ABSE 303
Homework (the effect of a tariff)
The demand curve and the supply curve for widgets at home are:
Qd = 100 – 4P
Qs = 20 +P
a)
b)
c)
d)
e)
f)
g)
h)
what are the equilibrium price and quantity if there is no trade
what are the equilibrium quantities if the nation can trade freely with abroad at a price of 5
what is the effect of the shift to free trade on the consumer surplus?
what is the effect of the shift to free trade on the producer surplus?
what is the net national gain?
what is the effect of a tariff of 5 on the consumer surplus?
what is the effect of the tariff on the producer surplus?
what is the net national loss from the shift from free trade to trade restriction?
a) equilibrium price – the one where Qd = Qs
100 – 4P = 20 +P
P = 16
Q = 36
b) if the price in the world market Pw = 5 and the nation can trade freely at this price
Qd = 100 – 4P = 100 – 4 x 5 = 80
Domestic sellers will supply Qs = 20 +P = 20 + 5 = 25
Qd - Qs = 55 imports
c) the effect on consumer surplus
before trade consumer surplus was the green area on the left graph below (Fig. 1)
with free trade consumer surplus is the yellow area on the right graph below (Fig. 2)
the effect on consumer surplus is the difference between consumer surplus under free trade
conditions and consumer surplus before trade. CS increased due to the lower price and greater
quantities bought. On fig. 2 it is shown by the red trapezium. We can calculate its area and we will
find the increase in consumer surplus.
ΔCS = SKLMN =
KL  MN
36  80
KN =
(16 – 5) = 638
2
2
CS before trade
CS under free trade
D
D
S
S
Pe = 16
Pw = 5
Imports = 55
Qe = 36
Qs = 25
Qd = 80
Fig. 1 Consumer surplus before and under free trade
CS before trade
Increase in CS under free
trade
D
D
S
S
L
K
Pe = 16
M
Pw = 5
N
Imports = 55
Qe = 36
Qs = 25
Fig. 2 Increase in consumer surplus under the free trade
Q =36
Qd = 80
d) the effect on the producer surplus
before trade producer surplus was the blue area on the left graph below (Fig. 3)
after trade producer surplus is the brown area on the right graph below (Fig 3)
PS before trade
PS under free trade
D
D
S
S
Pe = 16
Pw = 5
Qe = 36
Qs = 25
Fig. 3 Producer surplus before and under free trade
With the decrease in price producer surplus falls. The effect on producer surplus is the
difference between producer surplus before trade and producer surplus under free. On fig. 4 it is
shown by the grey trapezium. We can calculate its area and we will find the decrease in producer
surplus.
ΔPS = SKLTN =
KL  TN
36  25
KN =
(16 – 5) = 335.5
2
2
PS before trade
Loss of PS under free trade
D
D
S
S
L
Pe = 16
K
Pw = 5
N
Qe = 36
T
Qs = 25
Fig. 4. Loss of producer surplus with free trade
e) the net national gain is the difference between the gain in consumer surplus and the loss of
producer surplus = 638 – 335.5 = 302.5
Geometrically it is the area of the triangle LMT presented on Fig. 5 below. If we calculate the area
of the triangle, we will get the same 302.5 = (55 x 11) : 2
Net national gain from trade
D
S
L
P = 16
T
M
Pw = 5
Imports = 55
Qs = 25
Qe
Fig. 5 Net national gain from trade
Qd = 80
f) the effect of a tariff of 5 on consumer surplus
If the country sets a tariff of 5 on imports, foreign companies will have to pay it and therefore they
will raise the price by 5. Since the price under free trade was 5, now it will rise by 5 up to 10. Now
buyers will be willing to buy less. How much exactly we can find from the equation for the
demand curve:
Qd = 100 – 4P = 100 – 4 X 10 = 60
Consumers will have a lower consumer surplus, because of the increase in price and reduction in
the quantity bought.
The reduction in the consumer surplus is shown on Fig 6.
CS under free trade
Decrease in CS after the
tariff
D
D
S
S
Pt = 10
Pw = 5
Pw=5
Qe = 80
Qd =60
Qd = 80
Fig 6. Reduction in CS with the tariff
Geometrically this reduction is presented by the area of the trapezium UVMN, presented on Fig. 7.
Loss of CS after the tariff
P
U
V
Pt = 10
N
Pw = 5
M
Qdt = 60
Qd = 80
Q
Fig. 7 Loss of CS after the tariff
We will find the loss of CS = SUVMN =
UV  MN
60  80
UN =
x (10 – 5) = 350
2
2
g) the effect of the tariff on the producer surplus
Since foreign producers will have to raise the price and become less competitive, local producers
will be able to increase production. Now the new domestically supplied quantity will be:
Qs = 20 +P = 20 + 10 = 30
Due to the higher price and greater quantity sold, domestic producers will increase their producer
surplus. It is shown on Fig. 8 below
PS under free trade
PS after the tariff
D
D
S
S
Pt = 10
Pw = 5
Pw = 5
Qs = 25
Qs = 25
Qst = 30
Fig. 8 PS before and after the tariff
The increase in producer surplus can be found as the area of the trapezium UWZN, presented on
Fig. 9
Gain in PS after the tariff
P
W
U
Pt = 10
N
Pw = 5
Z
Qs = 25
Qst = 30
Q
Fig. 9. Gain in PS after the tariff
It is easy to find it. It will be the area of the trapezium UWZN =
25  30
x (10 – 5) = 137.5
2
i)
the net national loss from trade = gain in producer surplus + government collections from the
tariff– loss in CS.
Do not forget that the government has set the tariff to collect it from foreigners. Government
collections will be = tariff per unit 5 x the amount of imports (Qdt – Qst = 60 – 30) 30 = 150.
Geometrically it is the area of WVHG on Fig. 10 below.
Government collection from tariff
P
W
V
Pt = 10
Pw = 5
G
Qst = 30
H
Qdt = 80
Q
Fig. 10 Government collections from tariff
Therefore, the net national loss from tariff = 137.5 + 150 – 350 = - 63.5
Geometrically we can see the net national loss presented by the areas of two triangles WGZ and
VMH, presented on Fig. 11 below.
Net national loss from tariff
P
W
V
Pt = 10
Pw = 5
Z
G
Qst = 30
H
Qdt = 80
M
Q
Fig. 11. Net national loss from tariff
Since these net losses are lost by domestic buyers, but are not taken over by domestic sellers, or by
the government, these are deadweight losses.
The first deadweight loss – the area of the triangle WGZ is lost because of the shift in demand
from foreign to domestic producers. We call it production effect of tariff.
The second deadweight loss – the area of the triangle VMH is lost because of the reduction in
consumption due to the higher price. We call it consumption effect of the tariff.
Now, try to solve another problem like this one. I will change only the numbers and you will have
to answer the same questions.
Qd = 30 – 2P
Qs = 2 + 2P
a)
b)
c)
d)
e)
f)
g)
h)
what are the equilibrium price and quantity if there is no trade
what are the equilibrium quantities if the nation can trade freely with abroad at a price of 2
what is the effect of the shift to free trade on the consumer surplus?
what is the effect of the shift to free trade on the producer surplus?
what is the net national gain?
what is the effect of a tariff of 2 on the consumer surplus?
what is the effect of the tariff on the producer surplus?
what is the net national loss from the shift from free trade to trade restriction?