International Trade:
Comparative Advantage
Prof. Christopher Balding
February 20, 2014
Absolute Advantage
Absolute Advantage cont.
Can We Trade under Absolute
Absolute Advantage Trade in
What Happens to Total
The Purpose of DFS
“The distinguishing feature of the Ricardian
approach emphasized in this paper is the
determination of the competitive margin in
production between imported and exported goods.
The analysis advances the existing literature by
formally showing precisely how tariffs and
transport costs establish a range of commodities
that are not traded, and how the price-specie flow
mechanism does or does not give rise to
movements in relative cost and price levels.”
Equation (1)
A(z) = a*(z)/a(z)
A '(z) < 0
Equations (2’) and (4)
The home country will efficiently produce all those
commodities for which domestic unit labor costs
are less than or equal to foreign unit labor costs.
Accordingly, any commodity z will be produced at
home i
(2') ω< A (z)
It follows that for a given relative wage ω the home
country will efficiently produce the range of
(4) 0 < z < z(ω)
Summarizing Section 1
In summarizing the supply part of the model
we note that any specified relative real wage
is associated with an efficient geographic
specialization pattern characterized by the
borderline commodity z(w) as well as by a
relative price structure. (The pattern is
"efficient" in the sense that the world is out
on, and not inside, its production-possibility
Equation 8
We therefore prescribe for the continuum
case a given b(z) profile:
• (8) b(z) = P(z)C(z)/Y > 0
b(z) = b*(z)
∫b(z) dz = 1
Equation 9
Next we define the fraction of income spent
(anywhere) on those goods in which the
home country has a comparative advantage:
(9) ν(z) = ∫b(z)dbz > 0
ν’(z)= b(z) > 0
where again (0, 2) denotes the range of
commodities for which the home country
enjoys a comparative advantage.
The Demand Side
To interpret the B( ) schedule we note that it is
entirely a representation of the demand side; and
in that respect it shows that if the range of
domestically produced goods were increased at
constant relative wages, demand for domestic
labor (goods) would increase as the dividing line is
shifted -at the same time that demand for foreign
labor (goods) would decline.' A rise in the
domestic relative wage would then be required to
equate the demand for domestic labor to the
existing supply.
We assume (i) constant expenditure share
(ii) identical tastes for the two countries.
We specify a fraction
of income spent on the
commodities in the range
i.e. the commodities in
which home has a comparative advantage.
Similarly the fraction of income spent on foreign produced is:
Equilibrium Relative Wages and
• Equilibrium requires that:
• Domestic labour income = World
spending on domestic commodities
• So the eqm wage is:
Commodities produced by home
Commodities produced
by foreign
•The B( ) Schedule is a locus of trade
balance equilibria i.e.
Value of imports = Value of
Equilibrium Relative Wages and
Commodities produced by home
Commodities produced
by foreign
The B schedule is upward sloping as any trade
imbalance at constant relative wages will be met
by a change a in the relative wage to restore
If the home capacity to produce the range of
commodities increases at given relative wages
will lower our imports and increase our exports.
The resulting imbalance is corrected by an
increase in the relative wage which will increase
our import demand for goods and reduce our
exports and thus restore balance.
Equation 11
Substituting (5) in (10') yields as a solution
the unique relative wage 5, at which the
world is efficiently specialized, is in
balanced trade, and is at full employment
with all markets clearing:
(11) z = A(z) = B(-;L*/L)
The equilibrium relative wage defined in (11)
is represented in Figure 1 at the intersection
of the A( ) and B( ) schedules.2
Summarizing Section II
Among the characteristics of the equilibrium we
note that the equilibrium relative wages and
specialization pattern are determined by
technology, tastes, and relative size (as measured
by the relative labor force)…. We note that with
identical homothetic tastes across countries and no
distortions, the relative wage Z- is a measure of the
wellbeing of the representative person-laborer at
home relative to the well-being of the
representative foreign laborer.
Size Matters
Consider first the effect of an increase in the
relative size of the rest of the world. An increase in
L*/L by (10) shifts the B( ) trade balance
equilibrium schedule upward in proportion to the
change in relative size and must, therefore, raise
the equilibrium relative wage at home and reduce
the range of commodities produced domestically.
