Trade in a One-Factor World
To describe the pattern and effects of trade between two countries when each country has only
one factor of production is simple. Yet the implications of this analysis can be surprising.
Indeed, to those who have not thought about international trade, many of these implications
seem to conflict with common sense. Even this simplest of trade models can offer some
important guidance on real-world issues, such as what constitutes fair international competition
and fair international exchange.
Before we get to these issues, however, let us get the model stated. Suppose that there
are two countries. One of them we again call Home and the other we call Foreign. Each of
these countries has one factor of production (labor) and can produce two goods, wine and
cheese. As before, we denote Home’s labor force by L and Home’s unit labor requirements
in wine and cheese production by and respectively. For Foreign we will use a
convenient notation throughout this book: When we refer to some aspect of Foreign, we
will use the same symbol that we use for Home, but with an asterisk. Thus Foreign’s labor
force will be denoted by , Foreign’s unit labor requirements in wine and cheese will be
denoted by and , respectively, and so on.
In general, the unit labor requirements can follow any pattern. For example, Home
could be less productive than Foreign in wine but more productive in cheese, or vice versa.
For the moment, we make only one arbitrary assumption: that
(3-2)
or, equivalently, that
(3-3)
In words, we are assuming that the ratio of the labor required to produce a pound of
cheese to that required to produce a gallon of wine is lower in Home than it is in Foreign.
More briefly still, we are saying that Home’s relative productivity in cheese is higher than
it is in wine.
But remember that the ratio of unit labor requirements is equal to the opportunity cost
of cheese in terms of wine; and remember also that we defined comparative advantage
precisely in terms of such opportunity costs. So the assumption about relative productivities
embodied in equations (3-2) and (3-3) amounts to saying that Home has a comparative
advantage in cheese.
One point should be noted immediately: The condition under which Home has this
comparative advantage involves all four unit labor requirements, not just two. You might
think that to determine who will produce cheese, all you need to do is compare the two
countries’ unit labor requirements in cheese production, and . If , Home
labor is more efficient than Foreign in producing cheese. When one country can produce a
unit of a good with less labor than another country, we say that the first country has an
absolute advantage in producing that good. In our example, Home has an absolute advantage
in producing cheese.
aLC 6 aLC
a * LC
a * LC
aLC/aLC
* 6 aLW/aLW
* .
aLC/aLW 6 aLC
* /aLW
*
aLC
a * LW
*
L*
aLW aLC,
30 PART ONE International Trade Theory
What we will see in a moment, however, is that we cannot determine the pattern of
trade from absolute advantage alone. One of the most important sources of error in
discussing international trade is to confuse comparative advantage with absolute
advantage.
Given the labor forces and the unit labor requirements in the two countries, we can
draw the production possibility frontier for each country. We have already done this
for Home, by drawing PF in Figure 3-1. The production possibility frontier for
Foreign is shown as in Figure 3-2. Since the slope of the production possibility
frontier equals the opportunity cost of cheese in terms of wine, Foreign’s frontier is
steeper than Home’s.
In the absence of trade, the relative prices of cheese and wine in each country would be
determined by the relative unit labor requirements. Thus in Home the relative price of
cheese would be ; in Foreign it would be .
Once we allow for the possibility of international trade, however, prices will no longer
be determined purely by domestic considerations. If the relative price of cheese is higher
in Foreign than in Home, it will be profitable to ship cheese from Home to Foreign and to
ship wine from Foreign to Home. This cannot go on indefinitely, however. Eventually
Home will export enough cheese and Foreign enough wine to equalize the relative price.
But what determines the level at which that price settles?
Determining the Relative Price After Trade
Prices of internationally traded goods, like other prices, are determined by supply and
demand. In discussing comparative advantage, however, we must apply supply-and-demand
analysis carefully. In some contexts, such as some of the trade policy analysis in Chapters 9
through 12, it is acceptable to focus only on supply and demand in a single market. In assessing
the effects of U.S. import quotas on sugar, for example, it is reasonable to use partial
equilibrium analysis, that is, to study a single market, the sugar market. When we study
comparative advantage, however, it is crucial to keep track of the relationships between
aLC
* /aLW
a * LC/aLW
PF*
Foreign wine
production, QW,
in gallons
L*/aLW
L*/aLC Foreign cheese
production, QC,
in pounds
P*
*
*
*
* F*
Figure 3-2
Foreign’s Production Possibility
Frontier
Because Foreign’s relative unit
labor requirement in cheese is
higher than Home’s (it needs to
give up many more units of wine
to produce one more unit of
cheese), its production possibility
frontier is steeper.
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 31
markets (in our example, the markets for wine and cheese). Since Home exports cheese only
in return for imports of wine, and Foreign exports wine in return for cheese, it can be misleading
to look at the cheese and wine markets in isolation. What is needed is general
equilibrium analysis, which takes account of the linkages between the two markets.
One useful way to keep track of two markets at once is to focus not just on the quantities
of cheese and wine supplied and demanded but also on the relative supply and
demand, that is, on the number of pounds of cheese supplied or demanded divided by the
number of gallons of wine supplied or demanded.
