(Microeconomics) Clear instructions listed. 3 questions 200 word per question. Reading material attached.

1. During the spring when demand for lobster is relatively low, Maine lobster fishermen are able to sell their lobster catches for about $5.50 per pound. During the summer when demand for lobster is much higher, Maine lobster fishermen are able to sell their lobster catches for only about $4.00 per pound. It may seem strange that the market price is higher when demand is low than when demand is high. Use supply and demand analysis to describe why this situation exists. Illustrate with a graph if you are able to do so. (Note: you don’t need to know anything about lobster fishing to answer this question.)

2. Several years ago, health officials became very concerned about contaminated spinach, and recalled most of the produce that was available in supermarkets across the country. Answer one or more of the questions below—illustrate with a graph if you are able to do so.

What would this concern do to the demand curve for spinach?

How would it impact the demand curves for organic spinach or other edible greens?

3. As you know, gasoline prices have dropped significantly over the past year. Explain why this has occurred in terms of supply and demand; illustrate with a graph if possible. What impact will the lower prices have on supply in the long run (now to 2 years out)?

Your posts must contain a minimum of 200 words Per Question. You must include citations to support your responses.

USE ATTACHMENT AS REFERENCE: “PRINCIPLES OF ECONOMICS VERSION 3.0” (Chapter 5,6,7)

C H A P T E R 6
Markets, Maximizers, and
Efficiency
START UP: A DRIVE IN THE COUNTRY
Suppose you decide to take a drive. For purposes of this example, we will assume that you have a car available, that

the weather is pleasant, and that there is an area nearby that will be perfect for your drive.

Your decision to take this drive is a choice. Since economics deals with choices, we can put economics to work

in thinking about it. Economists assume that people make choices that maximize the value of some objective. You

are a consumer; we assume that taking a drive is a choice that maximizes your utility—the satisfaction you obtain

from your use of goods and services and from the activities you pursue.

You certainly plan to enjoy the drive; that enjoyment is the benefit you expect from it. But you will give up

some things as well. Your drive will take some time, time you could have spent doing something else. It will take

some gasoline; what you spend for the gasoline could have been used for something else. The drive will also gen-

erate some wear and tear on your car. That will cost you the price of repair and maintenance and reduced resale

value of your car. The opportunity cost of your drive will thus include the value of the best other use of your time

and the value of the best other use of the funds your drive will require. To maximize utility you will weigh the be-

nefits of the drive against the cost of the drive and maximize the difference between those benefits and costs.

This chapter introduces the method through which maximizing choices can be made. This method applies not

just to your decision to take a drive, but also to Wal-Mart’s decision to hire extra workers and to USX Corporation’s

to produce extra steel. The method we will learn can be applied to the analysis of any choice; we will use it

throughout our investigation of microeconomics.

We will also see how maximizing choices by individuals and by firms can lead to an allocation of resources that

generates the greatest gains possible for the economy as a whole. In this analysis, we will put a new item in our

toolkit, the method through which individuals and firms maximize, together with demand and supply analysis, to

see how the marketplace can guide resources to their best uses.

We will also examine cases in which maximizing choices do not guide resources to their best uses. That possib-

ility is suggested by another aspect of your choice to take a drive. In addition to the costs you will consider, there

will be costs imposed on others. Your drive will pollute the air, so part of the opportunity cost of the drive will be

the value of the slightly cleaner air people in your area might have had. Resources such as the air we breathe will al-

most certainly be misallocated as the result of maximizing choices. We will see just how misallocation of an eco-

nomy’s resources can occur and how this misallocation could be fixed.

economic profit

The difference between total
revenue and total cost.

net benefit

The total benefit of an activity
minus its opportunity cost.

marginal benefit

The amount by which an
additional unit of an activity
increases its total benefit.

marginal cost

The amount by which an
additional unit of an activity
increases its total cost.

marginal decision rule

If the marginal benefit of an
additional unit of an activity
exceeds the marginal cost,
the quantity of the activity
should be increased. If the
marginal benefit is less than
the marginal cost, the
quantity should be reduced.

1. THE LOGIC OF MAXIMIZING BEHAVIOR

L E A R N I N G O B J E C T I V E S

1. Explain the maximization assumption that economists make in explaining the behavior of con-
sumers and firms.

2. Explain and illustrate the concepts of marginal benefit and marginal cost and apply them to
understanding the marginal decision rule.

To say that individuals maximize is to say that they pick some objective and then seek to maximize its
value. A sprinter might want to maximize his or her speed; a politician might want to maximize the
probability that he or she will win the next election. Economists pay special attention to two groups of
maximizers: consumers and firms. We assume that consumers seek to maximize utility and that firms
seek to maximize economic profit, which is the difference between total revenue and total cost. The
costs involved in this concept of economic profit are computed in the economic sense—as the oppor-
tunity costs, or value of the best opportunity forgone.

The assumption of maximizing behavior lies at the heart of economic analysis. As we explore its
implications, however, we must keep in mind the distinction between models and the real world. Our
model assumes that individuals make choices in a way that achieves a maximum value for some clearly
defined objective. In using such a model, economists do not assume that people actually go through the
calculations we will describe. What economists do argue is that people’s behavior is broadly consistent
with such a model. People may not consciously seek to maximize anything, but they behave as though
they do.

1.1 The Analysis of Maximizing Behavior
The activities of consumers and firms have benefits, and they also have opportunity costs. We assume
that given these benefits and costs, consumers and firms will make choices that maximize the net
benefit of each activity—the total benefit of the activity minus its opportunity cost. The specific meas-
ures of benefit and cost vary with the kind of choice being made. In the case of a firm’s choices in pro-
duction, for example, the total benefit of production is the revenue a firm receives from selling the
product; the total cost is the opportunity cost the firm incurs by producing it. The net benefit is thus
total revenue minus total opportunity cost, or economic profit.

Economists maintain that in order to maximize net benefit, consumers and firms evaluate each
activity at the margin—they consider the additional benefit and the additional cost of another unit of
the activity. Should you “supersize” your order at McDonald’s? Will the additional beverage and the
additional french fries be worth the extra cost? Should a firm hire one more worker? Will the benefits
to the firm of hiring this worker be worth the additional cost of hiring him or her?

The marginal benefit is the amount by which an additional unit of an activity increases its total
benefit. It is the amount by which the extra french fries increase your satisfaction, or the extra revenue
the firm expects to bring in by hiring another worker. The marginal cost is the amount by which an
additional unit of an activity increases its total cost. You will pay more to supersize your McDonald’s
order; the firm’s labor costs will rise when it hires another worker.

To determine the quantity of any activity that will maximize its net benefit, we apply the marginal
decision rule: If the marginal benefit of an additional unit of an activity exceeds the marginal cost, the
quantity of the activity should be increased. If the marginal benefit is less than the marginal cost, the
quantity should be reduced. Net benefit is maximized at the point at which marginal benefit equals
marginal cost. The marginal decision rule is at the heart of the economic way of thinking. The rule ba-
sically says this: If the additional benefit of one more unit exceeds the extra cost, do it; if not, do not.
This simple logic gives us a powerful tool for the analysis of choice. Perhaps more than any other rule
in economic analysis, the marginal decision rule typifies the way in which economists analyze prob-
lems. We shall apply it in every chapter that follows in the microeconomics portion of this text.

138 PRINCIPLES OF ECONOMICS VERSION 3.0

constraint

A boundary that limits the
range of choices that can be
made.

Maximizing choices must be made within the parameters imposed by some constraint, which is a
boundary that limits the range of choices that can be made. We assume that a consumer seeks the
greatest satisfaction possible within the limits of his or her income or budget. A firm cannot produce
beyond the limits of its production capacity at a point in time.

The marginal decision rule forms the foundation for the structure economists use to analyze all
choices. At first glance, it may seem that a consumer seeking satisfaction from, say, pizza has little in
common with an entrepreneur seeking profit from the production of custom-designed semiconduct-
ors. But maximizing choices always follow the marginal decision rule—and that rule holds regardless of
what is being maximized or who is doing the maximizing.

To see how the logic of maximizing choices works, we will examine a specific problem. We will
then extend that problem to the general analysis of maximizing choices.

A Problem in Maximization

Suppose a college student, Laurie Phan, faces two midterms tomorrow, one in economics and another
in accounting. She has already decided to spend 5 hours studying for the two examinations. This de-
cision imposes a constraint on the problem. Suppose that Ms. Phan’s goal is to allocate her 5 hours of
study so that she increases her total score for the two exams by as much as possible.

Ms. Phan expects the relationship between the time she spends studying for the economics exam
and the total gain in her score to be as given by the second row of the table in Panel (a) of Figure 6.

We interpret the expected total gain in her score as the total benefit of study. She expects that 1 hour of
study will raise her score by 18 points; 2 hours will raise it by 32 points, and so on. These values are
plotted in Panel (b). Notice that the total benefit curve rises, but by smaller and smaller amounts, as she
studies more and more. The slope of the curve, which in this case tells us the rate at which her expected
score rises with increased study time, falls as we travel up and to the right along the curve.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 139

F I G U R E 6 . 1 The Benefits of Studying Economics

The table in Panel (a) shows the total benefit and marginal benefit of the time Laurie Phan spends studying for her
economics exam. Panel (b) shows the total benefit curve. Panel (c) shows the marginal benefit curve, which is given
by the slope of the total benefit curve in Panel (b).

140 PRINCIPLES OF ECONOMICS VERSION 3.0

F I G U R E 6 . 2 The Marginal Benefits of
Studying Accounting

The marginal benefit Laurie Phan expects from
studying for her accounting exam is shown by
the marginal benefit curve. The first hour of
study increases her expected score by 14
points, the second hour by 10 points, the third
by 6 points, and so on.

Now look at the third row in the table in Panel (a). It tells us the amount by which each additional hour
of study increases her expected score; it gives the marginal benefit of studying for the economics exam.
Marginal benefit equals the amount by which total benefit rises with each additional hour of study. Be-
cause these marginal benefits are given by the changes in total benefits from additional hours of study,
they equal the slope of the total benefit curve. We see this in the relationship between Panels (b) and (c)
of Figure 6.1. The decreasing slope of the total benefit curve in Panel (b) gives us the downward-slop-
ing marginal benefit curve in Panel (c).

The marginal benefit curve tells us what happens when we pass from one point to another on the
total benefit curve, so we have plotted marginal benefits at the midpoints of the hourly intervals in
Panel (c). For example, the total benefit curve in Panel (b) tells us that, when Ms. Phan increases her
time studying for the economics exam from 2 hours to 3 hours, her total benefit rises from 32 points to
42 points. The increase of 10 points is the marginal benefit of increasing study time for the economics
exam from 2 hours to 3 hours. We mark the point for a marginal benefit of 10 points midway between
2 and 3 hours. Because marginal values tell us what happens as we pass from one quantity to the next,
we shall always plot them at the midpoints of intervals of the variable on the horizontal axis.

We can perform the same kind of analysis to obtain the marginal benefit curve for studying for the
accounting exam. Figure 6.2 presents this curve. Like the marginal benefit curve for studying econom-
ics, it slopes downward. Once again, we have plotted marginal values at the midpoints of the intervals.
Increasing study time in accounting from 0 to 1 hour increases Ms. Phan’s expected accounting score
by 14 points.

Ms. Phan’s marginal benefit curves for studying typify a general phenomenon in
economics. Marginal benefit curves for virtually all activities, including the activities of
consumers and of firms, slope downward. Think about your own experience with
studying. On a given day, the first hour spent studying a certain subject probably gener-
ates a greater marginal benefit than the second, and the second hour probably generates
a greater marginal benefit than the third. You may reach a point at which an extra hour
of study is unlikely to yield any benefit at all. Of course, our example of Laurie Phan’s
expected exam scores is a highly stylized one. One could hardly expect a student to
have a precise set of numbers to guide him or her in allocating study time. But it is cer-
tainly the case that students have a rough idea of the likely payoff of study time in
different subjects. If you were faced with exams in two subjects, it is likely that you
would set aside a certain amount of study time, just as Ms. Phan did in our example.
And it is likely that your own experience would serve as a guide in determining how to
allocate that time. Economists do not assume that people have numerical scales in their
heads with which to draw marginal benefit and marginal cost curves. They merely as-
sume that people act as if they did.

The nature of marginal benefits can change with different applications. For a res-
taurant, the marginal benefit of serving one more meal can be defined as the revenue
that meal produces. For a consumer, the marginal benefit of one more slice of pizza can
be considered in terms of the additional satisfaction the pizza will create. But whatever
the nature of the benefit, marginal benefits generally fall as quantities increase.

Ms. Phan’s falling marginal benefit from hours spent studying accounting has spe-
cial significance for our analysis of her choice concerning how many hours to devote to
economics. In our problem, she had decided to devote 5 hours to studying the two sub-
jects. That means that the opportunity cost of an hour spent studying economics equals
the benefit she would have gotten spending that hour studying accounting.

Suppose, for example, that she were to consider spending all 5 hours studying accounting. The
marginal benefit curve for studying for her accounting exam tells us that she expects that the fifth hour
will add nothing to her score. Shifting that hour to economics would cost nothing. We can say that the
marginal cost of the first hour spent studying economics is zero. We obtained this value from the mar-
ginal benefit curve for studying accounting in Figure 6.

Similarly, we can find the marginal cost of the second hour studying economics. That requires giv-
ing up the fourth hour spent on accounting. Figure 6.2 tells us that the marginal benefit of that hour
equals 2—that is the marginal cost of spending the second hour studying economics.

Figure 6.3 shows the marginal cost curve of studying economics. We see that at first, time devoted
to studying economics has a low marginal cost. As time spent studying economics increases, however,
it requires her to give up study time in accounting that she expects will be more and more productive.
The marginal cost curve for studying economics can thus be derived from the marginal benefit curve
for studying accounting. Figure 6.3 also shows the marginal benefit curve for studying economics that
we derived in Panel (b) of Figure 6.1.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 141

F I G U R E 6 . 3 The Marginal Benefits and
Marginal Costs of Studying Economics

The marginal benefit curve from Panel (c) of
Figure 6.1 is shown together with the marginal
costs of studying economics. The marginal
cost curve is derived from the marginal benefit
curve for studying accounting shown in Figure
6.2.

Just as marginal benefit curves generally slope downward, marginal cost curves
generally slope upward, as does the one in Figure 6.3. In the case of allocating time, the
phenomenon of rising marginal cost results from the simple fact that, the more time a
person devotes to one activity, the less time is available for another. And the more one
reduces the second activity, the greater the forgone marginal benefits are likely to be.
That means the marginal cost curve for that first activity rises.

Because we now have marginal benefit and marginal cost curves for studying eco-
nomics, we can apply the marginal decision rule. This rule says that, to maximize the
net benefit of an activity, a decision maker should increase an activity up to the point at
which marginal benefit equals marginal cost. That occurs where the marginal benefit
and marginal cost curves intersect, with 3 hours spent studying economics and 2 hours
spent studying accounting.

Using Marginal Benefit and Marginal Cost Curves to Find Net Benefits

We can use marginal benefit and marginal cost curves to show the total benefit, the
total cost, and the net benefit of an activity. We will see that equating marginal benefit
to marginal cost does, indeed, maximize net benefit. We will also develop another tool
to use in interpreting marginal benefit and cost curves.

Panel (a) of Figure 6.4 shows the marginal benefit curve we derived in Panel (c) of
Figure 6.1. The corresponding point on the marginal benefit curve gives the marginal
benefit of the first hour of study for the economics exam, 18 points. This same value
equals the area of the rectangle bounded by 0 and 1 hour of study and the marginal be-
nefit of 18. Similarly, the marginal benefit of the second hour, 14 points, is shown by
the corresponding point on the marginal benefit curve and by the area of the shaded
rectangle bounded by 1 and 2 hours of study. The total benefit of 2 hours of study
equals the sum of the areas of the first two rectangles, 32 points. We continue this pro-

cedure through the fifth hour of studying economics; the areas for each of the shaded rectangles are
shown in the graph.

F I G U R E 6 . 4 The Benefits and Costs of Studying Economics

Panel (a) shows the marginal benefit curve of Figure 6.1. The total benefit of studying economics at any given
quantity of study time is given approximately by the shaded area below the marginal benefit curve up to that level
of study. Panel (b) shows the marginal cost curve from Figure 6.3. The total cost of studying economics at any given
quantity of study is given approximately by the shaded area below the marginal cost curve up to that level of study.

Two features of the curve in Panel (a) of Figure 6.4 are particularly important. First, note that the sum
of the areas of the five rectangles, 50 points, equals the total benefit of 5 hours of study given in the
table in Panel (a) of Figure 6.1. Second, notice that the shaded areas are approximately equal to the area
under the marginal benefit curve between 0 and 5 hours of study. We can pick any quantity of study
time, and the total benefit of that quantity equals the sum of the shaded rectangles between zero and
that quantity. Thus, the total benefit of 2 hours of study equals 32 points, the sum of the areas of the
first two rectangles.

Now consider the marginal cost curve in Panel (b) of Figure 6.4. The areas of the shaded rectangles
equal the values of marginal cost. The marginal cost of the first hour of study equals zero; there is thus
no rectangle under the curve. The marginal cost of the second hour of study equals 2 points; that is the

142 PRINCIPLES OF ECONOMICS VERSION 3.0

deadweight loss

The loss in net benefits
resulting from a failure to
carry out an activity at the
most efficient level.

area of the rectangle bounded by 1 and 2 hours of study and a marginal cost of 2. The marginal cost of
the third hour of study is 6 points; this is the area of the shaded rectangle bounded by 2 and 3 hours of
study and a marginal cost of 6.

Looking at the rectangles in Panel (b) over the range of 0 to 5 hours of study, we see that the areas
of the five rectangles total 32, the total cost of spending all 5 hours studying economics. And looking at
the rectangles, we see that their area is approximately equal to the area under the marginal cost curve
between 0 and 5 hours of study.

We have seen that the areas of the rectangles drawn with Laurie Phan’s marginal benefit and mar-
ginal cost curves equal the total benefit and total cost of studying economics. We have also seen that
these areas are roughly equal to the areas under the curves themselves. We can make this last statement
much stronger. Suppose, instead of thinking in intervals of whole hours, we think in terms of smaller
intervals, say, of 12 minutes. Then each rectangle would be only one-fifth as wide as the rectangles we
drew in Figure 6.4. Their areas would still equal the total benefit and total cost of study, and the sum of
those areas would be closer to the area under the curves. We have done this for Ms. Phan’s marginal
benefit curve in Figure 6.5; notice that the areas of the rectangles closely approximate the area under
the curve. They still “stick out” from either side of the curve as did the rectangles we drew in Figure 6.4,
but you almost need a magnifying glass to see that. The smaller the interval we choose, the closer the
areas under the marginal benefit and marginal cost curves will be to total benefit and total cost. For
purposes of our model, we can imagine that the intervals are as small as we like. Over a particular range
of quantity, the area under a marginal benefit curve equals the total benefit of that quantity, and the
area under the marginal cost curve equals the total cost of that quantity.

F I G U R E 6 . 5 The Marginal Benefit Curve and Total Benefit

When the increments used to measure time allocated to studying economics are made smaller, in this case 12
minutes instead of whole hours, the area under the marginal benefit curve is closer to the total benefit of studying
that amount of time.

Panel (a) of Figure 6.6 shows marginal benefit and marginal cost curves for studying economics, this
time without numbers. We have the usual downward-sloping marginal benefit curve and upward-slop-
ing marginal cost curve. The marginal decision rule tells us to choose D hours studying economics, the
quantity at which marginal benefit equals marginal cost at point C. We know that the total benefit of
study equals the area under the marginal benefit curve over the range from A to D hours of study, the
area ABCD. Total cost equals the area under the marginal cost curve over the same range, or ACD. The
difference between total benefit and total cost equals the area between marginal benefit and marginal
cost between A and D hours of study; it is the green-shaded triangle ABC. This difference is the net be-
nefit of time spent studying economics. Panel (b) of Figure 6.6 introduces another important concept.
If an activity is carried out at a level less than the efficient level, then net benefits are forgone. The loss

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 143

in net benefits resulting from a failure to carry out an activity at the efficient level is called a
deadweight loss.

F I G U R E 6 . 6 Using Marginal Benefit and Marginal Cost Curves to Determine Net Benefit

In Panel (a) net benefits are given by the difference between total benefits (as measured by the area under the
marginal benefit curve up to any given level of activity) and total costs (as measured by the area under the marginal
cost curve up to any given level of activity). Maximum net benefits are found where the marginal benefit curve
intersects the marginal cost curve at activity level D. Panel (b) shows that if the level of the activity is restricted to
activity level E, net benefits are reduced from the light-green shaded triangle ABC in Panel (a) to the smaller area
ABGF. The forgone net benefits, or deadweight loss, is given by the purple-shaded area FGC. If the activity level is
increased from D to J, as shown in Panel (c), net benefits declined by the deadweight loss measured by the area
CHI.

Now suppose a person increases study time from D to J hours as shown in Panel (c). The area under
the marginal cost curve between D and J gives the total cost of increasing study time; it is DCHJ. The
total benefit of increasing study time equals the area under the marginal benefit curve between D and J;
it is DCĲ. The cost of increasing study time in economics from D hours to J hours exceeds the benefit.
This gives us a deadweight loss of CHI. The net benefit of spending J hours studying economics equals
the net benefit of studying for D hours less the deadweight loss, or ABC minus CHI. Only by studying
up to the point at which marginal benefit equals marginal cost do we achieve the maximum net benefit
shown in Panel (a).

We can apply the marginal decision rule to the problem in Figure 6.6 in another way. In Panel (b),
a person studies economics for E hours. Reading up to the marginal benefit curve, we reach point G.
Reading up to the marginal cost curve, we reach point F. Marginal benefit at G exceeds marginal cost at
F; the marginal decision rule says economics study should be increased, which would take us toward
the intersection of the marginal benefit and marginal cost curves. Spending J hours studying econom-
ics, as shown in Panel (c), is too much. Reading up to the marginal benefit and marginal cost curves, we
see that marginal cost exceeds marginal benefit, suggesting that study time be reduced.

144 PRINCIPLES OF ECONOMICS VERSION 3.0

This completes our introduction to the marginal decision rule and the use of marginal benefit and
marginal cost curves. We will spend the remainder of the chapter applying the model.

Heads Up!

It is easy to make the mistake of assuming that if an activity is carried out up to the point where marginal be-
nefit equals marginal cost, then net benefits must be zero. Remember that following the marginal decision
rule and equating marginal benefits and costs maximizes net benefits. It makes the difference between total
benefits and total cost as large as possible.

K E Y T A K E A W A Y S

< Economists assume that decision makers make choices in the way that maximizes the value of some objective.

< Maximization involves determining the change in total benefit and the change in total cost associated with each unit of an activity. These changes are called marginal benefit and marginal cost, respectively.

< If the marginal benefit of an activity exceeds the marginal cost, the decision maker will gain by increasing the activity.

< If the marginal cost of an activity exceeds the marginal benefit, the decision maker will gain by reducing the activity.

< The area under the marginal benefit curve for an activity gives its total benefit; the area under the marginal cost curve gives the activity’s total cost. Net benefit equals total benefit less total cost.

< The marginal benefit rule tells us that we can maximize the net benefit of any activity by choosing the quantity at which marginal benefit equals marginal cost. At this quantity, the net benefit of the activity is maximized.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 145

T R Y I T !

Suppose Ms. Phan still faces the exams in economics and in accounting, and she still plans to spend a total of
5 hours studying for the two exams. However, she revises her expectations about the degree to which study-
ing economics and accounting will affect her scores on the two exams. She expects studying economics will
add somewhat less to her score, and she expects studying accounting will add more. The result is the table
below of expected total benefits and total costs of hours spent studying economics. Notice that several values
in the table have been omitted. Fill in the missing values in the table. How many hours of study should Ms.
Phan devote to economics to maximize her net benefit?

Hours studying economics 0 1 2 3 4 5

Total benefit 0 14 24 30 32

Total cost 0 2 8 32 50

Net benefit 0 12 12 0 −18

Now compute the marginal benefits and costs of hours devoted to studying economics, completing the table
below.

Draw the marginal benefit and marginal cost curves for studying economics (remember to plot marginal val-
ues at the midpoints of the respective hourly intervals). Do your curves intersect at the “right” number of hours
of study—the number that maximizes the net benefit of studying economics?

Case in Point: Preventing Oil Spills

146 PRINCIPLES OF ECONOMICS VERSION 3.0

Do we spill enough oil in our oceans and waterways? It is a question that perhaps only economists would
ask—and, as economists, we should ask it.

There is, of course, no virtue in an oil spill. It destroys wildlife and fouls shorelines. Cleanup costs can be tre-
mendous. However, preventing oil spills has costs as well: greater enforcement expenditures and higher costs
to shippers of oil and, therefore, higher costs of goods such as gasoline to customers. The only way to prevent
oil spills completely is to stop drilling for and shipping oil. That is a cost few people would accept. But what is
the right balance between environmental protection and the satisfaction of consumer demand for oil?

Vanderbilt University economist Mark Cohen examined the U.S. Coast Guard’s efforts to reduce oil spills when
transporting oil through its enforcement of shipping regulations in coastal waters and on rivers. He focused on
the costs and benefits resulting from the Coast Guard’s enforcement efforts in 1981. On the basis of the fre-
quency of oil spills before the Coast Guard began its enforcement, Mr. Cohen estimated that the Coast Guard
prevented 1,159,352 gallons of oil from being spilled in 1981.

