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4 Trade and Resources: The Heckscher–Ohlin Model

Notes to Instructor

Chapter Summary

This chapter presents the Heckscher–Ohlin model with two factors (capital and labor),

two goods (computers and shoes), and two countries (Home and Foreign). A test of the

model is discussed with Leontief ’s paradox. Additionally this chapter, like the last,

discusses the affect of trade on factor prices. The “sign test” in the Heckscher-Ohlin

model is discussed in the Appendix.

Comments

Note that this chapter covers only two theorems of the Heckscher–Ohlin model—the

Heckscher–Ohlin theorem and the Stolper–Samuelson theorem. The other two

theorems—the Rybczynski theorem and Factor Price Insensitivity—are deferred to the

next chapter, in an effort to break the material into smaller pieces.

Unlike the previous chapters, a discussion of the theory is followed by an empirical

test. This concept is possibly new to students and could be highlighted to generate

interest in the topic. Moreover, although students are quite familiar with graphing supply

and demand from their principles course, place emphasis on teaching the export supply

and import demand curves, particularly because the derivation of these curves requires an

understanding of the relationship between the no-trade and free–trade relative prices.

Similarly, the topic of relative demand and supply may also benefit from additional

attention as the shift of the curves due to changes in the relative price may not be

immediately obvious to the students because the curves are in ratios (i.e., horizontal axis

Lecture Notes

Introduction

We begin the chapter with a comparison between the Ricardian model, in which trade

occurs due to differences in technology between countries giving rise to their

comparative advantage, and the Heckscher–Ohlin model, in which uneven distribution

in resources leads countries to trade with one another. The Heckscher–Ohlin model also

differs from the specific-factors model in that factors of production can move between

industries because the model is set in the long run. The model was developed to explain

the “golden age” of international trade between 1890 and 1914, during which there was

an increase in the ratio of trade to gross domestic product (GDP) coinciding with

improvements in transportation.

1 Heckscher–Ohlin Model

The Heckscher-Ohlin model consists of two factors (capital and labor), two goods

(computers and shoes), and two countries (Home and Foreign). The total amount of

Assumptions of the Heckscher–Ohlin Model

The six assumptions of the Heckscher–Ohlin model are as follows:

Assumption 1: Both factors can move freely between the industries.

The implication of the first assumption is that the rental on capital, R, is identical

across the two industries. If one industry has a higher rental, it would attract capital from

Assumption 2: Shoe production is labor-intensive, that is, it requires more labor per unit

of capital to produce shoes than computers, so that LS/KS > LC/KC.

The second assumption states how intensive the factors are in the production of each

good. Namely, computer production is capital-intensive, requiring more capital per

worker than the production of shoes. Because shoe production is labor-intensive, the

relative demand curve in shoes, LS/KS, is to the right of the relative demand curve in

computers, LC/KC, in Figure 4-1, where the horizontal axis gives the ratio of labor to

capital used in production and the vertical axis denotes the ratio of the labor wage to the

capital rental.

[FIGURE 4–1 MISSING FROM PDF TEXT]

Assumption 3: Foreign is labor-abundant, by which we mean that the labor–capital ratio

in Foreign exceeds that in Home, . Equivalently, Home is capital

abundant, so that .

The third assumption distributes the resources unevenly across the two countries, with

Home being capital-abundant, whereas Foreign is labor-abundant. Remember, labor- and

capital-abundance are always in relative terms. The textbook provides an example

Assumption 4: The final outputs, shoes and computers, can be traded internationally, but

labor and capital do not move between countries.

Assumption 5: The technologies used to produce the two goods are identical across the

countries.

From the fifth assumption, we see that each good is produced using the same

Assumption 6: Consumer tastes are the same across countries, and preferences for

computers and shoes do not vary with a country’s level of income.

The sixth assumption implies that although the poorer country would consume less of

APPLICATION

Are Factor Intensities the Same Across Countries?

In the United States, footwear production is more capital-intensive than call centers

because of the expensive automated–manufacturing machines used by a New Balance

plant. However, there is a “reversal” of factor intensities in India, where call centers are

N E T W O R K

The New Balance website can be found through the following link:

No–Trade Equilibrium

Production Possibility Frontiers Figure 4-2 shows the production possibility frontiers

(PPFs) for Home in panel (a) and Foreign in panel (b). The bowed-out PPF is biased

Indifference Curves With the assumption of common consumer tastes across the

countries, we add an identical indifference curve to each country’s PPF. The tangency of

No–Trade Equilibrium Price The no–trade equilibrium for Home is at point A, with

production of computers and shoes given by QC1 and QS1. The no-trade equilibrium for

Free–Trade Equilibrium

Home Equilibrium with Free Trade With free trade, the equilibrium relative price of

computers is between the no-trade relative prices found at Home and Foreign. More

specifically, panel (a) of Figure 4-3 shows that the free–trade equilibrium price of

computers, (PC/PS)W, is steeper than the no-trade price at Home (see Figure 4–2) because

Foreign Equilibrium with Free Trade In panel (a) of Figure 4-4, the Foreign no-trade

equilibrium is at point A*. Because the Foreign no–trade relative price is higher than at

Home, the world equilibrium price of computers, (PC/PS)W, is cheaper than the no-trade

Foreign price, (P*/P*S)A*. Facing a lower relative price of computers under free trade,

Equilibrium Price with Free Trade Putting together Home’s export supply curve for

computers and Foreign’s import demand curve for computers gives the equilibrium

relative price of computers with free trade as shown in Figure 4-5. At the world relative

Pattern of Trade The pattern of trade can be determined from the free–trade equilibrium.