Figure 3-3 shows world supply and demand for cheese relative to wine as functions of
the price of cheese relative to that of wine. The relative demand curve is indicated by
RD; the relative supply curve is indicated by RS. World general equilibrium requires that
relative supply equal relative demand, and thus the world relative price is determined by
the intersection of RD and RS.
The striking feature of Figure 3-3 is the funny shape of the relative supply curve RS: It’s
a “step” with flat sections linked by a vertical section. Once we understand the derivation
of the RS curve, we will be almost home-free in understanding the whole model.
First, as drawn, the RS curve shows that there would be no supply of cheese if the world
price dropped below . To see why, recall that we showed that Home will specialize
in the production of wine whenever . Similarly, Foreign will specialize
in wine production whenever . At the start of our discussion of equation
(3-2), we made the assumption that . So at relative prices of cheese
below , there would be no world cheese production.
Next, when the relative price of cheese is exactly , we know that workers
in Home can earn exactly the same amount making either cheese or wine. So Home
will be willing to supply any relative amount of the two goods, producing a flat section to
the supply curve.
We have already seen that if is above , Home will specialize in the production
of cheese. As long as PC/PW 6 aLC , however, Foreign will continue to specialize in
* /aLW
*
PC/PW aLC/aLW
PC/PW aLC/aLW
aLC/aLW
aLC/aLW 6 aLC
* /aLW
*
PC/PW 6 aLC
* /aLW
*
PC/PW 6 aLC/aLW
aLC/aLW
Relative price
of cheese, PC/PW
aLC /aLW
L /aLC Relative quantity
of cheese,
RD
*
RD
L*/aLW *
Q
*
aLC /aLW
QC + QC
QW +QW *
1
2
RS
*
(2 in our
example)
(1/2 in our
example)
Figure 3-3
World Relative Supply and
Demand
The RD and RD¿ curves show that
the demand for cheese relative to
wine is a decreasing function of
the price of cheese relative to that
of wine, while the RS curve shows
that the supply of cheese relative
to wine is an increasing function
of the same relative price.
32 PART ONE International Trade Theory
producing wine. When Home specializes in cheese production, it produces pounds.
Similarly, when Foreign specializes in wine, it produces gallons. So for any relative
price of cheese between and , the relative supply of cheese is
(3-4)
At we know that Foreign workers are indifferent between producing
cheese and wine. Thus here we again have a flat section of the supply curve.
Finally, for , both Home and Foreign will specialize in cheese production.
There will be no wine production, so that the relative supply of cheese will
become infinite.
A numerical example may help at this point. Let’s assume, as we did before, that in
Home it takes one hour of labor to produce a pound of cheese and two hours to produce
a gallon of wine. Meanwhile, let’s assume that in Foreign it takes six hours to
produce a pound of cheese—Foreign workers are much less productive than Home
workers when it comes to cheesemaking—but only three hours to produce a gallon
of wine.
In this case, the opportunity cost of cheese production in terms of wine is 1/2 in Home—
that is, the labor used to produce a pound of cheese could have produced half a gallon of
wine. So the lower flat section of RS corresponds to a relative price of 1/2.
Meanwhile, in Foreign the opportunity cost of cheese in terms of wine is 2: The six
hours of labor required to produce a pound of cheese could have produced two gallons of
wine. So the upper flat section of RS corresponds to a relative price of 2.
The relative demand curve RD does not require such exhaustive analysis. The downward
slope of RD reflects substitution effects. As the relative price of cheese rises,
consumers will tend to purchase less cheese and more wine, so the relative demand for
cheese falls.
The equilibrium relative price of cheese is determined by the intersection of the relative
supply and relative demand curves. Figure 3-3 shows a relative demand curve RD
that intersects the RS curve at point 1, where the relative price of cheese is between the
two countries’ pretrade prices—say, at a relative price of 1, in between the pretrade prices
of 1/2 and 2. In this case, each country specializes in the production of the good in which
it has a comparative advantage: Home produces only cheese, while Foreign produces
only wine.
This is not, however, the only possible outcome. If the relevant RD curve were , for
example, relative supply and relative demand would intersect on one of the horizontal sections
of RS. At point 2 the world relative price of cheese after trade is , the same as
the opportunity cost of cheese in terms of wine in Home.
What is the significance of this outcome? If the relative price of cheese is equal to
its opportunity cost in Home, the Home economy need not specialize in producing
either cheese or wine. In fact, at point 2 Home must be producing both some wine and
some cheese; we can infer this from the fact that the relative supply of cheese (point
on the horizontal axis) is less than it would be if Home were in fact completely specialized.
Since is below the opportunity cost of cheese in terms of wine in Foreign,
however, Foreign does specialize completely in producing wine. It therefore remains
true that if a country does specialize, it will do so in the good in which it has a comparative
advantage.
For the moment, let’s leave aside the possibility that one of the two countries does not
completely specialize. Except in this case, the normal result of trade is that the price of a
PC/PW
Qoe
aLC/aLW
RDoe
PC/PW 7 aLC
* /aLW
*
PC/PW = aLC
* /aLW
* ,
1L/aLC2/1L*/aLW
* 2.
aLC
* /aLW
a * LC/aLW
L*/aLW
*
L/aLC
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 33
traded good (e.g., cheese) relative to that of another good (wine) ends up somewhere in
between its pretrade levels in the two countries.
