ECO364 - International Trade - Chapter 3 - Heckscher...

ECO364 - International TradeChapter 3 - Heckscher Ohlin

Christian Dippel

University of Toronto

Summer 2009

Christian Dippel (University of Toronto) ECO364 - International Trade Summer 2009 1 / 103

The Heckscher-Ohlin Model Model Set-Up

Difference To Ricardo

I In Ricardo:I everyone wins from Trade.I there is only one factor of productionI outcome is complete specialization

I This is very simplistic

I The Heckscher-Ohlin model aims to remedy some of theseshortcomings.

I It is more complex than Ricardo but gives far more subtle andnuanced predictions.



Framework

I 2x2x2 Model: 2 Countries, 2 Goods (Outputs), 2 Factors (Inputs).

I No productivity differences. All countries share the same technology.

I Identical Homothetic Preferences.

I Output can be produced with different input mixes (depending onrelative input prices).

I Factors are mobile across sectors.I Countries differ in the relative abundance of factors. This is the key

of Comparative Advantage in the HO Model.I HO is often referred to as the factor proportions theory.



Preview of Insights to Come

I Factor Abundance determined at Country Level

I Factor Intensity determined at Industry (=Sector) Level

I Specialization according to both Factor Abundance and Intensity

I Countries gain from Trade but Industries may loose and Factors mayloose

I Trade has Subtle Effects on Industrial Restructuring

I Under certain conditions, Factor Prices (e.g. wages) are equalizedacross countries



I Recall patterns of specialization from the first class:

Table: Trade by Commodities (1995)

Type of Goods Canada China Thailand United States

Machinery 0.383 0.230 0.382 0.472Food and Live Animals 0.066 0.045 0.190 0.072

Chemicals 0.059 0.041 0.031 0.109Misc. Manufactures 0.049 0.455 0.196 0.113

Source: Robert Feenstra, “World Trade Flows”

I Canada and the United States specialize in skilled labor/capitalintensive goods while China and Thailand specialize in goods that useunskilled labor relatively intensively.



Set-Up Again

1. Two countries.

2. Two goods.

3. Two productive factorsI Because of (1)-(3), this is referred to as the 2x2x2 model.

4. Constant returns to scale

5. Perfect competition (all agents are price takers).

6. Countries differ only in terms of their (relative) factor endowments.

7. Factors are immobile across countries but mobile across sectors.

8. Identical Homothetic Preferences



We first set up the equilibrium relations between goods prices, factorprices and factor inputs

1. Derive relationship between relative factor prices and relative factordemand.

I Based on firm profit maximization.I FF curves (to be derived).

2. Derive relationship between relative goods prices and relative factorprices.

I Based on iso-value and iso-cost curves from Lerner diagram (to bederived).

I SS curve (to be derived).

3. Use (1) and (2), derive three-way relationship between relative factorprices, relative factor demand and relative goods prices (see slide33/98 for an application).



This is a General Equilibrium (GE) Framework. It is important toremember what GE means (as opposed to Partial Equilibrium):

1. Firms maximize profits

2. Consumers maximize utilityI Utility/Preferences stay in the background throughout the analysisI Because of homothetic preferences: Relative Demand unaffected by

income

3. Labor markets clear

I This is the basic set-up for any GE Framework!

I The equilibrium is a set of (factor market clearing) factor prices,(goods market clearing) goods prices and sector-specific factorallocations.



We consider a small open economy where prices are exogenously given andpredict:

1. What happens to equilibrium relative factor prices and factor demandif goods prices change (can be interpreted as movement from autarkyto free trade).

I Stolper-Samuelson Theorem and Jones Magnification.

2. What happens to equilibrium relative factor prices and the productionstructure (sectorial composition) if the distribution of productivefactors changes (can interpret as immigration).

I Factor Price Insensitivity and Rybczynski Theorem.

