Managerial Economics-Charles W. Upton Arc Elasticity “eta”
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Managerial Economics-Charles W. Upton Arc Elasticity “eta ”
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Transcript of Managerial Economics-Charles W. Upton Arc Elasticity “eta”
Managerial Economics-Charles W. Upton
Arc Elasticity“eta”
Elasticity
Defining Arc ElasticityP
Q
50
100
20
60 64
18
icengeinPercentCha
ityngeinQuantPercentCha
Pr
Elasticity
Defining Arc ElasticityP
Q
50
100
20
60 64
18
icengeinPercentCha
ityngeinQuantPercentCha
Pr
Where:
Percent change is measured as percent of
average value
Elasticity
Defining Arc ElasticityP
Q
50
100
20
60 64
18
icengeinPercentCha
ityngeinQuantPercentCha
Pr
When P changes from 20 to 18, p = -2
Average value of P = 19
The % change is thus -2/19
Elasticity
The FormulaP
Q
50
100
20
60 64
18 ))((
))((
121
1
121
1
o
o
o
PP
PoPQQ
Elasticity
The FormulaP
Q
50
100
20
60 64
18 ))((
))((
121
1
121
1
o
o
o
PP
PoPQQ
Elasticity
The FormulaP
Q
50
100
20
60 64
18 ))((
))((
121
1
121
1
o
o
o
PP
PoPQQ
Elasticity
The FormulaP
Q
50
100
20
60 64
18 ))((
))((
121
1
121
1
o
o
o
PP
PoPQQ
Elasticity
The FormulaP
Q
50
100
20
60 64
18 ))((
))((
121
1
121
1
o
o
o
PP
PoPQQ
Elasticity
An ExampleP
Q
50
100
20
60 64
18
Compute the arc elasticity when P
changes from 20 to 18
Elasticity
An ExampleP
Q
50
100
20
60 64
18)1820)((
1820)6460)((
6460
21
21
Elasticity
An ExampleP
Q
50
100
20
60 64
18)1820)((
1820)6460)((
6460
21
21
192624
Elasticity
An ExampleP
Q
50
100
20
60 64
18)1820)((
1820)6460)((
6460
21
21
192624
= -0.6129
Elasticity
Reverse the CalculationP
Q
50
100
20
60 64
18
Compute the arc elasticity when P
changes from 18 to 20
Elasticity
Reverse the CalculationP
Q
50
100
20
60 64
18
= -0.6129
Elasticity
Second ExampleP
Q
50
100
20
60 64
18
Compute the arc elasticity when P
changes from 10 to 20
Elasticity
Second ExampleP
Q
50
100
20
60 64
18
= -4/7
Elasticity
Arc Elasticity and Tables
• 15,000 units were demanded when the price was $5.
• 12,000 units were demanded when the price was $7.
• Compute the elasticity
Elasticity
Arc Elasticity and Tables
• 15,000 units were demanded when the price was $5.
• 12,000 units were demanded when the price was $7.
• Compute the elasticity
))((
))((
121
1
121
1
o
o
o
o
PPPPQQQQ
Elasticity
Arc Elasticity and Tables
• 15,000 units were demanded when the price was $5.
• 12,000 units were demanded when the price was $7.
• Compute the elasticity
))((
))((
121
1
121
1
o
o
o
o
PPPPQQQQ
6
2500,13
3000
Elasticity
Arc Elasticity and Tables
• 15,000 units were demanded when the price was $5.
• 12,000 units were demanded when the price was $7.
• Compute the elasticity
))((
))((
121
1
121
1
o
o
o
o
PPPPQQQQ
6
2500,13
3000
3
2
Elasticity
Arc Elasticity and Tables
• 15,000 units were demanded when the price was $5.
• 12,000 units were demanded when the price was $7.
• Compute the elasticity
))((
))((
121
1
121
1
o
o
o
o
PPPPQQQQ
6
2500,13
3000
3
2
Note that we never said which price came first.
Elasticity
Which method is best?
• The concept of elasticity is defined without reference to any one method of calculation.
Elasticity
Which method is best?
• The concept of elasticity is defined without reference to any one method of calculation.
• There are occasions when the point elasticity formula is best and there are occasions when the arc elasticity formula is best.
Elasticity
Which method is best?
• The concept of elasticity is defined without reference to any one method of calculation.
• There are occasions when the point elasticity formula is best and there are occasions when the arc elasticity formula is best.
In general we tend to use point elasticities in class,
because we have the luxury of examples with
nice demand curves.
Elasticity
Extensions to other Elasticities
• Income elasticities (measuring the responsiveness of demand with respect to changes in income).
Elasticity
Extensions to other Elasticities
• Income elasticities (measuring the responsiveness of demand with respect to changes in income).
• Own price elasticities measuring the responsiveness of demand with respect to changes in the price of the good itself.
Elasticity
Extensions to other Elasticities
• Income elasticities (measuring the responsiveness of demand with respect to changes in income).
• Own price elasticities measuring the responsiveness of demand with respect to changes in the price of the good itself.
• Cross price elasticities (measuring the responsiveness of demand with respect to the price of other goods).
Elasticity
End
©2004 Charles W. Upton
