The HeckscherOhlinSamuelson Model

1
The Heckscher-Ohlin-Samuelson Model

• Factor Proportions Theory

2
Problems with the Generic Neoclassical Model

• What is the source of a countrys comparative
  advantage? Generic neoclassical theory doesnt
  really say
• Factors other than labor (especially capital) are
  not explicitly included

3
H-O-S In General

• Heckscher, and his student Ohlin, worked in the
  early part of the 20th century
• Samuelson refined their work after WWII
• Closer attention is paid in this model to each
  countrys resource endowment

4
H-O-S Assumptions

• 2 countries
• 2 commodities
• 2 factors (labor and capital)
• Perfect competition exists in all markets
• Each countrys endowment of factors is fixed
• Factors are mobile internally, but immobile
  internationally

5
H-O-S Assumptions (contd)

• Each producer has a wide range of options as to
  how to produce X or Y
• if K is cheap relative to labor, a relatively
  capital-intensive method will be adopted
• if K is expensive relative to labor, a relatively
  labor-intensive method will be adopted
• Each country has the same CRTS technology

6
H-O-S Assumptions (contd)

• Tastes and preferences are the same for both
  countries

7
Concepts and Terminology

• The capital-labor ratio for good X is simply
  KX/LX, and for Y is KY/LY
• If KX/LX gt KY/LY, production of good X is capital
  intensive relative to production of good Y
• For example, the amount of capital per worker in
  the U.S. petroleum and coal industry is 468,000
• The similar figure for apparel products is 8,274
• Therefore, petroleum and coal is produced in a
  relatively capital-intensive manner

8
Concepts and Terminology

• Also, production of Y must be relatively labor
  intensive (If KX/LX gt KY/LY, then LY/KY gt LX/KX)
• That is, apparel products are produced in a
  labor-intensive manner (as compared to petroleum
  and coal)

9
Relative Factor Intensities, Selected U.S.
Industries (1992)
10
Concepts and Terminology

• Country A is said to be capital abundant relative
  to Country B if (K/L)A gt (K/L)B
• For example, if the U.S. has a capital stock of
  4.3 trillion and a labor force of 121 million,
  then K/L is about 36,000.
• K/L for India works out to 607 billion/304
  million 2,000.
• Therefore, the U.S. is capital abundant relative
  to India India is relatively labor abundant.

11
Relative Factor Endowments, Selected Countries
(1992)
12
Concepts and Terminology

• To summarize
• goods are produced relatively K or L intensively
• countries are relatively K or L abundant

13
Concepts and Terminology

• The factor price of labor (the wage) is denoted w
• The factor price of capital is denoted r
• If labor is relatively expensive, w/r will be a
  relatively big number
• If labor is relatively cheap, w/r will be a
  relatively small number

14
More on Factor Prices

• What makes labor relatively expensive?
• If it is relatively scarce
• What makes labor relatively cheap?
• If it is relatively abundant
• So If (K/L)A is a relatively big number (that
  is, capital is relatively abundant), w/r will be
  a relatively big number, reflecting the relative
  scarcity of L and abundance of K

15
A Review of Trade in the Neoclassical Model

• Suppose the U.S. is capital abundant relative to
  Mexico
• This, of course, means that Mexico is relatively
  labor abundant
• These differences affect the shape of each
  countrys PPF
• Suppose that cars are produced rel.
  K-intensively, and textiles labor intensively

16
Autarky in Mexico and the U.S.
U.S.
Mexico
Cars
Cars
(PT/PC)Mex
E
e
Y1
Y4
(PT/PC)US
X1
Textiles
Textiles
X4
17
Autarky in Mexico and the U.S.

• The relative price of textiles in autarky is
  greater in the U.S. than in Mexico
• That is, the U.S.s autarky price line is steeper
  than Mexicos
• In symbols, (PT/PC)U.S. gt (PT/PC)Mex.
• This means that Mexico has the comparative
  advantage in textiles

18
Autarky in Mexico and the U.S.
U.S.
Mexico
Cars
Cars
(PT/PC)Mex
E
e
Y1
Y4
(PT/PC)US
X1
Textiles
Textiles
X4
19
Autarky in Mexico and the U.S.

