Dr. Bill W. S. Hung
1
Neoclassical Trade Theory:
The Heckscher-Ohlin Theorem
Basic Assumptions:
1. Two countries, two goods, two factors -- 2x2x2 mode
2. Identical technological in two countries
Production functions are same in two countries
3. Constant returns to scale
The sharp of PPC is unchanged
4. Two different factor abundance countries:
Labor-abundant and capital-abundant
And Two factor intensities commodities:
Labor-intensive and Capital-intensive
2
5. Identical preference and tastes
Two countries are facing the same utility functions
6. Perfect competition
Goods market and factors market
7. Factors are perfectly mobile only within a country
Factors are restricted to move across countries
8. No transportation costs
9. No restriction on trade
10. Increasing opportunity costs:
The PPF curve is concave but not a straight line.
3
Factor abundance:
Definition:
K
K
( )1  ( ) 2
L
L
Suppose:
Country 1 is relative abundance of capital
Country 2 is relative abundance of labor
or
Factor Price definition: w:
r:
L
L
( ) 1 ( ) 2
K
K
labor wage
rental rate of capital
r
r
( )  ( ) OR ( w )  ( w )
w1 w 2
r 1
r 2
The greater the relative abundance of a factor, the lower its relative price.
Since Country 1 has relative abundance of capital, thus its rental rate
of capital is relatively lower than its wage.
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Relative Factor Intensity:
Definition:
Commodity S (steel) is a capitalintensive goods.
K
K
(
)S  (
)C
L
L
Commodity C( clothes) is a
OR
L
L
( )S  ( ) C
K
K
labor-intensive goods.
Similarly in terms of factor prices:
(
r
)
w c
> (
r
)
w S
OR
(
w
) <
r c
(
w
r
)
S
5
L
The Edgeworth Box:
0s
K
C5
C4
C2
C3
C1
S5
0c
S1
K
S4
S3
S2
L
Contract curve: production efficiency locus
(Increasing opportunity cost)
6
Country I: Capital abundant country
Steel
S0
S1
K2
C3
steel
C2
S2
S3
PPFI
C1
C0
Clothes
L2
o
clothes7
Country II: Labor-abundant country
Steel
S0
S1
C3
KI
C2
S2
C1
S3
steel
C0
Clothes
PPF1I
LI
o
clothes
8
YSteel
The shape or pattern of CICs
represent the aggregate consumers’ taste
or preference
E
CI0
PX
PPF
0
Marginal rate
of transformation MRTXY
(MRT)
PY
(autarky price)
XClothes
Marginal rate
MCX PX MUX



 MRSXY Of substitution
MCY PY MUY
(MRS)
9
Combining two countries input space,
output space and consumer preference:
S
K
L I
or
L
K I
PI
PPFI
K
or
L II
I*
L
K II
II
CI0
K
PII
PPFII
0
C
L
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Increasing opportunity cost 
incomplete specialization
Different demand condition 
different autarky price ratio
Classical
analysis:
Two countries with identical PPF or
production condition are the same, there is
no incentive for trade and of course no
gains from trade.
Neoclassical Even two countries have the same
analysis
production condition, but when the
demand conditions are different the
increasing opportunity costs would drive
the two countries to trade.
The different prices in autarky indicates that there is a basis for
gainful trade between two countries.
11
Trade direction, incomplete specialization, and consumption
S
C
A
0
CI1
CI0
I
P P
PW
C
Only when PW > PI, Country-I has incentive to reallocate
the production from point A to point P and to trade with
other country (world), and through exchange (import) to
consume at point C.
12
The Heckscher-Ohlin Theorem
A country will have comparative advantage in, and therefore, will
export, that good whose production is relatively intensive in the
factor with which that country is relatively well endowed.
Labor abundant country
(i.e., China)
Capital abundant country
(i.e., U.S.A.)
