BA 187 – International Trade
Hecksher-Ohlin Model & Relative
Factor Endowments
1
Hecksher-Ohlin Model
• Two countries, two goods, X and Y, and two factors of
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•
•
•
•
•
•
prod’n, labor, L and capital, K. (2 x 2 x 2 model)
Technology identical between countries.
Production functions for both goods exhibit constant
returns to scale.
Each commodity has a different factor intensity, which are
not affected by relative factor prices.
Tastes and preferences identical between countries.
Perfect competition in both industries and both countries.
Factors are perfectly mobile within countries but perfectly
immobile between countries.
No transportation costs or tariffs or other barriers to trade.
2
Production Functions, Isoquants, and
Relative Factor Prices
3
Production Theory
• Production Function – Q = F(K, L)
– Shows amount of output produced for given inputs of capital & labor.
– Assume exhibits constant returns to scale (CRS), diminishing marg. returns.
• Production Isoquant – Q0 = F(K, L)
– Shows the various combination of capital & labor that can be used to produce a
chosen level of output, Q0.
– Bowed shape result of diminishing marginal returns as substitute capital for
labor to keep production level constant.
•
Isocost Line & Production Equilibrium
– Combination of K & L choose to produce any given level output Q depends on
relative prices of capital and labor, i.e. w/r, the relative wage.
– Isocost line shows all comb. of K & L with same total cost given w and r.
– Firm will choose production point (K & L) which minimizes total cost for any
desired level of output Q0.
•
With CRS prod’n function, these points fall on a straight line from origin.
•
Slope of this line depends on relative wage vs. return on capital.
4
Isoquants, Isocosts & Production
•Isoquants show all combinations of K & L
that produce certain amount of Good X.
1. Good X is “ labor-intensive”.
2. Good Y is “ capital-intensive”.
•Isocost line shows all combinations of K & L
with same cost given w and r.
Given (w/r)
–Slope is relative factor price, w/r.
Capital, K
•Prod’n Points for Good X where Isoquant tangent
[K/L] Y
to Isocost Line. Assuming CRS so these points are
on ray from origin.
2Y0
•Can do same exercise for Good Y.
Y0
[K/L] X
2X0
Note that Labor- or Capital-intensity of a good is
Determined by shape of Isoquants, i.e. prod’n.
X0
Relative Factor Price, (w/r)0
Labor, L
5
Factor Endowments and
Factor Intensities
6
Factor Intensities & Factor Abundance
• Factor Intensities: (A property of production technologies)
– A Good Y is said to be capital-intensive if the ratio of capital-labor in its
production is higher than the ratio of that used to produce Good X, at any
relative factor price ratio. i.e. (K/L)Y > (K/L)X .
– In a two good world, if Good Y is capital-intensive then Good X will be
labor-intensive, at any relative factor price ratio.
•
Factor Abundance: (A property of factor endowments)
– Physical Units definition: A nation is capital-abundant if its capital/labor
ratio (K/L) is larger than that of the other nation.
– Relative Factor Price definition: A nation is capital-abundant if its ratio
of wage rate for labor to rental price of capital (w/r) is larger than that of
the other nation.
– We assume these two def’ns are equivalent (although they aren’t exactly).
•
H-O model combines both factor intensities of goods and relative
factor abundance of nations to determine trade patterns.
7
Relative Factor Costs & Intensities
1. Good X is “ labor-intensive”.
2. Good Y is “ capital-intensive”.
Capital, K
Given (w/r) “high”
Given (w/r) “low”
[K/L]highY
Capital, K
[K/L]lowY
2Y0
2Y0
Y0
[K/L]lowX
[K/L]highX
Y0
2X0
2X0
X0
X0
Relative Factor Price, (w/r)low
Labor, L
Labor, L
Relative Factor Price, (w/r)high
8
Factor Prices and Input Choices
Note from previous slide:
Wage-rental ratio,
w/r
1.
Good X
Good Y
2.
(w/r)high
(w/r)lo
w
3.
Capital-Labor Ratio
K/L
As (w/r) increases from
“low” to “high”, K/L ratio
used to produce Good X
increases. The same is true
for Good Y.
Implies there is an upwardsloping relation between
relative factor price w/r and
K/L used in production of
each good.
