The specific factors model was developed by Paul Samuelson and Ronald Jones. Like the simple Ricardian model, it assumes an economy that produces two goods and that can allocate its labor supply between the two sectors. Unlike the Ricardian model,however, the specific factors model allows for the existence of factors of production besides labor. Whereas labor is a mobile factor that can move between sectors, these

other factors are assumed to be specific. That is, they can be used only in the production of particular goods.

Assumptions of the Model:

Imagine an economy that can produce two goods, cloth and food. Instead of one factor of production, however, the country has three: labor (L), capital (K), and land

(T for terrain). Cloth is produced using capital and labor (but not land), while food is produced using land and labor (but not capital). Labor is therefore a mobile factor that can be used in either sector, while land and capital are both specific factors that

can be used only in the production of one good. Land can also be thought of as a different type of capital, one that is specific to the food sector .

How much of each good does the economy produce? The economy’s output of cloth depends on how much capital and labor are used in that sector. 

In the model developed in this chapter, we assume

two factors of production—land and capital—

are permanently tied to particular sectors

of the economy. In advanced economies, however,

agricultural land receives only a small part

of national income. When economists apply the

specific factors model to economies like those of

the United States or France, they typically think

of factor specificity not as a permanent condition

but as a matter of time. For example, the vats

used to brew beer and the stamping presses used

to build auto bodies cannot be substituted for

each other, and so these different kinds of equipment

are industry-specific. Given time, however,

it would be possible to redirect investment from

auto factories to breweries or vice versa. As a result,

in a long-term sense both vats and stamping

presses can be considered two manifestations of a

single, mobile factor called capital.

In practice, then, the distinction between specific

and mobile factors is not a sharp line. Rather,

it is a question of the speed of adjustment, with

factors being more specific the longer it takes to

redeploy them between industries. So how specific

are the factors of production in the real economy?

Worker mobility varies greatly with the characteristics

of the worker (such as age) and the job

occupation (whether it requires general or jobspecific

skills). Nevertheless, one can measure an

average rate of mobility by looking at the duration

of unemployment following a worker’s displacement.

After four years, a displaced worker

in the United States has the same probability of

being employed as a similar worker who was not

displaced.* This four-year time-span compares

with a lifetime of 15 or 20 years for a typical

specialized machine, and 30 to 50 years for structures

(a shopping mall, office building, or production

plant). So labor is certainly a less specific

factor than most kinds of capital. However, even

though most workers can find new employment

in other sectors within a four-year time-span,

switching occupations entails additional costs: A

displaced worker who is re-employed in a different

occupation suffers an 18 percent permanent

drop in wages (on average). This compares with

a 6 percent drop if the worker does not switch

occupations.† Thus, labor is truly flexible only

before a worker has invested in any occupationspecific

skills.

Problems

1.

2.

This chapter introduces and discusses the Heckscher-Ohlin (H-O) theory of trade and its implications. The H-O theory is also known as the factor-proportions theory or factor-endowment theory. A principal result  of the H-O theory is the Heckscher-Ohlin Theorem which states the following.

A nation will export the product that uses its most abundant factor intensively.

This result will be explained in detail in developing the H-O theory. Both the Ricardian and opportunity-cost models demonstrate that comparative advantage is the basis of trade, but neither adequately explains the source of a country's comparative advantage. The H-O model explains comparative advantage in terms of the factor abundance of nations and the factor intensity of commodities.

Factor abundance is the resource richness of nations. In a two-factor model, where the factors are capital and labor, the factor abundance of one nation is defined by the relative endowment of capital to labor in the nation relative to another nation or nations.

The relative aspect of factor abundance is important. For example, the U.S. has more of both labor and capital than Mexico, but the quantity of capital advantage in the U.S. over Mexico is greater than the quantity of labor advantage in the U.S. over Mexico. The U.S., therefore, is capital abundant and Mexico is labor abundant. Letting K measure the quantity of capital and L the quantity of labor, (K/L)_US>(K/L)_MEX, or the amount of capital per laborer in the U.S. exceeds that of Mexico. (Verify that it is possible for L_US to be greater than L_MEX and (K/L)_US>(K/L)_MEX ). Now invert the ratios, which reverses the inequality, so (L/K)_US<(L/K)_MEX, which says that Mexico is labor abundant relative to the U.S. If one country is capital rich (more capital relative to labor) then the other is labor rich (more labor relative to capital).

Factor abundance can also be measured by relative factor prices. If Mexico is abundant in labor then, ceteris paribus, labor will be relatively cheaper in Mexico than in the U.S. Thus, (w/r)_M < (w/r)_US, where w is the wage rate and r is the cost of capital, usually taken to be the interest rate. If (w/r)_M < (w/r)_US the (r/w)_M > (r/w)_US, so capital is relatively cheaper in the US.

