chp3 slides economics
Post on 11-Oct-2015
23 Views
Preview:
DESCRIPTION
TRANSCRIPT
-
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. electric power: why did price shoot up in
2000?
2. inelastic: can demand be everywhere
inelastic?
-
What-if questions
how do equilibrium price and quantity
change when an underlying factor changes?
use graphs to predict qualitative effects of
changes: 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
-
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/ yearQ, million kg/yearp, cents/kg
Demand Curve
-
Review: Electric power
Why did Californias wholesale electric
power rates suddenly shoot up in 2000?
-
Answer
demand increased 5% more than expected
limited capacity short-run supply nearly
vertical
-
price per kWh
Quantity, million kWh per year
D
1
D
2
S
p
1
p
2
p*
S*
-
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 /
Q Q
p p
= =
/
/
Q Q Q p
p p pQ
= =
-
Linear demand curve
linear demand: Q = a bp
elasticity of demand:
pork demand curve: Q = 286 20p
d
d
Q p Q p p
b
p Q p Q Q
= = =
3.30
20 0.3
220
Q p p
b
p Q Q
= = = =
-
Interpretation of pork demand
elasticity
1% increase in price of pork leads to an %
= -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
-
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: < 1
= 4
Unitary: = 1
= 0.3
Inelastic: 0 > > 1
Perfectly
inelastic
Perfectly elastic
-
Downward-sloping linear
demand curve
perfectly elastic ( is -) where demand
curve hits vertical axis
unitary elasticity at midpoint:
p = a/(2b) and Q = a/2
therefore, = -bp/Q = -b(a/[2b])/(a/2) = -1
perfectly inelastic ( = 0) where demand
curve hits quantity axis
= -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
( = 0) everywhere: essential good
horizontal demand curve: perfectly elastic
(-): perfect substitutes
-
Constant Elasticity Demand Curves
-
Figure 3.3c Individuals Demand for Insulin
*
p, Price of
insulin dose
* Q, Insulin
doses per day
p
Q
-
Prove constant elasticity
demand function: Q = Ap
1
1
d
elasticity
d
Q p p
Ap
p Q Q
p p
Ap
Ap p
= =
= = =
-
Solved problem
Is it possible that a demand curve is
inelastic everywhere?
restatement: Does the assumption that a
demand curve is everywhere inelastic
contradicts some known fact?
-
Answer
1. assume that a demand curve is everywhere
inelastic, and determine the properties of
that demand curve:
if demand curve is perfectly inelastic, quantity
doesn't change as price increases so revenue
rises in proportion to price
as the price rise, the amount consumers spend
grows without limit
-
Answer (cont.)
2. check whether those properties violate a
known fact:
consumers cannot spend an infinite amount
on a single good: They don't have unlimited
wealth
therefore, a demand curve cannot be
everywhere inelastic (at a high enough
price, the demand must be elastic)
-
Solved problem
Will a profit-maximizing monopoly ever
operate in the inelastic section of its demand
curve?
restatement: Can a monopoly make more
money operating in a different section of its
demand curve?
-
Answer
1. show what happens to its revenue if the monopoly
raises its price and it is in the inelastic section of
its demand curve: quantity falls less than in
proportion to price, so revenue rises
2. discuss what happens to profit: cost falls with
quantity, so profit rises
3. conclude: monopoly raises its price when in the
inelastic section section of its demand curve until
its no longer in that section
-
Income elasticity of demand
% change in quantity demanded
% change in income
/
/
Q Q Q Y
Y Y Y Q
=
= =
-
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
= 2 x 12.5/220 = 0.114
2
Q Y Y
Y Q Q
= =
-
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
Q Q Q p
p p p Q
= =
-
Negative cross-price elasticity
as the other goods price increases, people
buy less of this good
demand curve shifts to the left
example: as price of cream rises, people
consume less coffee (cross-price elasticity
is negative)
-
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: demand for a Camry rises as the
price of a Taurus increases
-
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 b
o
Q p p
p Q Q
=
-
Price elasticity of supply
/
/
%change in quantity supplied
%change in price
Q Q Q p
p p pQ
=
= =
-
Sign of elasticity of supply
if supply curve slopes upward, p/Q > 0,
then > 0
if supply curve slopes downward, p/Q >
0, then < 0
supply curve is elastic if > 1
supply curve is inelastic if 0 < 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
Q p
p Q
= = =
-
Figure 3.4 Elasticity Varies Along Linear Pork Supply Curve
p, $ per kg
220 260176
S
0.71
0.66
0.6
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
-
OPEC restricts output
according to news reports 1/17/01, OPEC
planned to reduce its quantity of oil by 5%
how would the price change in SR and LR?
p/p = (Q/Q)/
= -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,
specific (unit) tax: a specified amount, , is
collected per unit of output
-
Tax on consumer
pQ QT = Qspecific tax
(1 - )pQT = pQad valorem tax p
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
seller receives p -
-
Question 1
What is the effect of a specific tax on the
equilibrium?
answer: See Figure 3.5 where we shift up
the after-tax supply curve
equilibrium price rises
equilibrium quantity falls
government collects tax revenues
-
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
= 2.95
= $1.05
S
1
e
1
e
2
S
2
D
-
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)
-
Question 2
Who is hurt by the tax?
