[Over the next week I might be posting stuff on trade theory. In part, I think readers will find some aspects of it interesting, but this is also a form of “note taking” for me — it helps me better remember the specifics of the different models.]
The Heckscher–Ohlin model of international trade, named after the Swedish economists Eli Heckscher and Bertil Ohlin — the latter later received a Nobel prize for his work on trade theory —, is an equilibrium model that helps us understand the importance of relative factor endowments in deciding the pattern of international trade. It has been criticized for “poor predictive power,” meaning that some think it doesn’t explain the real world very well, but I think it’s still interesting to study it and its implications. One of the things it implies is that international trade might contribute to wealth gaps in a countries that are not abundant in unskilled labor.
The Heckscher–Ohlin theory can be modeled relatively easily if you simplify some of the assumptions. This is usually called the “2 × 2 × 2” model: two outputs (bread [B] and cheese [C]), two factors of production (capital [K] and labor [L), and two countries (Home and Foreign, the latter denoted with an asterisk [*]). These factors are mobile in the long-run, meaning their rate of return will tend to equilibrate. This is an addition to the basic Ricardian model, which assumes that there is only one factor of production and that labor will specialize in the area it has a comparative advantage in.
First, we can see the effect of price changes on the distribution of factors of production in Home markets. Let’s establish some basic relationships and definitions,
- The mixture of factors of production to produce one unit of cheese ≡ QC (L, K); for bread ≡ QC (L, K);
- aKC ≡ the amount of capital used to produce one unit of cheese;
- aLC ≡ the amount of labor used to produce one unit of cheese;
- aKB ≡ the amount of capital used to produce one unit of bread;
- aLB ≡ the amount of labor used to produce one unit of bread;
- PC & PB ≡ the given prices of cheese and bread, respectively.
Let’s assume that cheese is a labor intensive industry and bread is capital intensive. Note, when we talk about intensity we’re talking about relative, not absolute, intensity. For example, suppose that each unit of bread requires two labor hours and six capital hours and that each unit of cheese uses five labor hours and ten capital hours. We see that cheese uses more of both goods, but bread is still capital intensive relative to cheese. This is more easily seen when we compare ratios of inputs: 1:3 for bread and 1:2 for cheese. This relationship between the two industries can be modeled algebraically: aLC/aKC > aLB/aKB (the relative amount of labor is greater in the production of cheese than it is in the production of bread).
In equilibrium the ratio of prices ( PC/PB ) is equal to the opportunity cost of the factors going towards the production of the two goods. The relationship between relative prices ( PC/PB ) and the production of the different outputs can be graphed abstractly on a production possibilities frontier (PPF). The point of production will have a slope of –PC/PB (the opportunity cost),
Another set of relationship we can graph are those between relative prices, relative returns to the factors of production (wages [w] for labor and rent [r] for capital), and the relative allocation of these factors in each industry,
The left hand panel (where a leftward movement along the abscissa [x-axis] represents increase) shows a hypothetical relationship between the relative price of cheese and the relative price of wages. It depicts relative wages increasing as does the relative price of cheese. Why is this? Remember that we said cheese is labor intensive and bread is capital intensive. An increase in the relative price of cheese will impact labor more than capital, because the change in relative prices is favoring a labor intensive industry.
The panel on the right (where a rightward movement along the abscissa represents increase) shows the relationship for each output between the ratio of labor to capital (L/K). The CC curve shows different L/K ratios corresponding to different w/r ratios for the cheese industry, and BB for the bread industry. Note that curve CC is to the right of curve BB. We know this because we assumed that cheese is the labor intensive industry — this condition will always be true: LC/KC > LB/KB (it’s the same as saying aLC/aKC > aLB/aKB). An increase in relative wages will induce producers to increase the employment of capital relative to labor, which makes sense if you think of a demand curve for labor: the higher the price of labor the less of its quantity will be demanded.
There is an interesting implication of the model relevant to the subject of economic inequality. An increase in relative wages means that the return to labor will rise and the return to capital will fall. Remember that wages are equal to marginal product in equilibrium. A fall in L/K implies an increase in the marginal product of labor. This is because the capital intensity of that industry is rising. Since this is true for both industries, we see that capitalists (capital owners) lose and laborers gain purchasing power in terms of both goods.
Second, how does all of this relate to international trade. Take a look at the following graph,
This graph may be a little difficult to follow at first, because relative supply and demand curves are not customary. The logic is that as the relative price of cheese falls, the relative quantity of cheese demanded rises. Think about like this: if the price of cheese (the numerator) falls, all else equal quantity demanded will increase. If the price of bread rises, all else equal the quantity demanded for bread will fall — there is only one other good, so people substitute bread with cheese. Think of relative supply in similar terms. This graph assumes that relative demand in both countries is the same, and that foreign (RS*) is better endowed in capital than home. This means that, all else equal, at any price ratio home will produce more of the labor intensive good than foreign. This follows from our previous explanation of the relationship between relative prices and resource allocation: countries will tend to produce goods that use factors of production they’re relatively well endowed with.
The main takeaway, though, is that relative prices will tend to converge with trade — it has to do with the equalization of the rate of profits. People will take advantage of price differences until prices are the same. Following the graph, we see that the relative price of cheese in foreign falls (they can buy it for relatively cheaper prices from Home) and it rises at Home (they can sell cheese for higher prices at Foreign). How does this impact the distribution of income at Home? Well, we know from the previous graphs that a rise in PC/PB will, all else equal, raise relative wages: laborers gain at the expense of capitalists. In Foreign the opposite is true: capitalists gain at the expense of laborers.
This version of the Heckscher–Ohlin model predicts that laborers in capital abundant countries will suffer as a result of international trade, and capitalists will gain. That is, there will be a bifurcation of income. If we think about skilled labor versus unskilled labor, as opposed to capital versus labor, then unskilled labor in countries well endowed with skilled labor will suffer from international trade. To put this in the context of the real world, it means that unskilled labor in the United States (a capital intensive economy) will be hurt by globalization that lowers the prices of the goods unskilled labor produces (if countries like, say, China are relatively abundant in unskilled labor). In other words, this model predicts that trade will contribute to a growing inequality gap.
My challenge to this prediction is that it ignores the fact that the use of “skilled” and “unskilled” is often relative, not absolute. For example, let’s say that a U.S. farmer represents unskilled labor, and a U.S. computer engineer represents skilled labor. The same is true in Mexico: farmers are unskilled labor and computer engineers are skilled labor. But, farming in the U.S. is still much more capital intensive than farming in Mexico. U.S. farmers have better equipment. The same is probably true of U.S. computer engineers. Another way of saying the same thing is that the U.S. benefits from better technology. So, it doesn’t follow that skilled/unskilled labor in the U.S. are analogous to their counterparts in Mexico.
If we assume that the skills gap will continue to exist with trade, but that these gaps are somewhat incomparable between countries, then what we’d see is an increase in the domain of goods being manufactured. Both nations still gain: unskilled labor in countries where it’s abundant gain from an increase in demand for their products, and skilled labor in countries well endowed with it gain from an increased demand for their products. Note that if PC/PB converge internationally, then so will w/r. In other words, labor will tend to allocate where the returns are highest. It’s important to remember, though, that demand for a particular skill is dependent on the profitability of producing goods which use this skill. It also depends on the fact that the skill can be employed given certain endowments. This suggests that increases in skill follow increases in capital accumulation, which is consistent with the observation that different countries tend to have different absolute capital endowments.