[PDF] 14.581 International Trade — Lecture 2: Ricardian Theory (I)—

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14.581 International Trade

| Lecture 2: Ricardian Theory (I)|

14.581

Week 2

Fall 2018

14.581

Week 2

)Ricardian Theory (I)Fall 20181 / 34

Today's Plan

1Taxonomy of neoclassical trade models

2Standard Ricardian model: DFS 1977

1Free trade equilibrium

2Comparative statics

3Multi-country extensions

4The origins of cross-country technological dierences

14.581

Week 2

)Ricardian Theory (I)Fall 20182 / 34

Taxonomy of Neoclassical Trade Models

In a neoclassical trade model, comparative advantage, i.e. dierences

in relative autarky prices, is the rationale for tradeDierences in autarky prices may have two origins:

1Demand (periphery of the eld)

2Supply (core of the eld)

1Ricardian theory:Technological dierences2Factor proportion theory: Factor endowment dierences14.581( Week 2)Ricardian Theory (I)Fall 20183 / 34

Taxonomy of Neoclassical Trade Models

In order to shed light on the role of technological and factor endowment dierences:Ricardian theory assumes only one aggregate factor of production Factor proportion theory rules out technological dierences across countriesNeither set of assumptions is realistic, but both may be useful

depending on the question one tries to answer:If you want to understand the impact of the rise of China on real

incomes in the US, Ricardian theory is the natural place to startIf you want to study its eects on the skill premium, more factors will

be neededNote that: Technological and factor endowment dierences are exogenously given No relationship between technology and factor endowments (Skill-biased technological change?)

14.581

Week 2

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Standard Ricardian Model

DFS 1977Consider a world economy withtwo countries: Home and ForeignAsterisks denote variables related to the Foreign country

Ricardian models dier from other neoclassical trade models in that

there only isone aggregate factorof productionThere can be many (nontradable) factors, but they can all be

aggregated into a single composite inputWe denote by: LandLthe endowments of labor (in eciency units) in the two

countrieswandwthe wages (in eciency units) in the two countries14.581( Week 2)Ricardian Theory (I)Fall 20185 / 34

Standard Ricardian Model

Supply-side assumptionsThere is acontinuumof goods indexed byz2[0,1]Since there are CRS, we can dene the (constant) unit labor

requirements in both countries:a(z)anda(z)a (z)anda(z)capture all we need to know about technology in the two countriesW.l.o.g, we order goods such thatA(z)a(z)a

(z)is decreasingHence Home has a comparative advantage in the low-zgoodsFor simplicity, we'll assume strict monotonicity

14.581

Week 2

)Ricardian Theory (I)Fall 20186 / 34

Standard Ricardian Model

Free trade equilibrium (I): Ecient international specializationPrevious supply-side assumptions are all we need to make qualitative

predictions about pattern of tradeLetp(z)denote the price of goodzunder free tradeProt-maximization requires

p (z)wa(z)0, with equality ifzproduced at home(1) p

(z)wa(z)0, with equality ifzproduced abroad(2) PropositionThere existsez2[0,1]such that Home produces all

goodszez14.581( Week 2)Ricardian Theory (I)Fall 20187 / 34

Standard Ricardian Model

Free trade equilibrium (I): Ecient international specializationProof:By contradiction. Suppose that there existsz0 zproduced at Home andz0is produced abroad.(1)and(2)imply p (z)wa(z)=0 pz0waz00 pz0waz0=0 p (z)wa(z)0

This implies

wa (z)waz0=p(z)pz0waz0wa(z), which can be rearranged as a z0/az0a(z)/a(z) This contradictsAstrictly decreasing.14.581( Week 2)Ricardian Theory (I)Fall 20188 / 34

Standard Ricardian Model

Free trade equilibrium (I): Ecient international specializationProposition simply states that Home should produce and specialize in

the goods in which it has a CANote that:

Proposition does not rely on continuum of goods

Continuum of goods + continuity ofAis important to derive A (ez)=ww w(3)Equation

(3)is the rst of DFS's two equilibrium conditions:Conditional on wages, goods should be produced in the country where

it is cheaper to do soTo complete characterization of free trade equilibrium, we need to

look at the demand side to pin down the relative wagew14.581( Week 2)Ricardian Theory (I)Fall 20189 / 34

