The Heckscher-Ohlin-Samuelson
Model
Factor Proportions Theory
Problems with the Generic
Neoclassical Model
• What is the source of a country’s
comparative advantage? Generic
neoclassical theory doesn’t really say
• Factors other than labor (especially capital)
are not explicitly included
H-O-S In General
• Heckscher, and his student Ohlin, worked in
the early part of the 20th century
• Samuelson refined their work after WWII
• Closer attention is paid in this model to
each country’s resource endowment
H-O-S Assumptions
•
•
•
•
•
2 countries
2 commodities
2 factors (labor and capital)
Perfect competition exists in all markets
Each country’s endowment of factors is
fixed
• Factors are mobile internally, but immobile
internationally
H-O-S Assumptions (cont’d)
• Each producer has a wide range of options
as to how to produce X or Y
– if K is cheap relative to labor, a relatively
capital-intensive method will be adopted
– if K is expensive relative to labor, a relatively
labor-intensive method will be adopted
• Each country has the same CRTS
technology
H-O-S Assumptions (cont’d)
• Tastes and preferences are the same for both
countries
Concepts and Terminology
• The capital-labor ratio for good X is simply
KX/LX, and for Y is KY/LY
• If KX/LX > KY/LY, production of good X is
capital intensive relative to production of
good Y
• Also, production of Y must be relatively
labor intensive (If KX/LX > KY/LY, then
LY/KY > LX/KX)
Concepts and Terminology
• Country A is said to be capital abundant
relative to Country B if (K/L)A > (K/L)B
• In such a case, Country B must be relatively
labor abundant
• So:
– goods are produced relatively K or L
intensively
– countries are relatively K or L abundant
Concepts and Terminology
• The factor price of labor (the wage) is
denoted w
• The factor price of capital is denoted r
• If labor is relatively expensive, w/r will be a
relatively big number
• If labor is relatively cheap, w/r will be a
relatively small number
More on Factor Prices
• What makes labor relatively expensive?
– If it is relatively scarce
• What makes labor relatively cheap
– If it is relatively abundant
• So: If (K/L)A is a relatively big number (that
is, capital is relatively abundant), w/r will
be a relatively big number, reflecting the
relative scarcity of L and abundance of K
A Review of Trade in the
Neoclassical Model
• Suppose the U.S. is capital abundant
relative to Mexico
• This, of course, means that Mexico is
relatively labor abundant
• These differences affect the shape of each
country’s PPF
• Suppose that cars are produced rel. Kintensively, and textiles labor intensively
Autarky in Mexico and the U.S.
Cars
Mexico
Cars
U.S.
Y4
e
(PT/PC)Mex
E
Y1
(PT/PC)US
X1
Textiles
X4
Textiles
Autarky in Mexico and the U.S.
• The relative price of textiles in autarky is
greater in the U.S. than in Mexico
• That is, the U.S.’s autarky price line is
steeper than Mexico’s
• In symbols, (PT/PC)U.S. > (PT/PC)Mex.
• This means that Mexico has the comparative
advantage in textiles
Autarky in Mexico and the U.S.
• This also means that the relative price of
cars in autarky is lower in the U.S. than in
Mexico
• That is, (PC/PT)U.S. < (PC/PT)Mex.
• This means that the U.S. has the
comparative advantage in cars
Production in Trade
Cars
Mexico
(PX/PY)T
Y5
Y1
U.S.
Cars
E
Y4
e'
e
E'
Y2
X1
X2 Textiles
X5 X4
Textiles
Consumption in Trade
Cars
Mexico
(PX/PY)T
Y5
C'
Y1
U.S.
Cars
E
Y4
e'
e
c'
E'
Y2
X1
X2 Textiles
X5 X4
Textiles
The Result
• The relatively capital abundant country
(U.S.) exports the relatively capital
intensive good (cars)
• The relatively labor abundant country
(Mexico) exports the relatively labor
intensive good (textiles)
The Heckscher-Ohlin Theorem
• A country will export the commodity that
uses relatively intensively the factor that
country has in relative abundance
• A country will import the commodity that
uses relatively intensively the factor that is
relatively scarce in that country
The Source of Comparative
Advantage
• If a country has a lot of labor relative to K,
its wage rates will be relatively low, so
• the product that uses a lot of labor in its
production (relatively speaking) will be
produced at a relatively low cost, so
• the country should export the labor
intensive good
The Source of Comparative
Advantage
• If a country has a lot of capital relative to L,
its capital price will be relatively low, so
• the product that uses a lot of K in its
production (relatively speaking) will be
produced at a relatively low cost, so
• the country should export the capital
intensive good
The Source of Comparative
Advantage
• So it is a country’s relative factor
endowment that determines its comparative
advantage
• This is why the H-O-S model is also called
the factor proportions theory
Changes in Relative Commodity
Prices
• As we learned before,
– (PT/PC)US falls as the U.S. moves to trade. That
is, the international relative textile price is
lower than the U.S.’s autarky price.
