ECO364 - International Trade - Chapter 2 - Ricardohomes.chass.utoronto.ca/~cdippel/LNRicardo.pdf · ECO364 - International Trade Chapter 2 - Ricardo Christian Dippel University of

ECO364 - International TradeChapter 2 - Ricardo

Christian Dippel

University of Toronto

Summer 2009

Christian Dippel (University of Toronto) ECO364 - International Trade Summer 2009 1 / 73

Ricardian Comparative Advantage Comparative Advantage

Comparative Advantage: The Ricardian Model

I Why do countries specialize in different commodities/goods?

I Is trade a good thing?



The Ricardian Model: Definitions

start with:

I Unit Labor Requirement: the amount of labor required to increaseoutput by one unit.

I aj is the amount of labor needed to produce one unit of good j . Withone factor (labor), 1/aj is the marginal product of labor.

I Arithmetically, if Y = F (L), then the unit labor requirement is

1MPL = 1

∂Y∂L

= ∂L∂Y



The Ricardian Model: Motivating Example

I Suppose that Canada and China each have 100 workers andtechnology manifested by the following unit labor requirements:

Table: Unit Labor Requirements

Country Textiles Computers

Canada 10 5

China 5 10



The Ricardian Model: Motivating Example

I Suppose that each country divides its labor force in half so that thereare 50 workers in each sector...

Table: Output


Canada 5 10

China 10 5

World 15 15



I Examine two other possibilities.

1. Canada specializes in computers and China in textiles.2. Canada specializes in textiles and China in computers.

Canada: C, China: T Canada: T, China: C

Country C T C T

Canada 20 0 0 10

China 0 20 10 0

World 20 20 10 10



I If countries specialize in the “right” sector, world output can increase.

I But how do we know what the “right” sector is?



The Ricardian Model: Definitions

I Constant Returns to Scale (CRS): If one increases all inputs by someproportion, output increases by the same proportion.

I y=ouput and l= labor.I y = f (l) is CRS if y = f (γl) = γf (l) where γ > 0.I y = l is a CRS production function.I y = l0.4, y = l1.1, and y = l + 5 are all not CRS production functions.

I Homothetic Preferences: The form of the utility function does notdepend on income (linear Engels Curves).

I Autarky: When economies are “closed” and do not trade at all.



The Ricardian Model: Assumptions

I Two countries, two goods, one factor (labor),

I Labor is immobile across countries and mobile across sectors,

I Constant returns to scale (CRS) production,

I Identical and homothetic preferences,

I Perfect Competition (all agents are price takers).



The Ricardian Model: Opportunity Costs

I Opportunity costs (OC) formalize the tradeoffs implicit in the unitlabor requirements.

I Recall that an opportunity cost is the cost associated with forgoingone’s next best option.

I The OC of production turns out to be the ratio of unit laborrequirements.



Canada 10 5China 5 10



I 10 Canadian workers needed to produce 1 unit of textile and 5 neededto produce a computer.

I Consequently, the opportunity cost of producing a computer in Canadais the 0.5 of a textile that is forgone.

I 5 Chinese workers needed to produce one unit of textiles and 10needed to produce a computer.

I Consequently, the opportunity cost of producing a computer in China isthe 2 textiles that are forgone.

I Because the opportunity cost of producing a computer is lower inCanada than China, Canada has a comparative advantage incomputers and China possesses a comparative advantage in textiles.



I An absolute advantage is when a country has a lower unit laborrequirement than another country for a given good.

I Absolute advantage involves comparing unit labor requirements fora good across countries. Comparative advantage involvescomparing unit labor requirements across countries and goods.

I This distinction is at the heart of Ricardian Theory. Do not confusethe two.



I More generally, rename Canada and China to be N(orth) and S(outh),With the same two goods, C(omputers) and T(extiles), the North willpossess a comparative advantage in computers if and only if:

aNC

aNT

<aSC

aST

I The South will possess a comparative advantage in computers if andonly if:

aNC

aNT

>aSC

aST



I Is this confirmed in the earlier data?

Country aT aC

Canada 10 5China 5 10

aCan.C

aCan.T

=1

2

aChinaC

aChinaT

= 2

IaCan.C

aCan.T

<aChinaC

aChinaT

and Canada has a comparative advantage in computers!



I With only two goods, if a country possesses a comparative advantagein one good, the other country will possess the comparativeadvantage in the other good.

I With only two goods, a country cannot have a comparative advantagein both goods !!

I In the above example, suppose one country has a set of aj ’s that arelower for both goods. Are there still gains from specialization, if onecountry has an absolute advantage in which it possesses lower unitlabor requirements in both sectors?