3. Who specializes in what:I Heckscher-Ohlin Theorem


The Heckscher-Ohlin Model General Equilibrium in a Small Open Economy

I To determine the optimal factor-intensity, we use the iso-value andiso-cost lines in the following Lerner Diagram.

Figure: Lerner Diagram



I The iso-value curves map combinations of capital and labor thatyield $1 of output.

I Start with 1 = pxF x(K , L).I For a given value of px , what values of K and L produce $1 of output?



I Some iso-value schedules where px ,3 < px ,2 < px ,1... (at a lowerprice, firm needs more inputs to yield $1 of input)




I The iso-cost curve gives combinations of capital and labor that (as abundle) cost $1. Values of w and r are taken as given. It is derivedfrom the following equation

wL + rK = 1

K = 1r −

wr L



I If w and r rise by the same proportion, the iso-cost curve shifts inparallel. Using less K and L now costs $1




With zero profits, both revenue and costs are equal to 1. Therefore, K andL must lie on both curves.




I Equilibrium has to be at point of tangency (demonstrated on next fewslides)

I The straight line from the origin to the point of tangency is called theOutput Expansion Path (OEP)

I The slope of the OEP gives us the factor intensity in a sector.I A flatter OEP in our graph means a sector is more labor intensive



I Value of output is $1 and costs are less than $1. Positive profits (firmentry). Not an equilibrium.



I Could use a different mix of K and L to attain positive profits. Notan equilibrium.



I Value of output is $1 and costs are more than $1. Negative profitsand firm exit. Not an equilibrium.



I With a second good of another factor intensity, we can add a secondiso-value curve.




I The preceding slide determines equilibrium factor intensities (KTLT, KC

LC)

in both sectorsI for a given set of goods prices pC , pT

I and a given set of input prices w , r

I These goods prices and input prices are an equilibrium because bothiso-value lines are tangent to the iso-cost curve

I Suppose that pT increases. In order to produce $1 worth of textiles,fewer inputs are needed.

I Consequently, the iso-value curve T shifts in while the iso-valuecurve C does not move



I Now, there are profit opportunities in the textile sector because costsare unchanged but revenue has increased.

I Capital and labor flow into the textile sector.

I Because textiles are relatively labor intensive (flatter OEP), labor’swage is bid up more than capital’s rental rate.

I (w/r) rises in response to pT/pc increasing.I Importantly, r actually falls in this case to allow for non-negative

profits in the Computer-sectorI Intuition: for every unit of labor that shifts from the Computer to

Textile-sector, Computer-firms want to free up more capital thantextile-firms are demanding.



I note that r has to fall if pC is fixed.




This relationship between goods and factor prices is represented in the SScurve:



I This SS curve gives us the relationship between goods prices andfactor prices

I What about the relationship between factor prices and factorintensities?

I We saw that a rise in PT/PC raises w/rI This makes labor more expensive and naturally leads to substitution

effects where each firm demands a higher K/L ratioI Note that for markets to clear this has to imply that the labor-intensive

sector expands (intuition: PT rises)

I There is therefore a positive relationship between w/r and K/L inboth sectors



restructuring if w/r increases




I There is therefore a positive relationship between w/r and K/L inboth sectors

I Supposing computers are relatively capital intensive (FCFC is belowand to the right of FTFT ):



I We can soon combine the graphs on slides 27 and 30 to have agraphical representation of the General Equilibrium in a Small OpenEconomy (with prices exogenous)

I But first, let’s make this more formal through the firm’s profitmaximization problem.

I In competition, the nominal wage paid to a factor in production ofgood X equals its marginal revenue product such that where w is thewage and r is the rental rate of capital

w = pxmpl(K , L) r = pxmpk(K , L)



We can divide these two expressions such that

w

r=

px

px

mpl(K/L)

mpk(K/L)=

mpl(K/L)

mpk(K/L)

Because the marginal product of labor is increasing in and the marginalproduct of capital is decreasing in K/L, we can rewrite the right hand sideinto a single expression that is increasing in K/L.

w

r= f (K/L) ,

∂ wr

∂(K/L)= f ′(K/L) > 0



Example: Suppose that computers are capital intensive and textiles arelabor intensive with Cobb-Douglas production functions.

