The cost of taxes
Lecture 7 – academic year 2014/15
Introduction to Economics
Fabio Landini
The cost of taxes
• Past classes: a tax on a good affects its price
and quantity exchanged.
• Moreover: buyers and sellers share in the tax
burden in different ways.
• The objective of this lecture is to answer the
following question: what are the effects of a
tax on the welfare of market participants?
2
Market equilibrium and
allocative efficiency
• A free market produces the quantity of
goods that maximizes the total welfare(=
consumer surplus + producer surplus).
• When an allocation of resources maximizes
the total welfare, we say that such
allocation is economically efficient.
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The costs of imposing taxes
• When the government imposes a tax on a
particular good, the equilibrium quantity of
that good diminishes and its price increases.
• The size of the market for that particular
good decreases.
• Therefore: in a perfectly competitive market,
taxes have a cost in terms of diminished
welfare experienced by individuals.
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Market equilibrium in
presence of a tax
Price
Consumer Price
Tax levy
(T x Q)
Value of
the tax
(T)
Supply
Producer price
Quantity
sold (Q)
0
Q.ty with Q.ty without
the tax
the tax
Demand
Quantity
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The costs of imposing taxes
• The tax introduces a mark-up between
the price paid by the consumer and the
price earned by the producer.
• The cost of the tax for consumers and
producers exceeds the tax levy (earned
by the government), generating a net
loss.
• The net loss is the reduction in total
welfare caused by the introduction of a
tax.
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Consumer surplus:
from A+B+C to A
Price
Price paid by
consumer = PB
Tax levy: from
none to B+D
Supply
A
B
Total surplus (social
welfare): from
A+B+C+D+E+F to
A+B+D+F
C
Price without
tax = P1
E
D
Price earned by
producer = PS
Producer surplus:
from D+E+F to F
Net loss of social
welfare: C+E
F
Demand
0
Q2
Q1
Quantity
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Net loss: an example
• At the current price of 0.50 € per unit, the
quantity sold is 1.000 units.
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Net loss: an example
Price
Supply
0.50
demand
0
1000
Quantity
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Net loss: an example
• The government introduces a tax of 0.20 € on
the production of each unit of the good. The
producers “collect” the tax and then they pay
it back to the government.
• Let’s assume the tax burden is shared equally
– Consumers and producers pay 0.10 € each.
– Remember: taxes are not necessarily paid
only by those who are supposed to pay the
government (previous lessons).
• The higher price for consumers and the smaller
price for producers translates into a smaller
quantity that is exchanged in the market.
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Net loss: an example
Price
Supply
0.60
0.50
0.40
Demand
0
800
1000
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Quantity
Net loss: an example
• The tax impair both consumers and producers,
so that the quantity exchanged diminishes of
200 units(= 1.000 - 800).
• The area of the triangle included between the
demand curve and the supply curve and
delimited by the quantity exchanged is a
measure of the net loss.
• Example: = (0.10 x 200)/2 + (0.10 x 200)/2 = 20 €.
• Tax levy= (0.60 - 0.40) x 800 = 160
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Net loss: an example
Price
Tax levy = 160
Supply
0.60
Net loss of social
welfare = 20
0.50
0.40
Decrease in Demand
quantity = 200
0
800
1000
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Quantity
Effects of taxes
• Taxes -> loss of welfare
– They induce the market participants (producers and
consumers) to change their behaviour.
• Prices (PD, PS) change makes some some
exchanges not profitable any more.
– Higher price induces consumers to purchase less.
– Lower price induces producers to produce less.
• The size of the market reduces and
becomes smaller than the optimal level.
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Price
Loss of exchange
benefits
P
B
Price
without tax
Supply
Value of
the tax
P
S
Cost of
supplier
Value for
consumer
0
Q2
Q1
Decrease in quantity
due to the tax
Demand
Quantity
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Why the net loss?
• Even if the tax levy is redistributed
entirely to producers and consumers,
the fiscal revenue is not sufficient to
compensate for the reduction in the
volume of exchange due to the tax.
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How big is the net loss?
Theory
• The size of the net loss depends on Q*
caused by T.
• At the same time: Q* depends on the
price elasticity of demand and supply.
– If price elasticity, then net loss.
– If price elasticity, then net loss.
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Effects of taxes and
elasticity of supply
(a) Inelastic supply
Price
(b) Elastic supply
Price
If the supply is
elastic, the net
loss is large
Supply
Value of
the tax
If the supply is
inelastic, the net
loss is small
.