Namely, a country will export the good that uses intensively the factor of which it has an

Heckscher–Ohlin Theorem With two goods and two factors, each country will export

2 Testing the Heckscher–Ohlin Model

Testing the Heckscher–Ohlin Theorem: Leontief’s Paradox

Using 1947 data for the United States, Leontief measured the amount of capital and labor

required to produce $1 million worth of U. S. exports. The measurement indicated that

the capital–labor ratio used in export production was $14,000 per worker. Applying U. S.

technology to measure the labor and capital used in producing imports, Leontief found

Explanations Many explanations have been offered to explain Leontief ’s paradox,

including the following:

• Technologies in the United States and rest of the world may not have been the

same as the Heckscher–Ohlin theorem assumes.

Many of these explanations focus on the importance of more than two factors or the

ability of factors (such as skilled vs. unskilled labor). In the remainder of this section, we

Endowments in the New Millennium

The method for measuring factor abundance differs when we consider more than two

factors of production. The general definition of factor abundance is given by the

country’s share of that factor, as compared with its share of world GDP. A country is

Capital Abundance Using the general definition and data from Figure 4-6, we see that in

2013 the United States was physical–capital scarce because its share of the world’s capital

Labor and Land Abundance Using a similar comparison, Figure 4-6 shows that the

United States is abundant in research and development (R&D) scientists and skilled

Differing Productivities Across Countries

Although the extended Heckscher–Ohlin model is better at predicting the pattern of

international trade by allowing for many goods, factors, and countries, we can further

examine the accuracy of the model by dropping the assumption of identical technologies

Measuring Factor Abundance Once Again Measuring whether a country is abundant

in that effective factor or scarce in that effective factor is similar to the method we

Effective R&D Scientists To account for the differences in productivities across

countries due to the availability of laboratory equipment, we measure effective R&D

scientists by multiplying the actual number of R&D scientists by the amount of R&D

Effective Arable Land The effective amount of arable land is defined as the actual

arable land in a country times its productivity in agriculture. After accounting for the

differing productivities in arable land, we find that the U.S. was abundant in effective

arable land in 2013 because its share of effective arable land (20.7%) was greater than its

H E A D L I N E S

China Drawing High–Tech Research from the United States

Applied Materials, a U.S. firm that is currently the world’s largest supplier of equipment

Leontif’s Paradox Once Again

Going back to data from the time periods studied by Leontief, with our newly developed

concepts of effective abundance, we can redo Leontief ’s factor calculations, taking into

account the productivity of the U. S. workforce. To do this, we estimate productivity with

3 Effects of Trade on Factor Prices

In this section, we determine the impact of trade on the wage and rental earned by labor

Effect of Trade on the Wage and Rental of Home

Economy-Wide Relative Demand for Labor Recall that the total amount of labor

(capital) in an economy is equal to the sum of the labor (capital) in each industry, i.e., LC

+ LS = (KC + KS + ). Dividing total labor by total capital, we get the supply of labor

relative to capital or relative supply:

Increase in the Relative Price of Computers Because of free trade, Home faces a

higher relative price of computers, which drives it to further specialize in the production

of computers, shifting away resources from the production of shoes. The increase in the

production of the capital-intensive good (computers) leads to a change in the relative

demand for labor. More specifically, for the relative demand for labor in the economy,

we put more weight toward computers, a rise in (KC/ ), and less weight toward the shoe

exceeds the requirement necessary to operate the capital in computers. The change in the

relative supply and relative demand due to an increase in the relative price of computers

can be summarized by the following:

Determination of the Real Wage and Real Rental

Change in the Real Rental The rental on capital in computers (shoes) is equal to its

marginal product multiplied by the price of computers (shoes):

R = PC • MPKC and R = PS • MPKS

Because the labor–capital ratio increases in both industries due to the higher world

relative price of computers, the marginal product of capital also increases in both shoes

and computers. Rearranging the previous equations, we get

Change in the Real Wage Similarly, the wage in computers (shoes) is equal to its

marginal product multiplied by the price of computers (shoes):

W = PC • MPLC and W = PS • MPLS

However, unlike the case for capital, the law of diminishing returns tells us that the

increase in the labor–capital ratio (i.e., more labor per unit of capital) will lead to a

decrease in marginal produce of labor in both industries. Re arranging the preceding

Stolpe–Samuelson Theorem In the long run, when all factors are mobile, an increase in

the relative price of a good will increase the real earnings of the factor used intensively in

Changes in the Real Wage and Rental: A Numerical Example

Suppose the following:

Computers: Sales revenue = PC • QC = $100

Earnings of labor = W • LC = $50

Note that shoes are more labor-intensive than computers because the share of total

revenue paid to labor in shoes (60/100 = 60%) is more than that share in computers

(40/100 = 40%). Under free trade, the relative price of computers rises as follows:

To determine the impact of the higher relative price of computers on the rental on

capital for each industry, we subtract the payments to labor from total sales revenue and

divide the difference by the amount of capital:

We now add in the information pertaining to the increase in the price of computers:

Rewriting the previous equations in terms of percentage changes, we have the

following:

where ∆PC/PC is the percentage change in the price of computers, ∆W/W is the

percentage change in the wage, and ∆R/R is the percentage change in the rental on

capital.

Substituting the numbers given and subtracting one equation from the other, we get

which gives the change in wages as

Solving the equation, we get that the rental on capital increases by 60% when the

price of computers rises by 10%. The capital owner is better off from trade because the

General Equation for the Long-Run Change in Factor Prices The long-run results due

to an increase in the price of computers are given by the following: