Resources, Comparative Advantage and Income Distribution

1
Chapter 4

• Resources, Comparative Advantage and Income
  Distribution

2
CHAPTER 4 Overview

• Introduction
• Factor constraints and Production possibilities
• Relationship between factor endowments and output
  
• Rybczynski Theorem (holding prices constant) an
  increase in the relative abundance of one factor
  of production will lead to an increase in the
  relative supply of the good that uses that factor
  intensely.
• When factors are substitutable/ not substitutable
• Comparative advantage, pattern of trade, gains
  from trade
• Heckscher-Ohlin Theorem Countries will export
  goods that are relatively intense in their
  relatively abundant factors.

3
CHAPTER 4 Overview

• Relationship between goods prices and factor
  prices
• Stopler Samuelson Theorem if the relative price
  of a good increases, this will raise the real
  return of the factor that is used intensively in
  the production of that good, and will lower the
  real return of the other good
• Factor price equalization
• Income distribution and income inequality the
  effects of trade
• Empirical evidence

4
Introduction

• Ricardian model trade is explained by
  differences in labor productivity,
• Heckscher-Ohlin Theory
• Assumes that productivity and technology is the
  same across countries (i.e. no productivity
  differences across countries)
• Two Important Components argues that trade
  explained by
• differences in relative abundances of resources
  (factors of production) across countries.
• labor (skilled versus unskilled), physical
  capital, land, etc
• differences in intensity in which resources are
  used to produce goods
• example silicon chips are skilled intense,
  shirts are unskilled intense

5
Basic Assumptions in the Two Factor
Heckscher-Ohlin Model

• Two countries domestic and foreign
• Two goods cloth and food
• Two factors of production labor and land
• The amount of labor and land (factor endowments)
  varies across countries
• The supply of labor and land in each country is
  constant.
• Perfect Competition
• Zero profits
• Wage of each factor Marginal Product of the
  factor Price
• Factors are mobile across sectors
• Countries have the same technology and consumer
  tastes

6
Notation

• There are two factors of production labor and
  land.
• Unit labor requirements same in domestic and
  foreign.
• aTC units of land used to produce one unit of
  cloth
• aLC units of labor used to produce one unit of
  cloth
• aTF units of land used to produce one unit of
  food
• aLF units of labor used to produce one unit of
  food
• L,L total amount of labor available in
  dom/foreign
• T,T total amount of land available in
  dom/foreign

7
No Factor Substitutability

• We first look at the case when factors of
  production can not be substituted for one
  another.
• Unit factor requirements are fixed and can not
  change.
• Recipe Industries
• Example To produce 1 loaf of bread need exactly
• 1 cup of water
• 2 cups of flour
• 1 package of yeast
• No matter if water is cheap and flour is
  expensive, cannot substitute for each other
• (We will later allow for factor substitutability
  and this will yield a different looking PPF)

8
Relative Factor Intensity

• Relative factor intensity of an industry
• Cloth production is said to be labor-intense
  relative to food production if cloth production
  uses more labor for each acre of land than food
  production.
• ie. The labor to land ratio in the cloth industry
  exceeds that in the food industry

9
Relative Factor Intensity

• Assume that cloth production uses labor
  relatively intensively
• aLC /aTC gt aLF/aTF
• Implies that food production uses land relatively
  intensively
• aTF / aLF gt aTC /aLC

10
Production Possibilities

• Because there are two factors, have two factor
  market clearing conditions in each country.
• Total use of each factor total supply of each
  factor

11
Land and Labor constraints

• Production possibilities are influenced by both
  land and labor (requirements)
• Total use of land/labor Total supply
• aTFQF aTCQC T
• aLFQF aLCQC L

12
Land and Labor constraints

• Re-writing in the normal form of a line (food on
  the y-axis and cloth on the x-axis)
• Land constraint
• aTFQF aTCQC T
• (1) QF T/aTF -aTC/aTFQC
• Labor constraint
• aLFQF aLCQC L
• (2) QF L/aLF -aLC/aLFQC
• Notice that labor constraint is steeper than land
  because land is relatively labor intense.

13
Land and Labor constraints

• Endpoints of land constraint
• Cloth endpoint is maximum cloth production if
  constrained only by land.
• Food endpoint is maximum food production if
  constrained only by land.

14
Land and Labor constraints

QF
QF
LAND CONSTRAINT
LABOR CONSTRAINT
L/aLF
T/aTF
QC
QC
L/aLC
T/aTC

• Both conditions must hold.

15
PRODUCTION POSSIBILITIES

QF
LABOR CONSTRAINT
L/aLF
PPF
T/aTF
LAND CONSTRAINT
T/aTC
L/aLC
QC
16
Production Possibilities

• Production possibilities frontier
• Production possibilities are the interior of the
  factor constraints as must have enough labor and
  land
• Equilibrium production/ Full employment
• A country will produce at the intersection of the
  labor and the land constraints if its factors are
  fully employed.

