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Externalities:

Explain the difference between a positive and negative externality. In your analysis, make sure to

provide an example of each type of externality. Why does the government need to get involved

with externalities to bring about market efficiency? What solutions need to be provided for your

examples?

Your initial post should be at least 250 words in length. Utilize the required reading material as

well as the article to support your claims.

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4

Elasticity: The Measure of

Responsiveness

Learning Objectives

By the end of this chapter, you will be able to:

• Review the most important concepts in supply and demand analysis.

• Define elasticity as a measure of responsiveness.

• Define and calculate the coefficient of price elasticity of demand.

• Define and calculate the income elasticity of demand and the cross elasticity of demand.

• Define and calculate the price elasticity of supply.

• Determine the incidence of an excise tax.

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Section 4.1 Supply and Demand Revisited

CHAPTER 4

Introduction

C

onsider this. . . One day while shopping you notice an old oil lamp in the window

of a consignment store. Intrigued, you go into the store and pick up the lamp. When

you rub it, a genie appears and offers you three wishes. For one of your wishes,

you ask to be the sole inventor, owner, and producer of a revolutionary new smartphone

device. Your wish is granted.

You now are in a position to be very rich. What price should you charge for the smartphones? How many should you sell? For the sake of argument let’s assume you want to be

as rich as possible and that you can produce the devices at no cost—they just appear like

the genie. Now, what price should you charge and how many should you sell? You know

that demand curves slope downward to the right, so in order to sell more you will have to

lower your price. What a dilemma! This chapter will show you how to be as rich as possible!

To do so we extend the concepts of supply and demand by developing another tool of the

microeconomist—the elasticity measurement. Elasticity is the measure of the sensitivity,

or responsiveness, of quantity demanded or quantity supplied to changes in price (or

other conditions). We will develop several elasticity measures and then demonstrate their

usefulness in the analysis of public policy—and selling smartphones.

4.1 Supply and Demand Revisited

S

upply and demand are basic to economic analysis. It is worth reviewing them before

beginning to expand your kit of economic tools.

When developing the concept of

demand, we stressed the distinction between shifts in demand

curves and movement along

demand curves. Any movement

along a demand curve occurs

in response to a change in price

and is referred to as a change in

quantity demanded. Any shift of

the demand curve itself is called

a change in demand. Changes in

demand occur in response to

changes in one or more of the

iStockphoto/Thinkstock

ceteris paribus conditions that

underlie the demand curve: the Gasoline prices can shift the demand for automobiles, which

can also affect automobile production.

tastes of the group demanding

the good or service, the size of

that group, the income and wealth of that group, the prices of other goods and services, or

expectations about any of these conditions.

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CHAPTER 4

Section 4.1 Supply and Demand Revisited

Similarly, there is an important difference between changes in supply and changes in

quantity supplied. The phrase change in quantity supplied indicates to the economist that

the change that occurred was in response to a change in price. The phrase change in supply

means that the change occurred in response to a change in one or more of the ceteris paribus conditions affecting supply: the prices of the productive factors, the number of sellers,

the technology used to produce the good, or expectations about any of these conditions.

These principles and terms are useful in explaining economic events. Figure 4.1 is a diagram of supply and demand in the market for automobiles. Stable ceteris paribus conditions have been assumed, and differences in autos’ quality, size, and gas mileage have

been ignored, so that a demand curve for like units can be drawn. The market determines

an equilibrium price of P1 and quantity of Q1. Now suppose the price of gasoline increases.

Since gasoline and automobiles are complements, you know that the increase in the price

of gasoline is going to cause the demand for automobiles to shift from D1 to D2 in Figure

4.1. That is, with gasoline being more expensive, people drive less, reducing the demand

for automobiles. This decrease in demand for autos causes the price to fall to P2 and the

quantity supplied to decrease to Q2. Remember that quality and other factors are held

constant. Thus, the decrease in the demand for automobiles could represent a switch to

smaller cars or less frequent trade-ins for newer models.

Figure 4.1: The market for automobiles

Price/

Auto

S

P1

P2

D1

D2

0

Q2

Q1

Autos/Year

Gasoline is a complementary good to automobiles. If the price of gasoline rises, there will be a decrease

in the demand for automobiles. The price of autos will fall from P1 to P2, and the equilibrium quantity

will decrease from Q1 to Q2. There has been a decrease in the quantity supplied.