What is the incidence of the tax?
-
In-class problem
When a specific tax is imposed on pork,
what happens to prices? Price consumers
pay rises by
A. more than the tax
B. by the amount of the tax
C. by less than the tax
-
Price impact of tax
amount by which tax affects equilibrium
price depends on elasticities of supply and
demand
government raises tax by = - 0 =
price consumers pay increases by
p
=
-
Pork example
Figure 3.5 shows p = $4 - $3.30 = $0.70
demand elasticity: = -0.3
supply elasticity, = 0.6
= = $1.05
therefore:
0.6
($1.05) $0.70
0.6 ( 0.3)
p
= = =
-
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
= 2.95
= $1.05
S
1
e
1
e
2
S
2
D
-
Tax incidence
incidence of a tax on consumers is share of
tax that consumers pay
p
=
-
Incidence of a tax on pork
figure 3.5 shows consumer incidence is
p/ = $0.70/$1.05 = 2/3
using elasticities, consumer incidence is
/( - ) = 0.6/(0.6 - [-0.3]) = 2/3
-
Restaurant tax incidence
estimated demand and supply for restaurant
meals (Brown 1980):
constant elasticity demand curve: = -0.188
constant elasticity supply curve: = 6.47
original equilibrium:
Q
1
= 8.14 billion meals per year
p
1
= $10.47 per meal ($1992)
-
Restaurant tax incidence
most of the incidence falls on consumers:
2 1
$11.44 - $10.47
= = = 97%
$1
6.47
= =97%
- 6.47 + 0.188
p p p
=
-
Overall effect of $1 meal tax
raises $8 billion in tax revenues
causes little drop in the number of
restaurant meals purchased
-
Specific gasoline taxes
federal range from nearly 11 and 20 per
gallon
state from 7 to 36 per gallon
-
Incidence of gas tax
0-wholesale price
+1+retail price
statefederal
1 increase in specific gasoline tax
-
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 from 0 to 5%
retail price 3.6
wholesale price 1.8.
-
Solved problem
if supply curve is perfectly elastic,
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?
[for simplicity, assume demand is a
downward-sloping straight line]
-
Restatement
what changes: specific tax, , goes from $0
to $1 per unit
this change affects equilibrium price and
quantity
use pretax and post-tax price to consumers
to determine the incidence of the tax
-
p, Price per unit
Q, Quantity per time period
p
2
p
2
- = p
1
D
e
1
e
2
S
1
S
2
-
Question 3
Does equilibrium depend on who is taxed?
-
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
= $1.05
Wedge,
D
1
D
2
e
1
e
2
S
T
-
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
= 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
-
Tax on automobiles
worked better than planned
expected: luxury tax would raise $25 million in 1991
and $1.5 billion over 5 years
actual: brought in $98.4 million in first year alone
most tax revenue came from sales of expensive,
foreign cars, whose sales fell
27%, Mercedes
10%, Lexus
few lost jobs for Americans except for auto
dealers
-
Taxes on other luxury goods
raised relatively little revenue
caused substantial loss of domestic output
and jobs
four bills brought before Congress within a
year to remove those taxes
in mid 1993, the taxes were revoked
-
Yacht tax harmed industry
substantially
in the first year sales of yachts costing over
$100,000 fell by 71%;
whereas, sales of unaffected less-expensive
yachts fell only 28% (due to the recession)
employment fell from 160,000 to 115,000
workers
loss in payroll taxes far outweighed the
increase in the luxury tax revenues
-
Yacht tax raised only $7 million
(well below the forecast)
Congressional analysts underestimated the
demand elasticity: ignored tax-avoiding
behavior and ability of consumers to
substitute
wealthy consumers escaped the boat tax by
buying yachts in the Bahamas
buying yachts that cost just under $100,000
(avoiding the luxury tax)
-
1 Shapes of demand and supply
curves matters
shapes determine the size of the effect
-
2 Elasticity of demand
= 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
= 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
top related