• This also means that the relative price of cars
  in autarky is lower in the U.S. than in Mexico
• That is, (PC/PT)U.S. lt (PC/PT)Mex.
• This means that the U.S. has the comparative
  advantage in cars

20
Autarky to Trade
U.S.
Mexico
Cars
Cars
(PX/PY)trade
E
e
Y1
Y4
X1
Textiles
Textiles
X4
21
Production in Trade
U.S.
Mexico
Cars
Cars
(PX/PY)T
e'
Y5
E
e
Y1
Y4
E'
Y2
X1
X2
Textiles
Textiles
X4
X5
22
Consumption in Trade
U.S.
Mexico
Cars
Cars
e'
Y5
C'
Y3
E
e
Y1
Y4
c'
Y6
E'
Y2
X1
X2
Textiles
Textiles
X5
X6
X3
X4
23
The Result

• The relatively capital abundant country (U.S.)
  exports the relatively capital intensive good
  (cars)
• The relatively labor abundant country (Mexico)
  exports the relatively labor intensive good
  (textiles)

24
The Heckscher-Ohlin Theorem

• A country will export the commodity that uses
  relatively intensively the factor that country
  has in relative abundance
• A country will import the commodity that uses
  relatively intensively the factor that is
  relatively scarce in that country

25
The Source of Comparative Advantage

• If a country has a lot of labor relative to K,
  its wage rates will be relatively low, so
• the product that uses a lot of labor in its
  production (relatively speaking) will be produced
  at a relatively low cost, so
• the country should export the labor intensive good

26
The Source of Comparative Advantage

• If a country has a lot of capital relative to L,
  its capital price will be relatively low, so
• the product that uses a lot of K in its
  production (relatively speaking) will be produced
  at a relatively low cost, so
• the country should export the capital intensive
  good

27
The Source of Comparative Advantage

• So it is a countrys relative factor endowment
  that determines its comparative advantage
• This is why the H-O-S model is also called the
  factor proportions theory

28
Changes in Relative Commodity Prices

• As we learned before,
• (PT/PC)US falls as the U.S. moves to trade. That
  is, the international relative textile price is
  lower than the U.S.s autarky price.
• (PT/PC)Mex rises as Mexico moves to trade. That
  is, the international relative textile price is
  higher than Mexicos autarky price.

29
Changes in Factor Prices

• In autarky, the K-intensive product (cars) is
  less expensive to produce in the U.S. as compared
  to Mexico
• this is because K is relatively abundant in the
  U.S., which makes the price of capital
  relatively low
• As trade commences, r will rise since demand for
  capital will rise

30
Changes in the Price of Capital in the U.S.
r
SK
D1K
QK
31
Changes in the Price of Capital in the U.S.
r
SK
In autarky, the price of capital (r1) is
determined by supply of and demand for capital
in the U.S
r1
D1K
QK
32
Changes in the Price of Capital in the U.S.
r
SK
When trade starts, the U.S. increases its
production of the capital intensive product, and
therefore demand for capital increases in the U.S.
r2
r1
D2K
D1K
QK
33
Changes in Factor Prices

• In autarky, the L-intensive product (textiles) is
  more expensive to produce in the U.S. as compared
  to Mexico
• this is because L is relatively scarce in the
  U.S., which makes the price of labor relatively
  high.
• As trade commences, w will fall since demand for
  labor will fall

34
Changes in the Price of Labor in the U.S.
w
SL
D1L
QL
35
Changes in the Price of Labor in the U.S.
w
SL
In autarky, the price of labor (w1) is determined
by supply of and demand for labor in the U.S
w1
D1L
QL
36
Changes in the Price of Labor in the U.S.
w
SL
When trade starts, the U.S. decreases its
production of the labor intensive product, and
therefore demand for labor decreases in the U.S.
w1
w2
D1L
QL
37
Commodity and Factor Prices In Trade A Summary

• When trade begins, the relative price of the good
  intensive in the abundant factor rises (e.g.,
  (PC/PT)US rises)
• The relative price of the good intensive in the
  scarce factor falls (e.g., (PT/PC)US falls)
• Also, the price of the abundant factor rises, and
  the price of the scarce factor falls (i.e., w
  falls, r rises in the U.S.)