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CHAPTER 4

Section 4.3 Price Elasticity of Demand

4.2 Elasticity as a General Concept

E

lasticity measures the way one variable responds to changes in other variables. One

variable is described as the dependent variable because it depends upon, or changes

in response to, some other variable, called the independent variable.

Elasticity is a measure of how the dependent variable responds to changes in any one of

the independent variables. The general formula to determine this responsiveness is

Elasticity 5

Percent change in the dependent variable

Percent change in the independent variable

Using the symbol D (the Greek letter delta) to represent change, this is written:

E5

%Dy

%Dx

In examining demand, economists are interested in how the quantity demanded responds

to changes in price and to changes in certain other ceteris paribus conditions that can

affect demand. The quantity demanded of good A (QAd) is thus the dependent variable.

The independent variables include factors such as the price of good A (PA), income (I),

tastes (T), the price of complements (Pc ), and the price of substitutes (Ps ).

4.3 Price Elasticity of Demand

I

n order to determine how quantity demanded Qd responds to change in any of the

independent variables, we hold all but one of them constant and calculate the elasticity coefficient using the equation above. For example, to see how quantity demanded

responds to price, we use

Elasticity coefficient 5

Percent change in the quantity of good A demanded

Percent change in the price of good A

Ed 5

%DQ Ad

%DPA

where Ed is the coefficient of price elasticity of demand. This formula gives us the price

elasticity of demand. Price elasticity of demand is the measure of the relative responsiveness of the quantity demanded to changes in price. Note an important advantage of

measuring in terms of percentage change. There are no units associated with the elasticity

coefficient; it is simply a ratio.

In the late nineteenth century, the famous English economist Alfred Marshall developed

the concept of elasticity to compare the demands for various products. When comparisons

are made, the coefficient indicates the relative responsiveness of the quantity demanded

to price changes. The slope of the demand curve, calculated as DP/DQ, is used to calculate

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CHAPTER 4

Section 4.3 Price Elasticity of Demand

absolute responsiveness. Relative comparisons make it possible to measure and then

describe the sensitivity of the demand relationship.

The coefficient of price elasticity of demand (Ed) is the numerical measure of price elasticity of demand. It is the percent change in quantity demanded of a good divided by the

percent change in price. That is, as you have seen, for good A,

Ed 5

%DQ Ad

%DPA

Since the percent change is calculated by dividing the change in the variable by the base

amount of the variable, this can be rewritten as

Ed 5

DQ Ad@Q Ad

DPA @PA

Types of Elasticity

Most straight-line demand curves look like those illustrated in Figure 4.1. Demand curve

D1 has a range of elasticity coefficients from infinity (at the intersection with the vertical

axis) to zero (at the intersection with the horizontal axis). No two points on a straight line

demand curve have the same elasticity coefficient. When the coefficient is less than 1,

demand is said to be inelastic; the percent change in quantity demanded is less than the

percent change in price. When the coefficient is greater than 1, the quantity demanded

changes relatively more than the price and the demand is thus described as elastic. Of

course, there are degrees of responsiveness. The larger the coefficient, the greater the

responsiveness.

With most demand curves, the elasticity coefficient varies along the curve. However, some

demand curves have a constant price elasticity of demand. We will examine three special

cases.

Figure 4.2 shows a vertical demand curve. With this curve, quantity demanded is totally

unresponsive to changes in price. As price changes from P1 to P2, there is no change in the

quantity demanded. The elasticity coefficient is

Ed 5

ama80571_04_c04_099-130.indd 103

DQd @Q 1

DP@P1

50

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CHAPTER 4

Section 4.3 Price Elasticity of Demand

Figure 4.2: Perfectly inelastic demand curve

Price/

Unit

D

P1

P2

0

Q1

Quantity/Time Period

On a perfectly inelastic demand curve, such as D, the quantity demanded has no responsiveness to

changes in price.

This vertical demand curve is a limiting case that violates the law of demand and is not

known to exist in the real world. This curve is called a perfectly inelastic demand curve.

Perfectly inelastic demand occurs when the coefficient of price elasticity of demand is

zero. There is no response of quantity demanded to changes in price. To illustrate this,

consider the plight of a person who is wandering lost in the desert, slowly succumbing to

thirst. If that person should arrive at an oasis and find water for sale, they will be willing

to pay any price for a drink. An increase in price will not have any effect whatsoever on

the quantity demanded. Similarly, the parents of a sick child whose survival depends on

a life saving drug will not be deterred by a price increase.

