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The Heckscher-Ohlin Model
Udayan Roy
http://myweb.liu.edu/~uroy/eco41
October 2009
BASIC ASSUMPTIONS
The Heckscher-Ohlin Assumptions—
Basics
• There are
– two countries, Home and Foreign
– two goods, Cloth and Food, and
– two resources, Labor and Land
• these are used to produce Cloth and Food
The Heckscher-Ohlin Assumptions—
Preferences
• The preferences of all consumers in the world are
identical.
• The preferences of any individual are such that the
Marginal Rate of Substitution is independent of the scale
of consumption.
– The MRS of Wine for Cheese is the additional amount of Wine
that would keep the individual's level of happiness unchanged
even after the consumption of Cheese is reduced by one unit.
Under this assumption, if the amounts of Cheese and Wine being
consumed are, say, doubled, then the MRS remains unchanged. In
other words, the MRS does not change if the ratio of the amounts
of Cheese and Wine consumed, Cheese/ Wine, does not change.
The Ricardian Assumptions—
Preferences
• The preferences of all consumers in the world are
identical.
• For any individual, the Marginal Rate of Substitution
is independent of the scale of consumption.
– An individual’s MRS of wine for cheese is the maximum
amount of wine that he/she would be willing to pay for
one unit of cheese.
– Under this assumption, if the amounts of Cheese and Wine
being consumed are, say, doubled, then the MRS remains
unchanged.
– In other words, the MRS does not change if the ratio of the
amounts of Cheese and Wine consumed, Cheese/ Wine,
does not change.
Marginal Rate of Substitution
Cheese
consumed
(C)
10
600
10
Wine
consumed
(W)
20
1200
5
CheeseWine Ratio
(C/W)
0.5
0.5
2
MRSWC
2
2
1.6
The Heckscher-Ohlin Assumptions—
Markets
• All markets are perfectly competitive.
– That is, no buyer or seller of a commodity has the
power to affect the price of the commodity by himself.
– More specifically, the market for a commodity is said
to be perfectly competitive if:
• There are many sellers
• There are many buyers
• All sellers sell the exact same product
• Individuals make decisions so as to maximize
happiness, whereas
• Firms make decisions so as to maximize profits
The Heckscher-Ohlin Assumptions—
Governments
• Governments do not interfere with the
smooth functioning of markets
– There are no taxes, subsidies, tariffs, quotas,
etc.
• However, although there is free trade in
goods and services, there is no crossborder movement of resources, such as
labor
The Heckscher-Ohlin Assumptions—
Technology
• Technological knowledge is the same in
both countries
• Goods are produced (with land and labor)
using technologies that satisfy Constant
Returns to Scale.
– That is, if the producer of a commodity, say,
doubles the amounts used of all resources,
then the amount produced will have to double
also.
The Heckscher-Ohlin Assumptions—
Factor Abundance
• Home has a higher ratio of labor to land than
Foreign does.
– That is, if TH, TF, LH, and LF denote the amounts of T
(land or territory) and L (labor) that Home and Foreign
are endowed with, then LH / TH > LF/ TF.
– L/T may be informally interpreted as the number of
workers per acre of land.
– Home is said to be the “labor-abundant” country and
Foreign is the “land-abundant” country.
The Heckscher-Ohlin Assumptions—
Factor Intensities
• The production of food is land-intensive
and the production of cloth is laborintensive
– That is, the number of workers per acre (L/T) is
always higher in cloth production than in food
production
Prices of Goods
• Let PC and PF denote the nominal prices of
cloth and food.
• Then, PC/PF is the relative price of cloth (in
units of food) and
• PF/PC is the relative price of food (in units of
cloth)
Prices of Factors
• Let w be the nominal price (or, wage) of labor.
• Let r be the nominal price (or, rent) of land
• Then w/r is the relative price of labor (in units of
land) and
• r/w is the relative price of land (in units of labor)
– Example: If w = $10 per hour for one worker and r =
$100 per hour for one acre of land, then the relative
wage for one worker is 1/10 acres of land and the
relative rent on an acre of land is 10 hours of labor.
