Trade ch2 1

Ricardian Model

Trade ch2 2

Ricardian Model

Some terms used:No (international) trade: autarky or closed

economy(International) trade: open economy.Basic premise: trade fosters specialization

and specialization is at the root of the gainsfrom trade.

Trade ch2 3

Example:In England, a specific amount of resources can produce

Either 1,000,000 m of clothOr 1,000 hl of wine

The opportunity cost of 1,000 hl of W is 1,000,000 m of C

In Portugal, a specific amount of resources can produceEither 100,000 m of clothOr 1,000 hl of wine

The opportunity cost of 1,000 hl of W is 100,000 m of C

Trade ch2 4

• The opportunity cost of producing wine is clearlylower in Portugal: Portugal has a comparativeadvantage in the production of wine.

• What happens if the 2 countries alter theirproduction in preparation for exchanging 1,000hl of wine?

• Before trade actually takes place, the followingtable illustrates the potential gains fromspecialization.

Trade ch2 5

Hypothetical change in production

+ 9000Change in worldproduction

- 100+ 1,000Portugal

+ 1,000- 1,000England

Cloth (1,000 m)Wine (hl)

Next question: will trade be mutually beneficial?Let’s now set up a formal model.

Trade ch2 6

Formal model2 countries: France and Germany2 goods: Bread and Machines1 factor: LaborPerfect competition and constant costsDefinition: aLi labor input requirement is the # of labor

hours needed to produce one unit of output i.Notation: aLB and aLM are # of labor hours to produce

respectively a unit of bread or of machine in France. Anasterisk is added for Germany (a*LB and a*LM)

Definition: 1/a corresponds to the units of output producedby one unit of input (productivity of labor)

L and L* are the total amount of labor hours available ineach country.

Trade ch2 7

France has 900 L and needs:2 labor/ h to produce 1 unit of B so aLB = 26 labor/ h to produce 1 unit of M so aLM = 6Production possibilities:i. All the resources are used to produce B,

France can produce 450B (C)ii. All the resources are used to produce M,

France can produce 150M (A)iii. Some resources can be allocated to each

production (e.g. 600L in B and 300L in M) then France can produce 300B and 50M (B)

Trade ch2 8

Construction of the production possibilityfrontier for France

M

B

50

300

150

450

Slope -1/3

The absolute value ofthe slope is theopportunity cost of breadin terms of machines.A

BC

Trade ch2 9

• Limits to production: labor in B + labor in M ≤ L

• With full employment of resources, theproduction possibility frontier (PPF) is

aLB*B + aLM*M = L i.e. + =

equation of line M = f(B)

• The opportunity cost of one extra unit of bread interms of machines forgone is and it is constant.

Trade ch2 10

All the possible mix of production are exhibited onthe PPF. How will the supply decisions be made?To figure it out, we need to make two assumptions.i. Perfect competition Profit =value of production = total = total costssince with one input there is only one kind of costSo value of production in 1 hour =ii. Workers are maximizers and choose to workwhere wages are

Trade ch2 11

Notation: PB is the price of bread and PM is theprice of machines.

As 1/a is the output of 1 labor/hour1/aLB * PB or PB/aLB

is the of 1 labor/hour in the breadindustry or the this output i.e.the hourly in the bread industry

Equivalently PM/aLM

is the hourly wage in the machine industry

Trade ch2 12

Supply possibilitiesIf PB/aLB > PM/aLM OR PB/PM > aLB/aLM

only is producedIf PB/aLB < PM/aLM OR PB/PM < aLB/aLM

only are producedIf PB/aLB = PM/aLM OR PB/PM = aLB/aLM

are produced

In sum, when the relative price of a good is smaller than itsopportunity cost, the good is produced.

In autarky, relative prices are toopportunity cost, so goods are produced.

Trade ch2 13

Same analysis for GermanyL* = 800 a*LB = 5 and a*LM = 2

0C*

(w/ )100 (w/500L)B*

0A*

MachinesBreadM

B

400

160

150

100

A*

B*

C*

Slope -2.5

Absolute value of slope is opportunitycost of B in terms of M i.e. to produce oneextra unit of B one must take laborhours from the machine production andgive up producing machines.

Trade ch2 14

In France aLB/aLM = 1/3In Germany a*LB/a*LM = 2.5

So aLB/aLM a*LB/a*LM

France has a comparative advantage (CA) inbecause the opportunity cost of producing

is lower in France than in Germany.Germany has a comparative advantage inIn autarky, the opportunity cost in each country is

_____ to the relative prices i.e. aLB/aLM PB/PMand each country produces both bread andmachine.

Trade ch2 15

Gain from trade1st approach: indirect method of productionFrance can either produce M or produce B and trade it for MIf France uses 1 labor/h to produce M:

it gets 1/aLM = (French productivity inM)

If France uses 1 labor/h to produce B: it produces 1/aLB =

that France can trade at some world price (assumePB/PM = 1) for (or 1/aLB * PB/PM )

Trade ch2 16

If 1/aLB * PB/PM > 1/aLM or PB/PM >France gains from tradingAnd at this relative world price (equal to 1) PB/aLB > PM/aLM

the French wage in the bread industry is _____that in the machine industry, so all theworkers move into _____ making and Franceonly produces (specializes into) ______.

Trade ch2 17

2nd approach: based on consumptionpossibilities (CPF) with and without trade.

