Unit IV
Tax Incidence (Chapter7)
In this chapter, look for the
answers to these questions:
 How do taxes affect market outcomes?
How does the outcome depend on whether
the tax is imposed on buyers or sellers?
 What is the incidence of a tax?
What determines the incidence?
 How does a tax affect consumer surplus, producer
surplus, and total surplus?
 What is the deadweight loss of a tax?
In this chapter, look for the
answers to these questions:
What factors determine the size of this
deadweight loss?
How does tax revenue depend on the size of
the tax?
What are the efficiency costs of taxes?
How can we evaluate the equity of a tax
system?
Government Policies That Alter the
Private Market Outcome
• Price controls
– Price ceiling: a legal maximum on the price
of a good or service. Example: rent control.
– Price floor: a legal minimum on the price of
a good or service. Example: minimum wage.
• Taxes
– The govt can make buyers or sellers pay a
specific amount on each unit bought/sold.
We will use the supply/demand model to see
how tax policy affects the market outcome
(the price buyers pay, the price sellers receive,
and eq’m quantity).
Taxes
• The govt levies taxes on many goods &
services to raise revenue to pay for national
defense, public schools, etc.
• The govt 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 1: The Market for Pizza
P
Eq’m
w/o
tax
S1
$10.00
D1
500
Q
A Tax on Buyers
A tax on
buyers shifts
the D curve
down by the
amount of the
tax.
The price
buyers pay
rises, the
price sellers
receive falls,
eq’m Q
falls.
Effects of a $1.50 per
unit tax on buyers
P
PB = $11.00
S1
Tax
$10.00
PS = $9.50
D1
D2
430 500
Q
The Incidence of a Tax:
how the burden of a tax is shared among
market participants
P
Because
of the tax,
buyers pay
$1.00 more,
sellers get
$0.50 less.
PB = $11.00
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
buyers pay
rises, the
price sellers
receive falls,
eq’m Q falls.
Effects of a $1.50 per
unit tax on sellers
P
PB = $11.00
S2
S1
Tax
$10.00
PS = $9.50
D1
430 500
Q
The Outcome Is the Same in Both Cases!
The effects on P and Q, and the tax incidence are the
same whether the tax is imposed on buyers or sellers!
P
What matters
is this:
A tax drives
a wedge
between the
price buyers
pay and the
price sellers
receive.
PB = $11.00
S1
Tax
$10.00
PS = $9.50
D1
430 500
Q
A C T I V E L E A R N I N G 1:
The market for
Effects of a tax P
140
130
hotel rooms
S
120
Suppose govt
imposes a tax
on buyers of
$30 per room.
Find new
Q, PB, PS,
and incidence
of tax.
110
100
90
80
D
70
60
50
40
0
Q
50 60 70 80 90 100 110 120 130
A C T I V E L E A R N I N G 1:
Answers
P
140
The market for
hotel rooms
130
PB = $110
Q = 80
PS = $80
Incidence
buyers: $10
sellers: $20
S
120
PB = 110
100
90
PS = 80
Tax
D
70
60
50
40
0
Q
50 60 70 80 90 100 110 120 130
Elasticity and Tax Incidence
CASE 1: Supply is more elastic than
demand
In this case,
buyers bear
most of the
burden of
the tax.
P
Buyers’ share
of tax burden
PB
S
Tax
Price if no tax
Sellers’ share
of tax burden
PS
D
Q
Elasticity and Tax Incidence
CASE 2: Demand is more elastic than supply
P
Buyers’ share
of tax burden
S
PB
Price if no tax
Sellers’ share
of tax burden
In this case,
sellers bear
most of the
burden of
the tax.
Tax
PS
D
Q
Elasticity and Tax Incidence
• If buyers’ price elasticity > 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 > 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?
CASE STUDY: Who Pays the
Luxury Tax?
Demand is
price-elastic.
The market for yachts
P
Buyers’ share
of tax burden
S
In the short run,
supply is inelastic.
PB
Tax
Sellers’ share
of tax burden
PS
D
Q
Hence,
companies
that build
yachts pay
most of
the tax.
So, what do we know so far?
• A tax is a wedge between the price
buyers pay and the price sellers
receive.
• A tax raises the price buyers pay and
lowers the price sellers receive.
• A tax reduces the quantity bought &
sold.
The Effects of a Tax
P
With no tax,
eq’m price is PE
and quantity is QE .
Govt imposes a
tax of $T per unit.
The price buyers
pay is PB ,
Size of tax = $T
S
PB
PE
PS
D
the price sellers
receive is PS ,
and quantity is QT .
