Advanced International Trade: Theory and Evidence, Second Edition - Chapter 1
1
Preliminaries:
Two-Sector Models
We begin our study of international trade with the classic Ricardian model, which has two goods and one factor (labor). The Ricardian model intro-
duces us to the idea that technological differences across countries matter. In com-
parison, the Heckscher-Ohlin model dispenses with the notion of technological
differences and instead shows how factor endowments form the basis for trade.
While this may be fine in theory, the model performs very poorly in practice: as
we show in the next chapter, the Heckscher-Ohlin model is hopelessly inadequate
as an explanation for historical or modern trade patterns unless we allow for tech-
nological differences across countries. For this reason, the Ricardian model is as
elevant today as it has always been. Our treatment of it in this chapter is a simple
eview of undergraduate material, but we will present a more sophisticated version
of the Ricardian model (with a continuum of goods) in chapter 3.
After reviewing the Ricardian model, we turn to the two-good, two-factor
model that occupies most of this chapter and forms the basis of the Heckscher-
Ohlin model. We shall suppose that the two goods are traded on international mar-
kets, but do not allow for any movements of factors across borders. This reflects
the fact that the movement of labor and capital across countries is often subject to
controls at the border and is generally much less free than the movement of goods.
Our goal in the next chapter will be to determine the pattern of international trade
etween countries. In this chapter, we simplify things by focusing primarily on one
country, treating world prices as given, and examine the properties of this two-
y-two model. The student who understands all the properties of this model has
already come a long way in his or her study of international trade.
RICARDIAN MODEL
Indexing goods by the subscript i, let ai denote the labor needed per unit of produc-
tion of each good at home, while ai
) is the labor need per unit of production in the
foreign country, ,i 1 2= . The total labor force at home is L and a
oad is L). Labor
is perfectly mobile between the industries in each country, but immobile across
countries. This means that both goods are produced in the home country only if
the wages earned in the two industries are the same. Since the marginal product
of labor in each industry is 1/ai, and workers are paid the value of their marginal
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2 • Chapter 1
products, wages are equalized across industries if and only if / /p pa a1 1 2 2= , where pi is
the price in each industry. Letting /p pp 21= denote the relative price of good 1 (using
good 2 as the numeraire), this condition is /p a a1 2= .
These results are illustrated in figure 1.1(a) and (b), where we graph the production
possibility frontiers (PPFs) for the home and foreign countries. With all labor devoted
to good i at home, it can produce L/ai units, ,i 1 2= , so this establishes the intercepts
of the PPF, and similarly for the foreign country. The slope of the PPF in each country
(ignoring the negative sign) is then a1/a2 and /a a1 2
) ). Under autarky (i.e., no interna-
tional trade), the equili
ium relative prices pa and pa) must equal these slopes in order
to have both goods produced in both countries, as argued above. Thus, the autarky
equili
ium at home and a
oad might occur at points A and A). Suppose that the
home country has a comparative advantage in producing good 1, meaning that a1/a2
/a a1 2
) ). This implies that the home autarky relative price of good 1 is lower than that
a
oad.
Now letting the two countries engage in international trade, what is the equilib-
ium price p at which world demand equals world supply? To answer this, it is helpful
to graph the world relative supply and demand curves, as illustrated in figure 1.2. For
the relative price satisfying /p p a a a 1 2= and /p p a a
a
1 2=
) ) ) both countries are fully
specialized in good 2 (since wages earned in that sector are higher), so the world rela-
tive supply of good 1 is zero. For p p p a a), the home country is fully specialized
in good 1 whereas the foreign country is still specialized in good 2, so that the world
elative supply is ( / )/( / )a L aL 1 2
) ) , as labeled in figure 1.2. Finally, for p p a and p p a),
oth countries are specialized in good 1. So we see that the world relative supply curve
has a “stair-step” shape, which reflects the linearity of the PPFs.
To obtain world relative demand, let us make the simplifying assumption that tastes
are identical and homothetic across the countries. Then demand will be independent
of the distribution of income across the countries. Demand being homothetic means
that relative demand d1/d2 in either country is a downward-sloping function of the
elative price p, as illustrated in figure 1.2. In the case we have shown, relative demand
intersects relative supply at the world price p that lies between pa and pa), but this does
L ∕ a1 y1 L* ∕ a1 y1
(a) Home Country (b) Foreign Country
y2
L ∕ a2
y2
L* ∕ a2
pa*
p
C*
A*
B*
p
pa
C
A
B
*
*
* *
Figure 1.1
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Preliminaries: Two-Sector Models • 3
not need to occur: instead, we can have relative demand intersect one of the flat seg-
ments of relative supply, so that the equili
ium price with trade equals the autarky
price in one country.1
Focusing on the case where p p p a a), we can go back to the PPF of each country
and graph the production and consumption points with free trade. Since p p a, the
home country is fully specialized in good 1 at point B, as illustrated in figure 1.1(a),
and then trades at the relative price p to obtain consumption at point C. Conversely,
since p p a), the foreign country is fully specialized in the production of good 2 at
point B) in figure 1.1(b), and then trades at the relative price p to obtain consumption
at point C). Clearly, both countries are better off under free trade than they were in
autarky: trade has allowed them to obtain a consumption point that is above the PPF.
Notice that the home country exports good 1, which is in keeping with its com-
parative advantage in the production of that good, / /a a a a1 1 22
) ). Thus, trade patterns
are determined by comparative advantage, which is a deep insight from the Ricardian
model. This occurs even if one country has an absolute disadvantage in both goods,
such as a a1 1
) and a a2 2
), so that more labor is needed per unit of production of either
good at home than a
oad. The reason that it is still possible for the home country
to export is that its wages will adjust to reflect its productivities: under free trade, its
wages are lower than those a
oad.2 Thus, while trade patterns in the Ricardian model
are determined by comparative advantage, the level of wages across countries is deter-
mined by absolute advantage.
1 This occurs if one country is very large. Use figures 1.1 and 1.2 to show that if the home country is very
large, then p pa= and the home country does not gain from trade.
2 The home country exports good 1, so wages earned with free trade are /w p a1= . Conversely, the foreign
country exports good 2 (the numeraire), and so wages earned there are / /w a p a1 2 1=
) ) ), where the inequal-
ity follow since /a ap 1 2
) ) in the equili
ium being considered. Then using a a1 1
), we obtain /w p a1= <
p a w1
) ).
(L ∕ a1) ∕ (L* ∕ a2)
Relative Supply
Relative Demand
pa*
p
p
pa
(y1 + y1) ∕ (y2 + y2)* * *
Figure 1.2
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4 • Chapter 1
TWO-GOOD, TWO-FACTOR MODEL
While the Ricardian model focuses on technology, the Heckscher-Ohlin model,
which we study in the next chapter, focuses on factors of production. So we now
assume that there are two factor inputs—labor and capital. Restricting our attention
to a single country, we will suppose that it produces two goods with the production
functions ( , )y f L Ki i i i= , ,i 1 2= , where yi is the output produced using labor Li and
capital Ki. These production functions are assumed to be increasing, concave, and
homogeneous of degree one in the inputs (Li, Ki).
3 The last assumption means that
there are constant returns to scale in the production of each good. This will be a main-
tained assumption for the next several chapters, but we should be point out that it is
ather restrictive. It has long been thought that increasing returns to scale might be an
important reason to have trade between countries: if a firm with increasing returns
is able to sell in a foreign market, this expansion of output will
ing a reduction in
its average costs of production, which is an indication of greater efficiency. Indeed,
this was a principal reason why Canada entered into a free-trade agreement with
the United States in 1989: