The Heckscher-Ohlin modelSources: Mucchielli Mayer; Feenstra Taylor.

Eleni ILIOPULOS

Paris 1

Class 5

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Aim of this lecture

Understand the Heckscher-Ohlin Model.

Understand how the HO Model contrasts with the Ricardian model.

Understand the No-Trade and the Free Trade equilibrium of the HOmodel.

Understand the e¤ects of trade on factor prices.

Understand how we can extend the Heckscher-Ohlin model.

References:

Mucchielli Mayer (2005); Feenstra Taylor (2008).

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The model: basic assumptions

Two countries: H, FTwo goods: X, YTwo (homogeneous) factors: L, KIdentical technologies in H and F for each good (but techX 6=techY,of course!).Factor intensities di¤er from sector to sector: KxLx 6=

KyLy.For instance,

we suppose here KxLx >KyLy

CRSNo distortions to production and/or to perfect competition.Production factors are fully employed.Perfect factor mobility across sectors; however, factors do not crossborders.Identical and homogeneous preferences (same indi¤erence curves).Di¤erent factors endowments!

�KL

�h 6=

�KL

�f . For instance, we

suppose here�KL

�h >

�KL

�f

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Specialization?

Since KxLx 6=KyLyand

�KL

�h 6=

�KL

�f ,

countries have an incentive to produce the good that is intensive in thedomestically abundant factor!

Factor intensities: result of producers optimization program, for agiven wrTechnical coe¢ cients can vary: aLx = Lx/X for a given wr . If ∆

wr !

producers optimize and can change factor intensities (NB: factors canbe substituted!)

However, irreversibility of factor intensities among sectors (i.e.,KxLx>

KyLy)

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Equilibrium in autharky

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Indi¤erence Curves

Consumer tastes are the same across countries, so the shape of theindi¤erence curves is the same in each country.

The tangencies with the two countriesPPFs are di¤erent because ofthe di¤erent shapes of the PPFs.

The relative price that consumers are willing to pay for computersequals the opportunity cost of producing them the no tradeequilibrium.

The slope at tangency equals the relative price of computers the steeper the slope, the higher the relative price of computers.

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Properties of autharky equilibrium: comparative advantage

KxLx>

KyLyand

�KL

�h >

�KL

�f entail:

Home PPF biased in favor of X (computers)

Foreign PPF biased in favor of Y (shoes).

Identical preferences in H and F ! the indi¤erence curves of bothcountries are parallel!

Therefore, since PPFs are biased:�PxPy

�ah<�PxPy

�af

! country H has a comparative advantage in producing X .!Comparative advantage: determined by factors endowments and factorintensities.

What if the size of country H changes? Comparative advantage is nota¤ected if

�KL

�h stay xed.

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Trade equilibrium with di¤erent autharky prices

relative prices are equalized.

relative prices allow markets to clear

consumers are on higher indi¤erence curves

Incomplete specialization (see the following slides)

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Country H

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International market for Home, good X

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Country F

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International market for Foreign, good X

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International equilibrium for the good X

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Equilibrium Price with Free Trade

The equilibrium free trade price is determined by the intersection ofthe Home export supply curve and the foreign import demand curve:Point D.

At that relative price, the quantity that Home wants to export equalsthe amount that Foreign wants to import.

This is a free-trade equilibrium since there is no reason for the relativeprice to change.

The trade triangles of the two countries are identical in size.

Heckscher-Ohlin Theorem:With two goods and two factors, each country will export the good thatuses intensively the factor of production it has in abundance, and willimport the other good.

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Factors and prices: what happens if the relative priceincrease?

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Factors and prices: what happens if the relative priceincrease?

Sector Y frees some L and K but in a proportion such that:�KL

�free <

KxLx

for an initial wrIn order to absorb the additional labor (and substitute capital): wr #More precisely, if the (relative) price of one good increases, theincome of the factor which is used intensively in its productionincreases as well.

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Factors income

�wr

�b <

�wr

�a !!