Note that it is possible for a nation with labor abundance to have a high relative wage rate if the wage has been pushed up by a high demand for products made with labor. The H-O model does, however, assumes that product demand is similar across nations, so the quantity definition of abundance will align with the factor-price definition of abundance. If, however, demand does differ across nations and the quantity definition does not align with the factor-price definition, then abundance should be defined using relative factor prices. (The term "relative factor price" refers to either w/r or r/w. The ratio w/r is the relative wage and r/w is the relative price of capital.)

Factor intensity refers to the relative amounts of capital and labor used in producing a good. Fig. 5.1 shows the use of capital and labor in the production of two commodities. The amount of capital per laborer in the production of a good is called the capital-labor ratio. For good Y, 2 units of capital are used with 10 units of capital, so the capital-labor ratio is 2/10, or 1/5. If the capital-labor ratio is constant, then a straight line, as in Fig. 5.1, shows capital-labor usage at different levels of K and L usage.

In Fig. 5.1, good Y is capital intensive because the amount of capital per laborer (1/2) in the production of Y is higher than the amount of capital per laborer in the production of X (1/5). This can be written as (K/L)_Y>(K/L)_X. Factor intensity is measured in relative terms so if good Y is a capital-intensive commodity, then good X must be a labor-intensive commodity because if (K/L)_Y>(K/L)_X, then (L/K)_Y<(L/K)_X.

The H-O model assumes that a good that is capital intensive in one nation is also capital intensive in another nation, although the capital-labor ratios could differ across nations as each nation adjusts factor usage to different factor prices. (See Fig. 5.1 in Chapter 5 of the International Economics.)

The H-O theory states that a commodity will be produced more cheaply by the nation that has a lot of the input that the commodity uses more of in production. If a commodity uses a relatively large amount of capital, then nations with abundant capital will have a comparative advantage in that commodity. A nation will export the product that uses its most abundant factor intensively. This implies that the nation will import that product that intensively uses the nation’s scarce factor.

The effect of abundance and factor intensity on the ppf of two nations is shown in Fig.5.2. It is assumed that Nation 1 is labor abundant, so by definition, Nation 2 is capital abundant. Good Y is assumed to be capital intensive in both nations, so by definition, Good X is labor intensive in both nations. The ppf of labor-abundant Nation 1 is biased towards Good X, the labor-intensive product. The ppf of capital-abundant Nation 2 is biased towards Good Y, the capital-intensive product.

For the same preferences in each nation, (the indifference curves shown in Fig. 5.2 have identical shapes), the opportunity cost of Good X is higher in Nation 2 than in Nation 1. (Recall that the slope of the ppf, DY/DX, is the opportunity cost of Good X.) Thus, Nation 1 with an abundance of labor will have a comparative advantage in the labor-intensive good. Nation 2, with an abundance of capital, will have a comparative advantage in the capital-intensive good.

Prior to trade, a labor-abundant country will have a comparative advantage in the labor-intensive product and so specialize in the labor-intensive product. The increased production of the labor-intensive produce will require more resources (capital and labor). The resources will come from the capital-intensive product, whose production will decrease as imports of the capital-intensive product increases. The capital-intensive product will release relatively more capital and relatively less labor than is demanded by the expanding production of the labor-intensive product. The consequence is an excess demand for labor and an excess supply of capital. The excess demand for labor will cause the wage rate to increase and the excess supply of capital will cause the price of capital to decrease. (It is useful to go back and review this argument until it's quite clear.) The conclusion is that in a labor-abundant country, trade will cause the price of labor to increase and the price of capital to decrease. In a capital-abundant country the reverse reallocation occurs, so trade will cause the price of capital to increase in a capital-abundant country and cause the price of labor to decrease. This change in the price of labor and the price of capital applies to both nominal and real wages.

This statement about trade and factor prices is what is known as the Stolper-Samuelson Theorem. Although the Stolper-Samuelson Theorem was originally applied to changes in tariffs, the Theorem also applies to changes in resource use to due to trade. The Stolper-Samuelson Theorem in the context of tariffs is developed in Chapter 8 of International Economics.

This conclusion suggests that a labor-abundant nation that has a low relative wage will find that trade increases its relative wage, approaching the falling relative wage of the capital-abundant nation. In fact, a second principal conclusion of the H-O model is that trade equalizes relative factor prices. If the source of different product prices is different factor prices, then when trade equalizes relative product prices, it also equalizes relative factor prices. This is demonstrated in Fig.5.3.

Nation 1 has a low relative wage because it is labor abundant. Because Nation 1 has a low relative wage, it can produce Good X at a relatively cheaper price than can Nation 2. Note a positive relationship between the relative wage and the price of Good X: as the relative wage increases the relative price of the labor-intensive good increases. The upward-sloping line in Fig. 5.3 shows this positive relationship between w/r and P_X/P_Y. Because trade equalizes prices, shown at (P_X/P_Y)* in Fig. 5.3, trade must also equalize the factor-price ratio, shown as (w/r)* in Fig. 5.3. (Note that (P_X/P_Y)* in Fig. 5.3 is the equilibrium terms of trade, the determination of which was described in Chapter 4.)

