Exercises Lecture 8: Trade policies
Exercise 1, from KOM
1. Home’s demand and supply curves for wheat are:
D = 100 − 20P
S = 20 + 20P
Derive and graph Home’s import demand schedule. What would the price of wheat
be in the absence of trade?
2. Now add Foreign, which has a demand curve
D∗ = 80 − 20P
and a supply curve
S ∗ = 40 + 20P
Derive and graph Foreign’s export supply curve and find the price of wheat that
would prevail in Foreign in the absence of trade
3. Now allow Foreign and Home to trade with each other, at zero transportation cost.
Find and graph the equilibrium under free trade. What is the world price? What is
the volume of trade?
4. Assume that Home imposes a specific tariff t = 0.5 on wheat imports.
(a) Determine and graph the effects of the tariff on the following:
(i) the price of wheat in each country;
(ii) the quantity of wheat supplied and demanded in each country;
(iii) the volume of trade.
(b) Determine the effect of the tariff on the welfare of each of the following groups:
(i) Home import-competing producers;
(ii) Home consumers;
(iii) the Home government.
(c) Show graphically and calculate the terms of trade gain, the efficiency loss, and
the total effect on welfare of the tariff.
1
Exercise 2, from KOM
Suppose that Foreign had been a much larger country, with domestic demand and supply
D∗ = 800 − 200P
S ∗ = 400 + 200P
Notice that this assumption implies that the Foreign price of wheat in the absence of trade
would have been the same as in the previous problem.
1. Recalculate the free trade equilibrium and the effects of a 0, 5 specific tariff by Home.
2. Relate the difference in results to the discussion of the small country case in the text.
Exercise 3
Consider Fig. 1 and answer to the following questions.
P
14
S
8
World price + tariff
6
3
World price
2
D
10
40
60
80
Figure 1
2
100
Q
1. In the absence of Trade how many units of the good does this country produce and
consume?
2. In the absence of trade what is the country’s consumer plus producer surplus?
3. With free trade and no tariffs, what is the amount of the good imported?
4. With a specific tariff t = 3 per unit, what is the amount of the good imported?
5. What is the effect of the tariff on the welfare of producers, consumers and government?
Exercise 4, from KOM
The nation of Acirema is “small” and unable to affect world prices. It imports peanuts at
the price of $10 per bag. The demand and supply curves are:
D = 400 − 10P
S = 50 + 5P.
Determine the free trade equilibrium. Then calculate and graph the following effects of an
import quota that limits imports to 50 bags.
1. The increase in the domestic price.
2. The quota rents.
3. The consumption distortion loss.
4. The production distortion loss.
3
Solutions Exercise 1
1. Home’s import demand schedule M D is given by:
M D = D − S = 100 − 20P − 20 − 20P = 80 − 40P
Q
and graphically it is given by:
HOME
P
P
S
5
2
2
1,75
1,5
1,75
1,5
1
1
MD
D
20
40 50 55
65 70 80
100
20
Q
40 50 55
65 70 80
Figure 2. Home’s Import Demand Curve
The price of wheat be in the absence of trade is given by the intersection of the
curves D and S and it equal to P = 2.
Algebraically, it is obtained from D = S (or M D = 0), hence:
80 − 40P = 0
4
⇒
P =2
100
Q
2. Foreign’s export supply curve XS is given by:
XS = S ∗ − D∗ = 40 + 20P − 80 + 20P = −40 + 40P
and graphically it is given by:
FOREIGN
P
XS
P
S
4
3
2
1
1
D
40
60
80 Q
40
80
Figure 3. Foreign’s export supply curve
As previously, the price of wheat be in the absence of trade is given by the intersection
of the curves D and S and it equal to P = 1.
Algebraically, it is obtained from D = S (or XS = 0), hence:
−40 + 40P = 0
5
⇒
P∗ = 1
Q
3. The equilibrium under free trade is given by M D = XS, that is:
80 − 40P = −40 + 40P
⇒
120 = 80P
⇒
PW = 1, 5
To find the volume of trade, it suffices to substitute the world price PW into either
the M D or the XS, so as to obtain:
80 − 40 × 1, 5 = 20 = Volume of trade without tariff (free trade)
Graphically, it is represented in Fig. 4
WORLD EQUILIBRIUM
P
XS
t
{
2
1,75
1,5
1,25
1
MD
10
80
20
Q
Figure 4. World equilibrium
4. (a) When Home imposes a tariff t = 0.5 on wheat imports, only the M D modifies
(the XS remains unchanged), and becomes:
M D = 80 − 40 (P + t) = 80 − 40(P + 0, 5) = 80 − 20 − 40P = 60 − 40P
| {z }
PT
6
hence the new price, namely PT∗ , is given by:
M D = XS
⇒
60 − 40P = −40 + 40P
⇒
PT∗ = 1, 25
while the price in Home, PT is given by
PT = PT∗ + t = 1, 25 + 0, 5 = 1, 75
To determine the the quantity of wheat supplied and demanded in each country
as well as the new volume of trade, it suffices to substitute the correct price,
either PT or PT∗ in the demand and supply functions.
Hence, substituting PT in D and S you obtain, for Home:
D = 100 − 20 × 1, 75 = 65
S = 20 + 20 × 1, 75 = 55
while, by substituting PT∗ in D∗ and S ∗ you obtain, for Foreign:
D∗ = 80 − 20 × 1, 25 = 55
S ∗ = 40 + 20 × 1, 25 = 65
where it should be clear that the new volume of trade is equal to 10, as shown
by Fig. 4.