It is apparent from Figure 2 that the domestic
relative wage increases proportionally less than the
decline in domestic relative size.
Income Share and Wages
We observe, too, that from the definition of the
home country's share in world income and (10), we
(12) wL/(wL + w*L*) =ν(z)
It is apparent, as noted above, that a reduction in
domestic relative size in raising the domestic
relative wage (thereby reducing the range of
commodities produced domestically) must under
our Cobb-Douglas demand assumptions lower the
home country's share in total world income and
spendingeven though our per capita income rises.
Technological Progress
An alternative form of technical progress that can be
studied is the international transfer of the least cost
technology. Such transfers reduce the discrepancies in
relative unit labor requirements-by lowering them for each
z in the relatively less efficient country-and therefore flatten
the A (z) schedule in Figure 1. It can be shown that such
harmonization of technology must benefit the innovating
low-wage country, and that it may reduce real income in
the high-wage country whose technology comes to be
adopted. In fact, the high-wage country must lose if
harmonization is complete so that relative unit labor
requirements now become identical across countries and all
our consumer's surplus from international trade vanishes.
Not Everything is Tradable
To introduce nontraded goods into the analysis we
assume that a fraction k of income is everywhere
spent on internationally traded goods, and a
fraction (1 - k) is spent in each country on
nontraded commodities. With b(z) continuing to
denote expenditure densities for traded goods, we
have accordingly
(14) k = ∫ b (z) dz < 1
where z denotes traded goods. As before the
fraction of income spent on domestically
exportable commodities is O(z), except that t now
reaches a maximum value of (1)= k.
Wages and Non-Tradables
The equilibrium relative wage again
depends on conditions. In this case demand
conditions explicitly include the fraction of
income spent on traded goods:
(11’) ω = ν(z)/[k – ν(z)] L*/L = A(z)
This nicely generalizes our previous
equilibrium of (11) to handle exogenously
given nontraded goods
The home country will produce
commodities for which domestic unit labor
cost falls short of foreign unit labor costs
adjusted for shrinkage, and we modify (2')
• (17) wa(z) < (1/g)w*a*(z)
or w < A(z)/g
Who Produces What?
In Figure 3 we show the adjusted relative unit
labor requirement schedules A (z)/g and A (z)g. It
is apparent from (17) and (18) that for any given
relative wage the home country produces and
exports commodities to the left of the A (z)g
schedule, both countries produce as nontraded
goods commodities in the intermediate range, and
the foreign country produces and exports
commodities in the range to the right of A (z)/g.
Wages, Traders, and Tariffs
(26) ω = ω (L*/L, t, t*)
From (26) and (23) it is apparent now that the
range of nontraded goods will be a function of
both tariff rates. It is readily shown that an
increase in the tariff improves the imposing
country's relative wage and terms of trade.
Furthermore, as is well known, when all countries
but one are free traders, then one country can
always improve its own welfare by imposing a tariff
that is not too large.
Money, Exchange Rates, and Trade
We return to the assumption that a fraction (1 - k)
of spending in each country falls on nontraded
goods, and accordingly equations (32)- and (33)
(32') WL = ν(ω) VG + (1 - k) γVG
(33') eW*L* = [k – ν(ω)]VG + (1 - γ)(1 - k)VG
These hold both in final equilibrium, and in
transient equilibrium where specie is flowing.
Equations (32') and (33') imply that the
equilibrium relative wage does depend on the
distribution of the world money supply.
Solving for Money…
Solving these equations for the equilibrium
relative wage we have:
(35) ω = ω(γ) ∂ω/∂γ > 0
An increase in the home country's initial
share in the world money supply γ raises our
relative wage.
Accounting for Money
We note, however, that now W and W* are
endogenous variables whose levels in the short run
do depend on the distribution of the world money
supply. A redistribution of money toward the home
country would raise our spending and demand for
goods, and reduce foreign spending and demand.
