A Partial Walk through the Lectures on Heckscher-Ohlin Theory
1. The Setting: This theory allows us to accomplish two objectives: (1) explain the
patterns of trade based in factor endowments and (2) analyze the implications of trade for
income distribution. Recall the Ricardian theory allows for only one factor, labor, which
rules out any income distribution effects of trade within a country.
There are two factors, labor and land, and two goods, C and W, and two countries,
HC and FC. Goods are distinguished according to factor intensity and countries
according to factor abundance. Initially, we assume a fixed-coefficients technology
meaning that labor and land cannot be substituted for each other. Substitution is
introduced later. Table 1 summarizes the basic information for HC.
Table 2.1
Factor of Production
Labor
Land
Factor use per-unit of
C
W
aLC (4)
aLW (2)
aTC (1)
aTW (2)
Total Endowment
L (100)
T (60)
We say that C is labor intensive relative to W if aLC/aTC > aLW/aTW. In words, C is
called labor intensive if it uses more labor per unit of land than does W. Given the
specific numbers shown in Table 1, aLC/aTC = 4/1 = 4 and aLW/aTW = 2/2 = 1 so that C is
labor intensive. You can readily verify that this means W is land intensive.
We also define FC to be labor abundant relative to HC if L*/T* > L/T. We will
assume FC has 120 units of labor and 60 units of land, making it labor abundant (120/60
> 100/60). HC is then automatically land abundant. The theory assumes that HC and
FC have access to the same technology.
2. The Production Possibilities Frontier in HC: Suppose for a moment that we have as
much land as we want and that labor is the only constraining factor of production. Then,
we can produce a maximum of L/aLC of C or L/aLW of W or a combination of C and W on
the (steeper) line joining these two points in Figure 1. Algebraically, this line is given by
(1)
aLC QC + aLW QW = L or 4QC + 2QW = 100
Next, suppose we have as much labor as we want and land is the only
constraining factor. Then we can produce a maximum of T/aTC of C or T/aTW of W or a
combination of C and W on the (flatter) line joining these two points in Figure 1.
Algebraically, the line is given by
(2)
aTC QC + aTW QW = T or QC + 2QW = 60
Observe that the labor constraint is steeper than the land constraint because C is labor
intensive and QC is measured along the horizontal axis.
Q
W
50
L
30 T
Q
L'
25
T'
60
Q
C
Figure 1: PPF of HC (Solid Line). Full employment at Q, Only
Given we need both factor of production, the only feasible outputs are along the
solid lines, TQL’. Along TQ (excluding point Q) labor is unemployed, while along QL
(excluding Q) land is unemployed. This is due to the assumed lack of substitutability in
production. If substitution between labor and land were allowed (as is true in reality), we
could get some extra output out of the unemployed factor by changing the ratio in which
labor and land must be combined. In that case, except at Q, the PPF will lie everywhere
outside TQL and we will have full employment everywhere. Seen this way, Q is not
unique but instead represents the more general case of full employment along the PPF.
Hence we will focus on Q in our analysis below.
3. The PPF in FC and the Rybczynski Theorem: FC is assumed to have the same
technology and the same amount of land as HC. Therefore, its land constraint is the same
as of HC. But FC has more labor. Therefore, its labor constraint lies outside that of HC
but is parallel to the latter. Q* gives the full employment point.
Comparing Q and Q*, we observe something surprising. FC has more labor but
the same amount of land as HC. Intuitively, we might have thought that the extra labor
will be used partially in the production of C and partially in the production of W. But
that is not how it works out. Instead, FC produces much more of C and absolutely less of
W. We want to state this dramatic outcome as
Rybczynski Theorem: Holding other things fixed, an increase in the supply of a factor
leads to a proportionately larger increase in the output of the good using the factor more
intensively and an absolute decline in the output of the other factor.
Q
W
60 L*
50
L
30 T
Q
Q*
L' L*'
25 30
T'
60
Q
C
Figure 2: PPF of HC and FC: FC has more labor. At the full-employment point,
it produces more of C and less of W than HC
[Convince yourselves that given the coefficients in Table 1, the only way to achieve full
employment of both resources in FC is for FC to produce more of C and less of W than
HC.]