• Without trade, consumption and productionpossibilities coincide: a country cannotconsume beyond its PPF

• With trade, the CPF lies ______ the PPF asa country can specialize in its CA good andtrade it at a higher relative price (for moreof the other good than in autarky)

Trade ch2 18

M

B

M

B

PPF-1/3

CPF

-1

PPF*

CPF*

-2.5

-1

FranceGermany

With world price PB/PM = 1

Trade ch2 19

Small country caseEngland (60M inhabitants) and New Zealand (4M)Trucks and wool

We have aLT/aLW PT/PW a*LT/a*LWwhere the a’s are for England and the a*’s for NZIn this case England produces ____ trucks and wool

while NZ now specializes in wool.Rationale: Although NZ has a CA in wool and fully

specializes in its production, the resulting level ofproduction is too small to meet the demand ofboth NZ and England, so England must continueto produce wool.

Trade ch2 20

trucks

wool

trucks

Wool

England

New ZealandPPF and CPF

PPF CPF

In this case, NZ trades at the English relative price

Trade ch2 21

Trade and relative wagesAustralia and the UK - Flour and cars Labor input requirement

CA

aLF/aLC

a*LC = 3aLC = 2cars

a*LF = 6aLF = 1flour

UKAustraliaTo produce 1 unit of

Trade ch2 22

1/a*LC =1/aLC =Units of cars

1/a*LF =1/aLF =Units of flour

UKAustralia

Productivity

Units of output produced by 1 labor/hour

Trade ch2 23

i. If PF = $15 and PC = $15 PF/PC =With perfect competition, wageswA = = in AustraliawUK = = in the UK

So wA/wUK=ii. If PW = $20 and PC = $15 PF/PC =wA = =wUK = =

So wA/wUK=

[we can transform relative price into relative wagebecause of perfect competition assumption]

Trade ch2 24

Trade takes placebecause aLF/aLC < PF/PC< a*LF/a*LC (1)As countries specialize in their CA good wA = (CA ) and wUK = (CA )so wA/wUK =Multiply every term in (1) by a*LC/aLF

we get a*LC/aLC < wA/wUK< a*LF/aLF

In the example (slide 23), trade takes place whenEither 0.5< PF/PC<2 Or 1.5< wA/wUK<6

Trade ch2 25

The data of case i. and case ii. yield a relative wagewithin the bonds for trade to take place. This isnot always the case:

If wA = $20 and wUK = $2 wA/wUK= $10 > $6The wage in Australia is too ___ and the Australian

productivity advantage cannot compensate forsuch a high wage

If wA = $20 and wUK = $20 wA/wUK= $1 < $1.5The wage in the UK is too ____ and the UK needs a

_____ wage to account for its low productivity.

Trade ch2 26

Comparative advantage with manygoods

In this case, we can’t use use relative prices todetermine CA (there is one between any 2 goods).

Instead we will use the concept of relative wage forthe 2 countries.

Then we can focus on the relative productivity foreach good (instead of the relative inputrequirements).

Trade ch2 27

The cost of producing 1 unit of good i is equal to the wagew multiplied by the number of hours required aLi

At home the cost is and abroad it isIf waLi < w*a*Li or a*Li/aLi > w/w*

good i should be produced in the _______ country If waLi > w*a*Li or a*Li/aLi < w/w*good i should be produced in the _______ country

Rationale:

is the relative ________ which is compared to the relative_______ (i.e. cost) w/w*.

�

a*Li/aLi

=1/a

Li

1/a *Li

Trade ch2 28

Example:France and GermanyCalculators, bread, cheese, wine and appleswe only need to know the relative wage to

figure out which good each country willexport.

Assume that w/w* = 2.5

Trade ch2 29

w/w* CA a*Li/aLia*Li (G)aLi (Fr)Good

303Apples

205Wine

93Cheese

21Bread

2550Calculator

For calculators, the relative productivity in France ( ) is _____than the relative wage (2.5), so France is ___ competitive and___________ has the comparative advantage.

2.5

Trade ch2 30

Similarly for bread, France has relative wages thatare ______ than its relative productivity (2.5 2)so France has a comparative _________ in bothcomputers and bread.

However in the case of cheese, wine and apple,France’s relative productivity is _______ thanthe relative wage so France has the comparative_______ in these 3 goods and will ______ themto Germany while Germany will ______computers and bread to France.

Trade ch2 31

Comparative advantage with manygoods - with transportation cost.

Let’s assume that the cost of the good doubleswhen shipped abroad - all the a’s double foreach country’s export good.

In the previous analysis we have determinedthat calculators and bread are Germany’sexport goods while cheese, wine, and applesare France’s export goods when shippingcosts are negligeable.

Trade ch2 32

w/w* CA a*Li/aLia*Li (G)aLi (Fr)Good

306Apples2010Wine96Cheese41Bread5050Calculator

The relative productivity for apple from France is still greaterthan the relative wage for France (5 > 2.5) so France still has aCA in apple and export them. .

2.5

Same table including shipping costs

Trade ch2 33

The relative productivity for computer from Germany isalso greater than the relative wage for Germany

(1/1 > 1/2.5 or 1 > .4) so Germany still has a CA incomputers and export them.

When we consider the other three goods that werepreviously traded (bread, cheese and wine), we find thefollowing:

the relative productivity has become smaller than therelative wage due to the inclusion of the shipping costs.

It is now prohibitive to export these goods.These are categorized as non-tradables.

Trade ch2 34

Multi country case

CA

205Sweden

155Germany

104France

PF/PcaLF/aLCChicken:

aLC

Fish:aLF

GoodCountry

.3

Trade ch2 35

In the case of Sweden and of France, the answer isstraightforward: they have a comparative advantageover the other 2 countries in fish and chickenrespectively.

Unless we know the relative world price, the answer forGermany is unclear.

If aGLF/aG

LC PF/PC Germany has a CA in fish overFrance only (but not over Sweden).

If aGLF/aG

LC PF/PC Germany has a CA in chickenover Sweden only (but not over France): this is thecase if the relative price is 0.3