Application: The Costs
of Taxation
Deadweight Loss of Taxation
Tax on a good
– Levied on buyers
• Demand curve shifts downward by the size of tax
– Levied on sellers
• Supply curve shifts upward by the size of tax
– Same outcome: price wedge
• Price paid by buyers rises
• Price received by sellers falls
• Lower quantity sold
Deadweight Loss of Taxation
• Tax burden
– Distributed between producers and
consumers
– Determined by elasticities of supply and
demand
• Market for the good becomes smaller
The effects of a tax
Price
Supply
Price buyers pay
Size
of tax
Price without tax
Price sellers receive
Demand
0
Quantity
with tax
Quantity
without tax
Quantity
A tax on a good places a wedge between the price that buyers pay
and the price that sellers receive. The quantity of the good sold falls.
The Deadweight Loss of Taxation
• How a tax affects market participants
• Gains and losses from a tax on a good
– Buyers: consumer surplus
– Sellers: producer surplus
– Government: total tax revenue
• Tax times quantity sold
• Public benefit from the tax
Tax revenue
Price
Size of tax (T)
Supply
Price buyers pay
Tax
revenue
TˣQ
Price sellers receive
Demand
Quantity
sold (Q)
0
Quantity
with tax
Quantity
without tax
Quantity
The tax revenue that the government collects equals T × Q, the size of the tax T times
the quantity sold Q. Thus, tax revenue equals the area of the rectangle between the
supply and demand curves
The Deadweight Loss of Taxation
• Welfare without a tax
– Maximum Consumer Surplus
– Maximum Producer Surplus
– Total tax revenue = zero
• Welfare with tax
– Smaller Consumer Surplus
– Smaller Producer Surplus
– Total tax revenue > zero
– Smaller overall welfare
How a tax affects welfare
Price
Price
buyers
pay =PB
Supply
A
B
Price
without =P1
tax
D
Price =PS
sellers
receive
C
•
E
•
F
Demand
0
Consumer Surplus
Producer Surplus
Tax Revenue
Total Surplus
•
Q2
Q1
A tax on a good reduces
consumer surplus (by the
area B + C)
The tax reduces producer
surplus (by the area D + E).
Because the fall in producer
and consumer surplus
exceeds tax revenue (area B
+ D), the tax is said to
impose a deadweight loss
(area C + E).
Quantity
Without Tax
With Tax
Change
A+B+C
D+E+F
None
A+B+C+D+E+F
A
F
B+D
A+B+D+F
-(B+C)
-(D+E)
+(B+D)
-(C+E)
The area C + E shows
the fall in total surplus
and is the deadweight
loss of the tax
The Deadweight Loss of Taxation
• Losses of surplus to buyers and sellers from a
tax exceeds the revenue raised by the
government
• Deadweight loss: The fall in total surplus that
results from a market distortion, such as a tax
• Taxes distort incentives
– Markets now allocate resources inefficiently
How a tax affects welfare
Hamburger Market
Price
Price
buyers
pay =$11
Price
without =$10
tax
Supply
$180
$20
•
Price =$9
sellers
receive
Demand
0
•
•
•
•
•
•
•
90
100
Tax ($2 times 90) = $180
C+E = $20
Government revenue
increased by $180 but the
tax damaged the market by
$200
If the government fails to
take $180 and create $200
or more in value, then policy
lowered overall economic
value
Quantity
Hamburger sellers create a lower price
Hamburger consumers pay a higher price
The hamburger market is now smaller
Even if the government manages to create economic value buyers and sellers in the
hamburger market are unlikely to be better off (redistribution of income)
Determinants of the Deadweight Loss
• Price elasticities of supply and demand
– When the supply curve is more elastic
• Deadweight loss is larger
– When the demand curve is more elastic
• Deadweight loss is larger
• The greater the elasticities of supply and
demand
– The greater the deadweight loss of a tax
Tax distortions and elasticities
Inelastic Supply
When supply is
relatively inelastic,
the deadweight loss
of a tax is small
Price
Elastic Supply
Price
When supply is
relatively elastic, the
deadweight loss of
a tax is large
Supply
Supply
Size
of tax
Size
of tax
Demand
0
Quantity
Demand
0
Quantity
In the above illustrations the demand curve and the size of the tax are the same,
but the price elasticity of supply is different. Notice that the more elastic the
supply curve, the larger the deadweight loss of the tax.
Tax distortions and elasticities
Inelastic Demand
When demand is relatively
inelastic, the deadweight
loss of a tax is small
Price
Elastic Demand
When demand is relatively
elastic, the deadweight
loss of a tax is large
Price
Supply
Size
of tax
Supply
Size
of tax
Demand
Demand
0
Quantity
0
Quantity
In the above illustrations, the supply curve and the size of the tax are the same,
but the price elasticity of demand is different. Notice that the more elastic the
demand curve, the larger the deadweight loss of the tax.
The deadweight loss debate
• Size of Government
– The larger the deadweight loss of taxation
• The larger the cost of any government program
– If taxes cause a large deadweight losses
• Strong argument for a leaner government
– Do less and taxes less
– If taxes cause a small deadweight losses
• Government programs are less costly
Deadweight Loss & Tax Revenue
As the tax increases
– Deadweight loss increases
• Even more rapidly than the size of the tax
– Tax revenue
• Increases initially
• Then decreases
– Higher tax – drastically reduces the size of the market
Deadweight Loss & Tax Revenue
Medium tax
Small tax
Price
Price
Deadweight
loss
Deadweight
loss
Supply
Supply
PB
PB
Tax
revenue
Tax
revenue
PS
Deadweight
loss
Demand
Demand P
S
Supply
Tax revenue
Price
PB
Large tax
Demand
PS
0
Q2 Q1
Quantity
0
Q2
Quantity
Q1
0 Q2
Q1
Quantity
The deadweight loss is the reduction in total surplus due to the tax. Tax revenue is the
amount of the tax times the amount of the good sold. A small tax has a small deadweight
loss and raises a small amount of revenue. A somewhat larger tax has a larger deadweight
loss and raises a larger amount of revenue. A very large tax has a very large deadweight
loss, but because it has reduced the size of the market so much, the tax raises only a small
amount of revenue.
Deadweight Loss & Tax Revenue
• 1974, economist Arthur Laffer
– Tax rates were so high
• Reducing them would actually raise tax revenue
• Ronald Reagan ran for president in 1980
• Taxes were so high that they were discouraging hard work
• Lower taxes would give people the proper incentive to work
• Raise economic well-being
• Perhaps increase tax revenue
Deadweight Loss & Tax Revenue
Tax
Revenue
Laffer curve
Tax revenue
first
increases
0
then
decreases
Tax size