Transcript PPF under Capital Constraint

Week 3: Part 1
Resources and
Trade: The
Heckscher-Ohlin
Model
Copyright © 2012 Pearson Education. All rights reserved.
Introduction
• In the Ricardian model, trade is explained by
differences in labor productivity that gives rise to
comparative advantage.
• Differences in resources across countries can also
give rise to international trade.
• The Heckscher-Ohlin theory (or factor-proportions
theory) argues that differences in resources (labor,
labor skills, physical capital, land or other factors of
production) across countries create productive
differences that explain why trade occurs.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-2
Two Factor Heckscher-Ohlin Model
We discuss the two factor Heckscher-Ohlin model using the
following simplifying assumptions:
1. Labor and capital are the resources important for production (two
factors of production = labor and capital).
2. The amount of labor services and capital varies across countries,
and this variation influences productivity.
3. The supply of labor services and capital in each country is
constant.
4. Only two goods are important for production and consumption:
cloth and food.
5. Competition allows factors of production to be paid a
“competitive” wage, a function of their productivities and the
price of the good that they produce, and allows factors to be used
in the industry that pays the most.
6. Only two countries are modeled: Home and Foreign.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-3
What an economy can produce?
• When there is more than one factor of production, the
opportunity cost in production is no longer constant and
the PPF is no longer a straight line. Why??
• Let’s expand the Ricardian model to include two factors
of production, labor (L) and capital (K).






aKC
aLC
aKF
aLF
K
L
=2
=2
=3
=1
= 3000
= 2000
capital used to produce one yard of cloth
labor used to produce one yard of cloth
capital used to produce one calorie of food
labor used to produce one calorie of food
total amount of capital available for production
total amount of labor available for production
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-4
Production possibilities are influenced by both land and
labor (requirements):
aKF QF + aKC QC ≤ K
Capital used for
each calorie of
food production
Total calories
of food
production
Capital used for
each yard of cloth
production
aLF QF + aLC QC ≤ L
Labor used for
each calorie of
food production
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
Total amount of
capital resources
Total yards
of cloth
production
Total amount of
labor resources
Labor used for
each yard of cloth
production
4-5
Using the numbers on Slide 4, we have:
Capital:
aKF QF + aKC QC ≤ K
3 QF + 2 QC ≤ 3000
Labor:
aLF QF + aLC QC ≤ L
1 QF + 2 QC ≤ 2000
The economy must produce subject to both constraints,
i.e., it must have enough capital and labor.
Given 2 factor of production, how to draw the
PPF?
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-6
PPF under Capital Constraint
aKF QF + aKC QC ≤ K
When QC = 0, aKF QF = K
When QF = 0,
QF = K / aKF
Given that:
3 QF + 2 Q C
When QC = 0, 3 QF = 3000
QF = 1000
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
aKC QC = K
QC = K / aKC
≤ 3000
When QF = 0,
2 QC = 3000
QC = 1500
3-7
Slope of PPF
= ΔQF / ΔQC
(y-axis: QF; x-axis: QC)
= (K/aKF) ÷ (K/aKC)
= aKC /aKF
Slope of PPF = Opportunity Cost of Cloth (in terms of Food)
= Ratio of Unit Capital Requirements (aKC /aKF )
The opportunity cost of cloth (in terms of food) is defined as the
number of calories of food to be given up for producing an extra yard
of cloth.
In our example,
Slope of PPF = -2/3
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
3-8
PPF under Labor Constraint
aLF QF + aLC QC ≤ L
When QC = 0, aLF QF = L
When QF = 0,
QF = L / aLF
Given that:
1 QF + 2 QC
When QC = 0, 1 QF = 2000
QF = 2000
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
aLC QC = L
QC = L / aLC
≤ 2000
When QF = 0,
2 QC = 2000
QC = 1000
3-9
Slope of PPF
= ΔQF / ΔQC
(y-axis: QF; x-axis: QC)
= (L/aLF) ÷ (L/aLC)
= aLC /aLF
Slope of PPF = Opportunity Cost of Cloth (in terms of Food)
= Ratio of Unit Labor Requirements (aLC /aLF )
The opportunity cost of cloth (in terms of food) is defined as the
number of calories of food to be given up for producing an extra yard
of cloth.
In our example,
Slope of PPF = -2
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
3-10
Fig. 4-1: The PPF Without Factor Substitution
Without factor substitution, the PPF
is the interior of the two factor
constraints (red kinked PPF)
Why PPF is a kinked line?
The economy can’t use more than the available supply
of capital and labor (in our example, K = 3000, L =
2000).
Subject to both capital and labor constraints:
(1) When QC = 0, what is the maximum food production?
1000 or 2000 units?
1000 calories of food? K = 3 x 1000 = 3000
✔
L = 1 x 1000 = 1000
✔
2000 calories of food? K = 3 x 2000 = 6000
✗
L = 1 x 2000 = 2000
✔
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-12
(2) When QF = 0, what is the maximum cloth production?
