HECKSCHER-OHLIN MODEL
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1.  INTRODUCTION
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Drawbacks Ricardian Trade Model
§  All agents gain from trade in Ricardo. Thus, we would not be able to explain why some
agents are against free trade, nor why there are barriers to trade.
§
§
§
In Ricardo (as in other trade models) both countries gain from trade.
Since there is only one factor of production (labor), it implies that if a country gains, then all individuals in that
country also gain.
Therefore, no one loses from trade liberalization.
§  In the Ricardian model there is typically complete specialization (unless in the case of
economies of very different sizes). In the real world, specialization is not complete.
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The Answer of Heckscher-Ohlin
§  To explain why some agents are against trade liberalization, we need at least 2 factors of
production.
§  The introduction of 2 factors of production also implies decreasing returns to each factor,
which typically results in incomplete specialization.
§  Basic assumptions Heckscher-Ohlin:
§
§
§
§
§
§
Perfect competition
2 countries
2 sectors
2 factors of production (e.g., capital and labor) perfectly mobile across sectors (but not across countries)
Identical technologies across countries
The only difference between countries is their relative factor endowment.
§  In this model comparative advantage comes from differences in relative factor
endowments.
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2. ROAD MAP
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Road Map
Theory
§  Closed Economy
§
§
§
§
Isoquants and isocosts.
Lerner diagram.
Stolper-Samuelson Theorem.
Rybczynski Theorem.
§  Open Economy
§
§
§
§
Trade patterns and Heckscher-Ohlin Theorem.
Application of Stolper-Samuelson Theorem.
Factor price equalization (FPE).
Exceptions to FPE.
Exercises
§  Graphical and numerical applications of the Heckscher-Ohlin model.
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3. THEORY LECTURES
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3.1. CLOSED ECONOMY (AUTARKY)
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Assumptions
§  2 countries: Spain and Poland.
§  2 factors of production (mobile across sectors, but not across countries):
capital (K)
labor (L)
§  2 sectors (identical technologies in both countries):
food (relatively L-intensive)
computers (relatively K-intensive)
§  Spain is relatively abundant in capital and Poland is relatively abundant in labor:
K / L > K*/ L*
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Production of Food
KF
An isoquant represents the amount of
capital and labor needed to produce a
certain number of units of food
(for example, the unit isoquant represents the
Isocost lines,
slope w/r
KF/LF
quantity of capital and labor needed to produce one
unit of food).
Unit isoquant
An isocost shows all combinations of
capital and labor which cost the same total
amount.
C = rK + wL
LA
Given w and r, the firm minimizes the
cost subject to the constraint of
producing one unit. It corresponds to the
lowest isocost tangent to the unit isoquant.
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K = C/r - (w/r)L
Thus, they are lines with slope -w/r
The line which goes from the origin through
the tangency point represents the KF/LF ratio
used to produce food, given factor prices w/
r.
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Relationship between Prices and Use of Inputs
Start in the equilibrium point 1.
KF
KF1/LF1
Now increase the cost of capital, r.
The optimal amount of inputs shifts
to point 2: the firm uses more labor
and less capital.
1
That is, KF2/LF2 < KF1/LF1
-(w/r)1
2
KF2/LF2
-(w/r)2
LF
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The same comparative statics take
place if the cost of labor, w,
decreases.
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Relationship between Prices and the
Relative Use of Inputs
w/r
Food
Computers
For each good, food and computer,
there exists a relationship between the
relative price of inputs, w/r, and the
relative use of inputs, K/L
Assume that the computer curve is to
the right of the food curve: that is, given
a ratio w/r, computers use relatively
more capital.
K/L
As we have just seen, an increase in the
relative cost of labor (w/r) increases the
relative use of capital (K/L).
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In that case, the production of
computers is relatively intensive in
capital and the production of food
is relatively intensive in labor.
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Determination of the Relative Price of Inputs:
the Lerner Diagram
K
Each isovalue corresponds to an isoquant. For
example, if PF = 0.5 , the isovalue of 1 €
corresponds to isoquant 2.
Isovalue computers (1 €)
KC/LC
When the price of any good changes, the position of
the isovalue curve shifts.
Isovalue food (1 €)
KF/LF
-(w/r)
L
Isovalue curves: combination of inputs
needed to produce a given value of each
good, for example, one euro.
If the economy produces both goods and
there is perfect competition, the cost of
producing each good will also be one euro.
(ΠF = 0 y ΠC = 0)
That is, the lowest possible cost that allows us
to produce one euro of each of the goods is
the same. Thus, producing 1 euro of each of
the goods must happen on the same isocost,
rKF + wLF = rKC + wLC
There is a UNIQUE isocost, tangent to the
two isovalue curves.
The slope of this isocost is the relative price of
inputs, -w/r.
