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Transcript
Chapter 6
Factor Endowments
and Trade II: The
Heckscher-Ohlin
Model
© 2007 Pearson Addison-Wesley.
All rights reserved
Contents
•
•
•
•
•
•
Heckscher-Ohlin Theorem
Factor Price Equalization Theorem
Stolper-Samuelson Theorem
Rybczynski Theorem
Factor Price Insensitivity Lemma
Factor Intensity Reversal
Copyright © 2007 Pearson Addison-Wesley. All rights reserved.
6-2
Methodology
• Diagram Analysis
• Mathematical Proof
• Empirical Analysis
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6-3
Two-Factor Heckscher-Ohlin Model
1.
2.
3.
4.
5.
6.
Labor and capital are resources important for production.
The amount of labor and capital varies across countries, and this variation
influences productivity.
The supply of labor and capital in each country is constant.
Only two goods are important for production and consumption: cloth and
food.
Competition allows factors of production to be paid a “competitive”
wage, a function of their productivities and the price of the good that it
produces, and allows factors to be used in the industry that pays the
highest wage/rental.
Only two countries are modeled: domestic and foreign
Copyright © 2007 Pearson Addison-Wesley. All rights reserved.
6-4
Production Possibilities
• When there is more than one factor of production, the PPF
(opportunity cost in production) is no longer a straight line.
Why?
• Let’s expand the previous chapter’s model to include two
factors of production, labor and capital.
–
–
–
–
–
–
aTC = hectares of capital used to produce one m2 of cloth
aLC = hours of labor used to produce one m2 of cloth
aTF = hectares of capital used to produce one calorie of food
aLF = hours of labor used to produce one calorie of food
L = total amount of labor available for production
K= total amount of capital (terrain) available for production
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6-5
Production Possibilities (cont.)
• Production possibilities are influenced by both
capital and labor (requirements):
Total amount of
aTFQF + aTCQC ≤ K
capital
resources
capital required
for each unit of
food production
Total units
of food
production
capital required
for each unit of
cloth production
aLFQF + aLCQC ≤ L
Labor required for
each unit of food
production
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Total units
of cloth
production
Total amount of
labor resources
Labor required for
each unit of cloth
production
6-6
Production Possibilities (cont.)
• Let’s assume that each unit of cloth production uses labor
intensively and each unit of food production uses capital
intensively:
– aLC /aKC > aLF/aKF
– Or aLC /aLF > aKC /aKF
– Or, we consider the total resources used in each industry and say that
cloth production is labor intensive and food production is capital
intensive if LC /KC > LF /KF.
• This assumption influences the slope of the production
possibility frontier:
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6-7
Production Possibilities (cont.)
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6-8
Production Possibilities (cont.)
• The opportunity cost of producing cloth in terms of
food is not constant in this model:
– it’s low when the economy produces a low amount of
cloth and a high amount of food
– it’s high when the economy produces a high amount of
cloth and a low amount of food
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6-9
Production Possibilities (cont.)
• The above PPF equations do not allow substitution of capital
for labor in production or vice versa.
– Unit factor requirements are constant along each line segment of the
PPF.
• If we allow substitution of inputs, then the PPF becomes
curved.
– For example, many laborers could work on a small plot of capital or a
few labors could work on a large plot of capital to produce the same
amount of output.
– Unit factor requirements are not constant at every quantity of cloth and
food produced.
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6-10
A simple HO Model with rigid technology
•
•
•
•
•
Assume home country is relatively labor-abundant country.
L/K>L*/K*
alcC+alfF=L; akcC+akfF=K;
alcC*+alfF*=L*; akcC*+akfF*=K*
Remember that techonology is assumed to be the same in both
countries.
• Preference are identical in both countries.
• Assume same capital endowment in both countries, but home
has 50% more labor force.
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6-11
Figure 6.1 Production Possibilities:
Rigid Technology
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6-12
A simple HO Model with rigid technology
• The K-constraint line is assumed to intersect the laborconstraint line instead of lying everywhere above or below.
• Given clothing is relative labor-intensive, the capital-constraint
line is flatter than the labor-constraint line.
• Point A is the only output combination for which both labor
and capital are fully employed in foreign.
• Point S is the only output combination for which both labor
and capital are fully employed at home.
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6-13
Two conclusions of a simple HO Model
• The relatively labor-abundant country produces relatively
larger quantities of the labor-intensive commodity.
