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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

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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

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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...

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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

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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

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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..

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TYPES OF ELASTICITY

Hypothetical Demand Elasticities for 4 Products

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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?

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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

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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

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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?

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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

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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

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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

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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

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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

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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.

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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

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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

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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?

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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

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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

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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.

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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

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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

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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

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