38
Commodity and Factor Prices In Trade A Summary

• In our example, (PT/PC)US falls as trade
  commences
• (w/r)US also falls
• In Mexico, the opposite is happening
• (PT/PC)Mex rises
• (w/r)Mex also rises
• Therefore relative commodity and factor prices
  move together as trade commences

39
The Relative Cost Curve

• Since relative factor and commodity prices move
  together as countries move from autarky to trade,
  we can look at a picture of these two sorts of
  prices
• We also know that in autarky (PT/PC)Mex is lower
  than (PT/PC)US
• (w/r)Mex is also lower in autarky than (w/r)US
  since Mexico is relatively labor abundant

40
The Relative Cost Curve
PT/PC
(PT/PC)US
(PT/PC)Mex
(w/r)Mex
w/r
(w/r)US
41
The Relative Cost Curve
PT/PC
(PT/PC)US
(PT/PC)Mex
(w/r)Mex
w/r
(w/r)US
42
The Relative Cost Curve
PT/PC
(PT/PC)US
As trade commences, (PT/PC)US falls, and
(PT/PC)Mex rises
(PT/PC)Mex
(w/r)Mex
w/r
(w/r)US
43
The Relative Cost Curve
PT/PC
(PT/PC)US
In addition, as trade commences (w/r)US falls,
and (w/r)Mex rises
(PT/PC)Mex
(w/r)Mex
w/r
(w/r)US
44
Factor Price Equalization

• In fact, each country moves along the relative
  cost curve to a common point
• We know this because there is only one
  international price
• If the countries wind up with a common
  international price, they must also wind up with
  a common set of relative factor prices

45
The Relative Cost Curve
PT/PC
(PT/PC)US
(PT/PC)Int
Both relative commodity and factor prices
equalize in trade
(PT/PC)Mex
(w/r)Mex
(w/r)US
w/r
(w/r)Int
46
The Factor Price Equalization Theorem

• In equilibrium, with both countries facing the
  same relative product prices, relative costs will
  be equalized. This can only happen if relative
  factor prices are equalized between countries.

47
H-O-S and the Distribution of Income

• The H-O theorem, together with the FPE theorem,
  also tell us about how the incomes of different
  groups within a country change as trade starts
• This provides insight into the politics of free
  trade

48
The Stolper-Samuelson Theorem

• As trade commences, the owners of the relatively
  abundant factor will find their real incomes
  rising the owners of the relatively scarce
  factor will find their real incomes falling.

49
H-O-S and the Distribution of Income

• According to the S-S theorem, if the U.S. is a
  relatively K-abundant country, who in America
  should favor free trade?
• Who in America should favor protectionism?

50
Theoretical Qualifications to H-O-S

• Suppose we relax some of the many assumptions.
  Will the implications of the H-O-S model still be
  the same?

51
Qualification 1 Demand Reversal

• Normally, the relative price of the commodity
  that uses intensively the abundant factor will be
  lower
• In our example, (PC/PT)US lt (PC/PT)Mex
• Or, (PT/PC)US gt (PT/PC)Mex
• What causes this difference in autarky prices?
  Differences in supply conditions

52
Qualification 1 Demand Reversal

• Suppose we let demand conditions differ
• Suppose domestic demand for the good that uses
  relatively intensively the relatively abundant
  factor is very strong in each country
• That is, suppose demand for cars is very strong
  in the U.S., and that demand for textiles is very
  strong in Mexico

53
Qualification 1 Demand Reversal

• Such strong demand makes the autarky car price in
  the U.S. higher, and the textile price in Mexico
  higher
• In the extreme, demand reversal could occur
  (PC/PT)US gt (PC/PT)Mex, and
• (PT/PC)US lt (PT/PC)Mex
• So what?

54
Qualification 1 Demand Reversal

• When trade begins, as usual the intl price will
  lie between the two countries APRs
• Therefore (PC/PT) for Mexico will rise as it
  moves to trade
• Mexico, then, would export cars
• Meanwhile, (PT/PC) for the U.S. will rise as it
  moves to trade
• The U.S., then, would export textiles

55
Bottom Line on Demand Reversals

• If demand reversals occur, the H-O theorem no
  longer holds the K-abundant country is exporting
  the L-intensive good, and the L-abundant country
  is exporting the K-intensive good
• If demand reversals are common in the real world,
  wed better find a new theory

56
Qualification 2 Factor Intensity Reversal

• Implicitly, weve assumed that if good X is
  K-intensive relative to good Y at one factor
  price ratio, it will be K-intensive at all factor
  prices
• A FIR is when a good is relatively K-intensive at
  one set of factor prices, but relatively labor
  intensive at another

