The Heckscher-Ohlin Model Udayan Roy uroy/eco41 October 2009

The Heckscher-Ohlin Model

Udayan Royhttp://myweb.liu.edu/~uroy/eco41

October 2009

http://myweb.liu.edu/~uroy/index.html

http://myweb.liu.edu/~uroy/eco41

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)

Wine consumed

(W)

Cheese-Wine Ratio

(C/W)

MRSWC

10 20 0.5 2600 1200 0.5 210 5 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 cross-border 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 labor-intensive– 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

Wage-rent ratio, w/r

Relative price of cloth, PC/PF

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

FPGP

As both Home and Foreign use the same technologies, the same FPGP curve is applicable in both countries

5

17




Under free trade, the relative price of cloth will be the same in both countries

FPGP

Therefore, the wage-rent ratio will also be the same in the two countries

5

17

Figure 4-5: Factor Prices and Input Choices


Acres of Land per worker, T/L

Cloth production

Food production

As labor becomes relatively more expensive, relatively more land is used in production…

But the number of acres of land per worker is always higher in food production, reflecting the assumption that food production is land intensive

… of both food and cloth

4 12

5

Figure 4-5: Factor Prices and Input Choices



Cloth production

Food production

As both Home and Foreign use the same technologies, these two curves must be true in both countries.

4 12

5

As free trade equalizes the wage-rent ratio worldwide, acres of land per worker in cloth production must be the same worldwide.

Therefore, Foreign, which has more land per worker than Home, must produce relatively more food …

Same must be true for food production.

Figure 4-11: Relative Supplies


Yards of cloth produced per calorie of food produced, QC/QF

RSFOREIGN

RSHOME

17

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.

17

3

Figure 4-11: Relative Demand


Yards of cloth consumed per calorie of food consumed, QC/QF

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 isn’t the latter ratio different for different people?

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

RSHOME

RSFOREIGN

RD

Foreign

Home

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


Yards of cloth produced per calorie of food produced, QC/QF

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

Foreign

Home

Free Trade

PC/PF

autarky

Foreign : land abundant, labor scarceHome: land scarce, labor abundantCloth: labor intensive productionFood: 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 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.

Foreign

Home

Free Trade

PC/PF

autarky



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


Relative price of cloth, PC/PF FPGP

Foreign

Foreign

Home

Home

Free Trade

Free Trade

Factor Prices: from autarky to free trade

• 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

Home

Free Trade

w/r

autarky

PC/PF


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

CL

C

MPP

w

FT

F

MPP

r

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

• 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



Cloth production

Food production


Foreign

Home

Free trade

Factor Use and Factor Productivity—Land-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



Cloth production

Food production


Foreign

Home

Free trade

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

• 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



Cloth production

Food production


Foreign, autarky

Home, autarky

Free trade

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

Documents

The Heckscher-Ohlin Model Udayan Roy uroy/eco41 October 2009