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
