International Trade Lecture 2: The Ricardian Modelhomepage.fudan.edu.cn/yiqingxie/files/2016/07/IntlTrade_2.pdf · International Trade Lecture 2: The Ricardian Model Yiqing Xie School

International TradeLecture 2: The Ricardian Model

Yiqing Xie

School of EconomicsFudan University

July, 2016

Yiqing Xie (Fudan University) Int’l Trade - Ricardian July, 2016 1 / 32

Outline

The Gains From Trade

The Causes of International Trade

Absolute and Comparative Advantage

Excess Demand and International Equilibrium

Absolute Advantage and Wage

Distribution of Gains between Countries

Summary


Gains from Trade

The ability to trade (voluntarily) leads to mutual gains from trade.

Point of departure:

The ability to trade at any prices other than the country’s autarky pricesmust make the country better off.

The optimal direction of trade depends only on the difference betweenthe country’s autarky prices and world prices:

Sell high, buy low: sell to the world what is more valuable to them thanat home; buy from the world what is more costly and difficult to produceat home.

Gains from trade are mutual for two countries: it is not the case that onegains at the expense of the other.


Gains from TradeFigure 5.1


Gains from Exchange VS Gains from Specialization

Total Gains = Gains from Exchange + Gains from Specialization

Gains from exchange

When two traders have similar preferences but different endowments,trade allows them to have a more diverse consumption basket or a morebalanced consumption basket.

Gains from specialization

Typically countries have the ability to produce different bundles of goods(the production possibility curve). Further gains can be captured byspecializing in what a country is good at.


Gains from Exchange VS Gains from Specialization

Total Gains = Gains from Exchange + Gains from Specialization

Gains from exchange

When two traders have similar preferences but different endowments,trade allows them to have a more diverse consumption basket or a morebalanced consumption basket.

Gains from specialization

Typically countries have the ability to produce different bundles of goods(the production possibility curve). Further gains can be captured byspecializing in what a country is good at.


Gains from Exchange VS Gains from SpecializationFigure 5.2


Gains-from-Trade Theorem – Free Trade VS Autarky

An undistorted, competitive economy must be better off in free trade than inautarky.

vector of free trade prices, p∗i

vector of free trade outputs, X∗i

vector of free trade consumption, D∗i

vector of autarky outputs, Xai

vector of autarky consumption, Dai


Gains-from-Trade Theorem – Free Trade VS Autarky1 Production efficiency in a competitive, undistorted economy∑

i

p∗i X∗i ≥

∑i

p∗i Xai

The free-trade production bundle yields a higher income at free-tradeprices than the autarky bundle.

2 Autarky market clearing and trade balance

Xai = Da

i ,∑

i

p∗i X∗i =

∑i

p∗i D∗i

3 Substitute (2) into (1) ∑i

p∗i D∗i ≥

∑i

p∗i Dai

Free trade is "Revealed Preferred" to autarky.



i

p∗i X∗i ≥

∑i

p∗i Xai



Xai = Da

i ,∑

i

p∗i X∗i =

∑i

p∗i D∗i


p∗i D∗i ≥

∑i

p∗i Dai




i

p∗i X∗i ≥

∑i

p∗i Xai



Xai = Da

i ,∑

i

p∗i X∗i =

∑i

p∗i D∗i


p∗i D∗i ≥

∑i

p∗i Dai



Distribution of GainsDistribution of gains between countries (Figure 5.3)

Distribution of gains within a countryI Heterogeneous preferencesI Heterogeneous endowments – revisit in H-O Model


Distribution of GainsDistribution of gains between countries (Figure 5.3)

Distribution of gains within a countryI Heterogeneous preferencesI Heterogeneous endowments – revisit in H-O Model


No Trade Model

1 Identical production functions in all countries

2 Same relative factor endowments in all countries

3 Constant returns to scale

4 Identical, Homogeneous preferences in all countries

5 No Distortions (imperfect competition, externalities, taxes).

In this world, there would be no trade and no gains from trade.


