Topics:
A Model of a Two-Factor Economy
Effects of International Trade between Two-factor Economies
Empirical Evidence on the Heckscher-Ohlin Model
 International trade reflects not only differences in labor productivity, but also differences in national resources.
 A more realistic view of trade must encompass other factors of production, as in Chapter 3.
 The model in this chapter considers that resource differences are the only impetus towards trade. Different factors have different relative abundance, and different nations have different technologies, reflected in the intensity with which they utilize these factors. This model is also called the factor-proportions theory.
1.
A Model of a Two-factor Economy a) Assumptions of the Model
Unlike in Chapter 3, here we no longer assume that any factor is specific to an industry. Instead, every industry uses all of the factors to some degree, and these factors are present to some degree in every country.
There are two goods, cloth (C) and food (F). Production of either good requires both land and labor.
Define:
α
TC
= acres of land used to produce one yard of cloth
α
LC
= acres of labor used to produce one yard of cloth
α
TF
= hours of labor used to produce one calorie of food
α
TF
= acres of land used to produce one calorie of food
L = the economy’s supply of labor
T = the economy’s supply of land
No specific amount of either factor is required to produce a good (no fixed input requirements); instead, the intensity with which a factor is utilized is a choice variable. Alternative combinations are shown in Figure 4-1.
If w is the wage paid to labor and r is the rent paid to land, then this input choice is sensitive to the factor-price ratio , w / r .
Figure 4-2 shows the relationship between the ratio of factor prices and the ratio of land to labor use in production is shown in Figure 4-2: The FF curve pertains to food production, and the CC curve pertains to cloth production. Note that since
CC lies to the left of FF for every value of w / r , the land-labor use ratio is always

(for any given factor-price ratio) higher for food production. Thus, the production of food is relatively land-intensive and the production of cloth is relatively laborintensive . b) Factor Prices and Goods Prices
If we assume that cloth and food are both produced, (perfect) competition among producers should reduce the price of the good produced to the cost of production.
It should be clear that a factor’s price will be reflected in the price of a good to the extent that the factor is actually used in producing that good. So a change in the relative price ratio will be reflected in the wage-rental ratio, and vice versa . This is shown in Figure 4-3.
Putting these two Figures together with one of the tricks of this trade, we have
Figure 4. Here the left half of Figure 4 is Figure 3 rotated 90 degrees counterclockwise. What is interesting about this diagram is: 1) When the relative price of cloth increases, the land/labor ratio used in production increases for both food and cloth production, and 2) An increase in the wage-rental ratio unambiguously makes workers better off and landowners worse off.
This is true because the MPL for labor for production of a good goes up when relatively less labor is used in production of that good (recall the diminishing marginal productivity). Since this is true for both goods, the real wage is higher in terms of both goods. Equivalently, the real rental rate for land is lower in terms of both goods.
So in this model, we get very strong distributional consequences as a result of a change in relative prices. There is no group for which the change has ambiguous effects, unlike with the specific factors model, where there are three factors and three groups. c) Resources and Output
We can determine the complete allocation of resources given any relative price of cloth, since we assume that all resources are used (the marginal productivity is always positive).
We use an “Edgeworth box” type of approach to show this works. In Figure 4-5, the length represents the total amount of labor available and the height represents the total amount of land available. O
C
is the cloth origin and O
F
is the food origin.
Since all of each is used, any point inside the box is a division of land and labor between cloth production and food production.
Since we have the relative prices, we know the land/labor ratio in both cloth production and food production. These land-labor ratios effectively give trade-offs from the respective origins, and these trade-offs are embodied in the slopes of lines drawn from these origins. The intersection (unique if these lines are not collinear, and this is ruled out by the assumption (Figure 4-2) that different factors ratios prevail) is the resulting resource allocation.

