ECO364 - International Trade
Chapter 2 - Ricardo
Christian Dippel
University of Toronto
Summer 2009
Christian Dippel (University of Toronto)
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Ricardian Comparative Advantage
Comparative Advantage
Comparative Advantage: The Ricardian Model
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Why do countries specialize in different commodities/goods?
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Is trade a good thing?
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Ricardian Comparative Advantage
Comparative Advantage
The Ricardian Model: Definitions
start with:
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Unit Labor Requirement: the amount of labor required to increase
output by one unit.
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aj is the amount of labor needed to produce one unit of good j. With
one factor (labor), 1/aj is the marginal product of labor.
Arithmetically, if Y = F (L), then the unit labor requirement is
1
MPL
Christian Dippel (University of Toronto)
=
1
∂Y
∂L
=
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Ricardian Comparative Advantage
Comparative Advantage
The Ricardian Model: Motivating Example
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Suppose that Canada and China each have 100 workers and
technology manifested by the following unit labor requirements:
Table: Unit Labor Requirements
Country
Textiles
Computers
Canada
10
5
China
5
10
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Ricardian Comparative Advantage
Comparative Advantage
The Ricardian Model: Motivating Example
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Suppose that each country divides its labor force in half so that there
are 50 workers in each sector...
Table: Output
Country
Textiles
Computers
Canada
5
10
China
10
5
World
15
15
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Ricardian Comparative Advantage
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Comparative Advantage
Examine two other possibilities.
1. Canada specializes in computers and China in textiles.
2. Canada specializes in textiles and China in computers.
Canada: C, China: T
Canada: T, China: C
Country
C
T
C
T
Canada
20
0
0
10
China
0
20
10
0
World
20
20
10
10
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Ricardian Comparative Advantage
Comparative Advantage
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If countries specialize in the “right” sector, world output can increase.
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But how do we know what the “right” sector is?
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Ricardian Comparative Advantage
Comparative Advantage
The Ricardian Model: Definitions
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Constant Returns to Scale (CRS): If one increases all inputs by some
proportion, output increases by the same proportion.
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I
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y =ouput and l= labor.
y = f (l) is CRS if y = f (γl) = γf (l) where γ > 0.
y = l is a CRS production function.
y = l 0.4 , y = l 1.1 , and y = l + 5 are all not CRS production functions.
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Homothetic Preferences: The form of the utility function does not
depend on income (linear Engels Curves).
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Autarky: When economies are “closed” and do not trade at all.
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Comparative Advantage
The Ricardian Model: Assumptions
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Two countries, two goods, one factor (labor),
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Labor is immobile across countries and mobile across sectors,
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Constant returns to scale (CRS) production,
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Identical and homothetic preferences,
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Perfect Competition (all agents are price takers).
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Ricardian Comparative Advantage
Comparative Advantage
The Ricardian Model: Opportunity Costs
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Opportunity costs (OC) formalize the tradeoffs implicit in the unit
labor requirements.
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Recall that an opportunity cost is the cost associated with forgoing
one’s next best option.
The OC of production turns out to be the ratio of unit labor
requirements.
Table: Unit Labor Requirements
Country
Canada
China
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Textiles
10
5
Computers
5
10
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Ricardian Comparative Advantage
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10 Canadian workers needed to produce 1 unit of textile and 5 needed
to produce a computer.
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Consequently, the opportunity cost of producing a computer in Canada
is the 0.5 of a textile that is forgone.
5 Chinese workers needed to produce one unit of textiles and 10
needed to produce a computer.
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Comparative Advantage
Consequently, the opportunity cost of producing a computer in China is
the 2 textiles that are forgone.
Because the opportunity cost of producing a computer is lower in
Canada than China, Canada has a comparative advantage in
computers and China possesses a comparative advantage in textiles.
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Ricardian Comparative Advantage
Comparative Advantage
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An absolute advantage is when a country has a lower unit labor
requirement than another country for a given good.
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Absolute advantage involves comparing unit labor requirements for
a good across countries. Comparative advantage involves
comparing unit labor requirements across countries and goods.
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This distinction is at the heart of Ricardian Theory. Do not confuse
the two.
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Ricardian Comparative Advantage
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More generally, rename Canada and China to be N(orth) and S(outh),
With the same two goods, C(omputers) and T(extiles), the North will
possess a comparative advantage in computers if and only if:
N
aC
N
aT
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Comparative Advantage
<
S
aC
S
aT
The South will possess a comparative advantage in computers if and
only if:
N
aC
N
aT
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>
S
aC
S
aT
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Ricardian Comparative Advantage
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Is this confirmed in the earlier data?
