payment services. In
response, economists have developed the theory of such two-sided
markets, which has been important to the ongoing evolution of these
markets and to government policy toward them. This book describes
economic theories of the internet and of two-sided markets, along with
other recent developments in economics.
5

1.3 Using Economic Skills in
Your Career
This book will help you develop skills in economic analysis that are
crucial in business decision-making. Some readers will get jobs that
use economic analysis intensively, as in assessing financial investment
options for financial institutions. Others may work in setting prices or
planning other actions based on formal analyses, such as spreadsheet-
based economic modeling. Other students will get jobs that emphasize
different skills, but economic decisions come up everywhere in
business.
All readers will benefit from familiarity with the applications of
economics presented in this book. Many managers as well as
concerned citizens regularly use these skills to predict the likely
outcomes from government actions and other events. Readers will also
find that much of the analysis in the book is relevant to their own
personal decisions, such as investment or educational choices.

Summary
1. Managerial Decision Making. Economic analysis helps
managers develop strategies to pursue their objectives
effectively in the presence of scarcity. Various managers within
a firm face different objectives and different constraints, but
the overriding objective in most private-sector firms is to
maximize profits. Making decisions subject to constraints
implies making trade-offs. To make good managerial decisions,
managers must understand how consumers, workers, other
managers, and governments will act. Economic theories
normally (but not always) assume that all decision makers
attempt to maximize their well-being given the constraints
they face.
2. Economic Models. Managers use models based on economic
theories to help make predictions and decisions, which they
use to run their firms. A good model is simple to use and
makes clear, testable predictions that are supported by
evidence. Economists use models to construct positive
hypotheses such as causal statements linking changes in one
variable, such as income, to its effects, such as purchases of
automobiles. These positive propositions can be tested. In
contrast, normative statements, which are value judgments,
cannot be tested.
3. Using Economic Skills in Your Career. A knowledge of
economics will be valuable to you in a career in management,
8

economics, or other fields. It will also be useful in your
everyday life.
MyLab Economics: Chapter 1 Study Plan
Open the MyLab Economics Study Plan to work the
exercises.

Chapter 2
Supply and Demand
Talk is cheap because supply exceeds demand.
Managerial Problem
Carbon Taxes
Burning fossil fuels such as gasoline, coal, and heating oil
releases gases containing carbon into the air. These
“greenhouse” gases are widely believed to contribute to
global warming. To reduce this problem and raise tax
revenues, many environmentalists and political leaders have
proposed levying a carbon tax on the carbon content in
fossil fuels.
When governments impose carbon taxes on gasoline,
managers of firms that sell gasoline need to think about how
much of the tax they have to absorb and how much they can
pass through to firms and consumers who buy gasoline.
Similarly, managers of firms that purchase gasoline must
consider how any pass-through charges will affect their
costs of shipping, air travel, heating, and production. This
pass-through analysis is critical in making managerial
1
2
9

decisions concerning how much to produce, how to set
prices, whether to undertake long-run capital investments,
and whether to operate or shut down.
Finland and Sweden implemented the first broad-based
carbon taxes on fuels containing carbon (such as gasoline)
in the early 1990s. Various other countries followed suit,
including Ireland and India in 2010 and the United Kingdom
in 2013. However, strong opposition to carbon taxes has
limited adoption in other parts of the world.
The first North American carbon tax was introduced in 2006
in Boulder, Colorado (where it was applied to only electricity
generation), and this tax was renewed in 2012. In 2007 and
2008, the Canadian provinces of Quebec and British
Columbia became the first provinces or states in North
America to impose a broad-based carbon tax. Canada is set
to impose a national carbon tax in 2018.
10

Such carbon taxes harm some industries and help others.
The tax hurts owners and managers of gasoline retailing
firms, who need to consider whether they can stay in
business in the face of a significant carbon tax. Shippers
and manufacturers that use substantial amounts of fuel in
production, as well as other firms, would also see their
operating costs rise.
In contrast, a carbon tax creates opportunities for other
firms and industries. For example, wind and solar power,
which are alternatives to fossil fuels in generating electricity,
would become much more attractive. Anticipating greater
opportunities in this market in the future, PacifiCorp, a utility
owned by Warren Buffett, announced a plan in 2017 to
spend $3.5 billion over three years to bring hundreds of new
wind turbines online. It also plans to greatly expand its use
of solar power. In 2018, the Solar Corporation of India (SECI)
called for bids (“tenders”) to build two large solar power
projects.
Managers in the motor vehicle industry would need to
consider whether to change their product mix in response to
a carbon tax, perhaps focusing more on fuel-efficient
vehicles. Even without a carbon tax, when gas prices rise,
many consumers switch from sports utility vehicles (SUVs)
to smaller cars. A carbon tax would favor fuel-efficient
vehicles even more.
At the end of this chapter, we will return to this topic and
answer a question of critical importance to managers in the

To analyze the effects of carbon taxes on gasoline prices and other
variables, managers use an economic tool called the supply-and-
demand model. Managers who use this model to anticipate the effects of
events make more profitable decisions.
The supply-and-demand model provides a good description of many
markets and applies particularly well to those with many buyers and
many sellers, as in most agricultural markets, much of the construction
industry, many retail markets (such as gasoline retailing), and several
other major sectors of the economy. In markets where this model is
applicable, it allows us to make clear, testable predictions about the
effects of new taxes or other shocks on prices and additional market
outcomes.
motor vehicle industry and in other industries affected by
gasoline prices: What would be the effect of imposing a
carbon tax on the price of gasoline?
Learning Objectives

1. Explain how the quantity of a good or service that consumers
want depends on its price and other factors.
2. Describe how the quantity of a good or service that firms want
to sell depends on its price and other factors.
3. Show how the interaction between consumers’ demand curve
and producers’ supply curve determines the market price and

quantity of a good or service.
4. Predict how an event that affects consumers or firms changes
the market price and quantity.
5. Analyze the market effects of government policy using the
supply-and-demand model.
6. Discuss when to use the supply-and-demand model.

2.1 Demand
Consumers decide whether to buy a particular good or service and, if
so, how much to buy based on its price and on other factors, including
their incomes, the prices of other goods, their tastes, and the
information they have about the product. Government regulations and
other policies also affect buying decisions. Before concentrating on the
role of price in determining quantity demanded, let’s look briefly at
some other factors.
Income plays a major role in determining what and how much to
purchase. People who suddenly inherit great wealth might be more
likely to purchase expensive Rolex watches or other luxury items and
would probably be less likely to buy inexpensive Timex watches and
various items targeted toward lower-income consumers. More broadly,
when a consumer’s income rises, that consumer will often buy more of
many goods.
The price of a related good might also affect consumers’ buying
decisions. Related goods can be either substitutes or complements.
Substitutes are a pair of goods or services for which an increase in
the price of one causes a consumer to demand a larger quantity of the
other. Before deciding to go to a movie theater, a consumer considers
the price of a substitute, such as streaming a movie online. The more
expensive a trip to a movie theater is, the more likely that the
consumer purchases a streamed movie to watch at home instead.