No Trade ModelFigure 6.1


No Trade ModelFigure 6.2

Assumptions 1-5 are sufficient for no trade, not necessary.Yiqing Xie (Fudan University) Int’l Trade - Ricardian July, 2016 12 / 32

Absolute and Comparative AdvantageRicardian Model

Differences in Technology across Countries

One Factor of Production: Labor (L)

a special case of same relative factor endowments in all countries

CRS and Perfect Competition

X1 = F(L1) specifically X1 = α1L1 (1)

X2 = F(L2) specifically X2 = α2L2 (2)

L = L1 + L2 (3)


Absolute and Comparative AdvantageDefinition

There are two countries – country h and country f .

Absolute Advantage

the comparison of the α’s for a given industry across countries

αh2 > αf 2 (4)

defines country h as having an absolute advantage in good X2.

Comparative Advantage

the relative productivity in the two industries across countries

αh2

αh1>αf 2

αf 1(5)

defines country h as having a comparative advantage in good X2.


Absolute and Comparative AdvantageDefinition

There are two countries – country h and country f .

Absolute Advantage

the comparison of the α’s for a given industry across countries

αh2 > αf 2 (4)

defines country h as having an absolute advantage in good X2.

Comparative Advantage

the relative productivity in the two industries across countries

αh2

αh1>αf 2

αf 1(5)

defines country h as having a comparative advantage in good X2.


Absolute and Comparative AdvantageProposition

A pattern of comparative advantage (inequality of the productivity ratios is anecessary and a sufficient condition for gains from specialization.

Proof: (assuming comparative advantage αh2αh1

>αf 2αf 1

)

Reallocate labor in each country toward the comparative-advantageindustry.

dLh2 = −dLh1 > 0 dLf 1 = −dLf 2 > 0 (6)

The changes in the total world output of the two goods will be

dX1 = −αh1dLh2 − αf 1dLf 2 dX2 = αh2dLh2 + αf 2dLf 2 (7)





>αf 2αf 1

)


dLh2 = −dLh1 > 0 dLf 1 = −dLf 2 > 0 (6)







>αf 2αf 1

)


dLh2 = −dLh1 > 0 dLf 1 = −dLf 2 > 0 (6)





Proof: (cont’d)

Set the first equation in (7) to zero, reallocating labor within eachcountry to hold world X1 output constant, and solve for

dLf 2 = −αh1

αf 1dLh2 ⇔ dX1 = dXh1 + dXf 1 = 0 (8)

Substitute (8) into the right-hand equation of (7), replacing dLf 2 with (8).

dX2 =

[αh2 −

αh1

αf 1αf 2

]dLh2 = αh1

[αh2

αh1−αf 2

αf 1

]dLh2 > 0 (9)

Gains from specialization: X2 increases with X1 constant.



Proof: (cont’d)

Set the first equation in (7) to zero, reallocating labor within eachcountry to hold world X1 output constant, and solve for

dLf 2 = −αh1

αf 1dLh2 ⇔ dX1 = dXh1 + dXf 1 = 0 (8)

Substitute (8) into the right-hand equation of (7), replacing dLf 2 with (8).

dX2 =

[αh2 −

αh1

αf 1αf 2

]dLh2 = αh1

[αh2

αh1−αf 2

αf 1

]dLh2 > 0 (9)

Gains from specialization: X2 increases with X1 constant.


Absolute and Comparative AdvantagePPF

The slopes of PPFs reflect comparative advantage.

dX1 = α1dL1 dX2 = α2dL2 = −α2dL1dX2

dX1= −α2

α1

The differences in slopes between two countries reflects comparativeadvantage.

The intercepts of PPFs reflect absolute advantage.

The differences in intercepts between two countries reflect absoluteadvantage.



The slopes of PPFs reflect comparative advantage.

dX1 = α1dL1 dX2 = α2dL2 = −α2dL1dX2

dX1= −α2

α1

The differences in slopes between two countries reflects comparativeadvantage.

The intercepts of PPFs reflect absolute advantage.

The differences in intercepts between two countries reflect absoluteadvantage.



Figure 7.1 Figure 7.2


Excess Demand and International EquilibriumDirection of Trade and Specialization

Comparative Advantage predicts thedirection of trade and specialization.

