International Economics Lecture 2: The Ricardian...

International EconomicsLecture 2: The Ricardian Model

Min Hua & Yiqing Xie

School of EconomicsFudan University

Mar. 5, 2014

Min Hua & Yiqing Xie (Fudan University) Int’l Econ - Ricardian Mar. 5, 2014 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 autarkyprices must make the country better off.

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

Sell high, buy low: sell to the world what is more valuable to themthan at home; buy from the world what is more costly and difficultto produce at home.

Gains from trade are mutual for two countries: it is not the casethat one gains 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 differentendowments, trade allows them to have a more diverseconsumption basket or a more balanced consumption basket.

Gains from specialization

Typically countries have the ability to produce different bundles ofgoods (the production possibility curve). Further gains can becaptured by specializing 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 differentendowments, trade allows them to have a more diverseconsumption basket or a more balanced consumption basket.

Gains from specialization

Typically countries have the ability to produce different bundles ofgoods (the production possibility curve). Further gains can becaptured by specializing 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 tradethan in autarky.

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∑

p∗iX∗i ≥

p∗iXai

The free-trade production bundle yields a higher income atfree-trade prices than the autarky bundle.

2 Autarky market clearing and trade balance

Xai = Da

i ,∑i

p∗iX∗i =

p∗iD∗i

3 Substitute (2) into (1) ∑i

p∗iD∗i ≥

p∗iDai

Free trade is "Revealed Preferred" to autarky.

p∗iX∗i ≥

p∗iXai

Xai = Da

i ,∑i

p∗iX∗i =

p∗iD∗i

p∗iD∗i ≥

p∗iDai

p∗iX∗i ≥

p∗iXai

Xai = Da

i ,∑i

p∗iX∗i =

p∗iD∗i

p∗iD∗i ≥

p∗iDai

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.Min Hua & Yiqing Xie (Fudan University) Int’l Econ - Ricardian Mar. 5, 2014 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 AdvantageDefinitionThere are two countries – country h and country f .

Absolute Advantage

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

αh2 > αf2 (4)

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

Comparative Advantage

the relative productivity in the two industries across countries

αh2αh1

>αf2αf1

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

Absolute and Comparative AdvantageDefinitionThere are two countries – country h and country f .

Absolute Advantage

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

αh2 > αf2 (4)

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

Comparative Advantage

the relative productivity in the two industries across countries

αh2αh1

>αf2αf1

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

Absolute and Comparative AdvantagePropositionA pattern of comparative advantage (inequality of the productivity ratiosis a necessary and a sufficient condition for gains from specialization.

Proof: (assuming comparative advantage αh2αh1

Reallocate labor in each country toward thecomparative-advantage industry.

dLh2 = −dLh1 > 0 dLf1 = −dLf2 > 0 (6)

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

dX1 = −αh1dLh2 − αf1dLf2 dX2 = αh2dLh2 + αf2dLf2 (7)

dLh2 = −dLh1 > 0 dLf1 = −dLf2 > 0 (6)

Absolute and Comparative AdvantagePropositionProof: (cont’d)

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

dLf2 = −αh1αf1

dLh2 ⇔ dX1 = dXh1 + dXf1 = 0 (8)

Substitute (8) into the right-hand equation of (7), replacing dLf2with (8).

[αh2 −

αh1αf1

]dLh2 = αh1

[αh2αh1−αf2αf1

]dLh2 > 0 (9)

Gains from specialization: X2 increases with X1 constant.

Absolute and Comparative AdvantagePropositionProof: (cont’d)

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

dLf2 = −αh1αf1

dLh2 ⇔ dX1 = dXh1 + dXf1 = 0 (8)

Substitute (8) into the right-hand equation of (7), replacing dLf2with (8).

[αh2 −

αh1αf1

]dLh2 = αh1

[αh2αh1−αf2αf1

]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

The differences in slopes between two countries reflectscomparative advantage.

The intercepts of PPFs reflect absolute advantage.

The differences in intercepts between two countries reflectabsolute advantage.

The slopes of PPFs reflect comparative advantage.

dX1 = α1dL1 dX2 = α2dL2 = −α2dL1dX2

dX1= −α2

The differences in slopes between two countries reflectscomparative advantage.

The intercepts of PPFs reflect absolute advantage.

The differences in intercepts between two countries reflectabsolute advantage.

Figure 7.1 Figure 7.2

Excess Demand and International EquilibriumDirection of Trade and Specialization

Comparative Advantage predictsthe direction of trade andspecialization.

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 oncomparative advantage, not absolute advantage.

One country may have an absolute advantage in everything, but itcan still 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, andso the wage rate in each country is determined by the competitiveconditions that the value of the marginal product of labor equalsthe wage rate.

p∗2αh2 = wh p∗1αf1 = wf thuswhwf

=p∗2αh2p∗1αf1

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

αh2αh1≥ p∗1p∗2≥αf2αf1

=p∗2αh2p∗1αf1

Assume that country h is has an absolute advantage in bothgoods in addition to having a comparative advantage in good 2, asin Figure 7.2.

αh1 > αf1 and thusαh2αf1

>αh2αh1

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

αh2αf1

>αh2αh1≥ p∗1p∗2≥αf2αf1

⇒ p∗2p∗1

αh2αf1

> 1 (13)

The right-hand expression is, from (10), the ratio of the wage ratesin the two countries.

p∗2p∗1

αh2αf1

> 1 (14)

>αh2αh1

αh2αf1

⇒ p∗2p∗1

αh2αf1

> 1 (13)

p∗2p∗1

αh2αf1

> 1 (14)

>αh2αh1

αh2αf1

⇒ p∗2p∗1

αh2αf1

> 1 (13)

p∗2p∗1

αh2αf1

> 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 anequilibrium because there isno 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 willexist gains from trade.

Countries should specialize according to comparative advantage,their relative 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 fromtrade: technically, they trade further away from their autarky pricesthan large countries.

International Economics Lecture 2: The Ricardian...

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