(b) To determine the effect of the tariff on the welfare of the different groups, refer
to Fig. 5.
where the areas a, b, c, d and e are given by:
a=
(50 + 55) × 0.25
= 13, 125
2
b=d=
5 × 0.25
= 0, 625
2
c = e = 10 × 0.25 = 2, 5
The reduction in consumers’ surplus is equal to a + b + c + d, hence it is equal
to 16,875.
7
P
S
b
1,75
1,5
1,25
a
d
c
e
50 55 65 70
D
100 Q
Figure 5. Welfare, efficiency loss and terms of trade gain.
Producers gain the area a, which is equal to 13,125.
Government revenue is equal to the area c, hence it is equal 2,5.
(c) The efficiency loss is equal to b + d = 0, 625 × 2 = 1, 25
The terms of trade gain is equal to e = 2, 5
The total effect on welfare of the tariff is positive and equal to −(b + d) + e =
−1, 25 + 2, 5 = 1, 25.
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Solutions Exercise 2
To recalculate the free trade equilibrium and the effects of a 0, 5 specific tariff by Home
you need to determine the new XS, given by:
XS = S ∗ − D∗ = 400 + 200P − 800 + 200P = −400 + 400P
The free trade equilibrium is given by the intersection of the XS with the M D as
follows:
M D = XS :
80 − 40P = −400 + 400P
⇒
PW = 1, 09
The equilibrium with a tariff t = 0, 5 imposed by Home is given instead by:
M D = XS :
60 − 40P = −400 + 400P
⇒
PT∗ = 1, 045
while the price in Home, PT :
PT∗ + t = 1, 045 + 0, 5 = 1, 545
By following the same reasoning as the previous exercise, the volume of trade with no
tariff (P = 1, 09) is therefore equal to 36,4 (you just need to substitute the price into
either the M D or the XS), while the volume of trade with the tariff is equal to 18,2 (in
this case either you plug PT into the M D or PT∗ into the XS).
Notice that there is already an important difference in comparison to Exercise 1. When
Home is relatively small, the effect of a tariff on world price is much smaller than when
Home is relatively large. When Foreign and Home were closer in size, as in Exercise 1, a
tariff of 0, 5 imposed by Home lowered world price from 1, 5 to 1, 25, whereas in this case
the same tariff lowers world price only from 1, 09 to 1, 045.
There are important differences also when it comes to analyze welfare, as Fig. 6 shows.
The areas now are given by:
a=
(50, 9 + 41, 8) × 0, 455
= 21, 089
2
b=d=
9.1 × 0, 455
= 2, 07
2
c = 18, 2 × 0, 455 = 8, 28
9
e = 18, 2 × 0, 045 = 0, 819
where a represent the increase in producers’ surplus, a + b + c + d = 33,51 the reduction
in consumers’ surplus and c the government’s revenue.
It is important to underline that - given the assumptions of the exercise - now the efficiency
loss, b + d = 4, 14 is much bigger in comparison to the terms of trade gain, equal to
e = 0, 819, as a consequence of the different variation of prices.
This small country example where the distortionary losses from the tariff overcome the
terms of trade gains should then make it clear that the smaller the economy, the larger
the losses from a tariff due to smaller terms of trade gains.
Solutions Exercise 3
1. 60.
P
S
1,545
a
1,09
1,045
b
c
d
e
D
41,8 50,9 69,1
78,2
Figure 6. Welfare, efficiency loss and terms of trade gain.
10
Q
2. The consumers’ surplus is equal to
6 × 60
= 180
2
, which is also equal to producers’ surplus. Hence the total surplus (consumers +
producers) is equal to 360.
3. With free trade, you have to consider the world price PW = 3, thus the amount of
good imported is equal to 100 − 10 = 90
4. With a specific tariff t = 3 per unit the amount of good imported is equal to
80 − 40 = 40
5. The variation in consumers’ surplus can be calculated by considering the initial
surplus - the surplus with the tariff, that is:
100 × (14 − 3) 80 × (14 − 6)
100 × 11 80 × 8
−
=
−
= 550 − 320 = 230
2
2
2
2
By the same reasoning, the variation in producers’ surplus is:
40 × (6 − 2) 10 × (3 − 2)
−
= 80 − 5 = 75
2
2
Finally, the revenue for the government is given by:
amount imported × amount of the tariff = 40 × 3 = 120
Solutions Exercise 4
1. To determine the free trade equilibrium, you just have to substitute the price PW = 10
into the demand and supply functions as follows:
D = 400 − 10 × 10 = 300
S = 50 + 5 × 10 = 100.
Hence the M D is
M D = D − S = 300 − 100 = 200
which defines total imports of Acirema.
11
With a quota which limits imports to 50 bags, the increase in the domestic price can
be identified by equating the demand to the domestic supply + the quota, that is:
D = S + quota :
400 − 10P = 50 + 5P + |{z}
50
⇒
P = 20
quota
Hence, graphically, the equilibrium is as in Fig. 7:
P
S
23,3
20
a
10
b
D
50 100
150
200
300
Figure 7
2. Quota rents are therefore given by
(20 − 10) × quota = 10 × 50 = 500.
3. The consumption distortion loss is given by the area b, where
b=
100 × 10
= 500
2
12
Q
4. The production distortion loss is given by the area a, where
a=
50 × 10
= 250
2
13