QT = K 1/3L2/3 QC = K 2/3L1/3

Firms producing X maximize PXQX − wLX − rKX

First Order Conditions (FOC) give {KC ,KT , LC , LT} as functions of{w , r , pC , pT} :

(1) w = pT23K

1/3T L

−1/3T (3) w = pC

13K

2/3C L

−2/3C

(2) r = pT13K−2/3T L

2/3T (4) r = pC

23K−1/3C L

1/3C

But {w , r} are also unknown so we need 2 more equations given by theendowments. (5) KT + KC = K (6) LT + LC = L



Dividing (1)/(2) and (3)/(4) gives us: wr = 2KT

LT

wr = 1

2KCLC

Setting (1)=(3) (or (2)=(4)) gives us: pTpC

2 = (KTLT

)−1/3(KCLC

)2/3

Combining these expressions gives us a solution for w/r (as a function ofprices): pT

pC= (w/r)1/3 which we can plug back in to solve for

{KC ,KT , LC , LT}



I We can now combine these two graphs into one picture.



I For a given set of relative goods prices, we can now predict:I Relative factor pricesI Factor intensities

I For a given set of relative factor prices, we can now predictI Relative goods prices.I Factor intensities

I In a small open economy (where prices are exogenous) we predictrelative factor prices and factor intensities given output prices.

I This can be represented in the following picture:


The Heckscher-Ohlin Model Stolper Samuelson and Rybczynski Theorems

I The SS curve is the graphical representation of theStolper-Samuelson theorem:

I As the relative price of a good increases, the nominal wages of thefactor used relatively intensively in that good increase relative to thenominal wages of the other factor.

I Jones Magnification is an important corrollary that the real wagesof the factor used relatively intensively in that good increase and thereal wage to the other factor decreases.



I Example 1: If pT rises relative to pC , then the relative return tolabor over capital rises, the real wages of workers increase and thereal return to capital falls.

I Example 2: If pT falls relative to pC , then the relative return tolabor over capital falls, the real wages of workers falls and the realreturn to capital rises.

I Using “Jones’ Hat-Notation”, denote a change in x by x

I Then it can be shown for Example 1, that: w > pT > pC > r



Figure: The Price of Textiles Rises Relative to the Price of Computers pT

pC↑



Figure: The Price of Textiles Falls Relative to the Price of Computers pT

pC↓



I If the price of textiles rises and the price of computers staysunchanged, how do we know...

1. that the nominal wage of labor rises and falls for capital?2. that the real wage of labor rises and falls for capital?



Figure: nominal wage changes follow from the Lerner Diagram



I We now know that r falls and w rises.

I But how do we know that the real wage of labor rises and falls forcapital?

I wpC

and wpT

are not real wages!

I If consumers consume both goods, the price level that consumers facewill be a combination of the price of textiles and computers.

I e.g p = 12 (pC + pT )

I If pT rises and pC stays unchanged, the aggregate price level (p) thatconsumers face must go up!

I Because r falls, rp must fall!



I How do we know that the real wage of labor rises?

I Label the cost share of labor in textile production as α and the costshare of capital in textile production as (1− α) (see Question 2c on2nd HO Problem Set)

I Recalling “Jones’ Hat-Notation” from previous slide and with zeroprofits, we have:

I pT = αw + (1− α)r

I Because r falls, w has to rise by more than pT

I Therefore wpC

and wpT

must both rise and wp must rise!



I The results on real wages and return to capital are an extension tothe Stolper-Samuelson Theorem called Jones Magnification.

I Jones Magnification holds very generally (i.e. without holding PC

constant) but that is harder to show.

I Jones Magnification matters because it is real wages (i.e. purchasingpower) that determine welfare!

I It can be shown more generally than here but the algebra gets a bitinvolved.