– (PT/PC)Mex rises as Mexico moves to trade. That
is, the international relative textile price is
higher than Mexico’s autarky price.
Changes in Factor Prices
• In autarky, the K-intensive product (cars) is
less expensive to produce in the U.S. as
compared to Mexico
– this is because K is relatively abundant in the
U.S., which makes the price of capital
relatively low
• As trade commences, r will rise since
demand for capital will rise
Changes in the Price of Capital in
the U.S.
r
SK
In autarky, the price of capital
(r1) is determined by supply of
and demand for capital in the U.S
r1
D1K
QK
Changes in the Price of Capital in
the U.S.
r
r2
r1
SK
When trade starts, the U.S. increases
its production of the capital intensive
product, and therefore demand for
capital increases in the U.S.
D2K
D1K
QK
Changes in Factor Prices
• In autarky, the L-intensive product (textiles)
is more expensive to produce in the U.S. as
compared to Mexico
– this is because L is relatively scarce in the U.S.,
which makes the price of labor relatively high.
• As trade commences, w will fall since
demand for labor will fall
Changes in the Price of Labor in
the U.S.
w
SL
D1L
QL
Changes in the Price of Labor in
the U.S.
w
w1
SL
In autarky, the price of labor
(w1) is determined by supply of
and demand for labor in the U.S
D1L
QL
Changes in the Price of Labor in
the U.S.
w
w1
SL
When trade starts, the U.S. decreases
its production of the labor intensive
product, and therefore demand for
labor decreases in the U.S.
w2
D1L
QL
Commodity and Factor Prices In
Trade: A Summary
• When trade begins, the relative price of the
good intensive in the abundant factor rises
(e.g., (PC/PT)US rises)
• The relative price of the good intensive in
the scarce factor falls (e.g., (PT/PC)US falls)
• Also, the price of the abundant factor rises,
and the price of the scarce factor falls (i.e.,
w falls, r rises in the U.S.)
Commodity and Factor Prices In
Trade: A Summary
• In our example, (PT/PC)US falls as trade
commences
• (w/r)US also falls
• In Mexico, the opposite is happening:
– (PT/PC)Mex rises
– (w/r)Mex also rises
• Therefore relative commodity and factor
prices move together as trade commences
The Relative Cost Curve
• Since relative factor and commodity prices
move together as countries move from
autarky to trade, we can look at a picture of
these two sorts of prices
• We also know that in autarky (PT/PC)Mex is
lower than (PT/PC)US
• (w/r)Mex is also lower in autarky than
(w/r)US since Mexico is relatively labor
abundant
The Relative Cost Curve
PT/PC
(PT/PC)US
As trade commences, (PT/PC)US
falls, and (PT/PC)Mex rises
(PT/PC)Mex
(w/r)Mex
(w/r)US
w/r
The Relative Cost Curve
PT/PC
(PT/PC)US
In addition, as trade commences
(w/r)US falls, and (w/r)Mex rises
(PT/PC)Mex
(w/r)Mex
(w/r)US
w/r
Factor Price Equalization
• In fact, each country moves along the
relative cost curve to a common point
• We know this because there is only one
international price
• If the countries wind up with a common
international price, they must also wind up
with a common set of relative factor prices
The Relative Cost Curve
PT/PC
(PT/PC)US
(PT/PC)Int
(PT/PC)Mex
Both relative commodity and
factor prices equalize in trade
(w/r)Mex (w/r)Int (w/r)US
w/r
The Factor Price Equalization
Theorem
In equilibrium, with both countries facing
the same relative (and absolute) product
prices, both having the same technology,
and with constant returns to scale, relative
(and absolute) costs will be equalized. This
can only happen if factor prices are
equalized between countries.
H-O-S and the Distribution of
Income
• The H-O theorem, together with the FPE
theorem also tell us about how the incomes
of different groups within a country change
as trade starts
• This provides insight into the politics of free
trade
The Stolper-Samuelson Theorem
The increase in the price of the relatively
abundant factor and the fall in the price of
the relatively scarce factor because of trade
implies that the owners of the abundant
factor will find their real incomes rising;
the owners of the scarce factor will find
their real incomes falling.
H-O-S and the Distribution of
Income
• According to the S-S theorem, if the U.S. is
a relatively K-abundant country, who in
America should favor free trade?
• Who in America should favor
protectionism?
Theoretical Qualifications to
H-O-S
• Suppose we relax some of the many
assumptions. Will the implications of the
H-O-S model still be the same?
