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The factor proportions model was originally developed by two Swedish economists, Eli Heckscher and his student Bertil Ohlin, in the 1920s. Many elaborations of the model were provided by Paul Samuelson after the 1930s, and thus sometimes the model is referred to as the Heckscher-Ohlin-Samuelson (HOS) model. In the 1950s and 1960s, some noteworthy extensions to the model were made by Jaroslav Vanek, and so occasionally the model is called the Heckscher-Ohlin-Vanek model. Here we will simply call all versions of the model either the Heckscher-Ohlin (H-O) model, or simply the more generic “factor proportions model.”
The H-O model incorporates a number of realistic characteristics of production that are left out of the simple Ricardian model. Recall that in the simple Ricardian model only one factor of production, labor, is needed to produce goods and services. The productivity of labor is assumed to vary across countries, which implies a difference in technology between nations. It was the difference in technology that motivated advantageous international trade in the model.
The standard H-O model begins by expanding the number of factors of production from one to two. The model assumes that labor and capital are used in the production of two final goods. Here, capital refers to the physical machines and equipment that are used in production. Thus machine tools, conveyers, trucks, forklifts, computers, office buildings, office supplies, and much more are considered capital.
All productive capital must be owned by someone. In a capitalist economy, most of the physical capital is owned by individuals and businesses. In a socialist economy, productive capital would be owned by the government. In most economies today, the government owns some of the productive capital, but private citizens and businesses own most of the capital. Any person who owns common stock issued by a business has an ownership share in that company and is entitled to dividends or income based on the profitability of the company. As such, that person is a capitalist—that is, an owner of capital.
The H-O model assumes private ownership of capital. Use of capital in production will generate income for the owner. We will refer to that income as capital “rents.” Thus, whereas the worker earns “wages” for his or her efforts in production, the capital owner earns rents.
The assumption of two productive factors, capital and labor, allows for the introduction of another realistic feature in production: differing factor proportions both across and within industries. When one considers a range of industries in a country, it is easy to convince oneself that the proportion of capital to labor applied in production varies considerably. For example, steel production generally involves large amounts of expensive machines and equipment spread over perhaps hundreds of acres of land, but it also uses relatively few workers. (Note that relative here means relative to other industries.) In the tomato industry, in contrast, harvesting requires hundreds of migrant workers to hand-pick and collect each fruit from the vine. The amount of machinery used in this process is relatively small.
In the H-O model, we define the ratio of the quantity of capital to the quantity of labor used in a production process as the capital-labor ratioThe ratio of the quantity of capital to the quantity of labor used in a production process.. We imagine, and therefore assume, that different industries producing different goods have different capital-labor ratios. It is this ratio (or proportion) of one factor to another that gives the model its generic name: the factor proportions model.
In a model in which each country produces two goods, an assumption must be made as to which industry has the larger capital-labor ratio. Thus if the two goods that a country can produce are steel and clothing and if steel production uses more capital per unit of labor than is used in clothing production, we would say the steel production is capital intensiveAn industry is capital intensive relative to another industry if it has a higher capital-labor ratio in the production process. relative to clothing production. Also, if steel production is capital intensive, then it implies that clothing production must be labor intensiveAn industry is labor intensive relative to another industry if it has a higher labor-capital ratio in the production process. relative to steel.
Another realistic characteristic of the world is that countries have different quantities—that is, endowments—of capital and labor available for use in the production process. Thus some countries like the United States are well endowed with physical capital relative to their labor force. In contrast, many less-developed countries have much less physical capital but are well endowed with large labor forces. We use the ratio of the aggregate endowment of capital to the aggregate endowment of labor to define relative factor abundancy between countries. Thus if, for example, the United States has a larger ratio of aggregate capital per unit of labor than France’s ratio, we would say that the United States is capital abundant relative to France. By implication, France would have a larger ratio of aggregate labor per unit of capital and thus France would be labor abundant relative to the United States.
The H-O model assumes that the only differences between countries are these variations in the relative endowments of factors of production. It is ultimately shown that (1) trade will occur, (2) trade will be nationally advantageous, and (3) trade will have characterizable effects on prices, wages, and rents when the nations differ in their relative factor endowments and when different industries use factors in different proportions.