Also, at any level of (w/r)
Good Y always uses higher
K/L in prod’n. Thus its
relation is below that for
Good X.
9
Deriving a Nation’s PPF in
the H-O Model
10
Edgeworth Box – Joint Prod’n
Labor, L
Capital, K
Labor, L
Y0
[K/L] Y
X0
2Y0
2Y0
2Y0
Labor, L
[K/L] Y
Y0
Capital, K
Y0
[K/L] Y
[K/L] Y
2X0
[K/L] Y
Capital, K
Capital, K
2Y0
Capital, K
Labor, L
Y0
[K/L] X
X0
Labor, L
Y0
2X0
Capital, K
2Y0
[K/L] X
Labor, L
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Allocation of Factors to Goods Prod’n
Labor, L
OY
Capital, K
OY
[K/L]HY
2Y
Total
Capital
1Y
[K/L]H
[K/L]HY
X
Capital, K
[K/L]HY
1X
OX
2X
Labor, L
Total Labor
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Allocation of Factors & Nation’s PPF
Y
1. Box below shows allocation of capital and labor
to each good, for a given w/r ratio.
2. Implicit in this allocation are prod’n levels of
both Y =QY(KY, LY) and X =QX(KX, LX).
3. Varying w/r picks out different allocations and
prod’n points, tracing out PPF.
Capital, K
LY
PPF
B
OY
X
B
[K/L]HX
KX
KY
[K/L]HY
OX
LX
Labor, L
13
Factor Endowments and
Factor Intensities in the H-O Model
of Trade
14
Relative Factor Endowments
Estimates for 1966
Capital/Labor
Capital/Land
Labor/Land
($ per worker)
($ per hectare)
(workers per hectare)
Argentina
$2,827.0
$101.7
.036
Australia
7,415.5
67.2
.009
Canada
10,583.1
198.0
.019
France
6,878.5
3,136.9
.456
Hong Kong
1,368.5
90,739.1
66.304
Japan
3,358.5
5,286.5
1.574
Mexico
1,684.8
122.9
.073
United Kingdom
4,359.6
5,169.8
1.186
United States
10,260.9
1,058.6
.103
Country
Source: Bowen, Leamer, & Sveikauskaus, AER 1987
15
Factor Endowments & Intensities
1. Good X is “ labor-intensive” in both nations.
2. Good Y is “ capital-intensive” in both nations.
Capital, K
Foreign, Capital-Abundant
K/L high & (w/r) high
Home, Labor-Abundant
K/L low & (w/r) low
[K/L]FY
Capital, K
[K/L]HY
2Y
2Y
1Y
[K/L]HX
[K/L]FX
1Y
2X
2X
1X
1X
Relative Factor Price, (w/r)Home
Labor, L
Labor, L
Relative Factor Price, (w/r)Foreign
16
Factor Prices and Input Choices
Note from previous slide:
Wage-rental ratio,
w/r
1.
Good X
Good Y
2.
3.
Capital-Labor Ratio
K/L
As (w/r) increases from
Home to Foreign, K/L ratio
used to produce Good X
increases. The same is true
for Good Y.
Implies there is an upwardsloping relation between
relative factor price w/r and
K/L used in production of
each good.
Also, at any level of (w/r)
Good Y always uses higher
K/L in prod’n. Thus its
relation is below that for
Good X.
17
Differences in PPF’s across Nations
in the H-O Model
18
Labor-Abundant Nation’s PPF
Y
1. Box below shows allocation of capital and labor
to each good, for a given w/r ratio.
2. Implicit in this allocation are prod’n levels of
both Y =QY(KY, LY) and X =QX(KX, LX).
3. Varying w/r picks out different allocations and
prod’n points, tracing out PPF.
Capital, K
LY
PPFHome
B
OY
X
B
[K/L]HX
KX
KY
[K/L]HY
OX
LX
Labor, L
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Capital -Abundant Nation’s PPF
Y
1. Assume Foreign has more capital than labor .
PPFForeig
Capital, K
LY
OY
n
PPFHome
B
X
[K/L]HY
B
[K/L]HX
KX
OX
KY
LX
Labor, L
20
Equilibrium in the
Hecksher-Ohlin Model
21
Differing Technology/Endowments
Assuming identical utility function for Home & Foreign
Y
Home & Foreign PPF’s differ due to differences in
technology or factor endowments.
