Elasticity
The degree to which one variable, Y, responds to a change in another variable, X, is the elasticity of the response variable Y.
Elasticity is the ratio of the percent (proportional) change in variable Y to the percent (proportional) change in variable X.
Absolute change versus relative (percent) change
The absolute change is simply the difference between the new value of the variable and the initial value. Using the symbol ∆
(delta) to denote “change” or “difference”, the absolute change in y is represented by:
∆y = y₁ − y₀
Relative or percent change in y is the absolute change relative to (divided by) the initial value:
Δy% 
y1  y 0
y0
Elasticity is the comparison of the percentage change in y to a percentage change in the variable x. The ratio of percent
change in y over the percent change in x is the called the coefficient of elasticity and is denoted by E.
E
Δy%
Δx%
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Price elasticity of demand
The price elasticity of demand is the ratio of percent change in Q (quantity demanded) to the percent change in P (price). It
measures the relative responsiveness of quantity demanded to a relative change in price.
E
ΔQ%
ΔP%
Demand equation: Q = 1500 – 500P
P₀ = $1.00
P₁ = $0.80
Q₀ = 1,000
Q₁ = 1,100
P₀ = $0.80
P₁ = $1.00
P
P
$1.00
$1.00
$0.90
$0.90
$0.80
$0.80
Q₀ = 1,100
Q₁ = 1,000
D
1,000
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1,050
1,100
Q
D
1,000
1,050
1,100
Q
Midpoint Formula for Coefficient of Price Elasticity of Demand
Using the “midpoint” formula, we obtain the same value for E regardless of the direction of price change.
P
$1.00
$0.90
$0.80
D
1,000
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1,050
1,100
Q
How Elastic is Elastic?
Elasticity of demand basically depends upon the availability of substitutes. If there are close substitutes for good X, then the
demand for that good is price elastic.
Perfectly Inelastice Demand
D
Price
Infinitely Elastic Demand
Price
P₁
D
P₀
P
Q
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Quantity
Q₀
Q₁
Quantity
Inelastic Demand
Elastic Demand
Unit Elastic Demand
Price
Price
Price
$1.20
$1.10
$1.10
$0.90
$0.90
D
$0.80
D
D
950
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1050
Quantity
800
1200
Quantity
800
1200
Quantity
Total revenue (expenditure) test of demand elasticity
Price effect and quantity effect of a change in price
Which is the dominant effect?
Inelastic Demand
Elastic Demand
Unit Elastic Demand
Price
Price
$1.20
$1.10
$0.90
$0.80
D
D
950
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1050
Quantity
800
1200
Quantity
Changes in price elasticity along the demand curve
Price
$9.0
$8.0
$6.0
$5.0
$3.0
$2.0
D
10
20
40
50
70
80
Quantity
Total Reveneu
240
250
250
240
210
210
200
160
160
150
100
90
90
50
0
10
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20
30
40
50
60
70
80
90
Factors determining the price elasticity of demand
 Availability of substitutes
 Luxury goods versus necessities
 Share of income spent on the good
 Time
Cross price elasticity of demand
Substitutes versus complements
Income elasticity of demand
Normal goods
 Goods with income elastic demand
 Goods with income inelastic demand
Inferior goods
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Price elasticity of supply
Factors determining the elasticity of supply
 Availability of inputs
 Time
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