Exports
Labor-intensive products
Imports
Capital-intensive products
Exports
Capital-intensive goods
Imports
Labor-intensive goods
13
(A) Trade between two countries with
Identical Demand & Different Production Structures:
Country I: capital abundant
The H -O Model
Country II: labor abundant
Good X-clothes: labor-intensive
Good Y-steel: capital-intensive
Good Y-Steel
(PX/PY)1 C0
y3
C1
e’
I’s exports (Y)
e1
CII’, cI’
y4,y2
II’s imports (Y)
EII
y1
(PX/PY)2
E’
PPFI
0
x3
I’s imports (X) x2,x4
PPFII
II’s exports (X)
x1
(PX/PY)3
Good X-Clothes
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The H-O Model: alternative case: Country I: capital abundant
(different consumption level)
Country II: labor abundant
Good Y-Steel
Good X: labor-intensive
(PX/PY)1
Good Y: capital-intensive
e’
I’s exports
I
I’s imports
e
C’I
C4
C’II
C3
II’s imports
C2
C1
E
II’s exports
(PX/PY)II
E’
PPFII
PPFI
0
II
(PX/PY)3
Good X-Clothes
15
(B) Trade between two countries with
Identical PPFs & Different Demand Conditions:
Good Y-Steel
C’
y2
(PX/PY)1
S2
PPFI
I’s imports (Y)
y1
E1
y3
S1
EI’, eI’
y4
II’s exports (Y)
e
c’
y5
W2
W1
PPFII (P /P )
X Y 2
0
x2
x1
I’s exports (X)
x3
x4
x5
(PX/PY)3
Good X-Cloth
II’s imports (X)
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(C) No Trade between two countries with
Identical PPFs & identical Demand Conditions:
Y-Steel
Community Indifferent
utility curves
A
E
CI2
CI1
B
CI0
No Incentive
to trade
Why?
PX
PPF
PY
(autarky price)
I,II
0
XClothes
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Gains From Trade
Good Y
C
I1
A
I0
P
PW
0
Good X
Good Y
3 important assumptions:
1. No costs of factor mobility
P*
2. Full employment of factors
3. No redistribution of income once trade
A*
C*
I0
0
*
I1
*
PW
Good X
open (the different curves can show
welfare changes)
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Gains from trade and specialization
Good Y
E  C: consumption gains
(or gains from exchange)
C’
C
E  E’ and C  C’:
production gains (or
gains from specialization)
CI3
E
CI1 CI2
PX
E’
( P )’
X
0
PY
Autarky price
PY
( P )’
X
PY
World
trade price
Good X
19
Concept Check:
Can you show that the production at less than
complete specialization leads to a lower level of
welfare than at complete specialization.
20
The Leontief Paradox
Leontief statistic is defined as
(K/L)M
(K/L)X
Leontief’s result were startling. He found that the hypothesized
reduction of US export would release $2.25 Million worth of capital
And 182.3 year of labor-time, for a (K/X)x of approximately $14,000
Per labor-year. On the import side, to produce the foregone
import would require $3.09 million worth of capital and 170,0 years of
Labor-time, yielding a (K/L)M of approximately $18,200 per labor-year.
Thus, the Leontief statistic for the US was 1.3 (= $18,200/$14,000),
Unexpected for a relatively capital-abundant country.
What are the implications of the Leontief Paradox?
21
Invalid assumptions to Heckscher-Ohlin Model
1. Demand reversal
2. Factor-intensity reversal
3. Transportation costs
4. Imperfect competition
5. Immobile or commodity-specific factors
6. US tariff structure
7. Different skill levels of labor
8. The role of natural resources
others
9. Income inequality
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1. The Factor Price Equalization Theorem:
Given all the assumptions of the H-O model, free trade will
lead to the international equalization of individual factor
prices.(The impact of trade on factor prices)
2. The Stolper-Samuelson Theorem:
Free trade benefits the abundant factor and harms the scarce
factor.(The impact of trade on income distribution)
3. The Rybczynski Theorem:
At constant world prices, if a country experiences an increase
in the supply of one factor, it will produce more of the product
intensive in that factor and loss of the other.(The effect of
economic growth on trade)
23
Factor price equalization theorem
When home and foreign country trade with each
other, the relative prices of goods converge. This
convergence, in turn, causes convergence of the
relative prices of factors.
Before trade: (w/r)II > (w/r)world > (w/r)I
(Country-I wage is lower)
After trade: (w/r)I = world factor price = (w/r)II
because the goods prices are equalized in two countries
Example: When trade open between China and Hong Kong,
Wages increase in China, Wage decline in Hong Kong
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After trade adjustment in Country II (labor-abundant) case:
Producer adjusts output due to relative factor prices changes.