The effect of this convergence in relative prices is that each country specializes in the production
of that good in which it has the relatively lower unit labor requirement. The rise in the
relative price of cheese in Home will lead Home to specialize in the production of cheese, producing
at point F in Figure 3-4a. The fall in the relative price of cheese in Foreign will lead
Foreign to specialize in the production of wine, producing at point F* in Figure 3-4b.
Comparative Advantage in Practice: The Case of Babe Ruth
Everyone knows that Babe Ruth was the greatest slugger
in the history of baseball. Only true fans of the
sport know, however, that Ruth also was one of the
greatest pitchers of all time. Because Ruth stopped
pitching after 1918 and played outfield during all the
time he set his famous batting records, most people
don’t realize that he even could
pitch. What explains Ruth’s lopsided
reputation as a batter? The
answer is provided by the principle
of comparative advantage.
As a player with the Boston
Red Sox early in his career, Ruth
certainly had an absolute advantage
in pitching. According to
historian Geoffrey C. Ward and
filmmaker Ken Burns:
In the Red Sox’s greatest
years, he was their greatest
player, the best left-handed
pitcher in the American League,
winning 89 games in six seasons. In 1916 he
got his first chance to pitch in the World Series
and made the most of it. After giving up a run
in the first, he drove in the tying run himself,
after which he held the Brooklyn Dodgers
scoreless for eleven innings until his teammates
could score the winning run. . . . In the
1918 series, he would show that he could still
handle them, stretching his series record to
scoreless innings, a mark that stood for
forty-three years.*
The Babe’s World Series pitching record was
broken by New York Yankee Whitey Ford in the
same year, 1961, that his teammate Roger Maris
shattered Ruth’s 1927 record of
60 home runs in a single season.
Although Ruth had an absolute
advantage in pitching, his skill as
a batter relative to his teammates’
abilities was even greater: His
comparative advantage was at the
plate. As a pitcher, however, Ruth
had to rest his arm between
appearances and therefore could
not bat in every game. To exploit
Ruth’s comparative advantage,
the Red Sox moved him to center
field in 1919 so that he could bat
more frequently.
The payoff to having Ruth
specialize in batting was huge. In 1919, he hit 29
home runs, “more than any player had ever hit in a
single season,” according to Ward and Burns. The
Yankees kept Ruth in the outfield (and at the plate)
after they acquired him in 1920. They knew a good
thing when they saw it. That year, Ruth hit 54 home
runs, set a slugging record (bases divided by at bats)
that remains untouched to this day, and turned the
Yankees into baseball’s most renowned franchise.
292/3
*See Geoffrey C. Ward and Ken Burns, Baseball: An Illustrated History (New York: Knopf, 1994), p. 155. Ruth’s career preceded
the designated hitter rule, so American League pitchers, like National League pitchers today, took their turns at bat. For a
more extensive discussion of Babe Ruth’s relation to the comparative advantage principle, see Edward Scahill, “Did Babe Ruth
Have a Comparative Advantage as a Pitcher?” Journal of Economic Education 21(4), Fall 1990, pp. 402–410.
34 PART ONE International Trade Theory
The Gains from Trade
We have now seen that countries whose relative labor productivities differ across industries
will specialize in the production of different goods. We next show that both countries
derive gains from trade from this specialization. This mutual gain can be demonstrated in
two alternative ways.
The first way to show that specialization and trade are beneficial is to think of trade as
an indirect method of production. Home could produce wine directly, but trade with
Foreign allows it to “produce” wine by producing cheese and then trading the cheese for
wine. This indirect method of “producing” a gallon of wine is a more efficient method
than direct production.
Consider our numerical example yet again: In Home, we assume that it takes one hour
to produce a pound of cheese and two hours to produce a gallon of wine. This means that
the opportunity cost of cheese in terms of wine is 1/2. But we know that the relative price
of cheese after trade will be higher than this, say 1. So here’s one way to see the gains
from trade for Home: Instead of using two hours of labor to produce a gallon of wine, it
can use that labor to produce two pounds of cheese, and trade that cheese for two gallons
of wine.
More generally, consider two alternative ways of using an hour of labor. On one side,
Home could use the hour directly to produce gallons of wine. Alternatively, Home
could use the hour to produce pounds of cheese. This cheese could then be traded
for wine, with each pound trading for gallons, so our original hour of labor yields
gallons of wine. This will be more wine than the hour could have
produced directly as long as
International trade allows Home and Foreign to consume anywhere within the colored lines,
which lie outside the countries’ production frontiers.
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 35
(3-5)
or
But we just saw that in international equilibrium, if neither country produces both goods,
we must have . This shows that Home can “produce” wine more efficiently
by making cheese and trading it than by producing wine directly for itself.
Similarly, Foreign can “produce” cheese more efficiently by making wine and trading it.
This is one way of seeing that both countries gain.
Another way to see the mutual gains from trade is to examine how trade affects each
country’s possibilities for consumption. In the absence of trade, consumption possibilities
are the same as production possibilities (the solid lines PF and in Figure 3-4). Once
trade is allowed, however, each economy can consume a different mix of cheese and wine
from the mix it produces. Home’s consumption possibilities are indicated by the colored
line TF in Figure 3-4a, while Foreign’s consumption possibilities are indicated by in
Figure 3-4b. In each case, trade has enlarged the range of choice, and therefore it must
make residents of each country better off.
