Section 2: The Ricardian model

• Model assumptions:– 2 countries: home and foreign– 1 factor of production: labor – 2 goods: wheat and cloth– Constant marginal product of labor

• General concepts:– Autarky equilibrium– International trade equilibrium– Home export supply curve– Foreign import demand curve

1

Technology• Home technology

– Labor is the only factor used to produce both goods.– One worker can produce either 4 bushels of wheat or 2

yards of cloth.– The Marginal Product of Labor is the extra output

obtained by using one more unit of labor.– Notation: MPLW = 4 and MPLC = 2.

– Alternatively, the production of 1 unit of wheat requires ¼ worker and the production of 1 unit of cloth requires ½ worker.

– Notation: aW = 1/4 and aC = 1/2.

(ai are called unit input coefficients)2

Production possibilities

• Home Production Possibilities Frontier (PPF)– We can use the marginal products of labor to construct

Home’s PPF. – Assume Home is endowed with 25 workers.– If all the workers were employed in wheat, the economy

could produce 100 bushels.– If they were all employed in cloth, it could produce a

maximum of 50 yards. – The PPF connects these two points.– Key insight: A country’s PPF is determined by its labor

productivity and its labor endowment.3

Production possibilities

• Home’s production data is given by:– L = 25, MPLW = 4, MPLC = 2

– Maximum wheat output: QW = MPLW(L) = 4x25 = 100

– Maximum cloth output: QC = MPLC(L) = 2x25 = 50

• This gives us a straight line PPF which is a unique feature of the Ricardian model.– It assumes the marginal products of labor are constant.– We consider the case where the marginal product of labor

is diminishing in the specific-factors model in section 3.

Slope of PPF• The slope of the PPF can be calculated as the ratio of marginal

products of the two goods.• The slope also equals the opportunity cost of wheat—the

amount of cloth that must be given up to obtain one more unit of wheat.

2

1

)(

)(

100

50

W

C

W

C

MPL

MPL

LMPL

LMPLSlopePPF

Home PPF

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Demand

• Home Indifference Curve– Given Home’s PPF, how much wheat and cloth will

home actually produce? The answer depends on demand.

– Demand can be represented with indifference curves.

– An indifference curve shows the combinations of two goods that the country can consume and be equally satisfied.

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Home preferences

• All points on an indifference curve have the same level of utility.

• Points on higher indifference curves have higher utility.

• Indifference curves are often used to show the preferences of an individual.

• But we use indifference curves to show the preferences of an entire economy.

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Autarky (no-trade) equilibrium

The country is indifferent between A and B.

The country would be better off on U2, but C is not feasible to produce.

U0<U1<U2

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Autarky equilibrium• Autarky equilibrium (at home)

– Without trade, the consumption opportunities are constrained by the production opportunities.

– With perfectly competitive markets, the country will produce at its highest level of utility within the limits of the PPF.

– The highest level of utility that can be reached within the PPF is U1 with production taking place at point A.

– Key insight: under autarky, the economy’s production point must coincide with its consumption point.

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Autarky equilibrium• Equlibrium prices and wage rate

– Zero profit condition in wheat (price=marginal cost):PW = w aW (price = wage rate * labor units)

– Zero profit condition in cloth (price=marginal cost):PC = w aC (price = wage rate * labor units)

PW /PC = aW /aC = MPLC/MPLW

Key insight: relative autarky prices depend only on relative productivities and not at all on consumer preferences.

=> w= PWMPLW= PCMPLC

Workers are paid a common wage which equals the value of their marginal productivity in each sector.

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Foreign Economy

– Foreign Economy’s production possibilities• Assume one foreign worker can produce either one

bushel of wheat or one yard of cloth.• MPL*W = 1, MPL*C = 1 (a*W = 1, a*C = 1) • Since MPL*W <MPLW and MPL*C < MPLW , Foreign has

an absolute productivity disadvantage in each good.• Assume Foreign is endowed with 100 workers. • If all foreign, workers were employed in the wheat

sector, they could produce 100 bushels. • If all workers were employed in cloth sector, they could

produce a maximum of 100 yards.

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Foreign PPF

13

Foreign autarky equilibrium

– Foreign’s preferences are also represented by indifference curves and production occurs at the point of highest utility within the foreign PPF.

– The slope of the foreign PPF is also the foreign opportunity cost of wheat.

– Foreign’s relative price of wheat is P*W/P*C = 1 and exceeds Home’s relative price of wheat (PW/PC = ½)

– The difference in relative autarky prices comes from the comparative advantage that Home has in wheat.

