Taxes
Preview
• Two ways to implement at tax
– Tax the producer
– Tax the consumer
• But who pays the tax by law, isn’t who really
pays the tax in practice.
–
–
–
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Show the effect of a tax on supply and demand.
Show the effect on equilibrium
Show welfare losses from taxation
Show who pays for those losses
Tax on the consumer
• Suppose every time you purchase a good
at price P, you also had to pay a tax T?
Demand
1) At price P, you wanted to buy Q.
P
P
D
Q
Q
Demand
1) At price P, you wanted to buy Q.
P
2) With a tax of T, the producer
would have to charge P-T for
you to still want to by Q.
P
P-T
T
D
Q
Q
Demand
1) At price P, you wanted to buy Q.
P
2) With a tax of T, the producer
would have to charge P-T for
you to still want to by Q.
P
3) Thus, a unit tax of T causes the
demand curve to shift down
everywhere by T.
T
D`
Q
D
Q
Equilibrium
1) Demand decreased
P
S
P*
T
D`
Q*
D
Q
2) Quantity demanded decreased
Equilibrium
1) Demand decreased
P
S
2) Quantity demanded decreased
3) The price charged by the firm
decreased.
T
P*
D`
Q*
D
Q
Equilibrium
1) Demand decreased
P
P*+T
S
3) The price charged by the firm
decreased.
T
T
P*
4) The price paid by the consumer
increased
D`
Q*
2) Quantity demanded decreased
D
Q
Pre-Tax Surplus
P
S
P*
D
Q*
Q
Post-Tax Consumer Surplus
1) Before the tax, consumer
surplus was a + b + c +d +e.
P
P*+T
S
a
b
c
d e
T
P*
D`
Q*
D
Q
Post-Tax Consumer Surplus
P
P*+T
S
a
b
c
d e
T
P*
D`
Q*
D
Q
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b
Post-Tax Producer Surplus
P
P*+T
S
a
b
c
f
P*
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
3) Before the tax, producer surplus
was f + g + h + i.
d e
hi
T
g
D`
Q*
D
Q
Post-Tax Producer Surplus
P
P*+T
S
a
b
c
f
P*
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
3) Before the tax, producer surplus
was f + g + h + i.
4) After the tax, producer surplus is
g.
d e
hi
T
g
D`
Q*
D
Q
Government Revenue
P
P*+T
S
a
b
c
f
P*
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
3) Before the tax, producer surplus
was f + g + h + i.
4) After the tax, producer surplus is
g.
d e
hi
T
g
D`
Q*
D
Q
5) Tax revenue is T*Q*: c + d + f +
h.
Government Revenue
P
P*+T
S
a
b
c
f
P*
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
3) Before the tax, producer surplus
was f + g + h + i.
4) After the tax, producer surplus is
g.
d e
hi
T
g
D`
Q*
D
Q
5) Tax revenue is T*Q*: c + d + f +
h.
6) The consumer provided c and d,
while the producer provided f
and h.
Social Losses of Taxation
P
P*+T
P*
S
c
f
3) BUT, e and i would be lost
forever.
d e
hi
T
D`
Q*
1) The government could give c
and d back to consumers.
2) The government could give f
and h back to producers.
D
Q
e + i is the deadweight loss of
taxation.
Equilibrium and the Firm
MC
P
S
P
ATC
P*
P*
P = MR
D`
Q*
D
Q
q*
Q
Equilibrium and the Firm
MC
P
S
P
ATC
P = MR=AR
P*
D`
Q*
D
Q
q*
Q
Equilibrium and the Firm
MC
P
S
P
ATC
P = MR=AR
P*
D`
Q*
D
Q
q*
Profit has gone down.
Q
Tax on the producer
• Suppose instead, every time a good was
sold, the producer had to pay a tax of T.
• Essentially, the marginal cost of producing
each unit has increased by T.
Supply
S`
P
S
D
Q
1) Since the supply curve is the
firm’s marginal cost curve, if the
MC curve shifts up by T, then S
shifts up by T.
Supply
S`
P
S
1) Since the supply curve is the
firm’s marginal cost curve, if the
MC curve shifts up by T, then S
shifts up by T.
2) Supply decreased
D
Q
“at any price paid by
consumers, firms are willing to
supply less.”
Supply
P
S`
1) Supply decreased
S
2) Quantity supplied decreased
P*
D
Q*
Q
Supply
P
S`
1) Supply decreased
S
2) Quantity supplied decreased
3) Equilibrium price increased.
P*
D
Q*
Q
Supply
P
S`
1) Supply decreased
S
2) Quantity supplied decreased
3) Equilibrium price increased.
P*
T
4) Since the firm has to pay T for
every unit sold, the price the
firm receives (P* - T) decreased.
P*-T
D
Q*
Q
Pre-Tax Surplus
P
S
P*
D
Q*
Q
Post-Tax Consumer Surplus
S`
P
P*
S
a
b
c
d e
T
P*-T
D
Q*
Q
1) Before the tax, consumer
surplus was a + b + c +d +e.
Post-Tax Consumer Surplus
S`
P
P*
S
a
b
c
d e
T
P*-T
D
Q*
Q
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b
Post-Tax Producer Surplus
S`
P
P*
S
a
b
c
f
P*-T
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
d e
hi
T
3) Before the tax, producer surplus
was f + g + h + i.
g
D
Q*
Q
Post-Tax Producer Surplus
S`
P
P*
S
a
b
c
f
P*-T
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
d e
hi
T
3) Before the tax, producer surplus
was f + g + h + i.
4) After the tax, producer surplus is
g.
g
D
Q*
Q
Government Revenue
S`
P
P*
S
a
b
c
f
P*-T
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
d e
hi
T
3) Before the tax, producer surplus
was f + g + h + i.
4) After the tax, producer surplus is
g.
g
D
Q*
Q
5) Tax revenue is T*Q*: c + d + f +
h.
Government Revenue
S`
P
S
1) Before the tax, consumer
surplus was a + b + c +d +e.
2) After the tax, consumer surplus
is a + b.
a
b
c
f
d e
hi
T
3) Before the tax, producer surplus
was f + g + h + i.
4) After the tax, producer surplus is
g.
g
D
Q*
Q
5) Tax revenue is T*Q*: c + d + f +
h.
6) The consumer provided c and d,
while the producer provided f
and h.
Social Losses of Taxation
S`
P
P*
P*-T
S
c
f
d e
hi
T
3) BUT, e and i would be lost
forever.
D
Q*
1) The government could give c
and d back to consumers.
2) The government could give f
and h back to producers.
Q
e + i is the deadweight loss of
taxation.
Equivalence
S`
P
P*
P*-T
S P
c
f
d e
hi
T
P*+T
P*
S
c
f
d e
hi
T
D
Q*
Q
D`
Q*
D
Q
Equivalence
S`
P
A “T shift up” in supply is the
same as a “T shift down” in
demand.
S
The consumer pays P* in both
cases.
P*
P*-T
c
f
d e
hi
Q*
T
The consumer gets P* - T in both
cases.
D`
D
Q
Equivalence
S`
P
A “T shift up” in supply is the
same as a “T shift down” in
demand.
S
The consumer pays P* in both
cases.
T
P*
P*-T
The consumer gets P* - T in both
cases.
T
Q*
D`
D
Q
The economic burden of the tax is independent
of the statutory burden of the tax.