Percentages and Elasticity
•Which of the following seem more serious:
– An increase of 50 cents or an increase of
50% in the price of a hamburger
– An increase of $100 or an increase of 1% in
the price of a new car
•Percentage changes are often more important
than the amount of change
– Therefore economists often use elasticities
to examine percentage change or
responsiveness
1
Price Elasticity
• Price Elasticity of Demand (Ep)
– The responsiveness of quantity demanded
of a commodity to changes in its price
– Related to the slope, but concerned with
percentage changes
2
Price (dollars per pizza)
Impact of a Change in Supply &
Therefore Price on the Quantity Demanded
S0
40.00 … a
30.00
large
fall in
price...
S1
An increase
in supply
brings ...
Large price
change and
small quantity
change
20.00
10.00
… and a small
increase in quantity
5.00
0
5
10 13 15
Da
20
25
Quantity (pizzas per hour)
3
Price (dollars per pizza)
Impact of a Change in Supply…
An increase
in supply
S0
brings ...
40.00
30.00 … a small
fall in price...
20.00
15.00
Small price
change and
large quantity
change
Db
10.00
0
S1
… and a large
increase in quantity
5
10
25
15 17 20
Quantity (pizzas per hour)
4
Price Elasticity
Price Elasticity of Demand
Ep 
Percentage change in quantity demanded
Percentage change in price
%Qd
Ep 
%P
The ratio of the two percentages is a
number without units.
5
Price Elasticity
• Example
– Price of oil increases 10%
– Quantity demanded decreases 1%
-1%
Ep 
 .1
10%
When calculating the price elasticity of
demand, we ignore the minus sign for
% change in Q.
6
TYPES OF ELASTICITY
Hypothetical Demand Elasticities for 4 Products
Product
% Change in
price (%P)
% Change in Elasticity
quantity
(%QD/%P)
demanded
(%QD)
Insulin
+ 10%
0%
0  Perfectly
inelastic
Basic
Telephone
service
+ 10%

-1%
.1  Inelastic
Beef
+ 10%

-10%
1.0 
Unitarily
elastic
Bananas
+ 10%

-30%
3.0Elastic
7
Price Elasticity Ranges: Extreme Price Elasticities
P1 never touches
the demand curve
D
Price
P1
P0
0
8
Quantity Demanded per Year
(millions of units)
P1
30
Price
Perfect
inelasticity,
zero elasticity,
no matter how
much Price
changes,
Quantity
stays the
same;
insulin
0
D
Perfect
elasticity,
infinite
elasticity,
the slightest
increase
in price will
lead to
zero sales.
Quantity Demanded per Year
(millions of units) 8
Price Elasticity Ranges
Summary from Table
 Elastic Demand
%Q  %P; EP  1
 Unit Elastic
%Q  %P; EP  1
 Inelastic Demand
%Q  %P; EP  1
9
Elasticity of Demand
• Calculating elasticity
Ep 
or
Change in Q
Sum of quantities/2
Change in P
Sum of prices/2
Change in Q
Ep 
(Q1  Q2 )/2
or
Change in P
(P1  P2 )/2
Q
P
Ep 
Avg. Q Avg. P
10
Calculating the Elasticity of Demand
Price (dollars/pizza)
Original
point
20.50
ΔP=1
Q /Qave 2/10
=
Elasticity =
=4
P/Pave 1/20
20.00
New
point
19.50
D
Qave =1/2(11+9)=10
Pave =1/2(20.50+19.50)=20
9
10
ΔQ=2
11
Quantity (pizzas/hour)
11
Elasticity of Demand (mid-point)
Q =2
% Q
=20%
X 100
Q1 + Q2 (9 + 11)
= 10
2
Ed =
= Ed =
 P = $1.00
% P
=5%
20%
=
5%
X 100
P1 + P2 ($20.50 + $19.50)
= $20
2
12
Always use the mid-point formula for calculating elasticity
4
Changes in Elasticity Along a Linear
Demand
1.10
Elastic (EP > 1)
1.00
Price per Minute ($)
.90
Unit-elastic (EP = 1)
.80
Inelastic (EP < 1)
.70
.60
.50
Demand,
or average
revenue curve
.40
.30
.20
D
.10
0
1
2
3
4
5
6
7
8
9
Quantity per Period (billions of minutes)
10
11
13
The Relationship Between Price Elasticity of Demand and
Total Revenues for Cellular Phone Service
Price
Quantity
Total
Elasticity
Demanded
Revenue
$1.10
0
0
1.00
1
1.0
.90
2
.80
3
.70
4
.60
5
.50
6
1.8
2.4
2.8
Ep
21.000
6.333
3.400
Elastic
2.143
3.0
1.144
1.000 Unit-elastic
.40
7
3.0
.30
8
2.8
.692
.20
9
2.4
.10
10
1.8
.467
.294
1.0
.158
Inelastic
14
Total Revenue and Elasticity
Total Revenue
=
Price Per Good
X
# of Goods Sold
TR = P X Q
Assumption : Costs are constant
15
Elastic
demand
Price
1.10
.80
Unit
elastic
.55
Inelastic
demand
0
55
Maximum
total revenue
(dollars)
Total Revenue
3.00
110
Quantity
When demand is
elastic, price cut
increases total
revenue
0
55
When demand
is inelastic,
price cut decreases
total revenue
110
Quantity
16
Relationship Between Price
Elasticity of Demand and Total Revenues
Price Elasticity
of Demand
Effect of Price Change
on Total Revenues (TR)
Price
Decrease
Inelastic
(EP < 1)
Unit-elastic (EP = 1)
> 1)
TR
TR 
No change
Price
Increase
TR
No change
Elastic (EP
TR 
17
Total Revenue and Elasticity
Total Revenue Test:
Estimate the price elasticity of
demand by observing the change in
total revenue that results from a
change in price (ceteris paribus).
Note that revenue is maximized
when elasticity of demand = -1.
18
Question
• 2 drivers - Tom & Jerry each drive to to a gas
station.
• Before looking at the price, each places an
order.
• Tom says, “I’d like 10 litres of gas”.
• Jerry says, “I’d like $10 of gas”.
• What is each driver’s price elasticity of
demand?
19
Determinants of
Price Elasticity of Demand
•
•
•
•
•
Existence of substitutes
The length of time allowed for
adjustment
More specifically a good is defined
(more specific = more substitutes)
Necessity or not
Share of budget
20
Demand Elasticity and Time
Price per Unit
D2
P1
Pe
As time passes, the
demand curve rotates
to D2 and then to D3
and quantity demanded
lowers first to Q1 and
then to Q2
Q3
Q2 Q1
Quantity Supplied per Period
21
Elasticity: Example
• You are the consulting economist to the Guelph
transportation commission,
• The current fare is $.80
• There are 25,000 riders per day
• For each $.01 increase (decrease) in the fare, rider
ship decreases (increases) by 500 riders per day.
• What is the price elasticity of demand at the current
fare?
• Should fares be raised or lowered?
• What fare will maximize revenue?
22
Elasticity of Supply
• Calculating elasticity
Ep 
Change in Q
Change in P
Sum of quantities/2
Sum of prices/2
or
Change in Q
Ep 
(Q1  Q2 )/2
or
Change in P
(P1  P2 )/2
Q
P
Ep 
Avg. Q Avg. P
23
Price (dollars per pizza)
How a Change in Demand Changes Price and Quantity
40.00
An increase
in demand
brings ...
Sa
Large price change and
small quantity change
30.00
20.00
10.00
0
… a large
price rise...
… and a small
quantity increase
5
10 13 15
D1
20
25
D0
Quantity (pizzas per hour)
24
Price (dollars per pizza)
How a Change in Demand Changes Price and Quantity
40.00
Small price
change and
large quantity
change
An increase
in demand
brings ...
30.00
21.00
20.00
Sb
… a small
10.00 price rise...
… and a large
quantity increase
D1
D0
0
5
10
15
20
25
Quantity (pizzas per hour)
25
Elasticity of Supply
• Elasticity of supply ranges
– (from) Perfectly Elastic Supply
• Quantity supplied falls to 0 when there is
any decrease in price
– (to) Perfectly Inelastic Supply
• Quantity supplied is constant no matter
what happens to price
Notice: There is no total revenue test for supply
since price and quantity are directly related
26
S
Elasticity of
supply = 0
Price
Price
Supply Elasticity Ranges
Elasticity of
supply =

