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:

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

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

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

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

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

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(

Full Employment Supply of X and Y:

XKYLYKXL

XLXK

XKYLYKXL

YLYK

YKXK

YLXL

aaaa

LaKaY

aaaa

KaLaX

KYaXa

LYaXa

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

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

YYKYL

XXKXL

PRaWa

PRaWa

Full Employment Factor Prices:

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

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.

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.

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.

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

*

Preferences

1)(

)(ln)(

1

0

1

0

dzzb

dzzQzbU

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

Transportation costs

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

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

National income and Spending

wsY )1(

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

World Demand

111

11

)*

(*)()()1()(

])*(*

)()1([1

11

G

pbYM

G

pbYM

G

pbYpq

pMn

pnMnpG

S

North-South relative price

1

1

)1(1,*

*)(

)1(*

1)(

MFp

pp

YYMW

qq

wszp

SS

p

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

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

Special Case

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

Perfect competition1

0

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

Producer prices

p=factory-gate price domestically;

p Sold in M-1 markets abroad