A Note on Relative Wages
Political discussions of international trade often focus on comparisons of wage rates in
different countries. For example, opponents of trade between the United States and
Mexico often emphasize the point that workers in Mexico are paid only about $2 per hour,
compared with more than $15 per hour for the typical worker in the United States. Our
discussion of international trade up to this point has not explicitly compared wages in the
two countries, but it is possible in the context of our numerical example to determine how
the wage rates in the two countries compare.
In our example, once the countries have specialized, all Home workers are employed
producing cheese. Since it takes one hour of labor to produce one pound of cheese, workers
in Home earn the value of one pound of cheese per hour of their labor. Similarly,
Foreign workers produce only wine; since it takes three hours for them to produce each
gallon, they earn the value of 1/3 of a gallon of wine per hour.
To convert these numbers into dollar figures, we need to know the prices of cheese and
wine. Suppose that a pound of cheese and a gallon of wine both sell for $12; then Home workers
will earn $12 per hour, while Foreign workers will earn $4 per hour. The relative wage of a
country’s workers is the amount they are paid per hour, compared with the amount workers in
another country are paid per hour. The relative wage of Home workers will therefore be 3.
Clearly, this relative wage does not depend on whether the price of a pound of cheese is
$12 or $20, as long as a gallon of wine sells for the same price. As long as the relative price
of cheese—the price of a pound of cheese divided by the price of a gallon of wine—is 1, the
wage of Home workers will be three times that of Foreign workers.
Notice that this wage rate lies between the ratios of the two countries’ productivities in
the two industries. Home is six times as productive as Foreign in cheese, but only one-and-ahalf
times as productive in wine, and it ends up with a wage rate three times as high as
Foreign’s. It is precisely because the relative wage is between the relative productivities that
each country ends up with a cost advantage in one good. Because of its lower wage rate,
Foreign has a cost advantage in wine even though it has lower productivity. Home has a cost
advantage in cheese, despite its higher wage rate, because the higher wage is more than
offset by its higher productivity.
T*F*
P*F*
PC/PW 7 aLC/aLW
PC/PW 7 aLC/aLW.
11/aLC21PC/PW2 7 1/aLW,
36 PART ONE International Trade Theory
We have now developed the simplest of all models of international trade. Even though
the Ricardian one-factor model is far too simple to be a complete analysis of either the
causes or the effects of international trade, a focus on relative labor productivities can be a
very useful tool for thinking about trade issues. In particular, the simple one-factor model
is a good way to deal with several common misconceptions about the meaning of comparative
advantage and the nature of the gains from free trade. These misconceptions appear
so frequently in public debate about international economic policy, and even in statements
by those who regard themselves as experts, that in the next section we take time out to discuss
some of the most common misunderstandings about comparative advantage in light
of our model.
The Losses from Nontrade
Our discussion of the gains from trade took the
form of a “thought experiment” in which we
compared two situations: one in which countries
do not trade at all and another in which they have
free trade. It’s a hypothetical case that helps us
to understand the principles of international
economics, but it does not have much to do with
actual events. After all, countries don’t suddenly
go from no trade to free trade or vice versa. Or
do they?
As economic historian
Douglas Irwin* has pointed out,
in the early history of the United
States the country actually did
carry out something very close to
the thought experiment of moving
from free trade to no trade.
The historical context was as follows:
In the early 19th century
Britain and France were engaged
in a massive military struggle, the Napoleonic
Wars. Both countries endeavored to bring economic
pressures to bear: France tried to keep European
countries from trading with Britain, while Britain
imposed a blockade on France. The young United
States was neutral in the conflict but suffered considerably.
In particular, the British navy often
seized U.S. merchant ships and, on occasion,
forcibly recruited their crews into its service.
In an effort to pressure Britain into ceasing these
practices, President Thomas Jefferson declared a
complete ban on overseas shipping. This embargo
would deprive both the United States and Britain of
the gains from trade, but Jefferson hoped that
Britain would be hurt more and would agree to stop
its depredations.
Irwin presents evidence suggesting that the embargo
was quite effective: Although some smuggling
took place, trade between the United States
and the rest of the world was drastically reduced. In
effect, the United States gave up
international trade for a while.
The costs were substantial.
Although quite a lot of guesswork
is involved, Irwin suggests
that real income in the United
States may have fallen by about
8 percent as a result of the
embargo. When you bear in mind
that in the early 19th century only
a fraction of output could be
traded—transport costs were still too high, for
example, to allow large-scale shipments of commodities
like wheat across the Atlantic—that’s a
pretty substantial sum.
Unfortunately for Jefferson’s plan, Britain did
not seem to feel equal pain and showed no inclination
to give in to U.S. demands. Fourteen months
after the embargo was imposed, it was repealed.
Britain continued its practices of seizing American
cargoes and sailors; three years later the two countries
went to war.
*Douglas Irwin, “The Welfare Cost of Autarky: Evidence from the Jeffersonian Trade Embargo, 1807–1809,” Review of
International Economics 13 (September 2005), pp. 631–645.