11

Different brands of a good are often close substitutes. Before buying a
pair of Levi’s jeans, a customer might check the prices of other brands
and substitute one of those brands for Levi’s if its price is sufficiently
attractive.
Complements are a pair of goods or services for which an increase in
the price of one causes a consumer to demand a smaller quantity of the
other. Smartphones, such as the iPhone and Samsung Galaxy, and
music purchased online and downloaded to the smartphone are
complements. A decline in the price of smartphones increases the
demand for online music.
Consumers’ tastes are important in determining their demand for a
good or service. Consumers do not purchase foods they dislike or
clothes they view as unfashionable or uncomfortable. The importance
of fashion illustrates how changing tastes affect consumer demand.
Clothing items that have gone out of fashion often languish in discount
sections of clothing stores even though they commanded high prices a
couple of years (or even a few weeks) earlier when they were in
fashion. Firms devote significant resources to trying to change
consumer tastes through advertising.
Similarly, information about the effects of a good has an impact on
consumer decisions. In recent years, positive health outcomes linked to
various food items have created greater demand for these healthy
foods (such as soy products and high-fiber breads) when the
information became well known.


Government rules and regulations affect demand. If a city government
bans the use of skateboards on its streets, demand for skateboards in
that city falls. Governments might also restrict sales to particular
groups of consumers. For example, many political jurisdictions do not
allow children to buy tobacco products, which reduces the quantity of
cigarettes consumed.
Other factors might also affect the demand for specific goods. For
example, consumers are more likely to use Facebook if most of their
friends use Facebook. This network effect arises from the benefits of
being part of a network and from the potential costs of being outside
the network.
Although many factors influence demand, economists focus most on
how a good’s own price affects the quantity demanded. The
relationship between price and quantity demanded plays a critical role
in determining the market price and quantity in supply-and-demand
analysis. To determine how a change in price affects the quantity
demanded, economists ask what happens to quantity when price
changes and other factors affecting demand, such as income and tastes,
are held constant.
The Demand Curve
The amount of a good that consumers are willing to buy at a given
price, holding constant the other factors that influence purchases, is
the quantity demanded . The quantity demanded of a good or service
can exceed the quantity actually sold. For example, as a promotion, a

12

Figure 2.1 A Demand Curve
local store might sell Ghirardelli dark chocolate bars for $1 each today
only. At that low price, you might want to buy 10 chocolate bars, but
because the store has only 5 remaining, you can buy at most 5
chocolate bars at this price. The quantity you demand at this price is 10
chocolate bars—it’s the amount you want—even though the amount
you actually buy is only 5.
Using a diagram, we can show the relationship between price and the
quantity demanded. A demand curve shows the quantity demanded
at each possible price, holding constant the other factors that influence
purchases. Figure 2.1 shows the estimated annual world demand
curve, for coffee, which is one of the world’s most valuable traded
commodities. The internationally traded commodity is unroasted
(“green”) coffee beans. These unroasted beans are sold to Starbucks,
Folgers, Maxwell House, and other firms that roast and sell coffee to
retail consumers. In this section, we analyze the market for unroasted
coffee beans, which we call coffee. Although this demand curve is a
straight line, demand curves may also be smooth curves or wavy lines.
By convention, the vertical axis of the graph measures the price, p, per
unit of the good. We measure the price of coffee in dollars per pound
(abbreviated lb). The horizontal axis measures the quantity, Q, of the
good, which is usually a physical measure per time period. This figure
measures the quantity of coffee in millions of tons (2,000 lb) per year.


,
D1
3

The estimated global demand curve, for coffee shows the relationship
between the quantity demanded per year in millions of tons and the price per lb.
The downward slope of the demand curve shows that, holding other factors that
influence demand constant, consumers demand a smaller quantity of a good
when its price is high and a larger quantity when the price is low. A change in
price causes a movement along the demand curve. For example, an increase in the
price of coffee causes consumers to demand a smaller quantity of coffee.
The demand curve hits the vertical axis at $12, indicating that the
quantity demanded is zero when the price is $12 per lb or higher. The
demand curve hits the horizontal (quantity) axis at 12 tons, the
quantity of coffee buyers would want each year if the price were zero.
,
D1
13

To find out how much consumers demand at a price between zero and
$12, say, $6, we draw a horizontal line from that price on the vertical
axis until we hit the demand curve, and then we draw a vertical line
down to the horizontal quantity axis. As the figure shows, the quantity
demanded at a price of $6 per lb is 6 million tons per year.
One of the most important things to know about a demand curve is
what it does not show. All relevant economic variables that the
demand curve graph does not explicitly display—income, prices of
related goods (such as tea or sugar), tastes, information, and so on—
are held constant. Thus, the demand curve shows how quantity varies
with price but not how quantity varies with income, the prices of
related goods, tastes, information, or other variables.
Effects of a Price Change on the Quantity
Demanded
One of the most important results in economics is the Law of
Demand : Consumers demand more of a good if its price is lower,
holding constant income, the prices of other goods, tastes, and other
factors that influence the amount they want to consume. According to
the Law of Demand, demand curves slope downward, as in Figure 2.1 .
A downward-sloping demand curve illustrates that consumers demand
a larger quantity of this good when its price is low and a smaller
quantity when its price is high. What happens to the quantity of coffee
demanded if the price of coffee drops and all other variables remain
constant? If the price falls from $6 per lb to $4 per lb in Figure 2.1 ,




the annual quantity buyers want to purchase increases from 6 million
tons to 8 million tons per year. Similarly, if the price drops from $4 to
$2 per lb, the quantity buyers demand increases from 8 to 10 million
tons.
These changes in the quantity demanded in response to changes in
price are movements along the demand curve. Thus, the demand curve is
a concise summary of the answer to the question “What happens to the
quantity demanded as the price changes, when all other factors are
held constant?”
Although we generally expect demand curves to have a clear
downward slope, as the coffee demand curve does, a vertical or
horizontal demand curve is possible. We can think of horizontal and
vertical demand curves as being extreme cases of downward-sloping
demand. The Law of Demand rules out demand curves that have an
upward slope.
The Law of Demand is an empirical claim—a claim about what actually
happens. It is not a claim about general theoretical principles. It is
theoretically possible that a demand curve could slope upward.
However, the available empirical evidence strongly supports the Law
of Demand.
Effects of Other Factors on Demand
If a demand curve shows how a price change affects the quantity
demanded, holding constant all other factors that affect demand, how
can we use demand curves to show the effects of a change in one of
4
14

Figure 2.2 A Shift of the Demand Curve
these other factors, such as income? One approach is to draw the
demand curve in a three-dimensional diagram with the price of coffee
on one axis, income on a second axis, and the quantity of coffee on the
third axis. But just thinking about drawing such a diagram probably
makes your head hurt.
Economists use a simpler approach to show the effect of factors other
than a good’s own price on demand. A change in any relevant factor
other than the price of the good causes a shift of the demand curve rather
than a movement along the demand curve. We illustrate such a shift in
Figure 2.2 . This figure shows that the coffee demand curve shifts to
the right from the original demand curve to a new demand curve
if average annual household income in high-income countries, which
consume most of the world’s coffee, increases by $15,000, from
$35,000 to $50,000. On the new demand curve, consumers demand
more coffee at any given price than on because income has risen,
encouraging consumers to buy more coffee. At a price of $2 per lb, the
quantity of coffee demanded goes from 10 million tons on before
the increase in income, to 11.5 million tons on after the increase.