I We will now derive a very important result called the RybczynskiTheorem.

I To do this, we will use an Edgeworth Box...

I First, note that LT + LC = L and KT + KC = K .



Figure: The Textile Sector is Relatively Large



Figure: The Computer Sector is Relatively Large



I Remember from the “relative prices graph” that we know the ratio ofK to L in each sector.



I For given factor and goods prices, the Lerner Diagram gives us theratio of K to L (slope of OEP) in each sector.

I We can use this information in the Edgeworth Box.



I Combinations of capital and labor in each sector must lie on the raysbelow:



I These curves only intersect at one location.

I Therefore we know what inputs will be in each sector (and, therefore,what output will be).



I How do production patterns change if we increase one of theendowments?

I To do this, we simply expand the Edgeworth Box along the dimensionwhose factor has increased in quantity

I Suppose we increase the amount of labor in the economy.



I Labor and capital employed in computers both fall.

I Labor and capital employed in textiles both increase.

I Production of computers falls and production of textiles increases.

I Rybczynski Theorem: As endowments of one factor change, acountry will produce more of the goods that use that factorintensively and less of those that don’t

I A corollary is that Migration leads to industrial restructuring becauseit changes relative factor abundance



Factor Price Insensitivity

I Notice that the OEP’s did not change slope as we expanded theEdgeworth Box. This means that w/r did not change and thisirresponsiveness of w/r with respect to changes in factor endowmentsis referred to as Factor Price Insensitivity (FPI) .

I When does it hold? Intuitively, w/r cannot change in the Lernerdiagram because goods prices are exogenously given to a SOE.

I The only way w/r can change is if the country specializes in only onegood.

I This implies that the condition for FPI is that both countries arediversified (produce both goods).



Diversification vs. Specialization

I The discussion of FPI is a good point to check your understanding ofproduction functions in the Ricardian and HO Model.

I Why is there a tendency to fully specialize in the Ricardian Model butnot in the HO Model although both models have CRS productionfunction?

I The reason is that the HO Model is a two-factor model and theproduction function has declining marginal products in each factor(despite being CRS - make sure you get the difference).

I This implies that as one sector expands at the expense of the other,the marginal product of the scarce factor will eventually tend toinfinity in the shrinking sector.



Recap

I We have learnt how wages and factor intensities respond to pricechanges

I This is Stolper Samuelson

I ... and how factor intensities and industry structure (how much laboremployed in each sector) respond to factor endowments

I This is Rybczynski

I Now we learn about the patterns of specialization.


The Heckscher-Ohlin Model Heckscher Ohlin

I Unlike the Ricardian model, the PPF in the HO model is bowed outto reflect imperfect substitutability across sectors...



I Optimal output will be attained when the value of output ismaximized.

V = pCQC + pTQT

We can rewrite this as

QT = VpT− pc

pTQT

We can also think of this as an isovalue line that keeps the value ofproduction constant while varying the composition of production. Utilitywill be maximized when the value of production is maximized and thiscurve is as far up and to the right as possible.Do not confuse this isovalue line with the isovalue curve in the Lernerdiagram.



I Value, and consequently utility, is higher as these curves shift up andto the right



I A key insight is that, when there is no trade (autarky), theconsumption bundle must lie on both the iso-value line and the PPF.

I This is similar to the Ricardian model in which a consumption bundlemust lie on both the PPF and the budget constraint.

I Of course, in autarky, the production point is actually determined bytangency of PPF and indifference curve and the price ratio adjusts tobe equal to the slope of both.

I In autarky, an economy can only consume what it produces.

I But under trade, the iso-value line can be thought of as a budgetconstraint in that it gives all the consumption bundle that a countrycan afford.



I As pCpT

increases, the economy produces more computers relative totextiles.



I This also gives us a relative supply curve for the two goods



I Combine with Relative Demand



I The relative supply (RS) curve comes from the PPF and the iso-valuelines.

I The relative demand (RD) curve comes from utility maximization asin the Ricardian model.

