economics assignment

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Case 1: pWr > p H r

Case 2: pWr < p H r

Example

Example

I Dividing (2) by (1), we derive the relative demand curve:

C Hr ≡ C H 1 /C

H 2 = p2/p1 ≡ 1/pr (4)

I Substituting (4) into the budget constraint (3), we can solve for C H1 :

C H1 = 1

2

( X H1 + X

H 2 /pr

) (5)

I Substituting (5) into (4), we can solve for C H2 :

C H2 = 1

2

( pr X

H 1 + X

H 2

) (6)

I (5) and (6) imply that utility is equal to:

U H = 1

2

( X H1 + X

H 2 /pr

) 1 2 (

pr X H 1 + X

H 2

) 1 2

(7)

ECO 364 - International Trade Fall 2018 Exchange Economies 21

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Case 1: pWr > p H r

Case 2: pWr < p H r

Example

Example

I In autarky, market clearing requires:

C H1 = X H 1 (8)

C H2 = X H 2 (9)

I Substituting (8) and (9) into the relative demand equation (4), we can solve for the autarky relative price in Home:

pHr = X H 2 /X

H 1 (10)

I Substituting (10) into (7) implies that household utility under autarky is:

U Haut = (

X H1

) 1 2 (

X H2

) 1 2

(11)

ECO 364 - International Trade Fall 2018 Exchange Economies 22

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Case 1: pWr > p H r

Case 2: pWr < p H r

Example

Example

I Now compare utility under world prices pWr in SOE (7) with autarky utility (11):

U Hsoe = 1

2

( X H1 + X

H 2 /p

W r

) 1 2 (

pWr X H 1 + X

H 2

) 1 2

U Haut = (

X H1

) 1 2 (

X H2

) 1 2

I Can show that for any endowment X H1 , X H 2 and any world relative price p

W r :

U Hsoe ≥ U H aut

with U Hsoe = U H aut only when p

W r = X

H 2 /X

H 1 = p

H aut

I Gains from trade!

ECO 364 - International Trade Fall 2018 Exchange Economies 23

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Case 1: pWr > p H r

Case 2: pWr < p H r

Example

Example

I As a numerical example, suppose X H1 = 1 and X H 2 = 1

I In autarky:

I from (10), pHr = 1 I from (11), U Haut = 1

I In SOE:

I suppose pWr = 2 or p W r =

1 2

I then from (7), U Hsoe = 1.06

ECO 364 - International Trade Fall 2018 Exchange Economies 24

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Two-country Model

I The SOE assumption may be reasonable for small trading countries

I But we are also concerned about effects of trade between larger countries

I in particular, trade by “large” countries affects world prices

I Now consider a model of two countries: “Home” and “Foreign”

I Again, endowments in each country are fixed:

I Home has X H1 units of good 1, X H 2 units of good 2

I Foreign has X F1 units of good 1, X F 2 units of good 2

I Endowments are owned by representative households in each country

I Households in each country have identical preferences

ECO 364 - International Trade Fall 2018 Exchange Economies 25

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Two-country Model

I Now suppose Home and Foreign are allowed to trade their endowments

I Key questions:

1. Will the countries trade? 2. Which country will export/import which good? 3. Which country will gain/lose from trade? 4. How much will be traded and at what prices?

ECO 364 - International Trade Fall 2018 Exchange Economies 26

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Comparative Advantage

I Key to the analysis: the concept of comparative advantage

I one of the most fundamental ideas in trade theory

I A country has a comparative advantage in a good if...

I its autarky relative price is lower than the world relative price under trade I autarky relative price = relative price that results in autarky, i.e. pHr , p

F r

I From closed economy analysis, autarky prices depend on relative endowments:

X Hr ≡ X H 1 /X

H 2 , X

F r ≡ X

F 1 /X

F 2

ECO 364 - International Trade Fall 2018 Exchange Economies 27

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Comparative Advantage

I In this model, comparative advantage is therefore equivalent to...

I having a relative endowment greater than the world relative endowment

I With two countries, this is equivalent to...

I having a relative endowment greater than that of the other country

I “Law of Comparative Advantage”:

I countries export goods in which they have a comparative advantage

I Intuition: lower autarky relative price ≈ good is relatively less scarce

ECO 364 - International Trade Fall 2018 Exchange Economies 28

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Will the countries trade?

I From analysis of the SOE case, we know that:

I Home will export good 1, import good 2 if pWr > p H r

I Home will import good 1, export good 2 if pWr < p H r

I same logic applies to exports/imports by Foreign

I Therefore to determine if trade occurs, we can consider several possible cases

ECO 364 - International Trade Fall 2018 Exchange Economies 29

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Will the countries trade?

I Case 1: pWr > p H r and p

W r > p

F r

I both countries want to export good 1, import good 2 I world markets cannot clear

I Case 2: pWr < p H r and p

W r < p

F r

I both countries want to import good 1, export good 2 I world markets cannot clear

I Case 3: pHr < p W r < p

F r

I Home wants to export good 1, import good 2 I Foreign wants to import good 1, export good 2 I potential for trade

I Case 4: pFr < p W r < p

H r

I Home wants to import good 1, export good 2 I Foreign wants to export good 1, import good 2 I potential for trade

ECO 364 - International Trade Fall 2018 Exchange Economies 30

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Will the countries trade?