Given that there was a total of 824,921 gallons of oil actually spilled in 1981, should the Coast Guard have at-
tempted to prevent even more spillage? Mr. Cohen estimated that the marginal benefit of preventing one
more gallon from being spilled was $7.27 ($3.42 in cleanup costs, $3 less in environmental damage, and $0.85
worth of oil saved). The marginal cost of preventing one more gallon from being spilled was $5.50. Mr. Cohen
suggests that because the marginal benefit of more vigorous enforcement exceeded the marginal cost, more
vigorous Coast Guard efforts would have been justified.

More vigorous efforts have, indeed, been pursued. In 1989, the Exxon oil tanker Exxon Valdez ran aground,
spilling 10.8 million gallons of oil off the coast of Alaska. The spill damaged the shoreline of a national forest,
four national wildlife refuges, three national parks, five state parks, four critical habitat areas, and a state game
refuge. Exxon was ordered to pay $900 million in damages; a federal jury found Exxon and the captain guilty of
criminal negligence and imposed an additional $5 billion in punitive damages. In 2008, The Supreme Court re-
duced the assessment of punitive damages to $507 million, with the majority arguing that the original figure
was too high in comparison to the compensatory damages for a case in which the actions of the defendant,
Exxon, were “reprehensible” but not intentional.

Perhaps the most important impact of the Exxon Valdez disaster was the passage of the Oil Pollution Act of
1990. It increased shipper liability from $14 million to $100 million. It also required double-hulled tankers for
shipping oil.

The European Union (EU) has also strengthened its standards for oil tankers. The 2002 breakup of the oil tanker
Prestige off the coast of Spain resulted in the spillage of 3.2 million gallons of oil. The EU had planned to ban
single-hulled tankers, phasing in the ban between 2003 and 2015. The sinking of the Prestige led the EU to
move up that deadline.

Tanker spill crises have led both the United States and the European Union to tighten up their regulations of
oil tankers. The result has been a reduction in the quantity of oil spilled, which was precisely what economic
research had concluded was needed. Whereas the total quantity of oil spilled from tankers in the 1970s was
over 3 million tons, for the decade of the 2000s the total was 212,000 tons—a decline of over 90%—even as
the amount of oil shipped rose dramatically.

The year 2010 saw another kind of major oil spill resulting from offshore drilling. The explosion of the Deepwa-
ter Horizon oil rig in the Gulf of Mexico on April 20, 2010, in which 11 workers were killed and 17 injured, led to
a spill of 4.1 million barrels into the Gulf over a 3-month period. This spill was about 40% larger than the
second largest offshore drilling spill off the U.S. coast and 19 times bigger than the Exxon Valdez spill. So far,
no major legislation affecting oil drilling has passed, though, after a five-month drilling moratorium, the U.S.
Department of the Interior has made changes to its enforcement practices.

Whether or not new legislation concerning offshore oil drilling is needed and how it should be constructed is
being hotly debated. A preliminary study by Alan Krupnick, Sarah Campbell, Mark A. Cohen, and Ian W. H. Parry
for the organization Resources for the Future estimated the annual benefits of preventing a catastrophic spill
to be between $16.1 billion and $29.5 billion. The annual costs of a ban they estimate to be about $65 billion,
from which they conclude that cost-benefit analysis does not justify a ban. On the other hand, they argue that
regulation that would increase the costs of extraction by 10% or $11 billion annually would pass a cost-benefit
analysis test and that regulation that raises extraction cost by 20% or $22 billion would pass the test at the up-
per end of the benefits estimate only. It should be noted that the Oil Pollution Act of 1990 was passed about a
year and a half after the Exxon Valdez incident.

Sources: Based on Mark A. Cohen, “The Costs and Benefits of Oil Spill Prevention and Enforcement,” Journal of Environmental Economics and
Management 13:2(June 1986): 167–188; International Tanker Owners Pollution Federation Limited, Oil Tanker Spill Statistics 2010, available at
http://www.itopf.com;Alan Krupnick, Sarah Campbell, Mark A. Cohen, and Ian W. H. Parry, “Understanding the Costs and Benefits of Deepwater Oil
Drilling Regulation,”Discussion Paper Resources for the Future RFF DP 10–62 (January 2011); Rick S. Kurtz, “Coastal Oil Pollution: Spills, Crisis, and Policy
Change,” Review ofPolicy Research, 21:2 (March 2004): 201–219; David S. Savage, “Justices Slash Exxon Valdez Verdict,” Los Angeles Times, June 26,
2008, p. A1; GerardShields, “Gulf Oil Disaster: One Year Later,” The Advocate (Baton Rouge, Louisiana), April 20, 2011, p. 1; and Edwin Unsworth, “Europe
Gets Tougher onAging Oil Tankers,” Business Insurance, 36:48 (December 2, 2002): 33–34.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 147

efficient

The allocation of resources
when the net benefits of all
economic activities are
maximized.

A N S W E R T O T R Y I T ! P R O B L E M

Here are the completed data table and the table showing total and marginal benefit and cost.

Ms. Phan maximizes her net benefit by reducing her time studying economics to 2 hours. The change in her
expectations reduced the benefit and increased the cost of studying economics. The completed graph of
marginal benefit and marginal cost is at the far left. Notice that answering the question using the marginal de-
cision rule gives the same answer.

2. MAXIMIZING IN THE MARKETPLACE

L E A R N I N G O B J E C T I V E S

1. Explain what is meant by an efficient allocation of resources in an economy and describe the
market conditions that must exist to achieve this goal.

2. Define consumer and producer surplus.
3. Discuss the relationship between efficiency and equity.

In perhaps the most influential book in economics ever written, An Inquiry into the Nature and Causes
of the Wealth of Nations, published in 1776, Adam Smith argued that the pursuit of self-interest in a
marketplace would promote the general interest. He said resources would be guided, as if by an
“invisible hand,” to their best uses. That invisible hand was the

marketplace.

Smith’s idea was radical for its time; he saw that the seemingly haphazard workings of the market-
place could promote the common good. In this section, we will use the tools we have developed thus
far to see the power of Smith’s invisible hand. Efforts by individuals to maximize their own net benefit
can maximize net benefit for the economy as a whole.

When the net benefits of all economic activities are maximized, economists say the allocation of
resources is efficient. This concept of efficiency is broader than the notion of efficient production that
we encountered when discussing the production possibilities curve. There, we saw that the economy’s
factors of production would be efficient in production if they were allocated according to the principle
of comparative advantage. That meant producing as much as possible with the factors of production
available. The concept of an efficient allocation of resources incorporates production, as in that discus-
sion, but it includes efficiency in the consumption of goods and services as well.

148 PRINCIPLES OF ECONOMICS VERSION 3.0

property rights

A set of rules that specify the
ways in which an owner can
use a resource.

exclusive property right

A property right that allows
its owner to prevent others
from using the resource.

transferable property right

A property right that allows
the owner of a resource to
sell or lease it to someone
else.

efficiency condition

A situation that requires a
competitive market with
well-defined and transferable
property rights.

2.1 Achieving Efficiency
Imagine yourself arriving at the store to purchase some food. In your choice, you will weigh your own
benefits and costs to maximize your net benefit. The farmers, the distributors, and the grocer have
sought to maximize their net benefits as well. How can we expect that all those efforts will maximize
net benefits for the economy as a whole? How can we expect the marketplace to achieve an efficient al-
location of food, or of anything else?

One condition that must be met if the market’s allocation is to be efficient is that the marketplace
must be competitive or function as if it were. We will have a great deal more to say about competitive
markets versus less competitive ones in subsequent chapters. For now, we can simply note that a com-
petitive market is one with many buyers and sellers in each market and in which entry and exit are
fairly easy. No one controls the price; the forces of demand and supply determine price.

The second condition that must hold if the market is to achieve an efficient allocation concerns
property rights. We turn to that topic in the next section.

The Role of Property Rights

A smoothly functioning market requires that producers possess property rights to the goods and ser-
vices they produce and that consumers possess property rights to the goods and services they buy.
Property rights are a set of rules that specify the ways in which an owner can use a resource.

Consider the tomato market. Farmers who grow tomatoes have clearly defined rights to their land
and to the tomatoes they produce and sell. Distributors who purchase tomatoes from farmers and sell
them to grocers have clear rights to the tomatoes until they sell them to grocers. The grocers who pur-
chase the tomatoes retain rights to them until they sell them to consumers. When you buy a tomato,
you have the exclusive right to its use.

A system of property rights forms the basis for all market exchange. Before exchange can begin,
there must be a clear specification of who owns what. The system of property rights must also show
what purchasers are acquiring when they buy rights to particular resources. Because property rights
must exist if exchange is to occur, and because exchange is the process through which economic effi-
ciency is achieved, a system of property rights is essential to the efficient allocation of resources.

Imagine what would happen in the market for tomatoes if property rights were not clearly defined.
Suppose, for example, that grocers could not legally prevent someone from simply grabbing some to-
matoes and leaving without paying for them. If that were the case, grocers would not be likely to offer
tomatoes for sale. If it were the case for all grocery items, there would not be grocery stores at all.

Although property rights vary for different resources, two characteristics are required if the mar-
ketplace is to achieve an efficient allocation of resources:

1. Property rights must be exclusive. An exclusive property right is one that allows its owner to
prevent others from using the resource. The owner of a house, for example, has the right to
exclude others from the use of the house. If this right did not exist, ownership would have little
value; it is not likely that the property could be exchanged in a market. And the inability to sell
property would limit the incentive of owners to maintain it.

2. Property rights must be transferable. A transferable property right is one that allows the
owner of a resource to sell or lease it to someone else. In the absence of transferability, no
exchange could occur.

Markets and the Efficiency Condition

A competitive market with well-defined and transferable property rights satisfies the efficiency
condition. If met, we can assume that the market’s allocation of resources will be efficient.

Consider again your purchase of tomatoes. Suppose the curves of demand and supply for tomatoes
are those given in Figure 6.7; the equilibrium price equals $1.50 per pound. Suppose further that the
market satisfies the efficiency condition. With that assumption, we can relate the model of demand and
supply to our analysis of marginal benefits and costs.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 149

F I G U R E 6 . 7 Demand and Supply and
the Efficiency Condition

In a competitive market with exclusive and
transferable property rights, such as the market
for tomatoes, the efficiency condition is met.
Buyers and sellers are faced with all of the
relevant benefits and costs, and the
equilibrium price equals the marginal cost to
society of producing that good, here $2.50 per
pound. We can interpret the market demand
and supply curve as marginal benefit and
marginal cost curves, respectively.

consumer surplus

The amount by which the
total benefits to consumers
from consuming a good
exceed their total
expenditures on the good.

The demand curve tells us that the last pound of tomatoes was worth $1.50; we can
think of that as the marginal benefit of the last pound of tomatoes since that is how
much consumers were willing to pay. We can say that about any price on a market de-
mand curve; a demand curve can be considered as a marginal benefit curve. Similarly,
the supply curve can be considered the marginal cost curve. In the case of the tomato
market, for example, the price tells us that the marginal cost of producing the last
pound of tomatoes is $1.50. This marginal cost is considered in the economic
sense—other goods and services worth $1.50 were not produced in order to make an
additional pound of tomatoes available.

On what basis can we presume that the price of a pound of tomatoes equals its
marginal cost? The answer lies in our marginal decision rule. Profit-maximizing tomato
producers will produce more tomatoes as long as their marginal benefit exceeds their
marginal cost. What is the marginal benefit to a producer of an extra pound of toma-
toes? It is the price that the producer will receive. What is the marginal cost? It is the
value that must be given up to produce an extra pound of tomatoes.

Producers maximize profit by expanding their production up to the point at which
their marginal cost equals their marginal benefit, which is the market price. The price
of $1.50 thus reflects the marginal cost to society of making an additional pound of to-
matoes available.

At the equilibrium price and output of tomatoes, then, the marginal benefit of to-
matoes to consumers, as reflected by the price they are willing to pay, equals the mar-
ginal cost of producing tomatoes. Where marginal benefit equals marginal cost, net be-
nefit is maximized. The equilibrium quantity of tomatoes, as determined by demand
and supply, is efficient.

2.2 Producer and Consumer Surplus
Think about the last thing you purchased. You bought it because you expected that its benefits would
exceed its opportunity cost; you expected that the purchase would make you better off. The seller sold it
to you because he or she expected that the money you paid would be worth more than the value of
keeping the item. The seller expected to be better off as a result of the sale. Exchanges in the market-
place have a remarkable property: Both buyers and sellers expect to emerge from the transaction better
off.

Panel (a) of Figure 6.8 shows a market demand curve for a particular good. Suppose the price
equals OB and the quantity equals OE. The area under the demand curve over the range of quantities
from the origin at O to the quantity at E equals the total benefit of consuming OE units of the good. It
is the area OCDE. Consumers pay for this benefit; their total expenditures equal the rectangle OBDE,
which is the dark shaded region in the graph. Because the total benefits exceed total expenditures, there
is a consumer surplus given by the triangle BCD. Consumer surplus is the amount by which the total
benefits to consumers from consuming a good exceed their total expenditures on the good.

150 PRINCIPLES OF ECONOMICS VERSION 3.0

producer surplus

The difference between the
total revenue received by
sellers and their total cost.

F I G U R E 6 . 8 Consumer and Producer Surplus

Consumer surplus [Panel (a)] measures the difference between total benefit of consuming a given quantity of
output and the total expenditures consumers pay to obtain that quantity. Here, total benefits are given by the
shaded area OCDE; total expenditures are given by the rectangle OBDE. The difference, shown by the triangle BCD,
is consumer surplus.
Producer surplus [Panel b)] measures the difference between total revenue received by firms at a given quantity of
output and the total cost of producing it. Here, total revenue is given by the rectangle OBDE, and total costs are
given by the area OADE. The difference, shown by the triangle ABD is producer surplus.

Now consider the sellers’ side of transactions. Panel (b) of Figure 6.8 shows a market supply curve; re-
call that it gives us marginal cost. Suppose the market price equals OB and quantity supplied is OE;
those are the same values we had in Panel (a). The price times the quantity equals the total revenue re-
ceived by sellers. It is shown as the shaded rectangle OBDE. The total revenue received by sellers equals
total expenditures by consumers.

The total cost to sellers is the area under the marginal cost curve; it is the area OADE. That cost is
less than revenue. The difference between the total revenue received by sellers and their total cost is
called producer surplus. In Panel (b) it is the light-shaded triangle ABD.

F I G U R E 6 . 9 Net Benefit: The Sum of Consumer and Producer Surplus

The sum of consumer surplus and producer surplus measures the net benefit to society of any level of economic
activity. Net benefit is maximized when production and consumption are carried out at the level where the
demand and supply curves intersect. Here, the net benefit to society equals the area ACD. It is the sum of consumer
surplus, BCD, and producer surplus, ABD.

We put the demand and supply curves of Figure 6.8 Panels (a) and (b) together in Figure 6.9. The in-
tersection of the two curves determines the equilibrium price, OB, and the equilibrium quantity, OE.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 151

The shaded regions give us consumer and producer surplus. The sum of these two surpluses is net be-
nefit. This net benefit is maximized where the demand and supply curves intersect.

2.3 Efficiency and Equity
Consumer demands are affected by incomes. Demand, after all, reflects ability as well as willingness to
pay for goods and services. The market will be more responsive to the preferences of people with high
incomes than to those of people with low incomes.

In a market that satisfies the efficiency condition, an efficient allocation of resources will emerge
from any particular distribution of income. Different income distributions will result in different, but
still efficient, outcomes. For example, if 1% of the population controls virtually all the income, then the
market will efficiently allocate virtually all its production to those same people.

What is a fair, or equitable, distribution of income? What is an unfair distribution? Should every-
one have the same income? Is the current distribution fair? Should the rich have less and the poor have
more? Should the middle class have more? Equity is very much in the mind of the observer. What may
seem equitable to one person may seem inequitable to another. There is, however, no test we can apply
to determine whether the distribution of income is or is not equitable. That question requires a norm-
ative judgment.

Determining whether the allocation of resources is or is not efficient is one problem. Determining
whether the distribution of income is fair is another. The governments of all nations act in some way to
redistribute income. That fact suggests that people generally have concluded that leaving the distribu-
tion of income solely to the market would not be fair and that some redistribution is desirable. This
may take the form of higher taxes for people with higher incomes than for those with lower incomes. It
may take the form of special programs, such as welfare programs, for low-income people.

Whatever distribution society chooses, an efficient allocation of resources is still preferred to an in-
efficient one. Because an efficient allocation maximizes net benefits, the gain in net benefits could be
distributed in a way that leaves all people better off than they would be at any inefficient allocation. If
an efficient allocation of resources seems unfair, it must be because the distribution of income is unfair.

K E Y T A K E A W A Y S

< In a competitive system in which the interaction of demand and supply determine prices, the corresponding demand and supply curves can be considered marginal benefit and marginal cost curves, respectively.

< An efficient allocation of resources is one that maximizes the net benefit of each activity. We expect it to be achieved in markets that satisfy the efficiency condition, which requires a competitive market and well- defined, transferable property rights.

< Consumer surplus is the amount by which the total benefit to consumers from some activity exceeds their total expenditures for it.

< Producer surplus is the amount by which the total revenues of producers exceed their total costs.

< An inequitable allocation of resources implies that the distribution of income and wealth is inequitable. Judgments about equity are normative judgments.

152 PRINCIPLES OF ECONOMICS VERSION 3.0

T R Y I T !

Draw hypothetical demand and supply curves for a typical product, say coffee. Now show the areas of con-
sumer and producer surplus. Under what circumstances is the market likely to be efficient?

Case in Point: Bah Humbug!

Source: © Thinkstock

Professor Joel Waldfogel, in his book Scroogenomics, derides Christmas gift giving as only an economist would.
Based on repeated surveys from students in his classes (which asked them to compare value and price of gifts
they received and of items they bought for themselves) and estimates of annual Christmas spending in the
United States of $66 billion in 2007, he concludes that $12 billion, roughly 18% of the total, constituted dead-
weight loss. And that doesn’t count the 2.8 billion hours collectively spent shopping for the stuff.

The crux of his argument is that when you buy something for yourself, the price you pay is at least equal to the
value of the satisfaction you get from the item. For some items, the consumer surplus (the difference between
the value to you of the item and the price you pay), may be small or even zero, but for other items it may be
large. One example he gives where consumer surplus may be huge is the purchase of a $20 antibiotic for your
child with an ear infection who has been screaming all night. But what are the chances that consumer surplus
will be positive for an item you receive as a gift? “Relative to how much satisfaction their [gift givers] expendit-
ures could have given us, their choices destroy value. Take that, Santa,” writes Professor Waldfogel.

Doesn’t sentimental value make up for the differences between the price of an item you receive, say a $50
sweater, and the value you attach to it, say $25? If you attach $50 in sentimental value to the sweater, then it is
really worth $75 to you, which is more than the $50 price paid by the gift giver. The problem with this line of
argument is that if the gift giver had chosen a sweater for you that you actually liked—one that you valued at
least at the purchase price of $50—its total value to you would then have been $100. Compared to giving you
a sweater you actually liked, giving you the one you did not much care for destroyed value.

The surveys have also questioned the relationship of the gift giver to the gift recipient to see if giver know-
ledge of the recipient leads to more gift giving efficiency. The results are as one might expect. Gifts from aunts,
uncles, and grandparents generated between 75 and 80 cents of satisfaction per dollar spent. Friends gener-
ated 91 cents, parents 97 cents, siblings 99 cents, and significant others 102 cents of satisfaction per dollar
spent. In general, frequency of contact between giver and receiver increases the yield of a gift.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 153

While acknowledging that there are some situations in which gifts may create value for recipients beyond
what they could have purchased for themselves, such as when a recipient receives a CD of a band he or she
was unfamiliar with but turns out to love, overall Waldfogel’s estimates reveal a great loss for society. What to
do about it? Giving cash would work but there seems to be a stigma associated with doing so, especially for
certain kinds of relationships between givers and receivers. Gift registries solve the problem for newlyweds
and could do so for Christmas gifts if that idea caught on. Since outside of your immediate circle you are un-
likely to select a gift that does not destroy value, he suggests giving cash, if that is not too uncomfortable, or
gift cards, possibly ones for charitable causes. Of course, people often forget to use their gift cards. When that
happens, the benefit is not lost but rather goes to the retailer, which was not likely the intention of the gift
giver. He thus suggests that retailers team up with charities so that any amount not redeemed after a certain
time period goes to a charity stated on the gift card.

Parodying Karl Marx’s Communist Manifesto, he concludes, “A specter has been haunting the rich economies of
the West, and that specter is wasteful gift giving. Gift givers of the world unite. You have nothing to lose but
deadweight loss and a world of satisfaction to gain.”

Source: Based on Joel Waldfogel, Scroogenomics: Why You Shouldn’t Buy Presents for the Holidays (Princeton: Princeton University Press, 2009).

A N S W E R T O T R Y I T ! P R O B L E M

On the assumption that the coffee market is competitive and that it is characterized by well-defined exclusive
and transferable property rights, the coffee market meets the efficiency condition. That means that the alloca-
tion of resources shown at the equilibrium will be the one that maximizes the net benefit of all activities. The
net benefit is shared by coffee consumers (as measured by consumer surplus) and coffee producers (as meas-
ured by producer surplus).

154 PRINCIPLES OF ECONOMICS VERSION 3.0

market failure

The failure of private
decisions in the marketplace
to achieve an efficient
allocation of scarce resources.

public good

A good for which the cost of
exclusion is prohibitive and
for which the marginal cost
of an additional user is zero.

private good

A good for which exclusion is
possible and for which the
marginal cost of another user
is positive.

3. MARKET FAILURE

L E A R N I N G O B J E C T I V E S

1. Explain what is meant by market failure and the conditions that may lead to it.
2. Distinguish between private goods and public goods and relate them to the free rider problem

and the role of government.
3. Explain the concepts of external costs and benefits and the role of government intervention

when they are present.
4. Explain why a common property resource is unlikely to be allocated efficiently in the

marketplace.

Private decisions in the marketplace may not be consistent with the maximization of the net benefit of
a particular activity. The failure of private decisions in the marketplace to achieve an efficient allocation
of scarce resources is called market failure. Markets will not generate an efficient allocation of re-
sources if they are not competitive or if property rights are not well defined and fully transferable. Eith-
er condition will mean that decision makers are not faced with the marginal benefits and costs of their
choices.

Think about the drive that we had you take at the beginning of this chapter. You faced some, but
not all, of the opportunity costs involved in that choice. In particular, your choice to go for a drive
would increase air pollution and might increase traffic congestion. That means that, in weighing the
marginal benefits and marginal costs of going for a drive, not all of the costs would be counted. As a
result, the net benefit of the allocation of resources such as the air might not be maximized.

3.1 Noncompetitive Markets
The model of demand and supply assumes that markets are competitive. No one in these markets has
any power over the equilibrium price; each consumer and producer takes the market price as given and
responds to it. Under such conditions, price is determined by the intersection of demand and supply.

In some markets, however, individual buyers or sellers are powerful enough to influence the mar-
ket price. In subsequent chapters, we will study cases in which producers or consumers are in a posi-
tion to affect the prices they charge or must pay, respectively. We shall find that when individual firms
or groups of firms have market power, which is the ability to change the market price, the price will be
distorted—it will not equal marginal cost.

3.2 Public Goods
Some goods are unlikely to be produced and exchanged in a market because of special characteristics of
the goods themselves. The benefits of these goods are such that exclusion is not feasible. Once they are
produced, anyone can enjoy them; there is no practical way to exclude people who have not paid for
them from consuming them. Furthermore, the marginal cost of adding one more consumer is zero. A
good for which the cost of exclusion is prohibitive and for which the marginal cost of an additional
user is zero is a public good. A good for which exclusion is possible and for which the marginal cost
of another user is positive is a private good.

National defense is a public good. Once defense is provided, it is not possible to exclude people
who have not paid for it from its consumption. Further, the cost of an additional user is zero—an army
does not cost any more if there is one more person to be protected. Other examples of public goods in-
clude law enforcement, fire protection, and efforts to preserve species threatened with extinction.

Free Riders

Suppose a private firm, Terror Alert, Inc., develops a completely reliable system to identify and inter-
cept 98% of any would-be terrorists that might attempt to enter the United States from anywhere in the
world. This service is a public good. Once it is provided, no one can be excluded from the system’s pro-
tection on grounds that he or she has not paid for it, and the cost of adding one more person to the
group protected is zero. Suppose that the system, by eliminating a potential threat to U.S. security,
makes the average person in the United States better off; the benefit to each household from the added
security is worth $40 per month (about the same as an earthquake insurance premium). There are
roughly 113 million households in the United States, so the total benefit of the system is $4.5 billion per

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 155

free riders

People or firms that consume
a public good without paying
for it.

F I G U R E 6 . 1 0 Public Goods and Market
Failure

Because free riders will prevent firms from
being able to require consumers to pay for the
benefits received from consuming a public
good, output will be less than the efficient
level. In the case shown here, private
donations achieved a level of the public good
of Q1 per period. The efficient level is Q*. The
deadweight loss is shown by the triangle ABC.

month. Assume that it will cost Terror Alert, Inc., $1 billion per month to operate. The benefits of the
system far outweigh the cost.