D1
D2
,
D2
D1
,
D1
,
D2

The global demand curve for coffee shifts to the right from to as average
annual household income in high-income countries rises by $15,000, from
$35,000 to $50,000. As a result of the increase in income, more coffee is
demanded at any given price.
The prices of related goods—substitutes and complements—also affect
the quantity of coffee demanded. Consumers who view tea and coffee
as substitutes demand more coffee at any given price of coffee as the
price of tea rises. That is, their demand curve for coffee shifts to the
right.
Complements have the opposite effect. Consumers who view sugar
and coffee as complements demand less coffee at any given price of
coffee as the price of sugar rises. That is, their demand curve for coffee
shifts to the left.
D1
D2

In addition, changes in other factors that affect demand, such as
information, can shift a demand curve. Reinstein and Snyder (2005)
found that movie reviews affect the demand for some types of movies,
but not others. Holding price constant, they determined that if a film
received “two-thumbs-up” reviews on a popular movie-review
television program, the opening weekend demand curve shifted to the
right by 25% for a drama, but the demand curve did not significantly
shift for an action film or a comedy.
To properly analyze the effects of a change in some variable on the
quantity demanded, we must distinguish between a movement along a
demand curve and a shift of a demand curve. A change in the good’s own
price causes a movement along a demand curve. A change in any other
relevant factor besides the good’s own price causes a shift of the demand
curve.

The Demand Function
The demand curve shows the relationship between the quantity
demanded and a good’s own price, holding other relevant factors
constant at some particular levels. We illustrate the effect of a change
in one of these other relevant factors by shifting the demand curve. We
can also represent the same information—information about how price,
income, and other variables affect quantity demanded—using a
mathematical relationship called the demand function. This function
shows the effect of a good’s own price and other relevant factors on
the quantity demanded. Any factors not explicitly listed in the demand
function are assumed to be irrelevant or held constant. For example,
we could specify the demand for coffee as a function of the price of
coffee, income, the price of tea, the price of sugar, the prices of other
related goods, and possibly other factors as well. However, if we hold
constant all potentially relevant factors except the price of coffee, p, the
price of sugar, and income, Y, the demand function is
where Q is the quantity of coffee demanded, D is the demand function,
p is the price of coffee, and Y is income. This expression shows how
the quantity of coffee demanded varies with the price of coffee and the
income of consumers.
,
ps
Q = D (p, , Y) ,
ps
(2.1)
15

Equation 2.1 is a general functional form—it does not specify a
particular form for the relationship between quantity, Q, and the
explanatory variables, p and Y. The estimated demand function that
corresponds to the demand curve in Figures 2.1 and 2.2 has the
specific (linear) form
where Q is the quantity of coffee in millions of tons per year, p is the
price of coffee in dollars per lb, is the price of sugar in dollars per lb,
and Y is the average annual household income in high-income
countries in thousands of dollars.
When we draw the demand curve in Figures 2.1 and 2.2 , we set
and Y at specific values, per lb and thousand per
year. By substituting these values for and Y in Equation 2.2 , we
can express the quantity demanded as a function of only the price of
coffee:
The demand function in Equation 2.3 corresponds to the straight-line
demand curve in Figure 2.1 with The constant term, 12,
in Equation 2.3 is the quantity demanded (in millions of tons per
year) if the price is zero. Setting the price equal to zero in Equation

D1  
Q = 8.56 − p − 0.3 + 0.1Y,
ps
(2.2)
ps
D1  
ps = $0.20
ps Y = $35
ps 
Q =
=
=
8.56 − p − 0.3 + 0.1Y
ps
8.56 − p − (0.3 × 0.2) + (0.1 × 35)
12 − p.
(2.3)

D1  Y = 35.


2.3 , we find that the quantity demanded is Figure
2.1 shows that where hits the quantity axis—where price
is zero.
Equation 2.3 also shows us how quantity demanded varies with a
change in price: a movement along the demand curve. If the price falls
from to the change in price, equals (The symbol,
the Greek letter delta, means “change in” the variable following the
delta, so is the “change in the price.”) If the price of coffee falls from
to then Quantity demanded
changes from at a price of $4 to at a price of $2, so
million tons per year, as Figure 2.1
shows.
More generally, the quantity demanded at is and the
quantity demanded at is The change in the quantity
demanded, in response to the price change (using
Equation 2.3 ) is
Thus, the change in the quantity demanded, is in this case.
For example, if then That is, a
$2 decrease in price causes the quantity demanded to rise by 2 million
 Q = 12 − 0 = 12.
 Q = 12 D1

p1 ,
p2 Δp, − .
p2 p1 Δ
Δp
= $4
p1 = $2,
p2 Δp = $2 − $4 = −$2.
= 8
Q1 = 10
Q2
ΔQ = − = 10 − 8 = 2
Q2 Q1

p1 = D ( ) ,
Q1 p1
p2 = D ( ) .
Q2 p2
ΔQ = − ,
Q2 Q1

ΔQ =
=
=
=
=
−
Q2 Q1
D ( ) − D ( )
p2 p1
(12 − ) − (12 − )
p2 p1
− ( − )
p2 p1
−Δp.
ΔQ, −Δp
Δp = −$2, ΔQ = −1Δp = −1 (−2) = 2.
16

tons per year. The change in quantity demanded is positive—the
quantity demanded increases—when the price falls. This effect is
consistent with the Law of Demand. Similarly, raising the price would
cause the quantity demanded to fall.
Using Calculus
Deriving the Slope of a Demand Curve
We can use calculus to determine how the quantity changes
as the price increases. Given the demand function for coffee
of the derivative of the demand function with
respect to price is Therefore, the slope of the
demand curve in Figure 2.1 , which is
is also More generally, the Law of Demand states that
the derivative of the demand function with respect to price
is negative,
Q = 12 − p,
dQ/dp = −1.
 dp/dQ = 1/(dQ/dp),
−1.
dQ/dp < 0.