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Foreign autarky equilibrium

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Opportunity costs (or real prices)

Cloth

(1 Yard)

Wheat

(1 Bushel)

Home 2 Bushels

of Wheat

½ Yard

of Cloth

Foreign 1 Bushel

of Wheat

1 Yard

of Cloth

Comparative advantage

• Comparative Advantage– A country has a comparative advantage in a good

when it has a lower opportunity cost of producing it than another country.

– From the Table we can see that Foreign has a comparative advantage in producing cloth as Foreign’s opportunity cost of cloth is lower (1<2).

– Home has a comparative advantage in producing wheat as its opportunity cost of wheat is lower (1/2<1).

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Determining the Pattern of International Trade

• Autarky price comparisons:– Relative price of cloth in Foreign is P*C/P*W = 1.

– Relative price of cloth in Home is PC/PW = 2.

– Foreign would want to export its cloth to Home—as it can make it for the cost of 1 and export it for more than 1.

– The opposite is true for wheat.– Home will export wheat and Foreign will export cloth.– Both countries export the good in which they have a

comparative advantage.

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Price changes as the result of trade

• How trade affects domestic prices:– As Home exports wheat, the quantity of wheat sold at

Home falls. So the price of wheat at Home is bid up.– Since more wheat goes into Foreign’s market, the price of

wheat in Foreign falls.– As Foreign exports cloth, the quantity sold in Foreign falls,

and the price in Foreign for cloth rises. – Since foreign cloth goes home, the price of cloth at Home

falls.

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Determining the Pattern of International Trade

• International Trade Equilibrium– The relative price of wheat in the trade equilibrium (or the

international terms of trade) will be between the autarky relative prices in Home and Foreign [This result has been established by J.S. Mill (1848), see section 1 lecture notes].

– For now we will assume the free-trade price of wheat, PW/PC ,is 2/3. This is between the autarky price of ½ in Home and the autarky price of 1 in Foreign.

– Given this free trade price of wheat, we can now see how trade changes production and consumption in each country.

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International Trade Equilibrium

– Two countries are in a trade equilibrium when:• the relative price of each good is the same in the

two countries • the amount of each good that the countries want to

trade is equal – In understanding the trade equilibrium we need to do

two things:• Determine the relative price of wheat or cloth in the

trade equilibrium.• See how the shift from the autarky to the trade

equilibrium affects production and consumption in both Home and Foreign.

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Change in Production and Consumption

– Home producers of wheat can earn more than the opportunity cost of wheat by selling it to Foreign.

– Home will therefore shift labor resources toward the production of wheat and increase its production.

– Remember wages are calculated by the price of the good times its marginal product.

– Given the information from before, we can calculate the wage rates in the two sectors.

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Labor Market Condition (Home)

• All Home workers have an incentive to move into the wheat sector and no cloth will be produced.

• With trade, Home will be fully specialized in wheat production.

2 4 81

3 2 6W W

C C

W W C C

P MPLP MPL

Therefore

P MPL P MPL

Wages in wheat Wages in cloth

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Terms of trade and increased consumption opportunities

– Home can export wheat at the international relative price (or terms of trade) of 2/3.

– For each bushel of wheat it exports, it gets 2/3 yards of cloth in return.

– The world price line (or terms of trade line) shows the range of consumption possibilities that the country can achieve by specializing in wheat and trading it.

– International trade allows to separate production (point B) from consumption (point C).

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Enhanced consumption opportunities

U2

World price line (terms of trade line), slope = –2/3

U1

A

50 100 Wheat, QW (bushels)

Cloth, QC (yards)

B

Home production

50

25

• The new world price, PW/PC = 2/3, shows us the new range of consumption possibilities

• The country can now achieve a higher utility with the new consumption possibilities

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Free trade equilibrium (Home)

Home imports 40 yards of cloth

Home exports 60 bushels of wheat

Home consumption

A

B

Home production

25

C40 World price line (terms of trade line), slope = –2/3 U2

U1

50 100 Wheat, QW (bushels)

Cloth, QC (yards)

50

100

Home produces 100 bushels but consumes only 40, so it exports 60

50

Home produces 0 yards of cloth but consumes 40, so it imports 40.

40

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Terms of trade

– From the previous figure we can also see that Home’s exports and imports are equal when valued in the same units.

– Home exports 60 bushels of wheat; multiplying this by the price of wheat in terms of cloth, 2/3, gives 40. This equals the amount of cloth that is imported.

– Now consider Foreign.

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Free trade equilibrium (Foreign)

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Comparative advantage and the gains from trade

– Each country exports the good where it has a comparative advantage. This confirms that the pattern of trade is determined by comparative advantage.

– There are gains from trade for the home and the foreign economy

– The gains from trade can be captured in several ways:• Each country reaches a higher utility level (utilitarian

formulation).• Each country enlarges its consumption opportunities

(utility free formulation).• Workers receive higher real wages.