Suppose that Terror Alert installs its system and sends a bill to each household for $20 for the first
month of service—an amount equal to half of each household’s benefit. If each household pays its bill,
Terror Alert will enjoy a tidy profit; it will receive revenues of more than $2.25 billion per month.

But will each household pay? Once the system is in place, each household would recognize that it
will benefit from the security provided by Terror Alert whether it pays its bill or not. Although some
households will voluntarily pay their bills, it seems unlikely that very many will. Recognizing the op-
portunity to consume the good without paying for it, most would be free riders. Free riders are people
or firms that consume a public good without paying for it. Even though the total benefit of the system
is $4.5 billion, Terror Alert will not be faced by the marketplace with a signal that suggests that the sys-
tem is worthwhile. It is unlikely that it will recover its cost of $1 billion per month. Terror Alert is not
likely to get off the ground.

The bill for $20 from Terror Alert sends the wrong signal, too. An efficient market requires a price
equal to marginal cost. But the marginal cost of protecting one more household is zero; adding one
more household adds nothing to the cost of the system. A household that decides not to pay Terror
Alert anything for its service is paying a price equal to its marginal cost. But doing that, being a free
rider, is precisely what prevents Terror Alert from operating.

Because no household can be excluded and because the cost of an extra household is zero, the effi-
ciency condition will not be met in a private market. What is true of Terror Alert, Inc., is true of public
goods in general: they simply do not lend themselves to private market provision.

Public Goods and the Government

Because many individuals who benefit from public goods will not pay for them, private firms will pro-
duce a smaller quantity of public goods than is efficient, if they produce them at all. In such cases, it
may be desirable for government agencies to step in. Government can supply a greater quantity of the
good by direct provision, by purchasing the public good from a private agency, or by subsidizing con-
sumption. In any case, the cost is financed through taxation and thus avoids the free-rider problem.

Most public goods are provided directly by government agencies. Governments produce national
defense and law enforcement, for example. Private firms under contract with government agencies pro-
duce some public goods. Park maintenance and fire services are public goods that are sometimes pro-
duced by private firms. In other cases, the government promotes the private consumption or produc-
tion of public goods by subsidizing them. Private charitable contributions often support activities that
are public goods; federal and state governments subsidize these by allowing taxpayers to reduce their
tax payments by a fraction of the amount they contribute.

While the market will produce some level of public goods in the absence of gov-
ernment intervention, we do not expect that it will produce the quantity that maxim-
izes net benefit. Figure 6.10 illustrates the problem. Suppose that provision of a public
good such as national defense is left entirely to private firms. It is likely that some de-
fense services would be produced; suppose that equals Q1 units per period. This level of
national defense might be achieved through individual contributions. But it is very un-
likely that contributions would achieve the correct level of defense services. The effi-
cient quantity occurs where the demand, or marginal benefit, curve intersects the mar-
ginal cost curve, at Q*. The deadweight loss is the shaded area ABC; we can think of
this as the net benefit of government intervention to increase the production of nation-
al defense from Q1 up to the efficient quantity, Q*.

Heads Up!

Note that the definitions of public and private goods are based on characteristics of the goods
themselves, not on whether they are provided by the public or the private sector. Postal ser-
vices are a private good provided by the public sector. The fact that these goods are produced
by a government agency does not make them a public good.

156 PRINCIPLES OF ECONOMICS VERSION 3.0

external cost

A cost imposed on others
outside of any market
exchange.

external benefit

An action taken by a person
or firm that creates benefits
for others in the absence of
any market agreement.

F I G U R E 6 . 1 1 External Costs

When firms in an industry generate external
costs, the supply curve S1 reflects only their
private marginal costs, MCP. Forcing firms to
pay the external costs they impose shifts the
supply curve to S2, which reflects the full
marginal cost of the firms’ production, MCe.
Output is reduced and price goes up. The
deadweight loss that occurs when firms are
not faced with the full costs of their decisions
is shown by the shaded area in the graph.

3.3 External Costs and Benefits
Suppose that in the course of production, the firms in a particular industry generate air pollution.
These firms thus impose costs on others, but they do so outside the context of any market ex-
change—no agreement has been made between the firms and the people affected by the pollution. The
firms thus will not be faced with the costs of their action. A cost imposed on others outside of any mar-
ket exchange is an external cost.

We saw an example of an external cost in our imaginary decision to go for a drive. Here is another:
violence on television, in the movies, and in video games. Many critics argue that the violence that per-
vades these media fosters greater violence in the real world. By the time a child who spends the average
amount of time watching television finishes elementary school, he or she will have seen 100,000 acts of
violence, including 8,000 murders, according to the American Psychological Association. Thousands of
studies of the relationship between violence in the media and behavior have concluded that there is a
link between watching violence and violent behaviors. Video games are a major element of the prob-
lem, as young children now spend hours each week playing them. Fifty percent of fourth-grade graders
say that their favorite video games are the “first person shooter” type.[1]

Any tendency of increased violence resulting from increased violence in the media constitutes an
external cost of such media. The American Academy of Pediatrics reported in 2001 that homicides
were the fourth leading cause of death among children between the ages of 10 and 14 and the second
leading cause of death for people aged 15 to 24 and has recommended a reduction in exposure to me-
dia violence.[2] It seems reasonable to assume that at least some of these acts of violence can be con-
sidered an external cost of violence in the media.

An action taken by a person or firm can also create benefits for others, again in the absence of any
market agreement; such a benefit is called an external benefit. A firm that builds a beautiful building
generates benefits to everyone who admires it; such benefits are external.

External Costs and Efficiency

The case of the polluting firms is illustrated in Figure 6.11. The industry supply curve S1
reflects private marginal costs, MCp. The market price is Pp for a quantity Qp. This is
the solution that would occur if firms generating external costs were not forced to pay
those costs. If the external costs generated by the pollution were added, the new supply
curve S2 would reflect higher marginal costs, MCe. Faced with those costs, the market
would generate a lower equilibrium quantity, Qe. That quantity would command a
higher price, Pe. The failure to confront producers with the cost of their pollution
means that consumers do not pay the full cost of the good they are purchasing. The
level of output and the level of pollution are therefore higher than would be economic-
ally efficient. If a way could be found to confront producers with the full cost of their
choices, then consumers would be faced with a higher cost as well. Figure 6.11 shows
that consumption would be reduced to the efficient level, Qe, at which demand and the
full marginal cost curve (MCe) intersect. The deadweight loss generated by allowing the
external cost to be generated with an output of Qp is given as the shaded region in the
graph.

External Costs and Government Intervention

If an activity generates external costs, the decision makers generating the activity will
not be faced with its full costs. Agents who impose these costs will carry out their activ-
ities beyond the efficient level; those who consume them, facing too low a price, will
consume too much. As a result, producers and consumers will carry out an excessive
quantity of the activity. In such cases, government may try to intervene to reduce the
level of the activity toward the efficient quantity. In the case shown in Figure 6.11, for
example, firms generating an external cost have a supply curve S1 that reflects their
private marginal costs, MCp. A per-unit pollution fee imposed on the firms would in-
crease their marginal costs to MCe, thus shifting the supply curve to S2, and the efficient
level of production would emerge. Taxes or other restrictions may be imposed on the activity that gen-
erates the external cost in an effort to confront decision makers with the costs that they are imposing.
In many areas, firms and consumers that pollute rivers and lakes are required to pay fees based on the
amount they pollute. Firms in many areas are required to purchase permits in order to pollute the air;
the requirement that permits be purchased serves to confront the firms with the costs of their choices.

Another approach to dealing with problems of external costs is direct regulation. For example, a
firm may be ordered to reduce its pollution. A person who turns his or her front yard into a garbage
dump may be ordered to clean it up. Participants at a raucous party may be told to be quiet. Alternative
ways of dealing with external costs are discussed later in the text.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 157

common property resource

Resources for which no
property rights have been
defined.

3.4 Common Property Resources
Common property resources[3] are resources for which no property rights have been defined. The
difficulty with common property resources is that individuals may not have adequate incentives to en-
gage in efforts to preserve or protect them. Consider, for example, the relative fates of cattle and buffalo
in the United States in the nineteenth century. Cattle populations increased throughout the century,
while the buffalo nearly became extinct. The chief difference between the two animals was that exclus-
ive property rights existed for cattle but not for buffalo.

Owners of cattle had an incentive to maintain herd sizes. A cattle owner who slaughtered all of his
or her cattle without providing for replacement of the herd would not have a source of future income.
Cattle owners not only maintained their herds but also engaged in extensive efforts to breed high-qual-
ity livestock. They invested time and effort in the efficient management of the resource on which their
livelihoods depended.

Buffalo hunters surely had similar concerns about the maintenance of buffalo herds, but they had
no individual stake in doing anything about them—the animals were a common property resource.
Thousands of individuals hunted buffalo for a living. Anyone who cut back on hunting in order to help
to preserve the herd would lose income—and face the likelihood that other hunters would go on hunt-
ing at the same rate as before.

Today, exclusive rights to buffalo have been widely established. The demand for buffalo meat,
which is lower in fat than beef, has been increasing, but the number of buffalo in the United States is
rising rapidly. If buffalo were still a common property resource, that increased demand, in the absence
of other restrictions on hunting of the animals, would surely result in the elimination of the animal. Be-
cause there are exclusive, transferable property rights in buffalo and because a competitive market
brings buyers and sellers of buffalo and buffalo products together, we can be reasonably confident in
the efficient management of the animal.

When a species is threatened with extinction, it is likely that no one has exclusive property rights
to it. Whales, condors, grizzly bears, elephants in Central Africa—whatever the animal that is
threatened—are common property resources. In such cases a government agency may impose limits on
the killing of the animal or destruction of its habitat. Such limits can prevent the excessive private use
of a common property resource. Alternatively, as was done in the case of the buffalo, private rights can
be established, giving resource owners the task of preservation.

K E Y T A K E A W A Y S

< Public sector intervention to increase the level of provision of public goods may improve the efficiency of resource allocation by overcoming the problem of free riders.

< Activities that generate external costs are likely to be carried out at levels that exceed those that would be efficient; the public sector may seek to intervene to confront decision makers with the full costs of their choices.

< Some private activities generate external benefits.

< A common property resource is unlikely to be allocated efficiently in the marketplace.

158 PRINCIPLES OF ECONOMICS VERSION 3.0

T R Y I T !

The manufacture of memory chips for computers generates pollutants that generally enter rivers and streams.
Use the model of demand and supply to show the equilibrium price and output of chips. Assuming chip man-
ufacturers do not have to pay the costs these pollutants impose, what can you say about the efficiency of the
quantity of chips produced? Show the area of deadweight loss imposed by this external cost. Show how a re-
quirement that firms pay these costs as they produce the chips would affect the equilibrium price and output
of chips. Would such a requirement help to satisfy the efficiency condition? Explain.

Case in Point: Protecting Wildlife by Establishing Private Property Rights

Source: © Thinkstock

Imagine that you are a rural landowner in Kenya. You grow crops, sell them, and earn a return. You raise live-
stock, sell them, and earn a return on them as well. Wild animals, from birds to elephants, are also found on
your property, but you are severely restricted in terms of what you can do with them. In Kenya, wildlife owner-
ship and user rights are largely the property of the state (i.e., wildlife is owned by all the citizens of Kenya). But
if wild animals kill some of your cattle, the loss is entirely yours, as the state will not compensate you. And do
not seriously think about offering wildlife viewing on your property because that is restricted by the state to
about 5% of the rangelands where the wildlife are found. If crops and livestock were treated in the same way
as wildlife in Kenya, how much of their production would continue in these areas?

Mike Norton-Griffiths, a long-time resident of Kenya and researcher of conservation and land use policy, argues
that the lack of private property rights for wildlife explains why wild animal populations there have been
dwindling. Since 1977, when Kenya banned all sport hunting and all other consumptive uses of wildlife, the
large animal wildlife population there has fallen by 60 to 70%. Over the same period, human population has
grown by more than 3% per year, crop production by more than 8% per year, and livestock population has
been stable.

To reverse the decline in wildlife population, Norton-Griffiths argues that property rights for wildlife should be
changed so that returns to wildlife become competitive with returns to crops and livestock. This would mean
that rural landowners would be allowed to generate income from wildlife from activities such as sales of wild-
life between landowners and to the public sector, ranching for local and overseas and local trade, sales of
wildlife products, tanning, making of trophies and curios, and sport hunting.

Private property rights for wildlife (sometimes referred to as private sector conservation) have been estab-
lished in much of southern Africa (South Africa, Botswana, Namibia, and Zimbabwe). In those countries, there
exist over 9,000 private game ranches and 1,100 private nature reserves. These private areas engage in wildlife
viewing services, sport hunting, live game sales, and bush meat production.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 159

The bounce back in wildlife population in the southern African countries is remarkable, even though the anim-
als may move from property to property. For example, the wildlife population on private game ranches in
Namibia has increased by about 70%. Similarly in Europe, rural landowners have invested in raising game birds,
even though the birds can move freely from property to property, because they can sell the rights to game
bird hunting on their property.

Peter Kareiva, the chief scientist for the Nature Conservancy, and Michelle Marvier, a professor at Santa Clara
University, support a conservation-for-people approach. They argue that it does not make sense to pit people
against nature. Rather, human well-being should become a part of biodiversity conservation efforts. If humans
can benefit from managing wildlife, the wildlife may benefit as well.

Sources: Based on Peter Kareiva and Michael Marvier, “Conservation for the People,” Scientific American 297:4 (October 2007): 50–57; Mike Norton-
Griffiths, “How Many Wildebeest Do You Need?” World Economics, 8:2 (April–June 2007): 41–64.

A N S W E R T O T R Y I T ! P R O B L E M

In the absence of any regulation, chip producers are not faced with the costs of the pollution their operations
generate. The market price is thus P1 and the quantity Q1. The efficiency condition is not met; the price is
lower and the quantity greater than would be efficient. If producers were forced to face the cost of their pollu-
tion as well as other production costs, the supply curve would shift to S2, the price would rise to P2, and the
quantity would fall to Q2. The new solution satisfies the efficiency condition.

4. REVIEW AND PRACTICE

Summary

Economists insist that individuals do not make choices willy-nilly. Rather, economists assume that individuals
make choices in a purposeful way, one that seeks the maximum value for some objective. We assume that
consumers seek to maximize utility and that firms seek to maximize profits.

Whatever is being maximized, choices are based on the marginal decision rule. Following this rule results in an
allocation that achieves the greatest degree of utility or profit possible.

If utility- and profit-maximizing choices are made in the context of a price system that confronts decision
makers with all of the costs and all of the benefits of their choices, the allocation of resources will be efficient.
An efficient allocation is one that maximizes the net benefit of every activity. The concepts of consumer and
producer surplus show us how this net benefit is shared. Equity is a separate issue, one that calls for a normat-
ive evaluation of the fairness of the distribution of income.

160 PRINCIPLES OF ECONOMICS VERSION 3.0

The allocation of resources will be inefficient in the absence of competitive markets. It will also be inefficient if
property rights are not exclusive and transferable. These two conditions break down when there are public
goods, common property resources, or external benefits or costs. In each of these cases, public sector inter-
vention may improve the efficiency of resource allocation. When a market fails to achieve the efficient solu-
tion, net benefit falls short of the maximum possible. Deadweight loss is the amount by which net benefit falls
below the net benefit possible at the efficient solution.

C O N C E P T P R O B L E M S

1. What is achieved by selecting the quantity of an activity at which marginal benefit equals marginal cost?

2. Suppose the marginal benefit of an activity exceeds the marginal cost. What does the marginal decision
rule say a maximizing decision maker will do?

3. Suppose you are a discus hurler and your goal is to maximize the distance you achieve. You “produce”
discus hurls by practicing. The total benefit of practice is distance achieved, and the input that achieves
this distance is hours of practice. Describe the total benefit curve of practice. What point on the curve
would you select?

4. This chapter argues that consumers maximize utility and firms maximize profits. What do you suppose
each of the following might be presumed to maximize?

a. A minister or rabbi

b. A United States Senator

c. The manager of a major league baseball team

d. The owner of a major league baseball team

e. The director of a charitable organization

5. For each of the following goods, indicate whether exclusive, transferable property rights exist and whether
the good poses a problem for public policy. If it does, does the problem relate to a problem of property
rights?

a. Clean air

b. Tomatoes

c. Housing

d. Blue whales

6. The dry-cleaning industry is a major source of air pollution. What can you conclude about the price and
output of dry-cleaning services?

7. Economists often recommend that polluters such as dry-cleaning establishments be charged fees for the
pollution they emit. Critics of this idea respond that the establishments would simply respond by passing
these charges on to their customers, leaving the level of pollution unchanged. Comment on this
objection.

8. Government agencies often require that children be inoculated against communicable diseases such as
polio and measles. From the standpoint of economic efficiency, is there any justification for such a
requirement?

9. Which of the following goods or services are public? Why or why not?

a. Libraries

b. Fire protection

c. Television programs

d. Health care

e. Water for household consumption

10. If a village in Botswana is granted several licenses to kill elephants, how does this give it an incentive to
preserve elephants and increase the size of the herd? How does the international ban on ivory sales affect
the incentive in Botswana to preserve the elephant?

11. The number of fish caught in the ocean has fallen in recent years partly as a result of more intensive
fishing efforts and the use of more sophisticated equipment. Fish in the ocean are a common property
resource. How might this fact be related to declining fish catches? How do you think this drop in the catch
affects the price of seafood?

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 161

N U M E R I C A L P R O B L E M S

1. Joe Higgins is thinking about how much time to spend studying for a biology exam tomorrow. Using
“utility units” he measures the benefits and costs of study; his calculations are shown in the following
table.

a. Fill in the fourth row for net benefit in the table. Use the midpoint convention to emphasize that
the net benefit is a marginal value showing the gain as hours spent increase by one-hour
increments.

b. Using a graph similar to Panel (a) of Figure 6.1 show the marginal benefit curve and verify that
the area under the curve at 3 hours of study corresponds to the total benefit of that much study.
(Hint: Remember that marginal values are plotted at the midpoints of the corresponding intervals
on the horizontal axis.)

c. Use a graph similar to Panel (b) of Figure 6.1 to show the marginal cost curve and verify that the
area under the curve at 3 hours of study corresponds to the total cost of that much study.

d. Use a graph similar to Panel (a) of Figure 6.6 to combine the marginal benefit and marginal cost
curves you drew in parts (a) and (b).

e. Based on the marginal decision rule, how many hours should Joe spend studying for his biology
exam?

2. Now suppose some friends of Joe’s call to say they are having a party tonight. Joe calculates that the party
is now his best alternative to study, and he increases his estimate of the cost of each hour of study. One
hour of study now costs 70; two hours cost 140; three hours 210, four hours 280; five hours 350; and six
hours 470.

a. Draw the new marginal benefit and marginal cost curves as in Problem 1, part (d):

b. Based on the marginal decision rule, identify the new solution that maximizes the net benefit of
study time.

3. The local gasoline market in a particular city has demand and supply curves given by the following data.
(All quantities are in millions of gallons per month.)

Price per gallon $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 $4.00

Quantity demanded 6 5 4 3 2 1 0

Quantity supplied 0 1 2 3 4 5 6

a. Plot the demand and supply curves, and determine the equilibrium price and quantity.

b. Show the areas of consumer and producer surplus.

c. Now suppose that the community determines that each gallon of gasoline consumed imposes
$0.50 in pollution costs. Accordingly, a $0.50-per-gallon tax is imposed. The tax is imposed on
sellers of gasoline, and it has the effect of increasing by $0.50 the price required to induce the
quantities supplied in the table. For example, a price of $2.00 is now required for a quantity of 1
million gallons to be supplied each month. Plot the new supply curve.

d. Approximate the new equilibrium price and output.

e. Does the price increase by the full amount of the tax? If not, explain why.

f. Would your answer be different if the demand for gasoline were perfectly inelastic?

4. The flu vaccination market has the demand and supply curves given by the following data. (All quantities
are in thousands.)

Price per vaccination $10 $15 $20 $25 $30

Quantity demanded 90 80 70 60 50

Quantity supplied 50 60 70 80 90

a. Plot the demand and supply curves, and determine the equilibrium price and quantity.

162 PRINCIPLES OF ECONOMICS VERSION 3.0

b. Show the areas of consumer and producer surplus.

c. Now suppose that each vaccination given generates an external benefit, as those who do not get
vaccinated are less likely to get the flu when others do get vaccinated. As a result, suppliers
receive a $10 subsidy from the government for each vaccine. For example, if consumers pay $10
per vaccination, suppliers receive $20, so only $10 from consumers is required to induce suppliers
to offer 70,000 vaccinations per month. Plot the new supply curve.

d. Determine the new equilibrium price and quantity.

e. Does the price fall by the full amount of the subsidy? If not, explain why.

f. What is the total amount that consumers now pay for the new equilibrium quantity of
vaccinations?

g. What is the total subsidy that suppliers receive from the government at the new equilibrium
quantity of vaccinations?

5. Given the following information about the supply of and demand for apples:

Price per
pound

Quantity demanded (pounds per
month)

Quantity Supplied (pounds per
month

$0.50 12,000 0

0.75 10,000 2,000

1.00 8,000 4,000

1.25 6,000 6,000

1.50 4,000 8,000

1.75 2,000 10,000

2.00 0 12,000

a. Draw a graph similar to Figure 6.9

b. Assuming the market for apples meets the efficiency condition, show the equilibrium price and
quantity that maximizes net benefit to society.

c. Identify the area of consumer surplus and the area of producer surplus.

CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 163

1.
2.

ENDNOTES

See Report of the Committee on Commerce, Science, and Transportation, Children’s
Protection From Violent Programming Act, Senate Report 106–509 (October 26, 2000),
Washington, D.C.: U.S. Government Printing Office, 2000, and Michael Rich, “Violent

Video Games Testimony,” Chicago City Council, October 30, 2000, at
http://www.aap.org/advocacy/rich-videogameviolence .

Mark Rosenberg, “Successful State Strategies,” Adolescent Health Leadership Forum,
December 6, 2003, at http://www.aap.org/advocacy/ahproject/AHLSuccessful
StateStrategiesMRosenberg.pps.

Common property resources are sometimes referred to as open access resources.

164 PRINCIPLES OF ECONOMICS VERSION 3.0

Chapter 6: Markets, Maximizers, and Efficiency

Start Up: A Drive in the Country
The Logic of Maximizing Behavior
The Analysis of Maximizing Behavior
A Problem in Maximization
Using Marginal Benefit and Marginal Cost Curves to Find Net Benefits

Maximizing in the Marketplace
Achieving Efficiency
The Role of Property Rights
Markets and the Efficiency Condition
Producer and Consumer Surplus
Efficiency and Equity
Market Failure
Noncompetitive Markets
Public Goods
Free Riders
Public Goods and the Government
External Costs and Benefits
External Costs and Efficiency
External Costs and Government Intervention
Common Property Resources
Review And Practice
Endnotes

C H A P T E R 7
The Analysis of Consumer
Choice
START UP: A DAY AT THE GROCERY STORE
You are in the checkout line at the grocery store when your eyes wander over to the ice cream display. It is a hot

day and you could use something to cool you down before you get into your hot car. The problem is that you have

left your checkbook and credit and debit cards at home—on purpose, actually, because you have decided that you

only want to spend $20 today at the grocery store. You are uncertain whether or not you have brought enough

cash with you to pay for the items that are already in your cart. You put the ice cream bar into your cart and tell the

clerk to let you know if you go over $20 because that is all you have. He rings it up and it comes to $22. You have to

make a choice. You decide to keep the ice cream and ask the clerk if he would mind returning a box of cookies to

the shelf.

We all engage in these kinds of choices every day. We have budgets and must decide how to spend them. The

model of utility theory that economists have constructed to explain consumer choice assumes that consumers will

try to maximize their utility. For example, when you decided to keep the ice cream bar and return the cookies, you,

consciously or not, applied the marginal decision rule to the problem of maximizing your utility: You bought the ice

cream because you expect that eating it will give you greater satisfaction than would consuming the box of

cookies.

Utility theory provides insights into demand. It lets us look behind demand curves to see how utility-maximiz-

ing consumers can be expected to respond to price changes. While the focus of this chapter is on consumers mak-

ing decisions about what goods and services to buy, the same model can be used to understand how individuals

make other types of decisions, such as how much to work and how much of their incomes to spend now or to sock

away for the future.

We can approach the analysis of utility maximization in two ways. The first two sections of the chapter cover

the marginal utility concept, while the final section examines an alternative approach using indifference curves.

total utility

The number of units of utility
that a consumer gains from
consuming a given quantity
of a good, service, or activity
during a particular time
period.

1. THE CONCEPT OF UTILITY

L E A R N I N G O B J E C T I V E S

1. Define what economists mean by utility.
2. Distinguish between the concepts of total utility and marginal utility.
3. State the law of diminishing marginal utility and illustrate it graphically.
4. State, explain, and illustrate algebraically the utility-maximizing condition.

Why do you buy the goods and services you do? It must be because they provide you with satisfac-
tion—you feel better off because you have purchased them. Economists call this satisfaction utility.

The concept of utility is an elusive one. A person who consumes a good such as peaches gains util-
ity from eating the peaches. But we cannot measure this utility the same way we can measure a peach’s
weight or calorie content. There is no scale we can use to determine the quantity of utility a peach
generates.

