Chapter Three
Applying the Supplyand-Demand Model
Topics To Be Covered
ƒ How the shapes of demand and supply
curves matter?
ƒ Sensitivity of quantity demanded to
price.
ƒ Sensitivity of quantity supplied to price.
ƒ Long run versus short run
ƒ Effects of a sales tax.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-2
How shapes of demand and supply
matter?
ƒ The shapes of the demand and supply
curves determine by how much a shock
affects the equilibrium price and
quantity.
ƒ Example: processed pork (same as
Chapter 2)
Š Supply depends on the price of pork and
the price of hogs.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-3
1
Figure 3.1 How the Effect of a Supply Shock
Depends on the Shape of the Demand Curve
3.55
3.30
D1
A $0.25
increase in the
price of pork
causes the
supply of pork
to shift to the
left.
e2
e1
S2
A $0.25 increase in the price of pork
causes the supply of pork to shift to
the left
(b)
p, $ per kg
(a)
p, $ per kg
This shift of the supply curve causes a
movement along the demand curve…
3.675
3.30
176
e2
e1
S2
S1
S1
0
D2
0
215220
Q, Million kg of pork per year
and a reduction in quantity.
220
176
Q, Million kg of pork per year
But equilibrium quantity does not change
since consumption is not sensitive to price
3-4
© 2009 Pearson Addison-Wesley. All rights reserved.
Figure 3.1 How the Effect of a Supply Shock
Depends on the Shape of the Demand Curve
(cont’d)
Š a shift in the supply
curve to S2…
Š has no effect on the
equilibrium price
Š and a substantial effect
on the quantity
(c)
p, $ per kg
ƒ When demand is very
sensitive to price…
3.30
D3
e2
e1
S2
S1
0
176
205
220
Q, Million kg of pork per year
© 2009 Pearson Addison-Wesley. All rights reserved.
3-5
Sensitivity of quantity demanded to
price.
ƒ Elasticity – the percentage change in a
variable in response to a given
percentage change in another variable.
ƒ Price elasticity of demand (ε) – the
percentage change in the quantity
demanded in response to a given
percentage change in the price.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-6
2
Sensitivity of quantity demanded to
price (cont).
ƒ Formally,
ΔQ
%ΔQ Q ΔQ p
ε=
=
=
%Δp Δp Δp Q
p
Š where Δ indicates change.
ƒ Example
Š If a 1% increase in price results in a 3% decrease in
quantity demanded, the elasticity of demand is ε = 3%/1% = -3.
3-7
© 2009 Pearson Addison-Wesley. All rights reserved.
Sensitivity of quantity demanded to
price (cont).
ƒ Along linear demand curve with a function of:
Q = a − bp
Š Where -b is the slope or
−b =
ΔQ
Δp
Š the elasticity of demand is
ε=
ΔQ p
p
= −b
Δp Q
Q
(3.3)
© 2009 Pearson Addison-Wesley. All rights reserved.
3-8
Sensitivity of quantity demanded to
price: Example.
ƒ The estimated linear demand function for pork
is:
Q = 286 -20p
Š where Q is the quantity of pork demanded in million
kg per year and p is the price of pork in $ per year.
Š At the equilibrium point of p = $3.30 and Q = 220
the elasticity of demand for pork is
ε = −b
p
3.30
= −20 ×
= −0.3
Q
220
© 2009 Pearson Addison-Wesley. All rights reserved.
3-9
3
Elasticity: An Application and a
practice problem
ƒ Varian (2002) found that the price elasticity of
demand for internet use was
Š -2.0 for those who used a 128 Kbps service
Š -2.9 for those who used a 64 Kbps service.
ƒ Practice problem:
Š 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
© 2009 Pearson Addison-Wesley. All rights reserved.
Elasticity Along a Demand Curve
ƒ The elasticity of demand varies along most
demand curves.
Š Along a downward-sloping linear demand curve the
elasticity of demand is a more negative number the
higher the price is.