Another limiting case is a horizontal demand curve, as shown in Figure 4.3. When price

drops below P1 an infinite increase in quantity of the good is demanded.

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CHAPTER 4

Section 4.3 Price Elasticity of Demand

Figure 4.3: Perfectly elastic demand curve

Price/

Unit

P1

D

P2

0

Quantity/Time Period

On a perfectly elastic demand curve, such as D, the quantity demanded has an infinite response to

changes in price. If price rises above P1, no amount of the good will be purchased. If price falls to P2, all

that is available will be purchased.

If the price rises above P1, quantity demanded drops to zero. Calculating the elasticity

coefficient for a price change from P1 to P2 yields

Ed 5

DQd @Q 1

DP@P1

5 q

A farmer who is selling produce into an established commodity market may encounter a

horizontal demand curve. If the farmer should set an asking price for the crop that is even

slightly above the market price, they will find no purchasers for their goods. Conversely,

if they should set the price below the market they will immediately be overwhelmed by

infinite demand.

A horizontal demand curve is called a perfectly elastic demand curve because the response

to changes in price is infinite. Perfectly elastic demand occurs when the coefficient of

price elasticity of demand is infinite.

A third kind of demand curve is shown in Figure 4.4. Any percent decrease or increase

in price results in the exact same percent increase or decrease in the quantity demanded.

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CHAPTER 4

Section 4.3 Price Elasticity of Demand

A 15 percent price increase will produce a 15 percent decrease in quantity demanded, and

so on. This means that the elasticity coefficient at any point along this demand curve is

equal to 1. For example, if you calculated the elasticity coefficient for a price change from

P1 to P2, you would find that

Ed 5

DQd @Q 1

DP@P1

51

Figure 4.4: Unitary elastic demand curve

Price/

Unit

P1

P2

D

0

Q1

Q2

Quantity/Time Period

With a unitary elastic demand curve, a change in price brings about the same percentage change in

quantity demanded.

Such a demand curve is referred to as a unit elastic demand curve. Unit elastic demand

occurs when the coefficient of price elasticity of demand is unitary (equal to 1).

Most demand curves are not shaped like those in Figures 4.2, 4.3, and 4.4. Most straightline demand curves look like the one in Figure 4.5. Demand curve D has a range of

elasticity coefficients from infinity (at the intersection with the vertical axis) to zero (at

the intersection with the horizontal axis). When the coefficient is less than 1, demand

is inelastic because the percent change in quantity demanded is less than the percent

change in price. When the coefficient is greater than 1, demand is elastic because the

quantity demanded changes relatively more than the price. Of course, there are degrees

of responsiveness. The larger the coefficient, the greater the responsiveness.

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CHAPTER 4

Section 4.3 Price Elasticity of Demand

Figure 4.5: Straight-line demand curve with varying elasticity coefficients

Price/

Unit

$3.00

$2.20

$2.00

0.20

$1.20

$1.00

0.20

E d =2.34

E d =0.58

2

0

5

8 10

2

15

D

18 20

25

Quantity/Time Period

A straight-line demand curve has elasticity coefficients that vary from zero at the horizontal-axis

intercept to infinity at the vertical-axis intercept.

Check Point: A Guide to Elasticity Coefficient

Type of elasticity

Responsiveness of quantity demanded

to a change in price

Elasticity coefficient

Perfectly inelastic

No response

Ed 5 0

Inelastic

Quantity demanded changes by a smaller

percentage than the price changes

0 , Ed , 1

Unit elastic

Quantity demanded changes by the same

percentage as the price changes.

Ed 5 1

Elastic

Quantity demanded changes by a larger

percentage than the price changes.

1 , Ed , ∞

Perfectly elastic

Quantity demanded becomes infinite, or all

that is available is demanded.

Ed 5 ∞

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CHAPTER 4

Section 4.4 Calculating Elasticity

4.4 Calculating Elasticity

T

he best way to understand elasticity is to calculate and interpret some elasticity

coefficients. Before we do this, we need to clarify two points. Remember that elasticity varies along a demand curve and that no two points have the same coefficient.

