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3.Heckscher-Ohlin Mode of Trade

Econ 3150 York U2

Problems with Ricardian model:

1. It predicts complete specialization

2. It predicts that all workers will gain from free trade. Inreal life some workers oppose free trade. (E.g. U.S. steel

workers oppose free trade with China)

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Econ 3150 York U3

Heckscher-Ohlin Model:

2 factors: capital (K) and labour (L) => concaveproduction frontier => no complete specialization, inequilibrium each country produces both goods

Comparative advantage is based on national differencesin factor endowments. Countries have different factors

endowments (e.g. capital, labour (skilled or unskilled),

land etc.) Differences in relative factor endowmentsresult in differences in autarky prices. E.g. countries that

have relatively abundant supplies of agricultural land

(like Canada, USA) have cheaper autarky prices of

agricultural products and become exporters of

agricultural products.

The model predicts that trade leads to redistribution ofincome between capital and labour => explains

opposition to trade of some factors of production

This model is favoured by economists and issupported by the real world data. There is a great deal of

evidence that differences in factor endowments are

important in explaining trade patterns.

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Econ 3150 York U4

1. Setup

2 goods: X,Y

2 factors: K,L, capital gets rent r, labour gets wage w2 countries: H,F

Assumptions

1. Identical CRS production functions in H and F

2. Kh, Lh, Kf, Lf- fixed factor endowments factors are perfectly mobile within each country

between X and Y sectors;

factors are immobilebetween countries.3. H, F differ inrelative factor endowments. (This will give

rise to price differences in H and F.)

4. Consumers in H, F have identical, homogenous

preferences

5. No distortions (tariffs etc.)

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Econ 3150 York U5

Definition

Factor Endowments

If capital- labor ratio in country H is greater than it is in

country F (f

f

h

h

L

K

L

K> ), then country H is relatively capital-

abundant and labour-scarce, while country F is relatively

labour-abundant and capital-scarce.

Example

K stock

($b.)

L

(m)L

K

($)

Brazil 507 53 9, 566

US 3,696 116 32,421

Switzerland 120 3 40,000

=> U.S. is capital-abundant relative to Brazil, but capital-

scarce relative to Switzerland.

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Econ 3150 York U6

L

K

hK

fK

hL fL

hE

fE

slope=home capital-labour ratio

slope=foreign capital-labour ratio

A. Factor Endowments Graph

H is capital-abundant, F is labour-abundant

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Econ 3150 York U7

Definition

Factor Intensities

Good Y is relatively capital-intensive and good X isrelatively labour-intensive if the capital-labour ratio used in

production of good Y is higher:x

x

y

y

L

K

L

K>

Example

K $m L thousandsL

K, $

Petroleum 27,005 95 284,263

Footwear 514 107 4,804

Take some price ratio w/r. Producers minimize costs =>isoquant is tangent to w/r. For any price ratio, at optimum

xyL

K

L

K)()( > => good Y is relatively capital-intensive, X is

relatively labour-intensive.

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Econ 3150 York U8

Assume:

1. Country H is relatively K-abundant, county F is

relatively L-abundant

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

ffhhXYXY ,,, - maximum amounts of goods X, Y that H, F

can produce (i.e. if all resources are devoted to production

of one good)

L

K

yK

Kx

yL xL

slope=Ys capital-labour intensity

slope=Xs capital-labour intensity

B. Factor Intensities Graph

Y

X

r

w

Y is capital-intensive, X is labour-intensive

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Econ 3150 York U9

Result

f

f

h

h

X

Y

X

Y>

I.e. capital-abundant country can produce relatively more

of capital-intensive commodity.

Can be shown in 2 steps:

Step 1. Assume that H, F are similar in size, H is capital-

abundant, F is labour-abundant:

L

K

hK

fK

hL fL

hE

fE

A. Factor Endowments Graph,

Isoquants for Y and X

fX hX

hY

fY

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Econ 3150 York U10

fhfh XXYY ; =>f

f

h

h

X

Y

X

Y>

Step 2. CRS technology =>f

f

h

h

X

Y

X

Y, are independent of

sizes of the countries.