Summing Demand Curves
The overall demand for coffee is composed of the demand of many
individual consumers. If we know the demand curve for each of two
consumers, how do we determine the total demand curve for the two
consumers combined? The total quantity demanded at a given price is
the sum of the quantity each consumer demands at that price.
We can use individual demand functions to determine the total
demand of several consumers. Suppose that the demand function for
Consumer 1 is
and the demand function for Consumer 2 is
At price p, Consumer 1 demands units, Consumer 2 demands
units, and the total quantity demanded by both consumers is the sum
of these two quantities:
We can generalize this approach to look at the total demand for three,
four, or more consumers, or we can apply it to groups of consumers
rather than just to individuals. It makes sense to add the quantities
= (p)
Q1 D1
= (p) .
Q2 D2
Q1 Q2
Q = + = (p) + (p) .
Q1 Q2 D1
D2

demanded only when all consumers face the same price. Adding the
quantity Consumer 1 demands at one price to the quantity Consumer 2
demands at another price would not be meaningful for this purpose—
the result would not show us a point on the combined demand curve.
Mini-Case
Summing Corn Demand Curves
We illustrate how to sum individual demand curves to get a
summed or combined demand curve graphically, using
estimated demand curves for corn (McPhail & Babcock,
2012). The figure shows the U.S. feed demand (the use of
corn to feed animals) curve, the U.S. food demand curve,
and the summed demand curve from these two sources.5

To derive the sum of the quantity demanded for these two
uses at a given price, we add the quantities from the
individual demand curves at that price. That is, we add the
demand curves horizontally. At a price for corn of $7.40, the
quantity demanded for food is 1.3 billion bushels per year
and the quantity demanded for feed is 4.6 billion bushels.
Thus, the summed quantity demanded at that price is
billion bushels.
When the price of corn exceeds $27.56 per bushel, farmers
stop using corn for animal feed, so the quantity demanded
for this use equals zero. As a result, the summed demand
curve is the same as the food demand curve at prices above
$27.56.
Q = 1.3 + 4.6 = 5.9

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Fig. 669.
Fig. 670.
When it becomes necessary to cut square packing to reduce its
depth, place the packing in a vise, allowing the stock to be removed
to project above the jaws, as shown in Fig. 671. With the aid of a
draw-knife the work can be quickly and easily done. It is difficult to
cut the packing evenly. If the rings have an uneven bearing on the
bottom of the grooves leakage is likely to occur when the pump is
first started.
The follower type of water piston can readily be packed without
removing it from the cylinder, providing rings of the proper depth
and length are at hand. The old packing rings can be removed with
a packing hook. Take the new ring and start one end with a soft
stick, and push the remainder of the ring firmly against the collar or
flange at the inner end of the piston, as shown in the engraving, Fig.
672. Arrange the several rings so as to break joints.
Method of packing a follower piston. Coat the sides of the rings
with a thick paste of cylinder oil and Dixon’s Flake graphite, which

will prevent the rings from sticking together.
Fig. 671.
Pump packing cannot be readily examined and is liable to fail at
any time, therefore several rings, cut to the proper length, should be
kept on hand. This may be easily done by making a pattern ring,
which is nothing more or less than a ring of packing which has been
fitted into the piston and is known to be of the proper length. The
extra rings can then be cut at odd times, and when occasion
demands it the water piston can be packed very quickly and the
pump started.
Care should be taken when about to pack a boiler feed pump or
other pump subjected to high pressure to see that the cylinders are
relieved before loosening the cylinder head bolts. This may be
accomplished by closing the valve in the delivery pipe, and also in
the suction pipe; if the pump receives water under pressure, open
the air cock on the air chamber and cylinder cocks.

Fig. 672.
Pump slip or slippage represents the difference between the
calculated and the actual discharge of a pump, which is generally
expressed as a percentage of the calculated discharge. Thus, when
the slippage is given as fifteen per cent. it indicates that the loss due
to slip amounts to fifteen per cent. of the calculated discharge.
Slippage is due to two causes, the time required for the suction and
discharge valve to seat, due to excessive speed. When the piston
speed is so high that the water cannot enter the pump fast enough
to completely fill the cylinder only a partial cylinder full of water is
delivered at each stroke. High speeds also increase slippage, due to
the seating of the valves.

Graphite as a lubricant is almost without a rival. It is one of the
forms under which carbon appears in nature; it is also known under
the name of plumbago and black lead; it is soft and oily to the
touch; it is a conductor of electricity; it is a lubricant that allows pipe
joints to be screwed up to the tightest possible fit. Graphite remains
upon the threads preventing rust, and it so preserves its peculiar
properties that pipe can be unscrewed without effort eight or ten
years after the joints have been made.
It is difficult to lift hot water by suction, but not everyone can
explain the cause; the reason is as follows:
Figs. 673 and 674.

In Fig. 674, let A be a vessel in which a vacuum exists, and let it
communicate by a tube, as shown, to the lower vessel containing
water. The pressure of the atmosphere upon the surface will force
the water up into the pipe until the column is high enough to exert a
pressure per square inch equal to that of the atmosphere. A cubic
inch of water weighs about 1⁄28 of a pound, so that it will take 28
cubic inches to weigh a pound, or a column 28 inches high to exert a
pressure of one pound per square inch. The atmospheric pressure is
14.7 pounds, or to avoid fractions, say, 15 pounds. This pressure
would then support a column (15 × 28)/12 = 35 feet high; that is,
the column a-c in Fig. 674 would be 35 feet in height. Attach a
gauge at or above the top, a, of a column, and it will indicate a
perfect vacuum; if the gauge were attached 28 inches below a, it
would indicate a pressure of one pound above absolute zero, or a
vacuum of 15-1 = 14 pounds; and if the gauge were moved further
downward, it would indicate an increasing pressure, that is, a
diminishing vacuum, at the rate of one pound for every 28 inches of
the water column above it, until at the level of the water in the tank
the pressure would be 15 pounds absolute, and the vacuum would
be zero.
Now, suppose the pipe to be lowered until the distance from the
bottom of the vessel, A, to the water level, c, is 21 feet. In that case
we will have the pressure of the atmosphere (15 pounds) forcing the
water up into the vessel, and the column 21 feet high, or (21 ×
12)/28 = 9 pounds, opposing it. The difference, 15-9 = 6 pounds, is
available to force the water into the chamber. This arrangement is
shown in Fig. 673, where A is a pump cylinder; then the difference
in pressure, 6 pounds, lifts the valve, and the water enters the pump
chamber with a velocity due to that pressure. In order to insure
smooth and quiet running of the pump, it is necessary to keep the
speed of the piston inside of the velocity with which the cylinder
would fill under this pressure, reduced by the friction of the water,
the pressure required to lift the valves, etc.
But this supposes that there is a perfect vacuum in A, and we
cannot realize this in contact with hot water. Water at any

temperature will boil unless it is under a pressure equal to or greater
than that corresponding with the temperature. Water at 60 degrees
F. will boil if the pressure upon its surface is reduced to a quarter of
a pound per square inch, and in the case shown in Fig. 674, it would
boil and fill the space A with steam at that absolute pressure.
Note.—Water at 170 degrees F. will boil if its pressure is reduced below
6 pounds absolute, and if the water were at this temperature in Fig. 673,
the cylinder, A, would be filled with steam at 6 pounds pressure; and this
added to the 9 pounds pressure of the column would completely balance
the atmospheric pressure, and the water would not rise above the level,
A.