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The Heckscher-Ohlin-Samuelson theorem:

Under the above assumptions (and incomplete specialization, see thefollowing), relative prices equalization (i.e., the existence of an uniqueinternational relative price) implies the international equalization of therelative income of factors, w/r .Thus, in equilibrium:

There exist one unique relative price PxPyEach countriy will produce di¤erent quantities X, Y:

�XY

�h 6=

�XY

�f

Relative factor incomes are equalized internationally:�wr

�h =

�wr

�f�

KxLx

�h=�KxLx

�f,�KyLy

�h=�KyLy

�f

The price-factors equalization will not hold IF for a given wr the

corresponding ratio KxLx ,KyLyit is not feasible because of insu¢ cient

domestic factor endowment. In this case, the economy completelyspecializes in one sector. Thus, factors income are equalized IFFcountries can keep their production diversied.

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The cone of diversication

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Complete specialization

In H wara . In F:wfrf. Notice that: wara >

wfrf

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Empirical relevance:In reality, factors incomes are not equalized. Are the assumptions of the H-O-S theoremveried?

Transportation costs do not allow to equalize good prices

Tari¤s do not allow to equalize good prices

Distortions that a¤ect perfect competition do not allow to equalizegood prices

Do countries have the same technology? Do factors have the sameproductivity all around the world?

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The Stopler-Samuelson Theorem

Under the above assumptions, an increase of the relative price of one goodincreases the real income of the factor intensively used in its production; italso entails a decrease in the real income of the other factor.

Factors endowments are assumed to be xed.

Amplication e¤ect: the increase in the real income of the factor (i.e.,rw ) is greater than the one of the relative price of the factor-abundantgood (i.e., PxPy ).

Redistribution as an important issue for policy makers: is it better tolet r or w increase? It follows from scarcity vs abundance of factors.

If the production of one good cannot change (i.e., the country iscompletely specialized), the real income of factors cannot vary.

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The Theorem of Rybczynski

If the relative price of goods is xed and countries are not completelyspecialized, the increase of the endowment of a factor entails an increasein the production of the good, which is intensive in that factor; it alsoentails a reduction in the production of the other good the one intensivein the other factor.

Amplication e¤ect: the increase of the quantity of the good isgreater than the increase in the quantity of the factor.

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The growth of a factor in a country and terms of trade

If growth is biased in favor of the export sector (KxLx ") and H is a largecountry ! excess supply of X!

Relative price of X decreases (PxPy #)! ToT deteriorate!On the contrary, if growth is biased in favor of the import sector: ToTimprove!

Bhagwati (1985) stresses that developing countries may not benet offactors growth in open economy.

Small open economy: factorsgrowth does not have e¤ect on ToT.

Factor growth cannot but be benecial

If factors increase a lot you can have an inversion of specialization

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Empirical relevance: the paradox of Leontief

a =Kimp/LimpKexp/Lexp

if the country is abundant in capital, a < 1. Is it the case? No..(other tests have better results...still, they are not conclusive). Why?

Land and natural resources are not accounted as production factors

Tari¤s can bias results

The year the test was done was close to the end of IIWW (data arebiased)

What if we account for labor productivity? (the possible solution ofLeontief)

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Empirical relevance: the paradox of Leontief

The model Heckscher-Ohlin-Vanek (HOV): n factors, m goods anddi¤erent countries.Focus on the service provided by factors (countries export the serviceprovided by the abundant factor).In a two country framework (Vanek, 1968): if one country is abundant inone factor, it needs to be a net exporter of its services. Factor abundance:the share of a countrys factor in world amount of that factor OVER thecountrys GDP share in world GDP. If specialization does not occur inmore than n-m sectors and

F1f1� F1f1� ..Fn

fn

if free trade, then the Home country will export services F1,F2,Fj andimport services Fj+1,Fj+2,Fn (j 6= n) ; we can compute j, if we know theprices of factors. Results improve little..See your book (MM) for more and more discussion..

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Important corrections are needed (Treer 1995; Davis et Weinstein,2001..):

Home bias in agentspreferences

Di¤erent productivities (Ricardo?)

Better data

Transportation costs.

Can H-O really explain intra-industry trade??

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The Stopler-Samuelson theorem and inequality in theNorth

In the rich countries, the income gap between skilled and unskilledlabor increases (or, where wages are not exible, unemployment ofunskilled workers increases).

At the same time, unskilled-labor-intensive goods are imported frompoorer countries.

Is it because of the Stopler-Samuelson e¤ect?

However:

The share of manufactures coming from developing countries intoOECD countries is still very small (but increasing).

Does inequality come from a biased growth in favor of technologicalprogress?

However, even if international trade may contribute to inequality,protectionism is not the solution.

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The model: basic assumptionsTrade equilibrium