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Chapter 4
Technology and
International Income
Distribution: The
Ricardian Model
© 2007 Pearson Addison-Wesley.
All rights reserved
A One Factor Ricardian Model (cont.)
1.
Labor is the only resource important for production.
2.
Labor productivity varies across countries, usually due to
differences in technology, but labor productivity in each
country is constant across time.
3.
The supply of labor in each country is constant.
4.
Only two goods are important for production and
consumption: food and clothing.
5.
Labor Theory of Value: competition allows laborers to be
paid a “competitive” wage, a function of their productivity
and the price of the good that they can sell, and allows
laborers to work in the industry that pays the highest wage.
6.
Only two countries are modeled: domestic and foreign.
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A One Factor Ricardian Model (cont.)
• Because labor productivity is constant, define a unit
labor requirement as the constant number of hours
of labor required to produce one unit of output.

aLF is the unit labor requirement for food in the domestic
country. For example, if aLF = 2, then it takes 2 hours of
labor to produce one liter of food in the domestic country.

aLC is the unit labor requirement for clothing in the domestic
country. For example, if aLC = 1, then it takes 1 hour of labor
to produce one kg of clothing in the domestic country.

A high unit labor requirement means low labor productivity.
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A One Factor Ricardian Model (cont.)
• Because the supply of labor is constant,
denote the total number of labor hours
worked in the domestic country as a constant
number L.
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Production Possibilities
• The production possibility frontier (PPF) of an economy
shows the maximum amount of a goods that can be produced for
a fixed amount of resources.
• If QC represents the quantity of clothing produced and QW
represents the quantity of food produced, then the production
possibility frontier of the domestic economy has the equation:
aLCQC + aLFQF = L
Labor required for
each unit of
clothing
production
Total units
of clothing
production
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Labor required for
each unit of food
production
Total amount of
labor resources
Total units
of food
production
Production Possibilities (cont.)
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Production Possibilities (cont.)
aLCQC + aLFQF = L
• QC = L/aLC when QF = 0
• QF = L/aLF when QC = 0
• QF = L/aLF – (aLC /aLF )QC: the equation for the PPF, with a slope
equal to – (aLC /aLF )
• When the economy uses all of its resources, the opportunity cost
of clothing production is the quantity of food that is given up
(reduced) as QC increases: (aLC /aLF )
• When the economy uses all of its resources, the opportunity cost
is equal to the absolute value of the slope of the PPF, and it is
constant when the PPF is a straight line.
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The Ricardian Production Possibilities Schedule
• The slope is the ratio of labor coefficient aLC/aLF.
• Before International trade, the country produces and
consumes at A, with welfare level shown by the
indifference curve y0.
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The Ricardian Production Possibilities Schedule
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Production, Prices and Wages
• Let PC be the price of clothing and Pf be the price
of food.
• Because of competition,

hourly wages of clothing makers are equal to the market
value of the clothing produced in an hour: Pc /aLC

Price=Marginal cost=alc*W

hourly wages of food makers are equal to the market value of
the food produced in an hour: Pf /aLF
• Because workers like high wages, they will work in
the industry that pays a higher hourly wage.
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Production, Prices and Wages (cont.)
• If PC /aLC > Pf/aLF workers will make only clothing.

If PC /Pf > aLC /aLF workers will only make clothing.

The economy will specialize in clothing production if the
price of clothing relative to the price of food exceeds the
opportunity cost of producing clothing.
• If PC /aLC < Pf /aLF workers will make only food.

If Pf /PC > aLF /aLC workers will only make food.

The economy will specialize in food production if the price of
food relative to the price of clothing exceeds the opportunity
cost of producing food.
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Production, Prices and Wages (cont.)
• If the domestic country wants to consume both food
and clothing (in the absence of international trade),
relative prices must adjust so that wages are equal in
the food and clothing industries.

If PC /aLC = Pf /aLF workers will have no incentive to flock to
either the clothing industry or the food industry, thereby
maintaining a positive amount of production of both goods.

PC /Pf = aLC /aLF

Production (and consumption) of both goods occurs when
relative price of a good equals the opportunity cost of
producing that good.
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Trade in the Ricardian Model
• Suppose that the domestic country has a
comparative advantage in clothing production:
its opportunity cost of producing clothing is lower
than it is in the foreign country.
aLC /aLF < a*LC /a*LF
When the domestic country increases clothing production, it
reduces food production less than the foreign country does
because the domestic unit labor requirement of clothing
production is low compared to that of food production.

