Chapter 3
Applying the
Supply-andDemand Model
Topic
•  How the shapes of demand and supply
curves matter?
•  Sensitivity of quantity demanded to price.
•  Sensitivity of quantity supplied to price.
•  Long run versus short run.
•  Effects of a sales tax.
3-2
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How Shapes of Demand and Supply
Matter?
•  The shapes of the demand and supply
curves determine by how much a shock
affects the equilibrium price and quantity.
•  Example: processed pork (same as
Chapter 2)
w Supply depends on the price of pork and the
price of hogs.
3-3
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Figure 3.1 How the Effect of a Supply Shock
Depends on the Shape of the Demand Curve
3.55
3.30
0
D1
A $0.25 increase in the price of pork causes
the supply of pork to shift to the left
A $0.25 increase
in the price of
pork causes the
supply of pork to
shift to the left.
e2
176
3.675
3.30
e1
S2
S1
215 220
0
Q, Million kg of pork per year
and a reduction in quantity.
3-4
(b)
p, $ per kg
(a)
p, $ per kg
This shift of the supply curve causes a
movement along the demand curve… D2
e2
S2
S1
176
e1
220
Q, Million kg of pork per year
But equilibrium quantity does not change since
consumption is not sensitive to price
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Figure 3.1 How the Effect of a Supply Shock
Depends on the Shape of the Demand Curve
(cont.)
w  a shift in the supply
curve to S2…
w  has no effect on the
equilibrium price
w  and a substantial effect
on the quantity
p, $ per kg
§  When demand is very
sensitive to price…
(c)
3.30
D3
e2
e1
S2
S1
0
176
205
220
Q, Million kg of pork per year
3-5
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Sensitivity of Quantity Demanded to Price
•  Elasticity – the percentage change in a
variable in response to a given
percentage change in another variable.
•  Price elasticity of demand (e) – the
percentage change in the quantity
demanded in response to a given
percentage change in the price.
3-6
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Sensitivity of Quantity Demanded to Price
(cont.)
•  Formally,
ΔQ
%ΔQ
ΔQ p
Q
ε=
=
=
Δp
%Δp
Δp Q
p
w  where D indicates change.
•  Example
w  If a 1% increase in price results in a 3% decrease in quantity
demanded, the elasticity of demand is e = -3%/1% = -3.
3-7
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Sensitivity of Quantity Demanded to Price
(cont.)
•  Along linear demand curve with a function of:
Q = a − bp
w  Where -b is the slope or
ΔQ
−b =
Δp
w  the elasticity of demand is
ΔQ p
p
ε=
= −b
Δp Q
Q
3-8
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(3.3)
Sensitivity of Quantity Demanded to
Price: Example
•  The estimated linear demand function for pork
is:
Q = 286 -20p
w  where Q is the quantity of pork demanded in million
kg per year and p is the price of pork in $ per year.
w  At the equilibrium point of p = $3.30 and Q = 220
the elasticity of demand for pork is
p
3.30
ε = −b = −20 ×
= −0.3
Q
220
3-9
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Elasticity: An Application and a Practice
Problem
•  Varian (2002) found that the price elasticity of
demand for internet use was
w  -2.0 for those who used a 128 Kbps service
w  -2.9 for those who used a 64 Kbps service.
•  Practice problem:
w  A 1% increase in the price per minute reduced the
connection time by ________ for those with high
speed access, and by _______ for those with slow
phone line access.
3 - 10
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Solved Problem 3.1
•  Calculate the elasticity of demand for the linear
pork demand curve D in panel a of Figure 3.1 at
the equilibrium e1 where p=$3.30 and Q=220.
The estimated linear demand function for pork,
which holds constant other factors that influence
demand besides price (Equation 2.3), is Q=286
– 20p, where Q is the quantity of pork
demanded in million kg per year and p is the
price of pork in dollars per kg.
