1
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
2
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
3
Impact of a Change in Supply &
Therefore Price on the Quantity Demanded
S1
Quantity (pizzas per hour)
Price (dollars per pizza)
10.00 20.00 30.00 40.00
Da
0 5 10 13 15 20 25
5.00
S0
Large price change and small quantity change
An increase in supply brings ...
… and a small
increase in quantity
… a large fall in price...
4
Impact of a Change in Supply…
Quantity (pizzas per hour)
Price (dollars per pizza)
10.00 20.00 30.00 40.00
Db
0 5 10 15 17 20 25
S1
15.00
S0
Small price change and large quantity change
An increase in supply brings ...
… a small fall in price...
… and a large
increase in quantity
5
Price Elasticity
E
p %Q
d%P
Percentage change in price
Percentage change in quantity demanded
p E
The ratio of the two percentages is a number without units.
Price Elasticity of Demand
6
Price Elasticity
• Example
– Price of oil increases 10%
– Quantity demanded decreases 1%
E
p -1%
10% .1
When calculating the price elasticity of When calculating the price elasticity of demand, we ignore the minus sign for demand, we ignore the minus sign for
% change in
% change in QQ..
7
TYPES OF ELASTICITY
Hypothetical Demand Elasticities for 4 Products
8
Price Elasticity Ranges: Extreme Price Elasticities
Quantity Demanded per Year
(millions of units)
Price
0
D
8
Perfect
inelasticity, zero elasticity, no matter how much Price changes, Quantity stays the same;
insulin P0
P1
Quantity Demanded per Year (millions of units)
Price
0
Perfect elasticity, infinite elasticity, the slightest increase
in price will lead to
zero sales.
30 D
P1
P1 never touches the demand curve
9
Price Elasticity Ranges
Summary from Table
% Q %P; E P 1
% Q %P; E P 1
% Q %P; E P 1
Unit Elastic
Inelastic Demand
Elastic Demand
10
Elasticity of Demand
• Calculating elasticity
Ep Change in Q (Q1 Q2)/2
Change in P (P1 P2)/2
or
Ep Q Avg.Q
P Avg.P
or
Sum of prices/2 Change in P Sum of quantities/2
Change in Q p
E
Always use the mid-point
formula
11
Calculating the Elasticity of Demand
9 10 11 19.50
20.50
D New point
Quantity (pizzas/hour) Price (dollars/pizza)
20.00
Original point
Elasticity = = 4Q /Qave
P/Pave
2/10
= 1/20
ΔP=1
ΔQ=2
Qave =1/2(11+9)=10
Pave =1/2(20.50+19.50)=20
12
Elasticity of Demand (mid-point)
Ed =
P = $1.00
P1 + P2 ($20.50 + $19.50)
2
P
=5% = $20
Q = 2
Q1 + Q2 (9 + 11)
2
Q
=20% = 10
Always use the mid-point formula for calculating elasticity 20%
5% =
4
= Ed =
X 100
X 100
13
D
Demand, or average
revenue curve
Quantity per Period (billions of minutes)
Price per Minute ($)
0
.10 .20 .30 .40 .50 .60 .70 .80 .90 1.00 1.10
1 2 3 4 5 6 7 8 9 10 11
Elastic (EP > 1)
Inelastic (EP < 1)
Unit-elastic (EP = 1)
Changes in Elasticity Along a Linear
Demand
14
The Relationship Between Price Elasticity of Demand and Total Revenues for Cellular Phone Service
$1.10 0
1.00 1
.90 2
.80 3
.70 4
.60 5
.50 6
.40 7
.30 8
.20 9
.10 10
Quantity Total Elasticity Price Demanded Revenue Ep
21.000 6.333 3.400 2.143 1.144 1.000 .692 .467 .294 .158
Elastic
Inelastic Unit-elastic 00
1.01.0 1.81.8 2.42.4 2.82.8 3.03.0 3.03.0 2.82.8 2.42.4 1.81.8 1.01.0
15
Total Revenue and Elasticity
Total Revenue
=
Price Per Good
X
# of Goods Sold
TR = P X Q
Total Revenue
=
Price Per Good
X
# of Goods Sold
TR = P X Q
Assumption : Costs are constant
Assumption : Costs are constant
16
5555 110110 .55.55
1.101.10
3.003.00
(dollars)(dollars)
Maximum total revenue When demand is inelastic,
price cut decreases total revenue
Unit elastic Elastic
demand
Quantity Quantity
Inelastic demand 00
When demand is elastic, price cut increases total revenue
Total RevenueTotal Revenue PricePrice
0 55
0 55 110110
E la st ic ity a nd T ot al R ev en ue
Quantity Quantity .80
17
Relationship Between Price
Elasticity of Demand and Total Revenues
Inelastic (EP < 1) TR TR Unit-elastic (EP = 1) No change No change Elastic (EP > 1) TR TR
Price Elasticity Effect of Price Change
of Demand on Total Revenues (TR)
Price Price
Decrease Increase
18
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.
