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