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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
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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
$0.50
25
1.00
20
1.20
18
1.40
16
1.60
14
1.80
12
2.00
10
2.20
8
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(continued)
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CHAPTER 4
Section 4.4 Calculating Elasticity
Table 4.1: Demand curve schedule for straight-line demand curve in Figure 4.5 (continued)
Price
Quantity demanded
2.40
6
2.60
4
2.80
2
3.00
0
Since we are calculating arc elasticity, we use averages. The reason averages are used to
calculate elasticity can be illustrated using two points from the demand schedule in Table
4.1. First, consider the elasticity of a price increase as we move along the demand curve
from Point A ($.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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