I Note that Cases 3 and 4 are possible only if pHr 6= pFr I Trade therefore requires differences in autarky prices

I i.e. differences in comparative advantage

I Trade therefore requires differences in relative endowments, i.e. X Hr 6= X Fr I Key insight: in this model, countries trade only if they are different

I not enough to have different levels of endowments I differences in relative endowments are key

ECO 364 - International Trade Fall 2018 Exchange Economies 31

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Comparative vs. Absolute Advantage

I Important to differentiate comparative advantage from absolute advantage

I As an example, suppose that:

I X H1 = 100, X H 2 = 100

I X F1 = 1, X F 2 = 1

I Home has a greater endowment of both goods than Foreign

I Home has an absolute advantage in both goods

I Seems to suggest that Home should export both goods to Foreign

I But X Hr = X F r = 1:

I no difference in comparative advantage I model predicts that no trade occurs!

I Why?

I Home is richer than Foreign, hence it consumes more I but with identical preferences, same relative consumption I no need for trade

ECO 364 - International Trade Fall 2018 Exchange Economies 32

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Which country will export/import which good?

I As an example, suppose X Hr > X F r :

I Home is relatively abundant in good 1 vs. good 2 than Foreign

I Then pHr < p F r , and trade occurs at some world price p

W r ∈

( pHr , p

F r

) I Home has a comparative advantage in good 1 I Foreign has a comparative advantage in good 2

I Trade patterns are characterized by:

I Home exporting good 1 and importing good 2 I Foreign importing good 1 and exporting good 2

I Converse logic if X Hr < X F r

ECO 364 - International Trade Fall 2018 Exchange Economies 33

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Which country will gain/lose from trade?

I From SOE analysis:

I a country gains from being able to trade... I at any relative price different from its autarky relative price

I Immediately implies that both Home and Foreign must gain from trade!

I Calculation of welfare is exactly the same as in SOE given pWr

ECO 364 - International Trade Fall 2018 Exchange Economies 34

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

How much will be traded and at what prices?

I Export supply and import demand depend on world relative price pWr I For example, with pHr < p

W r < p

F r :

Home Foreign

I As pWr increases (from p H r to p

F r ):

I Home increases both exports of good 1 and imports of good 2 I Foreign reduces both imports of good 1 and exports of good 2

ECO 364 - International Trade Fall 2018 Exchange Economies 35

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

How much will be traded and at what prices?

I pWr must be such that export supply equals import demand

I For example, in the good 1 market:

ECO 364 - International Trade Fall 2018 Exchange Economies 36

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Example

I To determine trade volumes and prices, need to solve the equilibrium conditions

I Example with symmetric Cobb-Douglas utility U (C1, C2) = C 1 2

1 C 1 2

2 :

Home budget constraint: pWr C H 1 + C

H 2 = p

W r X

H 1 + X

H 2 (1)

Foreign budget constraint: pWr C F 1 + C

F 2 = p

W r X

F 1 + X

F 2 (2)

Home utility maximization: C H2 /C H 1 = p

W r (3)

Foreign utility maximization C F2 /C F 1 = p

W r (4)

Good 1 market clearing: C H1 + C F 1 = X

H 1 + X

F 1 (5)

Good 2 market clearing: C H2 + C F 2 = X

H 2 + X

F 2 (6)

ECO 364 - International Trade Fall 2018 Exchange Economies 37

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Solving for trade prices

I From (3) and (4), relative demand in each country is the same

I Therefore world relative demand is given by:

C Wr ≡ C H1 + C

F 1

C H2 + C F 2

= 1/pWr (7)

I World relative supply is:

X Wr = X H1 + X

F 1

X H2 + X F 2

(8)

I Market clearing (5) and (6) requires C Wr = X W r , which determines the world

relative price: pWr = 1/X

W r (9)

ECO 364 - International Trade Fall 2018 Exchange Economies 38

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Solving for trade flows

I Substituting (3) and (9) into (1), we can solve for C H1 and C H 2 :

C H1 = 1

2

( X H1 + X

H 2 X

W r

) C H2 =

1

2

( X H1 /X

W r + X

H 2

) I Substituting (4) and (9) into (2), we can solve for C F1 and C

F 2 :

C F1 = 1

2

( X F1 + X

F 2 X

W r

) C F2 =

1

2

( X F1 /X

W r + X

F 2

)

ECO 364 - International Trade Fall 2018 Exchange Economies 39

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Will the countries trade? Who will trade what? Which country will gain/lose from trade? How much will be traded and at what prices? Example

Solving for trade flows

I Exports (imports, if negative):

E H1 ≡ X H 1 − C

H 1 =

1

2 X H2

( X Hr − X

W r

) E H2 ≡ X

H 2 − C

H 2 =

1

2 X H1

( 1/X Hr − 1/X

W r

) E F1 ≡ X

F 1 − C

F 1 =

1

2 X F2

( X Fr − X

W r

) E F2 ≡ X

F 2 − C

F 2 =

1

2 X F1

( 1/X Fr − 1/X

W r

) I Note that pattern of trade depends on relative endowments I If X Fr < X

W r < X

H r , then E

H 1 > 0, E

H 2 < 0, E

F 1 < 0, and E

F 2 > 0

I Home exports good 1 and imports good 2 I Foreign imports good 1 and exports good 2

I If X Hr < X W r < X

F r , then E

H 1 < 0, E

H 2 > 0, E

F 1 > 0, and E

F 2 < 0

I Home imports good 1 and exports good 2 I Foreign exports good 1 and imports good 2

ECO 364 - International Trade Fall 2018 Exchange Economies 40

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Summary

I Studied trade between two countries with different endowments of two goods

I Pattern of trade determined by comparative advantage:

greater relative endowment

⇒ good is relatively less scarce ⇒ lower autarky relative price ⇒ comparative advantage

I Countries export goods in which they have a comparative advantage

I Model illustrates how both countries can gain from trade

I trade functions like a new technology I enables transformation of the endowment.... I into something preferred more by consumers

I But where do endowments come from?

I next lecture: introduce production ⇒ Ricardian models

ECO 364 - International Trade Fall 2018 Exchange Economies 41