where “*” notates foreign country variables
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Figure 4.2 Free-Trade Equilibrium
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4-14
Free-Trade Equilibrium
• Autarky equilibrium: point A for home and point A* for
foreign.
• Equilibrium terms of trade are the slope of dashed lines.
• Free trade: Home produces at E and consumes at B.
• Free trade: Foreign produces at E* and consumes at B*.
• Each country gains from trade.
• The trade triangles match.
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4-15
Country Size
• Does the assumption of constant labor costs necessarily
require each country to become completely specified with
trade?
• No.
• Country size matters.
• Two countries, a large one and a small one, trade.
• The small one cannot provide the good that it has comparative
advantage for the entire large (American) market.
• The states has to produce both goods.
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4-16
Figure 4.2 Free-Trade Equilibrium
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4-17
Figure 4.3 The World Transformation
Schedule
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4-18
World Production Possibilities
• Home has comparative advantage in clothing. If the world
wants to produce clothing, it should be first off the mark.
• Foreign enticed to do so only if the world relative price of
clothing reaches the height of its cost ratio, shown by the
world PPF.
• Point A adds up the maximum possible food output and point
C does the analogous job for clothing production.
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4-19
Trade in the Ricardian Model (cont.)
• Suppose the domestic country is more efficient in
food and clothing production.
• It has an absolute advantage in all production: its unit
labor requirements for food and clothing production
are lower than those in the foreign country:

aLC < a*LC and aLF < a*LF
• A country can be more efficient in producing both
goods, but it will have a comparative advantage in
only one good—the good that uses resources most
efficiently compared to alternative production.
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Trade in the Ricardian Model (cont.)
• Even if a country is the most (or least) efficient
producer of all goods, it still can benefit from trade.
• To see how all countries can benefit from trade, we
calculate relative prices when trade exists.

Without trade, relative price of a good equals the opportunity
cost of producing that good.
• To calculate relative prices with trade, we first
calculate relative quantities of world production:
(QC + Q*C )/(QW + Q*W)
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Relative Supply and Relative Demand
• Next we consider relative supply of clothing: the
quantity of clothing supplied by all countries relative to
the quantity of food supplied by all countries at each
relative price of clothing, Pc /PF.
• It is world relative price.
• Fix unit labor requirement, but allow price to move to
see the response of quantity.
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Relative Supply
Relative Price of clothing, Pc/Pf
alc/aLF
Rela. Supply yc+yc*/(yf+yf*)
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Relative Supply and Relative Demand (cont.)
• There is no supply of clothing if the relative price of
clothing falls below aLC /aLF .

Why? because the domestic country will specialize in food
production whenever PC /Pf < aLC /aLF

And we assumed that aLC /aLF < a*LC /a*LF so foreign workers
won’t find it desirable to produce clothing either.
• When PC /Pf = aLC /aLF , domestic workers will be
indifferent between producing food or clothing, but
foreign workers will still produce only food.
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Relative Supply
Relative Price of clothing, Pc/Pf
alc/aLF
Rela. Supply yc+yc*/(yf+yf*)
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Relative Supply and Relative Demand (cont.)
• When a*LC /a*LF > Pc / Pf > aLC /aLF , domestic workers
specialize in clothing production because they can
earn higher wages, but foreign workers will still
produce only food.
• When a*LC /a*LF = PC / Pf, foreign workers will be
indifferent between producing food or clothing, but
domestic workers will still produce only clothing.
• There is no supply of food if the relative price of
clothing rises above a*LC /a*LF
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Relative Supply
Relative Price of clothing, Pc/Pf
alc*/aLF*
alc/aLF
(L/alc)/(L*/aLF*)
Rela. Supply yc+yc*/(yf+yf*)
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Relative Supply and Relative Demand
(cont.)
Relative price
of clothing, PC/Pf
a*LC/a*LF
RS
aLC/aLF
L/aLC
L*/a*LF
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Relative quantity
of clothing, QC + Q*C
QW + Q*W
Relative Supply and Relative Demand (cont.)
• Relative demand of clothing is the quantity of clothing
demanded in all countries relative to the quantity of
food demanded in all countries at each relative price
of clothing, PC /Pf.
• As the relative price of clothing rises, consumers in all
countries will tend to purchase less clothing and more
food so that the relative quantity of clothing
demanded falls.
• Key assumption: the two countries shared the same
(homothetic) taste pattern.
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Relative Supply and Relative Demand
(cont.)
Relative price
of clothing, PC/Pf
a*LC/a*LF
RS
1
RD
aLC/aLF
L/aLC
L*/a*LF
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Relative quantity
of clothing, QC + Q*C
Q W + Q*W
Relative Supply
and Relative Demand (cont.)
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Figure 4.4 The World Market for Food
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The World Market for Food
• At point A, Foreign specifies to produce L*/alf*, which
corresponds to point B in Figure 4.3.
• At point B, both countries produce food only, therefore the
total production is fixed here.
• Suppose the equilibrium is point J’, then foreign produces both
clothing and food whereas home still produces clothing.
• Therefore, at J’, the production of food reduces. We get the
point in J on the world PPF in Figure 4.3.
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4-33
Figure 4.3 The World Transformation
Schedule
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4-34
Wages and Productivity
• The Perfect Competitive Profit Conditions:
• Unit costs may exceed price, but only if all producers leave the
industry.
• Unit costs cannot lower than price due to the free entry.
• If unit costs lower than price, the consequent profits would
signal new entrants into the industry.
• 1 /aLC , and 1/ aLF denote both labor’s average product and its
marginal product.
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4-35
Wages and Productivity
• In any industry with positive output, the wage rate must equal
the value of labor’s (average or marginal) productivity.
• In any industry forced to shut down because of international
competition, it is because the prevailing wage rate would
exceed the value of labor’s productivity.
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4-36
International Wage Comparisons
• Home country exports clothing.
• Suppose the world relative price of clothing is so low and even
the home produce food as well (like point B in Figure 4.4).
• No production at clothing.
• What happens for wages at home?
• If foreign worker is twice productive than home workers in
producing food, then foreign worker earns twice.
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4-37
International Wage Comparisons
• Suppose the world relative price of clothing lies between the
cost ratios in the two countries
• Now the wage ratio reflects (1) the productivity of labor force,
and (2) terms of exchange between commodity as well.
• Suppose the world relative price of clothing is so high so that
home and foreign produce clothing:
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4-38
Figure 4.5 Relative Wages and the Terms of
Trade
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4-39
Do Wages Reflect Productivity?
• In the Ricardian model, relative wages reflect
relative productivities of the two countries.
• Is this an accurate assumption?
• Some argue that low wage countries pay low
wages despite growing productivity, putting
high wage countries at a cost disadvantage.
• But evidence shows that low wages are
associated with low productivity.
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Do Wages Reflect Productivity? (cont.)
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Do Wages Reflect Productivity? (cont.)
• Other evidence shows that wages rise as
productivity rises.