Francis Edgeworth, one of the most important contributors to the theory of consumer behavior,
imagined a device he called a hedonimeter (after hedonism, the pursuit of pleasure):

“[L]et there be granted to the science of pleasure what is granted to the science of energy; to
imagine an ideally perfect instrument, a psychophysical machine, continually registering the
height of pleasure experienced by an individual…. From moment to moment the hedonimeter
varies; the delicate index now flickering with the flutter of passions, now steadied by intellectual
activity, now sunk whole hours in the neighborhood of zero, or momentarily springing up towards
infinity.”[1]

Perhaps some day a hedonimeter will be invented. The utility it measures will not be a character-
istic of particular goods, but rather of each consumer’s reactions to those goods. The utility of a peach
exists not in the peach itself, but in the preferences of the individual consuming the peach. One con-
sumer may wax ecstatic about a peach; another may say it tastes OK.

When we speak of maximizing utility, then, we are speaking of the maximization of something we
cannot measure. We assume, however, that each consumer acts as if he or she can measure utility and
arranges consumption so that the utility gained is as high as possible.

1.1 Total Utility
If we could measure utility, total utility would be the number of units of utility that a consumer gains
from consuming a given quantity of a good, service, or activity during a particular time period. The
higher a consumer’s total utility, the greater that consumer’s level of satisfaction.

Panel (a) of Figure 7.1 shows the total utility Henry Higgins obtains from attending movies. In
drawing his total utility curve, we are imagining that he can measure his total utility. The total utility
curve shows that when Mr. Higgins attends no movies during a month, his total utility from attending
movies is zero. As he increases the number of movies he sees, his total utility rises. When he consumes
1 movie, he obtains 36 units of utility. When he consumes 4 movies, his total utility is 101. He achieves
the maximum level of utility possible, 115, by seeing 6 movies per month. Seeing a seventh movie adds
nothing to his total utility.

166 PRINCIPLES OF ECONOMICS VERSION 3.0

FIGURE 7.1 Total Utility and Marginal Utility Curves

Panel (a) shows Henry Higgins’s total utility curve for attending movies. It rises as the number of movies increases,
reaching a maximum of 115 units of utility at 6 movies per month. Marginal utility is shown in Panel (b); it is the
slope of the total utility curve. Because the slope of the total utility curve declines as the number of movies
increases, the marginal utility curve is downward sloping.

Mr. Higgins’s total utility rises at a decreasing rate. The rate of increase is given by the slope of the total
utility curve, which is reported in Panel (a) of Figure 7.1 as well. The slope of the curve between 0

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 167

marginal utility

The amount by which total
utility rises with consumption
of an additional unit of a
good, service, or activity, all
other things unchanged.

law of diminishing
marginal utility

This tendency of marginal
utility to decline beyond
some level of consumption
during a period.

budget constraint

A restriction that total
spending cannot exceed the
budget available.

movies and 1 movie is 36 because utility rises by this amount when Mr. Higgins sees his first movie in
the month. It is 28 between 1 and 2 movies, 22 between 2 and 3, and so on. The slope between 6 and 7
movies is zero; the total utility curve between these two quantities is horizontal.

1.2 Marginal Utility
The amount by which total utility rises with consumption of an additional unit of a good, service, or
activity, all other things unchanged, is marginal utility. The first movie Mr. Higgins sees increases his
total utility by 36 units. Hence, the marginal utility of the first movie is 36. The second increases his
total utility by 28 units; its marginal utility is 28. The seventh movie does not increase his total utility;
its marginal utility is zero. Notice that in the table marginal utility is listed between the columns for
total utility because, similar to other marginal concepts, marginal utility is the change in utility as we go
from one quantity to the next. Mr. Higgins’s marginal utility curve is plotted in Panel (b) of Figure 7.1
The values for marginal utility are plotted midway between the numbers of movies attended. The mar-
ginal utility curve is downward sloping; it shows that Mr. Higgins’s marginal utility for movies declines
as he consumes more of them.

Mr. Higgins’s marginal utility from movies is typical of all goods and services. Suppose that you
are really thirsty and you decide to consume a soft drink. Consuming the drink increases your utility,
probably by a lot. Suppose now you have another. That second drink probably increases your utility by
less than the first. A third would increase your utility by still less. This tendency of marginal utility to
decline beyond some level of consumption during a period is called the law of diminishing
marginal utility. This law implies that all goods and services eventually will have downward-sloping
marginal utility curves. It is the law that lies behind the negatively sloped marginal benefit curve for
consumer choices that we examined in the chapter on markets, maximizers, and efficiency.

One way to think about this effect is to remember the last time you ate at an “all you can eat”
cafeteria-style restaurant. Did you eat only one type of food? Did you consume food without limit? No,
because of the law of diminishing marginal utility. As you consumed more of one kind of food, its mar-
ginal utility fell. You reached a point at which the marginal utility of another dish was greater, and you
switched to that. Eventually, there was no food whose marginal utility was great enough to make it
worth eating, and you stopped.

What if the law of diminishing marginal utility did not hold? That is, what would life be like in a
world of constant or increasing marginal utility? In your mind go back to the cafeteria and imagine that
you have rather unusual preferences: Your favorite food is creamed spinach. You start with that be-
cause its marginal utility is highest of all the choices before you in the cafeteria. As you eat more,
however, its marginal utility does not fall; it remains higher than the marginal utility of any other op-
tion. Unless eating more creamed spinach somehow increases your marginal utility for some other
food, you will eat only creamed spinach. And until you have reached the limit of your body’s capacity
(or the restaurant manager’s patience), you will not stop. Failure of marginal utility to diminish would
thus lead to extraordinary levels of consumption of a single good to the exclusion of all others. Since we
do not observe that happening, it seems reasonable to assume that marginal utility falls beyond some
level of consumption.

1.3 Maximizing Utility
Economists assume that consumers behave in a manner consistent with the maximization of utility. To
see how consumers do that, we will put the marginal decision rule to work. First, however, we must
reckon with the fact that the ability of consumers to purchase goods and services is limited by their
budgets.

The Budget Constraint

The total utility curve in Figure 7.1 shows that Mr. Higgins achieves the maximum total utility possible
from movies when he sees six of them each month. It is likely that his total utility curves for other
goods and services will have much the same shape, reaching a maximum at some level of consumption.
We assume that the goal of each consumer is to maximize total utility. Does that mean a person will
consume each good at a level that yields the maximum utility possible?

The answer, in general, is no. Our consumption choices are constrained by the income available to
us and by the prices we must pay. Suppose, for example, that Mr. Higgins can spend just $25 per
month for entertainment and that the price of going to see a movie is $5. To achieve the maximum
total utility from movies, Mr. Higgins would have to exceed his entertainment budget. Since we assume
that he cannot do that, Mr. Higgins must arrange his consumption so that his total expenditures do not
exceed his budget constraint: a restriction that total spending cannot exceed the budget available.

168 PRINCIPLES OF ECONOMICS VERSION 3.0

Suppose that in addition to movies, Mr. Higgins enjoys concerts, and the average price of a concert
ticket is $10. He must select the number of movies he sees and concerts he attends so that his monthly
spending on the two goods does not exceed his budget.

Individuals may, of course, choose to save or to borrow. When we allow this possibility, we con-
sider the budget constraint not just for a single period of time but for several periods. For example, eco-
nomists often examine budget constraints over a consumer’s lifetime. A consumer may in some years
save for future consumption and in other years borrow on future income for present consumption.
Whatever the time period, a consumer’s spending will be constrained by his or her budget.

To simplify our analysis, we shall assume that a consumer’s spending in any one period is based on
the budget available in that period. In this analysis consumers neither save nor borrow. We could ex-
tend the analysis to cover several periods and generate the same basic results that we shall establish us-
ing a single period. We will also carry out our analysis by looking at the consumer’s choices about buy-
ing only two goods. Again, the analysis could be extended to cover more goods and the basic results
would still hold.

Applying the Marginal Decision Rule

Because consumers can be expected to spend the budget they have, utility maximization is a matter of
arranging that spending to achieve the highest total utility possible. If a consumer decides to spend
more on one good, he or she must spend less on another in order to satisfy the budget constraint.

The marginal decision rule states that an activity should be expanded if its marginal benefit ex-
ceeds its marginal cost. The marginal benefit of this activity is the utility gained by spending an addi-
tional $1 on the good. The marginal cost is the utility lost by spending $1 less on another good.

How much utility is gained by spending another $1 on a good? It is the marginal utility of the good
divided by its price. The utility gained by spending an additional dollar on good X, for example, is

MUX
PX

This additional utility is the marginal benefit of spending another $1 on the good.
Suppose that the marginal utility of good X is 4 and that its price is $2. Then an extra $1 spent on

X buys 2 additional units of utility (MUX / PX = 4 / 2 = 2). If the marginal utility of good X is 1 and its
price is $2, then an extra $1 spent on X buys 0.5 additional units of utility (MUX / PX = 1 / 2 = 0.5).

The loss in utility from spending $1 less on another good or service is calculated the same way: as
the marginal utility divided by the price. The marginal cost to the consumer of spending $1 less on a
good is the loss of the additional utility that could have been gained from spending that $1 on the good.

Suppose a consumer derives more utility by spending an additional $1 on good X rather than on
good Y:

EQUATION 7.1
MUX

PX
>

MUY
PY

The marginal benefit of shifting $1 from good Y to the consumption of good X exceeds the mar-
ginal cost. In terms of utility, the gain from spending an additional $1 on good X exceeds the loss in
utility from spending $1 less on good Y. The consumer can increase utility by shifting spending from Y
to X.

As the consumer buys more of good X and less of good Y, however, the marginal utilities of the
two goods will change. The law of diminishing marginal utility tells us that the marginal utility of good
X will fall as the consumer consumes more of it; the marginal utility of good Y will rise as the consumer
consumes less of it. The result is that the value of the left-hand side of Equation 7.1 will fall and the
value of the right-hand side will rise as the consumer shifts spending from Y to X. When the two sides
are equal, total utility will be maximized. In terms of the marginal decision rule, the consumer will have
achieved a solution at which the marginal benefit of the activity (spending more on good X) is equal to
the marginal cost:

EQUATION 7.2
MUX

PX
=

MUY
PY

We can extend this result to all goods and services a consumer uses. Utility maximization requires
that the ratio of marginal utility to price be equal for all of them, as suggested in Equation 7.3:

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 169

utility-maximizing
condition

Utility is maximized when
total outlays equal the
budget available and when
the ratios of marginal utilities
to prices are equal for all
goods and services.

EQUATION 7.3
MUA

PA
=

MUB

=
MUC

PC
= … =

MUn
Pn

Equation 7.3 states the utility-maximizing condition: Utility is maximized when total outlays
equal the budget available and when the ratios of marginal utilities to prices are equal for all goods and
services.

Consider, for example, the shopper introduced in the opening of this chapter. In shifting from
cookies to ice cream, the shopper must have felt that the marginal utility of spending an additional dol-
lar on ice cream exceeded the marginal utility of spending an additional dollar on cookies. In terms
of Equation 7.1, if good X is ice cream and good Y is cookies, the shopper will have lowered the value of
the left-hand side of the equation and moved toward the utility-maximizing condition, as expressed by
Equation 7.

The Problem of Divisibility

If we are to apply the marginal decision rule to utility maximization, goods must be divisible; that is, it
must be possible to buy them in any amount. Otherwise we cannot meaningfully speak of spending

more or $1 less on them. Strictly speaking, however, few goods are completely divisible.

Even a small purchase, such as an ice cream bar, fails the strict test of being divisible; grocers gen-
erally frown on requests to purchase one-half of a $2 ice cream bar if the consumer wants to spend an
additional dollar on ice cream. Can a consumer buy a little more movie admission, to say nothing of a
little more car?

In the case of a car, we can think of the quantity as depending on characteristics of the car itself. A
car with a compact disc player could be regarded as containing “more car” than one that has only a cas-
sette player. Stretching the concept of quantity in this manner does not entirely solve the problem. It is
still difficult to imagine that one could purchase “more car” by spending $1 more.

Remember, though, that we are dealing with a model. In the real world, consumers may not be
able to satisfy Equation 7.3 precisely. The model predicts, however, that they will come as close to do-
ing so as possible.

K E Y T A K E A W A Y S

< The utility of a good or service is determined by how much satisfaction a particular consumer obtains from it. Utility is not a quality inherent in the good or service itself.

< Total utility is a conceptual measure of the number of units of utility a consumer gains from consuming a good, service, or activity. Marginal utility is the increase in total utility obtained by consuming one more unit of a good, service, or activity.

< As a consumer consumes more and more of a good or service, its marginal utility falls.

< Utility maximization requires seeking the greatest total utility from a given budget.

< Utility is maximized when total outlays equal the budget available and when the ratios of marginal utility to price are equal for all goods and services a consumer consumes; this is the utility-maximizing condition.

170 PRINCIPLES OF ECONOMICS VERSION 3.0

T R Y I T !

A college student, Ramón Juárez, often purchases candy bars or bags of potato chips between classes; he tries
to limit his spending on these snacks to $8 per week. A bag of chips costs $0.75 and a candy bar costs $0.50
from the vending machines on campus. He has been purchasing an average of 6 bags of chips and 7 candy
bars each week. Mr. Juárez is a careful maximizer of utility, and he estimates that the marginal utility of an ad-
ditional bag of chips during a week is 6. In your answers use B to denote candy bars and C to denote potato
chips.

1. How much is he spending on snacks? How does this amount compare to his budget constraint?

2. What is the marginal utility of an additional candy bar during the week?

Case in Point: Changing Lanes and Raising Utility

In preparation for sitting in the slow, crowded lanes for single-occupancy-vehicles, T. J. Zane used to stop at
his favorite coffee kiosk to buy a $2 cup of coffee as he headed off to work on Interstate 15 in the San Diego
area. Since 1996, an experiment in road pricing has caused him and others to change their ways—and to raise
their total utility.

Before 1996, only car-poolers could use the specially marked high-occupancy-vehicles lanes. With those lanes
nearly empty, traffic authorities decided to allow drivers of single-occupancy-vehicles to use those lanes, so
long as they paid a price. Now, electronic signs tell drivers how much it will cost them to drive on the special
lanes. The price is recalculated every 6 minutes depending on the traffic. On one morning during rush hour, it
varied from $1.25 at 7:10 a.m., to $1.50 at 7:16 a.m., to $2.25 at 7:22 a.m., and to $2.50 at 7:28 a.m. The increas-
ing tolls over those few minutes caused some drivers to opt out and the toll fell back to $1.75 and then in-
creased to $2 a few minutes later. Drivers do not have to stop to pay the toll since radio transmitters read their
FasTrak transponders and charge them accordingly.

When first instituted, these lanes were nicknamed the “Lexus lanes,” on the assumption that only wealthy
drivers would use them. Indeed, while the more affluent do tend to use them heavily, surveys have discovered
that they are actually used by drivers of all income levels.

Mr. Zane, a driver of a 1997 Volkswagen Jetta, is one commuter who chooses to use the new option. He ex-
plains his decision by asking, “Isn’t it worth a couple of dollars to spend an extra half-hour with your family?”
He continues, “That’s what I used to spend on a cup of coffee at Starbucks. Now I’ve started bringing my own
coffee and using the money for the toll.”

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 171

We can explain his decision using the model of utility-maximizing behavior; Mr. Zane’s out-of-pocket commut-
ing budget constraint is about $2. His comment tells us that he realized that the marginal utility of spending
an additional 30 minutes with his family divided by the $2 toll was higher than the marginal utility of the store-
bought coffee divided by its $2 price. By reallocating his $2 commuting budget, the gain in utility of having
more time at home exceeds the loss in utility from not sipping premium coffee on the way to work.

From this one change in behavior, we do not know whether or not he is actually maximizing his utility, but his
decision and explanation are certainly consistent with that goal.

Source: Based on John Tierney, “The Autonomist Manifesto (Or, How I learned to Stop Worrying and Love the Road),” New York Times Magazine,
September 26, 2004, 57–65.

A N S W E R S T O T R Y I T ! P R O B L E M S

1. He is spending $4.50 (= $0.75 × 6) on potato chips and $3.50 (= $0.50 × 7) on candy bars, for a total of $8.
His budget constraint is $8.

2. In order for the ratios of marginal utility to price to be equal, the marginal utility of a candy bar must be 4.
Let the marginal utility and price of candy bars be MUB and PB, respectively, and the marginal utility and
price of a bag of potato chips be MUC and PC, respectively. Then we want

MUC
PC

=
MUB

We know that PC is $0.75 and PB equals $0.50. We are told that MUC is 6. Thus

6
0.75 =

MUB
0.50

Solving the equation for MUB, we find that it must equal 4.

2. UTILITY MAXIMIZATION AND DEMAND

L E A R N I N G O B J E C T I V E S

1. Derive an individual demand curve from utility-maximizing adjustments to changes in price.
2. Derive the market demand curve from the demand curves of individuals.
3. Explain the substitution and income effects of a price change.
4. Explain the concepts of normal and inferior goods in terms of the income effect.

Choices that maximize utility—that is, choices that follow the marginal decision rule—generally
produce downward-sloping demand curves. This section shows how an individual’s utility-maximizing
choices can lead to a demand curve.

2.1 Deriving an Individual’s Demand Curve
Suppose, for simplicity, that Mary Andrews consumes only apples, denoted by the letter A, and or-
anges, denoted by the letter O. Apples cost $2 per pound and oranges cost $1 per pound, and her
budget allows her to spend $20 per month on the two goods. We assume that Ms. Andrews will adjust
her consumption so that the utility-maximizing condition holds for the two goods: The ratio of mar-
ginal utility to price is the same for apples and oranges. That is,

EQUATION 7.4
MUA

$2 =
MUO

Here MUA and MUO are the marginal utilities of apples and oranges, respectively. Her spending
equals her budget of $20 per month; suppose she buys 5 pounds of apples and 10 of oranges.

172 PRINCIPLES OF ECONOMICS VERSION 3.0

Now suppose that an unusually large harvest of apples lowers their price to $1 per pound. The
lower price of apples increases the marginal utility of each $1 Ms. Andrews spends on apples, so that at
her current level of consumption of apples and oranges

EQUATION 7.5
MUA

$1 >
MUO

Ms. Andrews will respond by purchasing more apples. As she does so, the marginal utility she re-
ceives from apples will decline. If she regards apples and oranges as substitutes, she will also buy fewer
oranges. That will cause the marginal utility of oranges to rise. She will continue to adjust her spending
until the marginal utility per $1 spent is equal for both goods:

EQUATION 7.6
MUA

$1 =
MUO

Suppose that at this new solution, she purchases 12 pounds of apples and 8 pounds of oranges. She
is still spending all of her budget of $20 on the two goods [(12 x $1)+(8 x $1)=$20].

FIGURE 7.2 Utility Maximization and an Individual’s Demand Curve

Mary Andrews’s demand curve for apples, d, can be derived by determining the quantities of apples she will buy at
each price. Those quantities are determined by the application of the marginal decision rule to utility maximization.
At a price of $2 per pound, Ms. Andrews maximizes utility by purchasing 5 pounds of apples per month. When the
price of apples falls to $1 per pound, the quantity of apples at which she maximizes utility increases to 12 pounds
per month.

It is through a consumer’s reaction to different prices that we trace the consumer’s demand curve for a
good. When the price of apples was $2 per pound, Ms. Andrews maximized her utility by purchasing 5
pounds of apples, as illustrated in Figure 7.2. When the price of apples fell, she increased the quantity
of apples she purchased to 12 pounds.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 173

Heads Up!

Notice that, in this example, Ms. Andrews maximizes utility where not only the ratios of marginal utilities to
price are equal, but also the marginal utilities of both goods are equal. But, the equal-marginal-utility outcome
is only true here because the prices of the two goods are the same: each good is priced at $1 in this case. If the
prices of apples and oranges were different, the marginal utilities at the utility maximizing solution would have
been different. The condition for maximizing utility—consume where the ratios of marginal utility to price are
equal—holds regardless. The utility-maximizing condition is not that consumers maximize utility by equating
marginal utilities.

2.2 From Individual to Market Demand
The market demand curves we studied in previous chapters are derived from individual demand curves
such as the one depicted in Figure 7.2. Suppose that in addition to Ms. Andrews, there are two other
consumers in the market for apples—Ellen Smith and Koy Keino. The quantities each consumes at
various prices are given in Figure 7.3, along with the quantities that Ms. Andrews consumes at each
price. The demand curves for each are shown in Panel (a). The market demand curve for all three con-
sumers, shown in Panel (b), is then found by adding the quantities demanded at each price for all three
consumers. At a price of $2 per pound, for example, Ms. Andrews demands 5 pounds of apples per
month, Ms. Smith demands 3 pounds, and Mr. Keino demands 8 pounds. A total of 16 pounds of
apples are demanded per month at this price. Adding the individual quantities demanded at $1 per
pound yields market demand of 40 pounds per month. This method of adding amounts along the hori-
zontal axis of a graph is referred to as summing horizontally. The market demand curve is thus the ho-
rizontal summation of all the individual demand curves.

FIGURE 7.3 Deriving a Market Demand Curve

The demand schedules for Mary Andrews, Ellen Smith, and Koy Keino are given in the table. Their individual
demand curves are plotted in Panel (a). The market demand curve for all three is shown in Panel (b).

174 PRINCIPLES OF ECONOMICS VERSION 3.0

income-compensated price
change

An imaginary exercise in
which we assume that when
the price of a good or service
changes, the consumer’s
income is adjusted so that he
or she has just enough to
purchase the original
combination of goods and
services at the new set of
prices.

substitution effect

The change in a consumer’s
consumption of a good in
response to an
income-compensated price
change.

Individual demand curves, then, reflect utility-maximizing adjustment by consumers to various market
prices. Once again, we see that as the price falls, consumers tend to buy more of a good. Demand
curves are downward-sloping as the law of demand asserts.

2.3 Substitution and Income Effects
We saw that when the price of apples fell from $2 to $1 per pound, Mary Andrews increased the quant-
ity of apples she demanded. Behind that adjustment, however, lie two distinct effects: the substitution
effect and the income effect. It is important to distinguish these effects, because they can have quite
different implications for the elasticity of the demand curve.

First, the reduction in the price of apples made them cheaper relative to oranges. Before the price
change, it cost the same amount to buy 2 pounds of oranges or 1 pound of apples. After the price
change, it cost the same amount to buy 1 pound of either oranges or apples. In effect, 2 pounds of or-
anges would exchange for 1 pound of apples before the price change, and 1 pound of oranges would
exchange for 1 pound of apples after the price change.

Second, the price reduction essentially made consumers of apples richer. Before the price change,
Ms. Andrews was purchasing 5 pounds of apples and 10 pounds of oranges at a total cost to her of $20.
At the new lower price of apples, she could purchase this same combination for $15. In effect, the price
reduction for apples was equivalent to handing her a $5 bill, thereby increasing her purchasing power.
Purchasing power refers to the quantity of goods and services that can be purchased with a given
budget.

To distinguish between the substitution and income effects, economists consider first the impact of
a price change with no change in the consumer’s ability to purchase goods and services. An
income-compensated price change is an imaginary exercise in which we assume that when the
price of a good or service changes, the consumer’s income is adjusted so that he or she has just enough
to purchase the original combination of goods and services at the new set of prices. Ms. Andrews was
purchasing 5 pounds of apples and 10 pounds of oranges before the price change. Buying that same
combination after the price change would cost $15. The income-compensated price change thus re-
quires us to take $5 from Ms. Andrews when the price of apples falls to $1 per pound. She can still buy
5 pounds of apples and 10 pounds of oranges. If, instead, the price of apples increased, we would give
Ms. Andrews more money (i.e., we would “compensate” her) so that she could purchase the same com-
bination of goods.

With $15 and cheaper apples, Ms. Andrews could buy 5 pounds of apples and 10 pounds of or-
anges. But would she? The answer lies in comparing the marginal benefit of spending another $1 on
apples to the marginal benefit of spending another $1 on oranges, as expressed in Equation 7.5. It
shows that the extra utility per $1 she could obtain from apples now exceeds the extra utility per $1
from oranges. She will thus increase her consumption of apples. If she had only $15, any increase in her
consumption of apples would require a reduction in her consumption of oranges. In effect, she re-
sponds to the income-compensated price change for apples by substituting apples for oranges. The
change in a consumer’s consumption of a good in response to an income-compensated price change is
called the substitution effect.

Suppose that with an income-compensated reduction in the price of apples to $1 per pound, Ms.
Andrews would increase her consumption of apples to 9 pounds per month and reduce her consump-
tion of oranges to 6 pounds per month. The substitution effect of the price reduction is an increase in
apple consumption of 4 pounds per month.

The substitution effect always involves a change in consumption in a direction opposite that of the
price change. When a consumer is maximizing utility, the ratio of marginal utility to price is the same
for all goods. An income-compensated price reduction increases the extra utility per dollar available
from the good whose price has fallen; a consumer will thus purchase more of it. An income-com-
pensated price increase reduces the extra utility per dollar from the good; the consumer will purchase
less of it.

In other words, when the price of a good falls, people react to the lower price by substituting or
switching toward that good, buying more of it and less of other goods, if we artificially hold the con-
sumer’s ability to buy goods constant. When the price of a good goes up, people react to the higher
price by substituting or switching away from that good, buying less of it and instead buying more of
other goods. By examining the impact of consumer purchases of an income-compensated price change,
we are looking at just the change in relative prices of goods and eliminating any impact on consumer
buying that comes from the effective change in the consumer’s ability to purchase goods and services
(that is, we hold the consumer’s purchasing power constant).

