sensitivity of quantity demanded to price 3.. sensitivity of quantity supplied to price 4.. What-if questions • how do equilibrium price and quantity change when an underlying factor ch
Trang 1Chapter 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 S1to S2
p, $ per kg
215 220 176
0
3.55 3.30
S1
D1
e2
Pork demand and supply curves
Trang 2If the demand curve is horizontal
p, $ per kg
220 205 176
0
Q, Million kg of pork per year
3.30
S1
S2
D3
e1
e2
If the demand curve is vertical
p, $ per kg
220 176
0
Q, Million kg of pork per year
3.675 3.30
S1
S2
D2
e1
e2
-49.5 -15
0 Horizontal
82.5 0
37.5 Vertical
37.25 -5
25 Actual:
Downward slope
R, $million/
year
Q, million kg/year
p, cents/kg
• summarize sensitivity of the quantity
demanded to price in a single statistic: price
elasticity of demand:
Q Q
p p
∆
/ /
Q Q Q p
p p p Q
ε ∆ = = ∆
Linear demand curve
• linear demand: Q = a – bp
• elasticity of demand:
• pork demand curve: Q = 286 – 20p
b
ε=∆ =−
∆
3.30
220
Q p b p
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
Trang 3Types 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 = 143 a/5 = 57.2
D
a = 286
220
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 p
Q
Trang 4Income elasticity of demand
% change in quantity demanded
% change in income
/
/
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
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
o o o
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
o
∆
Trang 5Price elasticity of supply
/
/
%change in quantity supplied
%change in price
Q Q Q p
p p p Q
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 b I < 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
220
Q p
p Q
∆
Figure 3.4 Elasticity Varies Along Linear Pork Supply Curve
p, $ per kg
176
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
Trang 6OPEC 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?
= -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
T = UQ
specific tax U
(1 -B)pQ
T = BpQ
ad 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
Trang 7Sin 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
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)
Figure 3.5 Effect of a $1.05 Specific Tax on the Pork Market
Collected from Producers
p, $ per kg
Q2= 206 Q1= 220 176
T = $216.3 million
Q, Million kg of pork per year
0
p2= 4.00
p1= 3.30
p2– τ = 2.95
τ = $1.05 S1
e1
e2
S2
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
Trang 8Incidence 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:
• Q1= 8.14 billion meals per year
• p1= $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?
Trang 9no: 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
Q2= 206 Q1= 220 176
= $216.3 million
Q, Million kg of pork per year
0
p2= 4.00
p1= 3.30
p2–
τ = $1.05 Wedge, τ
D1
D2
e1
e2
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
Q2 = 206 Q1 = 220 176
T = $216.3 million
Q, Million kg of pork per year
0
p2= 4.00
p1= 3.30
p2– τ = 2.95
e1 e2
Da
Ds
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
Trang 102 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