To describe the pattern and effects of trade between two countries when each country has only
one factor of production is simple. Yet the implications of this analysis can be surprising.
Indeed, to those who have not thought about international trade, many of these implications
seem to conflict with common sense. Even this simplest of trade models can offer some
important guidance on real-world issues, such as what constitutes fair international competition
and fair international exchange.
Before we get to these issues, however, let us get the model stated. Suppose that there
are two countries. One of them we again call Home and the other we call Foreign. Each of
these countries has one factor of production (labor) and can produce two goods, wine and
cheese. As before, we denote Home’s labor force by L and Home’s unit labor requirements
in wine and cheese production by and respectively. For Foreign we will use a
convenient notation throughout this book: When we refer to some aspect of Foreign, we
will use the same symbol that we use for Home, but with an asterisk. Thus Foreign’s labor
force will be denoted by , Foreign’s unit labor requirements in wine and cheese will be
denoted by and , respectively, and so on.
In general, the unit labor requirements can follow any pattern. For example, Home
could be less productive than Foreign in wine but more productive in cheese, or vice versa.
For the moment, we make only one arbitrary assumption: that
(3-2)
or, equivalently, that
(3-3)
In words, we are assuming that the ratio of the labor required to produce a pound of
cheese to that required to produce a gallon of wine is lower in Home than it is in Foreign.
More briefly still, we are saying that Home’s relative productivity in cheese is higher than
it is in wine.
But remember that the ratio of unit labor requirements is equal to the opportunity cost
of cheese in terms of wine; and remember also that we defined comparative advantage
precisely in terms of such opportunity costs. So the assumption about relative productivities
embodied in equations (3-2) and (3-3) amounts to saying that Home has a comparative
advantage in cheese.
One point should be noted immediately: The condition under which Home has this
comparative advantage involves all four unit labor requirements, not just two. You might
think that to determine who will produce cheese, all you need to do is compare the two
countries’ unit labor requirements in cheese production, and . If , Home
labor is more efficient than Foreign in producing cheese. When one country can produce a
unit of a good with less labor than another country, we say that the first country has an
absolute advantage in producing that good. In our example, Home has an absolute advantage
in producing cheese.
aLC 6 aLC
a * LC
a * LC
aLC/aLC
* 6 aLW/aLW
* .
aLC/aLW 6 aLC
* /aLW
*
aLC
a * LW
*
L*
aLW aLC,
30 PART ONE International Trade Theory
What we will see in a moment, however, is that we cannot determine the pattern of
trade from absolute advantage alone. One of the most important sources of error in
discussing international trade is to confuse comparative advantage with absolute
advantage.
Given the labor forces and the unit labor requirements in the two countries, we can
draw the production possibility frontier for each country. We have already done this
for Home, by drawing PF in Figure 3-1. The production possibility frontier for
Foreign is shown as in Figure 3-2. Since the slope of the production possibility
frontier equals the opportunity cost of cheese in terms of wine, Foreign’s frontier is
steeper than Home’s.
In the absence of trade, the relative prices of cheese and wine in each country would be
determined by the relative unit labor requirements. Thus in Home the relative price of
cheese would be ; in Foreign it would be .
Once we allow for the possibility of international trade, however, prices will no longer
be determined purely by domestic considerations. If the relative price of cheese is higher
in Foreign than in Home, it will be profitable to ship cheese from Home to Foreign and to
ship wine from Foreign to Home. This cannot go on indefinitely, however. Eventually
Home will export enough cheese and Foreign enough wine to equalize the relative price.
But what determines the level at which that price settles?
Determining the Relative Price After Trade
Prices of internationally traded goods, like other prices, are determined by supply and
demand. In discussing comparative advantage, however, we must apply supply-and-demand
analysis carefully. In some contexts, such as some of the trade policy analysis in Chapters 9
through 12, it is acceptable to focus only on supply and demand in a single market. In assessing
the effects of U.S. import quotas on sugar, for example, it is reasonable to use partial
equilibrium analysis, that is, to study a single market, the sugar market. When we study
comparative advantage, however, it is crucial to keep track of the relationships between
aLC
* /aLW
a * LC/aLW
PF*
Foreign wine
production, QW,
in gallons
L*/aLW
L*/aLC Foreign cheese
production, QC,
in pounds
P*
*
*
*
* F*
Figure 3-2
Foreign’s Production Possibility
Frontier
Because Foreign’s relative unit
labor requirement in cheese is
higher than Home’s (it needs to
give up many more units of wine
to produce one more unit of
cheese), its production possibility
frontier is steeper.
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 31
markets (in our example, the markets for wine and cheese). Since Home exports cheese only
in return for imports of wine, and Foreign exports wine in return for cheese, it can be misleading
to look at the cheese and wine markets in isolation. What is needed is general
equilibrium analysis, which takes account of the linkages between the two markets.
One useful way to keep track of two markets at once is to focus not just on the quantities
of cheese and wine supplied and demanded but also on the relative supply and
demand, that is, on the number of pounds of cheese supplied or demanded divided by the
number of gallons of wine supplied or demanded.