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 175

income effect

The change in consumption
of a good resulting from the
implicit change in income
because of a price change.

To complete our analysis of the impact of the price change, we must now consider the $5 that Ms.
Andrews effectively gained from it. After the price reduction, it cost her just $15 to buy what cost her
$20 before. She has, in effect, $5 more than she did before. Her additional income may also have an
effect on the number of apples she consumes. The change in consumption of a good resulting from the
implicit change in income because of a price change is called the income effect of a price change.
When the price of a good rises, there is an implicit reduction in income. When the price of a good falls,
there is an implicit increase. When the price of apples fell, Ms. Andrews (who was consuming 5 pounds
of apples per month) received an implicit increase in income of $5.

Suppose Ms. Andrews uses her implicit increase in income to purchase 3 more pounds of apples
and 2 more pounds of oranges per month. She has already increased her apple consumption to 9
pounds per month because of the substitution effect, so the added 3 pounds brings her consumption
level to 12 pounds per month. That is precisely what we observed when we derived her demand curve;
it is the change we would observe in the marketplace. We see now, however, that her increase in quant-
ity demanded consists of a substitution effect and an income effect. Figure 7.4 shows the combined
effects of the price change.

FIGURE 7.4 The Substitution and Income Effects of a Price Change

This demand curve for Ms. Andrews was presented in Figure 7.3. It shows that a reduction in the price of apples
from $2 to $1 per pound increases the quantity Ms. Andrews demands from 5 pounds of apples to 12. This graph
shows that this change consists of a substitution effect and an income effect. The substitution effect increases the
quantity demanded by 4 pounds, the income effect by 3, for a total increase in quantity demanded of 7 pounds.

The size of the substitution effect depends on the rate at which the marginal utilities of goods change as
the consumer adjusts consumption to a price change. As Ms. Andrews buys more apples and fewer or-
anges, the marginal utility of apples will fall and the marginal utility of oranges will rise. If relatively
small changes in quantities consumed produce large changes in marginal utilities, the substitution
effect that is required to restore the equality of marginal-utility-to-price ratios will be small. If much
larger changes in quantities consumed are needed to produce equivalent changes in marginal utilities,
then the substitution effect will be large.

The magnitude of the income effect of a price change depends on how responsive the demand for
a good is to a change in income and on how important the good is in a consumer’s budget. When the
price changes for a good that makes up a substantial fraction of a consumer’s budget, the change in the
consumer’s ability to buy things is substantial. A change in the price of a good that makes up a trivial

176 PRINCIPLES OF ECONOMICS VERSION 3.0

fraction of a consumer’s budget, however, has little effect on his or her purchasing power; the income
effect of such a price change is small.

Because each consumer’s response to a price change depends on the sizes of the substitution and
income effects, these effects play a role in determining the price elasticity of demand. All other things
unchanged, the larger the substitution effect, the greater the absolute value of the price elasticity of de-
mand. When the income effect moves in the same direction as the substitution effect, a greater income
effect contributes to a greater price elasticity of demand as well. There are, however, cases in which the
substitution and income effects move in opposite directions. We shall explore these ideas in the next
section.

2.4 Normal and

Inferior Goods

The nature of the income effect of a price change depends on whether the good is normal or inferior.
The income effect reinforces the substitution effect in the case of normal goods; it works in the opposite
direction for inferior goods.

Normal Goods

A normal good is one whose consumption increases with an increase in income. When the price of a
normal good falls, there are two identifying effects:

1. The substitution effect contributes to an increase in the quantity demanded because consumers
substitute more of the good for other goods.

2. The reduction in price increases the consumer’s ability to buy goods. Because the good is normal,
this increase in purchasing power further increases the quantity of the good demanded through
the income effect.

In the case of a normal good, then, the substitution and income effects reinforce each other. Ms.
Andrews’s response to a price reduction for apples is a typical response to a lower price for a normal
good.

An increase in the price of a normal good works in an equivalent fashion. The higher price causes
consumers to substitute more of other goods, whose prices are now relatively lower. The substitution
effect thus reduces the quantity demanded. The higher price also reduces purchasing power, causing
consumers to reduce consumption of the good via the income effect.

Inferior Goods

In the chapter that introduced the model of demand and supply, we saw that an inferior good is one for
which demand falls when income rises. It is likely to be a good that people do not really like very much.
When incomes are low, people consume the inferior good because it is what they can afford. As their
incomes rise and they can afford something they like better, they consume less of the inferior good.
When the price of an inferior good falls, two things happen:

1. Consumers will substitute more of the inferior good for other goods because its price has fallen
relative to those goods. The quantity demanded increases as a result of the substitution effect.

2. The lower price effectively makes consumers richer. But, because the good is inferior, this reduces
quantity demanded.

The case of inferior goods is thus quite different from that of normal goods. The income effect of a
price change works in a direction opposite to that of the substitution effect in the case of an inferior
good, whereas it reinforces the substitution effect in the case of a normal good.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 177

FIGURE 7.5 Substitution and Income Effects for Inferior Goods

The substitution and income effects work against each other in the case of inferior goods. The consumer begins at
point A, consuming q1 units of the good at a price P1. When the price falls to P2, the consumer moves to point B,
increasing quantity demanded to q2. The substitution effect increases quantity demanded to qs, but the income
effect reduces it from qs to q2.

Figure 7.5 illustrates the substitution and income effects of a price reduction for an inferior good.
When the price falls from P1 to P2, the quantity demanded by a consumer increases from q1 to q2. The
substitution effect increases quantity demanded from q1 to qs. But the income effect reduces quantity
demanded from qs to q2; the substitution effect is stronger than the income effect. The result is consist-
ent with the law of demand: A reduction in price increases the quantity demanded. The quantity de-
manded is smaller, however, than it would be if the good were normal. Inferior goods are therefore
likely to have less elastic demand than normal goods.

K E Y T A K E A W A Y S

< Individual demand curves reflect utility-maximizing adjustment by consumers to changes in price.

< Market demand curves are found by summing horizontally the demand curves of all the consumers in the market.

< The substitution effect of a price change changes consumption in a direction opposite to the price change.

< The income effect of a price change reinforces the substitution effect if the good is normal; it moves consumption in the opposite direction if the good is inferior.

178 PRINCIPLES OF ECONOMICS VERSION 3.0

T R Y I T !

Ilana Drakulic has an entertainment budget of $200 per semester, which she divides among purchasing CDs,
going to concerts, eating in restaurants, and so forth. When the price of CDs fell from $20 to $10, her pur-
chases rose from 5 per semester to 10 per semester. When asked how many she would have bought if her
budget constraint were $150 (since with $150 she could continue to buy 5 CDs and as before still have $100
for spending on other items), she said she would have bought 8 CDs. What is the size of her substitution
effect? Her income effect? Are CDs normal or inferior for her? Which exhibit, Figure 7.4 or Figure 7.5, depicts
more accurately her demand curve for CDs?

Case in Point: Found! An Upward-Sloping Demand Curve

The fact that income and substitution effects move in opposite directions in the case of inferior goods raises a
tantalizing possibility: What if the income effect were the stronger of the two? Could demand curves be up-
ward sloping?

The answer, from a theoretical point of view, is yes. If the income effect in Figure 7.5 were larger than the sub-
stitution effect, the decrease in price would reduce the quantity demanded below q1. The result would be a
reduction in quantity demanded in response to a reduction in price. The demand curve would be upward
sloping!

The suggestion that a good could have an upward-sloping demand curve is generally attributed to Robert
Giffen, a British journalist who wrote widely on economic matters late in the nineteenth century. Such goods
are thus called Giffen goods. To qualify as a Giffen good, a good must be inferior and must have an income
effect strong enough to overcome the substitution effect. The example often cited of a possible Giffen good is
the potato during the Irish famine of 1845–1849. Empirical analysis by economists using available data,
however, has refuted the notion of the upward-sloping demand curve for potatoes at that time. The most
convincing parts of the refutation were to point out that (a) given the famine, there were not more potatoes
available for purchase then and (b) the price of potatoes may not have even increased during the period!

A recent study by Robert Jensen and Nolan Miller, though, suggests the possible discovery of at least one
Giffen good. They began their search by thinking about the type of good that would be likely to exhibit Giffen
behavior and argued that, like potatoes for the poor Irish, it would be a main dietary staple of a poor popula-
tion. In such a situation, purchases of the item are such a large percentage of the diet of the poor that when
the item’s price rises, the implicit income of the poor falls drastically. In order to subsist, the poor reduce con-
sumption of other goods so they can buy more of the staple. In so doing, they are able to reach a caloric in-
take that is higher than what can be achieved by buying more of other preferred foods that unfortunately sup-
ply fewer calories.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 179

Their empirical work shows that in Hunan province in southern China rice is a Giffen good for poor consumers.
Rice provides calories at a relatively low cost and dominates the diet, while meat is considered the tastier but
higher cost-per-calorie food. In order to look at individual household decision making, they conducted a field
experiment in which randomly selected poor households were given vouchers, redeemable with local mer-
chants, for price reductions of varying sizes on the staple good. Households and merchants were given explicit
instructions that selling the vouchers for cash or reselling the staple good would result in dismissal from the
program and audits of the program seemed to confirm that participants were conforming to the ground rules.
Overall about 1,300 households participated. Households also completed a detailed questionnaire reporting
what they ate and drank, as well as other characteristics of the family on income, employment, other expendit-
ures, and the like. They then divided the households into two categories: 1) those who were so poor that, prior
to the experiment, almost all of their calories were from the staple good (Households in this category would
not be expected to show Giffen behavior because their extreme poverty gives them no choice but to con-
sume less of the staple when its price rises.) and 2) those who were somewhat less poor in the sense that, prior
to the experiment, they got at least 20% of their calories from sources other than the staple good. Households
in this “poor-but-not-too-poor” group exhibited Giffen behavior. In particular, they estimated that a 1% in-
crease in the price of rice leads to a 0.45% increase in rice consumption.

A similar experiment by the authors on wheat consumption in Gansu province in northern China showed less
evidence of its being a Giffen good, probably because there are more substitutes available for the specific
form of wheat—wheat flour used to make wheat-based foods in the home—that was the subject of the ex-
periment. In Gansu, people also consume wheat noodles at restaurants or road-side stands or buy wheat-
based products from stores in prepared forms. A study by David McKenzie tested whether tortillas were a
Giffen good for poor Mexicans. He found that they were an inferior good but not a Giffen good and similarly
speculated that the availability of substitutes was the likely reason.

Jensen and Miller argue that despite the fact that their research is the first to uncover a real example of a
Giffen good, other examples are likely waiting to be discovered in areas of the world where the population is
poor but not-too-poor and where there are few substitutes for the staple good.

Sources: Based on Robert Jensen and Nolan Miller, “Giffen Behavior and Subsistence Consumption,” American Economic Review 98:4 (2008):
1553–1577; David McKenzie, “Are Tortillas a Giffen Good in Mexico?” Economics Bulletin 15:1 (2002): 1–7.

A N S W E R T O T R Y I T ! P R O B L E M

One hundred fifty dollars is the income that allows Ms. Drakulic to purchase the same items as before, and
thus can be used to measure the substitution effect. Looking only at the income-compensated price change
(that is, holding her to the same purchasing power as in the original relative price situation), we find that the
substitution effect is 3 more CDs (from 5 to 8). The CDs that she buys beyond 8 constitute her income effect; it
is 2 CDs. Because the income effect reinforces the substitution effect, CDs are a normal good for her and her
demand curve is similar to that shown in Figure 7.4.

3. INDIFFERENCE CURVE ANALYSIS: AN ALTERNATIVE
APPROACH TO UNDERSTANDING CONSUMER CHOICE

L E A R N I N G O B J E C T I V E S

1. Explain utility maximization using the concepts of indifference curves and budget lines.
2. Explain the notion of the marginal rate of substitution and how it relates to the utility-maximiz-

ing solution.
3. Derive a demand curve from an indifference map.

Economists typically use a different set of tools than those presented in the chapter up to this point to
analyze consumer choices. While somewhat more complex, the tools presented in this section give us a
powerful framework for assessing consumer choices.

We will begin our analysis with an algebraic and graphical presentation of the budget constraint.
We will then examine a new concept that allows us to draw a map of a consumer’s preferences. Then
we can draw some conclusions about the choices a utility-maximizing consumer could be expected to
make.

180 PRINCIPLES OF ECONOMICS VERSION 3.0

budget line

Graphically shows the
combinations of two goods a
consumer can buy with a
given budget.

3.1 The Budget Line
As we have already seen, a consumer’s choices are limited by the budget available. Total spending for
goods and services can fall short of the budget constraint but may not exceed it.

Algebraically, we can write the budget constraint for two goods X and Y as:

EQUATION 7.7
PXQX + PYQY ≤ B

where PX and PY are the prices of goods X and Y and QX and QY are the quantities of goods X and
Y chosen. The total income available to spend on the two goods is B, the consumer’s budget. Equation
7.7 states that total expenditures on goods X and Y (the left-hand side of the equation) cannot exceed
B.

Suppose a college student, Janet Bain, enjoys skiing and horseback riding. A day spent pursuing
either activity costs $50. Suppose she has $250 available to spend on these two activities each semester.
Ms. Bain’s budget constraint is illustrated in Figure 7.6.

For a consumer who buys only two goods, the budget constraint can be shown with a budget line.
A budget line shows graphically the combinations of two goods a consumer can buy with a given
budget.

The budget line shows all the combinations of skiing and horseback riding Ms. Bain can purchase
with her budget of $250. She could also spend less than $250, purchasing combinations that lie below
and to the left of the budget line in Figure 7.6. Combinations above and to the right of the budget line
are beyond the reach of her budget.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 181

FIGURE 7.6 The Budget Line

The budget line shows combinations of the skiing and horseback riding Janet Bain could consume if the price of
each activity is $50 and she has $250 available for them each semester. The slope of this budget line is −1, the
negative of the price of horseback riding divided by the price of skiing.

The vertical intercept of the budget line (point D) is given by the number of days of skiing per month
that Ms. Bain could enjoy, if she devoted all of her budget to skiing and none to horseback riding. She
has $250, and the price of a day of skiing is $50. If she spent the entire amount on skiing, she could ski
5 days per semester. She would be meeting her budget constraint, since:

$50 × 0 + $50 × 5 = $250

The horizontal intercept of the budget line (point E) is the number of days she could spend horseback
riding if she devoted her $250 entirely to that sport. She could purchase 5 days of either skiing or horse-
back riding per semester. Again, this is within her budget constraint, since:

$50 × 5 + $50 × 0 = $250

Because the budget line is linear, we can compute its slope between any two points. Between points D
and E the vertical change is −5 days of skiing; the horizontal change is 5 days of horseback riding. The
slope is thus − 5 / 5 = − 1 . More generally, we find the slope of the budget line by finding the vertical
and horizontal intercepts and then computing the slope between those two points. The vertical inter-
cept of the budget line is found by dividing Ms. Bain’s budget, B, by the price of skiing, the good on the
vertical axis (PS). The horizontal intercept is found by dividing B by the price of horseback riding, the
good on the horizontal axis (PH). The slope is thus:

182 PRINCIPLES OF ECONOMICS VERSION 3.0

indifference curve

Graph that shows
combinations of two goods
that yield equal levels of
utility.

EQUATION 7.8

Slope = −
B / PS
B / PH

Simplifying this equation, we obtain

EQUATION 7.9

Slope = − B
PS

×
PH
B = −

PH
PS

After canceling, Equation 7.9 shows that the slope of a budget line is the negative of the price of the
good on the horizontal axis divided by the price of the good on the vertical axis.

Heads Up!

It is easy to go awry on the issue of the slope of the budget line: It is the negative of the price of the good on
the horizontal axis divided by the price of the good on the vertical axis. But does not slope equal the change in
the vertical axis divided by the change in the horizontal axis? The answer, of course, is that the definition of
slope has not changed. Notice that Equation 7.8 gives the vertical change divided by the horizontal change
between two points. We then manipulated Equation 7.8 a bit to get to Equation 7.9 and found that slope also
equaled the negative of the price of the good on the horizontal axis divided by the price of the good on the
vertical axis. Price is not the variable that is shown on the two axes. The axes show the quantities of the two
goods.

3.2 Indifference Curves
Suppose Ms. Bain spends 2 days skiing and 3 days horseback riding per semester. She will derive some
level of total utility from that combination of the two activities. There are other combinations of the
two activities that would yield the same level of total utility. Combinations of two goods that yield equal
levels of utility are shown on an indifference curve.[2] Because all points along an indifference curve
generate the same level of utility, economists say that a consumer is indifferent between them.

Figure 7.7 shows an indifference curve for combinations of skiing and horseback riding that yield
the same level of total utility. Point X marks Ms. Bain’s initial combination of 2 days skiing and 3 days
horseback riding per semester. The indifference curve shows that she could obtain the same level of
utility by moving to point W, skiing for 7 days and going horseback riding for 1 day. She could also get
the same level of utility at point Y, skiing just 1 day and spending 5 days horseback riding. Ms. Bain is
indifferent among combinations W, X, and Y. We assume that the two goods are divisible, so she is in-
different between any two points along an indifference curve.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 183

FIGURE 7.7 An Indifference Curve

The indifference curve A shown here gives combinations of skiing and horseback riding that produce the same
level of utility. Janet Bain is thus indifferent to which point on the curve she selects. Any point below and to the left
of the indifference curve would produce a lower level of utility; any point above and to the right of the indifference
curve would produce a higher level of utility.

Now look at point T in Figure 7.7. It has the same amount of skiing as point X, but fewer days are spent
horseback riding. Ms. Bain would thus prefer point X to point T. Similarly, she prefers X to U. What
about a choice between the combinations at point W and point T? Because combinations X and W are
equally satisfactory, and because Ms. Bain prefers X to T, she must prefer W to T. In general, any com-
bination of two goods that lies below and to the left of an indifference curve for those goods yields less
utility than any combination on the indifference curve. Such combinations are inferior to combinations
on the indifference curve.

Point Z, with 3 days of skiing and 4 days of horseback riding, provides more of both activities than
point X; Z therefore yields a higher level of utility. It is also superior to point W. In general, any com-
bination that lies above and to the right of an indifference curve is preferred to any point on the in-
difference curve.

We can draw an indifference curve through any combination of two goods. Figure 7.8 shows in-
difference curves drawn through each of the points we have discussed. Indifference curve A from Fig-
ure 7.7 is inferior to indifference curve B. Ms. Bain prefers all the combinations on indifference curve B
to those on curve A, and she regards each of the combinations on indifference curve C as inferior to
those on curves A and B.

Although only three indifference curves are shown in Figure 7.8, in principle an infinite number
could be drawn. The collection of indifference curves for a consumer constitutes a kind of map illus-
trating a consumer’s preferences. Different consumers will have different maps. We have good reason

184 PRINCIPLES OF ECONOMICS VERSION 3.0

to expect the indifference curves for all consumers to have the same basic shape as those shown here:
They slope downward, and they become less steep as we travel down and to the right along them.

FIGURE 7.8 Indifference Curves

Each indifference curve suggests combinations among which the consumer is indifferent. Curves that are higher
and to the right are preferred to those that are lower and to the left. Here, indifference curve B is preferred to curve
A, which is preferred to curve C.

The slope of an indifference curve shows the rate at which two goods can be exchanged without affect-
ing the consumer’s utility. Figure 7.9 shows indifference curve C from Figure 7.8. Suppose Ms. Bain is
at point S, consuming 4 days of skiing and 1 day of horseback riding per semester. Suppose she spends
another day horseback riding. This additional day of horseback riding does not affect her utility if she
gives up 2 days of skiing, moving to point T. She is thus willing to give up 2 days of skiing for a second
day of horseback riding. The curve shows, however, that she would be willing to give up at most 1 day
of skiing to obtain a third day of horseback riding (shown by point U).

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 185

marginal rate of
substitution

The maximum amount of
one good a consumer would
be willing to give up in order
to obtain an additional unit of
another.

FIGURE 7.9 The Marginal Rate of Substitution

The marginal rate of substitution is equal to the absolute value of the slope of an indifference curve. It is the
maximum amount of one good a consumer is willing to give up to obtain an additional unit of another. Here, it is
the number of days of skiing Janet Bain would be willing to give up to obtain an additional day of horseback riding.
Notice that the marginal rate of substitution (MRS) declines as she consumes more and more days of horseback
riding.

The maximum amount of one good a consumer would be willing to give up in order to obtain an addi-
tional unit of another is called the marginal rate of substitution (MRS), which is equal to the abso-
lute value of the slope of the indifference curve between two points. Figure 7.9 shows that as Ms. Bain
devotes more and more time to horseback riding, the rate at which she is willing to give up days of ski-
ing for additional days of horseback riding—her marginal rate of substitution—diminishes.

3.3 The Utility-Maximizing Solution
We assume that each consumer seeks the highest indifference curve possible. The budget line gives the
combinations of two goods that the consumer can purchase with a given budget. Utility maximization
is therefore a matter of selecting a combination of two goods that satisfies two conditions:

1. The point at which utility is maximized must be within the attainable region defined by the
budget line.

2. The point at which utility is maximized must be on the highest indifference curve consistent with
condition 1.

186 PRINCIPLES OF ECONOMICS VERSION 3.0

FIGURE 7.10 The Utility-Maximizing
Solution

Combining Janet Bain’s budget line and
indifference curves from Figure 7.6 and Figure
7.8, we find a point that (1) satisfies the budget
constraint and (2) is on the highest
indifference curve possible. That occurs for Ms.
Bain at point X.

FIGURE 7.11 Applying the Marginal
Decision Rule

Suppose Ms. Bain is initially at point S. She is
spending all of her budget, but she is not
maximizing utility. Because her marginal rate of
substitution exceeds the rate at which the
market asks her to give up skiing for horseback
riding, she can increase her satisfaction by
moving to point D. Now she is on a higher
indifference curve, E. She will continue
exchanging skiing for horseback riding until
she reaches point X, at which she is on curve A,
the highest indifference curve possible.

Figure 7.10 combines Janet Bain’s budget line from Figure 7.6 with her indifference curves from Figure
7.8. Our two conditions for utility maximization are satisfied at point X, where she skis 2 days per
semester and spends 3 days horseback riding.

The highest indifference curve possible for a given budget line is tangent to the
line; the indifference curve and budget line have the same slope at that point. The abso-
lute value of the slope of the indifference curve shows the MRS between two goods. The
absolute value of the slope of the budget line gives the price ratio between the two
goods; it is the rate at which one good exchanges for another in the market. At the
point of utility maximization, then, the rate at which the consumer is willing to ex-
change one good for another equals the rate at which the goods can be exchanged in
the market. For any two goods X and Y, with good X on the horizontal axis and good Y
on the vertical axis,

EQUATION 7.10

MRSX,Y =
PX
PY

3.4 Utility Maximization and the Marginal Decision Rule
How does the achievement of The Utility Maximizing Solution in Figure 7.10 corres-
pond to the marginal decision rule? That rule says that additional units of an activity
should be pursued, if the marginal benefit of the activity exceeds the marginal cost. The
observation of that rule would lead a consumer to the highest indifference curve pos-
sible for a given budget.

Suppose Ms. Bain has chosen a combination of skiing and horseback riding at
point S in Figure 7.11. She is now on indifference curve C. She is also on her budget
line; she is spending all of the budget, $250, available for the purchase of the two goods.

An exchange of two days of skiing for one day of horseback riding would leave her
at point T, and she would be as well off as she is at point S. Her marginal rate of substi-
tution between points S and T is 2; her indifference curve is steeper than the budget line
at point S. The fact that her indifference curve is steeper than her budget line tells us
that the rate at which she is willing to exchange the two goods differs from the rate the
market asks. She would be willing to give up as many as 2 days of skiing to gain an extra
day of horseback riding; the market demands that she give up only one. The marginal
decision rule says that if an additional unit of an activity yields greater benefit than its
cost, it should be pursued. If the benefit to Ms. Bain of one more day of horseback rid-
ing equals the benefit of 2 days of skiing, yet she can get it by giving up only 1 day of
skiing, then the benefit of that extra day of horseback riding is clearly greater than the
cost.

Because the market asks that she give up less than she is willing to give up for an
additional day of horseback riding, she will make the exchange. Beginning at point S,
she will exchange a day of skiing for a day of horseback riding. That moves her along
her budget line to point D. Recall that we can draw an indifference curve through any
point; she is now on indifference curve E. It is above and to the right of indifference
curve C, so Ms. Bain is clearly better off. And that should come as no surprise. When
she was at point S, she was willing to give up 2 days of skiing to get an extra day of
horseback riding. The market asked her to give up only one; she got her extra day of
riding at a bargain! Her move along her budget line from point S to point D suggests a
very important principle. If a consumer’s indifference curve intersects the budget line,
then it will always be possible for the consumer to make exchanges along the budget
line that move to a higher indifference curve. Ms. Bain’s new indifference curve at point
D also intersects her budget line; she’s still willing to give up more skiing than the mar-
ket asks for additional riding. She will make another exchange and move along her
budget line to point X, at which she attains the highest indifference curve possible with
her budget. Point X is on indifference curve A, which is tangent to the budget line.