The equilibrium autarky priceratio will be the slope of theproduction frontier:comparative advantage ratio

Specialization and trade at p∗1

Specialization and trade at p∗2

Figure 7.3


Excess Demand and International EquilibriumExcess Demand (Figure 7.4)


Excess Demand and International EquilibriumInternational Equilibrium (Figure 7.5)


Absolute Advantage and WageAbsolute Advantage

The existence of mutual gains from trade depends only on comparativeadvantage, not absolute advantage.

One country may have an absolute advantage in everything, but it canstill gain from specializing in what it does relatively well.

Absolute advantage does not determine the pattern of trade or theexistence of gains from trade, but it does determine real incomecomparisons between countries.


Absolute Advantage and WageWage Determination

Absolute Advantage in all goods⇒ higher real wage.

Suppose that both countries are specialized as in Figure 7.5, and so thewage rate in each country is determined by the competitive conditionsthat the value of the marginal product of labor equals the wage rate.

p∗2αh2 = wh p∗1αf 1 = wf thuswh

wf=

p∗2αh2

p∗1αf 1(10)

The world price ratio lies (weakly) between the autarky price ratios ofthe two countries.

αh2

αh1≥ p∗1

p∗2≥αf 2

αf 1(11)






wf=

p∗2αh2

p∗1αf 1(10)


αh2

αh1≥ p∗1

p∗2≥αf 2

αf 1(11)






wf=

p∗2αh2

p∗1αf 1(10)


αh2

αh1≥ p∗1

p∗2≥αf 2

αf 1(11)



Assume that country h is has an absolute advantage in both goods inaddition to having a comparative advantage in good 2, as in Figure 7.2.

αh1 > αf 1 and thusαh2

αf 1>αh2

αh1(12)

We can then add an element to the left-hand side of the chain ofinequalities in (11) using (12).

αh2

αf 1>αh2

αh1≥ p∗1

p∗2≥αf 2

αf 1⇒ p∗2

p∗1

αh2

αf 1> 1 (13)

The right-hand expression is, from (10), the ratio of the wage rates in thetwo countries.

p∗2p∗1

αh2

αf 1=

wh

wf> 1 (14)





αf 1>αh2

αh1(12)


αh2

αf 1>αh2

αh1≥ p∗1

p∗2≥αf 2

αf 1⇒ p∗2

p∗1

αh2

αf 1> 1 (13)


p∗2p∗1

αh2

αf 1=

wh

wf> 1 (14)





αf 1>αh2

αh1(12)


αh2

αf 1>αh2

αh1≥ p∗1

p∗2≥αf 2

αf 1⇒ p∗2

p∗1

αh2

αf 1> 1 (13)


p∗2p∗1

αh2

αf 1=

wh

wf> 1 (14)


Absolute Advantage and Wage

Absolute advantage shows up in real wage comparisons betweencountries.

The more productive country will have the higher real wage.

If wages are market determined, a high wage is the result of highproductivity, and is not a deterrent to gains from trade.


Absolute Advantage and Wage: Empirical Evidence


Absolute Advantage and Wage: Empirical EvidenceWages versus value added: data from Table 7.1


Distribution of Gains between CountriesSmall Countries are the bigger gainers.

(1) Begin with the equilibrium in Figure 7.5.Figure 7.5



(2) Let country f grow: it’s production frontier shifts out.Figure 7.6



(3) Country f desires to trademore at any given price ratio.

But this cannot be an equilibriumbecause there is no change in h.

Figure 7.7



(4) To re-establish equilibrium,the price of country f ’s exportmust fall, the price of its importmust rise.

(5) Country h gains more, mayget all gains, Figure 7.8.

Figure 7.8


Summary

With international differences in production technology, there will existgains from trade.

Countries should specialize according to comparative advantage, theirrelative ability to produce different goods.

If a country is uniformly more productive (e.g., has an absoluteadvantage in everything), then it must have a higher real wage.

Theory suggests that small countries are major gainers from trade:technically, they trade further away from their autarky prices than largecountries.


Documents

International Trade Lecture 2: The Ricardian Modelhomepage.fudan.edu.cn/yiqingxie/files/2016/07/IntlTrade_2.pdf · International Trade Lecture 2: The Ricardian Model Yiqing Xie School