Value of
the tax
Demand
0
Quantity
Supply
Demand
0
Quantity
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Effects of taxes and
elasticity of supply
(c) Inelastic demand (d) Elastic demand
Price
Supply
Value of
the tax
Price
If the demand is
inelastic, the net Value of
the tax
loss is small
Demand
0
Quantity 0
Supply
Demand
If the demand is
elastic, the net
loss is large
Quantity
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How big is the net loss? Discussion
• While it is easy to compute the value of
taxes, it is not that easy to evaluate the net
loss caused by the taxes.
• Example: tax on labour:
• For some workers the supply of labour is
inelastic:
– 40 years-old head of household wants to
work full time, independently of the wage.
– In this case, a tax on labour causes a
relatively small net loss
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How big is the net loss? Discussion
• For other types of workers the supply is
elastic.
– Women, elderly people, students: react
positively to monetary incentives.
– In these cases, a tax on labour causes a
relatively large net loss (smaller
productivity, illegal work, early retirement).
• In general: there are different opinions
on the elasticity of labour supply.
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State and the economy
The debate on the net loss is not (only) an academic
discussion.
Different opinions on the elasticity and its effects often
derive from different visions concerning the role of the
State in the economy
The tax on labour represent a large part of the tax levy
in advanced countries. When people talk bout
reducing such taxes, the question is:
– Do we want to reduce taxes and public services?
– Or do we want higher taxes and more public
services?
The answer depend on how we think the role of the
State in the allocation of resources.
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Net loss and fiscal revenue
Following an increase in taxes, the fiscal
revenue rapidly increases up to a
maximum and, then, it diminishes.
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Net loss and fiscal revenue
Small tax
Price
Supply
Net loss
PB
Fiscal revenue
PS
Demand
0
Q2Q1
Quantity
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Net loss and fiscal revenue
Medium tax
Price
Supply
Net loss
PB
Fiscal
revenue
PS
Demand
0
Q2
Q1
Quantity
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Net loss and fiscal revenue
Large tax
Price
Supply
PB
Net loss
Demand
PS
0
Q2
Q1
Quantity
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Net loss
(a) Net loss
0
Value of
the tax
Fiscal revenue
(b) Revenue
(Laffer’s curve)
0
Value of
the tax
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The theory of Laffer’s curve …
Main idea: when taxes are too high they
discourage production.
• In the case of labour: if the tax on income is
too high, it discourage the supply of work.
• Smaller taxes create incentives to work
more, increasing social welfare and fiscal
revenue.
Hence: it is better to reduce taxes!
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…and the empirical evidence
In the 1980 , Reagan (USA president)
implemented a policy aimed at reducing
taxes. However, the fiscal revenue
decreased rather than increasing
In the period 1980-84, disposable income:
+4%, fiscal revenue: -9%
Fiscal deficit.
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…and the empirical evidence
What does this result tell us?
• The idea of Laffer can be correct if applied to
tax payers subject to high tax rates.
In the period 1980-84 the fiscal revenue produced
by high income tax payers increased (more work,
smaller evasion…)
• The idea of Laffer can be correct if applied to
countries with high tax rates.
In Sweden during the 1980s the tax rate on high
incomes was about the 80%, while in the USA was
much smaller .
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The debate…
But then why there are countries with high tax
rates and countries with low tax rates?
It depends on how one evaluates the
elasticity of some economic curves.
In reality it is really complex to determine the
real value of elasticity, and this creates a lack
of consensus on this issues.
Much depends on the preferences of
citizens/voters…
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The debate…
In some countries (northern Europe), high tax rates
are accepted because they create more
resources to be redistributed through public
services. This, in their view, compensate parts of
the net loss.
In other countries (USA), low tax rates and little
redistribution are preferred because it is generally
believed that poverty is not the result of unlucky
events but rather the consequence of individual
actions. Therefore the social expenditure is unfair
(beyond a certain limit) and it does not
compensate the net loss.
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Conclusion
• The reduction in the consumer surplus and
producer surplus caused by taxes exceeds the
the increase in fiscal revenue obtained by the
public administration. Therefore, taxes produce
a net loss.
• The higher the tax rate, the higher the net loss.
• The fiscal revenue first increase with the value of
the tax; then, as the tax rate increases, the
fiscal revenue starts to diminish following the
reduction in the size of the market.
• When the tax rate is very high, this can justify a
tax cut so as to reduce the net loss.
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