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Application: The
Costs of Taxation
Copyright©2004 South-Western
8
Application: The Costs of Taxation
• Welfare economics is the study of how the
allocation of resources affects economic wellbeing.
• Buyers and sellers receive benefits from taking part
in the market.
• The equilibrium in a market maximizes the total
welfare of buyers and sellers.
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THE DEADWEIGHT LOSS OF
TAXATION
• How do taxes affect the economic well-being of
market participants?
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THE DEADWEIGHT LOSS OF
TAXATION
• It does not matter whether a tax on a good is
levied on buyers or sellers
of the good . . . the price
paid by buyers rises, and
the price received by
sellers falls.
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Figure 1 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
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How a Tax Affects Market Participants
• A tax places a wedge between the price buyers
pay and the price sellers receive.
• Because of this tax wedge, the quantity sold
falls below the level that would be sold without
a tax.
• The size of the market for that good shrinks.
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How a Tax Affects Market Participants
• Tax Revenue
• T = the size of the tax
• Q = the quantity of the good sold
T  Q = the government’s tax revenue
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Figure 2 Tax Revenue
Price
Supply
Price buyers
pay
Size of tax (T)
Tax
revenue
(T × Q)
Price sellers
receive
Demand
Quantity
sold (Q)
0
Quantity
with tax
Quantity
without tax
Quantity
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Figure 3 How a Tax Effects Welfare
Price
Price
buyers = PB
pay
Supply
A
B
C
Price
without tax = P1
Price
sellers = PS
receive
E
D
F
Demand
0
Q2
Q1
Quantity
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How a Tax Affects Market Participants
• Changes in Welfare
• A deadweight loss is the fall in total surplus that
results from a market distortion, such as a tax.
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How a Tax Affects Welfare
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How a Tax Affects Market Participants
• The change in total welfare includes:
•
•
•
•
The change in consumer surplus,
The change in producer surplus, and
The change in tax revenue.
The losses to buyers and sellers exceed the revenue
raised by the government.
• This fall in total surplus is called the deadweight
loss.
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Deadweight Losses and the Gains from
Trade
• Taxes cause deadweight losses because they
prevent buyers and sellers from realizing some
of the gains from trade.
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Figure 4 The Deadweight Loss
Price
Lost gains
from trade
PB
Supply
Size of tax
Price
without tax
PS
Cost to
sellers
Value to
buyers
0
Q2
Demand
Quantity
Q1
Reduction in quantity due to the tax
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DETERMINANTS OF THE
DEADWEIGHT LOSS
• What determines whether the deadweight loss
from a tax is large or small?
• The magnitude of the deadweight loss depends on
how much the quantity supplied and quantity
demanded respond to changes in the price.
• That, in turn, depends on the price elasticities of
supply and demand.
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Figure 5 Tax Distortions and Elasticities
(a) Inelastic Supply
Price
Supply
When supply is
relatively inelastic,
the deadweight loss
of a tax is small.
Size of tax
Demand
0
Quantity
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Figure 5 Tax Distortions and Elasticities
(b) Elastic Supply
Price
When supply is relatively
elastic, the deadweight
loss of a tax is large.
Size
of
tax
Supply
Demand
0
Quantity
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Figure 5 Tax Distortions and Elasticities
(c) Inelastic Demand
Price
Supply
Size of tax
When demand is
relatively inelastic,
the deadweight loss
of a tax is small.
Demand
0
Quantity
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Figure 5 Tax Distortions and Elasticities
(d) Elastic Demand
Price
Supply
Size
of
tax
Demand
When demand is relatively
elastic, the deadweight
loss of a tax is large.
0
Quantity
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DETERMINANTS OF THE
DEADWEIGHT LOSS
• The greater the elasticities of demand and
supply:
• the larger will be the decline in equilibrium
quantity and,
• the greater the deadweight loss of a tax.
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DEADWEIGHT LOSS AND TAX
REVENUE AS TAXES VARY
• The Deadweight Loss Debate
• Some economists argue that labor taxes are highly
distorting and believe that labor supply is more
elastic.
• Some examples of workers who may respond more
to incentives:
•
•
•
•
Workers who can adjust the number of hours they work
Families with second earners
Elderly who can choose when to retire
Workers in the underground economy (i.e., those
engaging in illegal activity)
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DEADWEIGHT LOSS AND TAX
REVENUE AS TAXES VARY
• With each increase in the tax rate, the
deadweight loss of the tax rises even more
rapidly than the size of the tax.
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Figure 6 Deadweight Loss and Tax Revenue from Three
Taxes of Different Sizes
(a) Small Tax
Price
Deadweight
loss Supply
PB
Tax revenue
PS
Demand
0
Q2
Q1 Quantity
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Figure 6 Deadweight Loss and Tax Revenue from Three
Taxes of Different Sizes
(b) Medium Tax
Price
Deadweight
loss
PB
Supply
Tax revenue
PS
0
Demand
Q2
Q1 Quantity
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Figure 6 Deadweight Loss and Tax Revenue from Three
Taxes of Different Sizes
(c) Large Tax
Price
PB
Tax revenue
Deadweight
loss
Supply
Demand
PS
0
Q2
Q1 Quantity
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DEADWEIGHT LOSS AND TAX
REVENUE AS TAXES VARY
• For the small tax, tax revenue is small.
