# Document

```Topic 8 ：Taxation(1)Positive Principles of Taxation
Taxes
• The government levies taxes on many goods
&amp; services to raise revenue to pay for
national defense, public schools, etc.
• The government can make buyers or sellers
pay the tax.
• The tax can be a percentage of the good’s
price, or a specific amount for each unit sold.
– For simplicity, we analyze per-unit taxes only.
EXAMPLE : The Market for Pizza
P
S1
Equilibrium
without tax
\$10.00
D1
500
Q
• Without tax consumers
would buy 430 pizzas if the
price is \$11.
• For consumers it does not
matter if the increase in price
is due to price itself or tax.
• If the market price is \$10 but
consumers have to pay \$1 in
tax then at P=\$10 they would
demand as much as at P=\$11
without tax.
•The same is true for any price.
•Hence, \$1 tax would shift the
demand curve down to the left
by vertical distance \$1.
P
Tax
\$11.00
\$10.00
\$9.00
D1
D2
Q
430
500 470
Effects of a \$1.00 per
A tax on
the D curve
down by the
amount of the
tax.
The price
rises, the
price sellers
equilibrium
Q falls.
P
PB = \$11.00
S1
Tax
\$10.00
PS = \$9.50
D1
D2
430 500
Effects of a \$1.50 per
Q
how the burden of a tax is shared among
market participants
P
PB = \$11.00
Because
of the tax,
\$1.00 more,
sellers get
\$0.50 less.
S1
Tax
\$10.00
PS = \$9.50
D1
D2
430 500
Q
A Tax on Sellers
A tax on
sellers shifts
the S curve
up by the
amount of the
tax.
The price
rises, the
price sellers
equilibrium Q
falls.
P
PB = \$11.00
S2
S1
Tax
\$10.00
PS = \$9.50
D1
430 500
Effects of a \$1.50 per
unit tax on sellers
Q
The effects on P and Q, and the tax incidence
are the same whether the tax is imposed on
P
PB = \$11.00
What matters
is this:
A tax drives
a wedge
between the
pay and the
price sellers
S1
Tax
\$10.00
PS = \$9.50
D1
430 500
Q
incidence发生率； 影响范围
wedge楔形物
Elasticity and Tax Incidence
CASE 1: Supply is more elastic than demand
P
of tax burden
PB
In this case,
most of the
burden of
the tax.
S
Tax
Price if no tax
Sellers’ share
of tax burden
PS
D
Q
CASE 2: Demand is more elastic than supply
P
In this case,
sellers bear
most of the
burden of
the tax.
S
PB
of tax burden
Price if no tax
Sellers’ share
of tax burden
Tax
PS
D
Q
• If buyers’ price elasticity &gt; sellers’ price
elasticity, buyers can more easily leave the
market when the tax is imposed, so buyers
will bear a smaller share of the burden of the
tax than sellers.
• If sellers’ price elasticity &gt; buyers’ price
elasticity, the reverse is true.
CASE STUDY:
Who Pays the Luxury Tax?
• 1990: Congress adopted a luxury tax on
yachts, private airplanes, furs, expensive
cars, etc.
• Goal of the tax: to raise revenue from those
who could most easily afford to pay –
wealthy consumers.
• But who really pays this tax?
The market for yachts
P
Demand is
price-elastic.
S
In the short run,
supply is inelastic.
PB
of tax burden
Tax
Sellers’ share
of tax burden
PS
D
Q
Hence,
companies
that build
yachts pay
most of
the tax.
Review
• A tax is a wedge between the price buyers
pay and the price sellers receive.
• A tax raises the price buyers pay and lowers
• A tax reduces the quantity bought &amp; sold.
• These effects are the same whether the tax
is imposed on buyers or sellers, so we do
not make this distinction in this chapter.