It is worth emphasizing here a fundamental distinction between the H-O model and the Ricardian model. Whereas the Ricardian model assumes that production technologies differ between countries, the H-O model assumes that production technologies are the same. The reason for the identical technology assumption in the H-O model is perhaps not so much because it is believed that technologies are really the same, although a case can be made for that. Instead, the assumption is useful in that it enables us to see precisely how differences in resource endowments are sufficient to cause trade and it shows what impacts will arise entirely due to these differences.
There are four main theorems in the H-O model: the Heckscher-Ohlin (H-O) theorem, the Stolper-Samuelson theorem, the Rybczynski theorem, and the factor-price equalization theorem. The Stolper-Samuelson and Rybczynski theorems describe relationships between variables in the model, while the H-O and factor-price equalization theorems present some of the key results of the model. The application of these theorems also allows us to derive some other important implications of the model. Let us begin with the H-O theorem.
The H-O theorem predicts the pattern of trade between countries based on the characteristics of the countries. The H-O theorem says that a capital-abundant country will export the capital-intensive good, while the labor-abundant country will export the labor-intensive good.
Here’s why. A country that is capital abundantA country is capital abundant relative to another country if it has a higher capital endowment per labor endowment than the other country. is one that is well endowed with capital relative to the other country. This gives the country a propensity for producing the good that uses relatively more capital in the production process—that is, the capital-intensive good. As a result, if these two countries were not trading initially—that is, they were in autarky—the price of the capital-intensive good in the capital-abundant country would be bid down (due to its extra supply) relative to the price of the good in the other country. Similarly, in the country that is labor abundantA country is labor abundant relative to another country if it has a higher labor endowment per capital endowment than the other country., the price of the labor-intensive good would be bid down relative to the price of that good in the capital-abundant country.
Once trade is allowed, profit-seeking firms will move their products to the markets that temporarily have the higher price. Thus the capital-abundant country will export the capital-intensive good since the price will be temporarily higher in the other country. Likewise, the labor-abundant country will export the labor-intensive good. Trade flows will rise until the prices of both goods are equalized in the two markets.
The H-O theorem demonstrates that differences in resource endowments as defined by national abundancies are one reason that international trade may occur.
The Stolper-Samuelson theoremA theorem that specifies how changes in output prices affect factor prices in the H-O model. It states that an increase in the price of a good will cause an increase in the price of the factor used intensively in that industry and a decrease in the price of the other factor. describes the relationship between changes in output prices (or prices of goods) and changes in factor prices such as wages and rents within the context of the H-O model. The theorem was originally developed to illuminate the issue of how tariffs would affect the incomes of workers and capitalists (i.e., the distribution of income) within a country. However, the theorem is just as useful when applied to trade liberalization.
The theorem states that if the price of the capital-intensive good rises (for whatever reason), then the price of capital—the factor used intensively in that industry—will rise, while the wage rate paid to labor will fall. Thus, if the price of steel were to rise and if steel were capital intensive, the rental rate on capital would rise, while the wage rate would fall. Similarly, if the price of the labor-intensive good were to rise, then the wage rate would rise, while the rental rate would fall.
The theorem was later generalized by Ronald Jones, who constructed a magnification effect for prices in the context of the H-O model. The magnification effect allows for analysis of any change in the prices of both goods and provides information about the magnitude of the effects on wages and rents. Most importantly, the magnification effect allows one to analyze the effects of price changes on real wages and real rents earned by workers and capital owners. This is instructive since real returns indicate the purchasing power of wages and rents after accounting for price changes and thus are a better measure of well-being than the wage rate or rental rate alone.
Since prices change in a country when trade liberalization occurs, the magnification effect can be applied to yield an interesting and important result. A movement to free trade will cause the real return of a country’s relatively abundant factor to rise, while the real return of the country’s relatively scarce factor will fall. Thus if the United States and France are two countries that move to free trade and if the United States is capital abundant (while France is labor abundant), then capital owners in the United States will experience an increase in the purchasing power of their rental income (i.e., they will gain), while workers will experience a decline in the purchasing power of their wage income (i.e., they will lose). Similarly, workers will gain in France, but capital owners will lose.
What’s more, the country’s abundant factor benefits regardless of the industry in which it is employed. Thus capital owners in the United States would benefit from trade even if their capital is used in the declining import-competing sector. Similarly, workers would lose in the United States even if they are employed in the expanding export sector.
