The Heckscher-Ohlin Model:
Features, Flaws, and Fixes
I: What's the H-O Model
Like
Alan V. Deardorff
University of Michigan
Themes of the 3 Lectures
The HO Model is largely well behaved in 2
dimensions, even when you include trade
costs
• In higher dimensions, it is not so well
behaved, especially when you include
trade costs
• Various modifications and extensions of
the HO model offer some promise of
making it behave better
Nottingham I
2
Outline of Lecture I
• Overview of the H-O Model
• The 2×2 Model
– Without trade costs
– With trade costs
• The 2×2×2 Model
• Conclusions from the 2×2(×2) Model
Nottingham I
3
H-O Overview
• The Heckscher-Ohlin (H-O) Model Assumptions
– Homogeneous goods and factors
– Perfectly competitive market equilibrium throughout
(goods and factors)
– Production functions
• Constant returns to scale
• Non-joint
– Factors
• Perfectly mobile across industries
• Perfectly immobile across countries
– Countries differ in factor endowments
– Industries differ in factor intensities
Nottingham I
4
H-O Overview
• The Heckscher-Ohlin (H-O) Model Implications
– Countries export goods that use intensively their
abundant factors (H-O Thm)
– Trade draws factor prices closer together across
countries, becoming equal in certain circumstances
(FPE Thm)
– Trade changes real factor prices (S-S Thm)
• Benefiting owners of abundant factors
• Hurting owners of scarce factors
– Rybczynski Thm (output effects of factor
accumulation)
Nottingham I
5
The Textbook 2×2 H-O Model
•
•
•
•
•
Goods X, Y
Factors K, L
X is K-intensive
Goods are final goods
Trade is
– Free and frictionless, or
– Subject to simple, constant trade costs per
unit (perhaps “iceberg”)
Nottingham I
6
The Textbook 2×2 H-O Model
• Analysis: Expanded Lerner Diagram
shows
– Production
– Factor allocations
– Factor Prices
– Trade
• Thus
for given
– Goods prices
– Factor endowments
Nottingham I
– Full solution for
small open
economy
– Dependence on
prices for large
economy
7
Lerner Diagram
K
1/wK0
1/wL0
Nottingham I
L
8
Lerner Diagram
K
E0
X0
1/wK0
Y0
1/wL0
Nottingham I
L
9
Lerner Diagram
K
Export
E0
X0
1/wK0
EC = EW
XC
YC
Y0
Import
1/wL0
Nottingham I
L
10
The Textbook 2×2 H-O Model
• Behavior
– If Endowments inside Diversification Cone
• Both goods produced
• Factor prices independent of endowments
– If Endowments outside Diversification Cone
• One good produced
• Factor prices depend on endowments
Nottingham I
11
The Textbook 2×2 H-O Model
• Sensitivity
– All variables (outputs, trade, factor prices) are
uniquely determined and depend smoothly on
• Endowments
• Prices
– Adding trade costs vis a vis a single other
country
• Creates range of world prices for which country
does not trade
• Outside that range, all variables depend smoothly
on trade costs
Nottingham I
12
The Textbook 2×2 H-O Model
• Summary
– With free and frictionless trade:
S I  S I ( EK , EL , PX / PY ),
I  X ,Y
DI  DI ( EK , EL , PX / PY ),
I  X ,Y
TI ( S I  DI )  TI ( EK , EL , PX / PY ), I  X , Y
wJ  w j ( EK , EL , PX , PY ),
Nottingham I
J  K, L
13
The Textbook 2×2 H-O Model
• Summary
– With iceberg trade costs, t:
S I  S I ( EK , EL , PX / PY , t X , tY ),
I  X ,Y
DI  DI ( EK , EL , PX / PY , t X , tY ),
I  X ,Y
TI ( S I  DI )  TI ( EK , EL , PX / PY , t X , tY ), I  X , Y
wJ  w j ( EK , EL , PX , PY , t X , tY ),
Nottingham I
J  K, L
14
Effects of Increasing Capital