Let ),(),,( LKfYLKfX yx == be maximum amounts

of goods X and Y that can be produced.

A country grows and now has 3 times more capital and

labour. The outputs of X and Y are:

Commodity Space, Home and Foreign PPFs

Y

X

Home PPF

Foreign PPF

hY

fY

hX fX

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Econ 3150 York U11

XLKfLKf xx 3),(3)3,3( ==

YLKfLKf yy 3),(3)3,3( ==

before growth, the ratio was Y

X; after growth, the ratio

stays the same: Y

X

3

3= Y

X.

=> Independently of country sizes, PPF of a relatively

capital-abundant country will be more stretched along the

K-intensive axis.

Commodity Space, PPFsY

X

Home

PPF

Foreign PPF

hY

fY

hX fX

hY3

1

fY2

hX3

1 f

X2

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Econ 3150 York U12

2. Autarky Equilibrium

Assume: H is a capital-abundant country and Y is a

capital-intensive good.

Note: Identical homogenous preferences => H and F have

parallel indifference curves. Home and foreign production

and consumption in autarky are at Ah and Af.

Tangency between the PPF and indifference curve

determines autarky price ratios:

Autarky

Y

X

Home

PPF

Foreign PPF

Pf

Ph

hY

fY

hX fX

hA

fA

h

au

f

au

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Econ 3150 York U13

f

y

f

x

h

y

h

x

P

P

P

P>

=> Capital-intensive good Yis relatively cheaper in capital-

abundant country H, while labour-intensive good is cheaper

in labour-abundant country F.

3. Free Trade Equilibrium

If countries open to trade, H observes relatively cheaper X

abroad, F observe relatively cheaper Y abroad =>

H exports Y (k-intensive good) and imports X, F exports X

(l-intensive good) and imports Y. H produces more Y and

less X, and F produces less Y and more X.

Note: There is no complete specialization in this model,

both countries keep producing both goods after trade.

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Econ 3150 York U14

Trade equalizes prices in 2 countries

H, F produce both goods Both H and F gain from trade.

4. The Heckscher-Ohlin Theorem

Theorem

The Heckscher-Ohlin Theorem

A country will export the commodity that intensively uses

its relatively abundant factor

Move from Autarky to Free Trade

Y

X

P*

hY

fY

hX fX

hA

fA

*

hQ

*

fQ

P*

A

fu

*hu

*

hC

*

fC Ahu

*

fu

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Econ 3150 York U15

Note: Empirically HO theorem applies better to countries

with large differences in relative endowments (e.g. USA Mexico trade). This trade model predicts inter-industry

trade.

World price P* adjusts to keep trade balanced: Hs imports

of X= Fs exports of X and Hs exports of Y= Fs imports

of Y.

Free Trade, Trade Triangles

Y

X

P*

*hQ

*fQ

P*

*hu

*hC

*fC

Hs imports of X =Fs exports of X

Hs exports of Y

=

Fs imports of Y*fu

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Econ 3150 York U16

5. The Factor-Price-Equalization Theorem

After countries open to trade each country observes higher

relative price for its exports:

H: observes higher relative price of Y, exports Y (k-

intensive good), resources are reallocated from sector X to

sector Y => demand for capital, demand for labour =>

r and w => w/r

F: observes higher relative price of X, exports X (l-

intensive good), resources are reallocated from sector Y to

sector X => demand for labour, demand for capital =>

w and r => w/r

there is a relationship between prices of goods and factorprices:

)(y

x

P

PG

r

w= , such that

y

x

P

P=>

r

w.

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Econ 3150 York U17

Note: technology in H, F is identical =>function G(.) is

identical in H,F.

