Supplementary notes
Chapter 3
Unit Labor Requirements
C
W
Home
1
2
Labor
supply
120
Foreign
6
3
240
Opportunity cost
• To increase C production by one unit, aLC
hours are required. The resulting sacrifice
in W production is aLC/aLW.
• The opportunity cost of C in terms of W is
____ in Home.
• In Foreign, the opportunity cost of C is
____.
Relative price and Opportunity Cost
• Before trade, the relative price of C to W is the
same as the opportunity cost of C. Why?
• Perfect competition  No profits
 market price = production cost
Pc = aLC W
Pw = aLW W
(W is the wage rate)
 Pc/Pw = aLC / aLW
Absolute advantage and
Comparative advantage
• Home has absolute advantage in _____.
• Foreign has absolute advantage in _____.
• Home has comparative advantage in
_____.
• Foreign has comparative advantage in
_____.
Production Possibilities Frontier
• Production possibilities for Home.
1 Qc + 2 Qw = 120
Qw = 60 – ½ Qc
• Production possibilities for Foreign.
Try!
Production Possibilities Frontier
• Draw the PPF for Home. Show that the
(absolute value of the) slope is the same
as the opportunity cost of C.
• Do the same for Foreign.
Terms of Trade
• The terms of trade (ToT) is the relative price
(PC / PW) in international trade.
• ToT must be between the two OC’s.
– In our example, Home’s OC (= 1/2) < Foreign’s OC (=
2)
– What would happen if ToT is greater than 2?
– (ToT may be equal to one of OC’s in extreme cases.)
• Home’s OC (1/2) < ToT < Foreign’s OC (2)
– PC / PW > aLC / aLW = aLCW / aLWW
– PC / PW < a*LC / a*LW = a*LCW* / a*LWW*
Pattern of production
PC / PW > aLC / aLW
• Meaning of this inequality?
• Can you explain why Home will produce
only cheese and there will be no
production of wine?
What if PC / PW = aLC / aLW?
Consumption Possibilities Frontier
• Assume ToT = 1.
• For Home
– At the above ToT, Home produces only C. On PPF,
find the point of production after trade.
– Find the maximum amount of W Home can buy with
the amount of C.
– Connect the two points. The resulting line is the CPF
under trade.
– Note CPF under autarky is the same as PPF.
– This shows that trade expands the CPF.
• Do the same for Foreign.
Gains from trade
3 ways to show gains from trade
A. Trade brings an expansion of production
in the world as a whole.
– Suppose that each country reduces the
production of the good it has comparative
disadvantage by 1 unit and moves saved
resources to the good it has comparative
advantage. Show what happens to the world
production.
B. Trade leads to an expansion of CPF.
Gains from trade
3. For Home, it is cheaper to produce wine
indirectly through trade than to produce it
directly.
– Direction production of wine costs 2 hours.
– Indirect production of wine costs 1 hour if the
ToT = 1. (To get 1W in trade requires 1C at
the given ToT. 1C requires 1 hour of work in
Home.)
– Consider changes in real wages!
ToT and Relative Supply
• ToT is determined by relative supply (RS) and relative
demand (RD).
– Both RS and RD are “of C relative to W).
• To find RS (supply of C relative to W):
–
–
–
–
Remember OC < OC* in our case
If ToT < OC, both countries will produce only ___. So the RS = 0.
If ToT > OC*, both will produce only ___. So the RS  .
If OC < ToT < OC*, then each country produces the good in
which it has comparative advantage. RS = ____.
– If ToT = OC or OC*, the RS is indeterminate.
• Why?
• Consider the case where OC < ToT = OC*.
• Home will produce only cheese. But Foreign will produce both. The
exact amount of each good produced in Foreign depends on the
demand condition.
Determination of ToT
• Relative demand is like usual demand. It is
negatively sloping.
• Each country’s production pattern and ToT are
determined at the intersection of the RS and RD
curves.
• Show how the ToT changes in each of the
following cases.
– The demand for cheese declines.
– The demand for wine increases .
– Home’s production capacity shrinks as a result of a
natural disaster.
Wages and Productivities
• In our example
– aLC /a*LC = 1/6
– aLW /a*LW = 2/3
• Then W* / W cannot be lower than ___
and higher than ____.
• What if W* / W < aLC /a*LC ? _____
Prices and Wages
• In our example,
•
•
•
•
– PC = aLCW
– PW = a*LWW* (why?)
From the above, PC / PW = aLCW / a*LWW*
Rewrite and obtain
W / W* = (a*LW /aLC) (PC / PW )
Home’s relative wage is higher
–
–
–
–
The more productive is Home’s labor (smaller aLC)
The less productive is Foreign’s labor (greater a*LW)
The higher is the relative price of cheese or ToT.
(Note the ToT is determined by RS and RD.)
Exercises
Unit labor requirements for two goods butter
(B) and cheese (C) for two countries are
given below:
•
France
Germany
•
Butter
10
5
•
Cheese
4
3
•
Labor Supply
8000
6000
Exercises
1. Fill in blanks.
a) Under autarky, the relative price of butter to
cheese is ( ) in France.
b) Germany has comparative advantage in ( ).
c) ( ) has absolute advantage in cheese.
d) If the German hourly wage rate is $30, the
French wage rate cannot be higher than (
).
e) Draw the world relative supply curve for QB/QC.
Exercises
2. Suppose that according to a report, 400 units of butter
are traded for 800 units of cheese each period.
a) What is the terms of trade?
b) Which country exports butter? Cheese?
c) Find the amounts of consumption of butter and cheese
in France.
d) In the following diagram for France, show and mark (i)
“PPF” for the production possibility frontier, (ii) “CPF”
for the consumption possibilities frontier, (iii) “P” for the
production point in trade, and (iv) “C” for the
consumption point. Use the X-axis for butter as
indicated.
Exercises
3. At the terms of trade mentioned in (2), if
the German hourly wage rate is $30, the
French wage rate should be ______.
4. Is trade illustrated above beneficial for
France? Compare the cost of production
of butter in direct production and indirect
production.