As before, spending changes for traded goods
offset each other precisely so that the net effect is
an increase in demand for nontraded goods at
home and a decline abroad. As a consequence our
wages will rise and foreign wages decline.
Therefore, starting from full equilibrium, a
redistributi on of money toward the home
country will create a deficit equal to:
(36) dM/dM= -V(1 - δ) 0 <δ <1
where δ is the elasticity of our nominal
wages with respect to the quantity of money
and is less than unity. Equation (36) implies
that the price-specie flow mechanism is
It is interesting to observe in this context that the
presence of nontraded goods in fact slows down
the adjustment process by comparison with a
world of only traded goods (contrary to J. Laurence
Laughlin's turn. Of the century worries). As we
saw before, with all goods freely tradeable, wages
are independent of the distribution of money, and
accordingly 6 = 0. Further we observe that the
speed of adjustment depends on the relative size of
countries. Thus the more equal countries are in
terms of size, the slower tends to be the adjustment
Turning to Bernhofen
Why The Case of Japan?
Comparative Advantage, Trade, and Payments… by
Dornbusch, Fischer, and Samuelson is the
advanced theoretical version of comparative
A Direct Test…The Case of Japan is the empirical
test of whether or not the theory is actually valid
The two papers are complementary
What is the Framework Here?
A natural experiment for a country when there is
not free trade and when there is free trade
Since most countries trade with the world in
varying degrees there is not good natural
experiments for when countries open up
Japan provides a perfect natural experiment
because it opened up very rapidly which allows
us to test prices and consumption for a range of
goods with and without free trade
Laying the Groundwork
This paper provides a direct test of the theory of
comparative advantage in its autarky price
formulation. It exploits Japan’s dramatic 19th
century move from a state of near complete
isolation to one that was fully exposed to the
forces of international competition and argues
that the case of Japan provides a natural
experiment to explore the empirical validity of
the theory.
Specifying the Test
We test the correlation version of the law of
comparative advantage developed by Deardorff (1980).
It asserts that an economy’s net export vector evaluated
at autarky prices is negative.1 In a world with just two
goods (see fig. 1), this is equivalent to the proposition
that the economy will export the good with the lower
relative opportunity cost….The theory asserts that, on
average, a country will import what is dear and export
what is cheap, with the valuation taking place at autarky
How Do You Test Comparative
An empirical test of this proposition requires
only data on a country’s autarky prices and its
international trade flows. Autarky prices
incorporate all relevant information about a
country’s intrinsic supply and demand
conditions. The trading vector contains all the
necessary information about its trading partners.
Consequently, the value of a country’s trade at
autarky prices is a sufficient basis for a
comparative advantage proposition.
Beyond History, Why is this a Good
In contrast to the often complex and sophisticated
product characteristics of goods traded internationally
today, the commodities that initially entered into
Japanese trade after it opened up were predominantly
agricultural or simple manufactured goods. They can be
reasonably characterized as homogeneous goods. Since
the historical evidence suggests that these goods were
priced under fairly competitive market conditions, the
observed autarky prices appear to be excellent measures
of Japan’s relative opportunity costs at the time.
Building the Model
Consider a competitive economy with n goods, and
denote by pi the n-vector of equilibrium goods prices,
xi the n-vector of equilibrium production outputs, and
ci the n-vector of equilibrium consumption levels. The
superscript a is used to denote a variable under autarky,
and the superscript f denotes a variable under free trade
(i.e., i p a, f). The subscript t pertains to one of the two
time periods (i.e., t p 1, 2). In each period, production
points are constrained to lie in a technologically feasible
production set Ft (t p 1, 2).
The Model and Autarky
While the equilibrium prices under autarky, pa (t
p 1, 2), are determined solely by domestic supply
t and demand conditions, the equilibrium price
vector under free trade, pf , is exogenous to the
domestic economy.
We are Observing…
The subsequent analysis 2 pertains to three competitive
(autarky) regime A: (pa , xa , ca), xa F
(autarky) regime B: (pa , xa , ca), xa F
(free-trade) regime C: (pf , xf , c f), xf F
The discussion above implies that the law of comparative
advantage involves a comparison of Japan’s historical path under
free trade with its historical path if it had continued to operate
under autarky (i.e., regime C vs. regime B). The absence of
information on the unobservable autarky regime B will require
an assessment of the conditions under which what is observed in
autarky under regime A permits inferences about the validity of
the law of comparative advantage.