1000 or 1500 units?
1000 yards of cloth?
1500 yards of cloth?
K = 2 x 1000 = 2000
✔
L = 2 x 1000 = 2000
✔
K = 2 x 1500 = 3000
✔
L = 2 x 1500 = 3000
✗
To reiterate, due to the constraints of K and L, the PPF
is the kinked line shown in red.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-13
• The kinked PPF line implies that the opportunity cost
of producing cloth in terms of food is not constant.
• The opportunity cost rises as the economy’s mix of
production shifts toward cloth:
 It is low (2/3) when the economy produces less
cloth and more food.
 It is high (2) when the economy produces more
cloth and less food.
• The red kinked PPF does not allow the substitution of
capital for labor in production or vice versa.
 Unit factor requirements are constant along each line
segment of the PPF.
 In our example, Cloth: 2K, 2L; Food: 3K, 1L.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-14
What if factor substitution is allowed?
• If producers can substitute one input for another in the
production process, then the PPF becomes curved
(bowed shaped).
 For example, to produce one yard of cloth, the current ratio is
2K: 2L. If factor substitution is allowed, the production of cloth
can use different input choice, say 1K: 4L.
 Unit factor requirements can vary at every quantity of cloth
and food that could be produced.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-15
Fig. 4-2: The PPF with Factor Substitution
Still, the opportunity cost of cloth
in terms of food rises as the
economy produces more cloth
and less food.
Bowed Shaped
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-16
What an economy does produce?
• The PPF describes what an economy can produce,
but to determine what the economy does produce, we
must determine the prices of goods.
• In general, the economy should produce at the point
that maximizes the value of production, V:
V = PCQC + PFQF
 where PC is the price of cloth and PF is the price of food.
• Define an isovalue line as a line representing a
constant value of production, V.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-17
V = PCQC + PFQF
Since the PPF is plotted with QF on the y-axis, and
QC on the x-axis, we will specify the equation of the
isovalue in terms of QF.
PFQF = V – PCQC
QF = V/PF – (PC /PF)QC
The slope of an isovalue line is –(PC /PF), i.e. the
relative price of cloth.
The economy produces at the point that maximizes
V. Q is the point that the PPF touches the highest
possible isovalue line.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-18
Fig. 4-3: Prices and Production
At Q, the slope of the PPF is the
same as the slope of isovalue line,
i.e.,– (PC /PF).
Slope of PPF
= Opportunity cost of cloth
At Point Q:
Slope of PPF = Slope of Isovalue
Opportunity Cost = Relative Price
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-19
What determines inputs combination (capital
versus labor)?
• When producers can substitute one input for another
in the production process, then the PPF becomes
bowed shaped (see Slide 16).
• In our example, to produce one calorie of food,
farmers use 3K: 1L.
• A two-factor model allows farmers to use different mix
of inputs. For instance, 2K: 2L.
• Figure 4-4 shows different combinations of labor and
tanah in producing one calorie of food.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-20
Fig. 4-4: Input Combinations in Food Production
Unit factor
requirements of
capital and labor are
not constant in the
Heckscher-Ohlin
model
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-21
• Producers may choose different amounts of factors of
production (capital and labor) to produce cloth or
food.
• Their choice depends on the wage rate (w) for labor,
and the rental rate (r) for capital.
• As w increases relative to r (w/r ), producers will use
less labor and more capital (L/K ).
• This implies a negative relationship between wagerental ratio (w/r) and labor-capital ratio (L/K). See CC
and FF in Figure 4-5.
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-22
Fig. 4-5: Factor Prices and Input Choices
The graph shows that when w/r 
(wage increases), L/K  (less
labor used).
This applies to both food and
cloth production.
The graph also shows that, at
any given factor prices w/r, cloth
production uses more labor
relative to capital than food
production uses.
In other words, we assume:
Cloth: Labor Intensive
Food: Capital Intensive
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-23
Can a good be both labor- and capital-intensive?
• Using the numbers given on Slide 4:
Cloth:
aKC = 2
aLC = 2
Food:
aKF = 3
aLF = 1
To measure factor intensity, it is not the absolute
amount of capital and labor used, but their ratio.
Labor intensity (Cloth) = aLC / aKC = 2/2 = 1
Labor intensity (Food) = aLF / aKF = 1/3 = 0.33
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-24
Since
aLC / aKC > aLF / aKF
We say that cloth production is labor intensive.
Food production, on the other hand, is:
Capital intensity (Cloth) = aKC / aLC = 2/2 = 1
Capital intensity (Food) = aKF / aLF = 3/1 = 3
Since aKF / aLF > aKC / aLC, we say that food production
is tanah intensive.
So, what is your answer?
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-25
To be Continued…
Copyright © 2009 Pearson Addison-Wesley. All rights reserved.
4-26