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.
19
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?
20
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
21
D2
Quantity Supplied per Period
Price per Unit
D1
Pe P1
As time passes, the demand curve rotates to D2 and then to D3 and quantity demanded lowers first to Q1 and then to Q2
Demand Elasticity and Time
D3
Q2 Q1 Q3
22
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?
23
Elasticity of Supply
• Calculating elasticity
Ep Change in Q (Q1 Q2)/2
Change in P (P1 P2)/2
or
Ep Q Avg.Q
P Avg.P
or
Sum of prices/2 Change in P Sum of quantities/2
Change in Q p
E
Always use the mid-point
formula
24
How a Change in Demand Changes Price and Quantity
Quantity (pizzas per hour)
Price (dollars per pizza)
10.00 40.00
D0
0 5 10 15 20 25
Sa Large price change and small quantity change
… a large price rise...
20.00
D1 30.00
13
An increase in demand brings ...
… and a small quantity increase
25
How a Change in Demand Changes Price and Quantity
Quantity (pizzas per hour)
Price (dollars per pizza)
10.00 30.00 40.00
D0
0 5 10 15 20 25
Sb
Small price change and large quantity change
… a small price rise...
20.00
D1 An increase
in demand brings ...
21.00
… and a large quantity increase
26
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
27
Supply Elasticity Ranges
Price
Quantity
S Elasticity of supply = 0
0
Quantity supplied is the same for any
price!
PricePrice
Quantity Quantity
SS Elasticity of
supply =
00
Suppliers will offer ANY quantity at this
price
28
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.
29
S2
Quantity Supplied per Period
Price per Unit
S1
Qe Pe
P1
As time passes, the supply curve rotates to S2 and then to S3 and quantity supplied rises first to Q1 and then to Q2
Supply Elasticity and Time
S3
Q1 Q2
30
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
31
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?
32
S + tax
Sales Tax Imposed on the Sellers
Quantity (thousands of MP3 players per week)
Price (dollars per player)
3 4 5 6
95 100 105
110 S
DA Tax
revenue
$10 tax
After Tax Market Price Supply is affected
33
S + tax
Sales Tax: Who Pays?
Quantity (thousands of MP3 players per week)
Price (dollars per player)
3 4 5 6
95 100 105
110 S
DA
$10 tax
Original Market Price
Buyer pays
After Tax Market Price
Seller pays
After Tax
Price to Seller t
a x Tax Wedge
34
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.
35
S + tax
The Sales Tax: Who Pays?
Demand Relatively Inelastic
Quantity (thousands of MP3 players per week)
Price (dollars per player)
3 4 5 6
95 100 105
110 S
DA 98
108 $10 tax
36
S + tax
The Sales Tax: Who Pays? Demand Relatively More Elastic.
Quantity (thousands of MP3 players per week)
Price (dollars per player)
3 4 5 6
95 100 105
110 S
DA $10 tax
Original Market Price 103
93
Tax Wedge
37
D-tax
Sales Tax: Who Pays When Tax Is Imposed on the Buyer?
Quantity (thousands of MP3 players per week)
Price (dollars per player)
3 4 5 6
95 100 105
110 S
DA
$10 tax
Original Market Price