bài giảng kinh tế vi mô tiếng anh ch3 applying s&d model

1
Chapter 3
Applying the Supply-and-
Demand Model
Applying supply and demand
model
1. shapes matter
2. sensitivity of quantity demanded to price
3. sensitivity of quantity supplied to price
4. sensitivity is different in long run than in
the short run
5. effects of a sales tax
Questions
1. condoms: how much of a subsidy is necessary to
encourage French consumers to use 70% more
condoms?
2. cigarettes taxes: how big a tax is needed to
discourage a substantial number of people from
smoking?
3. health care: if Congress passes a law forcing firms
to provide health care, will firms pass on the full
amount of these mandatory fees to consumers?
What-if questions
• how do equilibrium price and quantity
change when an underlying factor changes?
• use graphs to predict qualitative effects of
changes: The direction of change
• need to know shape of demand and supply
curves to determine quantitative change:
amount equilibrium quantity and price
change

Shapes of demand and supply
curves matter
• supply shock (25¢ increase in price of hogs)
effect on Canadian processed pork depends
on shape of demand curve
• supply shock causes supply curve of pork to
shift left from S
1
to S
2
p, $ per kg
215 2201760
Q, Million kg of pork per year
3.55
3.30
S
1
D
1
S
2
e
1
e
2
Pork demand and supply curves
2
If the demand curve is horizontal
p, $ per kg
2202051760

Q, Million kg of pork per year
3.30
S
1
S
2
D
3
e
1
e
2
If the demand curve is vertical
p, $ per kg
2201760
Q, Million kg of pork per year
3.675
3.30
S
1
S
2
D
2
e
1
e
2
-49.5-150Horizontal
82.5037.5Vertical

37.25-525Actual:
Downward slope
R, $million/
year
Q, million
kg/year
p, cents/kg
Demand Curve
Elasticity of demand
• summarize sensitivity of the quantity
demanded to price in a single statistic: price
elasticity of demand:
% change in quantity demanded /
%change in price /
QQ
p
p
ε
∆
==
∆
/
/
QQ Qp
p
ppQ
ε
∆∆
==
∆∆

Linear demand curve
• linear demand: Q = a – bp
• elasticity of demand:
• pork demand curve: Q = 286 – 20p
Qp p
b
p
QQ
ε
∆
==−
∆
3.30
20 0.3
220
Qp p
b
pQ Q
ε
∆
==−=− =−
∆
Interpretation of pork demand
elasticity
• 1% increase in price of pork leads to an F%
= -0.3% change in the quantity demanded
• quantity falls less than in proportion to price
• negative price elasticity, -0.3, is consistent
with Law of Demand
3

Types of elasticities
• elastic: the quantity demanded changes
more than in proportion to a change in price
• inelastic: the quantity demanded changes
less than in proportion to a change in price
• elasticity of demand varies along most
linear demand curves
Figure 3.2 Elasticity Along the Pork Demand Curve
p, $ per kg
a/2 = 143a/5 = 57.2
D
a = 286220
Q, Million kg of pork per year
0
11.44
a/b = 14.30
3.30
a/(2b) = 7.15
Elastic: ε < –1
ε = –4
Unitary: ε = –1
ε = – 0.3
Inelastic: 0 > ε > –1
Perfectly
inelastic
Perfectly elastic
Downward-sloping linear
demand curve
• perfectly elastic (F is -<) where demand
curve hits vertical axis

• unitary elasticity at midpoint:
p = a/(2b) and Q = a/2
therefore, F = -bp/Q = -b(a/[2b])/(a/2) = -1
• perfectly inelastic (F = 0) where demand
curve hits quantity axis
ε = -bp/Q = -b0/Q = 0
Constant elasticity demand
curves
• elasticity same at every point along curve
• smooth curves:
• Q = Ap
.
, or,
• vertical demand curve: perfectly inelastic (F =
0) everywhere: essential good
• horizontal demand curve: perfectly elastic
(-d): perfect substitutes
Constant Elasticity Demand Curves
Figure 3.3c Individual’s Demand for Insulin
*
p, Price of
insulin dose
* Q, Insulin
doses per day
p
Q
4
Income elasticity of demand
% change in quantity demanded
% change in income