There are two methods to calculate an elasticity coefficient; elasticity can be calculated

at a single point or between two points. The elasticity between two points is the value

of the coefficient at the midpoint between the points. In other words, the average of the

two. This value is called arc elasticity. For the purpose of this discussion we will compute

values of arc elasticities which require only arithmetic to calculate particular coefficients.

Many economists use a different, but related, measure called point elasticity, which uses

calculus to evaluate the responsiveness of quantity demanded to price at a particular

point on a demand curve. Basically, the elasticity is measured at a point by assuming tiny

changes in price and quantity demanded.

The second important point is that the formula for an elasticity coefficient will always produce a negative number because demand curves are negatively sloped. That is, they slope

downward to the right. In practice, economists ignore the minus signs on coefficients of

price elasticity of demand. An Ed value of 25 is considered to be larger than an Ed value of

24, for example. That is, these coefficients are treated as absolute values. It will be important later when considering other measures of elasticity to keep track of their signs, but the

sign is not important for price elasticity of demand. Some economists put a negative sign

in front of the formula to change the sign of the calculated coefficient.

The Midpoint Method

The demand schedule of Table 4.1 can be used to calculate some coefficients of price elasticity of demand. Again, the formula is

Ed 5

Percent change in quantity demanded

Percent change in price

Table 4.1: Demand curve schedule for straight-line demand curve in Figure 4.5

Price

Quantity demanded

$0.50

25

1.00

20

1.20

18

1.40

16

1.60

14

1.80

12

2.00

10

2.20

8

ama80571_04_c04_099-130.indd 108

(continued)

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CHAPTER 4

Section 4.4 Calculating Elasticity

Table 4.1: Demand curve schedule for straight-line demand curve in Figure 4.5 (continued)

Price

Quantity demanded

2.40

6

2.60

4

2.80

2

3.00

0

Since we are calculating arc elasticity, we use averages. The reason averages are used to

calculate elasticity can be illustrated using two points from the demand schedule in Table

4.1. First, consider the elasticity of a price increase as we move along the demand curve

from Point A ($.50) to Point B ($1.00):

Price

Quantity demanded

A

B

% change

$.50

$1.00

100%

25

20

80%

Using the formula

Ed 5

Percent change in quantity demanded

Percent change in price

Ed 5 80/100 5 .80

Now consider the same two points, but use Point B as the starting point, and observe a

price decrease (from $1.00 to $.50):

Price

Quantity demanded

B

A

% change

$1.00

$.50

50%

20

25

125%

Now when we use the same formula and the same two points we get the following result:

Ed 5 125/50 5 2.5

As you can see, if, instead of average values, we used the beginning or ending price and

quantity as the bases, the formula would produce different elasticity measures between

the same two points. By using averages we don’t have to distinguish between price

increases and decreases.

To build these averages into our formula, we divide both the sum of the beginning price and

the ending price and the sum of the beginning quantity and the ending quantity by two.

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CHAPTER 4

Section 4.4 Calculating Elasticity

For our purposes, this expression can be written as

DQ

Q1 1 Q2

2

Ed 5

DP

P1 1 P2

2

Since we are calculating arc elasticity, we use averages. That is, we divide both the sum of

the beginning price and the ending price and the sum of the beginning quantity and the

ending quantity by two. This is called the midpoint method.

We can now compute the elasticity coefficients for two different price changes on the

demand curve in Figure 4.5. First, the elasticity coefficient for the increase in price from

$1.00 to $1.20:

20 2 18

20 1 18

2

2

19

0.105

Ed 5

5

5

5 0.58

$1.00 2 $1.20

2.20

20.182

$1.00 1 $1.20

$1.10

2

Recall that economists ignore the sign (whether positive or negative) and just look at the

absolute value of price elasticities of demand.

Now for the elasticity coefficient for the increase in price from $2.00 to $2.20:

10 2 8

10 1 8

2

2

9

0.222

Ed 5

5

5

5 2.34

$2.00 2 $2.20

2.20

20.095

$2.00 1 $2.20

$2.10

2

Note that the elasticity varies along this demand curve, which has a constant slope. In

fact, all linear demand curves, except those that are vertical or horizontal, have elasticity

coefficients that range from zero through infinity. On a demand curve such as the one

shown in Figure 4.6, all points above price P1 (which corresponds to th …

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