Nominal Prices
• The nominal price of a commodity is simply
the number of dollars (or any other
relevant unit of account) that must be paid
to buy one unit of the commodity
• For example, the nominal price of labor—
also called the nominal wage—may be $8
per hour
Real Prices
• The real price of commodity X, in units of
commodity Y, is the amount of Y that costs
the same as one unit of X
• For example, if the nominal price of labor is
$8 per hour and the nominal price of a cup
of coffee is $2, then the real price of labor
is 4 cups of coffee per hour
• Real prices are also called relative prices
Real and Nominal Prices
• Real Price of X, in units of Y, is equal to
Nominal Price of X / Nominal Price of Y
• So, if w is the nominal wage and P is the
nominal price of a cup of coffee, then the
real wage is w / P.
• For example, if w is $8 per hour and P is $2,
then the real wage is w / P = 8/2 = 4 cups of
coffee per hour, as in the previous slide.
Figure 4-6: Factor Prices and Goods
Prices
Relative
price of
cloth,
PC/PF
FPGP
17
5
Wage-rent
ratio, w/r
As labor becomes more
expensive relative to
land, cloth, which is
labor-intensive in
production, finds itself
at a disadvantage and
becomes relatively more
expensive compared to
food
As both Home and
Foreign use the same
technologies, the same
FPGP curve is applicable
in both countries
Figure 4-6: Factor Prices and Goods
Prices
Relative
price of
cloth,
PC/PF
FPGP
Under free trade, the
relative price of cloth
will be the same in both
countries
Therefore, the wagerent ratio will also be
the same in the two
countries
17
5
Wage-rent
ratio, w/r
Figure 4-5: Factor Prices and Input
Choices
Cloth
production
Wage-rent
ratio, w/r
Food
production
As labor becomes
relatively more
expensive, relatively
more land is used in
production…
… of both food and
cloth
5
4
12
Acres of
Land per
worker, T/L
But the number of acres
of land per worker is
always higher in food
production, reflecting
the assumption that
food production is land
intensive
Figure 4-5: Factor Prices and Input
Choices
Cloth
production
Wage-rent
ratio, w/r
Food
production
As both Home and
Foreign use the same
technologies, these two
curves must be true in
both countries.
As free trade equalizes the
wage-rent ratio worldwide,
acres of land per worker in
cloth production must be the
same worldwide.
5
Same must be true for food
production.
4
12
Acres of
Land per
worker, T/L
Therefore, Foreign, which has
more land per worker than
Home, must produce relatively
more food …
Figure 4-11: Relative Supplies
Relative
price of
cloth,
PC/PF
RSFOREIGN
17
RSHOME
In Figure 4-5, we saw that
at w/r = 5, Foreign must
produce relatively more
food and Home must
produce relatively more
cloth.
In Figure 4-6 we saw that
w/r =5 corresponds to
PC/PF = 17.
Therefore, Home must
produce relatively more
cloth at PC/PF = 17, or
indeed at any other relative
price.
As cloth becomes more expensive relative to
food, the output of cloth will increase relative
to food, Therefore, the relative supply curves
slope upward.
Yards of cloth produced
per calorie of food
produced, QC/QF
Figure 4-11: Relative Demand
The H-O assumptions
about preferences imply
that that consumer
behavior can be
summarized by this
Relative Demand curve
and that the same curve is
true in both Home and
Foreign
Relative
price of
cloth,
PC/PF
17
3
In this figure, when the price of a yard of cloth is 17
times the price of a calorie of food, the number of yards
of cloth consumed is 3 times the number of calories of
food consumed, for every individual worldwide. Why
isn’t the latter ratio different for different people?