Suppose we start at point 1 in Figure 5. What happens when the supply of one of the resources, say land, changes? This is shown in Figure 4-6. Since land is represented on the vertical axis, an increased supply of land (polders?) means there is added height to the box, and the O
F
origin moves up to the new corner. The slopes from the origins do not change here, so the new intersection is point 2.
Since there is less land being used for cloth production and also less labor used for cloth production, there is less cloth being produced. An increase in the supply of land leads to a fall in the output of the labor-intensive good (holding prices constant). The land and labor shifted away from cloth production must necessarily have shifted into food production, where the output must have risen more than proportionately to the fall of output for cloth (we have added to the supply of one factor and kept the other constant, so output must increase).
Check it out on the PPF (Figure 7). Those slopes are theoretically the same, although it looks like they fudged a little to make their point. Food production is way up and cloth production is slightly down. The manner in which the PPF shifts out in this case is not symmetric, and this is called biased expansion of production possibilities . This biased effect of resource changes on production is known as the
Rybczynski effect .
An increase in the supply of a factor expands possibilities most for the good where the factor is used more intensively. It follows that an economy will tend to be relatively best at producing the good that is intensive in the factor (or factors when there are more factors) that are relatively abundant. This leads immediately to an insight with respect to the effect of international trade.
2.
Effects of International Trade Between Two-factor Economies
We assume two countries, Home and Foreign. Home is labor-abundant and Foreign is land-abundant; these are relative terms, not absolute, think of ratios. Same relative demands, same prices for each good, same technology, same relative demand, only different relative resource abundance. a) Relative Prices and the Pattern of Trade
At any given price ratio, Home will produce relatively more cloth than Foreign;
Figure 4-8 shows this in terms of relative supply. In the absence of trade, Home would be at point 1 and Foreign would be at point 3; different relative prices and different relative quantities.
But with trade, prices converge (recall that we assume that the price of cloth and food is the same in both countries). In Home, the rise in the relative price of cloth means that more cloth will be produced; in Foreign, the decrease in the relative price of cloth

means it will produce less cloth. Parallel reasoning applies in the case of food. Thus, each country ends up trading their excess with the other country, at relative prices in between the original one – somewhere like point 2. b) Trade and the Distribution of Income
Changes in relative prices have strong and opposed effects on laborers and landowners. Where the relative price of cloth rises, workers (landowners) are better off (worse off) in real terms.
When your country engages in trade, it follows that you are better off being in the business of producing the good that uses more of the factor more abundant in your country.
This doesn’t get fixed over time. The relative prices change and the income distribution effects fall where they do. So in the U.S., if we assume that we have high-skilled workers in abundance and low-skilled workers are relatively scare, the low-skilled (poor) workers in the U.S. tend to suffer in the U.S. when trade is liberalized. This leads to conflict.
If you’re a high-skilled worker, you should benefit. But if you work in an industry that is intensive in low-skilled labor, you might have to find another job. c) Factor Price Equalization
Without trade, the difference in the relative prices of goods implies a larger difference in relative factor prices. When the prices of goods converge, factor prices also converge. What may seem surprising is that they must converge completely.
Recall from Figure 3 that the relative prices of goods completely determines the wage-rental ratio. Since Home and Foreign have the same relative good prices, they must therefore have the same relative factor prices.
You can think of exports as somehow embodying the abundant resource being shipped abroad.
But guess what? International wage rates differ across countries, by a lot. Factor prices are not equalized in the real world. While they may be quality differences, this can only account for portion of the divergence.
There are at least two major reasons:
1.
Countries may have different technologies, so that both the wage rate and the rental rate could be higher in one country than another. This comes into play with the North-South example.
2.
Factor price equalization requires goods price convergence, and we really don’t get this. There are barriers to trade, such as transportation costs, tariffs, and quotas.