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Real wages in the trade equilibrium

– As stated before, in competitive labor markets, firms will pay workers the value of their marginal product.

– Since Home produces and exports wheat, workers can be thought of being paid in wheat. As 1 unit of labor produces 4 bushels of wheat, the real wage of home workers is MPLW (= 4 bushels of wheat).

– Workers can sell wheat on the world market at a relative price of PW/PC = 2/3.

– We can use this to calculate their real wage in terms of cloth: (PW/PC)MPLW = (2/3)4 = 8/3 yards.

– Through trade, 1 unit of labor is able to buy 8/3 yards.

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Real wages in the trade equilibrium– Home real wage is

• 4 bushels of wheat or• 8/3 yards of cloth (> 2, the autarky level)

– Foreign real wage is• 1 yard of cloth or• 3/2 bushels of wheat (>1, the autarky level)

(since(PC/PW) MPL*C = (3/2)1 = 3/2)

– Trade leads to an increase in real wages in both countries, but the real wages do not converge.

– Home workers earn a higher real wage than foreign workers because of their absolute productivity advantage.

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Key insight: Real wages in the trade equilibrium

• Wages are determined by absolute advantage and trade is determined by comparative advantage.– The only way a country with poor technology can export at

a price others are willing to pay is by having low wages.• As a country develops better technologies, its wages will rise.

– Workers become better off by receiving higher wages.– As countries engage in trade, the Ricardian model predicts

that their real wages will rise.

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Application 1: Labor productivity and wages

• Labor productivity can be measured by the value-added per hour in manufacturing.– Value-added is the difference between sales revenue in an industry

and the costs of intermediate inputs.– Equals the payments to labor and capital in an industry.– The Ricardian model ignores capital so we can measure labor

productivity as value-added divided by the number of hours worked, or value-added per hour.

• The next figures show value-added per hour in manufacturing for several countries.– Countries with higher labor productivity pay higher wages, just as the

Ricardian model predicts.

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Application 1: Labor productivity and wages

Labor Productivity and Wages, 2001

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Application 1: Labor productivity and wages

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Application 2: Comparative advantage in apparel, textiles, and wheat

• U.S. Textile and apparel industries face intense import competition.

• Burlington Industries announced in January 1999 it would reduce production capacity by 25% due to increased imports from Asia.

• After layoffs they employed 17,400 persons in the U.S. with sales of $1.6 billion in 1999.

• Sales per employee were therefore $92,000.• This is the average for all U.S. apparel producers.• Textiles are even more productive with annual sales per

employee of $140,000 in the U.S.

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Application 2: Comparative advantage in apparel, textiles and wheat

• In China, however, sales per employee are only $13,500 in apparel and $9,000 in textiles.

• The U.S. is 7 times more productive in apparel and 16 times more productive in textiles.

• So the U.S. has an absolute productivity advantage in these industries.

• In the wheat sector, the U.S. produces 27.5 bushels of wheat per hour of labor.

• China produces only 0.1 bushels of wheat per hour of labor.• So the US has also an absolute productivity advantage in wheat.• But it is 275 times more productive in wheat than China.

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Application 2: Comparative advantage in apparel, textiles, and wheat

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Application 2: Comparative advantage in apparel, textiles and wheat

• Since the absolute advantage in wheat for the U.S. is even greater than in apparel and textiles, the US has a comparative advantage in the production of wheat.

• China has a comparative advantage in apparel and textiles because its productive disadvantage relative to the U.S. is less than in wheat.

• This explains why the U.S. imports apparel and textiles from China despite its higher productivity.

• The also explains why the US is an exporter of wheat.

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International equilibrium: Determination of the terms of trade

• In the previous analysis we assumed that the relative price of wheat, or the terms of trade was given by 2/3. Now we investigate what determines the terms of trade.

• The terms of trade is determined by export supply and import demand.• There are two international markets for wheat and cloth. But since only

relative prices matter, it is sufficient to look only at the international equilibrium in one market. So we can just focus on the export supply and import demand in the wheat market.

• According to Walras’ law, which is a key general equilibrium insight, if the international market for wheat is in equilibrium, then the market for cloth has to be in equilibrium also.

• export supply = excess supply (domestic supply - domestic demand)• import demand = excess demand (domestic demand - domestic supply)

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Home export supply curve• Derivation of the Home export supply curve

– The home excess supply of wheat Xw (horizontal axis) will depend on the relative price of wheat Pw/Pc (vertical axis).

– At Pw/Pc=2/3, Xw=60 (=100-40). (points C and C’)– At Pw/Pc=1/2, Xw=0 (=50-50) (points A and A’) which is the autarky

equilibrium– However, if Pw/Pc=1/2 and trade is allowed, workers earn the same

wage in wheat and cloth and production can be at any point between A and B on the Home PPF => Xw can take any value between 0 and 50 (horizontal segment).

