EC391
International Trade
Endowment Economies
Stefania Garetto
Introduction
Introduction
Setup
Autarky
Two Countries
2 / 19
What is an endowment economy?
It is an economy where each agent (individual, country) is exogenously
endowed with given quantities of consumption goods.
In an endowment economy:
• production is taken as given;
• agents exchange goods if their preferred (utility-maximizing) bundle
differs from the endowments.
Setup
Introduction
Setup
Autarky
Two Countries
3 / 19
• 2 goods: clothes (c) and food (f )
• a country has a fixed endowment of the two goods: (Ec, Ef )
E
EC
EF
XC
XF

Setup
Introduction
Setup
Autarky
Two Countries
4 / 19
• 2 goods: clothes (c) and food (f )
• a country has a fixed endowment of the two goods: (Ec, Ef )
E
EC
EF
XC
XF
• the country is populated by a large number of consumers with identical
homothetic preferences⇒ we study the aggregate demand of the
country as the demand of a consumer that owns the aggregate
endowment.
Autarky: Consumer Problem
Introduction
Setup
Autarky
• Consumer Problem
• RD and RS
Two Countries
5 / 19
• A country is in autarky when it is completely closed to international
trade.
⇓
The country must consume its endowment: xc = Ec and xf = Ef .
• The equilibrium relative price is given by the marginal rate of
substitution computed at the endowment.
E
XC=EC
XF=EF
XC
-pc/pf
XF
Autarky: Relative Demand and Relative Supply
Introduction
Setup
Autarky
• Consumer Problem
• RD and RS
Two Countries
6 / 19
• Under autarky, relative supply is fixed.
• The intersection of relative demand and relative supply determines the
equilibrium relative price.
pC/pF
A
EC/EF
pAC/pAF
XC/XF
RS
RD
Two-countries Equilibrium: Setup
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
7 / 19
• There are two countries (country 1 and country 2). Each of them is an
endowment economy as described above.
• Preferences are homothetic and identical across countries, but relative
endowments differ across countries. Assume WLOG
Ec1
Ef1
>
Ec2
Ef2
.
• A country’s income is given by the value of its endowment:
Ii = pciEci + pfiEfi
for i = 1, 2. Since relative endowments differ across countries, the two
countries have different income levels.
• Under homothetic preferences, relative demand is independent of
income, so the two countries have the same relative demand.
• Relative supply is given by the relative endowments, so relative supply
differs across countries.
Two-countries Equilibrium: Autarky
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
8 / 19
• Under autarky, each country consumes its endowment.
• As a result:
pc1
pf1
< pc2
pf2
pC/pF
E1C/E1F
p2C/p2F
XC/XF
RS2
RD
RS1
p1C/p1F
E2C/E2F
Two-countries Equilibrium: Free Trade
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
9 / 19
• If relative prices under autarky differ across countries, the two countries
have an incentive to trade!
• Under free trade, relative prices must be common across countries
◦ Denote free trade relative prices as
pTc
pT
f
• Equilibrium relative prices under free trade are such that ‘world’ relative
demand is equal to ‘world’ relative supply:
◦ Homothetic preferences⇒ RD is the same in the two countries, and
it is also equal to the RD for the aggregate of the two countries;
◦ World relative supply = world relative endowments:
Ewc
Ewf
=
Ec1 + Ec2
Ef1 + Ef2
• As a result:
pc1
pf1
<
pTc
pT
f
< pc2
pf2
Two-countries Equilibrium: Free Trade
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
10 / 19
pC/pF
E1C/E1F
p2C/p2F
XC/XF
RS2
RD
RS1
p1C/p1F
E2C/E2F
RSW
EWC/EWF
pTC/pTF
Comparative Advantage in an Endowment Economy
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
11 / 19
Differences in relative prices under autarky are related to the concept of
comparative advantage.
Definition. A country has a comparative advantage in a good if the relative
price of the good under autarky is lower than its relative price under free
trade.
Law of Comparative Advantage. A country exports the goods in which it
has a comparative advantage.
In this simple model, differences in relative endowments across countries
are a source of comparative advantage.
Country 1 has a comparative advantage in c, the good in which it is relatively
abundant, and similarly Country 2 has a comparative advantage in f .
Questions
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
12 / 19
• Is there an incentive to trade if the two countries have the same
endowments?
• Is there an incentive to trade if the two countries have different
endowments, but the same relative endowments?
Country 1 under Autarky
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
13 / 19
E1

E1F
XC
-p1c/p1f
E1C
X1F
XF

Country 1: comparison between autarky and free trade prices
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
14 / 19
E1

E1F
XC
-p1c/p1f
E1C
X1F
-pTc/pTf
XF
pc1
pf1
<
pTc
pT
f
Country 1 Trade Flows
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
15 / 19
E1E1F
XC
-p1c/p1f
C1
E1C
X1F
-pTc/pTf
X1C
X1F
XF
Ec1 −Xc1 = exports of clothes
Xf1 − Ef1 = imports of food
Country 2 under Autarky
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
16 / 19
E1
E2C
E2F
XC
-p2c/p2f
XF
Country 2: comparison between autarky and free trade prices
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
17 / 19
E1
E2C
E2F
XC
-p2c/p2f -pTc/pTf
XF
pTc
pT
f
< pc2
pf2
Country 2 Trade Flows
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
18 / 19
E1
E2C
E2F
XC
-p2c/p2f
C1
X2C
X2F
-pTc/pTf
XF
Xc2 − Ec2 = imports of clothes
Ef2 −Xf2 = exports of food
Trade Flows: Summary
Introduction
Setup
Autarky
Two Countries
• Autarky
• Free Trade
• Trade Flows
19 / 19
• Trade flows follow the law of comparative advantage:
◦ Each country exports the good in which it has a comparative
advantage.
◦ In an endowment economy: each country exports the good in which
it is relatively abundant, and for which the autarky price is lower than
the price under free trade.
• In this example: Country 1 exports c and country 2 exports f .