Case study: There was (and still is) growing income inequality between the late 70s and the early 90s. This isn’t ideal in a society. Why? Some people blame increased trade with NIEs such as South Korea and China. The low-skilled workers would suffer, as described above. In fact, the volume of exports form NIEs did increase tremendously in this span of time.
However, we’re still talking about small numbers. Factor content of trade between advance countries and NIEs is not a big portion of the total supplies of skilled and unskilled labor.
There was also no change in the distribution of income between capital and labor.
We also don’t see evidence of the change in relative prices of goods that is predicted by the model.
Finally, while income divergence should indeed be happening in countries such as the
U.S., the reverse should be true in the NIEs (the lot of low-skilled workers should improve relatively). But it isn’t. It’s the rich getting richer everywhere.
Mainly economists blame differences in technology for the growing gap between skilled and unskilled workers in the U.S. What do you think?
3.
Empirical Evidence on the Heckscher-Ohlin Model a) FPE: We don’t see FPE in the real world
. Why?
1.
The theory says get FPE only if countries are sufficiently similar in their factor endowments. If they aren’t similar, then one might specialize in production of single good.
2.
Factor Price Equalization (FPE) theorem won't hold if countries have different technologies -- we'll come back to this.
3.
FPE theorem requires that countries actually face same prices -- but very few countries actually have free trade. (Also transport costs).
What about policy questions? In particular, consider the income/wage gap .
Between late 1970s and early 1990s, income gap between America's richest and poorest grew. During the period from 1970-1989, the real wage of males at the 90 percentile rose 15 percent, while the real wage of males at the 10 th th
percentile fell 25%
Many people blame trade with NIEs (Newly Industrialized Economies) like South
Korea, Taiwan, China, and Hong Kong. People have also argued should restrict trade to protect the poorest workers.
One natural question is thus: Is trade the source of the US wage gap?

1.
If the wage gap derives from the rich owning more capital and the relative price of capital intensive goods rising because of trade, then should see more a higher proportion of income going to capital. But you don’t: share of wages in US income was same in 1993 as in 1973.
2.
In HO setting, trade can only explain divergence of payments to skilled and unskilled labor if prices of skilled-labor-intensive and unskilled-laborintensive goods also diverge. They didn't.
3.
HO model suggests that trade should bring convergence of wages. So if trade between US and trade partners is driven by US having relative abundance of skilled labor, or capital, if trade brings divergence between wages of skilled and unskilled workers, should see wage convergence in its trade partners
(NIEs) at same time as see divergence in USA. But we didn't: the NIEs also had a widening gap also.
Remaining explanations? Improvements in technology that benefit skilled workers more than unskilled workers -- how much more productive do faster computers make ditch-diggers?
Conclusion: Trade may not be the source of growing wage inequality in USA. b) Evidence For/Against the Factor Proportions Model
Leontief Paradox: Since the U.S. has been relatively capital-rich, we should see that the U.S. exports capital-intensive goods and imports labor-intensive goods.
But this didn’t happen during the 25 years after WWII, and is major evidence against the HO model (see Table 4-3). Possible explanation is that the U.S. advantage is actually w.r.t. innovative technologies and entrepreneurial capital.
Autos (which we import) are heavily capital-intensive, but not in this same sense.
Tests of Global Data: If we were to calculate the factors of production embodied in exports and imports, countries should be exporting factors that are abundant and importing factors that are scarce. But a test by Bowen, Leamer, Sveikauskas
(1987) for 27 countries, with 12 factors of production (324 comparisons), finds that the HO model predicted very poorly:
Volume of Trade: The HO model predicts there should be much more trade than there actually is. One explanation is that the effectiveness (and thus implicit endowments) of factors may differ from country to country.
Daniel Trefler (1995) found that factors, in particular workers, are vastly less productive in some countries that in the US. This can explain the “missing trade”
-- different levels of factor efficiency mean that differences across countries in factor abundance are overstated. This can also explain lack of wage convergence.

Comparison of relative labor productivities to relative wages. (Table not in text)
Labor Productivity othercountry
Labor Productivity
US w othercountry w
US
Switzerland
W. Germany
Japan
UK
Hong Kong
1.04
.86
.66
.66
.42
.94
.72
.71
.70
.26
Thailand
Bangladesh
.05
.02
.14
.05
Conclusions:
 HO model predicts pattern and volume of trade poorly.
 Does a good job of revealing impacts of trade on factor returns and industrial mix in long run.