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BA 187 – International Trade

Hecksher-Ohlin Model & Relative Factor Endowments

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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 intensityfactor 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.

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Production Functions, Isoquants, and Relative Factor Prices

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Production Theory

• Production Function 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 IsoquantProduction 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 EquilibriumIsocost 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.

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Isoquants, Isocosts & Production

Given (w/r)

Labor, L

Capital, K[K/L]

Y

1. Good X is “ labor-intensivelabor-intensive”.2. Good Y is “ capital-intensivecapital-intensive”.

Relative Factor Price, (w/r)0

•Isocost lineIsocost line shows all combinations of K & L with same cost given w and r.

–Slope is relative factor price, w/r.

2X0

X0

•IsoquantsIsoquants show all combinations of K & L that produce certain amount of Good X.

[K/L] X

•Prod’n Points for Good XProd’n Points for Good X where Isoquant tangent

to Isocost Line. Assuming CRS so these points are

on ray from origin.2Y0

Y0•Can do same exercise for Good Y.

Note that Labor- or Capital-intensity of a good isDetermined by shape of Isoquants, i.e. prod’n.

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Factor Endowments and Factor Intensities

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Factor Intensities & Factor Abundance

• Factor IntensitiesFactor Intensities: (A property of production technologies)

– A Good Y is said to be capital-intensivecapital-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)(K/L)YY > (K/L) > (K/L)XX .

– In a two good world, if Good Y is capital-intensive then Good X will be labor-intensivelabor-intensive, at any relative factor price ratio.

• Factor AbundanceFactor Abundance: (A property of factor endowments)

– Physical Units definition: A nation is capital-abundantcapital-abundant if its capital/labor ratio (K/LK/L) is larger larger than that of the other nation.

– Relative Factor Price definition: A nation is capital-abundantcapital-abundant if its ratio of wage rate for labor to rental price of capital (w/rw/r) is larger 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.

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Relative Factor Costs & Intensities

Relative Factor Price, (w/r)high

Given (w/r) “lowlow”

Labor, L

Capital, K

2X0

2Y0

Y0

X0

Relative Factor Price, (w/r)low

[K/L]lowY

[K/L]lowX

X0

2X0

[K/L]highX2Y0

Y0

[K/L]highY

1. Good X is “ labor-intensivelabor-intensive”.2. Good Y is “ capital-intensivecapital-intensive”.

Labor, L

Capital, KGiven (w/r) “highhigh”

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Good X

Good Y

K/LCapital-Labor Ratio

w/rWage-rental ratio,

Factor Prices and Input Choices

Note from previous slide:1. As (w/r) increases from

“low” to “high”, K/L ratio used to produce Good X increases. The same is true for Good Y.

2. Implies there is an upward-sloping relation between relative factor price w/r and K/L used in production of each good.

3. 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.

(w/r)low

(w/r)high

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

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Edgeworth Box – Joint Prod’n

Labor, L

Capital, K

2X0

X0

[K/L] X

[K/L] Y

2Y0

Y0

Labor, L

Capital, K[K/L]

Y

2Y0

Y0

Labor, L

Capital, K

[K/L

] Y

2Y0

Y0

Lab

or, L

Cap

ital

, K

[K/L] Y

2Y0

Y0

Labor, L

Capital, K

[K/L] Y

2Y0

Y0

Labor, L

Capital, K

Labor, L

Capital, K

2X0

X0

[K/L] X

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[K/L]HY

Allocation of Factors to Goods Prod’n

Labor, L

2X

2Y

1Y

1X

Capital, K

[K/L]HX

[K/L]HY

Labor, L

Capital, K

OY

OX

[K/L]HY

OY

Total Labor

Total Capital

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Allocation of Factors & Nation’s PPF

Labor, L

Capital, K

[K/L]HX

OX

[K/L]HY

OY

LX

LY

KX KY

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.

Y

X

2. Implicit in this allocation are prod’n levels of both Y =QY(KY, LY) and X =QX(KX, LX).

B

B

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Factor Endowments and Factor Intensities in the H-O Model

of Trade

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Relative Factor EndowmentsEstimates for 1966

CountryCountry

Capital/LaborCapital/Labor($ per worker)

Capital/LandCapital/Land($ per hectare)

Labor/LandLabor/Land(workers per hectare)

Argentina $2,827.0$2,827.0 $101.7$101.7 .036.036

Australia 7,415.5 67.2 .009

Canada 10,583.1 198.0 .019

France 6,878.5 3,136.9 .456

Hong Kong 1,368.51,368.5 90,739.190,739.1 66.30466.304

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 10,260.910,260.9 1,058.61,058.6 .103.103

Source: Bowen, Leamer, & Sveikauskaus, AER 1987

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Factor Endowments & Intensities

Home, Labor-AbundantHome, Labor-AbundantK/L low & (w/r) low

Labor, L

Capital, K

Labor, L

Capital, K

2X

2Y

1Y

Foreign, Capital-AbundantForeign, Capital-AbundantK/L high & (w/r) high

1X

Relative Factor Price, (w/r)Home Relative Factor Price, (w/r)Foreign

[K/L]HY

[K/L]HX

1X

2X

[K/L]FX2Y

1Y

[K/L]FY

1. Good X is “ labor-intensive” in both nations.2. Good Y is “ capital-intensive” in both nations.

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Good X

Good Y

K/LCapital-Labor Ratio

w/rWage-rental ratio,

Factor Prices and Input Choices

Note from previous slide:1. As (w/r) increases from

Home to Foreign, K/L ratio used to produce Good X increases. The same is true for Good Y.