Then, for each PF/PC we can find w/r (see
next slide).
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Relationship between Relative Prices and Inputs:
the Lerner Diagram
Assume that PC = 1. This normalization is the
same as representing all units in terms of
units of computers.
K
(1/r)2
CC
(1/r)1
The initial situation is represented by the red
curves. The relative price of inputs is (w/r)1.
-(w/r)1
Note: since the isocost is wL+rK=1, the
vertical intercept has slope (1/r)1 and the
horizontal (1/w)1.
Keeping PC=1, an increase in PF/PC
represents an increase in PF. To produce 1 €
of food, we need less capital and labor, so
that the isovalue shifts from FF1 to FF2.
The isocost also changes: (w/r)2 > (w/r)1.
Moreover, the change in the intercepts
implies that: w2 > w1 and r2 < r1.
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-(w/r)2
FF1
FF2
(1/w)2
(1/w)1
L
Given the normalization, an increase in PF/PC
means that the wage buys more food and
the rental rate buys less food.
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Stolper-Samuelson Theorem
§  In the above exercise, we saw that an increase in PF/PC implies that the wage buys more
food and the rental rate buys less food.
§  If we had chosen the other possible normalization (PF=1), we would have found that an
increase in PF/PC (which would be equivalent to a decrease in PC) implies that the wage
buys more computers and the rental rate buys less computers.
§  That is, an increase in PF/PC allows the workers to buy more of both goods and the capital
owners to buy less of both goods.
STOLPER SAMUELSON THEOREM
An increase in the relative price of a good will increase the real return to the factor
used intensively in the production of that good, and will decrease the real return to
the other factor.
IMPORTANT: The Stolper-Samuelson Theorem relates changes in the relative price of goods
to changes in the REAL return of factors (and not simply to the absolute price and/or the
relative price of factors).
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Alternative Analysis of Stolper-Samuelson
w/r
Food
Computers
(w/r)2
(w/r)1
PF/PC
(PF/PC)2
(PF/PC)1
The left-hand side panel represents the
relationship between the relative price of
goods and factors.
The right-hand side panel represents the
relationship between the relative price of
factors and their relative use.
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(KF/LF)1 (KF/LF)2 (KC/LC)1
(KC/LC)2
K/L
An increase in the relative price of the good
intensive in labor (food) increases the relative
price of labor (i.e., w/r).
Moreover, the production of each good
becomes more intensive in capital: KF/LF and
KC/LC increase.
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Alternative Analysis of Stolper-Samuelson.
§
In the last figure we saw that an increase in the relative price of food (PF/PC), raises the
relative reward of labor (w/r), which increases the optimal (K/L) ratio in both sectors.
§
In a competitive economy, nominal wages are equalized in both sectors:
w = PFMPLF = PCMPLC
§
We define the “real” wage in terms of food as
ωF= w / PF = MPLF
§
And the real wage in terms of computers as
ωC= w / PC = MPLC
•
An increase in PF/PC , raises KF/LF and therefore increases both MPLF, and ωF. For the
same reason, ωS also rises. Thus, the real wage rises.
•
Similarly, one can prove than an increase in PF/PC, reduces the real rental rate of capital.
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Allocation of Factors of Production
LC
OC
The width of the box represents the
amount of labor available in the
economy and the height represents
the capital. Each point in the box
represents a possible allocation of
inputs between sectors.
KF + KC = K
LF + L C = L
F
KF
KC
C
OF
LF
We have seen how the relative price of factors and
the ratio K/L was determined for each good. Now
we investigate how they are allocated between
sectors.
Given PF/PC, we know KF/LF and
KC/LC. From the origin OF we
draw a line with slope KF/LF and
from OC we draw a line with slope
KC/LC.
The intersection between both
lines is the allocation of inputs in
this economy.
Question: Can we end up outside the box?
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Introduction to the Rybczynski Theorem
L 2C
O2C An increase in the endowment
of capital, raises the height of
the box. The origin of the
1
O C production of computers is now
O2C.
L 1C
Keeping PF/PC constant, the line
with slope KC/LC shifts up in a
parallel fashion.
F
1
K1F
K2F
2
C1
L 2F
C
K2C
C2
OF
K1
L 1F
In the new equilibrium (point 2),
more of both inputs are used in
the production of computers.
Thus, the production of
computers increases.
Less of both inputs are devoted
to the production of food. So, its
production decreases.
In this exercise we see how an increase in the
endowment of capital changes the allocation of inputs
in each sector and the production of both goods.
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Alternative Analysis of Rybczynski
QC
Y2C
Y1C
Another way of interpreting an increase in the
endowment of capital is through the
production possibility frontier.
2
Slope -(PF/PC)
1
Y2F Y1F
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An increase in the endowment of capital
causes the production possibility frontier to
move outward, but more in the direction of
computers than in the direction of food. There
is a biased expansion of the production
possibility frontier.
