Comparative Advantage and the Ricardian Model

1
Comparative Advantage and the Ricardian Model

• Krugman Obstfeld Chapter 2
• Appleyard Field Chapter 3 4

Course website www.valt.helsinki.fi/katal/opiskel
u/ka6a_08.htm
2
Comparative Advantage
England has absolute advantage in both products
if e.g.
3
Relative Prices in Autraky

• Autarky (no trade) price of wine in terms of
  cloth
• England 1 bbl. wine 3 yd. cloth
• Portugal 1 bbl. wine 2 yd. cloth
• Autarky price of cloth in terms of wine
• England 1 yd. cloth 0,33 bbl. wine
• Portugal 1 yd. cloth 0,5 bbl. Wine
• ? Cloth is relatively cheaper in England, wine
  in Portugal the opportunity cost of producing
  wine is higher in England

4
Rationale for Trade

• If international trade is allowed
• England wants to buy wine if it costs less than 3
  yards of cloth per barrel of wine
• Portugal wants to sell wine if it gets more than
  2 yards of cloth per barrel of wine
• ? Both are willing to trade ( both gain) for
  any price between 2 - 3 yard per barrel

5
Gains from Trade for England

• Suppose that the international price turns out to
  be 2,5 yard per barrel
• In autarky England can produce a barrel of wine
  with 3 hours of labour
• In free trade England can produce 2,5 yard with
  2,5 hour of work and exchange it for a barrel of
  wine
• ? England can get a barrel of wine with ½ hour
  less work than in autarky

6
Gains from Trade for Portugal

• International price 2,5 yards per barrel
• In autarky Portugal can produce 2,5 yard of cloth
  with 5 hours of work
• In free trade Portugal can produce a barrel of
  wine with 4 hours of work
• ? Portugal gets 2,5 yards of cloth with an hour
  less work

7
Mutual Gains from Trade

• Suppose both countries want to consume five yards
  of cloth and two barrels of wine
• In autarky England needs 11 hours to do this,
  Portugal needs 18
• In free trade England produces ten yards of cloth
  in 10 hours and Portugal produces four barrels of
  wine in 16 hours
• ? The same total amount is produced with 3 hours
  less work
• ? Another (more standard) interpretation
• more output with constant labour input

8
Comparative Advantage

• A country has a comparative advantage in
  producing a good if the opportunity cost is lower
  than in other countries
• Samuelson comparative advantage is the best
  example of an economic principle that is
  undeniably true yet not obvious to intelligent
  people
• This is the fundamental source of mutual gains
  from trade (another source is economies of scale,
  which we will discuss later in the course)

9
Assumptions of the Basic Ricardian Model

• Fixed resources and technology
• Completely mobile factors of production (labour
  in the simplest case) inside each country
• Completely immobile factors of production between
  the countries
• Full utilization of resources
• Perfect competition
• Labour theory of value (not necessary for PPF
  analysis)
• Zero transportation costs
• Constant unit costs
• Policy options Complete autarky OR free trade

10
Resource Constraints
Productivity / technology

• Resource constraint Suppose that England has
  9,000 hours of labour available and Portugal has
  16,000 hours of labour
• England can produce 9,000 yards of cloth and no
  wine or 3,000 barrels of wine and no cloth or
  some combination of these two
• Similarly for Portugal (8,000 yd. or 4,000 bbl.
  or combination)

11
Production Possibilities Frontier (PPF)
Cloth
England
Limits of production aCQCAWQWL where aj
unit labour requirement of producing good j, Qj
quantity of good j and L total labour supply
9,000
4,500
Slope of the PPF the amount of production of
one good that must be given up to obtain one
additional unit of the other good
3,000
1,500
Wine
12
Production Possibilities Frontier (PPF)
Cloth
Portugal
8,000
4,000
4,000
2,000
Wine
13
Consumption Possibilities Frontier (CPF) under
free trade
Suppose that the international price turns out to
be 2,5 yard per barrel and England produces only
cloth
Slope of the CPF the amount of consumption of
one good that must be given up to obtain one
additional unit of the other good
England
14
Consumption Possibilities Frontier (CPF) under
free trade
PW 2,5 yard per barrel, Portugal produces only
wine
Slope of the CPF the amount of consumption of
one good that must be given up to obtain one
additional unit of the other good
Portugal
Wine
15
Impact of International Price Change from 2,5
yr./bbl. to 2,25
England
Portugal
Cloth
Cloth
10,000
9,000
9,000
8,000
2,25
2,5
3,600
4,000
4,000
Wine
Wine
16
Complete Specialization
Cloth

• Suppose England would use 3,000 hours to produce
  1000 bbl. wine and 6,000 hours to produce 6,000
  yr. of cloth
• PW 2,5 yr./bbl.