3-11
© 2009 Pearson Addison-Wesley. All rights reserved.
p, $ per kg
Figure 3.2 Elasticity Along the Pork
Demand Curve
a/b = 14.30
11.44
Perfectly elastic
Q = 286 -20p
p
3.30
= -20 x 11.44= -0.3
220 = -4
Q
57.2
ε = -b
Elastic ε < –1
ε = –4
D
a/(2b) = 7.15
Unitary: ε = -1
3.30
0
Inelastic 0 > ε > –1
ε = –0.3
a/5 = 57.2
© 2009 Pearson Addison-Wesley. All rights reserved.
a/2 = 143
Perfectly
inelastic
220
a = 286
Q, Million kg of pork per year
3-12
4
Elasticity Along The Demand Curve:
Practice Problem
ƒ 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.
Š In which countries is the demand for rice
inelastic?
y In all the countries, since in all cases ε > -1.
Š In which country is the least elastic?
y In Vietnam, where ε = -0.15
3-13
© 2009 Pearson Addison-Wesley. All rights reserved.
(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
Q*
p*
Q, Units per
time period
Q*
Q, Insulin
doses per day
© 2009 Pearson Addison-Wesley. All rights reserved.
3-14
Sensitivity of quantity demanded to
income.
ƒ Formally,
ΔQ
%ΔQ Q ΔQ Y
=
=
ξ=
%ΔY ΔY ΔY Q
Y
Š where Y stands for income.
ƒ Example
Š If a 1% increase in income results in a 3% decrease in
quantity demanded, the income elasticity of demand is
ξ = -3%/1% = -3.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-15
5
Sensitivity of quantity demanded to
price: Example.
ƒ The estimated demand function for pork is:
Q = 171 – 20p + 20pb + 3pc + 2Y
Š 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).
Š Question: what would be the income elasticity of
demand for Pork if Q = 220 and Y = 12.5
Š Answer:
y Since ΔQ = 2, then
ΔY
ΔQ Y
Y
⎛ 12.5 ⎞
ξ=
= 2 = 2⎜
⎟ ≈ 0.114
ΔY Q
Q
⎝ 220 ⎠
© 2009 Pearson Addison-Wesley. All rights reserved.
3-16
Sensitivity of quantity demanded to the
price of a related good.
ƒ Formally,
ΔQ
ΔQ po
%ΔQ
Q
=
=
Δ
p
Δpo Q
%Δpo
o
po
Š where Po stands for price of another good.
ƒ Example
Š 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.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-17
Sensitivity of quantity demanded to the
price of a related good.
ƒ If the cross-price elasticity is positive, the
goods are substitutes.
Š Question: can you think of any examples of two
goods that are substitutes?
y Roses and carnations.
ƒ If the cross-price elasticity is negative, the
goods are complements
Š Question: can you think of any examples of two
goods that are complements?
y Peanut butter and jelly
© 2009 Pearson Addison-Wesley. All rights reserved.
3-18
6
Sensitivity of quantity demanded to
price: Example.
ƒ Again, the estimated demand function for
pork is:
Q = 171 – 20p + 20pb + 3pc + 2Y
Š Question: what would be the cross-price elasticity
between the price of beef and the quantity of
pork if Q = 220 and pb = $4?
Š Answer:
y Since ΔQ = 20, then
Δpb
p
ΔQ pb
⎛ 4 ⎞
= 20 b = 20⎜
⎟ ≈ 0.364
Δpb Q
Q
⎝ 220 ⎠
© 2009 Pearson Addison-Wesley. All rights reserved.
3-19
Sensitivity of quantity supplied to
price.
ƒ Formally,
ΔQ
%ΔQ Q ΔQ p
η=
=
=
%Δp Δp Δp Q
p
Š where Q indicates quantity supplied.
ƒ Example
Š If a 1% increase in price results in a 3% decrease in
quantity demanded, the elasticity of supplied is η =
- 3%/1% = -3.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-20
Sensitivity of quantity demanded to
price: Example.
ƒ The estimated linear supply function for pork
is:
Q = 88 - 40p
Š where Q is the quantity of pork supplied in million
kg per year and p is the price of pork in $ per year.
Š At the equilibrium, where p = $3.30 and Q = 220,
the elasticity of supplied is:
η=
ΔQ P
3.30
= 40 ×
= 0.6
Δp Q
220
© 2009 Pearson Addison-Wesley. All rights reserved.