Figure 3-3 shows world supply and demand for cheese relative to wine as functions of
the price of cheese relative to that of wine. The relative demand curve is indicated by
RD; the relative supply curve is indicated by RS. World general equilibrium requires that
relative supply equal relative demand, and thus the world relative price is determined by
the intersection of RD and RS.
The striking feature of Figure 3-3 is the funny shape of the relative supply curve RS: It’s
a “step” with flat sections linked by a vertical section. Once we understand the derivation
of the RS curve, we will be almost home-free in understanding the whole model.
First, as drawn, the RS curve shows that there would be no supply of cheese if the world
price dropped below . To see why, recall that we showed that Home will specialize
in the production of wine whenever . Similarly, Foreign will specialize
in wine production whenever . At the start of our discussion of equation
(3-2), we made the assumption that . So at relative prices of cheese
below , there would be no world cheese production.
Next, when the relative price of cheese is exactly , we know that workers
in Home can earn exactly the same amount making either cheese or wine. So Home
will be willing to supply any relative amount of the two goods, producing a flat section to
the supply curve.
We have already seen that if is above , Home will specialize in the production
of cheese. As long as PC/PW 6 aLC , however, Foreign will continue to specialize in
* /aLW
*
PC/PW aLC/aLW
PC/PW aLC/aLW
aLC/aLW
aLC/aLW 6 aLC
* /aLW
*
PC/PW 6 aLC
* /aLW
*
PC/PW 6 aLC/aLW
aLC/aLW
Relative price
of cheese, PC/PW
aLC /aLW
L /aLC Relative quantity
of cheese,
RD
*
RD
L*/aLW *
Q
*
aLC /aLW
QC + QC
QW +QW *
1
2
RS
*
(2 in our
example)
(1/2 in our
example)
Figure 3-3
World Relative Supply and
Demand
The RD and RD¿ curves show that
the demand for cheese relative to
wine is a decreasing function of
the price of cheese relative to that
of wine, while the RS curve shows
that the supply of cheese relative
to wine is an increasing function
of the same relative price.
32 PART ONE International Trade Theory
producing wine. When Home specializes in cheese production, it produces pounds.
Similarly, when Foreign specializes in wine, it produces gallons. So for any relative
price of cheese between and , the relative supply of cheese is
(3-4)
At we know that Foreign workers are indifferent between producing
cheese and wine. Thus here we again have a flat section of the supply curve.
Finally, for , both Home and Foreign will specialize in cheese production.
There will be no wine production, so that the relative supply of cheese will
become infinite.
A numerical example may help at this point. Let’s assume, as we did before, that in
Home it takes one hour of labor to produce a pound of cheese and two hours to produce
a gallon of wine. Meanwhile, let’s assume that in Foreign it takes six hours to
produce a pound of cheese—Foreign workers are much less productive than Home
workers when it comes to cheesemaking—but only three hours to produce a gallon
of wine.
In this case, the opportunity cost of cheese production in terms of wine is 1/2 in Home—
that is, the labor used to produce a pound of cheese could have produced half a gallon of
wine. So the lower flat section of RS corresponds to a relative price of 1/2.
Meanwhile, in Foreign the opportunity cost of cheese in terms of wine is 2: The six
hours of labor required to produce a pound of cheese could have produced two gallons of
wine. So the upper flat section of RS corresponds to a relative price of 2.
The relative demand curve RD does not require such exhaustive analysis. The downward
slope of RD reflects substitution effects. As the relative price of cheese rises,
consumers will tend to purchase less cheese and more wine, so the relative demand for
cheese falls.
The equilibrium relative price of cheese is determined by the intersection of the relative
supply and relative demand curves. Figure 3-3 shows a relative demand curve RD
that intersects the RS curve at point 1, where the relative price of cheese is between the
two countries’ pretrade prices—say, at a relative price of 1, in between the pretrade prices
of 1/2 and 2. In this case, each country specializes in the production of the good in which
it has a comparative advantage: Home produces only cheese, while Foreign produces
only wine.
This is not, however, the only possible outcome. If the relevant RD curve were , for
example, relative supply and relative demand would intersect on one of the horizontal sections
of RS. At point 2 the world relative price of cheese after trade is , the same as
the opportunity cost of cheese in terms of wine in Home.
What is the significance of this outcome? If the relative price of cheese is equal to
its opportunity cost in Home, the Home economy need not specialize in producing
either cheese or wine. In fact, at point 2 Home must be producing both some wine and
some cheese; we can infer this from the fact that the relative supply of cheese (point
on the horizontal axis) is less than it would be if Home were in fact completely specialized.
Since is below the opportunity cost of cheese in terms of wine in Foreign,
however, Foreign does specialize completely in producing wine. It therefore remains
true that if a country does specialize, it will do so in the good in which it has a comparative
advantage.
For the moment, let’s leave aside the possibility that one of the two countries does not
completely specialize. Except in this case, the normal result of trade is that the price of a
PC/PW
Qoe
aLC/aLW
RDoe
PC/PW 7 aLC
* /aLW
*
PC/PW = aLC
* /aLW
* ,
1L/aLC2/1L*/aLW
* 2.
aLC
* /aLW
a * LC/aLW
L*/aLW
*
L/aLC
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 33
traded good (e.g., cheese) relative to that of another good (wine) ends up somewhere in
between its pretrade levels in the two countries.