4. Allowing Substitution between Labor and Land: The kinked PPFs in Figures 1 and 2
result from the assumed lack of substitutability between labor and land. The PPFs will be
smooth if substitution is permitted. But even then, at a given price, FC produces more of
C and less of W than HC. This is shown in Figure 3.
*
QW, QW
L*
L
Q
Q*
T
T*
*
QC, QC
Figure 3: PPFs are Smooth when Substitution
is allowed between labor and land
5. Relative Supplies and Demand: The Heckscher-Ohlin Theorem: From Figure 3, you
can see that the relative supply of HC is upward sloped. As the price of C rises (i.e., the
price line becomes stepper), the ratio of QC to Q W rises. You can also see that at a given
price, this ratio is higher for FC than HC (recall the Rybczynski theorem). Now suppose
that HC and FC have similar preferences in the sense that for a given price, they demand
the two goods in the same ratio. Therefore, from Figure 4 you can infer that under
autarky, C is cheaper in the labor abundant FC and W in land abundant HC. Therefore,
when trade opens, labor abundant FC exports labor intensive good C and land abundant
HC exports the land-intensive good W. We write this important result as:
Heckscher-Ohlin Theorem: Each country exports the good that uses its abundant
factor more intensively and imports the good that uses its scarce factor more
intensively.
PC/PW
RS
RS*
RD
QC/QW
Figure 4: Under autarky, C is cheaper in FC than HC
6. Factor Prices: Consider HC, which imports the labor-intensive good. Trade leads to a
decline in the relative price of C. This causes the output of C to shrink and that of W to
expand along the PPF. Since C is labor intensive, at the original factor prices, it releases
more labor per unit of land than the ratio in which W absorbs these factors. At the
original factor prices, we have excess supply of labor and excess demand for land. This
pushes the wage down and the return on land up. Denoting the wage by w and the return
on land by r, w/r declines. What is more surprising, however, is that the wage declines
proportionately more than the decline in the price of C. Thus, the wage declines not only
in terms of W but also in terms of C. On the other hand, r rises in terms of both C and W.
Workers are unambiguously worse off (regardless of whether they spend most of their
income on C or W) and landowners are unambiguously better off. This is
Stolper-Samuelson Theorem: A decrease in the price of a good makes the factor
used more intensively in that good unambiguously worse off and the factor used
more intensively in the good whose relative price rises unambiguously better off.
To explain why w falls in terms of both goods, note that the decline in w/r leads to
a rise in the labor-to-land ratio in both C and W. This means the marginal physical
product of labor (MPL) falls in terms of both C and W. But remember that in
equilibrium,
w = PC.MPLC = PW.MPLW or w/PC = MPLC and w/PW = MPLW
Therefore, a decline in both marginal physical products implies a decline in both w/PC
and w/PW. Likewise, since the marginal physical product of land rises in both goods, the
return to land rises in terms of both goods.
7. Factor-Price Equalization: Given identical technologies in HC and FC, trade leads to
the equalization of factor prices internationally. Recall that under autarky, C is more
expensive in HC. Since C is labor intensive, this makes the wage in HC higher than in
FC while the return to land lower. When trade opens, according to the StolperSamuelson theorem, w falls and r rise in HC while the opposite happens in FC. As trade
equalizes the goods prices, it also equalizes the factor prices between the two countries.
8. Trade and Wages: During 1980s, skilled wage rose and unskilled wages fell in the
United States, with the ratio of skilled-to-unskilled wages rising by almost 30 percent.
Labeling the two factors in the Heckscher-Ohlin theory as being skilled and unskilled
labor and by appeal to the Stolper-Samuelson theorem, many analysts argue that this
increase in wage inequality is the result of increased trade with the developing countries
that export unskilled-labor-intensive goods. Trade economists disagree with this claim
arguing that this trade cannot explain the bulk of the increase in the wage inequality.
They cite four reasons (read the details in the textbook, pp. 79-81) for this: (i) the relative
price of unskilled-labor-intensive goods rose during the relevant period; (ii) imports from
developing countries account for less than 2 percent of the total expenditure in the United
States; (iii) wage inequality rose in the developing countries as well; and (iv) technical
change which shifted labor demand in favor of skilled labor and away from unskilled
labor provides a better explanation.