Economics Chapter 5 Solve These Two Constraints For The Quantity

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Chapter 5

Resources and Trade: The Heckscher-Ohlin Model

◼ Chapter Organization

Model of a Two-Factor Economy

Prices and Production

Choosing the Mix of Inputs

Factor Prices and Goods Prices

Resources and Output

Effects of International Trade between Two-Factor Economies

Relative Prices and the Pattern of Trade

Trade and the Distribution of Income

◼ Chapter Overview

In Chapter 3, trade between nations was motivated by differences internationally in the relative productivity

of workers when producing a range of products. In Chapter 4, the Specific Factors model considered

additional factors of production, but only labor was mobile between sectors. In Chapter 5, this analysis

goes a step further by introducing the Heckscher-Ohlin theory.

22 Krugman/Obstfeld/Melitz • International Economics: Theory & Policy, Tenth Edition

The chapter begins by developing a general equilibrium model of an economy with two goods that are

each produced using two factors according to fixed coefficient production functions. The assumption of

fixed coefficient production functions provides an unambiguous ranking of goods in terms of factor

intensities. (A more realistic model allowing for substitution between factors of production is presented

later in the chapter with the same conclusions.) Two important results are derived using this model. The

first is known as the Rybczynski effect. Increasing the relative supply of one factor, holding relative goods

prices constant, leads to a biased expansion of production possibilities favoring the relative supply of the

good that uses that factor intensively.

The central message concerning trade patterns of the Heckscher-Ohlin theory is that countries tend to

export goods whose production is intensive in factors with which they are relatively abundantly endowed.

Comparing the United States and Mexico, for example, we observe a relative abundance of capital in the

United States and a relative abundance of labor in Mexico. Thus, goods that intensively use capital in

production should be cheaper to produce in the United States, and those that intensively use labor should

be cheaper to produce in Mexico. With trade, the United States should export capital-intensive goods like

After presenting the basic theory behind the Heckscher-Ohlin theory, the rest of the chapter examines empirical

tests of the model, beginning with a pair of case studies looking at income inequality in the United States.

Wages paid to skilled workers in the United States have been rising at a much faster rate than those paid to

unskilled workers over the past few decades. At the same time, there has been a large increase in

international trade. Given that the United States is relatively abundant in skilled labor, the Heckscher-

Chapter 5 Resources and Trade: The Heckscher-Ohlin Model 23

increased by nearly the same proportion as skilled wages. If rising wage inequality in a rich country like

the United States is driven by factor price equalization, then we should also observe a narrowing gap in

developing countries that are exporting low-skill intensive goods. However, income inequality in these

nations is actually larger than in rich countries. Finally, trade between rich and poor nations is simply not

large enough to be entirely responsible for the size of the income gap. Rather, the increasing skill premium

is most likely due to skill-biased technical innovations like computers that have increased the

productivities of skilled workers more than that of unskilled workers.

Another empirical observation testing the validity of the Heckscher-Ohlin theory is the Leontief paradox.

This is the observation that the capital intensity of U.S. exports is actually lower than that of U.S. imports,

exactly the opposite of what the theory would predict for a capital abundant country. Further evidence of this

◼ Answers to Textbook Problems

1. a. The first step is to compute the opportunity costs of both cloth and food. We are given the

following resource constraints:

aKC = 2, aLC = 2, aKF = 3, aLF = 1 L = 2,000; K = 3,000

Each unit of cloth is produced with 2 units of capital and 2 units of labor. Each unit of food is

produced with 3 units of capital and 1 unit of labor. Furthermore, the economy is endowed with

2,000 units of labor and 3,000 units of capital. Given these values, we can define the following

24 Krugman/Obstfeld/Melitz • International Economics: Theory & Policy, Tenth Edition

Looking at the diagram, we see that production of both food and cloth will take place when the

relative price of cloth is between the two opportunity costs of cloth. The opportunity cost of cloth

is given by the slopes of the two components of the production possibilities frontier above, 2/3

b. Note the input requirements for each good. One unit of cloth can be produced using 2 units of

capital and 2 units of labor. One unit of food is produced using 3 units of capital and 1 unit of

labor. In a competitive market, the unit cost of each good must be equal to the output price.

QC = 2K + 2L → PC = 2r + 2w

QF = 3K + L → PF = 3r + w

This gives us two equations and two unknowns (r and w). Solve for the factor prices:

w = PF − 3r

d. The capital stock increases to 4,000. The labor constraint will remain unchanged, keeping the

maximum price of cloth at 2 units of food. The new capital constraint is given by:

2QC + 3QF  4,000

Solving for QF yields:

QF  1,333 − 2/3QC

Thus, the minimum price of cloth is also unchanged at 2/3 units of food. The only difference now

is that the production possibilities frontier will have a larger horizontal intercept (if cloth is on the

horizontal axis). Compared to Figure 5-1, the new production possibilities frontier will intercept

the x-axis at 2,000 instead of 1,500.

Chapter 5 Resources and Trade: The Heckscher-Ohlin Model 25

2. The definition of cattle raising as land intensive depends on the ratio of land to labor used in

production, not on the ratio of land or labor to output. The ratio of land to labor in cattle exceeds the

3. This question is similar to an issue discussed in Chapter 4. What matters is not the absolute abundance

of factors but their relative abundance. Poor countries have an abundance of labor relative to capital

when compared to more developed countries. For example, consider a large, rich country like the

4. In the Ricardian model, labor gains from trade through an increase in its purchasing power. This

result does not support labor union demands for limits on imports from less affluent countries. The

Heckscher-Ohlin model directly addresses distribution effects by considering how trade impacts the

5. Specific programmers may face wage cuts due to the competition from India, but this is not inconsistent

with skilled labor wages rising. By making programming more efficient in general, this development

may have increased wages for others in the software industry or lowered the prices of the goods overall.

6. The factor proportions theory states that countries export those goods whose production is intensive

in factors with which they are abundantly endowed. One would expect the United States, which

26 Krugman/Obstfeld/Melitz • International Economics: Theory & Policy, Tenth Edition

7. If the efficiency of the factors of production differs internationally, the lessons of the Heckscher-

Ohlin theory would be applied to “effective factors,” which adjust for the differences in technology

or worker skills or land quality (for example). The adjusted model has been found to be more