9,000
8,500 (6,000 10002,5)
3,000
3,600
Wine
(1000 6000/2,5) 3,400
Note Optimality of complete specialization
follows from the assumption of constant labour
requirements of production (this is why PPF is
linear). Later (in the HO-model) we will drop
this assumption. Yet, this affects the
conclusions only in terms of degree, i.e.
countries will still increase their
specialization due to trade.
17
Monetizing the Model

• Domestic price labour time wage (labour
  theory of value)
• Assume that wage rate in England is 1/hr. and in
  Portugal 0.6
• The domestic prices are

18
Basis for Trade

• England is willing to sell cloth if price is more
  than 1 and to buy wine if price is less than 3
• Similarly Portugal is willing to buy cloth if
  price is less than 1.2 and to sell wine if price
  is more than 2.4
• If the exchange rate is e.g. 11, basis for
  trade exist

19
Exchange Rates

• The link between domestic and international
  prices
• The price of a currency in terms of another
  currency 2e1 ? e1/20.5
• Vocabulary If e0.5 ? e1, we say that the
  pound revaluated and the euro devaluated (when
  exchange rates are floating). When the exchange
  rates are fixed we say that the pound has been
  revaluated or the euro has been devaluated

20
Export Condition

• England will export good j if
• aE,jWEe lt aP,jWP
• where aE,j amount of labour required in to
  produce good j England, aP,j amount of labour
  required to produce good j in Portugal, WE wage
  in England, WP wage in Portugal, e exchange
  rate (/). That is, the left-hand-side is the
  autarky price (cost of production) in England and
  the right-hand-side the autarky price in Portugal
  expressed in the same currency
• Dividing both sides by WEeaP,j we can rewrite
  the export condition as
• aE,j/aP,jlt WP /(WEe)

21
Wage Rate Limits (1)

• What wages lead England to export cloth and
  Portugal to export wine? (when exchange rate is
  fixed)
• England exports if PW gt aE,jWe and imports if
  PW lt aE,jWe
• Indifference between autarky and trade if
• PW PE PP ? aEWEe aPWP
• where PW world price, PE autarky price in
  England, PP autarky price in Portugal, aE
  amount of labour required in England, aP amount
  of labour required in Portugal, WE wage in
  England, WP wage in Portugal

22
Wage Rate Limits (2)

• Assume for simplicity that the exchange rate is
  fixed at e1 (11)
• Labour required for cloth aE1, aP2
• ? Both are indifferent if 1WE2WP
• Labour required for wine aE3, aP4
• ? Indifferent if 3WE4WP ? WE1.333WP
• ? England exports cloth and imports wine if
  1.33WP lt WE lt 2WP (and e1)

23
Exchange Rate Limits

• What exchange rates result England exporting
  cloth and Portugal wine? (wages fixed at WE1,
  WP0.6)
• Cloth England exports if price is more than 1,
  Portugal imports if price is less than 1.2
• ? Both are indifferent if 11.2
• Wine Portugal exports if price is more than
  2.4, England imports if price is less than 3
• ? Both are indifferent if 32.4 ? 12.4/30.8
• ? Trade occurs if e is the range (0.8,1.2),
• that is, you can buy one euro for 0.8 to 1.2
  pounds

24
Extension Multiple Commodities

• Export condition aE,j/aP,jlt WP /(WEe)
• Plugging in the wage rates and assuming fixed
  exchange rate at e1 we can rewrite this as
  aE,j/aP,jlt 0.6 (0.6 /1e)

25
Multiple Commodities

• Thus we need to calculate the relative labour
  requirements and compare them to the export
  condition (England exports)
• aE,j/aP,jlt WP /(WEe) 0.6

26
Wage Rate Change

• Assume that the wage rate in England increases to
  1.2/hr. The export condition becomes
• aE,j/aP,jlt WP /(WEe) 0.5 ( 0.6/1.2 )

27
Exchange Rate Change

• Assume that after the wage rate in England has
  increased to 1.2/hr, the pound devaluates to
  21 (e1/20.5). The export condition becomes
• aE,j/aP,jlt WP /(WEe) 1 (0.6/(1.20.5))

28
Other Extensions

• Transportation costs
• Export condition (aE,jtrj)/aP,jlt WP /(WEe),
  where trj is the transportation cost for product
  j expressed in labour hours required for
  transportation
• Some goods may become nontradable
• Multiple countries
• More complicated trade patterns depend on terms
  of trade (will be discussed later in the course)

29
The most important lessons

• Countries have comparative advantage in producing
  different goods and hence they can get mutual
  benefits from trade
• This is because countries differ from each other.
  The more different they are, the larger the
  (potential) benefits from trade
• In the Ricardian model the source of comparative
  advantage is differences in productivity.