1
HO Model – Factor Proportions
• INTERNATIONAL
ECONOMICS,
ECO 486
Bertil Ohlin 1899-1979
Eli F. Heckscher, 1879-1952.
2
Learning Objectives
• Examine the need to build a new model
• Understand five more assumptions
• Prove Rybczynski Theorem
• Prove HO Theorem
• Prove Factor-Price Equalization Theorem
• Prove Stolper-Samuelson Theorem.
4
Classical Model
• Strengths
– Trade is mutually beneficial
– High & low wage countries may trade
– Explains some of the trade patterns we observe
• Weaknesses
– Why does so much trade occur among
developed countries?
– Why does technology differ across countries?
5
Heckscher-Ohlin (HO) Model
• Built upon observed differences among
– Factors that countries possess
– Factors required to produce various goods
• Insights
–
–
–
–
Causes of trade
Effects of trade on factor prices
Effect of economic growth on trade patterns
Political behavior
7
Assumptions for HO Model
• Keep assumptions 1 through 10
• Drop assumptions 11 & 12
• Add assumptions 13 through 17
8
Assumption #13
• There are two factors of production, labor
(L), and capital (K). Owners of capital are
paid a rental payment (R) for the services of
their assets, and labor receives a wage
payment (W).
9
Assumption #14
• The technologies available to each country
are identical.
– Any technology is available to any country
– Factor prices determine the technology chosen
– Assumes away the Ricardian explanation of the
source of comparative advantage.
A Model of a Two-Factor Economy
Input Possibilities in Soybean Production
Unit Capital input aTS ,
in machines per bushel
Input combinations
that produce one
bushel of Soybeans
//
Unit Labor input aLF ,
in hours per bushel
10
11
Assumption #15
• The production of T is labor intensive
relative to the production of S
– That is, T requires more labor per machine
• Implies that production of S is capital
intensive (relative to the production of T).
– That is, S requires more machines per worker
12
K per Worker for US Industries
Industry
1960 1980 2000
Apparel
1.5
3.2
8.3
Leather products
2.3
4.5 14.6
Chemicals
30.4 58.9 85.9
Petroleum & coal
93.8 161.2 266.7
Thousands of 1972 dollars. P. 89, 6th edition, Husted & Melvin, International Economics
13
The Magnification Effect
A change in the relative price of a good (say, T) results in a
proportionately larger change in the price of its intensive factor (Labor).
Relative price of
Textiles, PT/PS
PW
Wage-rental
ratio, w/r
The relative price of a resource
affects the intensity of its use.
Which line represents the Capital-intensive industry, 1 or 2?
Wage-rental
ratio, w/r
1
2
Capital-labor
ratio, K/L
14
Changes in relative prices affect the
distribution of income
16
Wage-rental
ratio, w/r
Mag. Effect
Textiles
Soybeans
(w/r)2
(w/r)1
Relative
price of
T, PT/PS
(PT/PS)2 (PT/PS)1
Increasing
(KT/LT)1 (KT/LT)2 (KS/LS)1(KS/LS)2Capitallabor
Increasing
Ratio, K/L
17
Assumption #16
• Country A is relatively capital abundant,
while B is labor abundant.
18
K per Worker: Selected Countries
Country
1980
1990
Switzerland (highest)
57,061
73,459
27,551
34,705
Columbia (27 of 51)
11,800
12,650
Sierra Leone (lowest)
178
223
th
United States (11 )
th
1985 international prices. Item 4.2, page 91, 6th edition Husted & Melvin
19
Quantity definition of factor abundance
• Country A is relatively capital abundant, if
the ratio of its capital stock to its labor force
(K/L) is greater than that of the other
country:
K
L
A
A
K