Standard Ricardian Model

Demand-side assumptionsConsumers haveidentical Cobb-Douglaspref around the worldWe denote byb(z)2(0,1)the share of expenditure on goodz:

b(z) =p(z)c(z)wL =p(z)c(z)w L wherec(z)andc(z)are consumptions at Home and AbroadBy denition, share of expenditure satisfy: R1

0b(z)dz=114.581( Week 2)Ricardian Theory (I)Fall 201810 / 34

Standard Ricardian Model

Free trade equilibrium (II): trade balanceLet us denote byq(ez)Rez

0b(z)dzthe fraction of income spent (in

both countries) on goods produced at HomeTrade balance requires q (ez)wL=[1q(ez)]wLLHSHome exports; RHSHome importsPrevious equation can be rearranged as w=q(ez)1q(ez) LL B(ez)(4)Note thatB0>0: an increase inezleads to a trade surplus at Home,

which must be compensated by an increase in Home's relative wagew14.581( Week 2)Ricardian Theory (I)Fall 201811 / 34

Standard Ricardian Model

Putting things together!FH~

zωB(z)z A(z)Ecient international specialization, Equation(3), and trade balance, (4), jointly determine(ez,w)14.581( Week 2)Ricardian Theory (I)Fall 201812 / 34

Standard Ricardian Model

A quick note on the gains from tradeSince Ricardian model is a neoclassical model, general results derived

in previous lecture holdHowever, one can directly show the existence of gains from trade in this environmentArgument:

Setw=1 under autarky and free tradeIndirect utility of Home representative household only depends onp()For goodszproduced at Home under free trade: no change compared

to autarkyFor goodszproduced Abroad under free trade: p (z)=wa(z)14.581

Week 2

)Ricardian Theory (I)Fall 201813 / 34 What Are the Consequences of (Relative) Country Growth?!FH~

zωB(z)z A(z)Suppose thatL/Lgoes up (rise of China):wgoes up andezgoes downAt initial wages, an increase inL/Lcreates a trade decit Abroad,

which must be compensated by an increase inw14.581( Week 2)Ricardian Theory (I)Fall 201814 / 34 What are the Consequences of (Relative) Country Growth? Increase inL/Lraises indirect utility, i.e. real wage, of representative

household at Home and lowers it Abroad:Setw=1 before and after the change inL/LFor goodszwhose production remains at Home: no change inp(z)For goodszwhose production remains Abroad:

w%)w&)p(z)=wa(z)&For goodszwhose production moves Abroad: w a(z)a(z))p(z)&So Home gains. Similar logic implies welfare loss Abroad

Comments:

In spite of CRS at the industry-level, everything is as if we had DRS at the country-levelAs Foreign's size increases, it specializes in sectors in which it is relatively less productive (compared to Home), which worsens its terms-of trade, and so, lowers real GDP per capitaThe atter theAschedule, the smaller this eect14.581( Week 2)Ricardian Theory (I)Fall 201815 / 34 What are the Consequences of Technological Change? There are many ways to model technological change:

1Global uniform technological change: for allz,ba(z)=ba(z)=x>02Foreign uniform technological change: for allz,ba(z)=0, but

ba(z)=x>03International transfer of the most ecient technology: for allz, a(z) =a(z)(Oshoring?)Using the same logic as in the previous comparative static exercise, one can easily check that:1Global uniform technological change increases welfare everywhere

2Foreign uniform technological change increases welfare everywhere (For

Foreign, this depends on Cobb-Douglas assumption)3If Home has the most ecient technology,a(z) it will lose from international transfer (no gains from trade)

14.581

Week 2

)Ricardian Theory (I)Fall 201816 / 34

Other Comparative Static Exercises

Transfer problem: Keynes versus OhlinSuppose that there isT>0 such that:Home's income is equal towL+T,Foreign's income is equal towLTIf preferences are identical in both countries, transfers do not aect

the trade balance condition:

1q(ez)](wL+T)q(ez)(wLT)=T

q (ez)wL=[1q(ez)]wLSo there are no terms-of-trade eect If Home consumption is biased towards Home goods,q(z)>q(z)quotesdbs_dbs2.pdfusesText_3

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