The HeckscherOhlin theorem states that a country which is capitalabundant will export the
capitalintensive good. Likewise, the country which is laborabundant will export the laborintensive good. Each country exports that good which it produces relatively better than the other
country. In this model a country's advantage in production arises solely from its relative factor
abundance.
The HeckscherOhlin Theorem  Graphical Depiction  Variable Proportions
The HO model assumes that the two countries (US and France) have identical technologies,
meaning they have the same production functions available to produce steel and clothing. The
model also assumes that the aggregate preferences are the same across countries. The only
difference that exists between the two countries in the model is a difference in resource
endowments. We assume that the US has relatively more capital per worker in the aggregate than
does France. This means that the US is capitalabundant compared to France. Similarly, France,
by implication, has more workers per unit of capital in the aggregate and thus is laborabundant
compared to the US. We also assume that steel production is capitalintensive and clothing
production is laborintensive.
The difference
in resource endowments is sufficient to generate different PPFs in the
two countries such that equilibrium price ratios would differ in autarky.
To see why, imagine first that the two countries are identical in every
respect. This means they would have the same PPF (depicted as the brown
PPF_{0} in the adjoining figure), the same set of aggregate indifference
curves and the same autarky equilibrium. Given the assumption about aggregate
preferences, that is U = C_{C}C_{S}, the indifference
curve, I, will intersect the countrys' PPFs at point A,
where the absolute value of the slope of the tangent line (not drawn),
(P_{C}/P_{S}), is equal to the slope of the ray from the
origin through point A.
The slope is given by C_{S}^{A}/C_{C}^{A}.
In other words, the autarky price ratio in each country will be given
by,
Next suppose that labor and capital are shifted between the two countries.
Suppose labor is moved from the US to France while capital is moved from
France to the US. This will have two effects. First, the US will now have
more capital and less labor, France will have more labor and less capital
than initially. This implies that K/L>
K*/L*, or that the US is
capitalabundant and France is laborabundant. Secondly, the two countries
PPFs will shift. To show how, we apply the Rybczynski theorem.
The US experiences an increase in K and a decrease in L. Both changes
will cause an increase in output of the good that uses capital intensively
(i.e. steel) and a decrease in output of the other good (clothing). The
Rybczynski theorem is derived assuming that output prices remain constant.
Thus if prices did remain constant, production would shift from point
A to B
in the diagram and the US PPF would shift from the brown PPF_{0}
to the green PPF.
Using the new PPF we can deduce what the US production point and price
ratio would be in autarky given the increase in the capital stock and
decline in labor stock. Consumption could not occur at point B
since, 1) the slope of the PPF at B
is the same as the slope at A
since the Rybczynski theorem was used to identify it, and 2) homothetic
preferences implies that the indifference curve passing through A
must have a steeper slope since it lies along a steeper ray from the origin.
Thus, to find the autarky production point we simply find the indifference
curve which is tangent to the US PPF. This occurs at point C
on the new US PPF along the original indifference curve, I.
(Note: the PPF was conveniently shifted so that the same indifference
curve could be used. Such an outcome is not necessary but does make the
graph less cluttered.) The negative of the slope of the PPF at C
is given by the ratio of quantities C_{S'}/C_{C'}_{
. } Since C_{S}'/C_{C}'
> C_{S}^{A}/C_{C}^{A},
it follows that the new US price ratio will exceed the one prevailing
before the capital and labor shift, i.e., P_{C}/P_{S}
> (P_{C}/P_{S)}^{0}.
In other words, the autarky price of clothing is higher in the US after
it experiences the inflow of capital and outflow of labor.
France experiences an increase in L and a decrease in K. These changes
will cause an increase in output of the laborintensive good (i.e. clothing)
and a decrease in output of the capitalintensive good (steel). If price
were to remain constant, production would shift from point A
to D in the diagram and
the French PPF would shift from the brown PPF_{0}
to the red PPF^{*}.
Using the new PPF we can deduce the French production point and price
ratio in autarky, given the increase in the capital stock and decline
in labor stock. Consumption could not occur at point D
since homothetic preferences implies that the indifference curve passing
through D must have a flatter
slope since it lies along a flatter ray from the origin. Thus to find
the autarky production point we simply find the indifference curve which
is tangent to the French PPF. This occurs at point E
on the new French PPF along the original indifference curve, I.
(As before, the PPF was conveniently shifted so that the same indifference
curve could be used.) The negative of the slope of the PPF at
C
is given by the ratio of quantities C_{S}"/C_{C}",
Since C_{S'}/C_{C}"
< C_{S}^{A}/C_{C}^{A},
it follows that the new French price ratio will be less than the one prevailing
before the capital and labor shift, i.e., P_{C}*/P_{S}*
< (P_{C}/P_{S)}^{0}.
This means that the autarky price of clothing is lower in France after
it experiences the inflow of labor and outflow of capital.
All of the above implies that as one country becomes laborabundant and the other capitalabundant, it causes a deviation in their autarky price ratios. The country with relatively more
labor (France) is able to supply relatively more of the laborintensive good (clothing) which in
turn reduces the price of clothing in autarky relative to the price of steel. The US with relatively
more capital can now produce more of the capitalintensive good (steel) which lowers its price in
autarky relative to clothing. These two effects together imply that
Any difference in autarky prices between the US and France is sufficient to
induce profitseeking firms to trade. The higher price of clothing in
the US (in terms of steel) will induce firms in France to export clothing
to the US to take advantage of the higher price. The higher price of steel
in France (in terms of clothing) will induce US steel firms to export
steel to France. Thus, the US, abundant in capital relative to France,
exports steel, the capitalintensive good. France, abundant in labor relative
to the US, exports clothing, the laborintensive good. This
is the HeckscherOhlin theorem. Each country exports the good intensive
in the country's abundant factor.
International Trade Theory and Policy Lecture
Notes:
©19972006 Steven M. Suranovic Last Updated on 7/31/06
