International Trade - ECON GU 4500
Recitation 8
Bryan Ge, Guglielmo Imperiali d’Afflitto, Advaith Jayakumar 1
Columbia University
November 26, 2025
1 The content is based on slides by Natalie Yang (Columbia)
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Logistics
• PS2 due Monday, November 24, 11:59 pm.
Today:
• Trade policy instruments (tariffs, quotas) in partial equilibrium
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Main point
Different trade policy instruments can generate the same impact on welfare, but through different
mechanisms, or they can generate different welfare impacts even when both result in the same
equilibrium prices and quantities.
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Practice problem: tariffs vs quotas
Consider two economies, Home and Foreign, with demand and supply for widgets given by
Qd = 60 − 5P
Qs = P
Qd∗ = 36 − 5P
Qs∗ = P
Home and Foreign are large enough to influence the world equilibrium.
Q1: Find the autarky price in both countries, and the free trade price. Identify the direction of
trade (which country imports?) and find the quantity of widget imports.
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Equilibrium in autarky and free trade I
A1: First, we solve for the autarky equilibrium in both countries.
In Home:
Qd = Qs
60 − 5P = P ⇐⇒ P aut = 10, Q aut = 10
In Foreign:
Qd∗ = Qs∗
36 − 5P = P ⇐⇒ P ∗,aut = 6, Q ∗,aut = 6
Foreign has a lower price in autarky, so we expect it to supply to the world market when the two
countries open up to trade.
Let’s find the equilibrium under free trade. Home import demand is:
MD = Qd − Qs
= (60 − 5P) − P = 60 − 6P
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Equilibrium in autarky and free trade II
∗
Now, let’s derive Foreign export supply carefully. Notice that if P ∗ > 36
5 =⇒ Qd < 0, which is
36
∗
∗
impossible. So, if P > 5 , then Qd = 0, which means:
XS ∗ =
Qs∗ − Qd∗
Qs∗ − 0
= −36 + 6P
=P
if P ≤ 36
5
if P > 36
5
Free trade equilibrium price is found by solving: MD = XS ∗ . However, the threshold price beyond
which Foreign does not consume is given by 36
5 = 7.2. So we know that for a free-trade equilibrium
price above that level, we need to use the function XS = P. If we were to solve MD = XS ∗ |P FT ≤ 365 ,
then we would find P FT = 8 > 7.2, which would tell us that we have used the wrong piece of XS ∗ .
So, let’s find the free-trade price by equating:
MD = XS ∗ |P FT > 365
60 − 6P = P =⇒ P FT =
60
≈ 8.57
7
which is the correct free-trade equilibrium price.
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Equilibrium in autarky and free trade III
60
60
At P FT = 60
7 , MD = 60 − 6 ∗ 7 = 7 . So Home imports, Foreign exports, and Foreign does not
consume.
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Remark: two equivalent methods for finding equilibrium with free trade I
Remark: recently we have been solving for the free-trade equilibrium by equating import demand
by one country, MD, to export supply by its trading partner(s), XS.
However, earlier in the class, we were solving for the equilibrium under free trade by deriving world
demand for a good and world supply for the same good and equating the two. World demand is
given by the sum of Home demand and demand from the rest of the world (ROW), and world
supply is given by the sum of supplies from Home and ROW.
Conceptually, how is it possible that we have two different methods to find the free-trade price? Is
the solution to the equilibrium price under free trade dependent on the method we use?
Not really, the two methods are mathematically the same thing! In fact, notice that:
MD = XS ∗
Qd − Qs = Qs∗ − Qd∗
⇐⇒ Qd + Qd∗ = Qs∗ + Qs
| {z }
| {z }
world demand
world supply
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Practice problem: tariffs vs quotas
Q2: The importing country imposes a specific tariff of t = 2 on widget imports. What is the new
world price? What is the price faced by consumers in the economy with the tariff? How many
widgets are imported?
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Equilibrium with import tariff I
A2: Home imposes tariff t = 2. Then, if Pt is the world price of widgets after the tariff is imposed,
Home consumers pays Pt + t on imports of widgets, so Home’s import demand becomes:
MDt = 60 − 6(Pt + t) = 48 − 6Pt
Let’s find the world price Pt as we did in A1. Let’s first equate Home import demand to Foreign
export supply, assuming first the equilibrium price in Foreign is still higher than the threshold price
at which Foreign does not consume.