QF
Given PF/PC, an increase in the endowment of
capital increases the production of computers
and decreases the production of food.
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Rybczynski Theorem
RYBCZYNSKI THEOREM
Given relative prices, an increase in a factor endowment will increase output in the
sector that uses that factor intensively, and will decrease output in the other sector.
Given relative prices, an increase in the relative endowment of a factor, will
relatively increase output in the sector that uses that factor intensively.
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Production Possibility Frontiers
Remember that we have two countries
(Spain and Poland).
YC
The only difference is that Spain is relatively
capital abundant: K/L > K*/L*.
The production possibility frontiers are such
that, given prices, Spain (Poland) produces
relatively more computers (food).
This is an illustration of the Rybczynski
Theorem.
Y*C
Production
possibility frontier
in Spain
YF
Production
possibility froniter
in Poland
Y*F
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Relative Prices under Autarky
Relative supply: the relative shapes of the
production possibility frontiers of both
countries imply that the relative supply of
food in Poland is higher than in Spain.
PF /PC
RS
RS*
PF /PC
Relative demand: if preferences are
identical and homothetic, then the relative
demand is the same in both countries.
P*F /P*C
RD=RD*
YF /YC
Prices under autarky: the relative price of
food is lower in Poland:
Y*F /Y*C
(PF /PC)A > (P*F /P*C)A
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3.2. OPEN ECONOMY (FREE TRADE)
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Relative Prices under Free Trade
Relative supply: will be between RS and
RS* (depending on the relative size of both
countries)
PF /PC
RS
RSFT
RS*
PF /PC
Relative demand: the same
(PF/PC)FT
P*F /P*C
RD=RD*=RDFT
Relative prices: relative prices will converge
(PF /PC)A ≥ (P*F /P*C)FT ≥ (P*F /P*C)A
Pattern of trade: given that (PF /PC
Poland exports food.
)A >
YF /YC
(P*F /P*C
)A,
Y*F /Y*C
Spain exports computers and
HECKSCHER-OHLIN THEOREM
Each country exports that good which intensively uses the factor the country is
relatively abundant with.
Gains from trade: the terms of trade of each country improves, thus, both countries
gain from trade.
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Gains from Trade
Autarky: Production (YA) equals
consumption (CA)
SPAIN
QC
YFT
CFT
YA=CA
Free Trade: The relative price PF/PC
falls.
- (PF/PC)FT
CA
- (PF/PC)A
QF
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Spain produces more computers than
before (the production point, YFT, moves
up).
The new consumption point is on a
higher indifference curve. Spain
consumes more food (substitution and
wealth effect go in the same direction).
The change in the consumption of
computers is indeterminate (substitution
and wealth effects go in opposite
directions).
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Income Distribution
§  After trade liberalization, the relative price of food falls (rises) in Spain (Poland).
§  The Stolper-Samuelson Theorem implies that:
§  Spain: real wage falls and rental rate rises.
§  Poland: real wage rises and rental rate falls
§  Workers in Spain will be against trade. In Poland capital owners will be against.
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Income Distribution: Application
§  From the mid 70s onwards, the wage inequality between skilled and unskilled workers has
steadily increased in several countries.
§  Can we blame globalization? Might this be due to the increased trade with developing and
emerging countries?
§  To see this, use the Heckscher-Ohlin model with skilled and unskilled labor as the two
factors of production (instead of capital and labor).
§  In this case, the Heckscher-Ohlin model would predict that wage inequality increases in the
developed world, and decreases in developing and emerging countries.
§  The former has happened, but not the latter. Should we conclude that globalization does
not matter? (Note: there are papers that rationalize these trends).
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Factor Price Equalization (FPE)
Food
w/r
Computers
(w/r)
(w/r)LC
(w*/r*)
PF/PC
(PF/PC)
(P*F/P*C)
(PF/PC)FT
(K*F/L*F)
(KF/LF)
(KF/LF)FT
(K*C/L*C)
(KC/LC)
K/L
(KC/LC)FT
Convergence in price of goods, due to free trade, implies convergence in relative factor returns
(w/r) and relative use of factors in each sector (KF/LF and KC/LC).
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FPE
§
In the last figure we saw that free trade brings about equalization of relative factor prices
(w/r) and relative use of factors (KA/LA y KS/LS).
§
It is straighforward to see that absolute factor prices also converge. Remember that
nominal wages can be written as
w = PFMPLF = PCMPLC
w* = P*FMPL*F = P*CMPL*C
§
With free trade, PF=P*F and PC=P*C, and since KF/LF=K*F/L*F and KC/LC=K*C/L*C, it follows
that PFMPLF = P*FMPL*F and PCMPLC,= P*CMPL*C , so that
w = w*
§
Obviously, given that prices and nominal wages converge, real wages also converge:
ω= ω*
§
Following the same steps, it is easy to see that the rental rate of capital also converges,
both in real and nominal terms.