Country
Canada
China
aCCan.
1
=
Can.
2
aT
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Comparative Advantage
Can.
aC
Can.
aT
<
China
aC
China
aT
aT
10
5
aC
5
10
aCChina
=2
China
aT
and Canada has a comparative advantage in computers!
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Ricardian Comparative Advantage
Comparative Advantage
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With only two goods, if a country possesses a comparative advantage
in one good, the other country will possess the comparative
advantage in the other good.
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With only two goods, a country cannot have a comparative advantage
in both goods !!
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In the above example, suppose one country has a set of aj ’s that are
lower for both goods. Are there still gains from specialization, if one
country has an absolute advantage in which it possesses lower unit
labor requirements in both sectors?
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Ricardian Comparative Advantage
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Comparative Advantage
Suppose that North possesses an absolute advantage in both sectors
such that the structure of unit labor requirements is as follows:
Table: Unit Labor Requirements
Country
North
South
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Textiles
10
20
Computers
5
40
For each good, the North has a lower unit labor requirement but
which good is it more better at?
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Ricardian Comparative Advantage
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Comparative Advantage
Opportunity costs.
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(aCN /aTN )=0.5
(aCS /aTS )=2.
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Opportunity costs are the same as before even though Canada is 4
times as productive as before in both goods !
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Comparative advantage is not necessarily affected by shifts in
Absolute Advantage.
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Ricardian Comparative Advantage
Comparative Advantage
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Are their gains from specialization?
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Suppose that the South wants an additional computer.
The South can:
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1. Forgo 2 textiles and produce the computer at home. Or,
2. Produce 0.5 textiles and then trade them to the North for, for example,
1 computer. (the North is willing to do this because 1 is less than its
own opportunity costs of producing textiles).
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Clearly, the South prefers producing the good they have a comparative
advantage in and the trading it relative to producing an additional
unit of the good at which they are at a comparative disadvantage.
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Ricardian Comparative Advantage
Comparative Advantage
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Despite the fact that the North has an absolute advantage in both
goods, the North has a comparative advantage in Computers and the
South has a comparative advantage in Textiles.
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Why is it inefficient for the North to produce everything? Suppose
they did....
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Both countries could always be better of by specializing and trading
at a price that lies in between the two opportunity costs.
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The South should produce what it is good at and the North should
produce what it is good at.
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Ricardian Comparative Advantage
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Comparative Advantage
What will the relative price of computers and textiles be?
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Remember that there is no money in this model. All prices are relative
prices of goods.
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Assume that trade occurs.
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Assertion: In equilibrium, the world price of computers will be
between 0.5 and 2 textiles per computer.
Start with the result that Canada produces computers and China
produces textiles.
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i.e. assume each country produces its comparative advantage good.
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Ricardian Comparative Advantage
Comparative Advantage
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Suppose that the world price of computers is less than 0.5 textiles per
computer. Computers are cheap for China relative to autarky. China
is happy but textiles are expensive for Canada relative to autarky.
Canada is better off producing its own textiles ⇒ the relative price
cannot be less than 0.5 textiles per computer.
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Suppose that the world price of computers is more than 2 textiles per
computer. Textiles are cheap for Canada relative to autarky. Canada
is happy but computers are now expensive relative to autarky. China
is better off producing its own computers ⇒ the relative price cannot
be more than 2.
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Consequently, the the relative price will be between 0.5 and 2.
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Ricardian Comparative Advantage
Comparative Advantage
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Can 1 (textile per of computer) be the equilibrium relative price?
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Canada produces computers. The one textile per computer it can
obtain through trade is better than the 1/2 of a textile it could get if
it produced its own textiles.
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China produces textiles. The one computer per textile it can obtain
through trade is better than the 1/2 of a computer it could get if it
produced its own computers.
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For yourself: verify that 0.75 and 1.5 are also both possible
equilibrium relative prices.
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Ricardian Comparative Advantage
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Comparative Advantage
More generally, an equilibrium relative price must satisfy the following
restriction where the North has a comparative advantage in good x
and the South has a comparative advantage in good y .
axSouth
axNorth
px
≤
≤
py
ayNorth
aySouth
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This only pins down a possible range of equilibrium factor prices.
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To narrow this range, we introduce demand.