3 - 11
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Solved Problem 3.1: Answer
•  Substitute the slope coefficient, the price, and the
quantity values into Equation 3.3.
•  By inspection, the slope coefficient for this demand
equation is b = 20 (and a = 286). Substituting b = 20, p =
$3.30, and Q = 220 into Equation 3.3, we find that the
elasticity of demand at the equilibrium e1 in panel a of
Figure 3.1 is
•  Comment: Thus, at the equilibrium, a 1% increase in the
price of pork leads to a –0.3% fall in the quantity of pork
demanded: A price increase causes a less than
proportionate fall in the quantity of pork demanded.
3 - 12
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Elasticity Along a Demand Curve
•  The elasticity of demand varies along most
demand curves.
w  Along a downward-sloping linear demand curve the
elasticity of demand is a more negative number the
higher the price is.
3 - 13
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p, $ per kg
Figure 3.2 Elasticity Along the Pork
Demand Curve
Q = 286 -20p
Perfectly elastic
p
a/
b
= 14.30
e = -b
= -20 x 3.30
11.44= -0.3
220
Q
= -4
57.2
Elastic
e < –1
11.44
e = –4
D
a/(2b) = 7.15
Unitary: e = -1"
3.30
Inelastic 0 > e > –1
e = –0.3
Perfectly"
inelastic
0
3 - 14
a/5 = 57.2
a/2 = 143
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220
a = 286
Q, Million kg of pork per year
Elasticity Along The Demand Curve:
Practice Problem
•  According to Agcaoli-Sombilla (1991), the
elasticity of demand for rice is -0.47 in
Austria; -0.8 in Bangladesh, China, India,
Indonesia, and Thailand; -0.25 in Japan;
-0.55 in the EU and the US; and -0.15 in
Vietnam.
w In which countries is the demand for rice
inelastic?
•  In all the countries, since in all cases e > -1.
w In which country is the least elastic?
•  In Vietnam, where e = -0.15
3 - 15
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Elasticity Along the Demand Curve
(cont.)
•  Along a horizontal demand curve,
elasticity is infinite – perfectly elastic
demand
w a increase in price causes an infinite
change in quantity demanded
•  Along a vertical demand curve, elasticity
is zero – perfectly inelastic demand
w A change in the price does not cause a
change in the quantity demanded
3 - 16
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(a) Perfectly Elastic Demand
(b) Perfectly Inelastic Demand
(c) Individual‘s Demand for Insulin
p, Price per unit
p, Price per unit
p, Price of
insulin dose
Figure 3.3 Vertical and Horizontal
Demand Curves
p*
Q , Units per
time period
3 - 17
Q*
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Q , Units per
time period
p*
Q*
Q , Insulin
doses per day
Demand Elasticity and Revenue
•  Any shock that changes the equilibrium
price will affect an industry’s revenue
•  Whether revenue increases or decreases
when the equilibrium price changes
depends on elasticity
w With elastic demand, a higher price reduces
revenue
w With inelastic demand, a higher price
increases revenue
3 - 18
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Figure 3.4 Effect of a Price Change
on Revenue
Revenue decreases by B, but
increases by C, resulting in
revenue of A+C
An increase in price to
p2 reduces quantity
Revenue = A + B
3 - 19
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Solved Problem 3.2
•  Does revenue increase or decrease if the
demand curve is inelastic at the initial price?
How does it change if the demand curve is
elastic?
•  Answer
w  Consider the extreme case where the demand curve
is perfectly inelastic and then generalize to the
inelastic case.
w  Show that if the demand curve is elastic at the initial
price, then area C is relatively small.
3 - 20
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Solved Problem 3.2: Answer
3 - 21
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Solved Problem 3.2
•  Does revenue increase or decrease if the
demand curve is inelastic at the initial
price? How does it change if the demand
curve is elastic?