Assumption #1
First, it assumes that competitive producers
maximize the value of production on a
production possibility set Ft,
pixi ≥ pix for all x F (i = a, f; t = 1, 2).
Assumption #2
Second, we assume that aggregate consumer
preferences in period 2 are in accord with the
weak axiom of revealed preference, that is,
pf c f ≥ pf ca ⇒ pa c f > pa ca
meaning that if c f was preferred to ca at pf ,
then c f must not have been affordable to the
economy at pa
Assumption #3
Finally, we need to rule out any trade surplus,
that is,
pfT ≤ 0,
where T denotes the net export vector, defined
as T p xf c f .7 Given these conditions, we can
state the law of comparative advantage.
Fourth Assumption
The final assumption posited that had it remained closed, Japanese
growth would not have been biased toward importable goods during
the 1859-1868 period (Identification condition, εT≤0 holds.)
Historical record of ongoing shift of land and labor out of rice into tea
and raw silk (key exports)
Lack of land with suitable climate constrained increased production
of another key import, sugar
Absence of sheep ruled out the domestic production of woolen goods
Limited technological expertise and skill precluded rapid adoption of
foreign technologies
Lemma and the Proof
Lemma. Law of comparative advantage.—The value
of net exports in period 2, evaluated at the
(unobserved) autarky prices in period 2, is
negative: paT < 0.
Proof. Expressions (1) and (3) imply that pf c f p
pf xf ≥ pf xa p =pf ca. From (1) and (2), we then
obtain pa c f 1 pa ca p pa xa ≥ pa xf ⇒paT ! 0.
The Historical Example
In his survey on the empirical literature of international
trade, Deardorff (1984, p. 470) argued that tests of the
theory of comparative advantage remain virtually
impossible to carry out because “almost all countries
have engaged in trade throughout history, so that there
is no experience with autarky from which to draw
data.” Japan’s economic history offers a remarkable
exception. As a well-developed market economy, which
experienced over two centuries of autarky, it generated
a rich record of price data.
Identifying the Data
For the construction of the autarky price vector,
we identified three groups of commodities. The
first group of commodities includes exportables
and importables for which we could identify
reasonably close domestic substitutes and for
which we could obtain autarky price
Identifying More Data
A second group of commodities includes goods
(primarily woolens) that were not produced in Japan
under autarky.
Finally, the calculation of the inner product required
estimating the prices of a third group: the one-twentieth
of exports and one-sixth of imports for which there
were domestic substitute, but for which price
information could not be found in Japanese or
contemporary European sources.
Appendix I
Comparative Advantage
Dornbusch, Fischer, and Samuelson
What is Comparative Advantage?
A country is said to have a comparative advantage
in the production of a good if the opportunity
cost of producing that good in terms of other
goods is lower in that country compared to the
other countries.
What is Opportunity Cost in the Ricardian
Opportunity cost in the Ricardian model is described by the relative
unit labor requirements.
Unit labor requirements are the number of hours of labour taken to
produce the good.
For a two good model:
or equivalently
It implies that Home can produce x with a lower oppurtunity cost
i.e. has a comparative advantage in x.
Foreign can produce y with a lower oppurtunity cost i.e. has a
comparative advantage in y.
A Simple Model of Comparative
Lets assume:
In the US, the opportunity cost of 10 million roses is 100,000 computers.
Whereas in South America, with the resources used to produce 10 million
computers, only 30,000 computers can be produced.
What will happen if US decides to specialize in Computers and South America
decides to specialize in Roses.
United States
- 10 Million
+ 100,000
South America
+10 Million
- 30,000
+ 70,000
The world production increases, as each country specializes and trades the good it has a
comparative advantage in.