• The relatively labor-abundant country will tend to export the
relatively labor-intensive commodity.
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6-14
A Numerical Example
•
•
•
•
•
•
Factor requirements:
alc=3, alf=1; akc=1, akf=2
Factors Market clear condition for foreign:
Labor: 3C*+F*=200
Capital: C*+2F*=200
Question: how do goods’ price changes alter the distribution of
income?
• Suppose food’s price doesn’t change before and after trade, 10
• Clothing price differs in both countries before trade, but equals
10 after trade (assumed free trade)
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6-15
Price changes alter the distribution of income?
• Unit-cost equilibrium conditions:
• At home 3w+r=8 (clothing)
• At home w+2r=10 (food)
• At foreign 3w*+r*=12 (clothing)
• At foreign w*+2r*=10 (food)
• Autarky Solution: at home: w=6/5; r=22/5
•
Abroad: w*=14/5; r*=16/5.
• Clothing is more expensive abroad at autarky
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6-16
Two Important Results
•
•
•
•
•
After trade,
At home 3w+r=10 (clothing)
At home w+2r=10 (food)
At foreign 3w*+r*=10 (clothing)
At foreign w*+2r*=10 (food)
• Solution: w=2; r=4 (for both countries)
• Free trade benefits the abundant factor of production and
harms the relatively scarce factor of production.
• Stopler-Samuelson Theorem
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6-17
Factor Price Equalization
• Trading countries’ factor prices should equalize after trade if
they satisfy:
• (1) Both products are produced in both countries
• (2) Common technology
• (3) Free Trade
• (4) No Factor Intensity Reversal (FIR)
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6-18
Figure 6.2 Factor-Intensity Comparison
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6-19
Factor-Intensity Comparison
• When technology is flexible, one can use iso-quant to denote.
• When costs are minimized in each, clothing is relatively labor
intensive.
• Food is presumed to be produced by capital-intensive
techniques compared with clothing.
• When both industries face the same set of factor prices, the
least-cost K/L ratio for food (at A) exceeds that chosen for
clothing (at B)
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6-20
Figure 6.3 Factor Intensities and
Factor Endowments
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6-21
Factor Intensities and Factor Endowments
• If the K/L ratio at home is k, the w/r ratio must lie in the range
BC.
• Why?
• If the w/r is higher than point c, too much demand for capital,
which exceeds its maximum.
• If the capital-abundant foreign country has the endowment
ratio k*, there is an overlap of possible w/r ratio in the two
countries, DC.
• Free trade may equalize factor prices.
• If the foreign endowment ratio be at the higher value k**, the
relative wage rate abroad must be higher than at home.
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6-22
Production Possibilities (cont.)
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6-23
Input Possibilities
In the production of each
unit of food, unit factor
requirements of capital
and labor are not
constant in the
Heckscher-Ohlin model
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6-24
Production and Prices
• The production possibility frontier describes what an economy
can produce, but to determine what the economy does produce,
we must determine the prices of goods.
• In general, the economy should produce at the point that
maximizes the value of production, V:
V = PCQC + PFQF
– where PC is the price of cloth and PF is the price of food.
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6-25
Production and Prices (cont.)
• Define an iso-value line as a line representing a
constant value of production.
– V = PCQC + PFQF
– PFQF = V – PCQC
– QF = V/PF – (PC /PF)QC
– The slope of an iso-value line is – (PC /PF)
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6-26
Production and Prices (cont.)
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6-27
Production and Prices (cont.)
• Given prices of output, one iso-value line represents
the maximum value of production, say at a point Q.
• At that point, the slope of the PPF equals
– (PC
/PF), so the opportunity cost of cloth equals the
relative price of cloth.
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6-28
Factor Prices, Goods Prices and Factor Levels
• Producers may choose different amounts of factors of
production used to make cloth or food.
• Their choice depends on the wage rate, w, and the
(opportunity) cost of using capital, the rental rate r.
• As the wage rate increases relative to the rental rate, producers
are willing to use more capital and less labor in the production
of food and cloth.
– Recall that food production is capital intensive and cloth production is
labor intensive.
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6-29
Factor Prices, Goods Prices
and Factor Levels (cont.)
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6-30
Factor Prices, Goods Prices
and Factor Levels (cont.)
• Under competition, the price of a good equals the cost of
production, and the cost of production depends on the wage
rate and the rental rate.