/
/
QQ QY
YY YQ
ξ
=
∆∆
==
∆∆
Pork income elasticity of demand
pork demand function is
Q = 171 – 20p + 20p
b
+ 3p
c
+ 2Y
so pork income elasticity is
at Q = 220 and Y = 12.5
Y = 2 x 12.5/220 = 0.114
2
QY Y
YQ Q
ξ
∆
==
∆
Cross-price elasticity of demand
how quantity of one good changes as price
of another good increases
%change in quantity demanded

%change in price of another good
/
/
o
oo o
QQ Qp
pp pQ
∆∆
==
∆∆
Negative cross-price elasticity
• as the other good’s price increases, people buy
less of this good
• demand curve shifts to the left
•examples
• as price of cream rises, people consume less coffee
(cross-price elasticity is negative)
• Ford wants to know how much a change in the price of
a Camry affects the demand for a Taurus
Positive cross-price elasticity
• as the price of the other good increases,
people buy more of this good
• demand curve shifts to the right
• example: cross-price elasticity of pork with
respect to the price of beef is positive
Pork-beef example
• pork demand function is
Q = 171 – 20p + 20p
b
+ 3p

c
+ 2Y
• so cross-price elasticity of demand for pork
and the the price of beef is
•at Q = 220 and p
b
= $4 per kg, cross-price
elasticity is 20 x 4/220 = 0.364
20
ob
o
Qp p
p
QQ
∆
=
∆
5
Price elasticity of supply
/
/
%change in quantity supplied
%change in price
QQ Qp
pp pQ
η
=
∆∆
==
∆∆

Sign of elasticity of supply
• if supply curve slopes upward, %p/%Q > 0,
then
I > 0
• if supply curve slopes downward,
%p/%Q >
0, then
I < 0
• supply curve is elastic if
I > 1
• supply curve is inelastic if 0
bI< 1
Pork supply elasticity
• pork supply curve is
Q = 88 + 40p
• so pork supply elasticity is
• as price of pork increases by 1%, the quantity
supplied rises by nearly two-thirds of a percent
3.30
40 0.6
220
Qp
pQ
η
∆
== =
∆
Figure 3.4 Elasticity Varies Along Linear Pork Supply Curve
p, $ per kg
220 260176

S
η
≈ 0.71
η
≈ 0.66
η
≈ 0.6
η
≈ 0.5
300
Q, Million kg of pork per year
0
3.30
2.20
4.30
5.30
Constant Elasticity Supply Curves
Long run versus short run
• SR and LR elasticities may differ
substantially
• gasoline demand elasticities:
• SR elasticity = -0.35
• 5-year intermediate-run elasticity = -0.7
• 10-year, LR elasticity = -0.8
• if a good can be easily stored, SR demand
curve may be more elastic than LR curve
6
OPEC restricts output
• according to news reports 1/17/01, OPEC
may reduce quantity of oil by 5%

• How does the price change in SR and LR?
•
%p/p = (%Q/Q)/F
= -5%/(-0.35) = 14.3% (SR)
= -5%/(-0.7) = 7.1% (intermediate run)
= -5%/(-0.8) = 6.3% (LR)
Predictions based on elasticities
knowing only the elasticities of demand and
supply, we can make accurate predictions
about the effects of a new tax and determine
how much of the tax falls on consumers
Two types of sales taxes
• ad valorem tax (the sales tax): for every
dollar the consumer spends, the government
keeps a fraction,
B
• specific (unit) tax: a specified amount, U, is
collected per unit of output
Tax on consumer
pQ – UQT = UQspecific tax U
(1 - B)pQT = BpQad valorem tax Bp
Firms’ after-tax
revenue
Total tax
revenue
Per unit tax
4 Questions about sales taxes
1. What effect does a specific sales tax have on
equilibrium prices and quantity?
2. Are sales taxes assessed on producers "passed

along" to consumers? (do consumers pay entire
tax?)
3. Do equilibrium price and quantity depend on
whether the consumers or producers are taxed?
4. Do both types of sales taxes have the same effect
on equilibrium?
Specific tax
• assume the specific tax is assessed on firms
at the time of sale
• consumer pays p
• government takes
U
• seller receives p - U
7
Sin taxes
• because output falls after tax, governments
can use taxes to discourage "sin" activities
• federal specific taxes have been used for:
• cigarettes
• alcohol
• playing cards (in an earlier day)
Price impact of tax
• amount by which tax affects equilibrium
price depends on elasticities of supply and
demand
• government raises tax by
%U = U -0 = U
• price consumers pay increases by
p
η