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First, let’s think more deeply about the gains from trade in this
Ricardian model.
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Ricardian Comparative Advantage
Comparative Advantage
Conjecture: Suppose that the North has a comparative advantage in
good x:
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I
N
S
N
S
ax
= ppyx < aaxS
then the North neither gains nor loses from
If
ayN
y
trade and the South gains.
ax
If
< ppyx = aaxS
then the North gains from trade and the
ayN
y
South neither gains nor loses.
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Ricardian Comparative Advantage
Comparative Advantage
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Can we illustrate this graphically?
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The North’s Production Possibility Frontier (PPF) is as follows
where LN is the amount of labor that the North possesses:
N Q N ≤ LN
aCN QCN + aT
T
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Assuming full employment of all factors, simple arithmetic gives:
QTN =
Christian Dippel (University of Toronto)
LN
N
aT
−
N
aC
N
N QC
aT
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
Comparative Advantage
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A key insight is that in autarky, the PPF and the budget constraint
will be the same line.
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In autarky, what you consume/purchase must be what you produce.
With trade, you need not consume what you produce.
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Therefore, in a trading equilibrium, the budget constraint and PPF
need not be the same line.
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Ricardian Comparative Advantage
Comparative Advantage
Autarky Relative Prices
w = Pk MPLk =
Pk
ak
for k = {C , T }
Because the same wage w is paid in both sectors, this implies
PC
PT
I
=
aC
aT
Autarky relative prices will be equal to the ratio of unit labor
requirements in that country.
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Ricardian Comparative Advantage
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Comparative Advantage
Now introduce Trade
I
I
I
I
aN
The PPF will look the same as before and will have a slope of − aCN .
T
The budget constraint will now be based on the equation
PC QC + PT QT ≤ Y and will have the slope − PPTC .
aN
Let’s examine the case where PPTC > aCN .
T
Does the North gain from trade if it specializes in computers?
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
Comparative Advantage
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Now let’s examine the Southern case.
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Let’s examine the case where
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Does the South gain from trade if it specializes in textiles?
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Starting from autarky...
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PC
PT
<
S
aC
S
aT
.
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Ricardian Comparative Advantage
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Comparative Advantage
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Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
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Comparative Advantage
Suppose that (for either country) world relative prices more closely
resemble autarky relative prices.
aN
= aCN .
The gains from trade will diminish until PPTC
0
I
T
At this point, utility will be the same as in autarky.
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Ricardian Comparative Advantage
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Comparative Advantage
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Comparative Advantage
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If world relative prices equal autarky relative prices for one country,
that country does not gain from trade. The other country does gain
from trade.
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If world relative prices are in between autarky relative prices, both
countries gain from trade.
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The more “different” a country’s ratio of unit labor requirements are
from world relative prices, the more a country gains from trade.
If both countries have the same opportunity costs there is no
comparative advantage
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I
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Then there is no gains from trade for either country.
Even though there might still be absolute advantage.
Large differences mean larger gains from specialization.
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Ricardian Comparative Advantage
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Comparative Advantage
Let’s introduce demand....
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Ricardian Comparative Advantage
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Comparative Advantage
We are going to use the following graph to solve for equilibrium
(relative) output and prices (note the axes labels !!).
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Ricardian Comparative Advantage
Comparative Advantage
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The vertical axis gives the price of good X relative to Y . The
horizontal axis gives the relative World quantities where the World is
simply to aggregation of the North and South.
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Recall that the equilibrium relative price of goods X and Y must lie
between the autarky relative prices/unit labor requirements of the two
countries.
Assume that the North has a comparative advantage in good x,
therefore the South possesses a comparative advantage in good y .
I
I
I
an
as
Arithmetically, axn < axs .
y
y
We can represent this graphically as....
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
px
py
=
Comparative Advantage
axS
.
ayS
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Now suppose that
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The North completely specializes in good x because it can produce x
and then trade for y at better terms than if it produced its own y .
Consequently X N = LN /axn and Y N = 0.
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The South is indifferent between specializing in Y (and then trading
for X ) and producing both X and Y .
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The South will produce some combination of (X S , Y S ) that satisfies
0<
I
Consequently, when
segment.
Christian Dippel (University of Toronto)
px
py
=
axS
ayS
XS
YS
<∞
, the relative quantity supplied will be a
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
px
py
=
Comparative Advantage
axN
.
ayN
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Suppose that
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The South completely specializes in good y because it can produce y
and then trade for x at better terms than if it produced its own x.