Example taken from: International Economics: Theory and Policy (Paul Krugman)
Technical Progress
Technical progress in foreign:
• uniform decrease in the unit
labour requirements in foreign i.e.
a*(z) falls
•A(z) shifts down
•The loss of comparative
advantage due to lower foreign unit
labour requirements means the
range of commodities at home
•Causes a trade deficit
•The relative wage decreases to
restore to equilibrium and offset
the fall in comparative advantage.
Demand Shifts
Demand shifts from high z
commodities to low z
i.e. demand shifts towards goods
with weaker comparative
•Trade imbalance
•Relative wage increases
•Home now produces a lower
range of goods but consumes
them more intensely
•Foreign produces more goods
which is each consumed less
Unilateral Transfers
A continual unilateral transfer
from Foreign to Home.
•No change in any curve
•Assumption of homothetic
tastes means that we spend
the transfer exactly as
foreigners would have spent.
•Home incurs a recurring
trade deficit, but terms of
trade remains unchanged.
Transport Costs
•We assume that transport costs are categorized as shrinkage i.e. a fraction g(z) of the
shipment arrives.
•g(z) is identical for all commodities and for both countries.
The home country produces commodities which have a
lower unit labour cost adjusted for shrinkage i.e.
The Foreign country produces commodities which
have a lower unit labout cost adjust for shrinkage
Is the home country’s borderline commodity
Is the foreign country’s borderline commodity
Flexible Exchange Rates
We assume trade balance equilibrium and therefore the equality
of income and spending is assured in each country i.e.
We denote e as the exchange rate and hence foreign wages can
be measured in terms of domestic currency and relative wage is
given as:
So the equilibrium exchange rate under the equilibrium relative
wage can be written as:
Appendix II
Bernhofen Slides
The Theory of Comparative Advantage
[With Two Goods]
Under autarky
Economy’s production
point coincides with its
consumption point : xa=ca
International trade
 Economy has a
comparative advantage in
good 2
 Trade vector evaluated at
autarky prices is negative :
paT <0
Autarky versus Free Trade
Two comparative histories of an economy in Japan:Regime C vs Regime B
Regime A : Actual path under autarky (pa1,xa1,ca1), xa1 Є F1
Regime B : Putative path under autarky (pa2,xa2,ca2), xa2 Є F2
Regime C : Actual path under free trade (pf2,xf2,cf2), xf2 Є F2
Regime A
Regime B
Regime C
Pti: n-vector of equilibrium goods prices
Xit: n-vector of equilibrium production outputs
Cit: : n-vector of equilibrium consumption level
i= a(under autarky),f(under free trade),
t = time period 1 (1850-1858) and period 2 (1868-1875)
Identification Condition
Competitive producers maximize the value of production on Ft
pti xti ≥ pti xt for all xt Є Ft (i = a, f : t =1, 2)
Weak axiom of revealed preference holds:
pf2 cf2 ≥ pf2 c2a
pa2 cf2 > pa2 c2a
No trade surplus pf2 T ≤ 0, T: net export vector, T = xf2 - cf2
Law of comparative advantage: pa2 T < 0
pa2 = pa1+ ε ,
Then Pa1T < 0
As long as the identification condition ε T ≤ 0 holds,
pa2T < 0
Empirical Findings
Empirical Findings
Approximate Inner Product In Various Test Years (Millions of Ryo)
Year of Net Export Vector
Imports with observed
autarky prices
Imports of woolen goods
Imports with approximated
autarky prices (Shinbo index)
Exports with observed
autarky prices
Exports with approximated
autarky prices (Shinbo index)
Total inner product
(sum of rows 1-5)
Empirical Finding
The autarky price prediction of the law of comparative
advantage holds in all the eight trading years. Note that
the result holds in years of current account surplus as
well as during a deficit.
With eight negative entries in a sample size of eight,
the p-value=0.004 , so we can reject the H2.
The case of Japan provides a natural experiment that
occurs in an environment that is transparent by any
reasonable measure.
The testable hypothesis derived from this approach
places no restriction on what accounts for comparative
advantage whether factor endowments, technologies,
tastes, or a combination of them.
The robustness of this paper’s findings suggests that the
autarky price formulation of comparative advantage is a
coherent and insightful theory that can also be validated

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