3-21
7
Sensitivity of quantity supplied to price
(cont).
ƒ Along linear supply curve with a function of:
Q = g − hp
Š Where -b is the slope or
h=
ΔQ
Δp
Š the elasticity of demand is
η=
ΔQ p
p
=h
Δp Q
Q
© 2009 Pearson Addison-Wesley. All rights reserved.
3-22
Figure 3.4 Elasticity Along the Pork
Supply Curve
© 2009 Pearson Addison-Wesley. All rights reserved.
3-23
Demand Elasticities Over Time
ƒ Elasticities tend to be larger in the longrun.
Š Can you think why?
y In the case of demand:
– Substitution and storage opportunities.
y In the case of supply:
– Converting fixed inputs into variable inputs.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-24
8
Solved Problem 3.1
ƒ 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 = 82 million barrels per day, the preANWR world price is p1 = $100 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.
© 2009 Pearson Addison-Wesley. All rights reserved.
3-25
Solved Problem 3.1
© 2009 Pearson Addison-Wesley. All rights reserved.
3-26
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?
© 2009 Pearson Addison-Wesley. All rights reserved.
3-27
9
Two Types of Sales Taxes
ƒ Ad valorem tax - for every dollar the
consumer spends, the government
keeps a fraction, α, which is the ad
valorem tax rate.
ƒ Unit tax - where a specified dollar
amount, τ, is collected per unit of output.
3-28
© 2009 Pearson Addison-Wesley. All rights reserved.
Figure 3.5 Effect of a $1.05 Specific Tax on the
Pork Market Collected from Producers
ƒ A tax on producers shifts
the supply curve
downward by the amount
of the tax (τ = $1.05)….
ƒ which causes the market
price to increase…
p, $ per kg
S2
e2
τ = $1.05 S1
p2 = 4.00
e1
p3 = 3.30
p2 – τ = 2.95
ƒ After the tax,
T = $216.3 million
0 176
D
Q2 = 206 Q1 = 220
Š buyers are worse off by
$0.70 ($4.00 - $3.30)…
Š sellers are worse off by
$0.35 ($3.30 - $2.95)
Š and the government
collects $216.3 in
revenue.
Q, Million kg of pork per year
© 2009 Pearson Addison-Wesley. All rights reserved.
3-29
How Specific Tax Effects Depend on
Elasticities.
ƒ The government raises the tax from zero to
τ, so the change in the tax is Δτ =τ – 0 = τ.
Š The price buyers pay increases by:
⎛ η ⎞
Δp = ⎜⎜
⎟⎟Δτ
⎝η − ε ⎠
ƒ If ε = -0.3 and η = 0.6, a change of a tax of
Δτ = $1.05 causes the price buyers pay to
rise by
⎛ η ⎞
0.6
Δp = ⎜⎜
⎟⎟Δτ = 0.6 − [−0.3] × $1.05 = $0.70
⎝η − ε ⎠
© 2009 Pearson Addison-Wesley. All rights reserved.
3-30
10
Solved Problem 3.2
ƒ 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?
3-31
© 2009 Pearson Addison-Wesley. All rights reserved.
Solved Problem 3.2
3-32
© 2009 Pearson Addison-Wesley. All rights reserved.
p, $ per kg
Figure 3.6 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 = 4.00
Wedge, τ = $1.05
S
e2
p = 3.30 T = $216.3 million
p2 – τ = 2.95
τ = $1.05
D1
The tax shifts the
demand curve down
by τ = $1.05…
0
176
Q2 = 206
© 2009 Pearson Addison-Wesley. All rights reserved.
D2
Q1 = 220
Q, Million kg of pork per year
3-33
11
Figure 3.7 Comparison of an Ad Valorem
and a Specific Tax on Pork
© 2009 Pearson Addison-Wesley. All rights reserved.
3-34
Solved Problem 3.3
ƒ 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?
© 2009 Pearson Addison-Wesley. All rights reserved.
3-35
Solved Problem 3.3
© 2009 Pearson Addison-Wesley. All rights reserved.
3-36
12