I Suppose that North possesses an absolute advantage in both sectorssuch that the structure of unit labor requirements is as follows:



North 10 5South 20 40

I For each good, the North has a lower unit labor requirement butwhich good is it more better at?



I Opportunity costs.I (aN

C /aNT )=0.5

I (aSC/a

ST )=2.

I Opportunity costs are the same as before even though Canada is 4times as productive as before in both goods !

I Comparative advantage is not necessarily affected by shifts inAbsolute Advantage.



I Are their gains from specialization?

I Suppose that the South wants an additional computer.I The South can:

1. Forgo 2 textiles and produce the computer at home. Or,2. Produce 0.5 textiles and then trade them to the North for, for example,

1 computer. (the North is willing to do this because 1 is less than itsown opportunity costs of producing textiles).

I Clearly, the South prefers producing the good they have a comparativeadvantage in and the trading it relative to producing an additionalunit of the good at which they are at a comparative disadvantage.



I Despite the fact that the North has an absolute advantage in bothgoods, the North has a comparative advantage in Computers and theSouth has a comparative advantage in Textiles.

I Why is it inefficient for the North to produce everything? Supposethey did....

I Both countries could always be better of by specializing and tradingat a price that lies in between the two opportunity costs.

I The South should produce what it is good at and the North shouldproduce what it is good at.



I What will the relative price of computers and textiles be?I Remember that there is no money in this model. All prices are relative

prices of goods.

I Assume that trade occurs.

I Assertion: In equilibrium, the world price of computers will bebetween 0.5 and 2 textiles per computer.

I Start with the result that Canada produces computers and Chinaproduces textiles.

I i.e. assume each country produces its comparative advantage good.



I Suppose that the world price of computers is less than 0.5 textiles percomputer. Computers are cheap for China relative to autarky. Chinais happy but textiles are expensive for Canada relative to autarky.Canada is better off producing its own textiles ⇒ the relative pricecannot be less than 0.5 textiles per computer.

I Suppose that the world price of computers is more than 2 textiles percomputer. Textiles are cheap for Canada relative to autarky. Canadais happy but computers are now expensive relative to autarky. Chinais better off producing its own computers ⇒ the relative price cannotbe more than 2.

I Consequently, the the relative price will be between 0.5 and 2.



I Can 1 (textile per of computer) be the equilibrium relative price?

I Canada produces computers. The one textile per computer it canobtain through trade is better than the 1/2 of a textile it could get ifit produced its own textiles.

I China produces textiles. The one computer per textile it can obtainthrough trade is better than the 1/2 of a computer it could get if itproduced its own computers.

I For yourself: verify that 0.75 and 1.5 are also both possibleequilibrium relative prices.



I More generally, an equilibrium relative price must satisfy the followingrestriction where the North has a comparative advantage in good xand the South has a comparative advantage in good y .

aNorthx

aNorthy

≤ px

py≤ aSouth

x

aSouthy

I This only pins down a possible range of equilibrium factor prices.

I To narrow this range, we introduce demand.

I First, let’s think more deeply about the gains from trade in thisRicardian model.



Conjecture: Suppose that the North has a comparative advantage ingood x :

I If aNx

aNy

= px

py< aS

x

aSy

then the North neither gains nor loses from

trade and the South gains.

I If aNx

aNy< px

py= aS

x

aSy

then the North gains from trade and the

South neither gains nor loses.



I Can we illustrate this graphically?

I The North’s Production Possibility Frontier (PPF) is as followswhere LN is the amount of labor that the North possesses:

aNC QN

C + aNTQN

T ≤ LN

I Assuming full employment of all factors, simple arithmetic gives:

QNT = LN

aNT

− aNC

aNT

QNC







I A key insight is that in autarky, the PPF and the budget constraintwill be the same line.

I In autarky, what you consume/purchase must be what you produce.With trade, you need not consume what you produce.

I Therefore, in a trading equilibrium, the budget constraint and PPFneed not be the same line.



Autarky Relative Prices

w = PkMPLk = Pkak

for k = {C ,T}

Because the same wage w is paid in both sectors, this implies

PCPT

= aCaT

I Autarky relative prices will be equal to the ratio of unit laborrequirements in that country.



I Now introduce TradeI The PPF will look the same as before and will have a slope of − aN

C

aNT

.

I The budget constraint will now be based on the equationPCQC + PTQT ≤ Y and will have the slope −PC

PT.

I Let’s examine the case where PC

PT>

aNC

aNT

.

I Does the North gain from trade if it specializes in computers?





I Now let’s examine the Southern case.

I Let’s examine the case where PCPT

<aSC

aST

.

I Does the South gain from trade if it specializes in textiles?

I Starting from autarky...