QT
QE
Q
The Effects of a Tax
P
The tax generates
revenue equal to
$T x QT .
Size of tax = $T
S
PB
PE
PS
D
QT
QE
Q
The Effects of a Tax
• Next, we use the tools of welfare economics
to measure the gains and losses from a tax.
• We will determine consumer surplus (CS),
producer surplus (PS), tax revenue, and
total surplus with and without the tax.
• Tax revenue is included in total surplus,
because tax revenue can be used to
provide services such as roads, police,
public education, etc.
The Effects of a Tax
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
The Effects of a Tax
With the tax,
CS = A
PS = F
Tax revenue
=B+D
Total surplus
=A+B+D+F
P
A
PB
S
B
D
C
E
PS
D
F
The tax causes
total surplus to
fall by C + E
QT
QE
Q
The Effects of a Tax
P
C + E is called the
deadweight loss
(DWL) of the tax,
the 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
About the Deadweight Loss
Because of the tax,
the units between
QT and QE are not
sold.
So, the tax has
prevented some
mutually beneficial
trades.
P
PB
S
PS
D
QT
QE
Q
A C T I V E L E A R N I N G 2:
The market for
Analysis of tax
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.
400
airplane tickets
P
$
350
300
S
250
200
150
D
100
50
0
Q
0
25
50
75 100 125
A C T I V E L E A R N I N G 2:
Answers to A
The market for
P
CS
= ½ x $200 x 100
= $10,000
airplane tickets
$ 400
350
300
S
250
PS
= ½ 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
A C T I V E L E A R N I N G 2:
Answers to B
A $100 tax on
P
CS
= ½ 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
airplane tickets
S
D
100
0
Q
0
25
50
75 100 125
What Determines the Size of the
DWL?
• The govt needs tax revenue to finance roads, schools,
police, etc., so it must tax some goods and services.
• Which ones? One answer is that govt should tax the
goods or services with the smallest DWL.
• So when is the DWL small vs. large? Turns out it
depends on the elasticities of supply and demand.
• Recall: The price elasticity of demand (or supply)
measures how much quantity demanded
(or supplied) changes when the price changes.
DWL and the Elasticity of Supply
When supply
is inelastic,
the DWL of a
tax is small.
P
S
Size
of tax
D
Q
DWL and the Elasticity of Supply
P
The more
elastic supply,
the larger the
DWL.
S
Size
of tax
D
Q
DWL and the Elasticity of Supply
When demand
is inelastic,
the DWL of a
tax is small.
P
S
Size
of tax
D
Q
DWL and the Elasticity of Supply
P
S
The more elastic
the demand,
the larger the
DWL.
Size
of tax
D
Q
Why Elasticity Affects the Size of
DWL
• A tax distorts the market outcome:
consumers buy less and producers sell
less, so eq’m Q is below the surplusmaximizing quantity.
• Elasticity measures how much buyers and
sellers respond to changes in price,
and therefore determines how much the
tax distorts the market outcome.
A C T I V E L E A R N I N G 3:
Elasticity and DWL of a tax
Would the DWL of a tax be larger if the
tax were on
A. Rice Krispies or sunscreen?
B. Gasoline in the Short Run vs. Gasoline in the
Long Run
C. Insulin vs. Caribbean Cruises
A C T I V E L E A R N I N G 3:
Answers
A. Rice Krispies or sunscreen
From Chapter 6:
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.
A C T I V E L E A R N I N G 3:
Answers
B. Gasoline in the short run or long run
From Chapter 6:
The price elasticities of demand and supply
for gasolline are larger in the long run than
in the short run.
So, a tax on gasoline would cause a larger
DWL in the long run than in the short run.
A C T I V E L E A R N I N G 3:
Answers
C. Insulin vs. Caribbean Cruises
From Chapter 6:
Insulin is a necessity and therefore less
price-elastic than a Caribbean Cruise
So, a tax on a Caribbean Cruise would
cause a larger DWL than a tax on insulin.
A C T I V E L E A R N I N G 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?
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? We explore this
next….
DWL and the Size of the Tax
Initially, the tax is
T per unit.
Doubling the tax
causes the DWL
to more than
double.
P
new
DWL
S
2T
T
D
initial
DWL
Q2
Q1
Q
DWL and the Size of the Tax
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
DWL and the Size of the Tax
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
When the
tax is small,
increasing it
causes tax
revenue to rise.