K
(K/L)s1
K
(w/r)1
(K/L)S0
IS0
IC1
IC0
(w/r)0
IS1
(K/L)c1
( K/L)c0
(w/r)1
Clothes
L
Steel
(w/r)0
L
(w/r)0   (w/r)1 Increase produce clothes
c Ic
i.e.,
I
When
r,
w
0
1
(labor-abundant)
Decrease produce steel
i.e., Is0 Is1
Both industries now employ more capital
In Country II :
25
Trade Condition
Pc/Ps
(Pc/Ps)II < (Pc/Ps) < (Pc/Ps) I
(Pc/Ps)I
world trade price
Pc/Ps
(w/r)II < (w/r)
(Pc/Ps)II
0
(w/r)II
w/r
(w/r)I
w/r
<(w/r)I
Labor
Capital
abundant
abundant
country
country
One important assumption is market perfect competition
But in real world it seems FPE theorem does not work well.
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The Stolper-Samuelson Theorem
With full employment both before and after trade, the
increase in the price of the abundant factor and the fall
in the price of the scare factor because of trade imply
that the owners of abundant factor will find their real
incomes rising and the owners of scarce factor will
find their real incomes falling.
In labor-abundant country:
if price of labor-intensive goods  ---> wage 
---> producer of labor-intensive goods and labor income 
In capital-abundant country:
if price of capital-intensive goods  ---> capital rent 
---> producer of capital-intensive goods and capital owner income 
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Steel
PC
( PS ) II
PC
( PS ) II
<
A to P :
PC
( P ) World price
S
PC  W 
PS 
P to T :
A
r
PC 

W
(PS+ t) 

r 
T
P
[Pc/(Ps+ tariff )]w
Country II’s PPF
0
PC
( P )World price
S
Clothes
Example: Tariffs can increase the trade prices. (From red to green line)
i.e., production point shifts from P point to T point
Policy implication:
Producer of steel and the capital owner will gain from the tariff.
(Pro-tariff or welcome any protection).
Producer of clothes and the labor will loss from the tariff.
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(Against tariff or reject any protection)
Rybczynski Theorem: The effect of factor endowment change
Example: The Growth Effects of Labor-Market Adjustment and
Migration ---Labor Endowment moves out, PPF shifts in.
Autos
(PT/PA)
(PT/PA)
a1
a0
0
t1
t0
Textiles
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Rybczynski Theorem:
Labor endowment increases, PPF shifts out
Autos
(PT/PA)
(PT/PA)
a0
a1
0
t0
t1
Textiles
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Exercise:
One of the important changes in the world economy over the
past three decades has been the rapid increase in capital
investment in the countries of the Pacific Basin (notably Japan,
Korea).
What are the implications of this investment for the
commodity patterns of trade of these two countries, say, with
respect to the United States? Explain.
(Hint: Think about Rybczynski theorem)
31
Invalid assumptions to Heckscher-Ohlin Model
Case of Demand Reversal
Steel
Prediction of trade pattern from H-O model
Country 2: exports C and imports S
Country 1: exports S and imports C
Now Country-1 prefers more steel
But Countyr-2 prefers more clothes
C1
Country 1’s
imports
of S
CI11
Demand Reversal outcome:
Country 2: now exports S and imports C
Country 1: now exports C and imports S
CI1
A1
0
P1
Country 1’s
exports of C
(Pc/Ps) world price
CI20
CI21
P2
Country 2’s
exports of S
A2
PPF1
Country-1: capital abundant
Country-2: labor abundant
PPF2
Country 2’s
imports of C
C2
Cloth
Steel: capital-intensive
32
Clothes: labor-intensive
Case of Factor-intensity: No matter factor prices change,
factor relative requirement ratio is always unchanged.
If steel is capital-intensive, cloth is labor-intensive,then at any factor
prices ratio, the factor input ratio is always (K/L)s > (K/L)c
At (w/r)2 :
K
W
( r) 2
K
( L ) S2
(
K
( L ) C2
K
) >
L S2
(
K
)
L C2
K
( L) S1
F
At (w/r)1 :
(
G
K
) >
L S1
(
K
)
L C1
K
(L ) C1
A
B
Steel
Cloth
0
W
( r) 1
Labor
Steel: capital-intensive
Clothes: labor-intensive
33
Invalid assumptions to Heckscher-Ohlin Model
Case of Factor intensity Reversal
K
(w/r) 2 (k/L) C2
At (w/r) 2 :
(k/L) S2
(
K
K
)
> ( )
L C2
L S2
F
At (w/r) 1 :
(k/L) S1
(
G
K
K
)
< ( )
L C1
L S1
Steel
B
0
A
(k/L) C1
Clothes
(w/r) 1
L
34
Question:
Can you give any example of tradable goods
that may have such factor-intensity-reversal
problem?
Exercise:
Show in a graph to illustrate that factorintensity reversal can also occur of the two
industry isoquants do not cross each other but
are tangent to one another.
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