A One-Factor Economy
To introduce the role of comparative advantage in determining the pattern of international
trade, we begin by imagining that we are dealing with an economy—which we call
Home—that has only one factor of production. (In Chapter 4 we extend the analysis to
models in which there are several factors.) We imagine that only two goods, wine and
cheese, are produced. The technology of Home’s economy can be summarized by labor
productivity in each industry, expressed in terms of the unit labor requirement, the number
of hours of labor required to produce a pound of cheese or a gallon of wine. For example,
it might require one hour of labor to produce a pound of cheese, two hours to produce
a gallon of wine. Notice, by the way, that we’re defining unit labor requirements as the
1The classic reference is David Ricardo, The Principles of Political Economy and Taxation, first published
in 1817.
TABLE 3-1 Hypothetical Changes in Production
Million Roses Thousand Computers
United States - 10 + 100
Colombia + 10 - 30
Total 0 + 70
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 27
inverse of productivity—the more cheese or wine a worker can produce in an hour, the
lower the unit labor requirement. For future reference, we define and as the unit
labor requirements in wine and cheese production, respectively. The economy’s total
resources are defined as L, the total labor supply.
Production Possibilities
Because any economy has limited resources, there are limits on what it can produce, and
there are always trade-offs; to produce more of one good, the economy must sacrifice
some production of another good. These trade-offs are illustrated graphically by a
production possibility frontier (line PF in Figure 3-1), which shows the maximum
amount of wine that can be produced once the decision has been made to produce any
given amount of cheese, and vice versa.
When there is only one factor of production, the production possibility frontier of an
economy is simply a straight line. We can derive this line as follows: If is the
economy’s production of wine and its production of cheese, then the labor used in producing
wine will be , and the labor used in producing cheese will be . The
production possibility frontier is determined by the limits on the economy’s resources—in
this case, labor. Because the economy’s total labor supply is L, the limits on production are
defined by the inequality
(3-1)
Suppose, for example, that the economy’s total labor supply is 1,000 hours, and that it
takes 1 hour of labor to produce a pound of cheese and 2 hours of labor to produce a gallon
of wine. Then the total labor used in production is
, and this total must be no more than the 1,000 hours of
labor available. If the economy devoted all its labor to cheese production, it could, as shown
in Figure 3-1, produce pounds of cheese (1,000 pounds). If it devoted all its labor to
wine production instead, it could produce L/aLW gallons—1000/2 = 500 gallons—of wine.
L/aLC
And it can produce any mix of wine and cheese that lies on the straight line connecting
those two extremes.
When the production possibility frontier is a straight line, the opportunity cost of a
pound of cheese in terms of wine is constant. As we saw in the previous section, this
opportunity cost is defined as the number of gallons of wine the economy would have to
give up in order to produce an extra pound of cheese. In this case, to produce another
pound would require person-hours. Each of these person-hours could in turn have
been used to produce gallons of wine. Thus the opportunity cost of cheese in terms
of wine is . For example, if it takes one person-hour to make a pound of cheese
and two hours to produce a gallon of wine, the opportunity cost of each pound of cheese is
half a gallon of wine. As Figure 3-1 shows, this opportunity cost is equal to the absolute
value of the slope of the production possibility frontier.
Relative Prices and Supply
The production possibility frontier illustrates the different mixes of goods the economy
can produce. To determine what the economy will actually produce, however, we need to
look at prices. Specifically, we need to know the relative price of the economy’s two
goods, that is, the price of one good in terms of the other.
In a competitive economy, supply decisions are determined by the attempts of individuals
to maximize their earnings. In our simplified economy, since labor is the only factor of
production, the supply of cheese and wine will be determined by the movement of labor to
whichever sector pays the higher wage.
Suppose, once again, that it takes one hour of labor to produce a pound of cheese and
two hours to produce a gallon of wine. Now suppose further that cheese sells for $4 a
pound, while wine sells for $7 a gallon. What will workers produce? Well, if they produce
cheese they can earn $4 an hour. (Bear in mind that since labor is the only input into production
here, there are no profits, so workers receive the full value of their output.) On the
other hand, if workers produce wine, they will earn only $3.50 an hour, because a $7 gallon
of wine takes two hours to produce. So if cheese sells for $4 a pound while wine sells for $7
a gallon, workers will do better by producing cheese—and the economy as a whole will
specialize in cheese production.