3 - 22
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Demand Elasticities Over Time
•  Demand elasticities may be different in
the short-run and the long-run
•  The difference depends on substitution
and storage opportunities
•  For most goods elasticities tend to be
larger in the long-run
•  For easily storable or durable goods, the
reverse is true
3 - 23
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Sensitivity of Quantity Demanded to
Income
•  Formally,
ΔQ
%ΔQ
ΔQ Y
Q
ξ=
=
=
%ΔY ΔY ΔY Q
Y
w  where Y stands for income.
•  Example
w  If a 1% increase in income results in a 3% increase in
quantity demanded, the income elasticity of demand is
x = 3%/1% = 3.
3 - 24
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Sensitivity of Quantity Demanded to
Income: Example
•  The estimated demand function for pork is:
Q = 171 – 20p + 20pb + 3pc + 2Y
w  where p is the price of pork, pb is the price of beef,
pc is the price of chicken and Y is the income (in
thousands of dollars).
w  Question: what would be the income elasticity of
demand for Pork if Q = 220 and Y = 12.5
w  Answer: ΔQ
•  Since
3 - 25
= 2, then
ΔY
ΔQ Y
Y
⎛ 12.5 ⎞
ξ=
= 2 = 2⎜
⎟ ≈ 0.114
ΔY Q
Q
⎝ 220 ⎠
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Sensitivity of Quantity Demanded to the
Price of a Related Good
•  Formally,
ΔQ
% ΔQ
ΔQ p o
Q
=
=
% Δ p o Δp o Δp o Q
po
w  where Po stands for price of another good.
•  Example
w  If a 1% increase in the price of a related good results in a
3% decrease in quantity demanded, the cross-price
elasticity of demand is = -3%/1% = -3.
3 - 26
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Sensitivity of Quantity Demanded to the
Price of a Related Good
•  If the cross-price elasticity is positive, the
goods are substitutes
w  Question: can you think of any examples of two
goods that are substitutes?
•  Roses and carnations
•  If the cross-price elasticity is negative, the
goods are complements
w  Question: can you think of any examples of two
goods that are complements?
•  Peanut butter and jelly
3 - 27
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Sensitivity of Quantity Demanded to the
Price of a Related Good: Example
•  Again, the estimated demand function for pork
is:
Q = 171 – 20p + 20pb + 3pc + 2Y
w  Question: what would be the cross-price elasticity
between the price of beef and the quantity of pork if
Q = 220 and pb = $4?
w  Answer: ΔQ
•  Since
Δpb = 20, then
pb
ΔQ pb
⎛ 4 ⎞
= 20
= 20⎜
⎟ ≈ 0.364
Δpb Q
Q
⎝ 220 ⎠
3 - 28
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Sensitivity of Quantity Supplied to Price
•  Formally,
ΔQ
%ΔQ
ΔQ p
Q
η=
=
=
Δp
%Δp
Δp Q
p
w  where Q indicates quantity supplied.
•  Example
w  If a 1% increase in price results in a 3% increase in quantity
supplied, the elasticity of supply is h = 3%/1% = 3.
3 - 29
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Sensitivity of Quantity Supplied to Price:
Example
•  The estimated linear supply function for pork
is:
Q = 88 - 40p
w  where Q is the quantity of pork supplied in million
kg per year and p is the price of pork in $ per year.
w  At the equilibrium, where p = $3.30 and Q = 220,
the elasticity of supply is:
ΔQ P
3.30
η=
= 40 ×
= 0.6
Δp Q
220
3 - 30
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Sensitivity of Quantity Supplied to Price
(cont.)