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Another Look at FPE
K
1/r
=1/r*
CC=CC*
KC/LC =K*C/L*C
Since both countries share the same
technologies and face the same prices, the
isovalue curves for computers and food are
also the same.
KF/LF =K*F/L*F
-(w/r)W
1/w=1/w*
FF=FF*
If both countries produce both goods
(incomplete specialization), the isocost that is
tangent to the two isovalue curves is the
same in both economies.
Remember that the intercept of the isocost
with the y-axis is 1/r =1/r* and with the x-axis
is 1/w=1/w*.
Therefore, w = w* y r = r*.
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FPE Theorem
FPE THEOREM
When there are no barriers to trade, technologies are identical and both countries
produce both goods, we have factor price equalization.
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Factor Mobility and Goods Mobility
Compare the following cases
§  Case 1: We allow factor mobility across countries but not trade in goods.
§  We know that in autarky ω > ω* (real wage) and ρ < ρ* (real return to capital).
§  With factor mobility, workers move to Spain and capital moves to Poland.
§  In equilibrium, ω = ω* and ρ = ρ* (this happens when K/L = K*/L*).
§  Case 2: We allow trade in goods but factors cannot move across countries.
§  We have seen that trade in goods brings about FPE, ω = ω* y ρ = ρ*, WITHOUT THE NEED OF
FACTOR MOBILITY.
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Factor Mobility and Goods Mobility
Intuition of FPE
Capital
POLAND
SPAIN
Labor
Capital
Computers
POLAND
SPAIN
Food
Labor
Spain, by exporting computers is also “exporting” capital to Poland, since computers are
capital-intensive. The same is true for labor and food for Poland.
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FPE Exceptions
We obtain FPE if the following conditions hold:
1.  Both countries produce both goods.
2.  Identical technologies across countries.
3.  No barriers to trade.
If any of these three assumptions does not hold, we will not obtain FPE.
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One Country Only Produces One Good
K*/L*
w/r
Food
Computers
(w/r)
(w/r)FT
(w*/r*)FT
(w*/r*)
PF/PC
(PF/PC)
(P*F/P*C)
(PF/PC)FT
(K*F/L*F)FT
(KC/LC)FT
K/L
(KF/LF)FT
Let us assume that the capital endowment in Poland is very low, that is, K*/L* is very small.
Remember that KF*/LF* ≤ K*/L* ≤ KC*/LC*. (Otherwise, one factor would be unemployed)
When there is convergence in goods prices, the relative wages in Poland increase, and so do the capital ratios KF*/LF*
and KC*/LC*. In order to have the weighted sum of KF*/LF* and KC*/LC* add up to K*/L*, the economy increases the
production of food and decreases the production of computers. When the economy reaches KF*/LF* = K*/L*, it becomes
completely specialized in food. At that point, relative wages stop converging. However, goods prices do converge.
Note: In the left-hand side panel we assume production of both goods. The right-hand side panel doesn’t hinge on that assumption. When
Poland stops prodcuing computers, the left-hand side panel isn’t longer useful to determine wages.
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One Country Produces Only One Good
K
With free trade, the isovalue curves are CC and FF.
To produce both goods we need an isocost that is
tangent to both curves.
(KS /LS)
CC
A country needs to have capital ratios between KC /LC
and KF /LF to produce both goods (cone of
diversification).
FF
Spain is within the cone of
diversification, and therefore produces
both goods, so that the relative wage is
w/r.
(K/L)
1
Poland is outside the cone of
diversification (see K*/L*), it only
produces food and the relative wage is
w*/r*.
(KF/LF)
(K*/L*)
1
Using the same reasoning as before, it is
easy to show that w < w*, r > r*, ω < ω*
and ρ > ρ*.
-(w/r)
-(w*/r*)
L
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Different Technologies
K
Assume that Spain has a technology
1.x times the technology of Poland in
both sectors.
CC*
1/r* CC
(KC /LC)
In this case, Poland needs 1.x times
the capital and labor of Spain to
produce the same.
1/r
Thus, the isovalue curves of Poland
are 1.x times the ones of Spain.
(KF/LF)
In equilbrium, w > w* and r > r*.
FF*
FF
1/w
-(w/r)
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1/w*
Actually, w = 1.x w* and r = 1.x r
L
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Barriers to Trade
If there are transportation costs and/or other barriers to trade, the price of goods will not
converge. Thus, factor returns will not converge either.
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4. EXERCISES
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Heckscher-Ohlin Problem Set
See Problem Set “Heckscher-Ohlin Model”.
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