TABLES AND DATA.
Miner’s Inch Measurement. The term miner’s inch is of California
origin, and not known or used in any other locality, it being a
method of measurement adopted by the various ditch companies in
disposing of water to their customers. The term is more or less
indefinite for the reason that the water companies do not all use the
same head above the center of the aperture, and the inch varies
from 1.36 to 1.73 cubic feet per minute each, but the most common
measurement is through an aperture 2 inches high and whatever
length is required, and through a plank 11⁄4 inches thick, as shown
in the engraving, Fig. 675. The lower edge of the aperture should be
2 inches above the bottom of the measuring box, and the plank 5
inches high above the aperture, thus making a 6-inch head above
the center of the stream. Each square inch of this opening
represents a miner’s inch, which is equal to a flow of 11⁄2 cubic feet
per minute. Time is not to be considered in any calculation based
upon a miner’s inch measurement.
Explanation of Weir Dam Measurement. Place a board or plank
edgewise across the stream to be measured as illustrated in Fig.
676.
This plank will be supported by posts sufficiently strong to resist
the pressure likely to be brought upon it by the head of water which
will form in the pond above this temporary dam, saw out a gap in
the top of the dam whose length should be from two to four times
its depth for small quantities of water and longer for larger
quantities. The edges of this gap should be beveled toward the
intake as represented. The over-fall below the bottom of gap should
be not less than twice its depth, that is, twelve inches if the gap is
six inches deep, etc.
Drive a stake above the dam at a distance of about six feet from
the face of the plank and then obstruct the water until it rises
precisely to the bottom of the gap and mark the water level on the

stake. Complete the dam so that all the water will be compelled to
flow through the gap and when the stream has assumed a regular
flow mark the stake at this new level.
Some would prefer to drive the stake with its top precisely level
with the bottom edge of gap in dam so that the depth of water in
stream may be measured with a rule or steel square placed upon top
of this stake at any time after the flow of water has reached its
average depth over dam. However the marks upon the stake are
preferred by most experts. After the stake has been marked it may
be withdrawn and the distance between the first and last marks
gives the theoretical flow according to the table, page 391.
Fig. 676.

Measurement in an open stream by velocity and cross section.
Measure the depth of the water at from 6 to 12 places across the
stream at equal distances apart. Add together all the depths in feet
and divide by the number of measurements made; this will be the
average depth of the stream, which, multiplied by its width, will give
its area or cross section. Multiply this by the velocity of the stream in
feet per minute which gives the cubic feet per minute of the stream.
Cubic Feet of water per minute that will flow over a Weir one-inch wide and
from 1⁄8 to 207⁄8-inches deep.
INCHES 1⁄8
1⁄4
3⁄8
1⁄2
5⁄8
3⁄4
7⁄8
0 .00 .01 .05 .09 .14 .19 .26 .32
1 .40 .47 .55 .64 .73 .82 .92 1.02
2 1.13 1.23 1.35 1.46 1.58 1.70 1.82 1.95
3 2.07 2.21 2.34 2.48 2.61 2.76 2.90 3.05
4 3.20 3.35 3.50 3.66 3.81 3.97 4.14 4.30
5 4.47 4.64 4.81 4.98 5.15 5.33 5.51 5.69
6 5.87 6.06 6.25 6.44 6.62 6.82 7.01 7.21
7 7.40 7.60 7.80 8.01 8.21 8.42 8.63 8.83
8 9.05 9.26 9.47 9.69 9.91 10.13 10.35 10.57
9 10.80 11.02 11.25 11.48 11.71 11.94 12.17 12.41
10 12.64 12.88 13.12 13.36 13.60 13.85 14.09 14.34
11 14.59 14.84 15.09 15.34 15.59 15.85 16.11 16.36
12 16.62 16.88 17.15 17.41 17.67 17.94 18.21 18.47
13 18.74 19.01 19.29 19.56 19.84 20.11 20.39 20.67
14 20.95 21.23 21.51 21.80 22.08 22.37 22.65 22.94
15 23.23 23.52 23.82 24.11 24.40 24.70 25.00 25.30
16 25.60 25.90 26.20 26.50 26.80 27.11 27.42 27.72
17 28.03 28.34 28.65 28.97 29.28 29.59 29.91 30.22
18 30.54 30.86 31.18 31.50 31.82 32.15 32.47 32.80
19 33.12 33.45 33.78 34.11 34.44 34.77 35.10 35.44
20 35.77 36.11 36.45 36.78 37.12 37.46 37.80 38.15
Example showing the application of the above table
Suppose the Weir to be 66 inches long, and the depth of water on it to
be 115⁄8 inches. Follow down the left hand column of the figures in the
table until you come to 11 inches. Then run across the table on a line with

the 11 until under 5⁄8 on top line you will find 15.85. This multiplied by
66, the length of Weir, gives 1046.10, the number of cubic feet of water
passing per minute.
FRICTION-LOSS IN POUNDS PRESSURE, FOR EACH 100 FEET OF
LENGTH IN DIFFERENT SIZE CLEAN IRON PIPES DISCHARGING
GIVEN QUANTITIES OF WATER PER MINUTE. ALSO VELOCITY OF
FLOW IN PIPE, IN FEET PER SECOND.
G. A. Ellis, C. E.
Gallons
discharged
per
minute.
1⁄2 Inch. 3⁄4 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
5 8.17 24.6 3.63 3.3
10 16.3 96.0 7.25 13.0
15 . . . . . . 10.9 28.7
20 . . . . . . 14.5 50.4
25 . . . . . . 18.1 78.0
Gallons
discharged
per
minute.
1 Inch. 11⁄4 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
5 2.04 0.84 1.31 0.31
10 4.08 3.16 2.61 1.05
15 6.13 6.98 3.92 2.38
20 8.17 12.3 5.22 4.07
25 10.2 19.0 6.53 6.40
30 12.3 27.5 7.84 9.15
35 14.3 37.0 9.14 12.04
40 16.3 48.0 10.4 16.1
45 . . . . . . 11.7 20.2
50 . . . . . . 13.1 24.9
75 . . . . . . 19.6 56.1
Gallons
discharged
per
minute.
11⁄2 Inch. 2 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
5 0.91 0.12 . . . . . .