The Effects of a Tax
Eq’m with no
tax:
price = PE
quantity = QE
Eq’m with
tax = \$T per unit:
P
Size of tax = \$T
S
PB
PE
PS
D
Quantity = QT
QT
QE
Q
P
Revenue from tax:
\$T x QT
Size of tax = \$T
S
PB
PE
PS
D
QT
QE
Q
• Next, we apply welfare economics to
measure the gains and losses from a tax.
• We determine consumer surplus (CS),
producer surplus (PS), tax revenue,
and total surplus with and without the tax.
• Tax revenue can fund beneficial services
so we include it in total surplus.
P
Without a tax,
CS = A + B + C
PS = D + E + F
Tax revenue = 0
Total surplus
= CS + PS
=A+B+C
+D+E+F
A
S
B
PE
D
C
E
D
F
QT
QE
Q
With the tax,
CS = A
PS = F
Tax revenue
=B+D
Total surplus
=A+B
+D+F
The tax
reduces total
surplus by
C+E
P
A
PB
S
B
D
C
E
PS
D
F
QT
QE
Q
P
C + E is called
loss (DWL无谓损

fall in total
surplus that
results from a
market distortion,
such as a tax.
A
PB
S
B
D
C
E
PS
D
F
QT
QE
Q
Because of the tax,
the units between
QT and QE are not
sold.
The value of these
greater than the
cost of producing
them,
so the tax prevents
some mutually
P
PB
S
PS
D
QT
QE
Q
ACTIVE LEARNING
1:
Analysis of tax
P
A. Compute
CS, PS, and
total surplus
without a tax.
B. If \$100 tax
per ticket,
compute
CS, PS,
tax revenue,
total surplus,
and DWL.
\$
The market for
airplane tickets
400
350
300
S
250
200
150
D
100
50
0
0
25
50
75 100 125
Q
ACTIVE LEARNING
1:
P
CS
= &frac12; x \$200 x 100
= \$10,000
The market for
airplane tickets
\$ 400
350
300
S
250
PS
= &frac12; x \$200 x 100 P = 200
= \$10,000
150
D
100
total surplus
= \$10,000 + \$10,000 50
= \$20,000
0
Q
0
25
50
75 100 125
ACTIVE LEARNING
1:
P
CS
= &frac12; x \$150 x 75
= \$5,625
\$ 400
350
300
PS = \$5,625
PB = 250
tax revenue
= \$100 x 75
= \$7,500
200
PS = 150
total surplus
= \$18,750
50
DWL = \$1,250
A \$100 tax on
airplane tickets
S
D
100
Q
0
0
25
50
75 100 125
What Determines the Size of the DWL?
• Which goods or services should government
tax to raise the revenue it needs?
– One answer: those with the smallest DWL.
• When is the DWL small vs. large?
– It depends on the price elasticities
of supply and demand.
Recall:
The price elasticity of demand (or supply)
measures how much QD (or QS) changes
when P changes.
DWL and the Elasticity of Supply
P
When supply
is inelastic,
the DWL of a
tax is small.
S
Size
of tax
D
Q
P
The more elastic
is supply, the
larger is the
DWL.
S
Size
of tax
D
Q
DWL and the Elasticity of Demand
P
When demand
is inelastic,
the DWL of a
tax is small.
S
Size
of tax
D
Q
P
The more
elastic is
demand, the
larger is
the DWL.
S
Size
of tax
D
Q
Why Elasticity Affects the Size of DWL
• A tax distorts the market outcome:
consumers buy less, producers sell less,
market Q is below the surplus-maximizing Q.
• Elasticity measures how much buyers and
sellers respond to changes in price,
and therefore determines how much the
tax distorts the market outcome.
2:
Elasticity and DWL of a tax
ACTIVE LEARNING
Would the DWL of a tax be larger if the
tax were on
A. Rice Krispies or sunscreen?
B. Hotel rooms in the short run or hotel rooms
in the long run?
C. Groceries or meals at fancy restaurants?
ACTIVE LEARNING
2:
A. Rice Krispies or sunscreen
•
Rice Krispies has many more close
substitutes than sunscreen, so demand for
Rice Krispies is more price-elastic than
demand for sunscreen.