QF
AF
Autarky Equilibrium at AH and AF
C*
Opening trade changes relative prices
New equilib. consumption at C*.
Each country has different prod’n ;point.
AH
QH
(PX/PY)
PPFF
PPFH
*
X
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Hecksher-Ohlin Theorem
•
Countries will export goods that use their abundant factors
intensively and import those goods that use their scarce
resources intensively.
–
Previous slides showed how factor endowments determine shape of
each nation’s PPF.
Assuming identical utilities, then Hecksher-Ohlin theorem result
arises for the pattern of trade.
–
•
Effects of trade:
1.
2.
3.
Trade results in mutual gains.
Countries reallocate factors to increase specialization in goods that
use their abundant factors intensively.
Relative commodity prices are equalized across nations after trade.
(This will have implications for relative factor prices across nations also.)
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Net Export (+) of Factor Services - 1967
Factor of Prod’n
U.S.
Germany
Japan
Mexico
Philippines
Capital Stock
+
-
-
-
-
Total Labor Force
-
-
+
+
-
Professional/technical labor
+
+
+
+
-
Managerial Labor
-
+
+
+
-
Clerical workers
-
+
+
+
-
Sales workers
-
-
-
+
+
Service workers
-
-
-
+
+
Agricultural workers
+
-
-
+
+
Production workers
-
+
+
-
-
Arable Land
+
-
-
+
+
Forest Land
-
-
-
+
-
Pasture Land
-
-
-
+
-
Source: Bowen, Leamer, & Sveikauskaus, AER 1987
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Trade, Distribution, and Welfare in
the H-O Model
25
Relative Product Prices & Factor Prices
• Relative product price (PX/PY) is linked to relative factor
returns (w/r) in the H-O model by the mobility of factors
between industries within a country.
• Assume relative price of X rises in Home from opening trade.
– Higher (PX/PY) leads Home producers to raise supply of X relative to Y.
– Good X is labor-intensive so generates larger increase in demand for
labor than labor released by fall in supply of capital-intensive Good Y.
– Result is increase in demand for labor, driving up real wage, w.
– Exact opposite result for capital in Home as prod’n shifts to Good X.
– Higher (PX/PY) thus leads to higher (w/r) as a result of different factor
intensities of the Goods combined with labor mobility between
industries within Home.
• Diagram on next slide illustrates this relationship between
relative product prices and relative factor prices in H-O model.
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Relative Factor Prices and Product Prices
1.
Relative Price of X,
PX/ PY
2.
SS
3.
4.
Wage-rental ratio
w/r
5.
As (PX/PY ) increases
suppliers switch production
from Good Y to Good X.
Good Y is capital-intensive,
while Good X is laborintensive.
Reducing production of Y
increases capital by more
than that needed for X.
Implies fall in return to
capital, r.
This also increases labor by
less than that needed for X.
Implies rise in return to
labor, w.
Rise in (PX/PY ) thus results
in rise in (w/r).
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From Relative Prices to Production
•
In the Hecksher-Ohlin Model:
1.
2.
•
Combining these two results allows us to examine what
capital/labor ratios are used in prod’n of each good in
each nation before trade.
–
•
For a given set of factor prices, firms choose specific, but
different, ratios of factor inputs (K/L) to produce each Good.
A given set of relative product prices (PX/PY) is associated with a
given relative factor price (w/r).
Provide diagrams linking the two results on next slide.
Will also be able to examine the consequences of the
equalization of relative product prices as result of trade
for the relative factor prices and capital/labor ratios across
countries.