Consequently X S = 0 and Y S = LS /ays .
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However, we cannot say how much the North will specialize because
the North is indiffernt indifferent between specializing in X (and then
trading for Y ) and producing both X and Y .
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Consequently, when
segment...
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px
py
=
axN
,
ayN
the relative quantity supplied will be a
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
axN
ayN
<
px
py
axS
.
ayS
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Now suppose that
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Complete specialization where the North specializes in X and the
South specializes in X .
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Note that any set of relative prices between the two autarky price
ratios will support this outcome.
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The relative supply curve will be vertical at this point.
Christian Dippel (University of Toronto)
<
Comparative Advantage
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
Comparative Advantage
At this point....
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The North prefers specializing in X and trading for Y to producing
both.
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I
Consequently, X N = LN /aXN and Y N = 0.
The South prefers specializing in Y and trading for X to producing
both.
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X S = 0 and Y S = LS /aYS .
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Ricardian Comparative Advantage
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Comparative Advantage
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Ricardian Comparative Advantage
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I
Comparative Advantage
The structure of demand determines the equilibrium.
This is done by introducing a relative demand curve
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As the relative price of a good rises, relative demand increases.
Reflects substitution effects.
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Ricardian Comparative Advantage
Comparative Advantage
Figure: Demand for X is high relative to Y
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Ricardian Comparative Advantage
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The North specializes in X and the South produces both X and Y .
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Why?
World demand for X is sufficiently high that the North cannot
produce enough X to satisfy high World demand for X .
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Comparative Advantage
The South satisfies for the remaining demand for X .
Because relative prices for the South are the same as in autarky, the
South does not gain from trade but the North does. In sum, the
World gains.
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Ricardian Comparative Advantage
Comparative Advantage
Figure: Demand for Y is high relative to X
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Ricardian Comparative Advantage
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The South specializes in Y and the North produces both X and Y .
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Why?
World demand for Y is sufficiently high that the South cannot
produce enough Y to satisfy high World demand for Y .
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Comparative Advantage
The North must provide for the remaining demand for Y .
Because prices for the North are the same as in autarky, the North
does not gain from trade but the South does. In sum, the World
gains.
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Ricardian Comparative Advantage
Comparative Advantage
Figure: Demand for X and Y is Relatively Even.
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Ricardian Comparative Advantage
Comparative Advantage
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The North specializes in X and the South specializes in Y .
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Because relative world prices are between autarky unit labor
requirements, both countries gain from trade
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General Rule in this model: a country that does not specialize does
not gain from trade !
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Ricardian Comparative Advantage
Comparative Advantage
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This analysis suggests that a country will produce more of its
comparative advantage good than its comparative disadvantage good
(specialization).
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One country produces a lot of one good, the other country produces a
lot of the other.
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If preferences are sufficiently similar (which we have assumed), they
will demand the same goods.
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A country will export its comparative advantage good and import its
comparative disadvantage good.
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See an upcoming problem set for concrete examples.
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Ricardian Comparative Advantage
Relative Wages
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Some commentators argue that high relative wages in the North
relative to the south are evidence of Northern exploitation of
Southern workers.
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Does the Ricardian model have anything to say about this?
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Ricardian Comparative Advantage
Relative Wages
Start with the profit maximizing condition that nominal wages equal the
marginal revenue product of labor.
w = p × MPL
Now suppose that Northern workers specialize in computers and Southern
workers specialize in textiles. This gives us two equilibrium conditions:
Christian Dippel (University of Toronto)
wN =
pC
N
aC
wS =
pT
S
aT
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Relative Wages
These conditions can be combined to give the following expression
wN
wS
I
S
aT
pC
N p
aC
T
=
MPLN
C pC
MPLST pT
Northern relative wages are determined by labor productivity and the
relative prices of the two goods.
I
I
I
=
If the two goods have the same price, labor productivity alone
determines relative wages.
If the two goods do not have the same price, the relative wage is higher
in the country that produces the relatively valuable good, holding labor
productivity constant.
But wages in both North and South are always higher under Trade
than under Autarky.
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Relative Wages
We can also offer strong rebuttals to common criticisms of free trade
if the Ricardian model possesses substantial validity.
1. Free Trade is beneficial only if your country is strong enough to stand
up to foreign competition.
2. Foreign competition is unfair and hurts other countries when it is based
on low wages.
3. Trade exploits a country and makes it worse off if its workers receive
much lower wages than workers in other nations.