Having reached point X, Ms. Bain clearly would not give up still more days of ski-
ing for additional days of riding. Beyond point X, her indifference curve is flatter than
the budget line—her marginal rate of substitution is less than the absolute value of the
slope of the budget line. That means that the rate at which she would be willing to exchange skiing for
horseback riding is less than the market asks. She cannot make herself better off than she is at point X
by further rearranging her consumption. Point X, where the rate at which she is willing to exchange
one good for another equals the rate the market asks, gives her the maximum utility possible.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 187

3.5 Utility Maximization and Demand
Figure 7.11 showed Janet Bain’s utility-maximizing solution for skiing and horseback riding. She
achieved it by selecting a point at which an indifference curve was tangent to her budget line. A change
in the price of one of the goods, however, will shift her budget line. By observing what happens to the
quantity of the good demanded, we can derive Ms. Bain’s demand curve.

Panel (a) of Figure 7.12 shows the original solution at point X, where Ms. Bain has $250 to spend
and the price of a day of either skiing or horseback riding is $50. Now suppose the price of horseback
riding falls by half, to $25. That changes the horizontal intercept of the budget line; if she spends all of
her money on horseback riding, she can now ride 10 days per semester. Another way to think about the
new budget line is to remember that its slope is equal to the negative of the price of the good on the ho-
rizontal axis divided by the price of the good on the vertical axis. When the price of horseback riding
(the good on the horizontal axis) goes down, the budget line becomes flatter. Ms. Bain picks a new
utility-maximizing solution at point Z.

188 PRINCIPLES OF ECONOMICS VERSION 3.0

FIGURE 7.12 Utility Maximization and Demand

By observing a consumer’s response to a change in price, we can derive the consumer’s demand curve for a good.
Panel (a) shows that at a price for horseback riding of $50 per day, Janet Bain chooses to spend 3 days horseback
riding per semester. Panel (b) shows that a reduction in the price to $25 increases her quantity demanded to 4 days
per semester. Points X and Z, at which Ms. Bain maximizes utility at horseback riding prices of $50 and $25,
respectively, become points X′ and Z′ on her demand curve, d, for horseback riding in Panel (b).

The solution at Z involves an increase in the number of days Ms. Bain spends horseback riding. Notice
that only the price of horseback riding has changed; all other features of the utility-maximizing solu-
tion remain the same. Ms. Bain’s budget and the price of skiing are unchanged; this is reflected in the
fact that the vertical intercept of the budget line remains fixed. Ms. Bain’s preferences are unchanged;
they are reflected by her indifference curves. Because all other factors in the solution are unchanged, we
can determine two points on Ms. Bain’s demand curve for horseback riding from her indifference
curve diagram. At a price of $50, she maximized utility at point X, spending 3 days horseback riding

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 189

per semester. When the price falls to $25, she maximizes utility at point Z, riding 4 days per semester.
Those points are plotted as points X′ and Z′ on her demand curve for horseback riding in Panel (b) of
Figure 7.12.

K E Y T A K E A W A Y S

< A budget line shows combinations of two goods a consumer is able to consume, given a budget constraint.

< An indifference curve shows combinations of two goods that yield equal satisfaction.

< To maximize utility, a consumer chooses a combination of two goods at which an indifference curve is tangent to the budget line.

< At the utility-maximizing solution, the consumer’s marginal rate of substitution (the absolute value of the slope of the indifference curve) is equal to the price ratio of the two goods.

< We can derive a demand curve from an indifference map by observing the quantity of the good consumed at different prices.

190 PRINCIPLES OF ECONOMICS VERSION 3.0

T R Y I T !

1. Suppose a consumer has a budget for fast-food items of $20 per week and spends this money on two
goods, hamburgers and pizzas. Suppose hamburgers cost $5 each and pizzas cost $10. Put the quantity of
hamburgers purchased per week on the horizontal axis and the quantity of pizzas purchased per week on
the vertical axis. Draw the budget line. What is its slope?

2. Suppose the consumer in part (a) is indifferent among the combinations of hamburgers and pizzas
shown. In the grid you used to draw the budget lines, draw an indifference curve passing through the
combinations shown, and label the corresponding points A, B, and C. Label this curve I.

Combination Hamburgers/week Pizzas/week

A 5 0

B 3 ½

C 0 3

3. The budget line is tangent to indifference curve I at B. Explain the meaning of this tangency.

Case in Point: Preferences Prevail in P.O.W. Camps

Economist R. A. Radford spent time in prisoner of war (P.O.W.) camps in Italy and Germany during World War II.
He put this unpleasant experience to good use by testing a number of economic theories there. Relevant to
this chapter, he consistently observed utility-maximizing behavior.

In the P.O.W. camps where he stayed, prisoners received rations, provided by their captors and the Red Cross,
including tinned milk, tinned beef, jam, butter, biscuits, chocolate, tea, coffee, cigarettes, and other items.
While all prisoners received approximately equal official rations (though some did manage to receive private
care packages as well), their marginal rates of substitution between goods in the ration packages varied. To in-
crease utility, prisoners began to engage in trade.

Prices of goods tended to be quoted in terms of cigarettes. Some camps had better organized markets than
others but, in general, even though prisoners of each nationality were housed separately, so long as they
could wander from bungalow to bungalow, the “cigarette” prices of goods were equal across bungalows.
Trade allowed the prisoners to maximize their utility.

Consider coffee and tea. Panel (a) shows the indifference curves and budget line for typical British prisoners
and Panel (b) shows the indifference curves and budget line for typical French prisoners. Suppose the price of
an ounce of tea is 2 cigarettes and the price of an ounce of coffee is 1 cigarette. The slopes of the budget lines
in each panel are identical; all prisoners faced the same prices. The price ratio is 1/2.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 191

Suppose the ration packages given to all prisoners contained the same amounts of both coffee and tea. But
notice that for typical British prisoners, given indifference curves which reflect their general preference for tea,
the MRS at the initial allocation (point A) is less than the price ratio. For French prisoners, the MRS is greater
than the price ratio (point B). By trading, both British and French prisoners can move to higher indifference
curves. For the British prisoners, the utility-maximizing solution is at point E, with more tea and little coffee. For
the French prisoners the utility-maximizing solution is at point E′, with more coffee and less tea. In equilibrium,
both British and French prisoners consumed tea and coffee so that their MRS’s equal 1/2, the price ratio in the
market.

Source: Based on R. A. Radford, “The Economic Organisation of a P.O.W. Camp,” Economica 12 (November 1945): 189–201; and Jack Hirshleifer, Price
Theory and Applications (Englewood Cliffs, NJ: Prentice Hall, 1976): 85–86.

A N S W E R S T O T R Y I T ! P R O B L E M S

1. The budget line is shown in Panel (a). Its slope is −$5/$10 = −0.5.

2. Panel (b) shows indifference curve I. The points A, B, and C on I have been labeled.

3. The tangency point at B shows the combinations of hamburgers and pizza that maximize the consumer’s
utility, given the budget constraint. At the point of tangency, the marginal rate of substitution (MRS)
between the two goods is equal to the ratio of prices of the two goods. This means that the rate at which
the consumer is willing to exchange one good for another equals the rate at which the goods can be
exchanged in the market.

192 PRINCIPLES OF ECONOMICS VERSION 3.0

4. REVIEW AND PRACTICE

Summary

In this chapter we have examined the model of utility-maximizing behavior. Economists assume that con-
sumers make choices consistent with the objective of achieving the maximum total utility possible for a given
budget constraint.

Utility is a conceptual measure of satisfaction; it is not actually measurable. The theory of utility maximization
allows us to ask how a utility-maximizing consumer would respond to a particular event.

By following the marginal decision rule, consumers will achieve the utility-maximizing condition: Expenditures
equal consumers’ budgets, and ratios of marginal utility to price are equal for all pairs of goods and services.
Thus, consumption is arranged so that the extra utility per dollar spent is equal for all goods and services. The
marginal utility from a particular good or service eventually diminishes as consumers consume more of it dur-
ing a period of time.

Utility maximization underlies consumer demand. The amount by which the quantity demanded changes in
response to a change in price consists of a substitution effect and an income effect. The substitution effect al-
ways changes quantity demanded in a manner consistent with the law of demand. The income effect of a
price change reinforces the substitution effect in the case of normal goods, but it affects consumption in an
opposite direction in the case of inferior goods.

An alternative approach to utility maximization uses indifference curves. This approach does not rely on the
concept of marginal utility, and it gives us a graphical representation of the utility-maximizing condition.

C O N C E P T P R O B L E M S

1. Suppose you really, really like ice cream. You adore ice cream. Does the law of diminishing marginal utility
apply to your ice cream consumption?

2. If two commodities that you purchase on a regular basis carry the same price, does that mean they both
provide the same total utility? Marginal utility?

3. If a person goes to the bowling alley planning to spend $15 but comes away with $5, what, if anything,
can you conclude about the marginal utility of the alternatives (for example, bowl another line, have a
soda or a sandwich) available to the person at the time he or she leaves?

4. Which do you like more—going to the movies or watching rented DVDs at home? If you engage in both
activities during the same period, say a week, explain why.

5. Do you tend to eat more at a fixed-price buffet or when ordering from an a la carte menu? Explain, using
the marginal decision rule that guides your behavior.

6. Suppose there is a bill to increase the tax on cigarettes by $1 per pack coupled with an income tax cut of
$500. Suppose a person smokes an average of 500 packs of cigarettes per year—and would thus face a tax
increase of about $500 per year from the cigarette tax at the person’s current level of consumption. The
income tax measure would increase the person’s after-tax income by $500. Would the combined
measures be likely to have any effect on the person’s consumption of cigarettes? Why or why not?

7. How does an increase in income affect a consumer’s budget line? His or her total utility?

8. Why can Ms. Bain not consume at point Y in Figure 7.10?

9. Suppose Ms. Bain is now consuming at point V in Figure 7.10. Use the marginal decision rule to explain
why a shift to X would increase her utility.

10. Suppose that you are a utility maximizer and so is your economics instructor. What can you conclude
about your respective marginal rates of substitution for movies and concerts?

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 193

N U M E R I C A L P R O B L E M S

1. The table shows the total utility Joseph derives from eating pizza in the evening while studying.

Pieces of pizza/evening Total Utility

0 0

1 30

2 48

3 60

4 70

5 78

6 80

7 76

a. How much marginal utility does Joseph derive from the third piece of pizza?

b. After eating how many pieces of pizza does marginal utility start to decline?

c. If the pizza were free, what is the maximum number of pieces Joseph would eat in an evening?

d. On separate diagrams, construct Joseph’s total utility and marginal utility curves for pizza. Does
the law of diminishing marginal utility hold? How do you know?

2. Suppose the marginal utility of good A is 20 and its price is $4, and the marginal utility of good B is 50 and
its price is $5. The individual to whom this information applies is spending $20 on each good. Is he or she
maximizing satisfaction? If not, what should the individual do to increase total satisfaction? On the basis of
this information, can you pick an optimum combination? Why or why not?

3. John and Marie settle down to watch the evening news. Marie is content to watch the entire program,
while John continually switches channels in favor of possible alternatives. Draw the likely marginal utility
curves for watching the evening news for the two individuals. Whose marginal utility curve is likely to be
steeper?

4. Li, a very careful maximizer of utility, consumes two services, going to the movies and bowling. She has
arranged her consumption of the two activities so that the marginal utility of going to a movie is 20 and
the marginal utility of going bowling is 10. The price of going to a movie is $10, and the price of going
bowling is $5. Show that she is satisfying the requirement for utility maximization. Now show what
happens when the price of going bowling rises to $10.

5. The table shows the total utility (TU) that Jeremy receives from consuming different amounts of two
goods, X and Y, per month.

Quantity TU X MU X MUX/PX TU Y MU Y MUY/PY

0 0 0

1 50 75

2 88 117

3 121 153

4 150 181

5 175 206

6 196 225

7 214 243

8 229 260

9 241 276

a. Fill in the other columns of the table by calculating the marginal utilities for goods X and Y and
the ratios of marginal utilities to price for the two goods. Assume that the price of both goods X
and Y is $3. Be sure to use the “midpoint convention” when you fill out the table.

b. If Jeremy allocates $30 to spend on both goods, how many units will he buy of each?

c. How much will Jeremy spend on each good at the utility maximizing combination?

d. How much total utility will Jeremy experience by buying the utility-maximizing combination?

e. Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize
his utility now?

f. Draw Jeremy’s demand curve for good Y between the prices of $6 and $3.

194 PRINCIPLES OF ECONOMICS VERSION 3.0

6. Sid is a commuter-student at his college. During the day, he snacks on cartons of yogurt and the “house
special” sandwiches at the Student Center cafeteria. A carton of yogurt costs $1.20; the Student Center
often offers specials on the sandwiches, so their price varies a great deal. Sid has a budget of $36 per week
for food at the Center. Five of Sid’s indifference curves are given by the schedule below; the points listed in
the tables correspond to the points shown in the graph.

a. Use the set of Sid’s indifference curves shown as a guide in drawing your own graph grid. Draw
Sid’s indifference curves and budget line, assuming sandwiches cost $3.60. Identify the point at
which he maximizes utility. How many sandwiches will he consume? How many cartons of
yogurt? (Hint: All of the answers in this exercise occur at one of the combinations given in the
tables on this page.)

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 195

b. Now suppose the price of sandwiches is cut to $1.20. Draw the new budget line. Identify the
point at which Sid maximizes utility. How many sandwiches will he consume? How many cartons
of yogurt?

c. Now draw the budget lines implied by a price of yogurt of $1.20 and sandwich prices of $0.90
and $1.80. With the observations you’ve already made for sandwich prices of $3.60 and $1.20,
draw the demand curve. Explain how this demand curve illustrates the law of demand.

7. Consider a consumer who each week purchases two goods, X and Y. The following table shows three
different combinations of the two goods that lie on three of her indifference curves—A, B, and C.

Indifference
Curve

Quantities of goods X and
Y, respectively

Quantitities of goods X and
Y, respectively

Quantities of goods X and
Y, respectively

A 1 unit of X and 4 of Y 2 units of X and 2 of Y 3 units of X and 1 of Y

B 1 unit of X and 7 of Y 3 units of X and 2 of Y 5 units of X and 1 of Y

C 2 units of X and 5 of Y 4 units of X and 3 of Y 7 units of X and 2 of Y

a. With good X on the horizontal axis and good Y on the vertical axis, draw the implied indifference
curves. Be sure to label all curves and axes completely.

b. On Curve A, what is the marginal rate of substitution (MRS) between the first two combinations of
goods X and Y?

c. Suppose this consumer has $500 available to spend on goods X and Y and that each costs $100.
Add her budget line to the graph you drew in part (a). What is the slope of the budget line?

d. What is the utility-maximizing combination of goods X and Y for this consumer? (Assume in this
exercise that the utility-maximizing combination always occurs at one of the combinations
shown in the table.)

e. What is the MRS at the utility-maximizing combination?

f. Now suppose the price of good X falls to $50. Draw the new budget line onto your graph and
identify the utility-maximizing combination. What is the MRS at the utility-maximizing
combination? How much of each good does she consume?

g. Draw the demand curve for good X between prices of $50 and $100, assuming it is linear in this
range.

196 PRINCIPLES OF ECONOMICS VERSION 3.0

2.ENDNOTES

Francis Y. Edgeworth, Mathematical Psychics: An Essay on the Application of Mathemat-
ics to the Moral Sciences (New York: Augustus M. Kelley, 1967), p. 101. First Published
1881.

Limiting the situation to two goods allows us to show the problem graphically. By
stating the problem of utility maximization with equations, we could extend the ana-
lysis to any number of goods and services.

CHAPTER 7 THE ANALYSIS OF CONSUMER CHOICE 197

Chapter 7: The Analysis of Consumer Choice

Start Up: A Day at the Grocery Store

The Concept of Utility

Total Utility

Marginal Utility

Maximizing Utility

The Budget Constraint

Applying the Marginal Decision Rule

The Problem of Divisibility

Utility Maximization and Demand

Deriving an Individual’s Demand Curve

From Individual to Market Demand

Substitution and Income Effects

Normal and Inferior Goods

Normal Goods

Inferior Goods

Indifference Curve Analysis: An Alternative Approach to Understanding Consumer Choice

The Budget Line

Indifference Curves

The Utility-Maximizing Solution

Utility Maximization and the Marginal Decision Rule

Utility Maximization and Demand

Review and Practice

Endnotes

elasticity

The ratio of the percentage
change in a dependent
variable to a percentage
change in an independent
variable.

C H A P T E R 5
Elasticity: A Measure of
Response
START UP: RAISE FARES? LOWER FARES? WHAT’S A
PUBLIC TRANSIT MANAGER TO DO?
Imagine that you are the manager of the public transportation system for a large metropolitan area. Operating

costs for the system have soared in the last few years, and you are under pressure to boost revenues. What do you

do?

An obvious choice would be to raise fares. That will make your customers angry, but at least it will generate the

extra revenue you need—or will it? The law of demand says that raising fares will reduce the number of passengers

riding on your system. If the number of passengers falls only a little, then the higher fares that your remaining pas-

sengers are paying might produce the higher revenues you need. But what if the number of passengers falls by so

much that your higher fares actually reduce your revenues? If that happens, you will have made your customers

mad and your financial problem worse!

Maybe you should recommend lower fares. After all, the law of demand also says that lower fares will increase

the number of passengers. Having more people use the public transportation system could more than offset a

lower fare you collect from each person. But it might not. What will you do?

Your job and the fiscal health of the public transit system are riding on your making the correct decision. To do

so, you need to know just how responsive the quantity demanded is to a price change. You need a measure of

responsiveness.

Economists use a measure of responsiveness called elasticity. Elasticity is the ratio of the percentage change

in a dependent variable to a percentage change in an independent variable. If the dependent variable is y, and the

independent variable is x, then the elasticity of y with respect to a change in x is given by:

ey, x =
% change in y
% change in x

A variable such as y is said to be more elastic (responsive) if the percentage change in y is large relative to the per-

centage change in x. It is less elastic if the reverse is true.

As manager of the public transit system, for example, you will want to know how responsive the number of

passengers on your system (the dependent variable) will be to a change in fares (the independent variable). The

concept of elasticity will help you solve your public transit pricing problem and a great many other issues in eco-

nomics. We will examine several elasticities in this chapter—all will tell us how responsive one variable is to a

change in another.

price elasticity of demand

The percentage change in
quantity demanded of a
particular good or service
divided by the percentage
change in the price of that
good or service, all other
things unchanged.

1. THE PRICE ELASTICITY OF DEMAND

L E A R N I N G O B J E C T I V E S

1. Explain the concept of price elasticity of demand and its calculation.
2. Explain what it means for demand to be price inelastic, unit price elastic, price elastic, perfectly

price inelastic, and perfectly price elastic.
3. Explain how and why the value of the price elasticity of demand changes along a linear de-

mand curve.
4. Understand the relationship between total revenue and price elasticity of

demand.

5. Discuss the determinants of price elasticity of demand.

We know from the law of demand how the quantity demanded will respond to a price change: it will
change in the opposite direction. But how much will it change? It seems reasonable to expect, for ex-
ample, that a 10% change in the price charged for a visit to the doctor would yield a different percent-
age change in quantity demanded than a 10% change in the price of a Ford Mustang. But how much is
this difference?

To show how responsive quantity demanded is to a change in price, we apply the concept of elasti-
city. The price elasticity of demand for a good or service, eD, is the percentage change in quantity
demanded of a particular good or service divided by the percentage change in the price of that good or
service, all other things unchanged. Thus we can write

E Q U A T I O N 5 . 1

eD =
% change in quantity demanded

% change in price

Because the price elasticity of demand shows the responsiveness of quantity demanded to a price
change, assuming that other factors that influence demand are unchanged, it reflects movements along
a demand curve. With a downward-sloping demand curve, price and quantity demanded move in op-
posite directions, so the price elasticity of demand is always negative. A positive percentage change in
price implies a negative percentage change in quantity demanded, and vice versa. Sometimes you will
see the absolute value of the price elasticity measure reported. In essence, the minus sign is ignored be-
cause it is expected that there will be a negative (inverse) relationship between quantity demanded and
price. In this text, however, we will retain the minus sign in reporting price elasticity of demand and
will say “the absolute value of the price elasticity of demand” when that is what we are describing.

Heads Up!

Be careful not to confuse elasticity with slope. The slope of a line is the change in the value of the variable on
the vertical axis divided by the change in the value of the variable on the horizontal axis between two points.
Elasticity is the ratio of the percentage changes. The slope of a demand curve, for example, is the ratio of the
change in price to the change in quantity between two points on the curve. The price elasticity of demand is
the ratio of the percentage change in quantity to the percentage change in price. As we will see, when com-
puting elasticity at different points on a linear demand curve, the slope is constant—that is, it does not
change—but the value for elasticity will change.

1.1 Computing the Price Elasticity of Demand
Finding the price elasticity of demand requires that we first compute percentage changes in price and
in quantity demanded. We calculate those changes between two points on a demand curve.

Figure 5.1 shows a particular demand curve, a linear demand curve for public transit rides. Sup-
pose the initial price is $0.80, and the quantity demanded is 40,000 rides per day; we are at point A on
the curve. Now suppose the price falls to $0.70, and we want to report the responsiveness of the quant-
ity demanded. We see that at the new price, the quantity demanded rises to 60,000 rides per day (point
B). To compute the elasticity, we need to compute the percentage changes in price and in quantity de-
manded between points A and B.

114 PRINCIPLES OF ECONOMICS VERSION 3.0

arc elasticity

Measure of elasticity based
on percentage changes
relative to the average value
of each variable between two
points.

F I G U R E 5 . 1 Responsiveness and Demand

The demand curve shows how changes in price lead to changes in the quantity demanded. A movement from
point A to point B shows that a $0.10 reduction in price increases the number of rides per day by 20,000. A
movement from B to A is a $0.10 increase in price, which reduces quantity demanded by 20,000 rides per day.

We measure the percentage change between two points as the change in the variable divided by the av-
erage value of the variable between the two points. Thus, the percentage change in quantity between
points A and B in Figure 5.1 is computed relative to the average of the quantity values at points A and
B: (60,000 + 40,000)/2 = 50,000. The percentage change in quantity, then, is 20,000/50,000, or 40%.
Likewise, the percentage change in price between points A and B is based on the average of the two
prices: ($0.80 + $0.70)/2 = $0.75, and so we have a percentage change of −0.10/0.75, or −13.33%. The
price elasticity of demand between points A and B is thus 40%/(−13.33%) = −3.00.

This measure of elasticity, which is based on percentage changes relative to the average value of
each variable between two points, is called arc elasticity. The arc elasticity method has the advantage
that it yields the same elasticity whether we go from point A to point B or from point B to point A. It is
the method we shall use to compute elasticity.

For the arc elasticity method, we calculate the price elasticity of demand using the average value of
price, P̄, and the average value of quantity demanded, Q̄. We shall use the Greek letter Δ to mean
“change in,” so the change in quantity between two points is ΔQ and the change in price is ΔP. Now we
can write the formula for the price elasticity of demand as

E Q U A T I O N 5 . 2

eD =
ΔQ / Q̄
ΔP / P̄

The price elasticity of demand between points A and B is thus:

eD =
20,000

(40,000 + 60,000)/2
-$0.10

($0.80 + $0.70)/2
= 40%-13.33% = -3.00

With the arc elasticity formula, the elasticity is the same whether we move from point A to point B or
from point B to point A. If we start at point B and move to point A, we have:

eD =
-20,000

(60,000 + 40,000)/2
0.10

($0.70 + $0.80)/2
= -40%13.33% = -3.00

The arc elasticity method gives us an estimate of elasticity. It gives the value of elasticity at the mid-
point over a range of change, such as the movement between points A and B. For a precise computa-
tion of elasticity, we would need to consider the response of a dependent variable to an extremely small
change in an independent variable. The fact that arc elasticities are approximate suggests an important

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 115

practical rule in calculating arc elasticities: we should consider only small changes in independent vari-
ables. We cannot apply the concept of arc elasticity to large changes.

Another argument for considering only small changes in computing price elasticities of demand
will become evident in the next section. We will investigate what happens to price elasticities as we
move from one point to another along a linear demand curve.

Heads Up!

Notice that in the arc elasticity formula, the method for computing a percentage change differs from the
standard method with which you may be familiar. That method measures the percentage change in a variable
relative to its original value. For example, using the standard method, when we go from point A to point B, we
would compute the percentage change in quantity as 20,000/40,000 = 50%. The percentage change in price
would be −$0.10/$0.80 = −12.5%. The price elasticity of demand would then be 50%/(−12.5%) = −4.00. Going
from point B to point A, however, would yield a different elasticity. The percentage change in quantity would
be −20,000/60,000, or −33.33%. The percentage change in price would be $0.10/$0.70 = 14.29%. The price
elasticity of demand would thus be −33.33%/14.29% = −2.33. By using the average quantity and average price
to calculate percentage changes, the arc elasticity approach avoids the necessity to specify the direction of
the change and, thereby, gives us the same answer whether we go from A to B or from B to A.

1.2 Price Elasticities Along a Linear Demand Curve
What happens to the price elasticity of demand when we travel along the demand curve? The answer
depends on the nature of the demand curve itself. On a linear demand curve, such as the one in Figure
5.2, elasticity becomes smaller (in absolute value) as we travel downward and to the right.

F I G U R E 5 . 2 Price Elasticities of Demand for a Linear Demand Curve

The price elasticity of demand varies between different pairs of points along a linear demand curve. The lower the price and the greater the quantity
demanded, the lower the absolute value of the price elasticity of demand.

