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## 5.14 Factor-Price Equalization

### Learning Objective

1. Understand the relationship between wages and rents across countries in the Heckscher-Ohlin (H-O) model.

The fourth major theorem that arises out of the Heckscher-Ohlin (H-O) model is called the factor-price equalization theorem. Simply stated, the theorem says that when the prices of the output goods are equalized between countries as they move to free trade, then the prices of the factors (capital and labor) will also be equalized between countries. This implies that free trade will equalize the wages of workers and the rents earned on capital throughout the world.

The theorem derives from the assumptions of the model, the most critical of which is the assumption that the two countries share the same production technology and that markets are perfectly competitive.

In a perfectly competitive market, the return to a factor of production depends on the value of its marginal productivity. The marginal productivity of a factor, like labor, in turn depends on the amount of labor being used as well as the amount of capital. As the amount of labor rises in an industry, labor’s marginal productivity falls. As the amount of capital rises, labor’s marginal productivity rises. Finally, the value of productivity depends on the output price commanded by the good in the market.

In autarky, the two countries face different prices for the output goods. The difference in prices alone is sufficient to cause a deviation in wages and rents between countries because it affects the marginal productivity. However, in addition, in a variable proportions model the difference in wages and rents also affects the capital-labor ratios in each industry, which in turn affects the marginal products. All of this means that for various reasons the wage and rental rates will differ between countries in autarky.

Once free trade is allowed in outputs, output prices will become equal in the two countries. Since the two countries share the same marginal productivity relationships, it follows that only one set of wage and rental rates can satisfy these relationships for a given set of output prices. Thus free trade will equalize goods’ prices and wage and rental rates.

Since the two countries face the same wage and rental rates, they will also produce each good using the same capital-labor ratio. However, because the countries continue to have different quantities of factor endowments, they will produce different quantities of the two goods.

This result contrasts with the Ricardian model. In that model, production technologies are assumed to be different in the two countries. As a result, when countries move to free trade, real wages remain different from each other; the country with higher productivities will have higher real wages.

In the real world, it is difficult to know whether production technologies are different, similar, or identical. Supporting identical production technology, one could argue that state-of-the-art capital can be moved anywhere in the world. On the other hand, one might counter by saying that just because the equipment is the same doesn’t mean the workforces will operate the equipment similarly. There will likely always remain differences in organizational abilities, workforce habits, and motivations.

One way to apply these model results to the real world might be to say that to the extent that countries share identical production capabilities, there will be a tendency for factor prices to converge as freer trade is realized.

### Key Takeaways

• The factor-price equalization theorem says that when the product prices are equalized between countries as they move to free trade in the H-O model, then the prices of the factors (capital and labor) will also be equalized between countries.
• Factor-price equalization arises largely because of the assumption that the two countries have the same technology in production.
• Factor-price equalization in the H-O model contrasts with the Ricardian model result in which countries could have different factor prices after opening to free trade.

### Exercises

1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”

1. This key technology assumption assures that factor-price equalization will occur in free trade in an H-O model.
2. The factor price equalization theorem says these will be equalized between countries if goods prices become equalized because of trade.
3. The factor price equalization theorem says these will be equalized between countries if factor prices become equalized because of factor migration.
2. Suppose there are two countries, Japan and the Philippines, described by a variable proportions H-O model. Suppose they produce two goods, rice and chicken, using two factors, labor and capital. Let rice be capital intensive and the Philippines be labor abundant.

1. If these are the only two countries and if they do not trade, explain how the price of rice and chicken will differ between the two countries.
2. If these are the only two countries and if they do not trade, explain how the wages and rental rates on capital will differ between the two countries.
3. When trade opens between the countries what happens to the price of rice and chicken in the Philippines?
4. When trade opens between the countries what happens to the wages and rents in the Philippines?
5. When trade opens between the countries what happens to the wages and rents in Japan?
6. When trade is free between the two countries, how do the wages and rents compare between the two countries?
3. Suppose there are two countries, Japan and the Philippines, as described in Exercise 2 above. Suppose goods trade is restricted between the countries and that factor mobility between countries suddenly becomes free.

1. Describe the pattern of factor flows that would occur between the two countries and explain why these flows occur.
2. Describe the effect of the factor flows on the wages and rents in the two countries.
3. Apply the magnification effect for quantities to explain how the outputs of rice and chicken will change in Japan and the Philippines.
4. After factor flows reach a new equilibrium, explain how goods’ prices will differ between the two countries.