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Krugman and Obstfeld, pp. 36-40
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Krugman “Ricardo’s Difficult Idea.” (optional).
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Ricardian Comparative Advantage
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Free Trade is beneficial only if your country is strong enough to stand
up to foreign competition.
I
I
Comparative and not absolute advantage is sufficient for gains from
trade
Foreign competition is unfair and hurts other countries when it is
based on low wages.
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I
Relative Wages
Low foreign wages are caused by low productivity.
Trade exploits a country and makes it worse off if its workers receive
much lower wages than workers in other nations.
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If wages are based on productivity, they will be low even if there is no
trade.
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Ricardian Comparative Advantage
Conclusions
1. Each country exports the good at which it possesses a comparative
advantage.
2. Each country imports the good at which it possesses a comparative
disadvantage.
3. In this setting, each country possesses a comparative advantage in
some good.
4. If free trade relative prices lie between autarky unit labor
requirements, both countries gain from trade.
5. If free trade relative prices equal the autarky price ratio for one
country, that country is no worse off from trade and the other country
is better off.
6. Increased utility comes from increased consumption possibilities that
allow consumer/workers to attain a higher indifference curve.
Christian Dippel (University of Toronto)
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Summer 2009
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The Multi-Good Extension
I
Let’s make the model more realistic by allowing more than one good.
I
This will also allow us to introduce the important notion of the the
intensive and extensive margin of trade.
I
Suppose there are N goods produced, indexed by i = 1,2,N.
I
The domestic countrys unit labor requirement for good i is ai , and
that of the foreign country is ai∗
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
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The Multi-Good Extension
I
Goods will be produced wherever it is cheaper to produce them.
I
Let w represent the wage rate in the domestic country and w*
represent the wage rate in the foreign country.
I
If wa1 < w ∗ a1∗ then only the domestic country will produce good 1,
since total wage payments are less there.
I
Equivalently, good i is produced in Home only if aa∗1 < ww (if Home’s
1
technology advantage is larger than its cost disadvantage)
I
Let’s consider an example:
∗
Christian Dippel (University of Toronto)
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Summer 2009
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The Multi-Good Extension
Figure: Demand for X and Y is Relatively Even.
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
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The Multi-Good Extension
I
Home has high productivity in apples, bananas, and caviar. That
gives Home a cost advantage.
I
Suppose Foreign has low wages. That gives it a cost advantage,
despite its low productivity.
I
How is the equilibrium relative wage determined?
I
the relevant equilibrium is equality of the relative supply and relative
(derived) demand of labor services.
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
68 / 73
The Multi-Good Extension
I
As domestic labor becomes more expensive relative to foreign labor,
goods produced in the domestic country become more expensive, and
demand of these goods and therefore derived demand for the labor to
produce them falls.
I
At certain threshold-levels, comparative advantage shifts from Home
to Foreign so that fewer goods will be produced in Home, further
reducing the demand of domestic labor services.
I
The relative (derived) demand of domestic labor services therefore
falls when w/w* rises.
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
69 / 73
The Multi-Good Extension
The Intensive and Extensive Margin of Trade
I
I
The intensive margin refers to a country exporting or importing a
larger quantity of the same goods
The extensive margin refers to a country exporting or importing new
goods
I
In later chapters, the intensive margin can also refer exporting firms
exporting more while the extensive margin refers to non-exporting firms
becoming exporters.
I
Suppose w/w* increases from 3 to 3.99: Home produces the same
goods but at higher prices so that the demand for these goods and
the labor to produce them falls (intensive margin).
I
Suppose w/w* increases from 3.99 to 4.01: The caviar industry now
moves to Foreign, causing a discrete drop in the demand of domestic
labor (extensive margin).
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
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The Multi-Good Extension
Figure: Demand for X and Y is Relatively Even.
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
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Empirical Evidence
I
What is the empirical evidence for technology-differences-based
comparative advantage?
I
Do countries export those goods in which their productivity is
relatively high?
I
The ratio of U.S. to British exports in 1951 compared to the ratio of
U.S. to British labor productivity in 26 manufacturing industries
suggests yes.
I
At this time the U.S. had an absolute advantage in all 26 industries,
yet the ratio of exports was low in the least productive sectors of the
U.S.
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
72 / 73
Empirical Evidence
Figure: Demand for X and Y is Relatively Even.
Christian Dippel (University of Toronto)
ECO364 - International Trade
Summer 2009
73 / 73