10 1.82 0.47 1.02 0.12
15 2.73 0.97 . . . . . .
20 3.63 1.66 2.04 0.42
25 4.54 2.62 . . . . . .
30 5.45 3.75 3.06 0.91
35 6.36 5.05 . . . . . .
40 7.26 6.52 4.09 1.60
45 8.17 8.15 . . . . . .
50 9.08 10.0 5.11 2.44
75 13.6 22.4 7.66 5.32
100 18.2 39.0 10.2 9.46
125 . . . . . . 12.8 14.9
150 . . . . . . 15.3 21.2
175 . . . . . . 17.1 28.1
200 . . . . . . 20.4 37.5
Gallons
discharged
per
minute.
21⁄2 Inch. 3 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
25 1.63 0.21 1.13 0.10
50 3.26 0.81 2.27 0.35
75 4.90 1.80 3.40 0.74
100 6.53 3.20 4.54 1.31
125 8.16 4.89 5.67 1.99
150 9.80 7.00 6.81 2.85
175 11.4 9.46 7.94 3.85
200 13.1 12.47 9.08 5.02
250 16.3 19.66 11.3 7.76
300 19.6 28.06 13.6 11.2
350 . . . . . . 15.9 15.2
400 . . . . . . 18.2 19.5
450 . . . . . . 20.4 25.0
500 . . . . . . 22.7 30.8
Gallons
discharged
per
minute.
4 Inch. 6 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
50 1.28 0.09 . . . . . .
75 . . . . . . . . . . . .

100 2.55 0.33 1.13 0.05
150 3.83 0.69 1.70 0.10
200 5.11 1.22 2.27 0.17
250 6.39 1.89 2.84 0.26
300 7.66 2.66 3.40 0.37
350 8.94 3.65 3.97 0.50
400 10.2 4.73 4.54 0.65
450 11.5 6.01 5.11 0.81
500 12.8 7.43 5.67 0.96
Note.—The quantity of a fluid discharged through a pipe or an orifice is
increased by heating the liquid: because heat diminishes the cohesion of
the particles, which exists to a certain degree, in all liquids.
FRICTION LOSS IN POUNDS PRESSURE, FOR EACH 100 FEET OF
LENGTH IN DIFFERENT SIZE CLEAN IRON PIPES DISCHARGING
GIVEN QUANTITIES OF WATER PER MINUTE. ALSO VELOCITY OF
FLOW IN PIPE, IN FEET PER SECOND.
G. A. Ellis, C. E.
Gallons
discharged
per
minute.
6 Inch. 8 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
250 2.84 0.26 1.59 0.07
500 5.67 0.98 3.19 0.25
750 8.51 2.21 4.79 0.53
1,000 11.3 3.88 6.38 0.94
1,250 . . . . . . . . 7.97 1.46
1,500 . . . . . . . . 9.57 2.09
Gallons
discharged
per
minute.
10 Inch. 12 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
250 1.02 0.03 0.71 0.01
500 2.04 0.09 1.42 0.04
750 3.06 0.18 2.13 0.08
1,000 4.08 0.32 2.84 0.13
1,250 5.10 0.49 3.55 0.20
1,500 6.12 0.70 4.26 0.29

1,750 7.15 0.95 4.96 0.38
2,000 8.17 1.23 5.67 0.49
2,250 . . . . . . . . 6.38 0.63
2,500 . . . . . . . . 7.09 0.77
3,000 . . . . . . . . 8.51 1.11
Gallons
discharged
per
minute.
14 Inch. 16 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
500 1.04 0.017 0.80 0.009
1,000 2.08 0.062 1.60 0.036
1,500 3.13 0.135 2.39 0.071
2,000 4.17 0.234 3.19 0.123
2,500 5.21 0.362 3.99 0.188
3,000 6.25 0.515 4.79 0.267
3,500 7.29 0.697 5.59 0.365
4,000 8.34 0.910 6.38 0.472
4,500 . . . . . . . . 7.18 0.593
5,000 . . . . . . . . 7.98 0.730
Gallons
discharged
per
minute.
18 Inch. 20 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
500 0.63 0.005 . . . . . . . .
1,000 1.26 0.020 1.02 0.012
1,500 1.89 0.040 . . . . . . . .
2,000 2.52 0.071 2.04 0.042
2,500 3.15 0.107 . . . . . . . .
3,000 3.78 0.150 3.06 0.091
3,500 4.41 0.204 . . . . . . . .
4,000 5.04 0.263 4.08 0.158
4,500 5.67 0.333 . . . . . . . .
5,000 6.30 0.408 5.11 0.244
6,000 7.56 0.585 6.13 0.348
7,000 . . . . . . . . 7.15 0.472
8,000 . . . . . . . . 8.17 0.612
Gallons
discharged
24 Inch. 30 Inch.
Veloc. in Pipe
per second.
Friction Loss
in pounds.
Veloc. in Pipe
per second.
Friction Loss
in pounds.

per
minute.
1,000 0.72 0.005 0.45 0.002
2,000 1.44 0.020 0.91 0.006
3,000 2.16 0.047 1.36 0.012
4,000 2.88 0.067 1.82 0.022
5,000 4.60 0.102 2.27 0.035
6,000 4.32 0.146 2.72 0.048
7,000 5.04 0.196 3.18 0.065
8,000 5.76 0.255 3.63 0.083
9,000 6.47 0.323 4.08 0.105
10,000 7.19 0.398 4.54 0.131
Note.—The velocity with which a liquid issues from an infinitely small
orifice in the bottom or sides of a vessel that is kept full is equal to that
which a heavy body would acquire by falling from the surface level to the
level of the orifice.
TABLE SHOWING FRICTIONAL HEADS AT GIVEN RATES OF
DISCHARGE IN CLEAN CAST IRON PIPES FOR EACH 1000 FEET OF
LENGTH, condensed from elaborate tables prepared by Messrs. Geo. A.
Ellis and A. H. Howland, Civil Engineers, Boston, Mass.
U. S.
gallons
discharged
per minute.
U. S. gallons
discharged
per
twenty-four
hours.
4-Inch Pipe. 6-Inch Pipe.
Velocity
in
Feet.
Friction
Head.
Velocity
in
Feet.
Friction
Head.
Feet. Pounds Feet. Pounds
25 36000 .64 .59 .26 .28 .11 .05
50 72000 1.28 2.01 .87 .57 .32 .14
100 144000 2.55 7.36 3.19 1.13 1.08 .47
150 216000 3.83 16.05 6.95 1.70 2.28 .99
200 288000 5.11 28.09 12.17 2.27 3.92 1.70
250 360000 6.37 43.47 18.83 2.84 6.00 2.60
300 432000 7.66 62.20 26.94 3.40 8.52 3.69
350 504000 8.94 84.26 36.50 3.97 11.48 4.97
400 576000 10.21 109.68 47.50 4.54 14.89 6.45
450 648000 11.49 138.43 59.96 5.11 18.73 8.11
500 720000 12.77 170.53 73.87 5.67 23.01 9.97
600 864000 15.32 244.76 106.02 6.81 32.89 14.25
700 1008000 17.87 332.36 143.98 7.94 44.54 19.08
800 1152000 . . . . . . . . . 9.08 57.95 25.10

