Four demand functions
P
η
D
Elasticity
“eta”
P
Q
P
P
D
D
Q
D
Q
D
Q
P
Q
Elasticity
Q
P
D
D
Four demand functions
P
P
D
Q
P
D
Q
Elasticity
Four demand functions
P
P
D
Q
Four demand functions
Q
P
D
Lectures in Microeconomics-Charles W. Upton
P
D
Q
Elasticity
Q
The notion of elasticity
P
D
Q
P
• The critical question: how responsive is the
quantity demanded to changes in price?
D
Q
P
D
D
Q
Elasticity
Q
Elasticity
1
The notion of elasticity
A Definition, Sort of
• The critical question: how responsive is the
quantity demanded to changes in price?
• And how do we measure that?
• We represent that by the price elasticity of
demand
η
the ratio of the percentage change in
quantity demanded to the percent change in
price
Elasticity
An Illustration
P
Elasticity
Q = 100 – 2P
P
Q = 100 – 2(20) = 60
50
50
Q = 100 – 2(18) =64
20
18
100
Q
60 64
Elasticity
New v. Old
P
= 100
2(20) = 60
But which isQthe
new– price
and which is the old price?
And does
Q it= make
100 – a2(18) =64
difference?
50
20
18
60 64
Q
Q
100
Elasticity
20
18
Elasticity
New v. Old
P
50
100
= 100
2(20) = 60
But which isQthe
new– price
and which is the old price?
And does
make
Q it=calculation
100 – a2(18) =64
Yes. Lets do the
difference?
assuming the price goes
from 20 to 18 and then from
60 64 100 18 to 20?
Q
Elasticity
2
Going from 20 to 18
P
η=
50
PercentChangeinQuantity
PercentChangein Pr ice
New Pr ice − Old Pr ice 18 − 20 − 2
=
=
= −10%
Old Pr ice
20
20
20
18
60 64
6 .7 %
= −0.67
− 10%
New Pr ice − Old Pr ice 18 − 20 − 2
=
=
= −10%
Old Pr ice
20
20
NewQuantity − OldQuantity 64 − 60 4
=
=
= 6.7%
OldQuantity
60
60
60 64
η=
50
60 64
Q
NewQuantity − OldQuantity 64 − 60 4
=
=
= 6.7%
60
60
OldQuantity
100
Elasticity
Going from 18 to 20
η=
PercentChangeinQuantity
PercentChangein Pr ice
50
20
18
60 64
100
Q
Elasticity
Going from 18 to 20
P
PercentChangeinQuantity
PercentChangein Pr ice
New Pr ice − Old Pr ice 20 − 18 2
=
=
= 11.1%
Old Pr ice
18
18
20
18
New Pr ice − Old Pr ice 18 − 20 − 2
= −10%
=
=
Old Pr ice
20
20
P
Elasticity
Going from 18 to 20
PercentChangeinQuantity
PercentChangein Pr ice
Q
100
Q
P
20
18
Elasticity
η=
20
18
50
60 64
Going from 20 to 18
50
η=
100
Q
P
Going from 20 to 18
P
η=
50
PercentChangeinQuantity
PercentChangein Pr ice
New Pr ice − Old Pr ice 20 − 18 2
=
=
= 11.1%
Old Pr ice
18
18
20
18 NewQuantity − OldQuantity
OldQuantity
100
60 64
Elasticity
Q
100
=
60 − 64 − 4
=
= −6.25%
64
64
Elasticity
3
Going from 18 to 20
P
− 6.25%
= −0.563
11.1%
η=
50
So what is it?
New Pr ice − Old Pr ice 20 − 18 2
=
=
= 11.1%
Old Pr ice
18
18
20
18 NewQuantity − OldQuantity
OldQuantity
60 64
Q
=
100
η=
60 − 64 − 4
=
= −6.25%
64
64
6.7%
− 6.25%
= −0.563
= −0.67 η =
11.1%
− 10%
Elasticity
Elasticity
Two computational methods
Point Elasticity of Demand
• Point Elasticity of Demand
• Arc Elasticity of Demand
• Defined by
η = Slope
Pr ice
Quantity
where Slope is the slope of the demand
function
Elasticity
Point Elasticity of Demand
• Defined by
In the case of a linear
Pr ice
demand function
η = Slope
Q = aQuantity
– bP
where Slope is the slope of the demand
The slope is -b
function
Elasticity
P
Computing the Point Elasticity
η = Slope
50
20
18
60 64
Elasticity
Pr ice
Quantity
Q
100
Elasticity
4
P
Computing the Point Elasticity
50
20
18
60 64
η = Slope
Pr ice
Quantity
Slope
= −2
20
18
60 64
Pr ice
Quantity
Slope
= −2
18
= −0.5625
64
50
50
20
18
= −2
100
η = Slope
Pr ice
Quantity
Slope
= −2
P
When P = 35, η= -2.333
20
= −0.67
60
Elasticity
η = Slope
Pr ice
Quantity
Slope
= −2
Compute the point price
elasticity of demand at
P = 25 and P = 35
60 64 100
Q
Elasticity
Elasticity
Slope
A Problem
Elasticity
η along the Demand Function
η = Slope
Compute the point price
elasticity of demand at
P = 25 When
and P =P35= 25, η= -1
60 64 100
Q
Pr ice
Quantity
η = (−2)
P
100
A Problem
P
20
18
η = Slope
η = (−2)
η = Slope
Q
Elasticity
50
Q
20
18
60 64
Computing at Q = 64
P
50
100
Q
Computing at Q = 60
P
100
Q
Pr ice
Quantity
• For a straight line
demand curve η
will vary over the
demand curve
Elasticity
5
P
η along the Demand Function
η = -∞
η = Slope
P
η along the Demand Function
Pr ice
Quantity
η = Slope
η=0
• When the curve hits
the price axis, η = -∞
• When the curve hits the
quantity axis, η = 0
100
Q
P
100
Q
Elasticity
η along the Demand Function
η = -1
Pr ice
Quantity
η = Slope
Pr ice
Quantity
Elasticity
Next Lecture
• Arc Elasticity
• Extensions
• At the midpoint,
η = -1
100
Q
Elasticity
Elasticity
End
©2004 Charles
W. Upton
Elasticity
6