P
PB
S
PB
2T
PS
T
D
PS
Q2
Q1
Q
Revenue and the Size of the Tax
P
PB
PB
When the
tax is larger,
increasing it
causes tax
revenue to fall.
S
3T
2T
D
PS
PS
Q3
Q2
Q
Revenue and the Size of the Tax
The Laffer curve
Tax
shows the
revenue
relationship
between
the size of the tax
and tax revenue.
The Laffer curve
Tax size
Taxes and Efficiency
• One tax system is more efficient than
another if it raises the same amount of
revenue at a smaller cost to taxpayers.
• The costs to taxpayers include:
– the tax payment itself
– deadweight losses
– administrative burden
Administrative Burden
• includes the time and money people
spend to comply with tax laws
• encourages the expenditure of resources
on legal tax avoidance
– e.g., hiring accountants to exploit “loopholes”
to reduce one’s tax burden
• is a type of deadweight loss
• could be reduced if the tax code were
simplified but would require removing
loopholes, politically difficult
Marginal vs. Average Tax Rates
• average tax rate
– total taxes paid divided by total income
– measures the sacrifice a taxpayer makes
• marginal tax rate
– the extra taxes paid on an additional dollar of
income
– measures the incentive effects of taxes
on work effort, saving, etc.
Lump-Sum Taxes
• A lump-sum tax is the same for every person
• Example: lump-sum tax = $4000/person
income
average tax rate
marginal tax
rate
$20,000
20%
0%
$40,000
10%
0%
Taxes and Equity
• Another goal of tax policy: equity –
distributing the burden of taxes “fairly.”
• Agreeing on what is “fair” is much
harder than agreeing on what is
“efficient.”
• Yet, there are several principles people
apply to evaluate the equity of a tax
system.
The Benefits Principle
• Benefits principle: the idea that people
should pay taxes based on the benefits they
receive from govt services
• Tries to make public goods similar to private
goods – the more you use, the more you pay.
• Example: Gasoline taxes
– the more you drive on public roads,
the more gas you buy,
so the more gas tax you pay
The Ability-To-Pay Principle
• Ability-to-pay principle: the idea that taxes
should be levied on a person according to
how well that person can shoulder the burden
• suggests that all taxpayers should make an
“equal sacrifice” to support govt
• recognizes that the magnitude of the sacrifice
depends not just on the tax payment, but on
the person’s income and other circumstances
– a $10,000 tax bill is a bigger sacrifice for a
poor person than a rich person
Three Tax Systems
• Proportional tax: taxpayers pay the same
fraction of income, regardless of income
• Regressive tax: high-income taxpayers
pay a smaller fraction of their income than
low-income taxpayers
• Progressive tax: high-income taxpayers
pay a larger fraction of their income than
low-income taxpayers
Examples of the Three Tax Systems
regressive
% of
income
proportional
tax
% of
income
progressive
tax
% of
income
income
tax
$50,000
$15,000
30%
$12,500
25%
$10,000
20%
$100,000
$25,000
25%
$25,000
25%
$25,000
25%
$200,000
$40,000
20%
$50,000
25%
$60,000
30%
U.S. Federal Income Tax Rates:
2010 (Married Filing Jointly)
The U.S. has a
progressive
income tax.
On taxable
income…
the tax rate
is…
0 – $16,750
10%
$16,750 - $68,000
15%
$68,000 - $137,300
25%
$137,300 - $209,250
28%
$209,250 - $373,650
33%
Over $373,650
35%
CHAPTER SUMMARY
 A tax on a good places a wedge between the price
buyers pay and the price sellers receive, and causes the
eq’m quantity to fall, whether the tax is imposed on
buyers or sellers.
 The incidence of a tax is the division of the burden of the
tax between buyers and sellers, and does not depend on
whether the tax is imposed on buyers or sellers.
 The incidence of the tax depends on the price elasticities
of supply and demand.
 Policymakers often face a tradeoff between the goals of
efficiency and equity in the tax system. Much of the
debate over tax policy arises because people give
different weights to these two goals.
CHAPTER SUMMARY
 The efficiency of a tax system refers to the costs it
imposes on taxpayers beyond their tax payments. One
cost is the deadweight loss caused by the distortion of
incentives from taxes. Another is the administrative
burden of complying with tax laws.
 The equity of a tax system refers to its fairness. The
benefits principle suggests that it is fair for people to be
taxed based on the amount of government benefits they
receive. The ability-to-pay principle suggests that it is
fair for people to pay taxes based on their ability to
handle the burden.
 The U.S. has a progressive tax system, in which high
income taxpayers face a higher average tax rate than
low income taxpayers.