03. The Heckscher-Ohlin Model

Learning objectives

By the end of this chapter, you should be able to:

  1. Explain how the Heckscher-Ohlin model differs from the Ricardian model.
  2. Define factor abundance and factor intensity.
  3. Derive simple labor and capital constraints for two goods.
  4. Explain why a country exports the good that uses its abundant factor intensively.
  5. Use pricing equations to show how a change in a product price affects wages and rents.
  6. Interpret the income distribution effects of trade.

Why this chapter matters

The Ricardian model explains trade using differences in technology. The Heckscher-Ohlin model explains trade using differences in resources.

This is important because many trade debates are not only about national gains. They are also about who gains and who loses inside the country. Farmers, workers, capital owners, consumers, and firms may be affected differently. The Heckscher-Ohlin model gives us a simple framework for thinking about these distributional effects.

For agricultural trade, this is especially relevant. Countries differ in land, labor, capital, water, technology, and natural resources. These differences help explain why countries specialize in different agricultural and non-agricultural products.

From Ricardian trade to resource-based trade

The Ricardian model assumes that labor is the only factor of production. Countries trade because labor productivity differs across countries.

The Heckscher-Ohlin model adds more structure. It assumes that production uses more than one factor, usually labor and capital. Countries trade because they have different relative factor endowments.

Model Main source of comparative advantage
Ricardian model Differences in technology and labor productivity
Heckscher-Ohlin model Differences in factor endowments

The Heckscher-Ohlin model is also called the factor proportions model.

Basic assumptions

The simple version of the model assumes:

  1. Two countries.
  2. Two goods.
  3. Two factors of production: labor and capital.
  4. Labor and capital are fixed in total supply within each country.
  5. Labor and capital can move between sectors inside a country.
  6. Factors do not move internationally.
  7. Goods differ in their factor intensity.
  8. Countries differ in their factor abundance.

This is a simplified model. It is not meant to describe every detail of the real world. Its purpose is to isolate one key mechanism: resources shape trade patterns.

Factor intensity

A good is labor intensive if it uses more labor relative to capital than another good.

A good is capital intensive if it uses more capital relative to labor than another good.

Suppose the production of cloth and food requires the following factor inputs.

Good Labor requirement Capital requirement Labor-capital ratio
Cloth 2 2 1.00
Food 1 3 0.33

Cloth uses 2 units of labor and 2 units of capital per unit of output. Its labor-capital ratio is:

\[ \frac{L_C}{K_C} = \frac{2}{2} = 1 \]

Food uses 1 unit of labor and 3 units of capital per unit of output. Its labor-capital ratio is:

\[ \frac{L_F}{K_F} = \frac{1}{3} \]

Because cloth has the higher labor-capital ratio, cloth is labor intensive relative to food. Food is capital intensive relative to cloth.

NoteKey distinction

Factor intensity refers to goods.

Factor abundance refers to countries.

Factor abundance

A country is labor abundant if it has more labor relative to capital than another country.

A country is capital abundant if it has more capital relative to labor than another country.

Suppose the USA and the EU have the following factor endowments.

Region Labor Capital Labor-capital ratio
USA 6,000 8,000 0.75
EU 4,000 8,000 0.50

The USA has a higher labor-capital ratio than the EU:

\[ \frac{L_{USA}}{K_{USA}} = \frac{6000}{8000} = 0.75 \]

\[ \frac{L_{EU}}{K_{EU}} = \frac{4000}{8000} = 0.50 \]

So, in this example, the USA is relatively labor abundant and the EU is relatively capital abundant.

Production constraints with labor and capital

Let:

  • \(Q_C\) be cloth output
  • \(Q_F\) be food output
  • \(L\) be total labor
  • \(K\) be total capital

Using the input requirements above:

Good Labor needed per unit Capital needed per unit
Cloth 2 2
Food 1 3

The labor constraint is:

\[ 2Q_C + Q_F \leq L \]

The capital constraint is:

\[ 2Q_C + 3Q_F \leq K \]

A country cannot produce output combinations that require more labor or capital than it has.