Figure 5.2 shows the same demand curve we saw in Figure 5.1. We have already calculated the price
elasticity of demand between points A and B; it equals −3.00. Notice, however, that when we use the
same method to compute the price elasticity of demand between other sets of points, our answer varies.
For each of the pairs of points shown, the changes in price and quantity demanded are the same (a
$0.10 decrease in price and 20,000 additional rides per day, respectively). But at the high prices and low
quantities on the upper part of the demand curve, the percentage change in quantity is relatively large,
whereas the percentage change in price is relatively small. The absolute value of the price elasticity of
demand is thus relatively large. As we move down the demand curve, equal changes in quantity repres-
ent smaller and smaller percentage changes, whereas equal changes in price represent larger and larger
percentage changes, and the absolute value of the elasticity measure declines. Between points C and D,
for example, the price elasticity of demand is −1.00, and between points E and F the price elasticity of
demand is −0.3

116 PRINCIPLES OF ECONOMICS VERSION 3.0

total revenue

A firm’s output multiplied by
the price at which it sells that
output.

On a linear demand curve, the price elasticity of demand varies depending on the interval over
which we are measuring it. For any linear demand curve, the absolute value of the price elasticity of de-
mand will fall as we move down and to the right along the curve.

1.3 The Price Elasticity of Demand and Changes in Total Revenue
Suppose the public transit authority is considering raising fares. Will its total revenues go up or down?
Total revenue is the price per unit times the number of units sold.[1] In this case, it is the fare times
the number of riders. The transit authority will certainly want to know whether a price increase will
cause its total revenue to rise or fall. In fact, determining the impact of a price change on total revenue
is crucial to the analysis of many problems in economics.

We will do two quick calculations before generalizing the principle involved. Given the demand
curve shown in Figure 5.2, we see that at a price of $0.80, the transit authority will sell 40,000 rides per
day. Total revenue would be $32,000 per day ($0.80 times 40,000). If the price were lowered by $0.10 to
$0.70, quantity demanded would increase to 60,000 rides and total revenue would increase to $42,000
($0.70 times 60,000). The reduction in fare increases total revenue. However, if the initial price had
been $0.30 and the transit authority reduced it by $0.10 to $0.20, total revenue would decrease from
$42,000 ($0.30 times 140,000) to $32,000 ($0.20 times 160,000). So it appears that the impact of a price
change on total revenue depends on the initial price and, by implication, the original elasticity. We
generalize this point in the remainder of this section.

The problem in assessing the impact of a price change on total revenue of a good or service is that
a change in price always changes the quantity demanded in the opposite direction. An increase in price
reduces the quantity demanded, and a reduction in price increases the quantity demanded. The ques-
tion is how much. Because total revenue is found by multiplying the price per unit times the quantity
demanded, it is not clear whether a change in price will cause total revenue to rise or fall.

We have already made this point in the context of the transit authority. Consider the following
three examples of price increases for gasoline, pizza, and diet cola.

Suppose that 1,000 gallons of gasoline per day are demanded at a price of $4.00 per gallon. Total
revenue for gasoline thus equals $4,000 per day (=1,000 gallons per day times $4.00 per gallon). If an
increase in the price of gasoline to $4.25 reduces the quantity demanded to 950 gallons per day, total
revenue rises to $4,037.50 per day (=950 gallons per day times $4.25 per gallon). Even though people
consume less gasoline at $4.25 than at $4.00, total revenue rises because the higher price more than
makes up for the drop in consumption.

Next consider pizza. Suppose 1,000 pizzas per week are demanded at a price of $9 per pizza. Total
revenue for pizza equals $9,000 per week (=1,000 pizzas per week times $9 per pizza). If an increase in
the price of pizza to $10 per pizza reduces quantity demanded to 900 pizzas per week, total revenue will
still be $9,000 per week (=900 pizzas per week times $10 per pizza). Again, when price goes up, con-
sumers buy less, but this time there is no change in total revenue.

Now consider diet cola. Suppose 1,000 cans of diet cola per day are demanded at a price of $0.50
per can. Total revenue for diet cola equals $500 per day (=1,000 cans per day times $0.50 per can). If an
increase in the price of diet cola to $0.55 per can reduces quantity demanded to 880 cans per month,
total revenue for diet cola falls to $484 per day (=880 cans per day times $0.55 per can). As in the case
of gasoline, people will buy less diet cola when the price rises from $0.50 to $0.55, but in this example
total revenue drops.

In our first example, an increase in price increased total revenue. In the second, a price increase left
total revenue unchanged. In the third example, the price rise reduced total revenue. Is there a way to
predict how a price change will affect total revenue? There is; the effect depends on the price elasticity
of demand.

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 117

price elastic

Situation in which the
absolute value of the price
elasticity of demand is
greater than

unit price elastic

Situation in which the
absolute value of the price
elasticity of demand is equal
to 1.

price inelastic

Situation in which the
absolute value of the price of
elasticity of demand is less
than 1.

Elastic, Unit Elastic, and Inelastic Demand

To determine how a price change will affect total revenue, economists place price elasticities of demand
in three categories, based on their absolute value. If the absolute value of the price elasticity of demand
is greater than 1, demand is termed price elastic. If it is equal to 1, demand is unit price elastic. And
if it is less than 1, demand is price inelastic.

Relating Elasticity to Changes in Total Revenue

When the price of a good or service changes, the quantity demanded changes in the opposite direction.
Total revenue will move in the direction of the variable that changes by the larger percentage. If the
variables move by the same percentage, total revenue stays the same. If quantity demanded changes by
a larger percentage than price (i.e., if demand is price elastic), total revenue will change in the direction
of the quantity change. If price changes by a larger percentage than quantity demanded (i.e., if demand
is price inelastic), total revenue will move in the direction of the price change. If price and quantity de-
manded change by the same percentage (i.e., if demand is unit price elastic), then total revenue does
not change.

When demand is price inelastic, a given percentage change in price results in a smaller percentage
change in quantity demanded. That implies that total revenue will move in the direction of the price
change: a reduction in price will reduce total revenue, and an increase in price will increase it.

Consider the price elasticity of demand for gasoline. In the example above, 1,000 gallons of gasol-
ine were purchased each day at a price of $4.00 per gallon; an increase in price to $4.25 per gallon re-
duced the quantity demanded to 950 gallons per day. We thus had an average quantity of 975 gallons
per day and an average price of $4.125. We can thus calculate the arc price elasticity of demand for
gasoline:

Percentage change in quantity demanded = −50 / 975 = −5.1%
Percentage change in price = 0.25 / 4.125 = 6.06%
Price elasticity of demand = −5.1% / 6.06% = −0.84

The demand for gasoline is price inelastic, and total revenue moves in the direction of the price change.
When price rises, total revenue rises. Recall that in our example above, total spending on gasoline
(which equals total revenues to sellers) rose from $4,000 per day (=1,000 gallons per day times $4.00) to
$4037.50 per day (=950 gallons per day times $4.25 per gallon).

When demand is price inelastic, a given percentage change in price results in a smaller percentage
change in quantity demanded. That implies that total revenue will move in the direction of the price
change: an increase in price will increase total revenue, and a reduction in price will reduce it.

Consider again the example of pizza that we examined above. At a price of $9 per pizza, 1,000 piz-
zas per week were demanded. Total revenue was $9,000 per week (=1,000 pizzas per week times $9 per
pizza). When the price rose to $10, the quantity demanded fell to 900 pizzas per week. Total revenue
remained $9,000 per week (=900 pizzas per week times $10 per pizza). Again, we have an average
quantity of 950 pizzas per week and an average price of $9.50. Using the arc elasticity method, we can
compute:

Percentage change in quantity demanded = − 100 / 950 = − 10.5%
Percentage change in price = $1.00 / $9.50 = 10.5%
Price elasticity of demand = − 10.5% / 10.5% = − 1.0

Demand is unit price elastic, and total revenue remains unchanged. Quantity demanded falls by the
same percentage by which price increases.

Consider next the example of diet cola demand. At a price of $0.50 per can, 1,000 cans of diet cola
were purchased each day. Total revenue was thus $500 per day (=$0.50 per can times 1,000 cans per
day). An increase in price to $0.55 reduced the quantity demanded to 880 cans per day. We thus have
an average quantity of 940 cans per day and an average price of $0.525 per can. Computing the price
elasticity of demand for diet cola in this example, we have:

Percentage change in quantity demanded = − 120 / 940 = − 12.8%
Percentage change in price = $0.05 / $0.525 = 9.5%
Price elasticity of demand = − 12.8% / 9.5% = − 1.3

The demand for diet cola is price elastic, so total revenue moves in the direction of the quantity change.
It falls from $500 per day before the price increase to $484 per day after the price increase.

A demand curve can also be used to show changes in total revenue. Figure 5.3 shows the demand
curve from Figure 5.1 and Figure 5.2. At point A, total revenue from public transit rides is given by the
area of a rectangle drawn with point A in the upper right-hand corner and the origin in the lower left-

118 PRINCIPLES OF ECONOMICS VERSION 3.0

hand corner. The height of the rectangle is price; its width is quantity. We have already seen that total
revenue at point A is $32,000 ($0.80 × 40,000). When we reduce the price and move to point B, the
rectangle showing total revenue becomes shorter and wider. Notice that the area gained in moving to
the rectangle at B is greater than the area lost; total revenue rises to $42,000 ($0.70 × 60,000). Recall
from Figure 5.2 that demand is elastic between points A and B. In general, demand is elastic in the up-
per half of any linear demand curve, so total revenue moves in the direction of the quantity change.

F I G U R E 5 . 3 Changes in Total Revenue and a Linear Demand Curve

Moving from point A to point B implies a reduction in price and an increase in the quantity demanded. Demand is
elastic between these two points. Total revenue, shown by the areas of the rectangles drawn from points A and B
to the origin, rises. When we move from point E to point F, which is in the inelastic region of the demand curve,
total revenue falls.

A movement from point E to point F also shows a reduction in price and an increase in quantity de-
manded. This time, however, we are in an inelastic region of the demand curve. Total revenue now
moves in the direction of the price change—it falls. Notice that the rectangle drawn from point F is
smaller in area than the rectangle drawn from point E, once again confirming our earlier calculation.

We have noted that a linear demand curve is more elastic where prices are relatively high and quantit-
ies relatively low and less elastic where prices are relatively low and quantities relatively high. We can
be even more specific. For any linear demand curve, demand will be price elastic in the upper half of the
curve and price inelastic in its lower half. At the midpoint of a linear demand curve, demand is unit price
elastic.

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 119

perfectly inelastic

Situation in which the price
elasticity of demand is zero.

perfectly elastic

Situation in which the price
elasticity of demand is
infinite.

1.4 Constant Price Elasticity of Demand Curves
Figure 5.4 shows four demand curves over which price elasticity of demand is the same at all points.
The demand curve in Panel (a) is vertical. This means that price changes have no effect on quantity de-
manded. The numerator of the formula given in Equation 5.1 for the price elasticity of demand
(percentage change in quantity demanded) is zero. The price elasticity of demand in this case is there-
fore zero, and the demand curve is said to be perfectly inelastic. This is a theoretically extreme case,
and no good that has been studied empirically exactly fits it. A good that comes close, at least over a
specific price range, is insulin. A diabetic will not consume more insulin as its price falls but, over some
price range, will consume the amount needed to control the disease.

F I G U R E 5 . 4 Demand Curves with Constant Price Elasticities

The demand curve in Panel (a) is perfectly inelastic. The demand curve in Panel (b) is perfectly elastic. Price elasticity
of demand is −1.00 all along the demand curve in Panel (c), whereas it is −0.50 all along the demand curve in Panel
(d).

As illustrated in Figure 5.4, several other types of demand curves have the same elasticity at every point
on them. The demand curve in Panel (b) is horizontal. This means that even the smallest price changes
have enormous effects on quantity demanded. The denominator of the formula given in Equation 5.1
for the price elasticity of demand (percentage change in price) approaches zero. The price elasticity of
demand in this case is therefore infinite, and the demand curve is said to be perfectly elastic.[2] This is
the type of demand curve faced by producers of standardized products such as wheat. If the wheat of
other farms is selling at $4 per bushel, a typical farm can sell as much wheat as it wants to at $4 but
nothing at a higher price and would have no reason to offer its wheat at a lower price.

120 PRINCIPLES OF ECONOMICS VERSION 3.0

The nonlinear demand curves in Panels (c) and (d) have price elasticities of demand that are neg-
ative; but, unlike the linear demand curve discussed above, the value of the price elasticity is constant
all along each demand curve. The demand curve in Panel (c) has price elasticity of demand equal to
−1.00 throughout its range; in Panel (d) the price elasticity of demand is equal to −0.50 throughout its
range. Empirical estimates of demand often show curves like those in Panels (c) and (d) that have the
same elasticity at every point on the curve.

Heads Up!

Do not confuse price inelastic demand and perfectly inelastic demand. Perfectly inelastic demand means that
the change in quantity is zero for any percentage change in price; the demand curve in this case is vertical.
Price inelastic demand means only that the percentage change in quantity is less than the percentage change
in price, not that the change in quantity is zero. With price inelastic (as opposed to perfectly inelastic) demand,
the demand curve itself is still downward sloping.

1.5 Determinants of the Price Elasticity of Demand
The greater the absolute value of the price elasticity of demand, the greater the responsiveness of
quantity demanded to a price change. What determines whether demand is more or less price elastic?
The most important determinants of the price elasticity of demand for a good or service are the avail-
ability of substitutes, the importance of the item in household budgets, and time.

Availability of Substitutes

The price elasticity of demand for a good or service will be greater in absolute value if many close sub-
stitutes are available for it. If there are lots of substitutes for a particular good or service, then it is easy
for consumers to switch to those substitutes when there is a price increase for that good or service. Sup-
pose, for example, that the price of Ford automobiles goes up. There are many close substitutes for
Fords—Chevrolets, Chryslers, Toyotas, and so on. The availability of close substitutes tends to make
the demand for Fords more price elastic.

If a good has no close substitutes, its demand is likely to be somewhat less price elastic. There are
no close substitutes for gasoline, for example. The price elasticity of demand for gasoline in the inter-
mediate term of, say, three–nine months is generally estimated to be about −0.5. Since the absolute
value of price elasticity is less than 1, it is price inelastic. We would expect, though, that the demand for
a particular brand of gasoline will be much more price elastic than the demand for gasoline in general.

Importance in Household Budgets

One reason price changes affect quantity demanded is that they change how much a consumer can buy;
a change in the price of a good or service affects the purchasing power of a consumer’s income and
thus affects the amount of a good the consumer will buy. This effect is stronger when a good or service
is important in a typical household’s budget.

A change in the price of jeans, for example, is probably more important in your budget than a
change in the price of pencils. Suppose the prices of both were to double. You had planned to buy four
pairs of jeans this year, but now you might decide to make do with two new pairs. A change in pencil
prices, in contrast, might lead to very little reduction in quantity demanded simply because pencils are
not likely to loom large in household budgets. The greater the importance of an item in household
budgets, the greater the absolute value of the price elasticity of demand is likely to be.

Time

Suppose the price of electricity rises tomorrow morning. What will happen to the quantity demanded?
The answer depends in large part on how much time we allow for a response. If we are interested

in the reduction in quantity demanded by tomorrow afternoon, we can expect that the response will be
very small. But if we give consumers a year to respond to the price change, we can expect the response
to be much greater. We expect that the absolute value of the price elasticity of demand will be greater
when more time is allowed for consumer responses.

Consider the price elasticity of crude oil demand. Economists Afshin Javan and Nahl Zahran es-
timated short- and long-run price elasticities of demand for crude oil in twenty-five nations for the
period 1993 to 2012. They found that for virtually every country, the price elasticities were negative and
the long-run price elasticities were greater (in absolute value) than were the short-run price elasticities.
Specifically, the short-run price elasticities ranged from -0.05 to -0.20, while the long run price elasticit-
ies ranged from -0.11 to -0.36. As you can see, the research was reported in a journal published by

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 121

OPEC (Organization of Petroleum Exporting Countries), an organization whose members have
profited greatly from the inelasticity of demand for their product. When it has chosen to restrict out-
put, OPEC, which produces about 40 percent of the world’s crude oil, has been able to put upward
pressure on the price of crude. That has increased OPEC’s (and all other oil producers’) total revenues
and reduced total cost.

T A B L E 5 . 1 Short- and Long-Run Price Elasticities of the Demand for Crude Oil
For most countries, price elasticity of demand for crude oil tends to be greater (in absolute value) in the long run
than in the short run.

Group Country Short-Run Price Elasticity of
Demand

Long-Run Price Elasticity of
Demand

North America United States −0.09 −0.24

Canada −0.06 −0.16

Mexico −0.08 −0.21

Europe Germany -0.11 −0.14

France −0.16 −0.22

Italy −0.20 −0.27

Spain −0.20 −0.28

United
Kingdom

−0.14 −0.19

Turkey -0.14 −0.18

Developed
Asia

Japan −0.16 −0.24

South Korea −0.14 −0.22

Emerging Asia Thailand −0.06 −0.14

Philippines −0.16 −0.36

Latin America Brazil −0.09 −0.19

Argentina −0.05 −0.11

Source: Based on data from Afshin Javan and Nahl Zahran, “Dynamic Panel Data Approaches for Estimating Oil Demand Elasticity,” OPEC Energy

Review 39:1 (March 2015): 62. The estimates are based on data for the period 1993 to 2012. Only countries for which both short-run and long-run

price elasticities of demand were estimated are shown above.

K E Y T A K E A W A Y S

< The price elasticity of demand measures the responsiveness of quantity demanded to changes in price; it is calculated by dividing the percentage change in quantity demanded by the percentage change in price.

< Demand is price inelastic if the absolute value of the price elasticity of demand is less than 1; it is unit price elastic if the absolute value is equal to 1; and it is price elastic if the absolute value is greater than 1.

< Demand is price elastic in the upper half of any linear demand curve and price inelastic in the lower half. It is unit price elastic at the midpoint.

< When demand is price inelastic, total revenue moves in the direction of a price change. When demand is unit price elastic, total revenue does not change in response to a price change. When demand is price elastic, total revenue moves in the direction of a quantity change.

< The absolute value of the price elasticity of demand is greater when substitutes are available, when the good is important in household budgets, and when buyers have more time to adjust to changes in the price of the good.

122 PRINCIPLES OF ECONOMICS VERSION 3.0

T R Y I T !

You are now ready to play the part of the manager of the public transit system. Your finance officer has just
advised you that the system faces a deficit. Your board does not want you to cut service, which means that
you cannot cut costs. Your only hope is to increase revenue. Would a fare increase boost revenue?

You consult the economist on your staff who has researched studies on public transportation elasticities. She
reports that the estimated price elasticity of demand for the first few months after a price change is about
−0.3, but that after several years, it will be about −1.

1. Explain why the estimated values for price elasticity of demand differ.

2. Compute what will happen to ridership and revenue over the next few months if you decide to raise fares
by 5%.

3. Compute what will happen to ridership and revenue over the next few years if you decide to raise fares by
5%.

4. What happens to total revenue now and after several years if you choose to raise fares?

Case in Point: Price Elasticity of Home Water Demand in Phoenix, Arizona

Like many other cities in the U.S. southwest, Phoenix, Arizona grew rapidly in the latter part of the twentieth
and first part of the twenty-first century. Located at the edge of a desert, Phoenix receives on average a mea-
ger eight inches of rain each year. Average temperature is about 75 degrees Fahrenheit and summer days of-
ten see temperatures over 100 degrees. Meeting increased water demand will be a challenge for the city un-
der any circumstance. If the National Resources Defense Council’s prediction of higher temperatures and less
precipitation pans out, the picture gets even worse. Thus, knowing how water consumption responds to price
changes is important for designing policies that will assure sustainable water use over time.

A study by James Yoo, Silvio Simonit, Ann P. Kinzig, and Charles Perrings investigated the price elasticity of res-
idential water demand in Phoenix from 2000 to 2008. Their findings conform closely to expectations regarding
factors that typically affect price elasticity of demand. In particular, with few substitutes for water, they were
expecting a fairly low price elasticity of demand and that it would be higher in absolute value in the long run
compared to the short run. Their estimate of price elasticity between 2000 and 2002 was -0.66. It rose to -1.155
over the interval 2000 to 2008. This suggests that over time consumers can adjust by such changes as buying
appliances with higher water efficiency and by redesigning their yards.

They also found that low-income/low-water users exhibited greater price responsiveness than high-income/
high-water users. Again, this result is expected since the water bill is more important in the budget of a low-in-
come family than it is in a high-income family’s budget. The policy implication of this finding is that, if policy
makers want to reduce water usage in the area, increasing price will alter the behavior of the low-income/low-

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 123

income elasticity of
demand

The percentage change in
quantity demanded at a
specific price divided by the
percentage change in
income that produced the
demand change, all other
things unchanged.

water users more than that of high-income/high-water users. To substantially alter the behavior of high-
income/high-waters users they would need to increase price even more for water consumption above a cer-
tain level. The authors point out that outdoor irrigation associated with relatively high-income/high-water us-
ing households accounts for most residential water use in Phoenix.

Source: Based on James Yoo, Silvio Simonit, Ann P. Kinzig, and Charles Perrings. “Estimating the Price Elasticity of Residential Water Demand: The Case
of Phoenix, Arizona,” Applied Economic Perspectives and Policy, 36:2 (June 2014): 333-350.

A N S W E R S T O T R Y I T ! P R O B L E M S

1. The absolute value of price elasticity of demand tends to be greater when more time is allowed for
consumers to respond. Over time, riders of the commuter rail system can organize car pools, move, or
otherwise adjust to the fare increase.

2. Using the formula for price elasticity of demand and plugging in values for the estimate of price elasticity
(−0.5) and the percentage change in price (5%) and then rearranging terms, we can solve for the
percentage change in quantity demanded as:
eD = %Δ in Q/%Δ in P; −0.5 = %Δ in Q/5%; (−0.5)(5%) = %Δ in Q = −2.5%.
Ridership falls by 2.5% in the first few months.

3. Using the formula for price elasticity of demand and plugging in values for the estimate of price elasticity
over a few years (−1.5) and the percentage change in price (5%), we can solve for the percentage change
in quantity demanded as:
eD = %Δ in Q/%Δ in P; −1.5 = %Δ in Q/5%; (−1.5)(5%) = %Δ in Q = −7.5%.
Ridership falls by 7.5% over a few years.

4. Total revenue rises immediately after the fare increase, since demand over the immediate period is price
inelastic. Total revenue falls after a few years, since demand changes and becomes price elastic.

2. RESPONSIVENESS OF DEMAND TO OTHER FACTORS

L E A R N I N G O B J E C T I V E S

1. Explain the concept of income elasticity of demand and its calculation.
2. Classify goods as normal or inferior depending on their income elasticity of demand.
3. Explain the concept of cross price elasticity of demand and its calculation.
4. Classify goods as substitutes or complements depending on their cross price elasticity of

demand.

Although the response of quantity demanded to changes in price is the most widely used measure of
elasticity, economists are interested in the response to changes in the demand shifters as well. Two of
the most important measures show how demand responds to changes in income and to changes in the
prices of related goods and services.

2.1 Income Elasticity of Demand
We saw in the chapter that introduced the model of demand and supply that the demand for a good or
service is affected by income. We measure the income elasticity of demand, eY, as the percentage
change in quantity demanded at a specific price divided by the percentage change in income that pro-
duced the demand change, all other things unchanged:

E Q U A T I O N 5 . 3

eY =
% change in quantity demanded

% change in income

The symbol Y is often used in economics to represent income. Because income elasticity of de-
mand reports the responsiveness of quantity demanded to a change in income, all other things un-
changed (including the price of the good), it reflects a shift in the demand curve at a given price.

124 PRINCIPLES OF ECONOMICS VERSION 3.0

cross price elasticity of
demand

It equals the percentage
change in the quantity
demanded of one good or
service at a specific price
divided by the percentage
change in the price of a
related good or service.

Remember that price elasticity of demand reflects movements along a demand curve in response to a
change in price.

A positive income elasticity of demand means that income and demand move in the same direc-
tion—an increase in income increases demand, and a reduction in income reduces demand. As we
learned, a good whose demand rises as income rises is called a normal good.

Studies show that most goods and services are normal, and thus their income elasticities are posit-
ive. Goods and services for which demand is likely to move in the same direction as income include
housing, seafood, rock concerts, and medical services.

If a good or service is inferior, then an increase in income reduces demand for the good. That im-
plies a negative income elasticity of demand. Goods and services for which the income elasticity of de-
mand is likely to be negative include used clothing, beans, and urban public transit. For example, the
studies we have already cited concerning the demands for urban public transit in France and in Madrid
found the long-run income elasticities of demand to be negative (−0.23 in France and −0.25 in Mad-
rid).[3]

When we compute the income elasticity of demand, we are looking at the change in the quantity de-
manded at a specific price. We are thus dealing with a change that shifts the demand curve. An increase
in income shifts the demand for a normal good to the right; it shifts the demand for an inferior good to
the left.

2.2 Cross Price Elasticity of Demand
The demand for a good or service is affected by the prices of related goods or services. A reduction in
the price of salsa, for example, would increase the demand for chips, suggesting that salsa is a comple-
ment of chips. A reduction in the price of chips, however, would reduce the demand for peanuts, sug-
gesting that chips are a substitute for peanuts.