I Two countries in autarky:

I Because preferences are identical and homothetic, the relativedemand curve is the same in both countries in autarky.

I Using the Rybczynski theorem, we know that the relative supply curvefor the North is to the left of the relative supply curve for the Southin autarky. To see this:..



I With free trade in goods, both pT and pC must equate acrosscountries. Therefore pT

pCmust equate across countries.



I With free trade and perfect competition, relative prices equate acrosscountries. The relative price of a given good will rise in one countryand fall in the other.



I For a given good, there will be excess relative supply in one countryand excess relative demand in the other country. This good will beexported by the first country and imported by the other.



I We can use the PPF graph to present the same information and toillustrate the gains from trade.

I The following equation presents a country’s balanced trade condition:

PCCC + PTCT = PCQC + PTQT

This can be rewritten as

CT − QT = pc

pT(QC − CC )

This is a budget constraint in that the value of goods consumed must beno greater than the value of goods produced.



I Looking at the South, recall that in Autarky, consumption equalsproduction.

I In equilibrium in autarky, we see production and consumption occurat the point where the indifference curve is tangent to the PPF.



I However, with trade, countries are no longer constrained to QC = CC

and QT = CT . Now, they can trade at any point along their budgetconstraint.

I pTpC

rises ( pCpT

falls) in the South. pTpC

falls ( pCpT

rises) in the North.



I For the South:



I For the North:



I In the above example, the price of computers relative to textiles risesin the North and falls in the South.

I More generally, the relative price of the good that intensively uses therelatively abundant factor rises. The relative price of the good thatintensively uses the relatively scarce factor falls.

I By the Stolper-Samuelson Theorem, the abundant factor wins andthe scarce factor loses.

I “Society” gains in each country because consumers can attain higherindifference curves

I This can be easily seen on the last two slides



I The Heckscher-Ohlin Theorem: Under all of the previously statedassumptions, a country will export the good that relatively intensivelyuses its relatively abundant good. The same country will import thegood that relatively intensively uses its relatively scarce factor.


The Heckscher-Ohlin Model Factor Price Equalization

I Stolper-Samuelson tells us what happens to relative factor prices ineach country.

I Owners of each country’s relatively abundant factor win as its factorwage rises.

I Owners of each country’s relatively scarce factor lose as its relativefactor wage falls.



I How far does this factor price convergence go?

I With Factor Price Equalization (FPE), goods price equalizingacross countries leads to factor prices equalizing across countries.

I Relative factor prices converge across countries even though factorsare immobile across countries!

I This is a striking result but when is it true?

I The next slides show that FPE will happen as long as endowments arenot “too” different.



I Recall the Lerner Diagram



I ... and the Edgeworth Box.



I Equilibrium Allocations can be found in two equivalent ways. PointsA and B are equivalent.



The “Integrated Equilibrium Approach”

I So far, we have considered how factors are divided across sectors inone country.

I Now, let’s engage in a thought experiment:I Suppose we combine 2 countries and drop all barriers between them

(we have already assumed free trade and ignore financial flows so theonly addition is free migration)

I The two countries are now “like one” and there will be a uniqueGeneral Equilibrium set of goods and factor prices.

I This can again be represented in an Edgeworth Box that looks exactlylike before.

I The boundaries given by the OEP’s mark the “Cone ofDiversification”.



Figure: the Cone of Diversification



I We can pick a factor allocation anywhere in the Edgeworth box toslice the country into two (drawing national boundaries).

I Claim: Any factor allocation inside the Cone of Diversification willlead to FPE.

I FPE is equivalent to saying the OEP’s in the two countries are thesame.

I The goods prices have to be the same under free tradeI Also, countries have the same technology.I Together, this implies the iso-value curves in each country’s Lerner

Diagram are the same.I The OEP’s can then only be the same under FPE (only then are the

iso-cost curves the same)



I Allocation α lies inside the Cone of Diversification and FPE is attained



I More intuitively, factor prices will be equalized if endowments are nottoo different.

