Taxes

1
Taxes
2
Preview

• Two ways to implement at tax
• Tax the producer
• Tax the consumer
• But who pays the tax by law, isnt who really
  pays the tax in practice.
• 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

3
Tax on the consumer

• Suppose every time you purchase a good at price
  P, you also had to pay a tax T?

4
Demand

• At price P, you wanted to buy Q.

P
P
D
Q
Q
5
Demand

• At price P, you wanted to buy Q.
• With a tax of T, the producer would have to
  charge P-T for you to still want to by Q.

P
P
T
P-T
D
Q
Q
6
Demand

• At price P, you wanted to buy Q.
• With a tax of T, the producer would have to
  charge P-T for you to still want to by Q.
• Thus, a unit tax of T causes the demand curve to
  shift down everywhere by T.

P
P
T
D
D
Q
Q
7
Equilibrium

• Demand decreased
• Quantity demanded decreased

P
S
P
T
D
D
Q
Q
8
Equilibrium

• Demand decreased
• Quantity demanded decreased
• The price charged by the firm decreased.

P
S
T
P
D
D
Q
Q
9
Equilibrium

• Demand decreased
• Quantity demanded decreased
• The price charged by the firm decreased.
• The price paid by the consumer increased

P
S
PT
T
T
P
D
D
Q
Q
10
Pre-Tax Surplus
P
S
P
D
Q
Q
11
Post-Tax Consumer Surplus

• Before the tax, consumer surplus was a b c d
  e.

P
S
a
b
PT
c
d
e
T
P
D
D
Q
Q
12
Post-Tax Consumer Surplus

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b

P
S
a
b
PT
c
d
e
T
P
D
D
Q
Q
13
Post-Tax Producer Surplus

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.

P
S
a
b
PT
c
d
e
i
h
f
T
P
g
D
D
Q
Q
14
Post-Tax Producer Surplus

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.
• After the tax, producer surplus is g.

P
S
a
b
PT
c
d
e
i
h
f
T
P
g
D
D
Q
Q
15
Government Revenue

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.
• After the tax, producer surplus is g.
• Tax revenue is TQ c d f h.

P
S
a
b
PT
c
d
e
i
h
f
T
P
g
D
D
Q
Q
16
Government Revenue

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.
• After the tax, producer surplus is g.
• Tax revenue is TQ c d f h.
• The consumer provided c and d, while the producer
  provided f and h.

P
S
a
b
PT
c
d
e
i
h
f
T
P
g
D
D
Q
Q
17
Social Losses of Taxation

• The government could give c and d back to
  consumers.
• The government could give f and h back to
  producers.
• BUT, e and i would be lost forever.
• e i is the deadweight loss of taxation.

P
S
PT
c
d
e
i
h
f
T
P
D
D
Q
Q
18
Equilibrium and the Firm
MC
P
P
ATC
S
P
P MR
P
D
D
Q
q
Q
Q
19
Equilibrium and the Firm
MC
P
P
ATC
S
P MRAR
P
D
D
Q
q
Q
Q
20
Equilibrium and the Firm
MC
P
P
ATC
S
P MRAR
P
D
D
Q
q
Q
Q
Profit has gone down.
21
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.

22
Supply

• Since the supply curve is the firms marginal
  cost curve, if the MC curve shifts up by T, then
  S shifts up by T.

S
P
S
D
Q
23
Supply

• Since the supply curve is the firms marginal
  cost curve, if the MC curve shifts up by T, then
  S shifts up by T.
• Supply decreased
• at any price paid by consumers, firms are
  willing to supply less.

S
P
S
D
Q
24
Supply

• Supply decreased
• Quantity supplied decreased

S
P
S
P
D
Q
Q
25
Supply

• Supply decreased
• Quantity supplied decreased
• Equilibrium price increased.

S
P
S
P
D
Q
Q
26
Supply

• Supply decreased
• Quantity supplied decreased
• Equilibrium price increased.
• Since the firm has to pay T for every unit sold,
  the price the firm receives (P - T) decreased.

S
P
S
P
T
P-T
D
Q
Q
27
Pre-Tax Surplus
P
S
P
D
Q
Q
28
Post-Tax Consumer Surplus

• Before the tax, consumer surplus was a b c d
  e.

S
P
S
a
b
T
P
c
d
e
P-T
D
Q
Q
29
Post-Tax Consumer Surplus

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b

S
P
S
a
b
T
P
c
d
e
P-T
D
Q
Q
30
Post-Tax Producer Surplus

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.

S
P
S
a
b
T
P
c
d
e
i
h
f
P-T
g
D
Q
Q
31
Post-Tax Producer Surplus

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.
• After the tax, producer surplus is g.

S
P
S
a
b
T
P
c
d
e
i
h
f
P-T
g
D
Q
Q
32
Government Revenue

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.
• After the tax, producer surplus is g.
• Tax revenue is TQ c d f h.

S
P
S
a
b
T
P
c
d
e
i
h
f
P-T
g
D
Q
Q
33
Government Revenue

• Before the tax, consumer surplus was a b c d
  e.
• After the tax, consumer surplus is a b.
• Before the tax, producer surplus was f g h
  i.
• After the tax, producer surplus is g.
• Tax revenue is TQ c d f h.
• The consumer provided c and d, while the producer
  provided f and h.

S
P
S
a
b
T
c
d
e
i
h
f
g
D
Q
Q
34
Social Losses of Taxation

• The government could give c and d back to
  consumers.
• The government could give f and h back to
  producers.
• BUT, e and i would be lost forever.
• e i is the deadweight loss of taxation.

S
P
S
T
P
c
d
e
i
h
f
P-T
D
Q
Q
35
Equivalence
S
P
P
S
S
T
P
PT
c
d
e
c
d
e
i
h
i
h
f
f
P-T
T
P
D
D
D
Q
Q
Q
Q
36
Equivalence
A T shift up in supply is the same as a T
shift down in demand. The consumer pays P in
both cases. The consumer gets P - T in both
cases.
S
P
S
T
P
c
d
e
i
h
f
P-T
D
D
Q
Q
37
Equivalence
A T shift up in supply is the same as a T
shift down in demand. The consumer pays P in
both cases. The consumer gets P - T in both
cases.
S
P
S
T
P
P-T
T
D
D
Q
Q
The economic burden of the tax is independent of
the statutory burden of the tax.