– The flat portion of the export supply curve is a special feature of the Ricardian model.

– Export supply Xw will increase in Pw/Pc (domestic production will stay the same, but domestic consumption will fall).

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Export supply curve (Home)

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Foreign import demand curve

• Derivation of the Foreign import demand curve– The foreign excess demand for wheat Mw (horizontal axis) will also

depend on the relative price of wheat Pw/Pc (vertical axis).– At Pw/Pc=2/3, Mw=60 (=60-0) (points C* and C*’)– At Pw/Pc=1/2, Mw=0 (=50-50) (points A* and A*’) which is the autarky

equilibrium– However, if Pw/Pc=1/2 and trade is allowed, workers earn the same

wage in wheat and cloth and production can be at any point between A* and B* on the Foreign PPF => Mw can take any value between 0 and 50 (horizontal segment).

– The flat portion of the import demand curve is also a special feature of the Ricardian model.

– Import demand Mw will decrease in Pw/Pc (domestic production will stay the same, but domestic consumption will fall).

43

Import demand curve (Foreign)

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International trade equilibrium

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International trade equilibrium– The export supply and import demand curves are both general

equilibrium concepts. If international prices change, this will affect the behavior of producers and consumers in the wheat and cloth market.

– The export supply curve captures the behavior of producers and consumers in the home country (i.e. the exporter of wheat).

– The import demand curve captures the behavior of producers and consumers in the foreign country (i.e. the importer of wheat).

– At the international equilibrium price all markets are balanced.– Because only relative prices matter for producers and consumers, we

only needed to focus on the market for one good. Walras’ law implies that if there are 2 markets, if the first market is in equilibrium than the second market must also be in equilibrium.

– The analysis has also demonstrated that the market clearing international price must lie between the autarky prices (i.e. 1<2/3<2).

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Terms of trade and the distribution of the gains from trade

– The terms of trade is defined as the price of a country’s exports divided by the price of its imports.

– For Home, PW/PC is their terms of trade.

– An increase in PW or a fall in PC will raise Home’s terms of trade.

– An increase in the terms of trade is welfare improving since• the country will either earn more from its exports or• the country will pay less for its imports.

– Although both countries will benefit from international trade, the terms of trade will determine how the gains from trade are distributed across countries.

– Changes in the terms of trade have different welfare effects on exporting and importing countries (see Application 3).

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Application 3: The Terms of Trade for Primary Commodities

• Latin American economist Raúl Prebisch and British economist Hans Singer each put forward the hypothesis that the price of primary commodities would decline over time relative to the price of manufactured goods (Prebisch-Singer Hypothesis).

• Since primary commodities are often exported by developing countries whereas industrial countries export manufactured goods, this hypothesis has received quite a bit of attention regarding the distribution of the gains from trade between developing and industrialized countries.

• Arguments for the hypothesis:– As countries become richer, they spend a smaller share of their

income on food.– As world income grows, demand for food falls relative to the demand

for manufactured goods. Therefore, the price of agricultural products can also be expected to fall relative to manufactured goods.

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Application 3: The Terms of Trade for Primary Commodities

• Arguments for the hypothesis (continued):– For mineral products, industrialized countries continually find

substitutes in the production of manufactured products.– The substitution away from mineral products is a form of

technological progress, and as it proceeds, can lead to a fall in the price of raw materials.

• Arguments against the hypothesis:– Technological progress in manufactured goods can certainly lead to a

fall in the price of these goods as they become easier to produce.– This is a fall in terms of trade for industrialized countries rather than

developing countries.– In the case of oil, OPEC’s cartel pricing has caused an increase in the

terms of trade for oil-exporting countries.• The long-term evidence (1900-2000) is mixed.

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The long-term evidence(price of primary relative to manufactured goods)

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Key insights• The Ricardian model is about the reallocation of a single factor, labor,

across alternative uses.• It is comparative (productivity) advantage, not absolute (productivity)

advantage, which matters for the direction of specialization and the realization of the gains from trade.

• Absolute productivity advantage determines wage rates.• Gains from trade can be captured in three different ways: increase in

utility, increase in consumption opportunities or increase in real wages. • Since the gains from trade are at the country level, the gains are

aggregate gains. Because of the one factor assumption, there can’t be any domestic conflict about the gains from trade in the Ricardian framework.

• The distribution of the gains from trade depends on the terms of trade.• Changes in the terms of trade will have different welfare effects.• To analyze potential domestic conflict from international trade, we need

to relax the one factor assumption. This leads to the specific-factors model.

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