900 1290000 . . . . . . . . . 10.21 73.12 31.67
1000 1440000 . . . . . . . . . 11.35 90.05 38.99
1200 1728000 . . . . . . . . . 13.61 129.20 55.96
1400 2016000 . . . . . . . . . 15.88 175.38 75.97
1600 2304000 . . . . . . . . . 18.15 228.62 99.0
1800 2592000 . . . . . . . . . 20.42 288.90 125.14
2000 2880000 . . . . . . . . . 22.69 356.22 154.30
U. S.
gallons
discharged
per minute.
U. S. gallons
discharged
per
twenty-four
hours.
Velocity
in
Feet.
Friction
Head.
Velocity
in
Feet.
Friction
Head.
25 36000 .16 .04 .02 .10 .02 .01
50 72000 .32 .10 .04 .20 .04 .02
100 144000 .64 .29 .13 .41 .11 .05
150 216000 .96 .60 .26 .61 .22 .10
200 288000 1.28 1.01 .44 .82 .36 .16
250 360000 1.60 1.52 .66 1.02 .54 .23
300 432000 1.91 2.13 .92 1.23 .75 .32
350 504000 2.23 2.85 1.24 1.43 .99 .43
400 576000 2.55 3.68 1.59 1.63 1.27 .55
450 648000 2.87 4.61 2.00 1.83 1.58 .69
500 720000 3.19 5.64 2.44 2.04 1.93 .84
600 864000 3.83 8.03 3.48 2.45 2.72 1.18
700 1008000 4.47 10.83 4.69 2.86 3.66 1.58
800 1152000 5.09 14.05 6.08 3.27 4.73 2.05
900 1290000 5.74 17.68 7.69 3.68 5.93 2.57
1000 1440000 6.38 21.74 9.41 4.08 7.28 3.15
1200 1728000 7.66 31.10 13.47 4.90 10.38 4.50
1400 2016000 8.94 42.13 18.25 5.72 14.02 6.07
1600 2304000 10.21 54.84 23.75 6.53 18.22 7.89
1800 2592000 11.47 69.22 29.98 7.35 22.96 9.95
2000 2880000 12.77 85.27 36.93 8.17 28.25 12.34
2500 3600000 15.96 132.70 57.49 10.21 43.87 19.00
3000 4320000 . . . . . . . . . 12.25 62.92 27.25
U. S.
gallons
discharged
per minute.
U. S. gallons
discharged
per
Velocity
in
Feet.
Friction
Head.
Velocity
in
Feet.
Friction
Head.

twenty-four
hours.
25 36000 .07 .01 . . . . . . . . . . . .
50 72000 .14 .02 .01 .10 .01 . . .
100 144000 .28 .05 .02 .21 .03 .01
150 216000 .43 .10 .04 .31 .05 .02
200 288000 .57 .16 .07 .42 .08 .04
250 360000 .71 .24 .10 .52 .12 .05
300 432000 .85 .32 .14 .63 .16 .07
350 504000 .99 .43 .18 .73 .21 .09
400 576000 1.13 .54 .23 .83 .27 .12
450 648000 1.28 .67 .29 .94 .33 .14
500 720000 1.42 .81 .35 1.04 .40 .17
600 864000 1.70 1.14 .49 1.25 .55 .24
700 1008000 1.98 1.52 .66 1.46 .73 .32
800 1152000 2.27 1.96 .85 1.67 .94 .41
900 1290000 2.55 2.45 1.06 1.88 1.17 .51
1000 1440000 2.84 3.00 1.30 2.08 1.43 .62
1200 1728000 3.40 4.26 1.85 2.50 2.02 .88
1400 2016000 3.97 5.74 2.49 2.91 2.72 1.18
1600 2304000 4.54 7.44 3.22 3.33 3.51 1.52
1800 2592000 5.11 9.36 4.06 3.75 4.41 1.91
2000 2880000 5.67 11.50 5.00 4.17 5.41 2.34
2500 3600000 7.09 17.82 7.72 5.21 8.35 3.62
3000 4320000 8.51 25.51 11.05 6.25 11.93 5.17
3500 5040000 9.93 34.58 14.98 7.29 16.14 6.99
4000 5760000 . . . . . . . . . 8.34 21.00 9.10
4500 6480000 . . . . . . . . . 9.38 26.49 11.47
Note.—There seems to be no form of water pipe so perfect as to make
it fit for use in any and all cases and open to no improvement, but, in the
present state of knowledge, tarred cast iron seems to come the nearest to
this desideratum.
TABLE SHOWING FRICTIONAL HEADS AT GIVEN RATES OF
DISCHARGE IN CLEAN CAST IRON PIPES FOR EACH 1000 FEET OF
LENGTH, condensed from elaborate tables prepared by Messrs. Geo. A.
Ellis and A. H. Howland, Civil Engineers, Boston, Mass.
U. S.
gallons
U. S. gallons
discharged

discharged
per minute.
per
twenty-four
hours.
Velocity
in
Feet.
Friction
Head.
Velocity
in
Feet.
Friction
Head.
Feet. Pounds. Feet. Pounds.
500 720000 .80 .22 .09 .63 .13 .06
1000 1440000 1.60 .76 .34 1.26 .44 .19
1500 2160000 2.39 1.63 .71 1.89 .93 .40
2000 2880000 3.19 2.82 1.22 2.52 1.60 .69
2500 3600000 3.99 4.34 1.88 3.15 2.45 1.06
3000 4320000 4.79 6.19 2.68 3.78 3.48 1.51
3500 5040000 5.59 8.37 3.63 4.41 4.70 2.03
4000 5760000 6.38 10.87 4.71 5.04 6.09 2.64
4500 6480000 7.18 13.70 5.93 5.67 7.67 3.32
5000 7200000 7.98 16.85 7.30 6.30 9.43 4.08
5500 7920000 8.78 20.33 8.71 6.93 11.38 4.92
6000 8640000 . . . . . . . . . 7.57 13.49 5.84
U. S.
gallons
discharged
per minute.
U. S. gallons
discharged
per
twenty-four
hours.
Velocity
in
Feet.
Friction
Head.
Velocity
in
Feet.
Friction
Head.
500 720000 .51 .08 .04 .35 .04 .02
1000 1440000 1.02 .27 .12 .71 .12 .05
1500 2160000 1.53 .56 .24 1.06 .24 .10
2000 2880000 2.04 .96 .42 1.42 .41 .18
2500 3600000 2.55 1.47 .64 1.77 .62 .27
3000 4320000 3.06 2.09 .90 2.13 .87 .38
3500 5040000 3.57 2.81 1.22 2.48 1.16 .50
4000 5760000 4.08 3.64 1.58 2.84 1.50 .65
4500 6480000 4.59 4.58 1.98 3.19 1.88 .82
5000 7200000 5.11 5.62 2.43 3.55 2.31 1.00
5500 7920000 5.62 6.77 2.93 3.90 2.77 1.20
6000 8640000 6.13 8.03 3.48 4.26 3.28 1.42
7000 10080000 7.15 10.86 4.71 4.96 4.43 1.92
8000 11520000 . . . . . . . . . 5.67 5.75 2.49
9000 12960000 . . . . . . . . . 6.38 7.25 3.14
U. S.
gallons
discharged
per minute.
U. S. gallons
discharged
per
Velocity
in
Feet.
Friction
Head.
Velocity
in
Feet.
Friction
Head.

