Application: The Costs of Taxation
Chapter 8
1
IN THIS CHAPTER
• A tax affect
− Consumer surplus, producer surplus, and total surplus
− Total surplus = economic well-being
• Maximized at equilibrium
• Deadweight loss(DWL) of a tax
• Factors determine the size of the deadweight loss
− Elastic vs inelastic
• Tax revenue depends on the size of the tax
2
A tax?
(an amount of) money paid to the government that
is based on your income or
the cost of goods or services you have bought.
3
The effects of a tax
• Total surplus = Consumer surplus + Producer surplus
− Maximized at equilibrium
• With taxes:
− CS decreases (higher PB, lower QT)
− PS decreases (lower PS, lower QT)
− Government gains tax revenue (per unit tax * QT)
• What happens to total surplus?
4
How a Tax Affects Market Participants
P
A. Equilibrium with no tax:
• Price = PE
• Quantity = QE
B. Equilibrium with tax = $T per unit:
• Buyers pay PB
• Sellers receive PS
• Quantity = QT
Revenue from tax: $T x QT
Size of tax = $T
S
PB
PE
PS
D
QT
QE
Q
5
How a Tax Affects Market Participants: without a tax
P
Without a tax,
CS = A + B + C
PS = D + E + F
Tax revenue = 0
A
S
B
C
E
PE
Total surplus
= CS + PS
=A+B+C
+D+E+F
D
D
F
QT
QE
Q
6
How a Tax Affects Market Participants: with a tax
With the tax,
• CS = A
• PS = F
• Tax revenue = B + D
• Total surplus
= CS + PS + tax revenue
=A+B+D+F
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.
P
A
PB
S
B
D
The tax reduces total surplus by
C+E
• QE – QT = units not sold
because of the tax
C
E
PS
D
F
QT
QE
Q
7
Deadweight loss(DWL)?
A loss occurs when a government raises taxes to get
more money, but then loses money as a result.
8
Deadweight Loss of Taxation
• Tax on a good levied on buyers
− Demand curve shifts to the left(=downward)
• By the size of tax
• Tax on a good levied on sellers
− Supply curve shifts to the left(=upward)
• By the size of tax
• Lower quantity sold
9
Deadweight Loss of Taxation
• A tax on sellers (Chapter 6)
10
Deadweight Loss of Taxation
• A tax on buyers (Chapter 6)
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Example 1: Analysis of a tax
A. Compute CS, PS, and
total surplus without a
tax.
P
$ 400
350
300
B. If a $200 tax per unit is
imposed, compute CS,
PS, tax revenue, total
surplus, and DWL.
S
250
200
150
D
100
50
0
0
25
50
Q
75 100 125
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Example 1: A. Without a tax
P
A. Without tax:
• CS = ½ x $200 x 100
= $10,000
$ 400
350
300
CS
250
• PS = ½ x $200 x 100
= $10,000
• TS = $20,000
S
P = 200
PS
150
D
100
50
0
0
25
50
Q
75 100 125
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Example 1: B. With $200 tax
B. With $200 tax:
• CS = ½ x $100 x 50
= $2,500
• PS = $2,500
• Tax revenue
= $200 x 50
= $10,000
• TS = $15,000
• DWL = $5,000
P
$ 400
350
CS
PB = 300
S
250
Tax
200
DWL
revenue
150
D
PS = 100
PS
50
0
0
25
50
Q
75 100 125
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EXAMPLE 2: DWL and the gains from trade
Tom is taking his laundry to Jerry’s dry cleaning and laundry services
business. For this arrangement, each month, Tom is willing to pay
$165, and Jerry’s cost is $140. They agree on a price of $150 per
month.
A. Calculate CS, PS, and TS.
B. The government imposes a $35 tax on all laundry service providers.
What happens to CS, PS, and TS?
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EXAMPLE 2: Solutions
Tom’s WTP = $165; Jerry’s cost = $140 P = $150 per month.
A. Calculate CS, PS, and TS.
• Tom’s CS = WTP – P = 165 – 150 = $15
• Jerry’s PS = P – cost = 150 – 140 = $10
• TS = CS + PS = $25
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EXAMPLE 2: Solutions
Tom’s WTP = $165;Jerry’s cost = $140 P = $150 per month.
B. $35 tax
• Jerry needs 140 + 35 = $175 to provide laundry services to Tom,
but Tom’s WTP = $165
• Trade doesn’t happen!
• The tax has made both worse off: DWL = $25
• How about the government? The government gets $0 in tax
revenue because Jerry and Tom are not trading.
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The Determinants of the Deadweight Loss
• Price elasticities of supply and demand
− More elastic supply curve
• Larger deadweight loss
− More elastic demand curve
• Larger deadweight loss
• The greater the elasticities of supply and demand
− The greater the deadweight loss of a tax
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DWL and elasticity of supply
P
S
When supply is inelastic,
A change in price leads to a
small change in quantity supplied.
DWL is small.
Size
of tax
D
Q
19
DWL and elasticity of supply
P
The more elastic is the supply,
The greater the change in
quantity supplied due to a
change in price...
The greater the DWL.
S
Size
of tax
D
Q
20
Tax Distortions and Elasticities (a, b)
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DWL and elasticity of demand
P
When demand is inelastic,
A change in price leads to a
small change in quantity
demanded.
DWL is small.
S
Size
of tax
D
Q
22
DWL and elasticity of demand
The more elastic is demand,
The greater the change in
quantity demanded due to a
change in price…
and the greater the DWL.
P
S
Size
of tax
D
Q
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Tax Distortions and Elasticities (c, d)
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DWL and Tax Revenue as Taxes Vary
• As the tax increases
− Deadweight loss increases
• Even more rapidly than the size of the tax
− Tax revenue
• Increases initially
• Then decreases
• The higher tax: drastically reduces the size of the
market
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DWL and the size of the tax
P
new
DWL
Initially, the tax is T per unit.
S
Increasing the tax to 2T per unit…
causes the DWL to more than double.
2T
T
D
initial
DWL
Q2
Q1
Q
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DWL and the size of the tax
P
new
DWL
Initially, the tax is T per unit.
Increasing the tax even more, to 3T
per unit…
S
T
3T
causes the DWL to more than triple.
D
initial
DWL
Q3
Q1
Q
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Revenue and the size of the tax
P
When the tax is small, increasing it
causes tax revenue to rise.
When the tax is larger, increasing it
causes tax revenue to fall.
PB3
PB2
S
PB1
3T
2T
PS1
T
D
PS2
PS3
Q3
Q2
Q1
Q
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How Deadweight Loss and Tax Revenue Vary with the
Size of a Tax (a, b, c)
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Deadweight Loss and tax revenue as taxes vary
Tax revenue
DWL
The Laffer curve
Tax size
When a tax increases,
DWL rises even more.
Tax size
When a tax increases, tax
revenue initially increases,
then decreases.
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CHAPTER IN A NUTSHELL
• A tax on a good reduces the welfare of buyers and sellers,
and the reduction in CS and PS usually exceeds the revenue
raised by the government.
− The fall in total surplus is DWL of a tax.
• Taxes have deadweight losses.
− Buyers consume less and pay a higher P.
− Sellers produce less and receive a lower P.
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CHAPTER IN A NUTSHELL
• Large S and D elasticities: larger DWL
• As a tax grows larger
− Distorts incentives more
− Its DWL grows larger
− Tax revenue first rises with the size of a tax, but if the tax
gets large enough, tax revenue starts to fall.
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