I Endowments that are similar lie inside the Cone of Diversificationbecause it is “centered around the diagonal” in the Edgeworth Box.

I Free Trade between Canada and the USA is likely to erasewage-differences.

I But Free Trade between Canada and China? The endowments arelikely too different.

I Let’s say the last point α sliced the world into Canada and the US.I Instead, let’s slice the world into Switzerland and Bangladesh:



I The North runs out of labor and the South runs out of capital


The Heckscher-Ohlin Model Volume of Trade

Volume of Trade

I With identical preferences, all countries consume on the diagonal ofthe global Edgeworth-Box (understand this!)

I The factor content of trade is determined by the endowment pointand the factor prices.

I To see this, note that Home is capital-abundant if its endowment liesabove the diagonal.

I It exports capital-intensive goods and imports labor-intensive goods.I factor content of trade is the labor and capital embedded in these

good-flows.

I Home exports good B and imports good A. Can read the importedand exported labor and capital of the Edgeworth-Box.



The aggregate volume of trade is larger, the more different endowmentsare.


The Heckscher-Ohlin Model Size and Gains from Trade

Size and Gains from Trade

I the integrated equilibrium graph suggests that the volume of trade islarger if countries are more similar in size (as you get to the corners ofthe box, the boundaries of the cone get closer to the diagonal)

I Hoe does country-size relate to gains from trade?

I Assertion: small countries gain more from the movement fromautarky to free trade than do large countries.

I Recall that the gains from trade come from free trade prices beingdifferent than autarky prices.

I The more different free trade relative prices, the larger the gains fromtrade.



I In autarky, relative factor prices are determined by aggregate relativefactor endowments in each country.

I In a free trade equilibrium, relative factor prices are determined byworld relative factor endowments.

I The larger a country, the closer its relative endowments are to worldrelative endowments.

I Suppose we look at the two countries as Canada and China...



I Let’s look at a couple of examples...

Table: Size and Equilibrium Factor Prices

Large Canada Large ChinaK L K/L K L K/L

Canada 200 100 2 20 10 2China 5 20 0.25 50 200 0.25World 205 120 1.71 70 210 0.33

I (integrated) World equilibrium factor prices will more closely resembleautarky factor prices in the large country than in the small country.



Figure: Size and Factor Prices: Large Canada



Figure: Size and Factor Prices: Large China


The Heckscher-Ohlin Model Wrapping Up

Wrapping Up

I Unlike the Ricardian model, there are winners and losers from tradeliberalization.

I Owners of the scare factor lose because they become relatively lessscarce.

I Owners of the abundant factor win because they become relativelymore scarce.

I Winners win by more than the losers lose due to the gains fromspecialization.

I In order for “everyone” to gain from trade, we must see transferpayments from the owners of the relatively abundant factor to theowners of the relatively scarce factor.

I Aggregate gains from trade come from the fact that consumers canattain a higher indifference curve.



I Combining the Rybczynski and Heckscher-Ohlin theorems, acountry will export the good that relatively intensively uses itsrelatively abundant factor and will import the other.

I As a country moves from autarky to free trade, the relative price ofthe good that relatively intensively uses its relatively abundant factorincreases.

I As a country moves from autarky to free trade, the relative price ofthe good that relatively intensively uses its relatively scarce factorfalls.



I As a country moves from autarky to free trade, we can use theStolper-Samuelson theorem to show that the nominal wages of acountry’s relatively abundant factor rise and the nominal wages of thecountry’s relatively scarce factor falls.

I Jones Magnification shows that the same is true for real wages.

I This will lead to owners of the relatively scarce factor ”losing” andowners of the relatively abundant factor ”winning.”

I However, winners win by more than losers lose so trade can lead togains for everyone.

I For everyone to gain from trade, there must therefore be transferpayments from the winners to the losers.

I Factors of production are immobile across countries but goods aremobile. Trade in goods is enough to lead to factor priceconvergence.


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