17
Production Possibilities

• If there is more than one factor of production,
  the PPF is no longer a straight line. Why?
• Slope of PPF is the opp cost of production (of
  x-axis good)
• The opportunity cost of producing cloth in terms
  of food is not constant in this model Increasing
  opportunity costs.
• Opportunity Cost of Clothing
• its low when the economy produces a low amount
  of cloth and a high amount of food (labor
  constraint is non-binding)
• its high when the economy produces a high amount
  of cloth and a low amount of food (labor
  constraint is binding)

18
Production Possibilities

• Clothing is labor intense, if already producing a
  lot of it then labor is relatively scarce. On the
  other hand, land is abundant and could easily
  produce a lot of food.
• Increasing opportunity costs
• as clothing production increases after a certain
  point, the opportunity cost of producing clothing
  increases (requires giving up more and more food)

19
Example 4.1 PPFs and Output

• Unit factor requirements and endowments for the
  US
• Clothing Food
• aLC2 aLF1
• aTC1 aTF2
• L300
• T300
• Clothing is labor intense and food is land
  intense.
• aLC /aTC 2 gt aLF/aTF 1/2

20
Example 4.1 PPFs and Output

• Derive and draw equations for the production
  possibility frontier
• aLC2 aLF1 L300
• aTC1 aTF2 T300
• Land
• QF T/aTF -aTC/aTF QC QF 150 -1/2 QC
• Labor
• QF L/aLF -aLC/aLF QC QF 300 - 2
  QC

21
Example 4.1 PPFs and Output

• What production bundle fully employs both
  factors?
• Both constraints must hold with equality
  simultaneously. Find Intersection
• Land QF 150 -1/2 QC
• Labor QF 300 - 2 QC
• 150 - 1/2 QC 300 - 2 QC QF 300 - 2
  QC
• 1.5 QC 150 300 - 2(100)100
• QC 100 QF 100

22
Example 4.1 PPFs and Output
The intersection of the two factor constraints is
where there is full employment of both resources.
This is where the economy would produce in
autarky and full employment of resources.
QF

300
150
100
150
100
300
QC
23
Increase in land

• What is the effect of an increase in the land
  endowment (T increases)
• Land constraint shifts out parallel -slope
  unchanged
• Both endpoints of the land constraint increase
  when T increases.

24
Increase in land
Land constraint shifts out parallel - slope
unchanged Both endpoints of the land constraint
increase when T increases.
QF
LABOR CONSTRAINT

L/aLF
T/aTF
LAND CONSTRAINT
T/aTC
L/aLC
QC
25
Increase in land
When land increases from T1 to T2, the land
constraints shifts out. This biases the
production possibilities curve towards food
production (the land intense good).
QF

L/aLF
T2/aTF
T1/aTF
New PPF
T2/aTC
T1/aTC
L/aLC
QC
26
Example 4.2 Increase in land

• Suppose the US land endowment expands from T1300
  to T2450.
• Recall,
• aLC2 aLF1 L300
• aTC1 aTF2 T1300
• The new land constraint is
• QC2QF450
• QF225-1/2QC

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Example 4.2 Increase in land

• What is the new production bundle that fully
  employs both factors?
• New Land QF225 - 1/2QC
• Labor QF 300 - 2 QC
• 225 - 1/2 QC 300 - 2 QC QF 300 - 2
  QC
• 1.5 QC 75 300 - 2(50)200
• QC 50 QF 200

28
Example 4.2 Increase in land
QF

300
200
150
100
150
100
300
450
QC
50
29
Factor Levels and Output Levels

• Rybczynski Theorem
• (Holding prices constant), if the relative
  endowment of a factor increases, then the
  relative supply of the good that uses this factor
  intensively increases.

30
Relative Factor Levels and Relative Output Levels

• Implication of Rybczynski Theorem
• A country will have a higher relative supply of
  the good that makes intensive use of its relative
  abundant factor.
• A country is relatively labor abundant if its
  labor to land ratio is higher.
• For example the domestic country will be labor
  abundant if L/T gt L/T

31
Example 4.3 Factors and Shapes of PPFs

• Consider two countries domestic and foreign
• aLC2 aLF1
• aTC1 aTF2
• L150, T100
• L 100, T 150
• Clothing is labor intense and food is land
  intense.
• aLC /aTC 2 gt aLF/aTF 1/2
• Domestic country is labor abundant and foreign is
  land abundant.
• L/T1.5 gt L/T 2/3

32
Example 4.3 Factors and Shapes of PPFs

• Derive and draw equations for the production
  possibility frontiers in the two countries.
• Domestic
• Land QF T/aTF -aTC/aTF QC QF 50 -
  1/2 QC
• Labor QF L/aLF -aLC/aLF QC QF 150
  - 2 QC
• Foreign
• Land QF T/aTF -aTC/aTF QC QF 75
  -1/2 QC
• Labor QF L/aLF -aLC/aLF QC QF
  100 - 2 QC

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Example 4.3 Factors and Shapes of PPFs

• Production under full employment/ No trade
• FOREIGN DOMESTIC
• QF 75 -1/2 QC QF 50 -1/2 QC
• QF 100 - 2 QC QF 150 - 2 QC
• 75-1/2 QC 100 - 2 QC 50-1/2 QC 150 -
  2 QC
• QC 16.7 QC 66.7
• QF 66.7 QF 16.7
• QC /QF gt QC /QF
• The relative supply of the labor intense good is
  greater in the labor abundant country.

34
Example 4.3 Factors and Shapes of PPFs

QF
QF
FOREIGN
DOMESTIC
150
100
75
50
QC
100
75
QC
150
50
Differences in shapes of PPFs driven by
differences in factor endowments, not
productivity differences
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END PART 1