The measure economists use to describe the responsiveness of demand for a good or service to a
change in the price of another good or service is called the cross price elasticity of demand, eA, B. It
equals the percentage change in the quantity demanded of one good or service at a specific price di-
vided by the percentage change in the price of a related good or service. We are varying the price of a
related good when we consider the cross price elasticity of demand, so the response of quantity deman-
ded is shown as a shift in the demand curve.

The cross price elasticity of the demand for good A with respect to the price of good B is given by:

E Q U A T I O N 5 . 4

eA, B =
% change in quantity demanded of good A

% change in price of good B

Cross price elasticities of demand define whether two goods are substitutes, complements, or unre-
lated. If two goods are substitutes, an increase in the price of one will lead to an increase in the demand
for the other—the cross price elasticity of demand is positive. If two goods are complements, an in-
crease in the price of one will lead to a reduction in the demand for the other—the cross price elasticity

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 125

of demand is negative. If two goods are unrelated, a change in the price of one will not affect the de-
mand for the other—the cross price elasticity of demand is zero.

An examination of the demand for local television advertising with respect to the price of local radio
advertising revealed that the two goods are clearly substitutes. A 10 percent increase in the price of loc-
al radio advertising led to a 10 percent increase in demand for local television advertising, so that the
cross price elasticity of demand for local television advertising with respect to changes in the price of
radio advertising was 1.0.[4]

Heads Up!

Notice that with income elasticity of demand and cross price elasticity of demand we are primarily concerned
with whether the measured value of these elasticities is positive or negative. In the case of income elasticity of
demand this tells us whether the good or service is normal or inferior. In the case of cross price elasticity of de-
mand it tells us whether two goods are substitutes or complements. With price elasticity of demand we were
concerned with whether the measured absolute value of this elasticity was greater than, less than, or equal to
1, because this gave us information about what happens to total revenue as price changes. The terms elastic
and inelastic apply to price elasticity of demand. They are not used to describe income elasticity of demand or
cross price elasticity of demand.

K E Y T A K E A W A Y S

< The income elasticity of demand reflects the responsiveness of demand to changes in income. It is the percentage change in quantity demanded at a specific price divided by the percentage change in income, ceteris paribus.

< Income elasticity is positive for normal goods and negative for inferior goods.

< The cross price elasticity of demand measures the way demand for one good or service responds to changes in the price of another. It is the percentage change in the quantity demanded of one good or service at a specific price divided by the percentage change in the price of another good or service, all other things unchanged.

< Cross price elasticity is positive for substitutes, negative for complements, and zero for goods or services whose demands are unrelated.

126 PRINCIPLES OF ECONOMICS VERSION 3.0

T R Y I T !

Suppose that when the price of bagels rises by 10%, the demand for cream cheese falls by 3% at the current
price, and that when income rises by 10%, the demand for bagels increases by 1% at the current price. Calcu-
late the cross price elasticity of demand for cream cheese with respect to the price of bagels and tell whether
bagels and cream cheese are substitutes or complements. Calculate the income elasticity of demand and tell
whether bagels are normal or inferior.

Case in Point: Various Demand Elasticities for Conventional and Organic Milk

Peruse the milk display at any supermarket and you will see a number of items that you would not have seen a
decade ago. Choices include fat content; with or without lactose; animal milks or milk substitutes, such as soy
or almond milk; flavors; and organic or conventional milk. Whereas in the 1990s only specialty stores stocked
organic milk, today it is readily available in most supermarkets. In fact, the market share for organic milk has
grown, as sales of conventional milk have been fairly constant while sales of organic milk have increased.

Professors Pedro Alviola and Oral Capps have estimated various demand elasticities associated with conven-
tional and organic milk, based on a study of 38,000 households. Their results are summarized in the following
table.

Elasticity Measure Organic Milk Conventional Milk

Own-price elasticity −2.00 −0.87

Cross-price elasticity 0.70 0.18

Income elasticity 0.27 −0.01

Organic milk is price elastic, while conventional milk is price inelastic. Both cross-price elasticities are positive,
indicating that these two kinds of milk are substitutes but their estimated values differ. In particular, a 1% in-
crease in the price of conventional milk leads to a 0.70% increase in the quantity demanded of organic milk,
while a 1% increase in the price of organic milk leads to an increase in the quantity demanded of conventional
milk of only 0.18%. This asymmetry suggests that organic milk consumers have considerable reluctance in
switching back to what they may perceive as a lower-quality product. Finally, the income elasticity estimates
suggest that organic milk is a normal good, while conventional milk is an inferior good. As might be expected,
in the sample used in the study, purchasers of organic milk are more affluent as a group than are purchasers of
conventional milk.

Being a fairly new product, organic milk studies are just becoming available and the authors point out that
other researchers using different data sets have calculated different values for these elasticities. Over time, as
more data become available and various studies are compared, this type of work is likely to influence milk
marketing and pricing.

Source: Based on Pedro A. Alviola IV and Oral Capps Jr., “Household Demand Analysis of Organic and Conventional Fluid Milk in the United States
Based on the 2004 Nielsen Homescan Panel,” Agribusiness 26:3 (2010): 369–388.

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 127

F I G U R E 5 . 5 Increase in Apartment
Rents Depends on How Responsive Supply
Is

The more responsive the supply of apartments
is to changes in price (rent in this case), the less
rents rise when the demand for apartments
increases.

price elasticity of supply

The ratio of the percentage
change in quantity supplied
of a good or service to the
percentage change in its
price, all other things
unchanged.

A N S W E R T O T R Y I T ! P R O B L E M

Using the formula for cross price elasticity of demand, we find that eAB = (−3%)/(10%) = −0.3. Since the eAB is
negative, bagels and cream cheese are complements. Using the formula for income elasticity of demand, we
find that eY = (+1%)/(10%) = +0.1. Since eY is positive, bagels are a normal good.

3. PRICE ELASTICITY OF SUPPLY

L E A R N I N G O B J E C T I V E S

1. Explain the concept of elasticity of supply and its calculation.
2. Explain what it means for supply to be price inelastic, unit price elastic, price elastic, perfectly

price inelastic, and perfectly price elastic.
3. Explain why time is an important determinant of price elasticity of supply.
4. Apply the concept of price elasticity of supply to the labor supply curve.

The elasticity measures encountered so far in this chapter all relate to the demand side of the market. It
is also useful to know how responsive quantity supplied is to a change in price.

Suppose the demand for apartments rises. There will be a shortage of apartments
at the old level of apartment rents and pressure on rents to rise. All other things un-
changed, the more responsive the quantity of apartments supplied is to changes in
monthly rents, the lower the increase in rent required to eliminate the shortage and to
bring the market back to equilibrium. Conversely, if quantity supplied is less responsive
to price changes, price will have to rise more to eliminate a shortage caused by an in-
crease in demand.

This is illustrated in Figure 5.5. Suppose the rent for a typical apartment had been
R0 and the quantity Q0 when the demand curve was D1 and the supply curve was either
S1 (a supply curve in which quantity supplied is less responsive to price changes) or S2
(a supply curve in which quantity supplied is more responsive to price changes). Note
that with either supply curve, equilibrium price and quantity are initially the same.
Now suppose that demand increases to D2, perhaps due to population growth. With
supply curve S1, the price (rent in this case) will rise to R1 and the quantity of apart-
ments will rise to Q1. If, however, the supply curve had been S2, the rent would only
have to rise to R2 to bring the market back to equilibrium. In addition, the new equilib-
rium number of apartments would be higher at Q2. Supply curve S2 shows greater re-
sponsiveness of quantity supplied to price change than does supply curve S1.

We measure the price elasticity of supply (eS) as the ratio of the percentage
change in quantity supplied of a good or service to the percentage change in its price,
all other things unchanged:

E Q U A T I O N 5 . 5

eS =
% change in quantity supplied

% change in price

Because price and quantity supplied usually move in the same direction, the price elasticity of sup-
ply is usually positive. The larger the price elasticity of supply, the more responsive the firms that sup-
ply the good or service are to a price change.

Supply is price elastic if the price elasticity of supply is greater than 1, unit price elastic if it is equal
to 1, and price inelastic if it is less than 1. A vertical supply curve, as shown in Panel (a) of Figure 5.6, is
perfectly inelastic; its price elasticity of supply is zero. The supply of Beatles’ songs is perfectly inelastic
because the band no longer exists. A horizontal supply curve, as shown in Panel (b) of Figure 5.6, is
perfectly elastic; its price elasticity of supply is infinite. It means that suppliers are willing to supply any
amount at a certain price.

128 PRINCIPLES OF ECONOMICS VERSION 3.0

F I G U R E 5 . 6 Supply Curves and Their Price Elasticities

The supply curve in Panel (a) is perfectly inelastic. In Panel (b), the supply curve is perfectly elastic.

3.1 Time: An Important Determinant of the Elasticity of Supply
Time plays a very important role in the determination of the price elasticity of supply. Look again at
the effect of rent increases on the supply of apartments. Suppose apartment rents in a city rise. If we are
looking at a supply curve of apartments over a period of a few months, the rent increase is likely to in-
duce apartment owners to rent out a relatively small number of additional apartments. With the higher
rents, apartment owners may be more vigorous in reducing their vacancy rates, and, indeed, with more
people looking for apartments to rent, this should be fairly easy to accomplish. Attics and basements
are easy to renovate and rent out as additional units. In a short period of time, however, the supply re-
sponse is likely to be fairly modest, implying that the price elasticity of supply is fairly low. A supply
curve corresponding to a short period of time would look like S1 in Figure 5.5. It is during such periods
that there may be calls for rent controls.

If the period of time under consideration is a few years rather than a few months, the supply curve
is likely to be much more price elastic. Over time, buildings can be converted from other uses and new
apartment complexes can be built. A supply curve corresponding to a longer period of time would look
like S2 in Figure 5.5.

3.2 Elasticity of Labor Supply: A Special Application
The concept of price elasticity of supply can be applied to labor to show how the quantity of labor sup-
plied responds to changes in wages or salaries. What makes this case interesting is that it has some-
times been found that the measured elasticity is negative, that is, that an increase in the wage rate is as-
sociated with a reduction in the quantity of labor supplied.

In most cases, labor supply curves have their normal upward slope: higher wages induce people to
work more. For them, having the additional income from working more is preferable to having more
leisure time. However, wage increases may lead some people in very highly paid jobs to cut back on the
number of hours they work because their incomes are already high and they would rather have more
time for leisure activities. In this case, the labor supply curve would have a negative slope. The reasons
for this phenomenon are explained more fully in a later chapter. The Case in Point in this section gives
another example where an increase in the wage may reduce the number of hours of work.

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 129

K E Y T A K E A W A Y S

< The price elasticity of supply measures the responsiveness of quantity supplied to changes in price. It is the percentage change in quantity supplied divided by the percentage change in price. It is usually positive.

< Supply is price inelastic if the price elasticity of supply is less than 1; it is unit price elastic if the price elasticity of supply is equal to 1; and it is price elastic if the price elasticity of supply is greater than 1. A vertical supply curve is said to be perfectly inelastic. A horizontal supply curve is said to be perfectly elastic.

< The price elasticity of supply is greater when the length of time under consideration is longer because over time producers have more options for adjusting to the change in price.

< When applied to labor supply, the price elasticity of supply is usually positive but can be negative. If higher wages induce people to work more, the labor supply curve is upward sloping and the price elasticity of supply is positive. In some very high-paying professions or other unusual circumstances, the labor supply curve may have a negative slope, which leads to a negative price elasticity of supply.

T R Y I T !

In the late 1990s, it was reported on the news that the high-tech industry was worried about being able to
find enough workers with computer-related expertise. Job offers for recent college graduates with degrees in
computer science went with high salaries. It was also reported that more undergraduates than ever were ma-
joring in computer science. Compare the price elasticity of supply of computer scientists at that point in time
to the price elasticity of supply of computer scientists over a longer period of, say, 1999 to 2009.

Case in Point: Child Labor in Pakistan

Professor Sonia Bhalotra investigated the role of household poverty in child labor. Imagine a household with
two parents and two children, a boy and a girl. If only the parents work, the family income may be less than an
amount required for subsistence. In order to at least raise the income of the family to subsistence, will the
labor of both children be added? If only one child will work, will it be the boy or the girl? How do the motiva-
tions of parents to send their children to work affect the design of policies to encourage education? Will a pro-
gram that reduces school fees or improves school quality lead to more education or would a program that
provides cash or food to households who send their children to school work better?

130 PRINCIPLES OF ECONOMICS VERSION 3.0

Using information on over 3,000 children in an area of rural Pakistan where their labor force participation is
high, child wage labor is common, and gender differences in education and work of children prevail, Professor
Bhalotra specifically estimated how changes in wages for boys and girls affect the number of hours they work.
She focused on wage work outside the home because it usually involves more hours and less flexibility than,
say, work on one’s own farm, which essentially rules out going to school.

She argues that if the work of a child is geared toward the family hitting a target level of income, then an in-
crease in the wage will lead to fewer hours of work. That is, the labor supply elasticity will be negative and the
labor supply curve will have a negative slope. For boys, she finds that the wage elasticity is about −0.5. For
girls, she finds that the wage elasticity is about 0, meaning the labor supply curve is vertical. To further her hy-
pothesis that the labor supply decision for boys but not for girls is compelled by household poverty, she notes
that separate estimates show that the income of the family from sources other than having their children work
reduces the amount that boys work but has no effect on the amount that girls work. Other research she has
undertaken on labor supply of children on household-run farms provides further support for these gender
differences: Girls from families that own relatively larger farms were both more likely to work and less likely to
go to school than girls from households with farms of smaller acreage.

Why the gender differences and how do these findings affect drafting of policies to encourage schooling? For
boys, cash or food given to households could induce parents to send their sons to school. For girls, household
poverty reduction may not work. Their relatively lower level of participating in schooling may be related to an
expected low impact of education on their future wages. Expectations about when they will get married and
whether or not they should work as adults, especially if it means moving to other areas, may also play a role.
For girls, policies that alter attitudes toward girls’ education and in the longer term affect educated female
adult earnings may be more instrumental in increasing their educational attainment.

Source: Based on Sonia Bhalotra, “Is Child Work Necessary?” Oxford Bulletin of Economics and Statistics 69:1 (2007): 29–55.

A N S W E R T O T R Y I T ! P R O B L E M

While at a point in time the supply of people with degrees in computer science is very price inelastic, over
time the elasticity should rise. That more students were majoring in computer science lends credence to this
prediction. As supply becomes more price elastic, salaries in this field should rise more slowly.

4. REVIEW AND PRACTICE

Summary

This chapter introduced a new tool: the concept of elasticity. Elasticity is a measure of the degree to which a
dependent variable responds to a change in an independent variable. It is the percentage change in the de-
pendent variable divided by the percentage change in the independent variable, all other things unchanged.

The most widely used elasticity measure is the price elasticity of demand, which reflects the responsiveness of
quantity demanded to changes in price. Demand is said to be price elastic if the absolute value of the price
elasticity of demand is greater than 1, unit price elastic if it is equal to 1, and price inelastic if it is less than 1.
The price elasticity of demand is useful in forecasting the response of quantity demanded to price changes; it
is also useful for predicting the impact a price change will have on total revenue. Total revenue moves in the
direction of the quantity change if demand is price elastic, it moves in the direction of the price change if de-
mand is price inelastic, and it does not change if demand is unit price elastic. The most important determin-
ants of the price elasticity of demand are the availability of substitutes, the importance of the item in house-
hold budgets, and time.

Two other elasticity measures commonly used in conjunction with demand are income elasticity and cross
price elasticity. The signs of these elasticity measures play important roles. A positive income elasticity tells us
that a good is normal; a negative income elasticity tells us the good is inferior. A positive cross price elasticity
tells us that two goods are substitutes; a negative cross price elasticity tells us they are complements.

Elasticity of supply measures the responsiveness of quantity supplied to changes in price. The value of price
elasticity of supply is generally positive. Supply is classified as being price elastic, unit price elastic, or price in-
elastic if price elasticity is greater than 1, equal to 1, or less than 1, respectively. The length of time over which
supply is being considered is an important determinant of the price elasticity of supply.

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 131

C O N C E P T P R O B L E M S

1. Explain why the price elasticity of demand is generally a negative number, except in the cases where the
demand curve is perfectly elastic or perfectly inelastic. What would be implied by a positive price elasticity
of demand?

2. Explain why the sign (positive or negative) of the cross price elasticity of demand is important.

3. Explain why the sign (positive or negative) of the income elasticity of demand is important.

4. Economists Dale Heien and Cathy Roheim Wessells found that the price elasticity of demand for fresh milk
is -0.63 and the price elasticity of demand for cottage cheese is -1.1.[5] Why do you think the elasticity
estimates differ?

5. The price elasticity of demand for health care has been estimated to be -0.2. Characterize this demand as
price elastic, unit price elastic, or price inelastic. The text argues that the greater the importance of an item
in consumer budgets, the greater its elasticity. Health-care costs account for a relatively large share of
household budgets. How could the price elasticity of demand for health care be such a small number?

6. Suppose you are able to organize an alliance that includes all farmers. They agree to follow the group’s
instructions with respect to the quantity of agricultural products they produce. What might the group
seek to do? Why?

7. Suppose you are the chief executive officer of a firm, and you have been planning to reduce your prices.
Your marketing manager reports that the price elasticity of demand for your product is -0.65. How will this
news affect your plans?

8. Suppose the income elasticity of the demand for beans is -0.8. Interpret this number.

9. Transportation economists generally agree that the cross price elasticity of demand for automobile use
with respect to the price of bus fares is about 0. Explain what this number means.

10. Suppose the price elasticity of supply of tomatoes as measured on a given day in July is 0. Interpret this
number.

11. The price elasticity of supply for child-care workers has been estimated to be quite high, about 2. What will
happen to the wages of child-care workers as demand for them increases, compared to what would
happen if the measured price elasticity of supply were lower?

12. Studies suggest that a higher tax on cigarettes would reduce teen smoking and premature deaths. Should
cigarette taxes therefore be raised?

132 PRINCIPLES OF ECONOMICS VERSION 3.0

N U M E R I C A L P R O B L E M S

1. Economist David Romer found that in introductory economics classes a 10% increase in class attendance
is associated with a 4% increase in course grade.[6] What is the elasticity of course grade with respect to
class attendance?

2. Refer to Figure 5.2 and

a. Using the arc elasticity of demand formula, compute the price elasticity of demand between
points B and C.

b. Using the arc elasticity of demand formula, compute the price elasticity of demand between
points D and E.

c. How do the values of price elasticity of demand compare? Why are they the same or different?

d. Compute the slope of the demand curve between points B and C.

e. Computer the slope of the demand curve between points D and E.

f. How do the slopes compare? Why are they the same or different?

3. Suppose a bumper crop of oranges in Florida drove down orange prices. As juice makers costs fell, they
cut prices by about 15%. Value oriented customers were tempted to buy more orange juice. In fact, the
unit volume of frozen juices rose by about 6%.

a. Given these numbers, and assuming there were no changes in demand shifters for frozen orange
juice, what was the price elasticity of demand for frozen orange juice?

b. What do you think happened to total spending on frozen orange juice? Why?

4. Suppose you are the manager of a restaurant that serves an average of 400 meals per day at an average
price per meal of $20. On the basis of a survey, you have determined that reducing the price of an average
meal to $18 would increase the quantity demanded to 450 per day.

a. Compute the price elasticity of demand between these two points.

b. Would you expect total revenues to rise or fall? Explain.

c. Suppose you have reduced the average price of a meal to $18 and are considering a further
reduction to $16. Another survey shows that the quantity demanded of meals will increase from
450 to 500 per day. Compute the price elasticity of demand between these two points.

d. Would you expect total revenue to rise or fall as a result of this second price reduction? Explain.

e. Compute total revenue at the three meal prices. Do these totals confirm your answers in (b) and
(d) above?

5. The text notes that, for any linear demand curve, demand is price elastic in the upper half and price
inelastic in the lower half. Consider the following demand curves:

The table gives the prices and quantities corresponding to each of the points shown on the two demand
curves.

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 133

Demand curve D1 [Panel (a)] Demand curve D2 [Panel (b)]

Price Quantity Price Quantity

A 80 2 E 8 20

B 70 3 F 7 30

C 30 7 G 3 70

D 20 8 H 2 80

a. Compute the price elasticity of demand between points A and B and between points C and D on
demand curve D1 in Panel (a). Are your results consistent with the notion that a linear demand
curve is price elastic in its upper half and price inelastic in its lower half?

b. Compute the price elasticity of demand between points E and F and between points G and H on
demand curve D2 in Panel (b). Are your results consistent with the notion that a linear demand
curve is price elastic in its upper half and price inelastic in its lower half?

c. Compare total spending at points A and B on D1 in Panel (a). Is your result consistent with your
finding about the price elasticity of demand between those two points?

d. Compare total spending at points C and D on D1 in Panel (a). Is your result consistent with your
finding about the price elasticity of demand between those two points?

e. Compare total spending at points E and F on D2 in Panel (b). Is your result consistent with your
finding about the price elasticity of demand between those two points?

f. Compare total spending at points G and H on D2 in Panel (b). Is your result consistent with your
finding about the price elasticity of demand between those two points?

6. Suppose Janice buys the following amounts of various food items depending on her weekly income:

Weekly Income Hamburgers Pizza Ice Cream Sundaes

$500 3 3 2

$750 4 2 2

a. Compute Janice’s income elasticity of demand for hamburgers.

b. Compute Janice’s income elasticity of demand for pizza.

c. Compute Janice’s income elasticity of demand for ice cream sundaes.

d. Classify each good as normal or inferior.

7. Suppose the following table describes Jocelyn’s weekly snack purchases, which vary depending on the
price of a bag of chips:

Price of bag of chips Bags of chips Containers of salsa Bags of pretzels Cans of soda

$1.00 2 3 1 4

$1.50 1 2 2 4

a. Compute the cross price elasticity of salsa with respect to the price of a bag of chips.

b. Compute the cross price elasticity of pretzels with respect to the price of a bag of chips.

c. Compute the cross price elasticity of soda with respect to the price of a bag of chips.

d. Are chips and salsa substitutes or complements? How do you know?

e. Are chips and pretzels substitutes or complements? How do you know?

f. Are chips and soda substitutes or complements? How do you know?

8. The table below describes the supply curve for light bulbs:

Price per light bulb Quantity supplied per day

$1.00 500

1.50 3,000

2.00 4,000

2.50 4,500

3.00 4,500
Compute the price elasticity of supply and determine whether supply is price elastic, price inelastic,
perfectly elastic, perfectly inelastic, or unit elastic:

a. when the price of a light bulb increases from $1.00 to $1.50.

b. when the price of a light bulb increases from $1.50 to $2.00.

134 PRINCIPLES OF ECONOMICS VERSION 3.0

c. when the price of a light bulb increases from $2.00 to $2.50.

d. when the price of a light bulb increases from $2.50 to $3.00.

CHAPTER 5 ELASTICITY: A MEASURE OF RESPONSE 135

ENDNOTES

Notice that since the number of units sold of a good is the same as the number of
units bought, the definition for total revenue could also be used to define total
spending. Which term we use depends on the question at hand. If we are trying to
determine what happens to revenues of sellers, then we are asking about total rev-
enue. If we are trying to determine how much consumers spend, then we are asking
about total spending.

Division by zero results in an undefined solution. Saying that the price elasticity of
demand is infinite requires that we say the denominator “approaches” zero.

See Georges Bresson, Joyce Dargay, Jean-Loup Madre, and Alain Pirotte, “Economic
and Structural Determinants of the Demand for French Transport: An Analysis on a
Panel of French Urban Areas Using Shrinkage Estimators.” Transportation Research:
Part A 38: 4 (May 2004): 269–285. See also Anna Matas. “Demand and Revenue Im-
plications of an Integrated Transport Policy: The Case of Madrid.” Transport Reviews
24:2 (March 2004): 195–217.

Robert B. Ekelund, S. Ford, and John D. Jackson. “Are Local TV Markets Separate Mar-
kets?” International Journal of the Economics of Business 7:1 (2000): 79–97.

Dale M. Heien and Cathy Roheim Wessels, “The Demand for Dairy Products: Struc-
ture, Prediction, and Decomposition,” American Journal of Agricultural Economics 70:2
(May 1988): 219–228.

David Romer, “Do Students Go to Class? Should They?” Journal of Economic Perspect-
ives 7:3 (Summer 1993): 167–174.

136 PRINCIPLES OF ECONOMICS VERSION 3.0

Chapter 5: Elasticity: A Measure of Response

Start Up: Raise Fares? Lower Fares? What’s a Public Transit Manager To Do?
The Price Elasticity of Demand
Computing the Price Elasticity of Demand
Price Elasticities Along a Linear Demand Curve
The Price Elasticity of Demand and Changes in Total Revenue
Elastic, Unit Elastic, and Inelastic Demand
Relating Elasticity to Changes in Total Revenue
Constant Price Elasticity of Demand Curves
Determinants of the Price Elasticity of Demand
Availability of Substitutes
Importance in Household Budgets
Time

Responsiveness of Demand to Other Factors
Income Elasticity of Demand
Cross Price Elasticity of Demand
Price Elasticity of Supply
Time: An Important Determinant of the Elasticity of Supply
Elasticity of Labor Supply: A Special Application
Review and Practice
Endnotes

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