• Pc=costc=w*a +r*a
CL
CK
• The effect of the rental rate of capital on the price of cloth
depends on the intensity of capital usage in
cloth production.
– An increase in the rental rate of capital will affect the price of food
more than the price of cloth.
• Under competition, changes in w/r are therefore directly
related to changes in PC /PF .
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6-31
Factor Prices, Goods Prices
and Factor Levels (cont.)
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6-32
Figure 6.4 Factor Prices and
Commodity Prices
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6-33
Factor Prices, Goods Prices
and Factor Levels (cont.)
• We have a relationship among factor prices and good prices and the
levels of factors used in production:
• Stolper-Samuelson theorem: if the relative price of a
good increases, then the real wage (or rate of return of the
factor) used intensively in the production of that good
increases, while the real wage (or rate of return of the other
factor) decreases.
– Pc/PF up  (K/L)C up; (K/L)F up.
– Note that clothing is labor intensive, therefore Lf relatively decreases.
– Marginal productivity of a factor increases as the level of that
factor used in production decreases: L down MPL up.
– Under competition, the real wage/return is equal to the marginal
productivity of the factor: W/Pc=MPL
– Pc/PF up w/Pc up, r/Pc down; W/PF up, r/PF down
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6-34
Factor
Prices,
Goods
Prices
and
Factor
Levels
(cont.)
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6-35
Factor Prices, Goods Prices
and Factor Levels (cont.)
• We have a theory that predicts changes in the distribution of
income when the relative price of goods changes, say because
of trade.
• An increase in the relative price of cloth, PC /PF , will:
– raise income of workers relative to that of capital owners, w/r.
– raise the ratio of capital to labor, K/L, in both industries and raise the
marginal product of labor in both industries and lower the marginal
product of capital in both industries.
– raise the real income of workers and lower the real income of capital
owners.
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6-36
Factor Prices, Goods Prices,
Factor Levels and Output Levels
• The allocation of factors used in production
determine the level of output at the economy’s PPF.
• We summarize the relationship between the levels of
factors used in production and output levels, using the
following diagram:
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6-37
Factor
Prices,
Goods
Prices,
Factor
Levels
and
Output
Levels
(cont.)
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6-38
Factor Prices, Goods Prices,
Factor Levels and Output Levels (cont.)
• How do output levels change when the economy’s
resources change?
• If we hold output prices constant as a factor
of production increases, then the supply of
the good that uses this factor intensively increases
and the supply of the other
good decreases.
– This proposition is called the Rybczynski theorem.
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6-39
Factor Prices,
Goods Prices,
Factor Levels
and Output
Levels (cont.)
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6-40
Factor Prices, Goods Prices,
Factor Levels and Output Levels (cont.)
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6-41
Factor Prices, Goods Prices,
Factor Levels and Output Levels (cont.)
• An economy with a high ratio of capital to labor is predicted
to have a high output of food relative to cloth and a low price
of food relative to cloth.
– It will be relatively efficient at (have a comparative advantage in)
producing food.
– The relative supply of food shifts to the right.
• An economy will be relatively efficient at producing goods
that are intensive in the factors of production in which the
country is relatively well endowed.
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6-42
Trade in the Heckscher-Ohlin Model
• Suppose that the domestic country has an abundant amount of
labor relative to the amount of capital.
– The domestic country is abundant in labor and the foreign country is
abundant in capital: L/T > L*/ K*
– Likewise, the domestic country is scarce in capital and the foreign
country is scarce in labor.
– However, the countries are assumed to have the same technology and
same consumer tastes.
• Because the domestic country is abundant in labor, it will be
relatively efficient at producing cloth because cloth is labor
intensive.
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6-43
Trade in the Heckscher-Ohlin Model
(cont.)
• Since cloth is a labor intensive good, the domestic
country’s PPF will allow a higher ratio of cloth to
food relative to the foreign county’s PPF.
• At each relative price, the domestic country will
produce a higher ratio of cloth to food than the
foreign country.
– The domestic country will have a higher relative supply of
cloth than the foreign country.
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6-44
Trade in the Heckscher-Ohlin Model
(cont.)
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6-45
Trade in the Heckscher-Ohlin Model
(cont.)
• Like the Ricardian model, the Heckscher-Ohlin model
predicts a convergence of relative prices with trade.
• With trade, the relative price of cloth will rise in the
domestic country and fall in the foreign country.