Yards of cloth consumed
per calorie of food
consumed, QC/QF
Relative Demands
• Let’s say that Alex consumes 3 times as
many yards of cloth as calories of food
(relative demand is QC/QF = 3) when a yard
of cloth is 17 times as expensive as a calorie
of food (relative price PC/PF = 17)
• If Alex’s income changes, his relative
demand should not change because MRS is
independent of the scale of consumption
Relative Demands
• Since identical preferences have been assumed, if
the relative price of cloth is PC/PF = 17, then
Betty’s relative demand must also be QC/QF = 3
irrespective of Betty’s income
• Therefore, the same relative demand curve
represents everybody
• Therefore, the same relative demand curve
represents both Home and Foreign
Figure 4-11: Relative Supplies and
Demands
Relative
price of
cloth,
PC/PF
RSFOREIGN
RSHOME
Foreign
Home
RD
• The relative supplies
and demands can be
combined to find the
autarky relative prices in
Home and Foreign
• Clearly, they are
different
• Therefore, trade will
occur if it is allowed
• Since Home and
Foreign differ only in
their relative factor
endowments, that
difference must be the
reason why trade
occurs
Yards of cloth
produced per calorie
of food produced,
QC/QF
Who will export what?
• In autarky, the laborintensive good is relatively
cheaper in the laborabundant country
• Therefore, under free
trade, the labor-intensive
good is exported by the
labor-abundant country…
• … and the land-intensive
good is exported by the
land-abundant country
PC/PF
Foreign
autarky
Free Trade
Home
Foreign : land abundant, labor scarce
Home: land scarce, labor abundant
Cloth: labor intensive production
Food: land intensive production
The Heckscher-Ohlin Theorem
• To repeat, when trade occurs, the labor-abundant
country (Home) exports the labor-intensive good
(cloth) and
• The land-abundant country (Foreign) exports the
land-intensive good (food)
• In general, each country exports the good that
makes intensive use of the resource that is
abundant in that country
• This is called the Heckscher-Ohlin Theorem
– See the section “Relative Prices and the Pattern of
Trade” in chapter 4 of the textbook
Goods Prices: from autarky to free
trade
• In autarky, the laborintensive good is relatively
cheaper in the laborabundant country
• Free trade makes relative
prices equal everywhere
• Therefore, the laborintensive good becomes
more expensive in the
labor-abundant country,
and less expensive in the
labor-scarce country.
PC/PF
Foreign
autarky
Free Trade
Home
Foreign : land abundant, labor scarce
Home: land scarce, labor abundant
Cloth: labor intensive production
Food: land intensive production
Figure 4-6: Factor Prices and Goods
Prices
Relative
price of
cloth,
PC/PF
FPGP
Fig. 4-11 showed that, in
autarky, the relative
price of cloth is higher in
Foreign
Therefore, in autarky,
the wage-rent ratio
must also be higher in
Foreign
Foreign
Free Trade
Free trade makes the
wage-rent ratio the
same in the two
countries
Home
Home
Foreign
Free Trade
Wage-rent
ratio, w/r
Factor Prices: from autarky to free
trade
PC/PF
w/r
• In autarky, the wage-rent
ratio is higher in the laborscarce country and lower in
Foreign
autarky
the labor-abundant country
Free Trade
• When autarky ends and free
trade begins, the wage-rent
Home
ratio falls in the labor-scarce
country and rises in the
labor abundant country
Foreign : land abundant, labor scarce
Home: land scarce, labor abundant
Cloth: labor intensive production
Food: land intensive production
WHO GAINS AND WHO LOSES
FROM GLOBALIZATION?
Real Wage and Real Rent
w
Nominal wage: currency earned per hour of a worker’s labor
w/PC
Real wage: yards of cloth purchasable with the nominal wage
w/PF
Real wage: calories of food purchasable with the nominal wage
r
Nominal rent: currency earned per hour per acre of land
r/PC
Real rent: yards of cloth purchasable with the nominal rent
r/PF
Real rent: calories of food purchasable with the nominal rent
Marginal Product of a Resource
• The Marginal Product (MP) of labor in cloth
production is the additional amount of
cloth that would be produced if an
additional unit of labor is employed
– We can similarly define
• Marginal Product of labor in food production,
• Marginal Product of land in cloth production, and
• Marginal Product of land in food production
Marginal Product of a Resource
• See page Figure 7-2 of the textbook for
more on the Marginal Product.
Example: Level of Resource Use
• Suppose an additional worker produces an
additional 5 yards of cloth in one hour’s work.
Then MP = 5.
– See page Figure 7-2 of the textbook for more on
the Marginal Product.
• Therefore, to make one additional yard of
cloth, you need only 1/5 of a worker.