Worked example: production possibilities

For the USA:

\[ L = 6000, \qquad K = 8000 \]

The constraints are:

\[ 2Q_C + Q_F \leq 6000 \]

\[ 2Q_C + 3Q_F \leq 8000 \]

For the EU:

\[ L = 4000, \qquad K = 8000 \]

The constraints are:

\[ 2Q_C + Q_F \leq 4000 \]

\[ 2Q_C + 3Q_F \leq 8000 \]

The PPF is the outer boundary of feasible production. With two constraints, the country is limited by whichever factor constraint is more restrictive at each output combination.

Python application: factor constraints and PPF

Code
import numpy as np
import matplotlib.pyplot as plt

# Unit factor requirements
labor_cloth = 2
capital_cloth = 2
labor_food = 1
capital_food = 3

countries = {
    "USA": {"Labor": 6000, "Capital": 8000},
    "EU": {"Labor": 4000, "Capital": 8000}
}

for country, endowment in countries.items():
    L = endowment["Labor"]
    K = endowment["Capital"]

    max_cloth = min(L / labor_cloth, K / capital_cloth)
    cloth = np.linspace(0, max_cloth, 300)

    food_labor = (L - labor_cloth * cloth) / labor_food
    food_capital = (K - capital_cloth * cloth) / capital_food
    ppf = np.minimum(food_labor, food_capital)
    ppf = np.maximum(ppf, 0)

    plt.figure()
    plt.plot(cloth, food_labor, linestyle="--", label="Labor constraint")
    plt.plot(cloth, food_capital, linestyle="--", label="Capital constraint")
    plt.plot(cloth, ppf, linewidth=2, label="PPF")
    plt.fill_between(cloth, 0, ppf, alpha=0.15)
    plt.xlabel("Cloth")
    plt.ylabel("Food")
    plt.title(f"{country}: PPF with labor and capital")
    plt.legend()
    plt.tight_layout()
    plt.show()
(a) Production possibilities with labor and capital constraints.
(b)
Figure 5.1

The Heckscher-Ohlin theorem

The main prediction is:

ImportantHeckscher-Ohlin theorem

A country exports the good that uses its abundant factor intensively and imports the good that uses its scarce factor intensively.

Using the example above:

  • Cloth is labor intensive.
  • Food is capital intensive.
  • The USA is relatively labor abundant.
  • The EU is relatively capital abundant.

Therefore:

Region Relative abundance Predicted export good
USA Labor abundant Cloth
EU Capital abundant Food

This is the key logic of the model.

Why trade affects income distribution

The Ricardian model has only one factor of production, labor. That makes it hard to discuss conflict between workers and capital owners.

The Heckscher-Ohlin model has at least two factors. This allows us to study income distribution.

If trade raises the relative price of the labor-intensive good, demand for labor rises. Wages tend to increase. If trade lowers the relative return to capital, capital owners may lose.

The opposite happens when the relative price of the capital-intensive good increases.

This is the basic intuition behind the Stolper-Samuelson result:

NoteStolper-Samuelson intuition

A rise in the relative price of a good increases the real return to the factor used intensively in that good and reduces the real return to the other factor.

Factor prices and output prices

In competitive markets, the price of a good equals its unit production cost.

Let:

  • \(w\) be the wage rate
  • \(r\) be the rental rate of capital
  • \(P_C\) be the price of cloth
  • \(P_F\) be the price of food

Using the factor requirements:

Good Labor requirement Capital requirement
Cloth 2 2
Food 1 3

The pricing equations are:

\[ P_C = 2w + 2r \]

\[ P_F = w + 3r \]

These equations say that the price of each good must cover the cost of labor and capital used to produce it.

Worked example: factor prices before trade

Suppose both goods have price 4:

\[ P_C = 4, \qquad P_F = 4 \]

Then:

\[ 2w + 2r = 4 \]

\[ w + 3r = 4 \]

Solving the two equations gives:

\[ w = 1, \qquad r = 1 \]

So the wage rate and rental rate are both equal to 1.

What happens when the price of cloth rises?

Now suppose the price of cloth rises from 4 to 6, while the price of food remains 4.

\[ P_C = 6, \qquad P_F = 4 \]

The new pricing equations are:

\[ 2w + 2r = 6 \]

\[ w + 3r = 4 \]

Solving gives:

\[ w = 2.5, \qquad r = 0.5 \]

This is a strong result. The price of cloth increased by 50 percent, but the wage increased by 150 percent. The rental rate decreased by 50 percent.