In 2000, South Korea’s labor productivity was 35%
of the US level and its average wages were about
38% of US average wages.

After the Korean War, South Korea was one of the
poorest countries in the world, and its labor
productivity was very low. In 1975, average
wages in South Korea were still only 5% of US
average wages.
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International Wage Comparisons
• If the terms of trade lie strictly between the cost ratios in the
two countries, an improvement in the home terms of trade has
a proportionally favorable effect on the home relative wage.
• If the terms of trade allow both countries to produce the same
commodity, relative wages reflect labor’s productivity in this
commodity.
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4-43
Winners/Losers from Productivity Shocks
•
•
•
•
•
From autarky to trade, each country gains.
But it is not necessarily true for the increased globalization.
Unskilled labor problem in advanced countries.
Environmental problem.
Ricardian model is not good enough to analyze winners and
losers within one country.
• But it is ideal to consider how growth (say, productivity
change) affect the international distribution of income.
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4-44
Winners/Losers from Productivity Shocks
• The productivity improvement for a commodity in a trading
country has three possible consequences:
– Both countries might gain
– The country that experiences the productivity shock might lose
– The other country might lose.
• Consider case 1 now.
• U.S. produces the first 14 commodities and China produces
the rest of the goods from 16.
• Both countries produce 15th good.
• The commodities are ranked by their relative costs.
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4-45
Both countries might gain
• Suppose China develops a superior technology in good 20th,
which does not change the rank of commodities by
comparative advantage.
• Normalize the 15th good’s price as a unity to fix the nominal
wage in each country.
• The price of commodity must fall due to its productivity
improvement (i.e., the supply curve shifts to the right).
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4-46
Both countries might gain
• In sector 20th, the real wage increases due to a fall of its price.
• But the real wage at Home should equal across sectors to
avoid the possible arbitrage.
• Therefore, in sector 15th, the real wage must increase.
• But this implies the real wage must increase in foreign country
as well.
• Therefore, both countries gain since wage income is the only
source of income.
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4-47
Some country might lose
• When no commodity produced in common, the nominal wage
is different from each other.
• Same story but good 15th now is produced in China.
• For the U.S., consider an aggregate price index for those 14
types of goods.
• Its supply is vertical since the American labor force is assumed
fixed and fully employed.
• After the production shock, if world real incomes increase, this
would ship the aggregate demand curve to the right (income
effect).
• But the substitution effect caused by the technological shock of
good 20th might shift the aggregated demand curve left.
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4-48
Figure 4.6 Technological Progress
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4-49
Some country might lose
• If the substitution effect is dominated by the income effect,
then the demand shifts right, ends up with a higher price Pa.
• If Pa increases very much, it leads to a strong deterioration of
TOT for China.
• Immiserizing growth happens in China.
• China loses!
• The reverse situation could happen for the U.S.
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4-50
Figure 3.3 Immiserizing Growth
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4-51
Comparative Advantage
With Many Goods (cont.)
• Goods will be produced wherever it is cheaper to
produce them.
• Let w represent the wage rate in the domestic country
and w* represent the wage rate in the foreign country.