• In general, the labor needed to make one unit
of cloth can be calculated as 1/MP
• Marginal Cost is the additional cost of an
additional unit of output
• Therefore, MC = w × (1/MP) = w/MP
Price = Marginal Cost
• If P > MC at the current level of production,
additional production would increase profit
• If P < MC at the current level of production,
reduced production would increase profit
• Therefore, profit is maximized only if P = MC
• Therefore, if a good is being produced, P = MC
must be true
Real Wage and Real Rent
• Therefore, P = MC = w / MP
• Therefore, w/P = MP
• This implies that the real wage in
units of, say, cloth is the Marginal
Product of labor in the
production of cloth
• Similarly, the real rent in units of
food is the Marginal Product of
land in food production
w
C
 MPL
PC
r
F
 MPT
PF
Real Factor Rewards and
Productivity
• In general, the real payment to a resource
is equal to its productivity (or, marginal
product)
– This is the main conclusion of the Marginal
Productivity Theory of Income Distribution
Factor Use and Factor Productivity—
Labor-Abundant Country
Wage-rent
ratio, w/r
Cloth
production
• We saw earlier that when
autarky ends and free trade
begins w/r rises in the labor- Foreign
abundant country (Home).
Therefore,
Free trade
• More land is used per worker
– in cloth production and in
food production
Food
production
Home
• This makes labor more
productive…
• …and land less productive
• Therefore,
•
•
w/PC and w/PF both increase, and
r/PC and r/PF both decrease.
• Abundant resource benefits
from globalization
• Scarce resource loses
Foreign : land abundant, labor scarce
Home: land scarce, labor abundant
Cloth: labor intensive production
Food: land intensive production
Acres of
Land per
worker, T/L
Factor Use and Factor Productivity—
Land-Abundant Country
Wage-rent
ratio, w/r
Cloth
production
• When autarky ends and free
trade begins w/r falls in the
land-abundant country
Foreign
(Foreign). Therefore,
• Less land is used per workerFree trade
Food
production
– in cloth production and in
food production
• This makes labor less
productive…
• …and land more productive
• Therefore,
•
•
Home
w/PC and w/PF both decrease,
and
r/PC and r/PF both increase.
• Abundant resource benefits
from globalization
• Scarce resource loses
Foreign : land abundant, labor scarce
Home: land scarce, labor abundant
Cloth: labor intensive production
Food: land intensive production
Acres of
Land per
worker, T/L
Trade: Who Gains and Who Loses?
• In short, each country’s abundant resource
benefits from trade and
• Each country’s scarce resource loses from
trade
Factor Price Equalization
Cloth
• Free trade equalizes Wage-rent
production
the wage-rent ratio ratio, w/r
• Therefore, the landper-worker ratio in
cloth production is Foreign, autarky
also equalized
Free trade
• This equalizes the
productivity of labor
in cloth production Home, autarky
in the two countries
• This equalizes w/PC
in the two countries
• In a similar way,
w/PF, r/PC, and r/PF
each become
equalized worldwide
Foreign : land abundant, labor scarce
Home: land scarce, labor abundant
Cloth: labor intensive production
Food: land intensive production
Food
production
Acres of
Land per
worker, T/L
Factor Price Equalization Theorem
• The Factor Price Equalization Theorem:
When there is free trade in goods, the real
reward for any resource (in units of either
good) becomes the same in both
countries!
– An implication of this result is that if there is
free trade in goods, resources will have no
incentive to move from one country to another
Factor Price Equalization Theorem
• Heckscher-Ohlin theory implies FPE.
• But does FPE imply that free trade will
make everybody equally rich?
• Certainly not!
– Not every individual is endowed with the same
amount of resources
How accurate is the Heckscher-Ohlin
theory?
• Sadly, it’s not very accurate by itself
– It explains North-South trade quite well…
– But not trade within the North
• But, if modified to take cross-country
differences in technology into account, it
fits the data well
• So, a theory that combines the insights of
Ricardo and Heckscher-Ohlin might be best
The contribution of Heckscher-Ohlin
theory
• The theory’s main contribution is to point
out that cross-country differences in
relative resource availability can explain
trade
• It does not claim that differences in relative
resource availability are the only reason
why trade occurs