Variable Initial value New value Percent change
Price of cloth 4.0 6.0 50%
Price of food 4.0 4.0 0%
Wage 1.0 2.5 150%
Rental rate 1.0 0.5 -50%

Because cloth is labor intensive, an increase in the price of cloth raises the return to labor and lowers the return to capital.

Python application: factor-price equations

Code
import numpy as np
import matplotlib.pyplot as plt

w = np.linspace(0, 3.5, 300)

# Initial prices
pc_initial = 4
pf = 4

# New cloth price
pc_new = 6

# Pricing equations solved for r
r_cloth_initial = (pc_initial - 2 * w) / 2
r_cloth_new = (pc_new - 2 * w) / 2
r_food = (pf - w) / 3

# Equilibrium points
w_initial, r_initial = 1.0, 1.0
w_new, r_new = 2.5, 0.5

plt.figure()
plt.plot(w, r_cloth_initial, label="Cloth price = 4")
plt.plot(w, r_cloth_new, linestyle="--", label="Cloth price = 6")
plt.plot(w, r_food, label="Food price = 4")
plt.scatter([w_initial, w_new], [r_initial, r_new])
plt.text(w_initial, r_initial + 0.08, "A: w=1, r=1", ha="center")
plt.text(w_new, r_new + 0.08, "B: w=2.5, r=0.5", ha="center")
plt.xlabel("Wage, w")
plt.ylabel("Rental rate, r")
plt.title("Output prices and factor prices")
plt.ylim(0, 3.2)
plt.xlim(0, 3.5)
plt.legend()
plt.tight_layout()
plt.show()
Figure 5.2: Factor-price equations before and after an increase in the price of cloth.

Economic interpretation

The increase in the price of cloth makes cloth production more profitable. Since cloth is labor intensive, firms demand more labor. This raises the wage.

At the same time, resources move away from the capital-intensive sector. The return to capital falls.

This shows why trade can increase total national welfare but still create conflict inside the country. Owners of the abundant factor tend to gain. Owners of the scarce factor may lose.

Empirical limitations

The Heckscher-Ohlin model is useful, but its predictions are not always perfectly observed in the real world.

Important reasons include:

  1. Countries differ in technology, not only factor endowments.
  2. Trade barriers prevent full price equalization.
  3. Transportation costs matter.
  4. Labor and capital are not perfectly mobile across sectors.
  5. Skills, land, water, and institutions also affect production.
  6. Some trade occurs between similar countries in similar products.

One famous empirical puzzle is the Leontief paradox. The United States was expected to export capital-intensive goods, but early empirical work found that U.S. exports appeared less capital intensive than U.S. imports. This does not make the model useless, but it reminds us that real trade patterns are shaped by more than one mechanism.

Key takeaway

The Heckscher-Ohlin model explains trade using differences in factor endowments. A country tends to export the good that uses its abundant factor intensively. This creates gains from trade, but it also affects income distribution. Owners of abundant factors tend to gain from trade, while owners of scarce factors may lose.

Review questions

  1. What is the main difference between the Ricardian model and the Heckscher-Ohlin model?
  2. Define factor abundance.
  3. Define factor intensity.
  4. Why is cloth labor intensive in the example used in this chapter?
  5. Why is food capital intensive in the example used in this chapter?
  6. State the Heckscher-Ohlin theorem.
  7. If a country is capital abundant, what type of good does the model predict it will export?
  8. Why can trade create winners and losers inside the same country?
  9. What happens to wages when the price of a labor-intensive good rises?
  10. Why might the model fail to perfectly predict real-world trade patterns?

Practice problem

Suppose a country produces two goods: textiles and machinery.

Good Labor required per unit Capital required per unit
Textiles 4 1
Machinery 2 5

The country has 8,000 units of labor and 4,000 units of capital.

  1. Which good is labor intensive?
  2. Which good is capital intensive?
  3. Write the labor constraint.
  4. Write the capital constraint.
  5. If this country is labor abundant relative to its trading partner, which good does the Heckscher-Ohlin model predict it will export?
  6. If the relative price of textiles rises after trade, what is likely to happen to wages?