Qualification #1: Demand
Reversal
• Normally, the relative price of the
commodity that uses intensively the
abundant factor will be lower
• In our example, (PC/PT)US < (PC/PT)Mex
• Or, (PT/PC)US > (PT/PC)Mex
• What causes this difference in autarky
prices? Differences in supply conditions
Qualification #1: Demand
Reversal
• Suppose we let demand conditions differ
• Suppose domestic demand for the good that
uses relatively intensively the relatively
abundant factor is very strong in each
country
• That is, demand for cars is very strong in
the U.S., and demand for textiles is very
strong in Mexico
Qualification #1: Demand
Reversal
• Such strong demand makes the autarky car
price in the U.S. higher, and the textile price
in Mexico higher
• In the extreme, demand reversal could
occur: (PC/PT)US > (PC/PT)Mex, and
• (PT/PC)US < (PT/PC)Mex
• So what?
Qualification #1: Demand
Reversal
• When trade begins, as usual the int’l price
will lie between the two countries’ APRs
• Therefore (PC/PT) for Mexico will rise as it
moves to trade
• Mexico, then, would export cars
• Meanwhile, (PT/PC) for the U.S. will rise as
it moves to trade
• The U.S., then, would export textiles
Bottom Line on Demand
Reversals
• If demand reversals occur, the H-O theorem
no longer holds: the K-abundant country is
exporting the L-intensive good, and the Labundant country is exporting the Kintensive good
• If demand reversals are common in the real
world, we’d better find a new theory
Qualification #2: Factor Intensity
Reversal
• Implicitly, we’ve assumed that if good X is
K-intensive relative to good Y at one factor
price ratio, it will be K-intensive at all
factor prices
• A FIR is when a good is relatively Kintensive at one set of factor prices, but
relatively labor intensive at another
Qualification #2: Factor Intensity
Reversal
• FIRs occur when capital and labor can be
substituted more easily in the production of
one good than another
• Example:
– Suppose butane production is very inflexible:
1K + 1L = 1 butane, and if you want more
butane you must add more of both K and L
– Suppose apple production is much more
flexible
Qualification #2: Factor Intensity
Reversal
• If w/r is very high, apple producers will
choose a relatively K-intensive method (as
compared with butane makers)
• If w/r starts to fall, apple producers will
start substituting L for K
• Eventually, it’s possible that apples might
be produced in a relatively L-intensive
manner (as compared with butane)
Factor Intensity Reversal:
Implications for Trade
• Suppose France is K-abundant relative to
Germany (that is (K/L)F > (K/L)G)
• This means that (w/r)F > (w/r)G
• Suppose further that there is a FIR: in
France, at (w/r)F apples are produced
relatively K-intensively but in Germany at
(w/r)G apples are produced in a relatively Lintensive way
Factor Intensity Reversal:
Implications for Trade
• If trade begins, according to the H-O
theorem the relatively K-abundant country
(France) will export the rel. K-intensive
good (apples) and the rel. L-abundant
country will export the rel. L-intensive good
(also apples)
• This can’t work
Factor Intensity Reversal: The
Bottom Line
• If FIRs are present, the H-O theorem breaks
down
• If FIRs are common, we’d better find a new
theory
Qualification #3: Transportation
Costs
• In the real world, it is costly to transport
goods internationally
• How do the implications of our model
change if we allow for transportation costs?
• Consider the supply and demand curves for
textiles in Mexico and the U.S.:
Basic Set-Up
PT
U.S.
SText
PT
Mexico
SText
PAUS
Exp.
PIntl
PIntl
Imp.
PAMex
DText
q1
q2
QT
DText
q1
q2
QT
Adding Transportation Costs
• Suppose Mexico tries to pass along 100% of
the transportation costs to the U.S.
consumers
• In this case, the U.S. textile price will rise,
and the quantity of imports demanded will
fall
• Mexico will have a surplus, and will
eventually lower their domestic price
Adding Transportation Costs
• Therefore, unless Mexico is the only seller
in the world, transportation costs will be
borne by both the consumer (the U.S.) and
the seller (Mexico).
• How does this look on the graph?
Adding Transportation Costs
PT
U.S.
SText
PT
Mexico
SText
PIntl
t-costs
Exp.
PIntl
Imp.
DText
q1 q2
QT
DText
q1 q2
QT
Adding Transportation Costs
• Notice: there is no longer a single
international textile price, but rather two
different ones
• That is, transportation costs drive a wedge
between the two countries’ prices
Adding Transportation Costs: the
Bottom Line
• In general, the H-O theorem will still hold
• The FPE theorem breaks down, since factor
prices only equalize if the commodity prices
do
• Therefore, in the presence of transportation
costs, factor prices have a tendency to move
towards each other, but we should expect
equalization
Relaxing Other Assumptions
• One can relax many other assumptions and
examine how the implications of the model
change:
–
–
–
–
–
perfect competition
CRTS
identical production technologies
lack of policy obstacles
factors being perfectly transferable
Relaxing Other Assumptions
• These issues have involved many
researchers for many years
• You can read a bit about this research in
your text, but we have other fish to fry
• Suffice it to say that relaxing these
assumptions can modify the basic H-O-S
model, but doesn’t lead us to scrap the
model