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Elasticities and the Quantitative
Analysis of Supply and Demand
Examples of Revenue Change Resulting
From a Change in Price
number of total revenue
price
per night
tickets sold
per
per night
ticket
$250
50
$5
Case A
$400
100
$4
Case B
$5
$4
500
550
$2,500
$2,200
Elasticity is a measure of responsiveness
to a stimulus.
What is the responsiveness of your grade-point
average to hours of study time?
What is the responsiveness of wheat
production to rain fall?
What is the responsiveness of electricity usage
to the average daily temperature?
The quantity demanded by a consumer
will depend upon the following factors:
The good’s own price.
The consumer’s income.
Prices of related goods.
The consumer’s tastes and and preferences.
Expectations and other special influences.
The quantity supplied will depend upon:
the good’s own price
prices of inputs used in producing the good.
technology
prices of other goods the seller could supply
expectations and other factors
The price elasticity of demand, ED, measures the
responsiveness of the quantity demanded to changes in
the good's own price.
percent changein the quantity demanded
ED 
percent changein price
ED 
6 percent change in Qd 3 percent change in Qd

2 percent change in P 1 percent change in P
ED is the percentage change in the quantity demanded that
results per one percent change in price.
Suppose that a 10% increase in the price of
cigarettes results in a 4% decrease in the
quantity demanded.
4%
ED 
 0.4
10 %
For each 1% increase in price, the quantity
demanded goes down 0.4%.
Suppose that a 10% increase in the price of tickets
to a Ry Cooder concert results in a 25% decrease in
the quantity demanded.
25 %
ED 
 2.5
10 %
The demand for concert tickets is more responsive to
price than is the demand for cigarettes.
We say the demand for concert tickets is more elastic
(w.r.t. price) than is the demand for cigarettes.
Calculating the Price Elasticity of Demand
P1  P2
Q1  Q2
P
P1
P2
D
Q1
Q2
Q
percentchangein the quantity demanded
percent change in price
Qd
Qd

Q2  Q1 
 100
%  Qd
Qd
Qd
Qd




P
P
( P2  P1 )
%P
 100
P
P
P
ED 
Qd  (Q1  Q2 ) / 2
Pd  ( P1  P2 ) / 2
Example
price per
number of tickets
ticket
sold per night
$5
50
$4
100
Case A
Qd
ED 
P
Qd
P
(100  50 )

( 4  5)
75 
4.5
50
1
75
4.5

2
1
3
 
4.5
ED
2 4.5
9

   3
3 1
3
Important points:
The minus sign is dropped when calculating ED.
The formula is based on percentage changes, not unit changes.
The average price and quantity (midpoints) are used.
Price
$7
Quantity
demanded
(1000s)
1
Price
elasticity
ED = 4.33
4.33
$6
$5
$4
$3
$2
8
2
2.20
7
1.29
6
5
0.78
4
3
0.45
2
1
3
4
5
6
0.23
$1
7
P
a
ED > 1
ED = 1
ED < 1
b
ED = 0.23
c
1
2
3
4
5
6
7
8 Q
% Qd
ED 
% P
Demand is said to be elastic with respect to price
if ED > 1.
%Qd > %P
Demand is said to be inelastic with respect to
price if ED < 1.
%Qd < %P
Demand is said to be unit elastic with respect to
price if ED = 1.
%Qd = %P
Goods that are necessities typically have price
elasticities of demand that are relatively smaller.
Example:
ED = 0.58 for food
ED = 1.26 for furniture.
Goods having ready substitutes typically have
higher price elasticities of demand.
Example:
ED = 0.4 for gasoline
ED = 1.4 for natural gas
ED typically will be larger as the market/good is
more narrowly defined.
Example:
The price elasticity of demand for food will be smaller than the
price elasticity of demand for ice cream.
ED typically will be larger as buyers have a
longer period of time to respond to price
changes.
Inferences that can be made when the
price elasticity of demand is known.
%Qd
ED 
%P
%Qd  E D  %P
Inferences that can be made when the
price elasticity of demand is known.
%Qd
ED 
%P
%Qd  E D  %P
Example 1:
Suppose that ED = 2.5 and that there is a 5% increase in price. What
will be the percentage increase in the quantity demanded?
%Qd  ED  %P
 2.5  5%  12.5%
%Qd
ED 
%P
Example 2:
Suppose that the price elasticity of demand for cigarettes
is 0.7 for teens. How much would the price have to
increase in order for teen smoking to be reduced 35%?
35%
0.7 
?
%Qd
ED 
%P
Example 2:
Suppose that the price elasticity of demand for cigarettes
is 0.7 for teens. How much would the price have to
increase in order for teen smoking to be reduced 35%?
35%
0.7 
?
%Qd 35%
%P 