S
Quantity supplied is
the same for any
price!
0
Quantity
Suppliers will offer
ANY quantity at this
price
0
Quantity
27
Elasticity of Supply: Depends On:
1. Resource substitution possibilities,
-The more unique the resource, the more
inelastic the supply.
2. Time frame for the supply decision,
Momentary supply
Long-run supply
Short-run supply
- The longer producers have to adjust to a price
change, the more elastic is supply.
28
Supply Elasticity and Time
Price per Unit
S1
S2
P1
Pe
As time passes, the
supply curve rotates
to S2 and then to S3
and quantity supplied
rises first to Q1 and
then to Q2
Q2
Qe
Q1
Quantity Supplied per Period
29
Elasticity: example-Tax Burden
• Government levies a tax on a good:
– who actually pays the tax,
– what is the incidence of the tax,
• who bears the burden of the tax.
• Suppose that the tax is levied on the seller;
i.e., the seller has to pay the tax
Supply is affected
30
Explain the Effects of the Sales Tax
• A $10 sales (excise) tax per MP3 player is imposed
on the sellers of MP3 players.
• There are now two “prices” for MP3 players: an
after- tax price faced by buyers, and an after-tax
price faced by sellers.
• Will the price faced by buyers increase $10 after
introducing the sales tax? By how much?
• Will the price faced by sellers change? By how
much?
31
Sales Tax Imposed on the Sellers
Price (dollars per player)
Supply is affected
S + tax
S
110
$10 tax
105
100
After Tax
Market Price
Tax
revenue
95
DA
3
4
5
6
Quantity (thousands of MP3 players per week)
32
Sales Tax: Who Pays?
Price (dollars per player)
Tax Wedge
S + tax
S
110
$10 tax
After Tax
Market Price
105
Buyer pays
100
t
a
Seller pays x
Original Market Price
After Tax
Price to Seller
95
DA
3
4
5
6
Quantity (thousands of MP3 players per week)
33
Summary:
• Taxes discourage market activity
• Burden is shared, buyers pay more,
sellers receive less,
and
•Tax burden falls most heavily on the
side of the market that is least elastic
in its response to a price change.
34
The Sales Tax: Who Pays?
Demand Relatively Inelastic
Price (dollars per player)
S + tax
S
110
108
105
$10 tax
100
98
95
DA
3
4
5
6
Quantity (thousands of MP3 players per week)
35
The Sales Tax: Who Pays? Demand
Relatively More Elastic.
Price (dollars per player)
Tax Wedge
S + tax
S
110
$10 tax
DA
105
103
Original Market Price
100
95
93
3
4
5
6
Quantity (thousands of MP3 players per week)
36
Price (dollars per player)
Sales Tax: Who Pays When Tax Is
Imposed on the Buyer?
S
110
D-tax
105
Original Market Price
100
95
DA
3
4
5
6
Quantity (thousands of MP3 players per week)
37