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Relative Factor Prices and Product Prices
2. Good X is L-intensive,
Good Y is K-intensive
Wage-rental ratio,
1. Assume Home is Labor-abundant,
Foreign Capital-abundant
w/r
Good X
SS
Good Y
(w/r)F
(w/r)H
PX/ PY
(PX/ PY)F (PX/ PY)H
(K/L)XH
(K/L)YH
(K/L)XF
K/L
(K/L)YF
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Capital/Labor Ratios by Industry
(For U.S. 1985)
Commodity
SIC Code
K/L ($ per employee)
Dairy Products
202
43,764.54
Grain Mill Products
204
91,328.55
Tobacco Products
21
102,560.98
Textile Mill Products
22
31,067.74
Apparel
23
5,918.62
Paper & Allied Products
26
102,355.57
Petroleum & Coal Products
29
425,090.20
Semiconductors & related devices
3674
70,183.82
Motor Vehicles & equipment
371
54,018.63
Aircraft
3721
27,481.39
Source: U.S. Dept. of Commerce, Annual Survey of Manufactures
30
Trade, Distribution & Welfare
• Factor Price Equalization Theorem
– International trade will bring about the equalization in the relative and
absolute returns to homogenous factors of production across nations.
– Trade in final goods essentially substitutes for movement of factors
between countries to equalize differences in relative factor returns.
• Stolper-Samuelson Theorem
– Free trade will result in an increase in the reward to the abundant factor
and a decrease in the reward to the scarce factor, i.e. the relative return
earned by the abundant factor will rise with the opening of trade.
– Assuming full employment before and after trade.
• Do not find complete factor price equalization of H-O theory.
– May be barriers to adjustment: trade barriers, transportation costs,
heterogeneous capital or labor, non-traded goods, imperfect
competition, unemployed factors, etc.
31
Relative Factor Prices and Product Prices
Wage-rental ratio,
w/r
SS
Factor Price
Equalization
StolperSamuelson
Good X
Good Y
PX/ PY
K/L
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Convergence of Real Wages
Real Hourly Wage in Manufacturing
(as Percentage of U.S. Wage)
Country
1959
1970
1983
1990
Japan
11
24
51
108
Italy
23
42
62
100
France
27
41
62
101
U.K.
29
35
53
82
Germany
29
56
84
118
Average
24
40
62
102
U.S.
100
100
100
100
Source: IMF, OECD, and US BLS
33
Factor Growth in the H-O Model
34
Rybczinski Theorem
• At constant product prices, an increase in the endowment of
one factor will increase by a greater proportion (magnification
effect) the output of the good intensive in that factor, and will
reduce the output of the other good.
• Intuition:
– Assume that the supply of capital increases.
– Constant product prices imply constant relative factor returns, (w/r).
– But relative factor returns can remain constant only if K/L and
productivity of K and L remain constant in prod’n of both goods.
– To fully employ new capital, while keeping K/L constant in both
goods, requires fall in output of labor-intensive Good X to release
enough labor to absorb increase in K in prod’n of Good Y.
– Thus output of capital-intensive Good Y increases while output of
labor-intensive Good X falls.
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Factor Growth & the Rybczinski Theorem
Good Y
+
L1Y
O1Y
+ DK
L0Y
O0Y
K0
[K/L]HX
K0
-
X
K1
X
OX
Good X
K1
[K/L]HY
L1X
K0Y
L0X
+
Y
Labor, L
-
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Changes in Relative Factor Endowments
Physical
Capital
R&D
Scientists
1963
41.9%
62.5%
29.4%
18.3%
0.60%
27.4%
1980
33.6
50.7
27.7
19.1
0.19
29.3
1963
7.1
16.2
7.8
12.6
0.30
0.9
1980
15.5
23.0
8.7
11.5
0.25
0.8
1963
9.1
7.5
7.1
6.8
0.14
1.3
1980
7.7
10.0
6.9
5.5
0.08
1.1
1963
7.1
6.1
6.6
5.3
0.11
3.2
1980
7.5
6.0
6.0
3.9
0.06
2.6
1963
5.6
6.1
7.0
6.5
0.14
1.0
1980
4.5
8.5
5.1
4.9
0.09
1.0
1963
3.8
1.6
2.5
1.7
0.06
6.5
1980
3.9
1.8
2.9
2.1
0.03
6.1
1963
25.4
0.0
39.6
48.8
98.65
59.6
1980
27.3
0.0
42.7
53.0
99.32
59.1
Country
U.S.
Japan
Germany
France
U.K.
Canada
ROW
Skilled
Labor
Semiskilled
Labor
Unskilled
Labor
Arable
Land
Source: Mutti & Morici, Changing Patterns of U.S. Economic Activity & Comparative Advantage
37