 50%
ED
0.7
The relationship between price and revenue changes:
The importance of ED
Price
$7
Quantity
demanded
(1000s)
1
Price
elasticity
Revenues
($1000s)
TR = PQ
$7
4.33
$6
2
$12
2.20
$5
3
$15
1.29
$4
4
$16
0.78
$3
5
$15
0.45
$2
6
$12
0.23
$1
7
$7
The relationship between price and revenue changes:
The importance of ED
Price
$7
Quantity
demanded
(1000s)
1
Price
elasticity
Revenues
($1000s)
TR = PQ
$7
4.33
$6
2
$12
2.20
$5
3
$15
1.29
$4
4
$16
0.78
$3
5
$15
0.45
$2
6
$12
0.23
$1
7
$7
Demand is elastic
ED = 4.33
P
8
a
ED > 1
ED = 1
7
Demand is inelastic
6
5
4
3
ED < 1
b
2
1
ED = 0.23
c
1
2
3
4
5
6
7
8 Q
Price
$7
Quantity
demanded
(1000s)
1
Price
elasticity
Revenues
($1000s)
TR = PQ
$7
4.33
$6
2
$5
3
4
$15
6
5
$16
0.78
$3
5
$15
0.45
$2
6
8
7
1.29
$4
P
$12
2.20
a
ED > 1
ED = 1
4
3
Demand is inelastic
ED < 1
b
2
1
7
1
$7
ED = 0.23
c
$12
0.23
$1
Demand is elastic
ED = 4.33
2
3
4
5
6
7
8 Q
When demand is elastic (ED > 1), there is an inverse relationship
between changes in price and changes in total revenue.
P  TR
P  TR
ED > 1 implies that %Qd > %P.
TR = P • Q
  
Price
$7
Quantity
demanded
(1000s)
1
Price
elasticity
Revenues
($1000s)
TR = PQ
$7
4.33
$6
2
$5
3
4
$15
6
5
$16
0.78
$3
5
$15
0.45
$2
6
8
7
1.29
$4
P
$12
2.20
a
ED > 1
ED = 1
4
3
Demand is inelastic
ED < 1
b
2
1
7
1
$7
ED = 0.23
c
$12
0.23
$1
Demand is elastic
ED = 4.33
2
3
4
5
6
7
8 Q
When demand is inelastic (ED < 1), there is a direct relationship
between changes in price and changes in total revenue.
P  TR
P  TR
ED < 1 implies that %Qd < %P.
TR = P • Q
  
“Good weather is often bad for farmers' incomes."
This follows from the “total revenue test” and demand for many
farm products being price inelastic.
P
D
S1
TR1 = P1  Q1
S2
P1
TR2 = P2  Q2
P2
P  TR
Q1 Q 2
Q
P
P
Figure 1a
Figure 1b
Q
Q
Consider two alternative demand curves for a particular good.
P
Figure 2
ED = .8182
ED =1.5
1.00
0.80
D2
D1
10 12 14
Q
At the point where two demand curves intersect, the flatter demand curve is
relatively more elastic with respect to price, as compared to the steeper
demand curve.
Figure 4
P
D1
Sa
Sb
P0
D2
P1
Q0
P
D1
Q2
Sa
Sb
Q
P
Sa
Sb
P0
P0
D2
P1
Q0
Q2
Q
Q0
Q2
Q
Figure 3
Figure 3
P
P
Sa
Sa
Sb
P0
P0
P2
P1
D2
P2
P1
D1
D1
Q0
P
Q1
Q2
D2
Q0
Q
P
Sa
Sb
P0
Q1
Q2
Q
Sa
Sb
P0
P2
P1
D2
D1
Q0
Q1
D1
Q
Q0
Q2
Q
FACT: For a given increase in supply the increase in
equilibrium quantity will be larger and the decrease in
equilibrium price will be smaller as the demand is more
elastic with respect to price.
Figure 3
P
Figure 3
P
Sa
Sb
P0
P2
P1
D2
Sa
Sb
P0
P2
P1
D2
D1
Q0
Q1
Q2
D1
Q
Q0
Q1
Q2
Q
FACT: For a given increase in demand, the increase in
equilibrium quantity will be larger and the decrease in
equilibrium price will be smaller as supply is more elastic
with respect to price.
S2
Sb
P
P2
P
Sa
P0
S1
P1
P0
Db
Da1
D1
Q0
Q
Q0
Q2
Q1
Q