The effect of this convergence in relative prices is that each country specializes in the production
of that good in which it has the relatively lower unit labor requirement. The rise in the
relative price of cheese in Home will lead Home to specialize in the production of cheese, producing
at point F in Figure 3-4a. The fall in the relative price of cheese in Foreign will lead
Foreign to specialize in the production of wine, producing at point F* in Figure 3-4b.
Comparative Advantage in Practice: The Case of Babe Ruth
Everyone knows that Babe Ruth was the greatest slugger
in the history of baseball. Only true fans of the
sport know, however, that Ruth also was one of the
greatest pitchers of all time. Because Ruth stopped
pitching after 1918 and played outfield during all the
time he set his famous batting records, most people
don’t realize that he even could
pitch. What explains Ruth’s lopsided
reputation as a batter? The
answer is provided by the principle
of comparative advantage.
As a player with the Boston
Red Sox early in his career, Ruth
certainly had an absolute advantage
in pitching. According to
historian Geoffrey C. Ward and
filmmaker Ken Burns:
In the Red Sox’s greatest
years, he was their greatest
player, the best left-handed
pitcher in the American League,
winning 89 games in six seasons. In 1916 he
got his first chance to pitch in the World Series
and made the most of it. After giving up a run
in the first, he drove in the tying run himself,
after which he held the Brooklyn Dodgers
scoreless for eleven innings until his teammates
could score the winning run. . . . In the
1918 series, he would show that he could still
handle them, stretching his series record to
scoreless innings, a mark that stood for
forty-three years.*
The Babe’s World Series pitching record was
broken by New York Yankee Whitey Ford in the
same year, 1961, that his teammate Roger Maris
shattered Ruth’s 1927 record of
60 home runs in a single season.
Although Ruth had an absolute
advantage in pitching, his skill as
a batter relative to his teammates’
abilities was even greater: His
comparative advantage was at the
plate. As a pitcher, however, Ruth
had to rest his arm between
appearances and therefore could
not bat in every game. To exploit
Ruth’s comparative advantage,
the Red Sox moved him to center
field in 1919 so that he could bat
more frequently.
The payoff to having Ruth
specialize in batting was huge. In 1919, he hit 29
home runs, “more than any player had ever hit in a
single season,” according to Ward and Burns. The
Yankees kept Ruth in the outfield (and at the plate)
after they acquired him in 1920. They knew a good
thing when they saw it. That year, Ruth hit 54 home
runs, set a slugging record (bases divided by at bats)
that remains untouched to this day, and turned the
Yankees into baseball’s most renowned franchise.
292/3
*See Geoffrey C. Ward and Ken Burns, Baseball: An Illustrated History (New York: Knopf, 1994), p. 155. Ruth’s career preceded
the designated hitter rule, so American League pitchers, like National League pitchers today, took their turns at bat. For a
more extensive discussion of Babe Ruth’s relation to the comparative advantage principle, see Edward Scahill, “Did Babe Ruth
Have a Comparative Advantage as a Pitcher?” Journal of Economic Education 21(4), Fall 1990, pp. 402–410.
34 PART ONE International Trade Theory
The Gains from Trade
We have now seen that countries whose relative labor productivities differ across industries
will specialize in the production of different goods. We next show that both countries
derive gains from trade from this specialization. This mutual gain can be demonstrated in
two alternative ways.
The first way to show that specialization and trade are beneficial is to think of trade as
an indirect method of production. Home could produce wine directly, but trade with
Foreign allows it to “produce” wine by producing cheese and then trading the cheese for
wine. This indirect method of “producing” a gallon of wine is a more efficient method
than direct production.
Consider our numerical example yet again: In Home, we assume that it takes one hour
to produce a pound of cheese and two hours to produce a gallon of wine. This means that
the opportunity cost of cheese in terms of wine is 1/2. But we know that the relative price
of cheese after trade will be higher than this, say 1. So here’s one way to see the gains
from trade for Home: Instead of using two hours of labor to produce a gallon of wine, it
can use that labor to produce two pounds of cheese, and trade that cheese for two gallons
of wine.
More generally, consider two alternative ways of using an hour of labor. On one side,
Home could use the hour directly to produce gallons of wine. Alternatively, Home
could use the hour to produce pounds of cheese. This cheese could then be traded
for wine, with each pound trading for gallons, so our original hour of labor yields
gallons of wine. This will be more wine than the hour could have
produced directly as long as
International trade allows Home and Foreign to consume anywhere within the colored lines,
which lie outside the countries’ production frontiers.
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 35
(3-5)
or
But we just saw that in international equilibrium, if neither country produces both goods,
we must have . This shows that Home can “produce” wine more efficiently
by making cheese and trading it than by producing wine directly for itself.
Similarly, Foreign can “produce” cheese more efficiently by making wine and trading it.
This is one way of seeing that both countries gain.
Another way to see the mutual gains from trade is to examine how trade affects each
country’s possibilities for consumption. In the absence of trade, consumption possibilities
are the same as production possibilities (the solid lines PF and in Figure 3-4). Once
trade is allowed, however, each economy can consume a different mix of cheese and wine
from the mix it produces. Home’s consumption possibilities are indicated by the colored
line TF in Figure 3-4a, while Foreign’s consumption possibilities are indicated by in
Figure 3-4b. In each case, trade has enlarged the range of choice, and therefore it must
make residents of each country better off.
