The HeckscherOhlin Model

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The Heckscher-Ohlin Model

• Udayan Roy
• http//myweb.liu.edu/uroy/eco41
• October 2009

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Basic assumptions
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The Heckscher-Ohlin AssumptionsBasics

• 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

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The Heckscher-Ohlin AssumptionsPreferences

• 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.

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The Ricardian AssumptionsPreferences

• 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 individuals 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.

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Marginal Rate of Substitution
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The Heckscher-Ohlin AssumptionsMarkets

• 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

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The Heckscher-Ohlin AssumptionsGovernments

• 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 cross-border movement
  of resources, such as labor

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The Heckscher-Ohlin AssumptionsTechnology

• 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.

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The Heckscher-Ohlin AssumptionsFactor 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 gt 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.

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The Heckscher-Ohlin AssumptionsFactor Intensities

• The production of food is land-intensive and the
  production of cloth is labor-intensive
• That is, the number of workers per acre (L/T) is
  always higher in cloth production than in food
  production

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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)
• See earlier lecture

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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.

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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 laboralso
  called the nominal wagemay be 8 per hour

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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

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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.

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Figure 4-6 Factor Prices and Goods Prices
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
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Figure 4-6 Factor Prices and Goods Prices
Under free trade, the relative price of cloth
will be the same in both countries
Therefore, the wage-rent ratio will also be the
same in the two countries
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Figure 4-5 Factor Prices and Input Choices
As labor becomes relatively more expensive,
relatively more land is used in production
of both food and cloth
But the number of acres of land per worker is
always higher in food production, reflecting the
assumption that food production is land intensive
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Figure 4-5 Factor Prices and Input Choices
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.
Same must be true for food production.
Therefore, Foreign, which has more land per
worker than Home, must produce relatively more
food
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Relative Supplies

• Therefore, if the same w/r prevails in both
  countries, then
• QF/QC must be higher in Foreign than in Home.
  Equivalently,
• QC/QF must be higher in Home than in Foreign.
• This result is called the Rybczynski effect see
  the section Resources and Output in the textbook

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Relative Supplies

• From the FPGP Curve in Fig. 4-6, any particular
  value of w/r is linked to a specific value of
  PC/PF.
• Therefore, if the same w/r prevails in the two
  countries, then the same PC/PF must also prevail
  in the two countries. And at that common value of
  PC/PF
• QF/QC must be higher in Foreign than in Home.
  Equivalently,
• QC/QF must be higher in Home than in Foreign.

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Figure 4-11 Relative Supplies
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.
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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
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 isnt the latter ratio
different for different people?
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Relative Demands

• Lets 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 Alexs income changes, his relative demand
  should not change because MRS is independent of
  the scale of consumption

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Relative Demands

• Since identical preferences have been assumed, if
  the relative price of cloth is PC/PF 17, then
  Bettys relative demand must also be QC/QF 3
  irrespective of Bettys income
• Therefore, the same relative demand curve
  represents everybody
• Therefore, the same relative demand curve
  represents both Home and Foreign

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Figure 4-11 Relative Supplies and Demands

• 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

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Who will export what?

• In autarky, the labor-intensive good is
  relatively cheaper in the labor-abundant 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 scarceHome land
scarce, labor abundant Cloth labor intensive
productionFood land intensive production
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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

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Goods Prices from autarky to free trade

• In autarky, the labor-intensive good is
  relatively cheaper in the labor-abundant country
• Free trade makes relative prices equal everywhere
• Therefore, the labor-intensive 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 scarceHome land
scarce, labor abundant Cloth labor intensive
productionFood land intensive production
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Figure 4-6 Factor Prices and Goods Prices
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 Free trade makes the wage-rent ratio
the same in the two countries
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Factor Prices from autarky to free trade
w/r
PC/PF

• In autarky, the wage-rent ratio is higher in the
  labor-scarce country and lower in the
  labor-abundant country
• When autarky ends and free trade begins, the
  wage-rent ratio falls in the labor-scarce country
  and rises in the labor abundant country

Foreign
autarky
Free Trade
Home
Foreign land abundant, labor scarceHome land
scarce, labor abundant Cloth labor intensive
productionFood land intensive production
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Who gains and who loses from globalization?
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Real Wage and Real Rent
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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

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Marginal Product of a Resource

• See page Figure 7-2 of the textbook for more on
  the Marginal Product.

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Example Level of Resource Use

• Suppose an additional worker produces an
  additional 5 yards of cloth in one hours 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

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Price Marginal Cost

• If P gt MC at the current level of production,
  additional production would increase profit
• If P lt 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

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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

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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

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Factor Use and Factor ProductivityLabor-Abundant
Country

• We saw earlier that when autarky ends and free
  trade begins w/r rises in the labor-abundant
  country (Home). Therefore,
• More land is used per worker
• in cloth production and in food production
• 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
Free trade
Home
Foreign land abundant, labor scarceHome land
scarce, labor abundant Cloth labor intensive
productionFood land intensive production
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Factor Use and Factor ProductivityLand-Abundant
Country

• When autarky ends and free trade begins w/r falls
  in the land-abundant country (Foreign).
  Therefore,
• Less land is used per worker
• in cloth production and in food production
• This makes labor less productive
• and land more productive
• Therefore,
• w/PC and w/PF both decrease, and
• r/PC and r/PF both increase.
• Abundant resource benefits from globalization
• Scarce resource loses

Foreign
Free trade
Home
Foreign land abundant, labor scarceHome land
scarce, labor abundant Cloth labor intensive
productionFood land intensive production
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Trade Who Gains and Who Loses?

• In short, each countrys abundant resource
  benefits from trade and
• Each countrys scarce resource loses from trade

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Factor Price Equalization

• Free trade equalizes the wage-rent ratio
• Therefore, the land-per-worker ratio in cloth
  production is also equalized
• This equalizes the productivity of labor in cloth
  production 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, autarky
Free trade
Home, autarky
Foreign land abundant, labor scarceHome land
scarce, labor abundant Cloth labor intensive
productionFood land intensive production
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Resource Use and Resource ProductivityCloth
Production
These curves reflect Diminishing Returns to each
resource, which, in turn, is a consequence of the
assumption of Constant Returns to Scale
Similar curves can be drawn for food production
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Factor Price Equalization

• We saw earlier that free trade makes w/r equal in
  Home and Foreign
• Since both countries use the same technology, the
  equalization of w/r implies that the number of
  workers used per acre of land in the production
  of, say, cloth will also become the same in both
  countries

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Factor Price Equalization

• Therefore, the productivity (or MP) of labor in
  the production of cloth will become the same in
  both countries and
• The productivity (or MP) of land in the
  production of cloth will become the same in both
  countries

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Factor Price Equalization

• Therefore, the real wage in units of cloth, w/PC,
  will become the same in both countries (since the
  real wage is equal to the marginal product) and
• r/PC will become the same in both countries
• In the same way, one can show that
• w/PF will become the same in both countries and
• r/PF will become the same in both countries.

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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

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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

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How accurate is the Heckscher-Ohlin theory?

• Sadly, its 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

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The contribution of Heckscher-Ohlin theory

• The theorys 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

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Were Done!

• Any questions or comments?