1. BA 187 – International Trade
Hecksher-Ohlin Model & Relative Factor Endowments

2. Hecksher-Ohlin Model
Two countries, two goods, X and Y, and two factors of 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.

3. Factor Endowments and Factor Intensities

4. 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).
H-O model combines both factor intensities of goods and relative factor abundance of nations to determine trade patterns.

5. Relative Factor Endowments
Country
Capital/Labor
($ per worker)
Capital/Land
($ per hectare)
Labor/Land
(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
Source: Bowen, Leamer, & Sveikauskaus, AER 1987

6. Factor Endowments & Intensities
1. Good X is “ labor-intensive” in both nations.
Foreign, K/L high
2. Good Y is “ capital-intensive” in both nations.
Capital, K
[Implies (w/r) high]
Home, K/L low
Relative Factor Price, (w/r)Foreign 2Y 1Y
[K/L]FY
[Implies (w/r) low]
Capital, K
[K/L]HY 2Y 1Y 1X 2X
[K/L]FX 2X
[K/L]HX 1X
Relative Factor Price, (w/r)Home
Labor, L
Labor, L

7. Factor Prices and Input Choices
Note from previous slide:
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 upward-sloping 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.
Wage-rental ratio,
w/r
Good X
Good Y
Capital-Labor Ratio
K/L

8. Deriving a Nation’s PPF in the H-O Model

9. Allocation of Factors to Goods Prod’n
[K/L]HY
Labor, L
Capital, K OY
Capital, K
[K/L]HY OY
Total Labor
Total Capital
[K/L]HY 2X 2Y 1Y 1X
[K/L]HX OX
Labor, L

10. Allocation of Factors & Nation’s PPFY X
2. Implicit in this allocation are prod’n levels of both Y =QY(KY, LY) and X =QX(KX, LX).
1. Box below shows allocation of capital and labor to each good, for a given w/r ratio.
PPF
3. Varying w/r picks out different allocations and prod’n points, tracing out PPF. B
Capital, K LX LY OY KX KY
[K/L]HX
[K/L]HY OX
Labor, L

11. Equilibrium in the Hecksher-Ohlin Model

12. Differing Technology/EndowmentsQF QH C*
New equilib. consumption at C*.
Each country has different prod’n ;point.
Assuming identical utility function for Home & Foreign
(PX/PY)*
Opening trade changes relative prices
PPFH
PPFF
Home & Foreign PPF’s differ due to differences in
technology or factor endowments. Y AH AF
Autarky Equilibrium at AH and AF X

13. Hecksher-Ohlin Theorem
Countries will export goods that use their abundant factors intensively and import those goods that use their scarce resources intensively.
Previous slide shows how factor endowments determines shape of each nation’s PPF.
Assuming identical utilities, then Hecksher-Ohlin theorem result arises for the pattern of trade.
Effects of trade:
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.)

14. 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

15. Trade, Distribution, and Welfare in the H-O Model

16. 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.

17. Relative Factor Prices and Product Prices
As (PX/PY ) increases suppliers switch production from Good Y to Good X.
Good Y is capital-intensive, while Good X is labor-intensive.
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).
Relative Price of X,
PX/ PY SS
Wage-rental ratio
w/r

18. From Relative Prices to Production
In the Hecksher-Ohlin Model:
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).
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.
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.

19. Relative Factor Prices and Product Prices
Good X
Good Y
2. Good X is L-intensive,
Good Y is K-intensive
Wage-rental ratio,
w/r
1. Assume Home is Labor-abundant,
Foreign Capital-abundant SS
(PX/ PY)F
(w/r)F
(K/L)XF
(K/L)YF
(PX/ PY)H
(w/r)H
(K/L)XH
(K/L)YH
PX/ PY
K/L

20. 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

21. 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.

22. Relative Factor Prices and Product Prices
Wage-rental ratio,
w/r
Good X
Stolper-
Samuelson
Factor Price
Equalization SS
Good Y
PX/ PY
K/L

23. 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
101
U.K. 29 35 53 82
Germany 56 84
118
Average 40
102
U.S.
Source: IMF, OECD, and US BLS

24. Factor Growth in the H-O Model

25. 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.

26. Factor Growth & the Rybczinski Theorem+ -
Good Y
[K/L]HY
L0X
L0Y
K0X
K0Y
O0Y
L1X
L1Y
K1X
K1Y
O1Y DK + K0
[K/L]HX OX
Labor, L
Good X

27. Changes in Relative Factor Endowments
Country
Physical Capital
R&D Scientists
Skilled Labor
Semiskilled Labor
Unskilled Labor
Arable Land
U.S.
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
Japan
7.1
16.2
7.8
12.6
0.30
0.9
15.5
23.0
8.7
11.5
0.25
0.8
Germany
9.1
7.5
6.8
0.14
1.3
7.7
10.0
6.9
5.5
0.08
1.1
France
6.1
6.6
5.3
0.11
3.2
6.0
3.9
0.06
2.6
U.K.
5.6
7.0
6.5
1.0
4.5
8.5
5.1
4.9
0.09
Canada
3.8
1.6
2.5
1.7
1.8
2.9
2.1
0.03
ROW
25.4
0.0
39.6
48.8
98.65
59.6
27.3
42.7
53.0
99.32
59.1
Source: Mutti & Morici, Changing Patterns of U.S. Economic Activity & Comparative Advantage