Chapter 5Elasticity

You are responsible for reading Chapter 4!!!

What have we done?• Chapter 3 gave us downward sloping

demand curves– Law of demand

• Now want to see how Qd changes when price changes

Elasticity

• Response of one variable to a change in another variable

• Price elasticity of demand– Measure of the responsiveness of Qd of a

product to a change in the price of that product

PQEd

%%

PPQQ

E

d

d

So…

• What if Ed = 3?– If price was increased from the prevailing

point the % change in Qd would be 3 times the change in price

• Shouldn’t it be negative?– So price increases and Qd decreases?

• Yes!!– For ease we look at the absolute value, but

know that the law of demand holds

Point elasticity

• Measures the change between two observed points.

a

ab

a

abd

d

PPP

QQQ

PPQQ

E

example

• P1 = 10• P2 = 12• Q1 = 100• Q2 = 50• Elasticity??• Which is Point A??? • Big Problem!!!

6

121210

5050100

;2

5.2

101012

10010050

;1

A

A

Problem

• Answers vary depending on where you start

• Becomes more important the larger the change

Arc Elasticity• To avoid the endpoint problem take elasticity at the

midpoint (average) of the two points

2

2

2

2

21

21

21

21

21

21

PPPP

QQQQ

PPP

QQQ

E

dd

dd

dd

d

d

Differences

• With arc elasticity it is clear which points are used

• P1 is the first price• P2 is the second price• Qd1 and Qd2 are the first and second

quantity demanded respectively

Price elasticity of demand can yield 5 basic results

• Numerator > Denominator• Numerator < Denominator • Numerator = Denominator • Numerator = 0 • Denominator = 0• Each has a specific name and result

Elastic Demand

• Ed > 1• % change in quantity demanded > %

change in price• FLATTER CURVE• What are some examples of an elastic

good???

Inelastic Demand

• Ed<1• % change in the price > percent change in

quantity demanded• STEEPER CURVE• What are some examples of an inelastic

good?

Price Elasticity of Demand

a

0

Quantity Demanded

Price

D

10%

20%

Q1

Part (a)

Q2

P1

P2

Ed > 1Elastic

0

Quantity Demanded

Price

D

10%

4%

Q1

Part (b)

Q2

P1

P2

Ed < 1Inelastic

Unit Elastic Demand

• Ed=1• % change in price = % change in quantity

demanded• Change in price brings a proportionate

change in quantity demanded• CURVE

Price Elasticity of Demand

a

0

Quantity Demanded

Price

D

10%

10%

Q1

Part (c)

Q2

P1

P2

Ed = 1Unit Elastic

Perfectly Elastic Demand

• Ed = (denominator = 0)• % change in quantity demanded is A LOT in

response to a change in price • Price increases and quantity demanded goes

to 0• Totally flat --- horizontal• Extreme• Examples???

Perfectly inelastic demand

• Ed = 0• % change in quantity demanded

DOESN’T CHANGE in response to a change in price

• Totally steep --- vertical• Extreme• Examples???

Price Elasticity of Demand

a

0Quantity Demanded

Price

D1%

Part (d)

Q1

P1P2

Ed = Perfectly Elastic

0Quantity Demanded

PriceD

10%

Part (e)

Q1

P1

P2

Ed = 0Perfectly Inelastic

Aren’t demand curve downward sloping?

• Because the extremes (perfectly inelastic and perfectly elastic) are not.

• Use as points of reference only

How does a change in price affect Total Revenue of a Firm?

• Revenue depends on elasticity• Michael Jordan and Nike shoes

– No substitutes -- inelastic demand• What happens to Qd if price increases?

– Substitutes – elastic demand• What happens to Qd if price increases?

What is total revenue??

• Total revenue = price*quantity

• Firm uses to decide if to produce more or less

examples• Elastic demand

– Price increase– Price decrease

• Inelastic demand– Price increase– Price decrease

• Unit elastic demand– Price increase– Price decrease

Elasticities, Price

Changes, and Total

Revenue

a

Ed > 1P TR

P TR

Ed < 1P TR

P TR

Ed = 1

P

P

TR

TR

Important to look at because…

• Elasticity of the demand determines if with a price increase…– Total revenue increases– Total revenue decreases– Total revenue remains the same

Price elasticity of demand and a straight line

• Demand is downward sloping• Along the line elasticity varies from highly

elastic to highly inelastic• But…remember SLOPE is constant

Point P Qd

A 8 3

B 7 4

C 6 5

D 5 6

E 4 7

F 3 8

G 2 9

Price Elasticity of Demand along a Demand Curve

a

(1)POINT

(2)PRICE

(3)QUANTITY

DEMANDED

A

B

C

D

E

F

G

(4)Ed

$8

7

6

5

4

3

2

3

4

5

6

7

8

9

2.14

1.44

1.00

0.69

0.47

0.29

(a)

Price (dollars)

8

7

6

5

4

3

2

1

1 2 3 4 5 6 7 8 9Quantity Demanded

A

B

C

D

E

F

G D

ElasticRange

Unit ElasticRange

InelasticRange

(b)

Summary• Upper end of Demand Curve

– Qd is low and price is high– Freak out more when price is high

• Lower end of Demand Curve– Qd is high and price is low– Freak out less when price is low