∆= ∆τ
η
−ε
Pork example
• Figure 3.5 shows %p = $4 - $3.30 = 70¢
• demand elasticity:
F = -0.3
• supply elasticity,
I = 0.6
• %U = U = $1.05
• therefore:
0.6
($1.05) $0.70
0.6 ( 0.3)
p
η
∆= ∆τ= =
η−ε − −
Figure 3.5 Effect of a $1.05 Specific Tax on the Pork Market
Collected from Producers
p, $ per kg
Q
2
= 206 Q
1
= 220176
T
=
$216.3 million
Q, Million kg of pork per year

0
p
2
= 4.00
p
1
= 3.30
p
2
–
τ
= 2.95
τ
= $1.05
S
1
e
1
e
2
S
2
D
Question 2
• Who is hurt by the tax?
• What is the incidence of the tax?
Tax incidence
incidence of a tax on consumers is share of
tax that consumers pay
p∆η

=
∆τ η− ε
8
Incidence of a tax on pork
• Figure 3.5 shows consumer incidence is
%p/%7 = $0.70/$1.05 = 2/3
• using elasticities, consumer incidence is
I/(I - F) = 0.6/(0.6 - [-0.3]) = 2/3
Restaurant tax incidence
• estimated demand and supply for restaurant
meals (Brown 1980):
• constant elasticity demand curve: F = -0.188
• constant elasticity supply curve: I = 6.47
• original equilibrium:
• Q
1
= 8.14 billion meals per year
• p
1
= $10.47 per meal ($1992)
Incidence specific gasoline taxes
• specific taxes
• federal range from nearly 11¢ and 20¢ per gallon
• state from 7¢ to 36¢ per gallon
• incidence: federal tax ³ 1¢ º
• retail price ³ ½¢
• wholesale price m ½¢
• incidence: state tax ³ 1¢ º
• retail price ³ 1¢
• no wholesale price effect

Incidence ad valorem gas tax
ad valorem gas tax
• CA, Georgia, IL, Indiana, Louisiana,
Michigan, Mississippi, NY
• range up to 7% of retail price
•tax rate
³ from 0 to 5% º
• retail price ³ 3.6¢
• wholesale price m 1.8¢.
Question 3
• does equilibrium depend on who is taxed?
9
Answer
no: equilibrium is same whether government
collects tax from firms or from consumers
in a competitive market
= $1.05
= 2.95
Figure 3.6 Effect of a $1.05 Specific Tax on Pork Collected from
Consumers
p , $ per kg
Q
2
= 206 Q
1
= 220176
= $216.3 million
Q, Million kg of pork per year0
p
2

= 4.00
p
1
= 3.30
p
2
–
τ
= $1.05
Wedge,
τ
D
1
D
2
e
1
e
2
S
T
τ
Question 4
how can an ad valorem and specific tax
have the same effect on equilibrium (in a
competitive market)?
Figure 3.7 A Comparison of an Ad Valorem and a Specific Tax
on Pork
p , $ per kg
Q

2
= 206 Q
1
= 220176
T
=
$216.3 million
Q
, Million kg of pork per year0
p
2
= 4.00
p
1
= 3.30
p
2
–
τ
= 2.95
e
1
e
2
D
a
D
s
S
D

Luxury taxes
• in 1990, an ad valorem tax was imposed on luxury
goods
• tax was 10% of the amount over
• $100,000 paid for yachts
• $250,000 for private planes
• $10,000 for furs and jewels
• $30,000 for cars
• objective: raise tax revenues without harming the
poor and middle class
1 Shapes of demand and supply
curves matters
shapes determine the size of the effect
10
2 Elasticity of demand
• F = percentage change in quantity demanded
due to an increase in price divided by
percentage change in price
• always negative due to the Law of Demand
3 Elasticity of supply
• I = percentage change in the quantity
supplied divided by the percentage change
in price
• may have any sign, but commonly positive
(upward-sloping supply curve)
4 LR and SR elasticities
frequently differ
usually more adjustment is possible in the
long run than in the short run
5 Sales taxes

• common types of sales taxes: ad valorem and
specific
• both types of taxes usually raise equilibrium price
and lower equilibrium quantity
• tax incidence depends on demand and supply
elasticities
• in competitive markets, effect of a tax on
equilibrium same whether collected from
consumers or producers