– In the domestic country, the rise in the relative price of cloth leads
to a rise in the relative production of cloth and a fall in relative
consumption of cloth; the domestic country becomes an exporter of
cloth and an importer of food.
– The decline in the relative price of cloth in the foreign country
leads it to become an importer of cloth and an exporter
of food.
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6-46
Trade in the Heckscher-Ohlin Model
(cont.)
• An economy will be relatively efficient at
(have a comparative advantage in) producing
goods that are intensive in its abundant factors of
production.
• An economy will export goods that are intensive in
its abundant factors of production and import
goods that are intensive in its scarce factors of
production.
– This proposition is called the Heckscher-Ohlin theorem
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6-47
Trade in the Heckscher-Ohlin Model
(cont.)
• Over time, the value of goods consumed is constrained to
equal the value of goods produced for each country.
PCDC + PFDF = PCQC + PFQF
where DC represents domestic consumption demand for cloth and DF
represents domestic consumption demand for food
(DF – QF) = (PC /PF)(QC – DC)
Quantity
of imports
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Price of exports
relative to imports
Quantity
of exports
6-48
Trade in the Heckscher-Ohlin Model
(cont.)
(DF – QF) = (PC /PF)(QC – DC)
• This equation is the budget constraint for an
economy, and it has a slope of – (PC /PF)
(DF – QF) – (PC /PF)(QC – DC) = 0
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6-49
Trade in the Heckscher-Ohlin Model
(cont.)
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6-50
Trade in the Heckscher-Ohlin Model
(cont.)
• Note that the budget constraint touches the PPF: a
country can always afford to consume what it
produces.
• However, a country need not consume
only the goods and services that it produces
with trade.
– Exports and imports can be greater than zero.
• Furthermore, a country can afford to consume more
of both goods with trade.
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6-51
Trade in the Heckscher-Ohlin Model
(cont.)
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6-52
Trade in the Heckscher-Ohlin Model
(cont.)
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6-53
Trade in the Heckscher-Ohlin Model
(cont.)
• Because an economy can afford to consume more with
trade, the country as a whole is made better off.
• But some do not gain from trade, unless the model accounts
for a redistribution of income.
• Trade changes relative prices of goods, which have effects
on the relative earnings of labor and capital.
– A rise in the price of cloth raises the purchasing power of domestic
laborers, but lowers the purchasing power of domestic capital
owners.
• The model predicts that with trade owners of abundant
factors gain, but owners of scarce
factors lose.
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6-54
Factor Price Equalization
• Unlike the Ricardian model, the Heckscher-Ohlin model
predicts that factor prices will be equalized among countries
that trade.
• Because relative prices are equalized and because of the direct
relationship between relative prices and factor prices, factor
prices are also equalized.
• Trade increases the demand for goods produced by abundant
factors, indirectly increasing the demand for the abundant
factors themselves, raising the factor prices of the abundant
factors across countries.
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6-55
Factor Price Equalization
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6-56
Factor Price Equalization (cont.)
• But factor prices are not really equal across countries.
• The model predicts that trading countries produce the same
goods, so that prices for those goods can equalize, but
countries may produce different goods.
• The model assumes that trading countries have the same
technology, but different technologies could affect the
productivities of factors and therefore the wages/rates paid to
these factors.
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6-57
Factor Price Equalization (cont.)
• Trade barriers and transportation costs may prevent goods
prices and factor prices from equalizing.
• After an economy liberalizes trade, factors of production may
not quickly move to the industries that intensively use
abundant factors.
– In the short run, the productivity of factors will be determined by their
use in their current industry, so that their wage/rate may vary across
countries.
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6-58
Does Trade Increase Income Inequality?
• Over the last 40 years, countries like South Korea,
Mexico and China have exported to the US goods
intensive in unskilled labor (e.g., clothing, shoes,
toys, assembled goods).
• At the same time, income inequality has increased in
the US, as wages of unskilled workers have grown
slowly compared to those of skilled workers.
• Did the former trend cause the latter trend?
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6-59
Does Trade Increase
Income Inequality? (cont.)
•
The Heckscher-Ohlin model predicts that owners of
abundant factors will gain from trade and owners of scarce
factors will lose from trade.
•
But little evidence supporting this prediction exists.
1. According to the model, a change in income distribution
occurs through changes in goods prices, but there is no
evidence of a change in the prices of skill-intensive goods
relative to prices of unskilled-intensive goods.
