heckscher ohlin model

The Heckscher-Ohlin Assumptions—Basics

There are two countries, Home and Foreign two goods, Cloth and Food, and two resources, Labor and Land (that

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.

Marginal Rate of Substitution

Note that a consumer’s MRS of Wine for Cheese is, simply, a measure of how much the consumer likes cheese.

We assume that MRSWC decreases as the consumption of Cheese (C) increases relative to the consumption of Wine (W)…

And remains unchanged if the consumption of Cheese remains unchanged relative to the consumption of Wine. (See next slide.)

Marginal Rate of Substitution

Cheese consume

d (C)

Wine consume

d (W)

Cheese-Wine Ratio (C/W)

MRSWC

10 20 0.5 2

600 1200 0.5 2

10 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)

See earlier lecture

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.

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

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

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

Factor Prices and Input Choices


Acres of Land per worker, T/L

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

When w/r = 5, cloth producers use 4 acres per worker in both countries and food producers use 12 acres per worker in both countries.

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

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.

Relative Supplies From the FPGP Curve in Fig. 4-3, 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.

Relative Supplies


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

RSFOREIGN

RSHOME

17

In Figure 4-2, we saw that at w/r = 5, Foreign must produce relatively more food and Home must produce relatively more cloth.

In Figure 4-3 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

Relative Demands


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

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

Relative Supplies and Demands


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

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

Autarky—Goods Prices

Note that the (relative) price of the labor-intensive good (cloth), PC/PF, is higher in the land-abundant (and, therefore, labor-scarce) country (Foreign).

Factor Prices and Goods Prices

Fig. 4-8 showed that, in autarky, the relative price of cloth is higher in Foreign

Fig. 4-3 then shows that, in autarky, the relative price of labor must also be higher in Foreign

Free trade makes the relative price of labor the same in both countries


Relative price of cloth, PC/PF FPGP

Foreign

Foreign

Home

Home

Free Trade

Free Trade

Autarky—Factor Prices

Note that the (relative) price of labor in units of land, w/r, is higher in Foreign, which is land-abundant (and, therefore, labor-scarce).

Free Trade—Goods Prices

From the earlier lectures we know that the free trade relative price of cloth will be somewhere between the two autarky prices

Therefore, the price of cloth will rise in Home and fall in Foreign

Free Trade—Factor Prices

From the FPGP curve, we see that the relative price of labor rises in the labor-abundant country (Home) and falls in the labor-scarce country (Foreign)

Home is labor-abundant. So labor is relatively cheap in autarky. Therefore, the labor-intensive good (cloth) is relatively cheap in autarky.

Free Trade—Factor Prices Therefore, when trade begins, Foreign

imports Home-made cloth. This raises the production of cloth in Home

Since cloth is labor-intensive the demand for labor increases faster than the demand for land

As a result, labor becomes relatively more expensive in Home when trade begins

Free Trade—Pattern

It is also clear that Home will export cloth (because, in autarky, it made cloth cheaper than Foreign) and

Foreign will export food.

The Heckscher-Ohlin Theorem Note that 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

Real Wage and Real Rent The purchasing power of the (nominal)

wage, w, whether in units of cloth or food, is the real wage: w/PC and w/PF.

The purchasing power of the (nominal) rent, r, whether in units of cloth or food, is the real rent: r/PC and r/PF.

To see who gains and who loses from trade, we need to focus on the real wage and the real rent and check what happens to these two things as autarky ends and free trade begins.

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

Example: Level of Resource Use

Suppose an additional worker produces an additional 5 yards of cloth in one hour’s work. Then MP = 5.

Therefore, to make one additional yard of cloth, you need only 1/5 of a worker.

This shows that the labor needed to make one unit of cloth can be calculated as 1/MP

Level of Resource Use

The amount of labor used in the production of an additional unit of cloth is then 1/MP or 1 divided by the marginal product of labor in cloth production

Marginal Cost The Marginal Cost (MC) of a commodity

is the additional cost of producing an additional unit of that commodity

MC of, say, cloth can be calculated by multiplying the labor required to produce a yard of cloth by the wage that the labor must be paid. 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,

Fewer workers would be used per acre of land (in cloth production and in food production) See Figure 4-2

Factor Use and Factor Productivity —Labor-Abundant Country

This increases the productivity of Labor (because each worker would now have more land to work with) …

… and decreases the productivity of Land (because each acre of land is now being utilized by fewer workers)

Therefore, w/PC and w/PF both increase, and r/PC and r/PF both decrease.

Resource Use and Resource Productivity—Cloth Production

Acres of land per worker, T/L

Marginal Productivity

Marginal Productivity of Land = Real Rent, r/PC

Marginal Productivity of Labor = Real Wage, w/PC

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

Factor Use and Factor Productivity —Land-Abundant Country

Similarly, when autarky ends and free trade begins w/r falls in the land-abundant country (Foreign).

Therefore, more workers are used per acre of land (in both cloth and food production)

This decreases the productivity of Labor… … and increases the productivity of Land Therefore,

w/PC and w/PF both decrease, and r/PC and r/PF both increase.

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 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

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

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.

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

heckscher ohlin model

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