A Note on Relative Wages
Political discussions of international trade often focus on comparisons of wage rates in
different countries. For example, opponents of trade between the United States and
Mexico often emphasize the point that workers in Mexico are paid only about $2 per hour,
compared with more than $15 per hour for the typical worker in the United States. Our
discussion of international trade up to this point has not explicitly compared wages in the
two countries, but it is possible in the context of our numerical example to determine how
the wage rates in the two countries compare.
In our example, once the countries have specialized, all Home workers are employed
producing cheese. Since it takes one hour of labor to produce one pound of cheese, workers
in Home earn the value of one pound of cheese per hour of their labor. Similarly,
Foreign workers produce only wine; since it takes three hours for them to produce each
gallon, they earn the value of 1/3 of a gallon of wine per hour.
To convert these numbers into dollar figures, we need to know the prices of cheese and
wine. Suppose that a pound of cheese and a gallon of wine both sell for $12; then Home workers
will earn $12 per hour, while Foreign workers will earn $4 per hour. The relative wage of a
country’s workers is the amount they are paid per hour, compared with the amount workers in
another country are paid per hour. The relative wage of Home workers will therefore be 3.
Clearly, this relative wage does not depend on whether the price of a pound of cheese is
$12 or $20, as long as a gallon of wine sells for the same price. As long as the relative price
of cheese—the price of a pound of cheese divided by the price of a gallon of wine—is 1, the
wage of Home workers will be three times that of Foreign workers.
Notice that this wage rate lies between the ratios of the two countries’ productivities in
the two industries. Home is six times as productive as Foreign in cheese, but only one-and-ahalf
times as productive in wine, and it ends up with a wage rate three times as high as
Foreign’s. It is precisely because the relative wage is between the relative productivities that
each country ends up with a cost advantage in one good. Because of its lower wage rate,
Foreign has a cost advantage in wine even though it has lower productivity. Home has a cost
advantage in cheese, despite its higher wage rate, because the higher wage is more than
offset by its higher productivity.
T*F*
P*F*
PC/PW 7 aLC/aLW
PC/PW 7 aLC/aLW.
11/aLC21PC/PW2 7 1/aLW,
36 PART ONE International Trade Theory
We have now developed the simplest of all models of international trade. Even though
the Ricardian one-factor model is far too simple to be a complete analysis of either the
causes or the effects of international trade, a focus on relative labor productivities can be a
very useful tool for thinking about trade issues. In particular, the simple one-factor model
is a good way to deal with several common misconceptions about the meaning of comparative
advantage and the nature of the gains from free trade. These misconceptions appear
so frequently in public debate about international economic policy, and even in statements
by those who regard themselves as experts, that in the next section we take time out to discuss
some of the most common misunderstandings about comparative advantage in light
of our model.
The Losses from Nontrade
Our discussion of the gains from trade took the
form of a “thought experiment” in which we
compared two situations: one in which countries
do not trade at all and another in which they have
free trade. It’s a hypothetical case that helps us
to understand the principles of international
economics, but it does not have much to do with
actual events. After all, countries don’t suddenly
go from no trade to free trade or vice versa. Or
do they?
As economic historian
Douglas Irwin* has pointed out,
in the early history of the United
States the country actually did
carry out something very close to
the thought experiment of moving
from free trade to no trade.
The historical context was as follows:
In the early 19th century
Britain and France were engaged
in a massive military struggle, the Napoleonic
Wars. Both countries endeavored to bring economic
pressures to bear: France tried to keep European
countries from trading with Britain, while Britain
imposed a blockade on France. The young United
States was neutral in the conflict but suffered considerably.
In particular, the British navy often
seized U.S. merchant ships and, on occasion,
forcibly recruited their crews into its service.
In an effort to pressure Britain into ceasing these
practices, President Thomas Jefferson declared a
complete ban on overseas shipping. This embargo
would deprive both the United States and Britain of
the gains from trade, but Jefferson hoped that
Britain would be hurt more and would agree to stop
its depredations.
Irwin presents evidence suggesting that the embargo
was quite effective: Although some smuggling
took place, trade between the United States
and the rest of the world was drastically reduced. In
effect, the United States gave up
international trade for a while.
The costs were substantial.
Although quite a lot of guesswork
is involved, Irwin suggests
that real income in the United
States may have fallen by about
8 percent as a result of the
embargo. When you bear in mind
that in the early 19th century only
a fraction of output could be
traded—transport costs were still too high, for
example, to allow large-scale shipments of commodities
like wheat across the Atlantic—that’s a
pretty substantial sum.
Unfortunately for Jefferson’s plan, Britain did
not seem to feel equal pain and showed no inclination
to give in to U.S. demands. Fourteen months
after the embargo was imposed, it was repealed.
Britain continued its practices of seizing American
cargoes and sailors; three years later the two countries
went to war.
*Douglas Irwin, “The Welfare Cost of Autarky: Evidence from the Jeffersonian Trade Embargo, 1807–1809,” Review of
International Economics 13 (September 2005), pp. 631–645.
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