But what if cheese prices drop to $3 a pound? In that case workers can earn more by
producing wine, and the economy will specialize in wine production instead.
More generally, let and be the prices of cheese and wine, respectively. It takes
person-hours to produce a pound of cheese; since there are no profits in our one-factor model,
the hourly wage in the cheese sector will equal the value of what a worker can produce in an
hour, . Since it takes person-hours to produce a gallon of wine, the hourly wage
rate in the wine sector will be . Wages in the cheese sector will be higher
if ; wages in the wine sector will be higher if
Because everyone will want to work in whichever industry offers the higher wage, the
economy will specialize in the production of cheese if . On the other
hand, it will specialize in the production of wine if . Only when
is equal to will both goods be produced.
What is the significance of the number ? We saw in the previous section that it
is the opportunity cost of cheese in terms of wine. We have therefore just derived a crucial
proposition about the relationship between prices and production: The economy will specialize
in the production of cheese if the relative price of cheese exceeds its opportunity
cost in terms of wine; it will specialize in the production of wine if the relative price of
cheese is less than its opportunity cost in terms of wine.
aLC /aLW
aLC /aLW
PC /PW 6 aLC /aLW PC /PW
PC /PW 7 aLC /aLW
PC /PW 7 aLC/aLW PC /PW 6 aLC /aLW.
PW/aLW
PC /aLC aLW
PC PW aLC
aLC /aLW
1/aLW
aLC
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 29
In the absence of international trade, Home would have to produce both goods for
itself. But it will produce both goods only if the relative price of cheese is just equal to its
opportunity cost. Since opportunity cost equals the ratio of unit labor requirements in
cheese and wine, we can summarize the determination of prices in the absence of international
trade with a simple labor theory of value: In the absence of international trade, the
relative prices of goods are equal to their relative unit labor requirements.
To introduce the role of comparative advantage in determining the pattern of international
trade, we begin by imagining that we are dealing with an economy—which we call
Home—that has only one factor of production. (In Chapter 4 we extend the analysis to
models in which there are several factors.) We imagine that only two goods, wine and
cheese, are produced. The technology of Home’s economy can be summarized by labor
productivity in each industry, expressed in terms of the unit labor requirement, the number
of hours of labor required to produce a pound of cheese or a gallon of wine. For example,
it might require one hour of labor to produce a pound of cheese, two hours to produce
a gallon of wine. Notice, by the way, that we’re defining unit labor requirements as the
1The classic reference is David Ricardo, The Principles of Political Economy and Taxation, first published
in 1817.
TABLE 3-1 Hypothetical Changes in Production
Million Roses Thousand Computers
United States - 10 + 100
Colombia + 10 - 30
Total 0 + 70
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 27
inverse of productivity—the more cheese or wine a worker can produce in an hour, the
lower the unit labor requirement. For future reference, we define and as the unit
labor requirements in wine and cheese production, respectively. The economy’s total
resources are defined as L, the total labor supply.
Production Possibilities
Because any economy has limited resources, there are limits on what it can produce, and
there are always trade-offs; to produce more of one good, the economy must sacrifice
some production of another good. These trade-offs are illustrated graphically by a
production possibility frontier (line PF in Figure 3-1), which shows the maximum
amount of wine that can be produced once the decision has been made to produce any
given amount of cheese, and vice versa.
When there is only one factor of production, the production possibility frontier of an
economy is simply a straight line. We can derive this line as follows: If is the
economy’s production of wine and its production of cheese, then the labor used in producing
wine will be , and the labor used in producing cheese will be . The
production possibility frontier is determined by the limits on the economy’s resources—in
this case, labor. Because the economy’s total labor supply is L, the limits on production are
defined by the inequality
(3-1)
Suppose, for example, that the economy’s total labor supply is 1,000 hours, and that it
takes 1 hour of labor to produce a pound of cheese and 2 hours of labor to produce a gallon
of wine. Then the total labor used in production is
, and this total must be no more than the 1,000 hours of
labor available. If the economy devoted all its labor to cheese production, it could, as shown
in Figure 3-1, produce pounds of cheese (1,000 pounds). If it devoted all its labor to
wine production instead, it could produce L/aLW gallons—1000/2 = 500 gallons—of wine.
