Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

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Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model The Explanation of International Trade: Differences across countries in relative abundance of factors of production. Assumptions: Identical Technologies Identical Demand Patterns The HOS Model:

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Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model. The HOS Model:. The Explanation of International Trade: Differences across countries in relative abundance of factors of production. Assumptions:Identical Technologies Identical Demand Patterns. Relative Factor - PowerPoint PPT Presentation

Transcript of Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Page 1: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Factor Proportions and the Structure of Trade: HOS-

Krugman-DFS Model

The Explanation of International Trade: Differences across countries inrelative abundance of factors of production.

Assumptions: Identical TechnologiesIdentical Demand Patterns

The HOS Model:

Page 2: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

RelativeFactorIntensity

:

Full employment:

Y

X

AB*YLa

L

XKa

KXLa

LYK

XK

a

a

YL

XL

a

aL constant

K constant

Structural Bias: The Transformation Curve( = ABC) shifts asymmetrically with unbalanced changes in K and L. A Rise in K, with no change in L, leads to an increase(fall) in X (Y)).

C

YL

XL

YK

XK

a

a

a

a

YL

YK

XL

XK

a

a

a

aor

D

B

YKa

K KYaXa

LYaXa

YKXK

YLXL

E

F

Page 3: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

AT POINT F

1) Labor is unemployed: W=0.(2) The X-industry is active The Y-industry is inactive. Therefore:

AT POINT A

1) Capital is unemployed: R=0.(2) Y-industry is active X-industry is inactive. Therefore:

Y

X

a

a

P

P

a

PRW

YPRaWa

XPRaWa

YK

XK

Y

X

XK

X

YYKYL

XXKXL

,0

0

0

Page 4: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

AT Point A (continue):

0

,0

0

0

Y

X

a

a

P

P

a

PWR

YPRaWa

XPRaWa

YL

XL

Y

X

YL

Y

YYKYL

XXKXL

Page 5: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

At Point B

Y

x

P

P

YK

XK

a

a

YL

XL

a

a

Y

X

Relative Supply

0,0

YX

a

a

P

P

a

a

PRaWa

PRaWa

YL

XL

Y

X

YK

XK

YYKYL

XXKXL

Page 6: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Two Countries: H and F: H is more capital abundant.

H’s Relative Supply is biased towards X:

Y

x

P

P

YK

XK

a

a

YL

XL

a

a

FRS

HRS

FH

FH

YY

XX

Page 7: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Free Trade and Autarkic Equilibria

Y

x

P

P

YK

XK

a

a

YL

XL

a

a

FRS

HRS

FH

FH

YY

XX

3 2

1

2=Free trade1=autarky in H3=autarky in F

FH

HH

F

FH

H

HH

FH

FH

YY

Y

Y

X

Y

X

YY

XX

)1(

Page 8: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Full Employment Supply of X and Y:

XKYLYKXL

XLXK

XKYLYKXL

YLYK

YKXK

YLXL

aaaa

LaKaY

aaaa

KaLaX

KYaXa

LYaXa

Page 9: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

The Heckscher-Ohlin Proposition #1:Any country will export the good

which makes intensive use in its production of relative abundant factor supply.

Page 10: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

YYKYL

XXKXL

PRaWa

PRaWa

Full Employment Factor Prices:

Page 11: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Income Distribution and International Trade

R

W

XK

X

a

P

YK

Y

a

P

XL

X

a

P

XL

XK

a

a

YL

YK

a

a

A

BB’

D C

ABC=factor price frontier

A rise in XP (X is capital intensive) will raise R and decrease W.

risesPX

YL

Y

a

P Industry X-Line

Industry Y-Line

Page 12: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

The Heckscher-Ohlin Proposition #2(dual to Proposition #1):

Free trade causes an increase in the factor price of the factor of production which is used intensively in the export industry and a fall in the factor price used intensively in the import competing industry.

Page 13: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Factor Price Equalization: Failures

Two ways to generate a failure of FPE:

• Assume that factor proportions are sufficiently different that they are outside the FPE set.

• Introduce costs to international trade, which could have strong effect on trade volume.

Page 14: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Romalis (AER, March 2004, 94, No.1, 67-97)

• Generalizes a Heckscher-Ohlin model of Dornbusch-Fischer-Samuelson framework, and explains trade structure;

• Assumes a many-country version of the Heckscher-Ohlin model;

• Integrates this with Krugman intra-industry trade;

• Allows for transportation costs.

Page 15: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

The Model

There are 2M countries, M each in the North and South.

Southern variables are marked with an asterisk.

There are two factors of production: skilled and unskilled labor.

The proportion of skilled labor is

Northern countries are abundant in skilled labor

*

Page 16: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Preferences

1)(

)(ln)(

1

0

1

0

dzzb

dzzQzbU

Page 17: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Monopolistic Competition

1

1)(

0

*

)),(()),((

),()(

)]()([)(

)(

),(

wsizqizqTC

diizqzQ

znznMzN

zN

izq

SS

zND

S= Production of variety i

Number of of varieties in industry z

Sub-utility function

Fixedcost

DualUnit cost

Number ofcountries

Page 18: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Transportation costs

1 Units of a good must be shipped for 1 unit to arrive in any other country

Page 19: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Equilibrium in an industry

Solve for the share of world production that each country commands, conditional on relative production costs. Countries with lower costs capture larger market shares.

1

1

)('

1

)('

1

)'),(()(

'),(

),(),(

1

1

zIi

zIi

D

diizpzG

diizp

izpizq

Consumer price

IdealPrice index

Page 20: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

National income and Spending

wsY )1(

A constant fraction of income b(z) is spent on industry z

Page 21: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model
Page 22: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

World Demand

111

11

)*

(*)()()1()(

])*(*

)()1([1

11

G

pbYM

G

pbYM

G

pbYpq

pMn

pnMnpG

S

Page 23: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

North-South relative price

1

1

)1(1,*

*)(

)1(*

1)(

MFp

pp

YYMW

qq

wszp

SS

p

Page 24: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

If is low, (1) is the solution;if is high, (2) is the solution

0*,)1(*

*)(*,0

0*,)1(

*)(

np

YYbnn

np

YYbn

p

(1)

(2)

p

Page 25: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

General Equilibrium

***(

*1))(1

()()1(

*))(1

()(*

1

1)()()1(1

)()(1

1

0

1

0

1

0

1

0

SS

S

qpnnpqM

npq

dzzM

Wzzb

dzzM

Wzzbs

dzzWzbzw

dzzWzzbs

Page 26: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Special Case

The Dornbusch-Fischer-Samuelson Model is a special case with no transportation costs

Perfect competition1

0

Page 27: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Transport costs

The addition of the transport costs leads a stark structure of production and trade:

Share ofindustry

Skill intensity of industry (z)

Unskilled goods produced in southNon-traded goods Produced In North

Non-traded goods Produced In South

Skill-intensive goods Produced In North

Page 28: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model

Producer prices

p=factory-gate price domestically;

p Sold in M-1 markets abroad