L
B
B
22
TEXTILES, T (millions of yards per year)
Increasing Opportunity Cost in A
S is K-intensive
A is K-abundant
20
18
14
12
America’s PPF
6
0
2
4
8
10
12
16
SOYBEANS, S (millions of bushels per year)
23
TEXTILES, T (millions of yards per year)
Increasing Opportunity Cost in B
T is L-intensive
B is L-abundant
40
20
Britain’s PPF
0
5
10
SOYBEANS, S (millions of bushels per year)
25
Assumption #17
• Tastes in the two countries are identical.
– Given same GDP & prices, same choice
• Implies that supply conditions alone
determine the direction of comparative
advantage (CA).
– Different tastes would imply different demand
– Could reverse the direction of CA.
The importance of assuming
identical tastes.
26
Tastes differ markedly, reversing the
direction of Comparative Adv.
Relative price
of S, PS/PT
RSB
RSWORLD
RSA
1
(PS/PT )A
(PS/PT )B
2
RDA
RDB
Relative quantity of S, QS
QT
Q*S
Q*T,
QS + Q*S
QT + Q*T
27
29
Rybczynski Theorem
• At constant world prices, if a country
experiences an increase in the supply of one
factor, it will produce more of the product
intensive in that factor and less of the other.
– See Figure 4.7 , page 103
– Read Item 10.1 “The Dutch Disease,” page 289,
7th edition of Husted & Melvin
30
Labor used in ________________ production
L__ Increasing
1
K_
__
__
O_
_
Labor used in ________________ L
production
Increasing
O_
K_
Capital used in _____ production
Capital used in ________ production
Which is the K-intensive industry?
32
Rybczynski Theorem
• How do the outputs of the two goods
change when the economy’s resources
change?
• Increase the amount of one factor, say K,
and observe the results
33
K increases. S (K int.) expands. S
needs more labor. T must contract
L2S
O2 S
L1S
O 1S
1
K1T
K2T
T
2
S2 S1
OT
L used in T production
Increasing
L2T
L1T
K1S
K2S
K used in S production
K used in T production
Increasing
L used in S production
An increase in K in Country A.
Output of
T, QT
Slope = -PS/PT
Q1 T
Q2 T
1
2
PPF1
Q1 S
Q2 S
Slope = -PS/PT
PPF2
Output of
S, QS
34
An increase in L in country B.
Output of
T, QT
Slope = -PS/PT
2
Q2 T
Slope = -PS/PT
Q1
1
T
PPF1 PPF2
Q2 S Q 1 S
Output of
S, QS
35
36
Rybczynski Theorem
• Also helps us to understand that an
economy will tend to be more productive in
industries that use its abundant factor
intensively.
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Heckscher-Ohlin Theorem
• A country will export the goods whose
production is intensive in the factor with
which that country is abundantly endowed.
General equilibrium for a closed
39
economy; increasing opportunity costs
Proof of the HO theorem
40
 PS 
P 
 T

A
 PS 
P 
 T

Trade
 PS 
P 
 T
41
B
• With free trade, there will be one world relative
price for S (PS/PT) and T (PT/PS).
• As PS/PT rises in Country A, their S industry
expands while their T industry contracts.
• As PS/PT falls in Country B, their S industry
contracts while their T industry expands.
• Tricky to draw the general equilibrium solution,
so let’s try it together.
HO Model: Trade Equilibrium in a special
case (easier to draw)
Textiles, QT
Q*
A*
D and D*
A
Q
B’s
PPF
A’s PPF
Soybeans, QS
42
43
TEXTILES, T (millions of yards per year)
Autarky in A
18
15
a
CIC0
12
0
10
13
16
SOYBEANS, S (millions of bushels per year)
45
TEXTILES, T (millions of yards per year)
Autarky in B
40
a
30
CIC0
20
Britain’s PPF
10
0
4
6.5
9
SOYBEANS, S (millions of bushels per year)
Trade Leads to a Convergence of
Relative Prices
Relative price
of S, ______
RSB
RSA
3
2
1
RD
Relative quality
of S,
47
Trade Leads to a Convergence of
Relative Prices
Relative price
of S, PS/PT
RSB
RSWORLD
RSA
3
4
5
2
1
RD
Relative quantity of S, QS
Q*S
QS + Q*S
QT
Q*T,
QT + Q*T
48
 PS 
P 
 T

A
 PS 
P 
 T

Trade
 PS 
P 
 T
49
B
• With free trade, there will be one world relative
price for S (PS/PT) and T (PT/PS).
• As PS/PT rises in Country A, their S industry
expands while their T industry contracts.
• As PS/PT falls in Country B, their S industry
contracts while their T industry expands.
• Tricky to draw the general equilibrium solution,
so let’s try it together.
50
International Trade Equilibrium
• Incomplete specialization in Comparative
Advantage good.
• Community Indifference Curve (CIC) &
Terms of Trade line (ToT) tangent at
consumption point
• Congruent trade triangles imply balanced
trade.
HO Trade Equilibrium
– general case
A produces more S, less T. Complete
specialization in their comparative
advantage good is unlikely.
A exports S, imports T
B produces more T, less S
B exports T, imports S
Their trade triangles are congruent.
51
Derivation of national supply and
52
demand curves; increasing opp. cost
National supply and national demand
54
in the classical and HO models.
National supply and national demand
55
in the HO model
57
Stolper-Samuelson Theorem
• Free international trade benefits the
abundant factor and harms the scarce factor.
 PS 
P 
 T

A
 PS 
P 
 T

Trade
 PS 
P 
 T
58
B
• As PS/PT rises in Country A, PT/PS and w/r fall.
– Look back at Slide 16.
– A is K abundant (L scarce)
• As PS/PT falls in Country B, PT/PS and w/r rise.
– B is L abundant (K scarce)
60
Factor-Price Equalization (FPE) Theorem
• Given all the assumptions of the HO model,
free trade will lead to the international
equalization of individual factor prices.
– Look again at Slide 16.
• One relative price for T, PT/PS
• One wage-rental ratio, w/r
61
Factor-Price Equalization?
“There isn’t any.” Why not?
1. Some goods are not produced in some countries.
2. Productivity (technology) does differ between
countries.
3. Goods’ prices differ due to natural and artificial
barriers to trade.
62
The End of Chapter 4
• See “Isocosts, Isoquants, and Proofs”in
eco486 main folder
• See Specific-Factors Model:
03specific_factors_jde.ppt in Krugman
folder