Not only are relative factor prices equalized as a result of trade, but absolute factor prices are also equalized, given the assumptions of the H-O model. This conclusion flows from the basic assumptions of perfectly competitive markets and similar technologies. In perfectly competitive markets, factors are paid the value of their marginal product. The value of marginal product is the dollar value of the additional units of a product produced by an additional worker. If an additional worker adds 10 units of production that sell for $40 each, then the value of the marginal product is $400. If a worker received a wage less than $400, then other firms would compete away the worker at a higher wage. If the wage were more than the value of the marginal product, then the worker would not be hired, causing the wage to fall.

Now, if technologies are identical across nations, as assumed in the H-O theory, then the marginal products of labor will be identical across countries and the marginal products of capital will be identical across countries. Product prices will be equalized by the act of trade, so the value of marginal products will be identical across countries. Competition will now force all wages to equal the value of labor's marginal product. Trade will cause the wage rate in Switzerland to be the same as the wage rate in Germany for the same kind of factors of production. Similarly, trade will cause the price of capital in the United States to be the same as the price of capital in Mexico. The conclusion that trade will equalize both absolute and relative factor prices is the factor-price equalization theorem, or the Heckscher-Ohlin-Samuelson (H-O-S) theorem.

The factor-price equalization theorem also indicates the effect of trade on income distribution within a country. In a capital-abundant nation, the price of capital (r) increases and the price of labor (w) decreases. (The reverse happens for a labor-abundant nation.) However, because trade increases overall income, the loss of income by workers is exceeded by the gain in income by owners of capital.

Research on the empirical relevance of the Heckscher-Ohlin model begins with a famous study by Vassily Leontief. Leontief measured the labor and capital content of a representative basket of exports and import-competing goods. Leontief's result, known as the Leontief Paradox, was that the United States imports capital-intensive goods and exports labor-intensive goods, in direct opposition to the predictions of the H-O model.

Attempts to explain the H-O model has resulted in significant new research, the most important of which is the extension of the H-O model to include other inputs besides capital and labor, especially human capital, research and development, and natural resources. Based on more recent research, the H-O model appears appropriate for trade between developed and developing countries, and for manufactured goods. Remaining trade patterns are explained by new trade theories that include economies of scale and imperfect competition, which are addressed in the next chapter.

The capital and labor requirements for the production of one unit of Textiles and one unit of Computers is provided in Table 1.

Table 1: Capital and Labor Production Requirements

a) Which good, textiles or computers, uses more units of capital in producing one unit?

b) Calculate the capital-labor ratios in the production of textiles and computers. Which good's production is capital intensive?

c) Which good uses more units of labor per unit of production?

d) Calculate the labor-capital ratios in the production of textiles and computers. Which good's production is labor intensive?

• 1. The factor-endowment model of international trade was developed by

•  a. Adam Smith. 
   b. David Ricardo. 
   c. John Stuart Mill. 
   d. Eli Heckscher and Bertil Ohlin. 
  

• 2. In the Heckscher-Ohlin model, a nation's comparative advantage is based on

•  a. consumer preferences. 
   b. the nation's relative endowments of productive resources such as labor and capital. 
   c. distance from the nation's most important trading partners. 
   d. trade barriers such as tariffs and quotas. 
  

• 3. According to the Heckscher-Ohlin model, a nation with a relative abundance of capital would be expected to

•  a. trade less than a labor-abundant nation. 
   b. trade more than a labor-abundant nation. 
   c. export capital-intensive products such as autos. 
   d. allow labor to immigrate from other nations. 
  

• 4. TRUE OR FALSE: The factor endowments model predicts that international trade will tend to equalize the prices of tradeable goods among nations, but to increase the wage gap between capital-abundant and labor-abundant nations.

•  a. True 
   b. False 
  

• 5. In a nation with a relative abundance of skilled labor and a relative scarcity of unskilled labor, international trade would tend to

•  a. widen or aggravate the income disparity between skilled and unskilled workers. 
   b. reduce the income disparity between skilled and unskilled workers. 
   c. lower the wages of both groups of workers. 
   d. raise the wages of both groups of workers. 
  

• 6. Empirical studies have found that the largest contribution to growing wage inequality in the United States has come from

•  a. international trade. 
   b. immigration. 
   c. technological change. 
   d. a decline in union influence. 
  

• 7. Leontief's 1954 study of U.S. trade patterns, resulting in the Leontief paradox, found that

•  a. U.S. trade volume declined even though U.S. GDP had been rising. 
   b. the United States was exporting mostly capital-intensive products. 
   c. the United States was trading more with distant than with near nations. 
   d. U.S. exports were labor-intensive compared with U.S. imports, even though the United States was widely regarded as a relatively capital-abundant nation. 
  

• 8. TRUE OR FALSE: Studies have found the United States to be a net exporter of technologically intensive manufactured goods and a net importer of more standardized and labor-intensive manufactured goods.

•  a. True 
   b. False