• As the size of the tax rises, tax revenue grows.
• But as the size of the tax continues to rise, tax
revenue falls because the higher tax reduces the
size of the market.
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Figure 7 How Deadweight Loss and Tax Revenue Vary with
the Size of a Tax
(a) Deadweight Loss
Deadweight
Loss
0
Tax Size
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Figure 7 How Deadweight Loss and Tax Revenue Vary with
the Size of a Tax
(b) Revenue (the Laffer curve)
Tax
Revenue
0
Tax Size
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DEADWEIGHT LOSS AND TAX
REVENUE AS TAXES VARY
• As the size of a tax increases, its deadweight
loss quickly gets larger.
• By contrast, tax revenue first rises with the size
of a tax, but then, as the tax gets larger, the
market shrinks so much that tax revenue starts
to fall.
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CASE STUDY: The Laffer Curve and Supplyside Economics
• The Laffer curve depicts the relationship
between tax rates and tax revenue.
• Supply-side economics refers to the views of
Reagan and Laffer who proposed that a tax cut
would induce more people to work and thereby
have the potential to increase tax revenues.
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A Policy Choice
• Suppose you are a legislator in the Maryland State
Assembly. To fund your large salary increase,
additional tax revenues must be assessed.
• The following alternatives are being considered:
•
•
•
•
A sales tax on food
A tax on families with school-age children
A property tax on vacation homes
A sales tax on jewelery.
• Rank these taxes in order of how you prefer them.
• Now rank these taxes in order of deadweight loss from
least to most.
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Summary
• A tax on a good reduces the welfare of buyers
and sellers of the good, and the reduction in
consumer and producer surplus usually exceeds
the revenues raised by the government.
• The fall in total surplus—the sum of consumer
surplus, producer surplus, and tax revenue — is
called the deadweight loss of the tax.
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Summary
• Taxes have a deadweight loss because they
cause buyers to consume less and sellers to
produce less.
• This change in behavior shrinks the size of the
market below the level that maximizes total
surplus.
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Summary
• As a tax grows larger, it distorts incentives
more, and its deadweight loss grows larger.
• Tax revenue first rises with the size of a tax.
• Eventually, however, a larger tax reduces tax
revenue because it reduces the size of the
market.
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Midterm 1, 2003Problem 1
• Suppose Country A has 40 workers and each can produce either
3 units of food or 1 unit of clothing. Country B has 100 workers
and each can produce either 6 units of food or 6 units of
clothing.
• a) Draw in separate diagrams the production possibilities
frontier for each country. Place clothing on the horizontal axis.
Be sure to label the intercepts and the slope on your diagrams.
• b) Which country has an absolute advantage in the production
of clothing? Defend your answer carefully.
• c) Which country has an comparative advantage in the
production of clothing? Defend your answer carefully.
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Midterm 1, 2003Problem 1
• d) In the absence of trade, Country A produces and consumers
60 units of food and 20 units of clothing, while B produces and
consumers 300 units of food and 300 units of clothing.
Someone proposes the following agreement:
• County A will produce only food and no clothing. A will give 60 units of
food to B in exchange for 30 units of cothing.
•
Suppose that B would like to continue to consumer 300 units of
food. How many units of clothing would B consume if it
accepts this agreement? Defend your answer carefully.
• e) Will both countries accept the agreement? Defend your
answer carefully.
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A) Production Possibility Frontiers
A
Food
Food
600
B
Slope=-1
120
Slope=-3
600
40
Clothing
Clothing
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Which country has an absolute advantage in
the production of clothing? Defend your
answer carefully.
• In Country B each worker can produce 6 units
of each good. This is more in each good than a
worker can produce in A.
• Therefore B has an ABSOLUTE advantage in
BOTH goods and thus in clothing.
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Which country has an Comparative
advantage in the production of clothing?
Defend your answer carefully.
• In Country A the opportunity cost of 1 unit of
clothing is 3 units of food.
• In Country B the opportunity cost of 1 unit of
clothing is 1 units of food. Since 1 < 3, B has
the comparative advantage in clothing.
• (Note we can also see this by noting the slopes
of the PPFs. Since A’s slope is steeper, more
units of food must be given up for a unit of
clothing.)
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d)
• If A only produces food, it can produce 120 units (see PPF in a)
above)
• It trades 60 units of food in return for 30 units of clothing. (Note
that it now has more clothing (30) than before trade was
allowed and the same amount of food (60)
• B would now have to produce 240 units of food to get to 300 in
total (240 + 60 =300).
• That takes 40 workers (40 times 6 =240). It now has 60 workers
to produce 6 times 60 =360 units of clothing.
• 30 units have to be given to A in trade but that leaves B with
330=360-30 > 300 units of clothing to consumer.
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e)
• Since A now has more clothing (30) than before trade was
allowed and the same amount of food (60)) it will also accept
the agreement.
• Since B has the same amount of food and more clothing, it will
accept.
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