57
Qualification 2 Factor Intensity Reversal

• FIRs occur when capital and labor can be
  substituted more easily in the production of one
  good than another
• Example
• Suppose butane production is very inflexible 1K
  1L 1 butane, and if you want more butane you
  must add more of both K and L
• Suppose apple production is much more flexible

58
Qualification 2 Factor Intensity Reversal

• If w/r is very high, apple producers will choose
  a relatively K-intensive method (as compared with
  butane makers)
• If w/r starts to fall, apple producers will start
  substituting L for K
• Eventually, its possible that apples might be
  produced in a relatively L-intensive manner (as
  compared with butane)

59
Factor Intensity Reversal Implications for Trade

• Suppose France is K-abundant relative to Germany
  (that is (K/L)F gt (K/L)G)
• This means that (w/r)F gt (w/r)G
• Suppose further that there is a FIR in France,
  at (w/r)F apples are produced relatively
  K-intensively but in Germany at (w/r)G apples are
  produced in a relatively L-intensive way

60
Factor Intensity Reversal Implications for Trade

• If trade begins, according to the H-O theorem the
  relatively K-abundant country (France) will
  export the rel. K-intensive good (apples) and the
  rel. L-abundant country will export the rel.
  L-intensive good (also apples)
• This cant work

61
Factor Intensity Reversal The Bottom Line

• If FIRs are present, the H-O theorem breaks down
• If FIRs are common, wed better find a new theory

62
Qualification 3 Transportation Costs

• In the real world, it is costly to transport
  goods internationally
• How do the implications of our model change if we
  allow for transportation costs?
• Consider the supply and demand curves for
  textiles in Mexico and the U.S.

63
Basic Set-Up
U.S.
SText
PT
PT
Mexico
SText
PAUS
PAMex
DText
DText
QT
QT
64
Basic Set-Up
U.S.
SText
PT
PT
Mexico
SText
PAUS
PIntl
PIntl
PAMex
DText
DText
q1
q2
QT
QT
q1
q2
65
Basic Set-Up
U.S.
SText
PT
PT
Mexico
SText
PAUS
Exp.
PIntl
PIntl
Imp.
PAMex
DText
DText
q1
q2
QT
QT
q1
q2
66
Adding Transportation Costs

• Suppose Mexico tries to pass along 100 of the
  transportation costs to the U.S. consumers
• In this case, the U.S. textile price will rise,
  and the quantity of imports demanded will fall
• Mexico will have a surplus, and will eventually
  lower their domestic price

67
Adding Transportation Costs
U.S.
SText
PT
PT
Mexico
SText
Exp.
t-costs
PIntl
PIntl
Imp.
DText
DText
q1
q2
q1
q2
QT
QT
68
Adding Transportation Costs

• Therefore, unless Mexico is the only seller in
  the world, transportation costs will be borne by
  both the consumer (the U.S.) and the seller
  (Mexico).
• How does this look on the graph?

69
Adding Transportation Costs
U.S.
SText
PT
PT
Mexico
SText
Exp.
PIntl
PIntl
Imp.
DText
DText
q1
q2
q1
q2
QT
QT
70
Adding Transportation Costs
U.S.
SText
PT
PT
Mexico
SText
Exp.
PIntl
PIntl
t-costs
Imp.
DText
DText
q1
q2
q1
q2
QT
QT
71
Adding Transportation Costs

• Notice there is no longer a single international
  textile price, but rather two different ones
• That is, transportation costs drive a wedge
  between the two countries prices

72
Adding Transportation Costs the Bottom Line

• In general, the H-O theorem will still hold
• The FPE theorem breaks down, since factor prices
  only equalize if the commodity prices do
• Therefore, in the presence of transportation
  costs, factor prices have a tendency to move
  towards each other, but we should not expect
  equalization

73
Relaxing Other Assumptions

• One can relax many other assumptions and examine
  how the implications of the model change
• perfect competition
• CRTS
• identical production technologies
• lack of policy obstacles
• factors being perfectly transferable

74
Relaxing Other Assumptions

• These issues have involved many researchers for
  many years
• You can read a bit about this research in your
  text, but we have other fish to fry
• Suffice it to say that relaxing these assumptions
  can modify the basic H-O-S model, but doesnt
  lead us to scrap the model