MDt = XS ∗ |Pt > 365
48 − 6P = P =⇒ Pt =
48
≈ 6.86
7
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Equilibrium with import tariff II
36
But Pt = 48
7 < 5 ! So, we know that Home import demand is intersecting Foreign import supply in
the region where Pt < 36
5 . Therefore, the world price (i.e., the price in Foreign) once Home
imposes the tariff is given by:
MDt = XS ∗ |Pt < 365
48 − 6P = −36 + 6P =⇒ Pt = 7
So, the price Home pays on imports is Pt + t = 9. Import demand with the tariff is
MDt = 48 − 6 ∗ Pt = 6.
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Practice problem: tariffs vs quotas
Q3: What is the welfare cost in Home of the tariff?
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Welfare costs of tariff I
A3: To measure the welfare cost, we can consider the change in the social surplus (∆TSS), which
is given by the sum of the changes in consumer surplus ∆CS, producer surplus ∆PS, government
revenue ∆GR, and any eventual externality ∆E . So, given QdFT the quantity demanded by Home
under free trade (i.e., without the tariff), Qdt the quantity demanded by Home after the tariff is
imposed, QsFT the quantity supplied by Home under free trade, and Qst the quantity supplied by
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Welfare costs of tariff II
Home with the tariff, we have:
1
∆CS = − [(Pt + t) − P FT ][QdFT + Qdt ]
2
1
60 120
675
= − [9 − ][
+ 15] = −
2
7
7
98
1
FT
FT
∆PS = + [(Pt + t) − P ][Qs + Qst ]
2
60 60
369
1
= + [9 − ][ + 9] =
2
7 7
98
∆GR = +t[Qdt − Qst ] = 2[6] = 12 =⇒ ∆TSS
675 369
870
=−
+
+ 12 =
≈ +8.88
98
98
98
= ∆CS + ∆PS + ∆GR
The tariff creates a welfare benefit!
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Practice problem: tariffs vs quotas
Q4: Suppose instead of imposing a tariff, the importing country imposed a trade quota instead.
What is the quota amount that is equivalent to this tariff?
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Equivalence between quota and tariff
A4: An import quota equivalent to the tariff is a quota which achieves the same imported quantity,
i.e., Q = MDt = 6, where Q is the quota.
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Practice problem: tariffs vs quotas
Q5: When implementing the quota, the importing country just gives away the license for free to
the first foreign exporters who ask. What is the welfare cost of the quota in Home?
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Welfare costs of quota I
A5: Because Home gives away the quota for free, no government revenue is raised with this
instrument. Hence, the change in total welfare amounts to the change in consumer and producer
surplus. The quantity demanded at home with the quota Qdq is such that Qdq = Qdt = 15 (that’s
because Home is raising a quota equivalent to the tariff of t = 2). The equilibrium price in Home
will be such that Home wants to import 6 widgets from abroad, i.e., P q = P t + t = 9. So, relative
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Welfare costs of quota II
to free trade, we have:
1
∆CS = − [P q − P FT ][QdFT + Qdq ]
2
widgets from abroad (quota)
demand for domestic widgets
z}|{
1
60 120
= − [9 − ][
+(
9
2
7
7
1
∆PS = + [P q − P FT ][QsFT + Qsq ]
2
1
60 60
369
= + [9 − ][ + 9] =
2
7 7
98
∆GR = 0
675 369
306
153
+
+0=−
=−
=⇒ ∆TSS = −
98
98
98
49
+
z}|{
6
)] = −
675
98
Because the “benefits” of the quota only accrue to foreign producers (the government is not selling
permits to export, but giving them out for free), the quota has welfare costs (negative change in
TSS) relative to free trade. This is different from the welfare benefits of the tariff (A5).
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Practice problem: tariffs vs quotas
Q6: What if, instead of giving the license away to foreign exporters, the importing country gives
import licenses to an importer-exporter located in Home. What is the welfare cost of the quota to
Home in this case?
Simplification: assume the price that the import-export firm pays to import widgets is the
free-trade price P FT . (This is not technically true in this case, as the equilibrium price at which
Foreign sells would respond to the quota – you could derive it by shifting up Foreign demand by the
value of the quota, Q = 6, and then find that the equilibrium price would become P = 7).
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Welfare costs of quota, revisited
A6: Now, the quota rents are gonna be collected by the import-export firm based in Home. The
rents amount to the difference between the world price paid to import the good, P FT ,2 and the
equilibrium selling price in Home, P q . Therefore, the quota rents QR are given by:
QR = (P q − P FT )Q
18
60
= (9 − )6 =
7
7
So, now ∆TSS is:
from A5
z }| {
153 18
27
∆TSS = −
+
=−
49
7
49
So, the effect of the quota on welfare is still negative, but less than before (which makes intuitive
sense: the profits from the quota are not handed out to foreign firms, but they remain inside
Home).
2 Remember the simplifying assumption we made
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