Look for the Answers

to These Questions:
• How does a tax affect consumer surplus, producer
surplus, and total surplus?
• What is the deadweight loss of a tax?
• What factors determine the size of this
deadweight loss?
• How does tax revenue depend on the size of the
tax?

2
 I. Review from Chapter 6
• A tax
– drives a wedge between the price buyers pay and the
price sellers receive.
– raises the price buyers pay and lowers the price sellers
receive.
– reduces the quantity bought & 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.
3
 II. The Effects of a Tax 1 of 6

P
Equilibrium with
no tax:
Price = PE Size of tax = $T
Quantity = QE S
PB
Equilibrium with
tax = $T per unit: PE
Buyers pay PB PS D
Sellers receive PS
Quantity = QT
Q
QT QE
 II. The Effects of a Tax 2 of 6

Revenue from tax:

$T x QT Size of tax = $T
PB S

PE

PS D

Q
QT QE
 II. The Effects of a Tax 3 of 6

• 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
(e.g., education, roads, police), so we include
it in total surplus.
 II. The Effects of a Tax 4 of 6

Without a tax, P

CS = A + B + C
PS = D + E + F A
Tax revenue = 0 S
B C
Total surplus PE
= CS + PS D E
=A+B+C D
F
+D+E+F

Q
QT QE
 II. The Effects of a Tax 5 of 6

With the tax, P

CS = A
PS = F
A
Tax revenue PB S
=B+D B C
Total surplus D E
=A+B PS D
+D+F F
The tax reduces
total surplus by Q
C+E QT QE
 III. The Effects of a Tax 6 of 6

P
C + E is called the
deadweight loss
(DWL) of the tax, A
PB S
the fall in total
B C
surplus that
results from a D E
market distortion, PS D
such as a tax. F

Q
QT QE
 IV. About the Deadweight Loss
P
Because of the tax,
the units between
QT and QE are not
sold. S
PB
The value of these
units to buyers is
greater than the cost PS D
of producing them,
so the tax prevents
some mutually
Q
beneficial trades. QT QE
Example: Analysis of a Tax The Market for
P Airplane Tickets
A. Compute $ 400
CS, PS, and
350
total surplus
without a tax. 300
S
250
B. If $100 tax
per ticket, 200
compute the 150
D
CS, PS, 100
tax revenue,
50
total surplus,
and DWL. 0 Q
0 25 50 75 100 125
Answers to A The Market for
P Airplane Tickets
CS $ 400
= ½ x $200 x 100 350
= $10,000 300
S
PS 250
= ½ x $200 x 100 P = 200
= $10,000 150
D
Total surplus 100
= $10,000 + $10,000 50
= $20,000 0 Q
0 25 50 75 100 125
Answers to B A $100 tax on
P Airplane Tickets
CS $ 400
= ½ x $150 x 75 350
= $5,625 300
PS = $5,625 S
PB = 250
Tax revenue 200
= $100 x 75 PS = 150
= $7,500 D
100
Total surplus 50
= $18,750
0 Q
DWL = $1,250
0 25 50 75 100 125
 V. What Determines the Size of the DWL?

• Which goods or services should the government tax

to raise the revenue it needs?
• One answer: those with the smallest DWL.
• When is the DWL small vs. large?
Turns out 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.
VI. DWL and the Elasticity of Supply
1 of 2

When supply is P
inelastic, it’s harder
S
for firms to leave the
market when the tax
reduces PS.
So, the tax only
reduces Q a little, Size
and DWL is small. of tax

D
Q
VI. DWL and the Elasticity of Supply
2 of 2

The more elastic is

P
supply, the easier for
firms to leave the
market when the tax
reduces PS, S

the greater Q falls Size

below the surplus- of tax
maximizing quantity,
the greater the DWL. D
Q
VII. DWL and the Elasticity of Demand
1 of 2

P When demand
is inelastic,
S
it’s harder for
Size consumers to
of tax leave the market
when the tax
raises PB.
So, the tax only
D reduces Q a little,
Q and DWL is small.
VII. DWL and the Elasticity of Demand
2 of 2

P The more elastic is

demand, the easier
S for buyers to leave
the market when the
tax increases PB,
Size
the more Q falls
of tax
D
below the surplus-
maximizing quantity,
and the greater the
DWL.
Q
 Example: Elasticity and the DWL of a Tax

Would the DWL of a tax be larger if the

tax were on:
A. Breakfast cereal or sunscreen?
B. Hotel rooms in the short run or
hotel rooms in the long run?
C. Groceries or meals at fancy restaurants?
 Example: Elasticity and the DWL of a tax

A. Breakfast cereal or sunscreen

From Chapter 5:
Breakfast cereal has more close substitutes
than sunscreen, so demand for breakfast
cereal is more price-elastic than demand for
sunscreen.
So, a tax on breakfast cereal would cause a
larger DWL than a tax on sunscreen.
 Example: Elasticity and the DWL of a Tax

B. Hotel rooms in the short run or long run

From Chapter 5:
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.
 Example: Elasticity and the DWL of a Tax

C. Groceries or meals at fancy restaurants

From Chapter 5:
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.
 VIII. How Big Should the Government Be?
1 of 3

• 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 the typical worker, the marginal tax rate
(the tax on the last dollar of earnings) is about 40%.
• How big is the DWL from this tax?
It depends on elasticity….
 VIII. How Big Should the Government Be?
2 of 3

• 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.
 VIII. How Big Should the Government Be?
3 of 3

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
wages they earn.
– Some people work in the “underground economy”
to evade high taxes.
IX. 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….
 X. DWL and the Size of the Tax 1 of 3
P
Initially, the tax is new
T per unit. DWL
Doubling the tax S
causes the DWL
to more than 2T T
double. D
initial
DWL

Q
Q2 Q1
 X. DWL and the Size of the Tax 2 of 3
P
Initially, the tax is new
T per unit. DWL

Tripling the tax S

causes the DWL
to more than 3T T
triple. D
initial
DWL

Q
Q3 Q1
 X. DWL and the Size of the Tax 3 of 3

Implication
Summary
When tax rates are
When a tax increases,
low, raising them DWL DWL rises even more.
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 Tax size
beneficial.
XI. Revenue and the Size of the Tax
1 of 3
P

PB
S
When the tax is PB
small, increasing it 2T T
causes the tax PS
revenue to rise. D
PS

Q
Q2 Q1
XI. Revenue and the Size of the Tax
2 of 3
P

PB
PB
When the S
tax is larger,
increasing it 3T 2T
causes tax D
revenue to fall. PS
PS
Q
Q3 Q2
 XI. Revenue and the Size of the Tax
3 of 3

Tax
The Laffer Curve
The Laffer curve
revenue
shows the
relationship
between
the size of the tax
and tax revenue.

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
govt.
• 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. 33
 Summary
• 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.
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