If waL1 < w*a*L1 then only the domestic country will produce
good 1, since total wage payments are less there.

Or equivalently, if a*L1 /aL1 > w/w*

If the relative productivity of a country in producing a good is
higher than the relative wage, then the good will be produced
in that country.
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Comparative Advantage
With Many Goods (cont.)
• Suppose there are 5 goods produced in the
world:
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Comparative Advantage
With Many Goods (cont.)
• If w/w* = 3, the domestic country will produce
apples, bananas, and caviar, while the foreign
country will produce dates and enchiladas.

The relative productivities of the domestic country
in producing apples, bananas and caviar are
higher than the relative wage.
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Comparative Advantage
With Many Goods (cont.)
• If each country specializes in goods that use
resources productively and trades the products for
those that it wants to consume, then each benefits.

If a country tries to produce all goods for itself, resources
are “wasted”.
• The domestic country has high productivity in apples,
bananas, and caviar that give it a cost advantage,
despite its high wage.
• The foreign country has low wages that give it a cost
advantage, despite its low productivity in dates.
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Comparative Advantage
With Many Goods (cont.)
• How is the relative wage determined?
• By the relative supply and relative (derived) demand
for labor services.
• The relative (derived) demand for domestic labor
services falls when w/w* rises. As domestic labor
becomes more expensive relative to foreign labor,


goods produced in the domestic country become more
expensive, and demand for these goods and the labor to
produce them falls.
fewer goods will be produced in the domestic country, further
reducing the demand for domestic labor.
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Comparative Advantage
With Many Goods (cont.)
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Comparative Advantage
With Many Goods (cont.)
• Suppose w/w* increases from 3 to 3.99:

The domestic country would produce apples, bananas, and
caviar, but the demand for these goods and the labor to
produce them falls as the relative wage rises.
• Suppose w/w* increases from 3.99 to 4.01:

Caviar is now too expensive to produce in the domestic
country, so the caviar industry moves to the foreign country,
causing a discrete (abrupt) drop in the demand for
domestic labor.
• Consider similar effects as w/w* rises from 0.75 to 10.
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Comparative Advantage
With Many Goods (cont.)
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Comparative Advantage
With Many Goods (cont.)
• Finally, suppose that relative supply of labor is
independent of w/w* and is fixed at an amount
determined by the populations in the domestic
and foreign countries.
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Comparative Advantage
With Many Goods (cont.)
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Transportation Costs
and Non-traded Goods
•
The Ricardian model predicts that countries
should completely specialize in production.
•
But this rarely happens for primarily
3 reasons:
More than one factor of production reduces the
tendency of specialization
2. Protectionism
3. Transportation costs reduce or prevent trade,
which may cause each country to produce the
same good or service
1.
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Transportation Costs
and Non-traded Goods (cont.)
• Non-traded goods and services (e.g.,
haircuts and auto repairs) exist due to
high transportation costs.

Countries tend to spend a large fraction of national
income on non-traded goods and services.

This fact has implications for the gravity model and
for models that consider how income transfers
across countries affect trade.
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Empirical Evidence
• Do countries export those goods in which their
productivity is relatively high?
• The ratio of US to British exports in 1951
compared to the ratio of US to British labor
productivity in 26 manufacturing industries
suggests yes.
• At this time the US had an absolute
advantage in all 26 industries, yet the ratio of
exports was low in the least productive
sectors of the US.
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Empirical Evidence (cont.)
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Summary
1. A country has a comparative advantage in producing
a good if the opportunity cost of producing that good
is lower in the country than it is in other countries.

A country with a comparative advantage in producing a
good uses its resources most efficiently when it produces
that good compared to producing other goods.
2. The Ricardian model focuses only on differences in
the productivity of labor across countries, and it
explains gains from trade using the concept of
comparative advantage.
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Summary (cont.)
3.
When countries specialize and trade according to
the Ricardian model; the relative price of the
produced good rises, income for workers rises and
imported goods are less expensive for consumers.
4.
Trade is predicted to benefit both high productivity
and low productivity countries, although trade may
change the distribution of income within countries.
5.
High productivity or low wages give countries a cost
advantage that allow them to produce efficiently.
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Summary (cont.)
7. Although empirical evidence supports
trade based on comparative advantage,
transportation costs and other factors
prevent complete specialization
in production.
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