Percentages and Elasticity

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
S0
40.00
30.00
Large price change and small quantity change
Price (dollars per pizza)
20.00
10.00
5.00
Da
0
25
5
10
15
20
13
Quantity (pizzas per hour)
4
Impact of a Change in Supply
40.00
S0
Small price change and large quantity change
30.00
Price (dollars per pizza)
20.00
Db
10.00
0
25
5
10
15
20
17
Quantity (pizzas per hour)
5
Price Elasticity
Price Elasticity of Demand
The ratio of the two percentages is a number
without units.
6
Price Elasticity

• Example
• Price of oil increases 10
• Quantity demanded decreases 1

7
TYPES OF ELASTICITYHypothetical Demand
Elasticities for 4 Products
8
Price Elasticity Ranges Extreme Price
Elasticities
9
Price Elasticity RangesSummary from Table

• Elastic Demand

• Unit Elastic

• Inelastic Demand

10
Elasticity of Demand

• Calculating elasticity

11
Calculating the Elasticity of Demand
Price (dollars/pizza)
20.50
20.00
19.50
D
Quantity (pizzas/hour)
9 10 11
12
Elasticity of Demand (mid-point)
D Q 2
X 100
Q1 Q2 (9 11)
D Q 20
10
2
Ed
D P 1.00
X 100
D P 5
P1 P2 (20.50 19.50)
20
2
Always use the mid-point formula for calculating
elasticity
13
Changes in Elasticity Along a Linear Demand
1.10
1.00
.90
.80
.70
.60
Price per Minute ()
.50
.40
.30
D
.20
.10
0
1
2
3
4
5
6
7
8
9
10
11
Quantity per Period (billions of minutes)
14
The Relationship Between Price Elasticity of
Demand andTotal Revenues for Cellular Phone
Service
Quantity Total Elasticity
Price Demanded Revenue
Ep
0 1.0 1.8 2.4 2.8 3.0 3.0 2.8 2.4 1.8 1.0

• 1.10 0
• 1.00 1
• .90 2
• .80 3
• .70 4
• .60 5
• .50 6
• .40 7
• .30 8
• .20 9
• .10 10

15
Total Revenue and Elasticity
Total Revenue Price Per GoodX of Goods
Sold TR P X Q
Assumption Costs are constant
16
Elasticity and Total Revenue
1.10
.80
Price
.55
Quantity
0
55 110
3.00
(dollars)
Total Revenue
Quantity
0 55 110
17
Relationship Between PriceElasticity of Demand
and Total Revenues
Price Elasticity Effect of Price Change of
Demand on Total Revenues (TR)
Price Price Decrease Increase

• Inelastic (EP lt 1) TR
  TR
• Unit-elastic (EP 1) No change No change
  Elastic (EP gt 1) TR
  TR

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.
19
Question

• 2 drivers - Tom Jerry each drive to to a gas
  station.
• Before looking at the price, each places an
  order.
• Tom says, Id like 10 litres of gas.
• Jerry says, Id like 10 of gas.
• What is each drivers price elasticity of demand?

20
Determinants ofPrice 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
Demand Elasticity and Time
D1
D2
D3
P1
Price per Unit
As time passes, the demand curve rotates to D2
and then to D3 and quantity demanded lowers first
to Q1 and then to Q2
Q2
Q1
Q3
Quantity Supplied per Period
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

24
How a Change in Demand Changes Price and Quantity
Sa
40.00
Large price change and small quantity change
Price (dollars per pizza)
20.00
10.00
D0
25
5
20
0
10
15
Quantity (pizzas per hour)
25
How a Change in Demand Changes Price and Quantity
Small price change and large quantity change
40.00
30.00
Price (dollars per pizza)
Sb
20.00
10.00
D0
25
5
20
0
10
15
Quantity (pizzas per hour)
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
S
Price
Price
S
Quantity supplied is the same for any price!
Suppliers will offer ANY quantity at this price
0
Quantity
0
Quantity
28
Elasticity of Supply Depends On

• Resource substitution possibilities,
  -The more unique the resource, the more
  inelastic the supply.
• 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
Supply Elasticity and Time
P1
Price per Unit
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
Q1
Quantity Supplied per Period
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
Sales Tax Imposed on the Sellers
Supply is affected
S
110
105
Price (dollars per player)
100
95
DA
3 4 5 6
Quantity (thousands of MP3 players per week)
33
Sales Tax Who Pays?
S tax
S
110
10 tax
105
Price (dollars per player)
100
95
DA
3 4 5 6
Quantity (thousands of MP3 players per week)
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
The Sales Tax Who Pays? Demand Relatively
Inelastic
S tax
S
110
10 tax
108
105
Price (dollars per player)
100
98
95
DA
3 4 5 6
Quantity (thousands of MP3 players per week)
36
The Sales Tax Who Pays? Demand Relatively More
Elastic.
S tax
S
110
10 tax
DA
105
103
Price (dollars per player)
100
95
93
3 4 5 6
Quantity (thousands of MP3 players per week)
37
Sales Tax Who Pays When Tax Is Imposed on the
Buyer?
S
110
105
Price (dollars per player)
100
95
DA
3 4 5 6
Quantity (thousands of MP3 players per week)