1.In autarky: Ph>Pf => fh rwrw )()( > i.e. labour isrelatively cheaper in labour-abundant country, capital is

relatively cheaper in capital-abundant country.

2.Trade: Ph=Pf=P* => fh rw

r

w)()( =

Theorem

The Factor-Price Equalization Theorem

Under identical CRS production technologies free trade in

commodities will equalize relative factor prices through

equalization of relative commodity prices so long as both

countries produce both goods.

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Econ 3150 York U19

Real wages:yxyx P

r

P

r

P

w

P

w,,,

SS: y

x

P

P=>

yx

yx

P

r

P

r

P

w

P

w

,

,

Note: in equilibrium, factor price=value of marginal

product

Recall labour market equilibrium conditions:

Sector X: Sector Y:

xx

xx

MPKPr

MPLPw

=

=

yy

yy

MPKPr

MPLPw

=

=

Real wages:

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Econ 3150 York U20

x

x

x

x

MPKP

r

MPLP

w

=

=

;y

y

y

y

MPKP

r

MPLP

w

=

=

We have to show that change in relative pricesy

x

P

Paffects

marginal products in X and Y sectors, so that y

x

P

P=>

MPL in both sectors, and MPK in both sectors.

2 steps (no rigorous proof required)

Step 1. y

x

P

P=> output of X => demand for labour

increases relative to demand for capital because X is alabour-intensive good => w/r labour becomes relatively

more expensive => K/L ratio both in production of X and

Y (producers substitute away from relatively more

expensive input).

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Econ 3150 York U21

(note: homothetic production function: same K/L ratio for

all levels of Y (or X) for any w/r)

Step 2.

K/L =>

MPL,

MPK (because of law ofdiminishing returns)

Recall Properties of Production Function:

Law of Diminishing Marginal Product. If use of L inthe production of X is increasing, total product of

L

K

yK

xK

yL xL

slope=Ys capital-labour intensity

slope=Xs capital-labour intensity

B. Factor Intensities Graph: change in w/r

Y

X

r

w

Y is capital-intensive, X is labour-intensiver

w

r

w

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Econ 3150 York U22

labour is increasing at a decreasing rate.

xL

),( 1KLTP xx

X

),( 1KLMPL xx

- slope of TP curve

1L 2L

1L 2L xL

),( 2KLTP xx

),( 2KLMPL xx

- slope of TP curve

X

A

A

C

C

B

B

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Econ 3150 York U23

1.Increase labour from L1 to L2 keeping capital fixed at1K , TPL increases, MPL falls. (Movement from A

to B on Total Product or Marginal Product graph).

2.Keep labour fixed at L1, increase 2K , TPLincreases, MPL increases. (Movement from A to C on

Total Product or Marginal Product graph).

Generally,)(

L

KfMPL =

: L

K

MPL ; L

K

MPL

Similarly, )(L

KfMPK = : L

K xMPK ; L

K

MPK

E.g. if K by 15%, and L by 10% MPL because

capital-labour ratio goes up, but MPKfalls.

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Econ 3150 York U25

workers protest free trade with developing countries and

demand protection.

7. The Rybczynski Theorem

The Rybczynski Theorem

If relative commodity prices are constant and if both

commodities continue to be produced, an increase in a

supply of a factor will lead to an increase in output of the

commodity using that factor intensively, and a decrease in

the output of the other commodity

E.g. immigration => increase in L - one may expect thatoutputs of X and Y will both increase. NO! Output of X

will increase, output of Y will decrease. If home country

increases its capital stock, it will produce more of good Y

and less of good X.

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The theorem is important as it predicts the impact of

economic growth on trade. The way in which country

growth has an impact on its production and trade mixes.

Countries with low saving rates but high population growth

would tend to produce goods and export goods with high

labour contents. Countries with high saving and investment

rates will produce and export more capital-intensive goods.

Y

X

Output expansion

PP

Y

X X

Growth in Labour Endowment (X is labour-intensive good)

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