L/aLC
And it can produce any mix of wine and cheese that lies on the straight line connecting
those two extremes.
When the production possibility frontier is a straight line, the opportunity cost of a
pound of cheese in terms of wine is constant. As we saw in the previous section, this
opportunity cost is defined as the number of gallons of wine the economy would have to
give up in order to produce an extra pound of cheese. In this case, to produce another
pound would require person-hours. Each of these person-hours could in turn have
been used to produce gallons of wine. Thus the opportunity cost of cheese in terms
of wine is . For example, if it takes one person-hour to make a pound of cheese
and two hours to produce a gallon of wine, the opportunity cost of each pound of cheese is
half a gallon of wine. As Figure 3-1 shows, this opportunity cost is equal to the absolute
value of the slope of the production possibility frontier.
Relative Prices and Supply
The production possibility frontier illustrates the different mixes of goods the economy
can produce. To determine what the economy will actually produce, however, we need to
look at prices. Specifically, we need to know the relative price of the economy’s two
goods, that is, the price of one good in terms of the other.
In a competitive economy, supply decisions are determined by the attempts of individuals
to maximize their earnings. In our simplified economy, since labor is the only factor of
production, the supply of cheese and wine will be determined by the movement of labor to
whichever sector pays the higher wage.
Suppose, once again, that it takes one hour of labor to produce a pound of cheese and
two hours to produce a gallon of wine. Now suppose further that cheese sells for $4 a
pound, while wine sells for $7 a gallon. What will workers produce? Well, if they produce
cheese they can earn $4 an hour. (Bear in mind that since labor is the only input into production
here, there are no profits, so workers receive the full value of their output.) On the
other hand, if workers produce wine, they will earn only $3.50 an hour, because a $7 gallon
of wine takes two hours to produce. So if cheese sells for $4 a pound while wine sells for $7
a gallon, workers will do better by producing cheese—and the economy as a whole will
specialize in cheese production.
But what if cheese prices drop to $3 a pound? In that case workers can earn more by
producing wine, and the economy will specialize in wine production instead.
More generally, let and be the prices of cheese and wine, respectively. It takes
person-hours to produce a pound of cheese; since there are no profits in our one-factor model,
the hourly wage in the cheese sector will equal the value of what a worker can produce in an
hour, . Since it takes person-hours to produce a gallon of wine, the hourly wage
rate in the wine sector will be . Wages in the cheese sector will be higher
if ; wages in the wine sector will be higher if
Because everyone will want to work in whichever industry offers the higher wage, the
economy will specialize in the production of cheese if . On the other
hand, it will specialize in the production of wine if . Only when
is equal to will both goods be produced.
What is the significance of the number ? We saw in the previous section that it
is the opportunity cost of cheese in terms of wine. We have therefore just derived a crucial
proposition about the relationship between prices and production: The economy will specialize
in the production of cheese if the relative price of cheese exceeds its opportunity
cost in terms of wine; it will specialize in the production of wine if the relative price of
cheese is less than its opportunity cost in terms of wine.
aLC /aLW
aLC /aLW
PC /PW 6 aLC /aLW PC /PW
PC /PW 7 aLC /aLW
PC /PW 7 aLC/aLW PC /PW 6 aLC /aLW.
PW/aLW
PC /aLC aLW
PC PW aLC
aLC /aLW
1/aLW
aLC
CHAPTER 3 Labor Productivity and Comparative Advantage: The Ricardian Model 29
In the absence of international trade, Home would have to produce both goods for
itself. But it will produce both goods only if the relative price of cheese is just equal to its
opportunity cost. Since opportunity cost equals the ratio of unit labor requirements in
cheese and wine, we can summarize the determination of prices in the absence of international
trade with a simple labor theory of value: In the absence of international trade, the
relative prices of goods are equal to their relative unit labor requirements.
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