•  Along linear supply curve with a function of:
Q = g + hp
w  Where h is the slope or
ΔQ
h=
Δp
w  the elasticity of supply is
ΔQ p
p
η=
=h
Δp Q
Q
3 - 31
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Figure 3.5 Elasticity Along the Pork
Supply Curve
3 - 32
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Supply Elasticities Over Time
•  Supply elasticities may differ in the shortrun and the long-run
•  The difference depends on the ability to
convert fixed inputs into variable inputs
3 - 33
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Solved Problem 3.3
•  What would be the effect of ANWR production
on the world price of oil given that ε = –0.4,η =
0.3, the pre-ANWR daily world production of oil
is Q1 = 84 million barrels per day, the preANWR world price is p1 = $70 per barrel, and
daily ANWR production would be 0.8 million
barrels per day? For simplicity, assume that the
supply and demand curves are linear and that
the introduction of ANWR oil would cause a
parallel shift in the world supply curve to the
right by 0.8 million barrels per day.
3 - 34
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Solved Problem 3.3
3 - 35
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Effects of a Sales Tax
1.  What effect does a sales tax have on
equilibrium prices and quantity?
2.  Is it true, as many people claim, that
taxes assessed on producers are
passed along to consumers?
3.  Do the equilibrium price and quantity
depend on whether the tax is assessed
on consumers or on producers?
3 - 36
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Two Types of Sales Taxes
•  Ad valorem tax - for every dollar the
consumer spends, the government keeps
a fraction, α, which is the ad valorem tax
rate
•  Specific tax - where a specified dollar
amount, t, is collected per unit of output
3 - 37
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Figure 3.6 Effect of a $1.05 Specific Tax on the
Pork Market Collected from Producers
p, $ per kg
S2
e2
p3 = 3.30
p2 – t = 2.95
t = $1.05 S1
p2 = 4.00
e1
•  After the tax,
T = $216.3 million
0 176
•  A tax on producers shifts
the supply curve
downward by the amount
of the tax (t = $1.05)….
•  which causes the market
price to increase…
Q2 = 206 Q1 = 220
D
Q, Million kg of pork per year
3 - 38
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w  buyers pay an additional
$.70 per unit ($4.00 $3.30)
w  sellers receive $0.35
less per unit ($3.30 $2.95)
w  and the government
collects $216.3 in
revenue.
How Specific Tax Effects Depend on
Elasticities
•  The government raises the tax from zero to t,
so the change in the tax is Dt =t – 0 = t.
w  The price buyers pay increases by:
⎛ η
Δp = ⎜⎜
⎝η − ε
⎞
⎟⎟Δτ
⎠
•  If e = -0.3 and h = 0.6, a change of a tax of Dt
= $1.05 causes the price buyers pay to rise by
⎛ η
Δp = ⎜⎜
⎝η − ε
3 - 39
⎞
0.6
⎟⎟Δτ =
× $1.05 = $0.70
0.6 − [−0.3]
⎠
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Solved Problem 3.4
•  If the supply curve is perfectly elastic and
demand is linear and downward sloping,
what is the effect of a $1 specific tax
collected from producers on equilibrium
price and quantity, and what is the
incidence on consumers? Why?
3 - 40
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Solved Problem 3.4
3 - 41
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p, $ per kg
Figure 3.7 Effect of a $1.05 Specific Tax
on Pork Collected from Consumers
but the new equilibrium is the same as
when the tax is applied to suppliers
e2
p = 3.30
T = $216.3 million
– t = 2.95
p = 4.00
p2
Wedge, t = $1.05
S
e2
t = $1.05
The tax shifts the
demand curve down
by τ = $1.05…
0
3 - 42
176
Q2 = 206
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Q1 = 220
D1
D2
Q, Million kg of pork per year
Figure 3.8 Comparison of an Ad Valorem
and a Specific Tax on Pork
3 - 43
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Solved Problem 3.5
•  If the short-run supply curve for fresh fruit
is perfectly inelastic and the demand
curve is a downward-sloping straight line,
what is the effect of an ad valorem tax on
equilibrium price and quantity, and what is
the incidence on consumers? Why?
3 - 44
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Solved Problem 3.5
3 - 45
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Figure 3.9 Effect of a Specific Gasoline
(Carbon) Tax in the Long Run and in the
Short Run
3 - 46
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