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6-60
Does Trade Increase
Income Inequality? (cont.)
2.
According to the model, wages of unskilled workers should
increase in unskilled labor abundant countries relative to
wages of skilled labor, but in some cases the reverse has
occurred:
–
3.
Wages of skilled labor have increased more rapidly in Mexico than
wages of unskilled labor.
Even if the model were exactly correct, trade is a small
fraction of the US economy, so its effects on US prices and
wages prices should be small.
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6-61
Trade and Income Distribution
• Changes in income distribution occur with every economic
change, not only international trade.
– Changes in technology, changes in consumer preferences, exhaustion of
resources and discovery of new ones all affect income distribution.
– Economists put most of the blame on technological change and the
resulting premium paid on education as the major cause of increasing
income inequality in the US.
• It would be better to compensate the losers from trade (or any
economic change) than prohibit trade.
– The economy as a whole does benefit from trade.
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6-62
Trade and Income Distribution (cont.)
• There is a political bias in trade politics: potential
losers from trade are better politically organized than
the winners from trade.
– Losses are usually concentrated among a few, but gains are
usually dispersed among many.
– Each of you pays about $8/year to restrict imports of sugar,
and the total cost of this policy is about $2 billion/year.
– The benefits of this program total about
$1 billion, but this amount goes to relatively
few sugar producers.
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6-63
Empirical Evidence of the
Heckscher-Ohlin Model
• Tests on US data
– Leontief found that US exports were less capital-intensive than US
imports, even though the US is the most capital-abundant country in the
world: Leontief paradox.
• Tests on global data
– Bowen, Leamer, and Sveikauskas tested the Heckscher-Ohlin model on
data from 27 countries and confirmed the Leontief paradox on an
international level.
• Tests on manufacturing data between low/middle income
countries and high income countries.
– This data lends more support to the theory.
– North-South trade pattern fits better with the theory
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6-64
Empirical Evidence of the
Heckscher-Ohlin Model (cont.)
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6-65
Empirical Evidence of the
Heckscher-Ohlin Model (cont.)
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6-66
Empirical Evidence of the
Heckscher-Ohlin Model (cont.)
• Because the Heckscher-Ohlin model predicts that factor prices
will be equalized across trading countries, it also predicts that
factors of production will produce and export a certain
quantity goods until factor prices are equalized.
– In other words, a predicted value of services from factors of
production will be embodied in a predicted volume of trade
between countries.
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6-67
Empirical Evidence of the
Heckscher-Ohlin Model (cont.)
• But because factor prices are not equalized across countries,
the predicted volume of trade is much smaller than actually
occurs.
– A result of “missing trade” discovered by Daniel Trefler.
• The reason for this “missing trade” appears to be the
assumption of identical technology among countries.
– Technology affects the productivity of labor and therefore the value of
labor services.
– A country with high technology and a high value of labor services
would not necessarily import a lot from a country with low technology
and a low value of labor services.
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6-68
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6-69
Summary
1.
Substitution of factors in the production process generates a
curved PPF.
–
–
2.
When an economy produces a low level of a good, the opportunity
cost of producing that good is low.
When an economy produces a high level of a good, the opportunity
cost of producing that good is high.
When an economy produces on its PPF, the opportunity cost
of producing a good equals the relative price of that good.
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6-70
Summary (cont.)
3. If the relative price of a good increases, then the real
wage or rate of return of the factor used intensively
in the production of that good increases, while the
real wage or rate of return of the other factor
decreases.
4. If we hold output prices constant as a factor of
production increases, then the supply
of the good that uses this factor intensively
increases, and the supply of the other
good decreases.
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6-71
Summary (cont.)
5.
An economy will export goods that are intensive in its
abundant factors of production and import goods that are
intensive in its scarce factors of production.
6.
The Heckscher-Ohlin model predicts that relative output
prices and factor prices will equalize, neither of which occurs
in the real world.
7.
The model predicts that owners of abundant factors gain, but
owners of scarce factors lose with trade.
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6-72
Summary (cont.)
8. A country as a whole will be better off with trade,
even though the model predicts that owners of
scarce factors will be worse off without
compensation.
9. Empirical support of the Heckscher-Ohlin model is
weak except for cases involving trade between high
income countries and low/middle income countries.
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6-73
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6-74
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6-75
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Figure 6.5 Unit-Value Iso-quants
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Figure 6.A.1 The Production Box
Diagram
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