1. Comparative Advantage and the Ricardian Model
Krugman & Obstfeld: Chapter 2
Appleyard & Field: Chapter 3 & 4
Course website:

2. Comparative Advantage
England has absolute advantage in both products if e.g.
Cloth
Wine
England
1 hr. / yd.
3 hrs. / bbl.
Portugal
2 hr. / yd.
4 hrs. / bbl.
In the book the other way around (England has absolute disadvantage in both goods)

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 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
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)
Productivity / technology:
Cloth
Wine
England
1 hr. / yd.
3 hrs. / bbl.
Portugal
2 hr. / yd.
4 hrs. / bbl.

11. Production Possibilities Frontier (PPF)
Cloth
England
Limits of production:
aC*QC+AW*QW≤L
where aj = unit labour requirement of producing good j, Qj = quantity of good j and L = total labour supply
Cloth
Wine
9,000
4,500
1,500
3,000
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
1,500
3,000
Wine

12. Production Possibilities Frontier (PPF)
Cloth
Portugal
Cloth
Wine
8,000
4,000
2,000
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
Cloth
Wine
3,000
9,000
3,600
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
Cloth
Wine
9,000
4,500
1,800
3,600

14. Consumption Possibilities Frontier (CPF) under free trade
Cloth
8,000
4,000
10,000
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
Cloth
Wine
10,000
5,500
1,800
4,000
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, *2,5)
wine = 6000/ = = 3400
cloth = 1000*2, = = 8500
3,000
3,600
Wine
( /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:
Cloth
Wine
England
1 hr.*1£
= £1
3 hrs*£1 = £3
Portugal
2 hr.*0.6 =€1.2
4 hr*0.6 =€2.4

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. £1=€1, basis for trade exist

19. Exchange Rates The link between domestic and international prices
The price of a currency in terms of another currency: £2*e=€1  e=€1/£2=0.5
Vocabulary: If e=0.5 → e=1, 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,j*WE*e < aP,j*WP
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 WE*e*aP,j we can rewrite the export condition as:
aE,j/aP,j< WP /(WE*e)

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 > aE,j*W*e and imports if PW < aE,j*W*e
Indifference between autarky and trade if:
PW = PE = PP  aE*WE*e = aP*WP
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: e=1 (£1=€1)
Labour required for cloth: aE=1, aP=2
→ Both are indifferent if 1*WE=2*WP
Labour required for wine: aE=3, aP=4
→ Indifferent if 3*WE=4*WP  WE=1.333*WP
→ England exports cloth and imports wine if 1.33WP < WE < 2WP (and e=1)

23. Exchange Rate Limits
What exchange rates result England exporting cloth and Portugal wine? (wages fixed at WE=£1, WP=€0.6)
Cloth: England exports if price is more than £1, Portugal imports if price is less than €1.2
→ Both are indifferent if £1=€1.2
Wine: Portugal exports if price is more than €2.4, England imports if price is less than £3
→ Both are indifferent if £3=€2.4  £1=2.4/3=€0.8
→ 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
Wage rate
Olives
Wine
Cider
Cloth
England
£1/hr.
10 hrs.
3 hrs.
2.9 hrs.
1 hrs.
Portugal
€0.6/hr.
4 hrs.
5 hrs.
Export condition: aE,j/aP,j< WP /(WE*e)
Plugging in the wage rates and assuming fixed exchange rate at e=1 we can rewrite this as: aE,j/aP,j< 0.6 (=€0.6 /£1*e)

25. Multiple Commodities aE,j/aP,j< WP /(WE*e) = 0.6
Thus we need to calculate the relative labour requirements and compare them to the export condition (England exports)
aE,j/aP,j< WP /(WE*e) = 0.6
Olives
Wine
Cider
Cloth
aE,j/aP,j
10/3=3.3
¾=0.75
2.9/5=0.58
1/3=0.33
Exporter
Portugal
England
If labour requirement for cider would be 3 in England, we would have a/a=0.6 = indifference (w/ arbitarily small transportation cost trade would not occur)

26. Wage Rate Change aE,j/aP,j< WP /(WE*e) = 0.5 (= 0.6/1.2 )
Assume that the wage rate in England increases to £1.2/hr. The export condition becomes
aE,j/aP,j< WP /(WE*e) = (= 0.6/1.2 )
Olives
Wine
Cider
Cloth
aE,j/aP,j
10/3=3.3
¾=0.75
2.9/5=0.58
1/3=0.33
Exporter
Portugal
England

27. Exchange Rate Change aE,j/aP,j< WP /(WE*e) = 1 (=0.6/(1.2*0.5))
Assume that after the wage rate in England has increased to £1.2/hr, the pound devaluates to £2=€1 (e=1/2=0.5). The export condition becomes
aE,j/aP,j< WP /(WE*e) = 1 (=0.6/(1.2*0.5))
Olives
Wine
Cider
Cloth
aE,j/aP,j
10/3=3.3
¾=0.75
2.9/5=0.58
1/3=0.33
Exporter
Portugal
England

28. Other Extensions Transportation costs Multiple countries
Export condition: (aE,j+trj)/aP,j< WP /(WE*e), 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.