Lecture 2: Comparative Advantage
Economics 2530a
Elhanan Helpman
Fall 2016
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Lecture 2: Comparative Advantage
Fall 2016
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Basic Law of Comparative Advantage
In our two-good example, the country exports the good (good 2) whose
relative price went up as a result of trade.
Intuitively, countries gain from trade because they export goods whose prices
are relatively higher in the trade equilibrium and import goods whose prices
are relatively lower.
Is this positive association between net imports and autarky prices robust?
Deardor¤ (1980) and Dixit and Norman (1980) show that it is.
Theorem: Let M k
C k X k denote the vector of net imports of country
k. The following conditions hold in a free-trade equilibrium:
1
2
3
p Ak M k
0 for all k;
p M k = 0 for all k;
∑k M k = 0.
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Proof: Conditions 2 and 3 simply re‡ect trade balance and market clearing.
As for condition 1, gains from trade imply (dropping superscripts k)
p A C A p A C . This is because C is preferred to C A and therefore C
cannot be a¤orded in autarky. Now, from the de…nition of M,
pA M = pA C
pA X
pA C A
pA X = pA X A
pA X
0,
where the last inequality results from the fact that X A maximizes GDP in
autarky.
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Basic Law of Comparative Advantage: Empirics
Bernhofen and Brown (2004) provide an empirical validation of this law,
using historical Japanese data from the second half of the 19th century.
Japan was in autarky for more than 200 years, until 1859, when it opened up
to trade.
Their main identifying assumption is that one can use autarky prices from
1851-53 to proxy the “counterfactual” autarky prices in 1868-75 (after the
Meiji restoration).
1.5
Silkworm Eggs
Net Exports in 1869
1
-100
Silk
Tea
0.5
Charcoal
Sake
Candy
Iron
-80
-60
Copper
0
-40
-20
0
20
Cotton40
60
80
100
120
Legumes
Brown Sugar
-0.5
Cotton Yarn
Rice
-1
-1.5
Change in Price
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Gains from Trade: Empirics
Bernhofen and Brown (2005) compute an upper bound on Japan’s gains from
trade: between 5.4% to 9.1% of GNP (depending on the initial GNP level).
Irwin (2005) uses a related formula to estimate U.S. losses from President
Je¤erson’s trade embargo of 1807-1809: 5% of GNP.
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Basic Law of Comparative Advantage: Further issues
The basic law of comparative advantage is often written as follows
p Ak
p
Mk
0 for all k.
According to this law there is a positive “association” across products
between the autarky-trade price di¤erence and net imports. On average,
every country imports (exports) goods with autarky prices relatively higher
(lower) than trading-equilibrium prices.
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Basic Law of Comparative Advantage: A Useful
Normalization
Alternatively, we can normalize prices to lie on the unit simplex:
∑i pi = ∑i piAk = 1 for all k. This is equivalent to …xing a bundle of one unit
of each good as the numeraire.
With this normalization, ∑i piAk pi = 0 and p Ak
that
0.
corr p Ak p, M k
p
Mk
0 imply
In the case of two countries, we can obtain a sharper result (only need
autarky prices):
0.
corr p Ak p A ( k ) , M k
And with 2 commodities and our choice of numeraire,
A( k )
Mik > 0 () piAk > pi
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Lecture 2: Comparative Advantage
for i = 1, 2.
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2 countries and 2 goods
In the case of 2 countries and 2 goods we can represent the net import
vectors as follows:
M 2H = − M 2F
M 1H = − M 1F
p FA
p HA
The vector M H =
()
M F has to be in the shaded cone.
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What Determines Autarky Prices?
Our treatment of the basic law of comparative advantage highlighted the role
of di¤erences in autarky prices in the determination of trade patterns and
trade volumes.
with p Ak = p A for all k, we have no trade
Following general equilibrium theory, we can identify three fundamental
sources of autarky price di¤erences across countries:
1
2
3
Di¤erences in tastes
Di¤erences in technologies
Di¤erences in endowments
Caveat: since most trade seems to ‡ow between similar countries, it may
seem that emphasizing cross-country di¤erences is not useful.
Still, neoclassical trade theories provide valuable insights into the structure of
trade ‡ows and are an essential benchmark for more realistic models.
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Taste Di¤erences
Preferences may shape comparative advantage if (i) preferences themselves
di¤er across countries, or (ii) preferences are identical worldwide but
non-homothetic.
An example of (i) is illustrated below. Both countries share the same
endowments and technologies, but country H shows a relative preference for
good 1, and consequently p1A /p2A is higher there.
good 2
XF
X
XH
good 1
As illustrated in the …gure, in a trading equilibrium country H will import
good 1 and export good 2.
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Taste Di¤erences (continued)
Now consider an example with non-homothetic preferences. Preferences are
such that the income elasticity is larger than one for good 1. Because H is
richer in terms of income per capita, its demand pattern is tilted towards
good 1 and again p1A /p2A is higher there.
good 2
Homothetic
XH
XH
Non-Homothetic
XF
good 1
As before, in a trading equilibrium country H imports good 1 and exports
good 2.
The …gure corresponds to preferences of the Stone-Geary type:
U = α log c1 + β log (c2
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Lecture 2: Comparative Advantage
b)
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Taste Di¤erences (continued)
The literature has largely downplayed the role of preferences in shaping
comparative advantage, because one can generate any trade pattern with
arbitrary di¤erences in preferences.
Still, there exist interesting contributions highlighting the role of
non-homotheticities in shaping trade ‡ows, e.g., Linder (1961), Flam and
Helpman (1987), Hunter (1991), Matsuyama (2000), Fieler (2011). Hunter
(1991) suggests that they can explain 20% of trade ‡ows.
More recently Fajgelbaum, Grossman and Helpman (2011) use a discrete
choice model together with vertical and horizontal product di¤erentiation to
highlight the role of income distribution di¤erences across countries as an
impetus for trade.
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Technological Di¤erences: Ricardo’s Insight
Consider a world with 2 countries (H and F ), two goods and one factor of
production, labor.
Technology is summarized by four unit input requirements: aik for k = H, F ,
i = 1, 2.
Result:
aH
aF
Country H exporters good 1 if 1H < 1F .
a2
a2
Proof.
Assume prices lie on the unit simplex. Because labor is the only factor,
piAk =
aik
∑` a`k
.
Now note that p1AH < p1AF () a1H /a2H < a1F /a2F . But from our previous results,
this implies M1H < 0.
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