Chapter
5
Elasticity and Its Application
The Elasticity of Demand
• Elasticity
– Measure of the responsiveness of quantity demanded or
quantity supplied
• Percentage change in quantity demanded (∆Qd/Qd)
• Percentage change in quantity supplied (∆Qs/Qs)
– To a change in one of its determinants (driver variables)
• Demand-side
– (own) price <-> demand elasticity (∆Qx/Qx)/ (∆Px/Px )
– Price of substitute/complement <-> cross-price
(∆Qx/Qx)/(∆Py/Py )
– Income <-> income elasticity ((∆Qx/Qx)/ (∆I/I )
2
The Elasticity of Demand
• (Own) Price elasticity of demand
– Elastic demand (e.g. price elasticity)
• Quantity demanded responds substantially to
changes in the price
– elasticity of demand > 1
– ∆Qd/Qd > ∆P/P %change in Qd > % change in P
– Inelastic demand
• Quantity demanded responds only slightly to
changes in the price
• elasticity < 1 (closer to zero)
• ∆Qd/Qd < ∆P/P
3
1
The price elasticity of demand (d, e)
(d) Elastic demand:
Elasticity > 1
(e) Perfectly elastic demand:
Elasticity equals infinity
Price
Price
1. A 22%
increase
in price…
1. At any price
above $4, quantity
demanded is zero
$5
Demand
1. an
4
2. At exactly $4,
consumers will
buy any quantity
1. an
$4
Demand
3. At any price
below $4, quantity
demanded is infinite
2. … leads to
a 67% decrease
in quantity
demanded
0
50
100
Quantity
0
Quantity
The price elasticity of demand determines whether the demand curve is steep or flat.
Note that all percentage changes are calculated using the midpoint method.
4
The Elasticity of Demand
• Determinants of (own) price elasticity of demand
• (∆Qx/Qx)/ (∆Px/Px )
– Availability of close substitutes
• Goods with close substitutes
– More elastic demand
– Necessities (0->1) vs. luxuries (>1) (defined by Income elasticity)
• Necessities – inelastic demand
• Luxuries – elastic demand
– Definition of the market
• Narrowly defined markets – more elastic demand
– Time horizon
– More elastic over longer time horizons
5
The Elasticity of Demand (own)
• Computing the price elasticity of demand
– Percentage change in quantity demanded
• Divided by percentage change in price
– Use absolute value (drop the minus sign)
• It’s always negative (own-price)
• Midpoint method
– Two points: (Q1, P1) and (Q2, P2)
(Q2  Q1 )/[(Q2  Q1 )/ 2 ]
Price elasticity of demand 
(P2  P1 )/[(P2  P1 )/ 2 ]
6
The Elasticity of Demand
• Variety of demand curves
– Demand is elastic
• Elasticity > 1
– Demand is inelastic
• Elasticity < 1
– Demand has unit elasticity
• Elasticity = 1
7
The Elasticity of Demand
• Cigarettes (US)[41]
– -0.3 to -0.6 (General)
– -0.6 to -0.7 (Youth) – proportion of income?
• Soft drinks
– -0.8 to -1.0 (general)[51] (broadly defined)
– -3.8 (Coca-Cola)[52] (narrow)
– -4.4 (Mountain Dew)[52] (narrow)
• Car fuel[45]
– -0.25 (Short run) (same car – reduce trips)
– -0.64 (Long run) (new car?)
8
The Elasticity of Demand
• Total revenue
– Amount paid by buyers
– Received by sellers of a good
– Computed as: price of the good times the
quantity sold (P ˣ Q)
9
Figure 2
Total revenue
Price
$4
1. an
P ˣ Q=$400
(revenue)
P
0
Demand
100
Quantity
Q
The total amount paid by buyers, and received as revenue by sellers, equals the
area of the box under the demand curve, P × Q. Here, at a price of $4, the
quantity demanded is 100, and total revenue is $400.
10
Figure 4
Elasticity of a linear demand curve (graph)
Price
Elasticity
is larger
than 1
$7
6
5
4
1. an
3
2
Demand
1
0
Elasticity
is smaller
than 1
2
4
6
8
10 12 14
Quantity
The slope of a linear demand curve is constant, but its elasticity is not. The demand
schedule in the table was used to calculate the price elasticity of demand by the midpoint
method. At points with a low price and high quantity, the demand curve is inelastic. At
points with a high price and low quantity, the demand curve is elastic.
11
Figure 4
Elasticity of a linear demand curve (schedule)
Price
Quantity
Total revenue
(Price ˣ Quantity)
$7
6
5
4
3
2
1
0
O
2
4
6
8
10
12
14
$0
12
20
24
24
20
12
0
Percentage
Change
in Price
Percentage
Change in
Quantity
Elasticity
Description
15
18
22
29
40
67
200
200
67
40
29
22
18
15
13.0
3.7
1.8
1.0
0.6
0.3
0.1
Elastic
Elastic
Elastic
Unit elastic
Inelastic
Inelastic
Inelastic
The slope of a linear demand curve is constant, but its elasticity is not. The
demand schedule in the table was used to calculate the price elasticity of
demand by the midpoint method. At points with a low price and high quantity,
the demand curve is inelastic. At points with a high price and low quantity, the
demand curve is elastic.
12
Figure
Elasticity and Total Revenue
The following equation holds:
where
R' is the marginal revenue (MR)
P is the price
Proof:
TR = Total Revenue
The Elasticity of Demand
• When demand is inelastic
– Price and total revenue move in the same
direction
• When demand is elastic
– Price and total revenue move in opposite
directions
• If demand is unit elastic
– Total revenue remains constant when the
price changes
14
Figure
The Elasticity of Demand
• Income elasticity of demand
– Measure of how much the quantity demanded of a good
responds
• To a change in consumers’ income
– Percentage change in quantity demanded
• Divided by the percentage change in income
– Normal goods: positive income elasticity
• Necessities: smaller income elasticities (~0, <1)
• Luxuries: large income elasticities ( > 1)
– Inferior goods: negative income elasticities (<0)
15
Figure
The Elasticity of Demand
• Cross-price elasticity of demand
– Measure of how much the quantity demanded of one good
responds
• To a change in the price of another/different good
– [∆Qx/Qx] / [∆Py/Py ]
– Sign matters -> tells whether substitute or complement
• Magnitude (<1 or >1) -> how “good” a substitute/essential a
complement
– Substitutes: Positive cross-price elasticity
• >1 -> “close” or good substitute as big shift with small price change
– Complements: Negative cross-price elasticity
• >1 -> “essential” to be used/consumed together (cars and gas)
16
The Elasticity of Supply
• Price elasticity of supply
– Measure of how much the quantity supplied
of a good responds
• To a change in the price of that good
– Percentage change in quantity supplied
• Divided by the percentage change in price
– Depends on the flexibility of sellers to change
the amount of the good they produce
17
The Elasticity of Supply
• Price elasticity of supply
– Elastic supply
• Quantity supplied responds substantially to
changes in the price
– Inelastic supply
• Quantity supplied responds only slightly to
changes in the price
• Determinant of price elasticity of supply
– Time period
• Supply is more elastic in long run
18
The Elasticity of Supply
• Computing price elasticity of supply
– Percentage change in quantity supplied
• Divided by percentage change in price
• Variety of supply curves
– Supply is perfectly inelastic
• Elasticity =0
• Supply curve – vertical
– Supply is perfectly elastic
• Elasticity = infinity
• Supply curve – horizontal
19
The Elasticity of Supply
• Variety of supply curves
– Unit elastic supply
• Elasticity =1
– Elastic supply
• Elasticity >1
– Inelastic supply
• Elasticity < 1
20
Figure 5
The price elasticity of supply (a, b)
(a) Perfectly inelastic supply:
Elasticity = 0
Price
(b) Inelastic supply:
Elasticity < 1
Price
Supply
Supply
1. An
increase
in price…
1. A 22%
increase
in price…
$5
4
$5
1. an
4
1. an
2. …leaves
the quantity
supplied
unchanged
0
100
Quantity
0
100 110
2. … leads to
a 10% increase
in quantity
supplied
Quantity
The price elasticity of supply determines whether the supply curve is steep or flat.
Note that all percentage changes are calculated using the midpoint method.
21
Figure 5
The price elasticity of supply (c)
(c) Unit elastic supply: Elasticity =1
Price
Supply
1. A 22%
increase
in price…
$5
4
0
1. an
100 125
2. … leads to
a 22% increase
in quantity
supplied
Quantity
The price elasticity of supply determines whether the supply curve is steep or flat.
Note that all percentage changes are calculated using the midpoint method.
22
Figure 5
The price elasticity of supply (d, e)
(d) Elastic supply:
Elasticity > 1
(e) Perfectly elastic supply:
Elasticity equals infinity
Price
Price
1. A 22%
increase
in price…
1. At any price
above $4, quantity
supplied is infinite
Supply
2. At exactly $4,
producers will
supply any quantity
$5
1. an
4
1. an
$4
Supply
2. … leads to
a 67% increase
in quantity
supplied
0
100
50
Quantity
3. At any price
below $4, quantity
supplied is zero
0
Quantity
The price elasticity of supply determines whether the supply curve is steep or flat.
Note that all percentage changes are calculated using the midpoint method.
23
Figure 6
How the price elasticity of supply can vary
Price
Elasticity is small
(less than 1).
$15
Supply
12
Elasticity is large 1. an
(greater than 1).
4
3
0
100
200
500 525
Quantity
Because firms often have a maximum capacity for production, the elasticity of supply may be
very high at low levels of quantity supplied and very low at high levels of quantity supplied.
Here an increase in price from $3 to $4 increases the quantity supplied from 100 to 200.
Because the 67 percent increase in quantity supplied (computed using the midpoint method) is
larger than the 29 percent increase in price, the supply curve is elastic in this range. By
contrast, when the price rises from $12 to $15, the quantity supplied rises only from 500 to
525. Because the 5 percent increase in quantity supplied is smaller than the 22 percent
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increase in price, the supply curve is inelastic in this range.
Applications of Supply, Demand, & Elasticity
• Why did OPEC fail to keep the price of oil
high?
– 1970s: OPEC reduced supply of oil
• Increase in prices 1973-1974 and 1971-1981
• Short-run: supply is inelastic
– Decrease in supply: large increase in price
– 1982-1990 – price of oil decreased
• Long-run: supply is elastic
– Decrease in supply: small increase in price
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Figure 8
A reduction in supply in the world market for oil
(a) The Oil Market in the Short Run
Price
1. In the short run, when supply and
demand are inelastic, a shift in supply. . .
S2
(b) The Oil Market in the Long Run
Price
1. In the long run, when supply and
demand are elastic, a shift in supply. . .
S1
S2 S
1
P2
P1
1. an
2. … leads to a
large increase
in price
1. an
P2
P1
2. … leads to a
small increase
in price
Demand
0
Quantity
0
Demand
Quantity
When the supply of oil falls, the response depends on the time horizon. In the short run,
supply and demand are relatively inelastic, as in panel (a). Thus, when the supply curve
shifts from S1 to S2, the price rises substantially. By contrast, in the long run, supply and
demand are relatively elastic, as in panel (b). In this case, the same size shift in the supply
curve (S1 to S2) causes a smaller increase in the price.
26