The reasons for this result are somewhat complicated, but the gist can be given fairly easily. When a country moves to free trade, the price of its exported goods will rise, while the price of its imported goods will fall. The higher prices in the export industry will inspire profit-seeking firms to expand production. At the same time, the import-competing industry, suffering from falling prices, will want to reduce production to cut its losses. Thus capital and labor will be laid off in the import-competing sector but will be in demand in the expanding export sector. However, a problem arises in that the export sector is intensive in the country’s abundant factor—let’s say capital. This means that the export industry wants relatively more capital per worker than the ratio of factors that the import-competing industry is laying off. In the transition there will be an excess demand for capital, which will bid up its price, and an excess supply of labor, which will bid down its price. Hence, the capital owners in both industries experience an increase in their rents, while the workers in both industries experience a decline in their wages.
The factor-price equalization theorem says that when the prices of the output goods are equalized between countries, as when countries move to free trade, 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 are the assumptions that the two countries share the same production technology and that markets are perfectly competitive. In a perfectly competitive market, factors are paid on the basis of the value of their marginal productivity, which in turn depends on the output prices of the goods. Thus when prices differ between countries, so will their marginal productivities and hence so will their wages and rents. However, once goods’ prices are equalized, as they are in free trade, the value of marginal products is also equalized between countries and hence the countries must also share the same wage rates and rental rates.
Factor-price equalization formed the basis for some arguments often heard in the debates leading up to the approval of the North American Free Trade Agreement (NAFTA) between the United States, Canada, and Mexico. Opponents of NAFTA feared that free trade with Mexico would lower U.S. wages to the level in Mexico. Factor-price equalization is consistent with this fear, although a more likely outcome would be a reduction in U.S. wages coupled with an increase in Mexican wages.
Furthermore, we should note that factor-price equalization is unlikely to apply perfectly in the real world. The H-O model assumes that technology is the same between countries in order to focus on the effects of different factor endowments. If production technologies differ across countries, as we assumed in the Ricardian model, then factor prices would not equalize once goods’ prices equalize. As such, a better interpretation of the factor-price equalization theorem applied to real-world settings is that free trade should cause a tendency for factor prices to move together if some of the trade between countries is based on differences in factor endowments.
The Rybczynski theoremA theorem that specifies how changes in endowments affect production levels in the H-O model. It states that an increase in a country’s endowment of a factor will cause an increase in the output of the good that uses that factor intensively and a decrease in the output of the other good. demonstrates the relationship between changes in national factor endowments and changes in the outputs of the final goods within the context of the H-O model. Briefly stated, it says that an increase in a country’s endowment of a factor will cause an increase in output of the good that uses that factor intensively and a decrease in the output of the other good. In other words, if the United States experiences an increase in capital equipment, then that would cause an increase in output of the capital-intensive good (steel) and a decrease in the output of the labor-intensive good (clothing). The theorem is useful in addressing issues such as investment, population growth and hence labor force growth, immigration, and emigration, all within the context of the H-O model.
The theorem was also generalized by Ronald Jones, who constructed a magnification effect for quantities in the context of the H-O model. The magnification effect allows for analysis of any change in both endowments and provides information about the magnitude of the effects on the outputs of the two goods.
The H-O model demonstrates that when countries move to free trade, they will experience an increase in aggregate efficiency. The change in prices will cause a shift in production of both goods in both countries. Each country will produce more of its export good and less of its import good. Unlike the Ricardian model, however, neither country will necessarily specialize in production of its export good. Nevertheless, the production shifts will improve productive efficiency in each country. Also, due to the changes in prices, consumers, in the aggregate, will experience an improvement in consumption efficiency. In other words, national welfare will rise for both countries when they move to free trade.
However, this does not imply that everyone benefits. As the Stolper-Samuelson theorem shows, the model clearly demonstrates that some factor owners will experience an increase in their real incomes, while others will experience a decrease in their factor incomes. Trade will generate winners and losers. The increase in national welfare essentially means that the sum of the gains to the winners will exceed the sum of the losses to the losers. For this reason, economists often apply the compensation principle.
The compensation principle states that as long as the total benefits exceed the total losses in the movement to free trade, then it must be possible to redistribute income from the winners to the losers such that everyone has at least as much as they had before trade liberalization occurred.
Note that the “standard” H-O model refers to the case of two countries, two goods, and two factors of production. The H-O model has been extended to many countries, many goods, and many factors, but most of the exposition in this text, and by economists in general, is in reference to the standard case.
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?”