twenty-four
hours.
500 720000 .23 .01 .00 .16 .01 .00
1000 1440000 .45 .04 .02 .32 .02 .01
1500 2160000 .68 .09 .04 .47 .04 .02
2000 2880000 .91 .15 .06 .63 .06 .03
2500 3600000 1.13 .22 .09 .79 .09 .04
3000 4320000 1.36 .30 .13 .95 .13 .06
3500 5040000 1.59 .40 .17 1.10 .17 .07
4000 5760000 1.82 .52 .22 1.26 .22 .09
4500 6480000 2.04 .64 .28 1.42 .27 .12
5000 7200000 2.27 .78 .34 1.58 .33 .14
5500 7920000 2.50 .94 .41 1.73 .39 .17
6000 8640000 2.72 1.11 .48 1.89 .46 .20
7000 10080000 3.18 1.49 .65 2.21 .62 .27
8000 11520000 3.63 1.93 .84 2.52 .80 .35
9000 12960000 4.08 2.43 1.05 2.84 1.00 .43
10000 14400000 4.54 2.98 1.29 3.15 1.23 .53
11000 15840000 5.00 3.59 1.55 3.46 1.47 .64
12000 17280000 5.44 4.25 1.84 3.78 1.74 .75
13000 18720000 5.90 4.97 2.15 4.09 2.03 .88
14000 20160000 6.36 5.75 2.49 4.41 2.35 1.02
15000 21600000 6.80 6.58 2.85 4.73 2.69 1.17
16000 23040000 . . . . . . . . . 5.05 3.46 1.32
17000 24480000 . . . . . . . . . 5.36 3.43 1.49
18000 25920000 . . . . . . . . . 5.68 3.83 1.66
20000 28800000 . . . . . . . . . . . . 6.30 4.71 2.04
Note.—A pressure of one lb. per sq. in. is exerted by a column of water
2.3093 feet or 27.71 inches high at 62° F.; and a pressure of one
atmosphere, or 14.7 lbs. per sq. in. is exerted by a column of water
33.947 feet high, or 10.347 meters at 62° F.
Table.
The pressure of water in pounds per square inch for every ft. in
height to 300 feet and then by intervals to 1,000 feet head. By this
table, from the pounds pressure per square inch, the feet head is
readily obtained and vice versa.
Feet Head. Pressure per sq. in.

1 0.43
2 0.86
3 1.30
4 1.73
5 2.16
6 2.59
7 3.03
8 3.46
9 3.89
10 4.33
11 4.76
12 5.20
13 5.63
14 6.06
15 6.49
16 6.93
17 7.36
18 7.79
19 8.22
20 8.66
21 9.09
22 9.53
23 9.96
24 10.39
25 10.82
26 11.26
27 11.69
28 12.12
29 12.55
30 12.99
31 13.42
32 13.86
33 14.29
34 14.72
35 15.16
36 15.59
37 16.02
38 16.45
39 16.89

40 17.32
41 17.75
42 18.19
43 18.62
44 19.05
45 19.49
46 19.92
47 20.35
48 20.79
49 21.22
50 21.65
51 22.09
52 22.52
53 22.95
54 23.39
55 23.82
56 24.26
57 24.69
58 25.12
59 25.55
60 25.99
61 26.42
62 26.85
63 27.29
64 27.72
65 28.15
66 28.58
67 29.02
68 29.45
69 29.88
70 30.32
71 30.75
72 31.18
73 31.62
74 32.05
75 32.48
76 32.92
77 33.35
78 33.78

79 34.21
80 34.65
81 35.08
82 35.52
83 35.95
84 36.39
85 36.82
86 37.25
87 37.68
88 38.12
89 38.53
90 38.98
91 39.42
92 39.85
93 40.28
94 40.72
95 41.15
96 41.58
97 42.01
98 42.45
99 42.88
100 43.31
101 43.75
102 44.18
103 44.61
104 45.05
105 45.48
106 45.91
107 46.34
108 46.78
109 47.21
110 47.64
111 48.08
112 48.51
113 48.94
114 49.38
115 49.81
116 50.24
117 50.68

118 51.11
119 51.54
120 51.98
121 52.41
122 52.84
123 53.28
124 53.71
125 54.15
126 54.58
127 55.01
128 55.44
129 55.88
130 56.31
131 56.74
132 57.18
133 57.61
134 58.04
135 58.48
136 58.91
137 59.34
138 59.77
139 60.21
140 60.64
141 61.07
142 61.51
143 61.94
144 62.37
145 62.81
146 63.24
147 63.67
148 64.10
149 64.54
150 64.97
151 65.40
152 65.84
153 66.27
154 66.70
155 67.14
156 67.57

157 68.00
158 68.43
159 68.87
160 69.31
161 69.74
162 70.17
163 70.61
164 71.04
165 71.47
166 71.91
167 72.34
168 72.77
169 73.29
170 73.64
171 74.07
172 74.50
173 74.94
174 75.37
175 75.80
176 76.23
177 76.67
178 77.10
179 77.53
180 77.97
181 78.40
182 78.84
183 79.27
184 79.70
185 80.14
186 80.57
187 81.00
188 81.43
189 81.87
190 82.30
191 82.73
192 83.17
193 83.60
194 84.03
195 84.47

196 84.90
197 85.33
198 85.76
199 86.20
200 86.63
201 87.07
202 87.50
203 87.93
204 88.36
205 88.80
206 89.21
207 89.66
208 90.10
209 90.53
210 90.96
211 91.39
212 91.83
213 92.26
214 92.69
215 93.13
216 93.56
217 93.99
218 94.43
219 94.86
220 95.30
221 95.73
222 96.16
223 96.60
224 97.03
225 97.46
226 97.90
227 98.33
228 98.76
229 99.20
230 99.63
231 100.00
232 100.49
233 100.93
234 101.36

235 101.79
236 102.23
237 102.66
238 103.09
239 103.53
240 103.96
241 104.39
242 104.83
243 105.26
244 105.69
245 106.13
246 106.56
247 106.99
248 107.43
249 107.86
250 108.29
251 108.73
252 109.15
253 109.59
254 110.03
255 110.46
256 110.89
257 111.32
258 111.76
259 112.19
260 112.62
261 113.03
262 113.49
263 113.92
264 114.36
265 114.79
266 115.22
267 115.66
268 116.09
269 116.52
270 116.96
271 117.39
272 117.82
273 118.26

274 118.69
275 119.12
276 119.56
277 119.99
278 120.42
279 120.85
280 121.29
281 121.73
282 122.15
283 122.59
284 123.02
285 123.45
286 123.89
287 124.32
288 124.75
289 125.18
290 125.62
291 126.05
292 126.48
293 126.92
294 127.35
295 127.78
296 128.22
297 128.65
298 129.08
299 129.51
300 129.95
310 134.28
320 138.62
330 142.95
340 147.28
350 151.61
360 155.94
370 160.27
380 164.61
390 168.94
400 173.27
500 216.58
600 259.90

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