I Suppose that (for either country) world relative prices more closelyresemble autarky relative prices.

I The gains from trade will diminish until(

PCPT

)0

=aNC

aNT

.

I At this point, utility will be the same as in autarky.





I If world relative prices equal autarky relative prices for one country,that country does not gain from trade. The other country does gainfrom trade.

I If world relative prices are in between autarky relative prices, bothcountries gain from trade.

I The more “different” a country’s ratio of unit labor requirements arefrom world relative prices, the more a country gains from trade.

I If both countries have the same opportunity costs there is nocomparative advantage

I Then there is no gains from trade for either country.I Even though there might still be absolute advantage.

I Large differences mean larger gains from specialization.



I Let’s introduce demand....



I We are going to use the following graph to solve for equilibrium(relative) output and prices (note the axes labels !!).



I The vertical axis gives the price of good X relative to Y . Thehorizontal axis gives the relative World quantities where the World issimply to aggregation of the North and South.

I Recall that the equilibrium relative price of goods X and Y must liebetween the autarky relative prices/unit labor requirements of the twocountries.

I Assume that the North has a comparative advantage in good x ,therefore the South possesses a comparative advantage in good y .

I Arithmetically,an

x

any<

asx

asy.

I We can represent this graphically as....





I Now suppose that px

py= aS

x

aSy

.

I The North completely specializes in good x because it can produce xand then trade for y at better terms than if it produced its own y .Consequently XN = LN/an

x and Y N = 0.

I The South is indifferent between specializing in Y (and then tradingfor X ) and producing both X and Y .

I The South will produce some combination of (X S ,Y S) that satisfies

0 < X S

Y S <∞

I Consequently, when px

py= aS

x

aSy

, the relative quantity supplied will be a

segment.





I Suppose that px

py= aN

x

aNy

.

I The South completely specializes in good y because it can produce yand then trade for x at better terms than if it produced its own x .Consequently X S = 0 and Y S = LS/as

y .

I However, we cannot say how much the North will specialize becausethe North is indiffernt indifferent between specializing in X (and thentrading for Y ) and producing both X and Y .

I Consequently, when px

py= aN

x

aNy

, the relative quantity supplied will be a

segment...





I Now suppose that aNx

aNy< px

py< aS

x

aSy

.

I Complete specialization where the North specializes in X and theSouth specializes in X .

I Note that any set of relative prices between the two autarky priceratios will support this outcome.

I The relative supply curve will be vertical at this point.





At this point....

I The North prefers specializing in X and trading for Y to producingboth.

I Consequently, XN = LN/aNX and Y N = 0.

I The South prefers specializing in Y and trading for X to producingboth.

I X S = 0 and Y S = LS/aSY .





I The structure of demand determines the equilibrium.I This is done by introducing a relative demand curve

I As the relative price of a good rises, relative demand increases.I Reflects substitution effects.



Figure: Demand for X is high relative to Y



I The North specializes in X and the South produces both X and Y .I Why?

I World demand for X is sufficiently high that the North cannotproduce enough X to satisfy high World demand for X .

I The South satisfies for the remaining demand for X .

I Because relative prices for the South are the same as in autarky, theSouth does not gain from trade but the North does. In sum, theWorld gains.



Figure: Demand for Y is high relative to X



I The South specializes in Y and the North produces both X and Y .I Why?

I World demand for Y is sufficiently high that the South cannotproduce enough Y to satisfy high World demand for Y .

I The North must provide for the remaining demand for Y .

I Because prices for the North are the same as in autarky, the Northdoes not gain from trade but the South does. In sum, the Worldgains.



Figure: Demand for X and Y is Relatively Even.



I The North specializes in X and the South specializes in Y .

I Because relative world prices are between autarky unit laborrequirements, both countries gain from trade

I General Rule in this model: a country that does not specialize doesnot gain from trade !



I This analysis suggests that a country will produce more of itscomparative advantage good than its comparative disadvantage good(specialization).

I One country produces a lot of one good, the other country produces alot of the other.

I If preferences are sufficiently similar (which we have assumed), theywill demand the same goods.

I A country will export its comparative advantage good and import itscomparative disadvantage good.

I See an upcoming problem set for concrete examples.


Ricardian Comparative Advantage Relative Wages

I Some commentators argue that high relative wages in the Northrelative to the south are evidence of Northern exploitation ofSouthern workers.

I Does the Ricardian model have anything to say about this?



Start with the profit maximizing condition that nominal wages equal themarginal revenue product of labor.

w = p ×MPL

Now suppose that Northern workers specialize in computers and Southernworkers specialize in textiles. This gives us two equilibrium conditions:

wN = pC

aNC

wS = pT

aST



These conditions can be combined to give the following expression

wN

wS =aST

aNC

pC

pT=

MPLNC

MPLST

pC

pT

I Northern relative wages are determined by labor productivity and therelative prices of the two goods.