2. Implies there is an upward-sloping relation between relative factor price w/r and K/L used in production of each good.

3. 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.

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Differences in PPF’s across Nations in the H-O Model

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Labor-Abundant Nation’s PPF

Labor, L

Capital, K

[K/L]HX

OX

[K/L]HY

OY

LX

LY

KX KY

1. Box below shows allocation of capital and labor to each good, for a given w/r ratio.

PPFHome

3. Varying w/r picks out different allocations and prod’n points, tracing out PPF.

Y

X

2. Implicit in this allocation are prod’n levels of both Y =QY(KY, LY) and X =QX(KX, LX).

B

B

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Capital -Abundant Nation’s PPF

Labor, L

Capital, K

OXLX

LY

KX KY

1. Assume Foreign has more capital than labor .

PPFForeign

Y

X

[K/L]HX

[K/L]HY

OY

B

BPPFHome

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Equilibrium in the Hecksher-Ohlin Model

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(PX/PY)*

Opening trade changes relative prices

Assuming identical utility function for Home & Foreign

PPFH

PPFF

Home & Foreign PPF’s differ due to differences intechnology or factor endowments.

Differing Technology/Endowments

Y

X

AH

AF Autarky Equilibrium at AH and AF

QF

QH

C*

New equilib. consumption at C*.Each country has different prod’n ;point.

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Hecksher-Ohlin Theorem• Countries will export goods that use their abundant factors Countries will export goods that use their abundant factors

intensively and import those goods that use their scarce intensively and import those goods that use their scarce resources intensively.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:Effects of trade:1. Trade results in mutual gains.

2. Countries reallocate factors to increase specialization in goods that use their abundant factors intensively.

3. 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 - 1967Factor of Prod’nFactor of Prod’n U.S.U.S. GermanyGermany JapanJapan MexicoMexico PhilippinesPhilippines

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

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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

w/rWage-rental ratio

PX/ PY

Relative Price of X,

1. As (PX/PY ) increases suppliers switch production from Good Y to Good X.

2. Good Y is capital-intensive, while Good X is labor-intensive.

3. Reducing production of Y increases capital by more than that needed for X. Implies fall in return to capital, r.

4. This also increases labor by less than that needed for X. Implies rise in return to labor, w.

5. Rise in (PX/PY ) thus results in rise in (w/r).

SS

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From Relative Prices to Production

• In the Hecksher-Ohlin Model:

1. For a given set of factor prices, firms choose specific, but different, ratios of factor inputs (K/L) to produce each Good.

2. A given set of relative product prices (P(PXX/P/PYY) ) is associated with a given relative factor price (w/r)(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.

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Relative Factor Prices and Product Prices

w/r

PX/ PYK/L

Wage-rental ratio,

SS

(PX/ PY)H

(w/r)H

(PX/ PY)F

(w/r)F

(K/L)XH (K/L)Y

H

(K/L)XF (K/L)Y

F

1. Assume Home is Labor-abundant, Foreign Capital-abundant Good X

Good Y

2. Good X is L-intensive, Good Y is K-intensive

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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

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Trade, Distribution & Welfare• Factor Price Equalization TheoremFactor Price Equalization Theorem

– International trade will bring about the equalization in the relative and International trade will bring about the equalization in the relative and absolute returns to homogenous factors of production across nations.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 TheoremStolper-Samuelson Theorem– Free trade will result in an increase in the reward to the abundant factor Free trade will result in an increase in the reward to the abundant factor

and a decrease in the reward to the scarce factorand 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.

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Relative Factor Prices and Product Prices

w/r

PX/ PY

Good X

Good Y

K/L

Wage-rental ratio,

SS

Factor Price Equalization

Stolper- Samuelson

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Convergence of Real Wages

CountryCountry 19591959 19701970 19831983 19901990

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

Real Hourly Wage in Manufacturing (as Percentage of U.S. Wage)

Source: IMF, OECD, and US BLS

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Factor Growth in the H-O Model

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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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Labor, L

K0

[K/L]HX

OX

Factor Growth & the Rybczinski Theorem

[K/L]HY

L0X

L0Y

K0X K0

Y

O0Y

L1X

L1Y

K1X K1

Y

+

-

-

+

O1Y

K+

Good X

Good Y

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Changes in Relative Factor EndowmentsCountryCountry

Physical Physical CapitalCapital

R&D R&D ScientistsScientists

Skilled Skilled LaborLabor

Semiskilled Semiskilled LaborLabor

Unskilled Unskilled LaborLabor

Arable Arable LandLand

U.S.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

JapanJapan 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

GermanyGermany 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

FranceFrance 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

U.K.U.K. 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

CanadaCanada 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

ROWROW 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

Source: Mutti & Morici, Changing Patterns of U.S. Economic Activity & Comparative Advantage