So…

• As move down the demand curve from higher prices to lower the price elasticity of demand goes from elastic to inelastic

Determinates of price elasticity of demand

• Number of substitutes available– Increase substitutes increases elasticity– More narrowly defined goods have more

substitutes (compared to broadly defined)• Example: Fords vs all cars

More determinates

• Percentage of one’s budget that is spent on the good– More expensive??? More elastic– More affected by price (even small changes)

Final determinate

• Amount of time that passed since price change– Increase time passed gives more opportunity

to change behavior or react to price change– Overtime can look for substitutes– Increase time increases elasticity– More elastic in long term than short

Cross Elasticity of Demand

• Measures the responsiveness of quantity demanded to a change in price of ANOTHER good

2

2%%

12

12

12

12

yy

yy

xx

xx

y

dxc

PPPP

QQQQ

PQE

When would you use Cross Price Elasticity?

• To determine if goods are substitutes or compliments• Ec>0 – substitutes

– % change in quantity demanded and price move in same direction

• Ec<0 – compliments– % change in quantity demanded and price move in

opposite directions• Ec=0 – goods unrelated

Income elasticity of demand

• Measures the responsiveness of quantity demanded to the change in income

2

2%

%

12

12

12

12

YYYY

QQQQ

incomeQE

xx

xx

dy

Why use income elasticity of demand?

• Use to determine if a good is normal or inferior

• Ey>0 – normal good– As income increases Qd increases

• Ey<0 – inferior good– As income increases Qd decreases

Can also say…

• If |Ey| > 1– % change in Qd > % change in Y– Income elastic

• If |Ey| < 1– % change in Qd < % change in Y– Income inelastic

• If |Ey| = 1– % change in Qd = % change in Y– Income unit elastic

Can we use income elasticity in the real world??

• If invest in the stock market do you want to invest in a normal or inferior good?

• Normal• Why• Increase income would increase quantity

bought and increase stock prices

Price Elasticity of Supply• Measures the responsiveness of quantity supplied of

a good to the change in the price of that good

2

2%

%

21

21

21

21

PPPP

QQQQ

PP

QQ

E

ss

ss

s

s

s

Classification is like demand

• Es > 1– Elastic

• Es < 1– Inelastic

• Es = 1– Unit elastic

• Each of these will result in a “normal” upward sloped supply curve

Any extreme elasticities???

• Yes!!• Es =

– Perfectly elastic or horizontal• Es = 0

– Perfectly inelastic or vertical

Price Elasticity of Supply

a

0

Quantity Supplied

Price

S

10%

20%

Q2

Part (a)

Q1

P1

P2

Es > 1Elastic

0

Quantity Supplied

Price

S

10%

4%

Q2

Part (b)

Q1

P1

P2Es < 1Inelastic

Price Elasticity of Supply

a

0Quantity Supplied

Price

S

10%

10%

Q2

Part (c)

Q1

P1

P2Es = 1Unit Elastic

Price Elasticity of Supply

a

0

Quantity Supplied

Price

S

Part (d)

Q1

P1

Es = Perfectly Elastic

0

Quantity Supplied

PriceS

10%

Part (e)

Q1

P1

P2

Es = 0PerfectlyInelastic

Does time play a role in elasticity of supply?

• Yes!!• Overtime producers are able to adjust their

behavior and production patterns• Supply becomes more elastic as time

passes

Elasticity and taxes

• If government levies a tax on a product who pays the tax??

• Producers?? Consumers?? Share??• Depends on the elasticity of demand and

supply

How find??• Find equilibrium price• Supply shifts left in the amount of the tax • Find new equilibrium• Find point of second equilibrium on ORGINAL

supply curve– Shows the actual price realized by firm or

equilibrium price – tax = point in question• Difference between points determines how much of

tax you pay

Who Pays the Tax?

a

0

8.00

7.50

8.50

9.00

Quantity of VCR Tapes

A

B

Q2

D1

$1 Tax

Q1

S2 (after tax)

S1 (before tax)

Price(dollars)

Part of tax paidby consumers interms of higher

price paid.

Part of tax paidby producers interms of lower

price kept.

Who pays more of the tax??

• Perfectly inelastic demand• Perfectly elastic demand• Demand more elastic than supply• Supply more elastic than demand

Different Elasticities and Who Pays the Tax

a

0

8.00

9.00

Quantity of VCR Tapes

A

B

Q1

D1 S2S1

Price (dollars)

Consumers payfull tax

Part (a)

$1 Tax

0

8.00

Quantity of VCR Tapes

AB

Q2

D1

$1 Tax

S2

S1

Price (dollars)

Producers payfull tax

Q1

Part (b)

Different Elasticities and Who Pays the Tax

a

0

8.00

9.00

Quantity of VCR Tapes

A

B

Q1

D1 S2S1

Price (dollars)

Consumers payfull tax

Part (a)

$1 Tax

0

8.00

Quantity of VCR Tapes

AB

Q2

D1

$1 Tax

S2

S1

Price (dollars)

Producers payfull tax

Q1

Part (b)

Summary

• Ed > Es producer bears most of the tax burden

• Ed < Es consumer bears most of the tax burden

• Ed = Es equally share the tax burden

Homework Numbers 5, 6, and 8

Working with Graphs and Numbers1, 2, and 4

Do we understand Chapter 5??