Factor Proportions and the
Structure of Trade: HOSKrugman-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
Intensity
a XK a XL
a XK aYK
or


a XL aYL
aYK aYL
Full employment:
a XL X  aYLY  L
Y
K
aYK
L
aYL
a XK X  aYK Y  K
E
A
K constant
B*
a XK
aYK
B
L constant
a
D
a
F
L
XL
C
YL
K
a XK
X
a XL
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)).
AT POINT F
1) Labor is unemployed: W=0.
(2) The X-industry is active
The Y-industry is inactive. Therefore:
Wa XL  Ra XK  PX  X  0
WaYL  RaYK  PY  Y  0
W  0, R 
AT POINT A
1) Capital is unemployed: R=0.
(2) Y-industry is active
X-industry is inactive. Therefore:
PX
a XK
PX a XK
X

 
PY aYK
Y
AT Point A (continue):
Wa XL  Ra XK  PX  X  0
WaYL  RaYK  PY  Y  0
PY
R  0, W 
aYL
PX a XL
X

 0
PY aYL
Y
At Point B
Wa XL  Ra XK  PX
WaYL  Ra YK  PY
Px
PY
a XK
aYK
a XK PX a XL


aYK
PY aYL
X  0, Y  0
Relative
Supply
a XL
aYL
X
Y
Two Countries: H and F: H is
more capital abundant.
H’s Relative Supply is biased
towards X:
Px
PY
a XK
aYK
a XL
aYL
RS F
RS H
XH XF
Y H Y F
Free Trade and Autarkic
Equilibria
Px
PY
a XK
aYK
a XL
aYL
2=Free trade
1=autarky in H
3=autarky in F
3
2
RS F
RS H
1
XH XF
Y H Y F
H
F
XH XF
H X
H X

 (1   ) F
H
F
H
Y Y
Y
Y
H
Y
H  H
Y Y F
Full Employment Supply of X and Y:
a XL X  aYLY  L
a XK X  aYK Y  K
aYK L  aYL K
X
a XL aYK  aYL a XK
a XK K  a XL L
Y
a XL aYK  aYL a XK
The Heckscher-Ohlin Proposition #1:
Any country will export the good
which makes intensive use in its production
of relative abundant factor supply.
Full Employment Factor Prices:
Wa XL  Ra XK  PX
WaYL  RaYK  PY
Income Distribution and
International Trade
W
PX
a XL
PY
aYL
A
PX rises
Industry X-Line
B
a XK
a XL
D
B’ Industry Y-Line
a
C
YK
aYL
PX
a XK
R
PY
aYK
ABC=factor price frontier
A rise in PX (X is capital intensive) will raise R and decrease W.
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
U   b( z ) ln Q ( z )dz
0
1
 b( z )dz  1
0
Monopolistic Competition
S
q ( z, i)
N ( z) 
= Production of variety i
Number of of varieties in industry z
N ( z )  M [n( z )  n ( z )]
*
1
Number of
countries

 N (z) D

Sub-utility function
Q( z )    q ( z , i ) di 
 0

TC (q S ( z , i ))  (  q S ( z , i )) s w1 Dual
Fixed
cost
Unit cost
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.

Consumer
price
1
1

p ( z , i ) 
q ( z, i) 
D

 p( z, i)
1
di '
i 'I ( z )
G( z)  (

 p( z, i)
1
di ')
1
1
i 'I ( z )
Ideal
Price index
National income and Spending
Y  s  (1   ) w
A constant fraction of income b(z) is spent on industry z
World Demand
G  [np1  ( M  1)n( p )1
1
Mn * ( p * )
]
1
1
p 1
p 1
p 1
pq  bY ( )  ( M  1)bY ( )  ( M )bY * ( )
G
G
G*
S
North-South relative price p
  1
p( z ) 
s w
 1
q S  q S *   (  1)
W  M (Y  Y *)
p
p
, F  1  ( M  1) 1
p*
If is low, (1) is the solution;
if p is high, (2) is the solution
p
(1)
(2)
b(Y  Y *)
n
, n*  0
p (  1)
b(Y  Y *)
n  0, n* 
, n*  0
p * (  1)
General Equilibrium
1
1
0 s zb( z )W ( z )dz  
1
1
0 w (1  z )b( z )W ( z )dz  1  
1
1
1
zb
(
z
)
W
(
 ( z )) dz   *
0 s *
M
1
 (1 ) zb( z )W (
0
1
 ( z )) dz  1   *
M
npq S

M (npq S  n * p * q S *
Special Case
The Dornbusch-FischerSamuelson Model is a
special case with no
transportation costs
 1
Perfect competition
 0
 
Transport costs
The addition of the transport costs leads a
stark structure of production and trade:
Skill intensity of industry (z)
Share of
industry
Unskilled goods produced in south
Non-traded goods
Produced In South
Skill-intensive goods
Produced In North
Non-traded goods
Produced In North
Producer prices
p=factory-gate price
domestically;
p
Sold in M-1 markets abroad