I If the two goods have the same price, labor productivity alonedetermines relative wages.

I If the two goods do not have the same price, the relative wage is higherin the country that produces the relatively valuable good, holding laborproductivity constant.

I But wages in both North and South are always higher under Tradethan under Autarky.



I We can also offer strong rebuttals to common criticisms of free tradeif the Ricardian model possesses substantial validity.

1. Free Trade is beneficial only if your country is strong enough to standup to foreign competition.

2. Foreign competition is unfair and hurts other countries when it is basedon low wages.

3. Trade exploits a country and makes it worse off if its workers receivemuch lower wages than workers in other nations.

I Krugman and Obstfeld, pp. 36-40

I Krugman “Ricardo’s Difficult Idea.” (optional).



I Free Trade is beneficial only if your country is strong enough to standup to foreign competition.

I Comparative and not absolute advantage is sufficient for gains fromtrade

I Foreign competition is unfair and hurts other countries when it isbased on low wages.

I Low foreign wages are caused by low productivity.

I Trade exploits a country and makes it worse off if its workers receivemuch lower wages than workers in other nations.

I If wages are based on productivity, they will be low even if there is notrade.


Ricardian Comparative Advantage Conclusions

1. Each country exports the good at which it possesses a comparativeadvantage.

2. Each country imports the good at which it possesses a comparativedisadvantage.

3. In this setting, each country possesses a comparative advantage insome good.

4. If free trade relative prices lie between autarky unit laborrequirements, both countries gain from trade.

5. If free trade relative prices equal the autarky price ratio for onecountry, that country is no worse off from trade and the other countryis better off.

6. Increased utility comes from increased consumption possibilities thatallow consumer/workers to attain a higher indifference curve.


The Multi-Good Extension

I Let’s make the model more realistic by allowing more than one good.

I This will also allow us to introduce the important notion of the theintensive and extensive margin of trade.

I Suppose there are N goods produced, indexed by i = 1,2,N.

I The domestic countrys unit labor requirement for good i is ai , andthat of the foreign country is a∗i



I Goods will be produced wherever it is cheaper to produce them.

I Let w represent the wage rate in the domestic country and w*represent the wage rate in the foreign country.

I If wa1 < w∗a∗1 then only the domestic country will produce good 1,since total wage payments are less there.

I Equivalently, good i is produced in Home only if a1a∗1< w∗

w (if Home’s

technology advantage is larger than its cost disadvantage)

I Let’s consider an example:






I Home has high productivity in apples, bananas, and caviar. Thatgives Home a cost advantage.

I Suppose Foreign has low wages. That gives it a cost advantage,despite its low productivity.

I How is the equilibrium relative wage determined?

I the relevant equilibrium is equality of the relative supply and relative(derived) demand of labor services.



I As domestic labor becomes more expensive relative to foreign labor,goods produced in the domestic country become more expensive, anddemand of these goods and therefore derived demand for the labor toproduce them falls.

I At certain threshold-levels, comparative advantage shifts from Hometo Foreign so that fewer goods will be produced in Home, furtherreducing the demand of domestic labor services.

I The relative (derived) demand of domestic labor services thereforefalls when w/w* rises.



The Intensive and Extensive Margin of Trade

I The intensive margin refers to a country exporting or importing alarger quantity of the same goods

I The extensive margin refers to a country exporting or importing newgoods

I In later chapters, the intensive margin can also refer exporting firmsexporting more while the extensive margin refers to non-exporting firmsbecoming exporters.

I Suppose w/w* increases from 3 to 3.99: Home produces the samegoods but at higher prices so that the demand for these goods andthe labor to produce them falls (intensive margin).

I Suppose w/w* increases from 3.99 to 4.01: The caviar industry nowmoves to Foreign, causing a discrete drop in the demand of domesticlabor (extensive margin).





Empirical Evidence

I What is the empirical evidence for technology-differences-basedcomparative advantage?

I Do countries export those goods in which their productivity isrelatively high?

I The ratio of U.S. to British exports in 1951 compared to the ratio ofU.S. to British labor productivity in 26 manufacturing industriessuggests yes.

I At this time the U.S. had an absolute advantage in all 26 industries,yet the ratio of exports was low in the least productive sectors of theU.S.


Empirical Evidence



Documents

ECO364 - International Trade - Chapter 2 - Ricardohomes.chass.utoronto.ca/~cdippel/LNRicardo.pdf · ECO364 - International Trade Chapter 2 - Ricardo Christian Dippel University of