• So, a tax on Rice Krispies would cause a
larger DWL than a tax on sunscreen.
ACTIVE LEARNING
2:
B. Hotel rooms in the short run or long
run
• The price elasticities of demand and supply
for hotel rooms are larger in the long run than
in the short run.
• So, a tax on hotel rooms would cause a larger
DWL in the long run than in the short run.
ACTIVE LEARNING
2:
C.Groceries or meals at fancy
restaurants
• Groceries are more of a necessity and
therefore less price-elastic than meals at
fancy restaurants.
• So, a tax on restaurant meals would cause a
larger DWL than a tax on groceries.
ACTIVE LEARNING
3:
Discussion question
• The government must raise tax
revenue to pay for schools, police, etc.
To do this, it can either tax groceries
or meals at fancy restaurants.
• Which should it tax?
How Big Should the Government Be?
• A bigger government provides more services,
but requires higher taxes, which cause DWLs.
• The larger the DWL from taxation,
the greater the argument for smaller government.
• The tax on labor income is especially important;
it’s the biggest source of government revenue.
• For many workers, the marginal tax rate (the tax on
the last dollar of earnings) is almost 50%.
• How big is the DWL from this tax?
It depends on elasticity….
• If labor supply is inelastic, then this DWL is
small.
• Some economists believe labor supply is
inelastic, arguing that most workers work
full time regardless of the wage.
•Other economists believe labor taxes are highly
distorting because some groups of workers
have elastic supply and can respond to
incentives:
– Many workers can adjust their hours,
e.g. by working overtime.
– Many families have a 2nd earner with discretion over
whether and how much to work.
– Many elderly choose when to retire based on the
wage they earn.
– Some people work in the “underground economy”
discretion判断力
The Effects of Changing the Size of the Tax
• Policymakers often change taxes, raising
some and lowering others.
• What happens to DWL and tax revenue when
taxes change?
DWL and the Size of the Tax
P
new
DWL
Initially, the tax
is T per unit.
S
Doubling the
tax
2T
T
causes the
DWL to more
than double.
D
initial
DWL
Q2
Q1
Q
Initially, the tax
is T per unit.
Tripling the tax
causes the
DWL to more
than triple.
P
new
DWL
S
T
3T
D
initial
DWL
Q3
Q1
Q
Implication
When tax rates are
low, raising them
doesn’t cause
much harm, and
lowering them
doesn’t bring
much benefit.
When tax rates are
high, raising them is
very harmful, and
cutting them is very
beneficial.
Summary
When a tax increases,
DWL rises even more.
DWL
Tax size
Revenue and the Size of the Tax
P
When the
tax is small,
increasing it
causes tax
revenue to rise.
PB
S
PB
2T
PS
T
D
PS
Q2
Q1
Q
P
PB
PB
When the
tax is larger,
increasing it
causes tax
revenue to fall.
S
3T
2T
D
PS
PS
Q3
Q2
Q
The Laffer curve
Tax
shows the
revenue
relationship
between
the size of the
tax and tax
revenue.
The Laffer curve
Tax size
SUMMARY
• A tax on a good reduces the welfare of
buyers and sellers. This welfare loss usually
exceeds the revenue the tax raises for the
government.
• The fall in total surplus (consumer surplus,
producer surplus, and tax revenue) is called
the deadweight loss (DWL) of the tax.
• A tax has a DWL because it causes
consumers to buy less and producers to sell
less, thus shrinking the market below the
level that maximizes total surplus.
• The price elasticities of demand and supply
measure how much buyers and sellers
respond to price changes. Therefore, higher
elasticities imply higher DWLs.
• An increase in the size of a tax causes the
DWL to rise even more.
• An increase in the size of a tax causes
revenue to rise at first, but eventually revenue
falls because the tax reduces the size of the
market.
```