Endowment, EK
K
1/wK0
EK
cone
1/wL0
Nottingham I
L
15
Effects of Increasing EK
SX
SX
Rybczynski Thm: SX/EK,
rises with EK
EK
cone
Nottingham I
16
Effects of Increasing EK
SY
SY
Rybczynski Thm: SY
Falls with EK
EK
cone
Nottingham I
17
Effects of Increasing EK
DX, DY
DX
DY
EK
cone
Nottingham I
18
Effects of Increasing EK
TX, TY
TX
EK
TY
cone
Nottingham I
19
Effects of Increasing EK
wK
wK0
wK
EK
wL
wL
wL0
EK
cone
Nottingham I
20
Effects of Increasing Labor
Endowment, EL
K
1/wK0
Effects are
mirror image of
increasing EK
EL
1/wL0
Nottingham I
L
21
Effects of Increasing Price of X, PX
K
1/wK0
1/wL0
Nottingham I
L
22
Effects of Increasing Price of X, PX
K
1/wK0
1/wL0
Nottingham I
L
23
Effects of Increasing Price of X, PX
K
1/wK0
1/wL0
Nottingham I
L
24
Effects of Increasing Price of X, PX
SX
SX
(cone)
Nottingham I
PX
25
Effects of Increasing Price of X, PX
SY
SY
(cone)
Nottingham I
PX
26
Effects of Increasing Price of X, PX
DX, DY
DY
DX
(cone)
Nottingham I
PX
27
Effects of Increasing Price of X, PX
TX, TY
TX
PX
TY
(cone)
Nottingham I
28
Effects of Increasing Price of X, PX
wK
wK
Stolper-Samuelson Thm:
wK/PX, wK/PY rise with PX
(cone)
Nottingham I
PX
29
Effects of Increasing Price of X, PX
Stolper-Samuelson Thm:
wL/PX, wL/PY fall with PX
wL
wL
(cone)
Nottingham I
PX
30
Effects of Increasing Price of Y, PY
• Effects are mirror image of increasing PX
Nottingham I
31
Effects of Presence of Trade Costs
• Assume iceberg trade cost t−1>0, equals
fraction of each good that disappears in transit to
world market (must ship t for 1 to arrive)
• Implication for domestic prices if world prices are
PXw, PYw:
– If country exports X: PX=PXw/t; PY=tPYw
– If country exports Y: PY=PYw/t; PX=tPXw
– If country does not trade:
(PXw/PYw)/t2 ≤ PX/PY ≤ t2(PXw/PYw)
Nottingham I
32
Presence of Trade Costs
1/wKw
X=1/PXw
K
EC
Y=1/PYw
1/wLw
Nottingham I
L
33
Presence of Trade Costs
1/wKw
X=1/PXw
K
If country exports X
…which it will if endowment
is above this line
ECX
EC
Y=1/PYw
1/wLw
Nottingham I
L
34
Presence of Trade Costs
1/wKw
X=1/PXw
K
EC
ECY
If country exports Y
…which it will if endowment
is below this line
Y=1/PYw
1/wLw
L
Nottingham I
35
Presence of Trade Costs
If country exports X
K
1/wKw
X=1/PXw
autarky
ECX
EC
ECY
If country exports Y
Y=1/PYw
1/wLw
Nottingham I
L
36
Effects of Increasing EK in
Presence of Trade Costs
If country exports X
K
1/wKw
X=1/PXw
autarky
ECX
EC
ECY
If country exports Y
Y=1/PYw
1/wLw
Nottingham I
L
37
Effects of Increasing EK in
Presence of Trade Costs
PX/PY
autarky
t2PXw/PYw
PXw/PYwt2
Y-export X-export
cone Nottingham
cone I
EK
38
Effects of Increasing EK in
Presence of Trade Costs
SX
autarky
Y-export X-export
cone Nottingham
cone I
EK
39
Effects of Increasing EK in
Presence of Trade Costs
SY
autarky
Y-export X-export
cone Nottingham
cone I
EK
40
Effects of Increasing EK in
Presence of Trade Costs
TX, TY
autarky
TX
EK
TY
Y-export X-export
cone Nottingham
cone I
41
Effects of Increasing EK in
Presence of Trade Costs
wK
autarky
wK
EK
wL
wL
Y-export X-export
cone Nottingham
cone I
EK
42
Effects of Increasing PXw/PYw in
Presence of Trade Costs
SX,SY
autarky
SX
(ρA =PXA/PYA =
autarky price)
ρA
Y-export X-export
cone Nottingham
cone I
SY
ρw =PXw/PYw
43
Effects of Increasing PXw/PYw in
Presence of Trade Costs
DX,DY
autarky
ρA
Y-export X-export
cone Nottingham
cone I
DY
DX
ρw =PXw/PYw
44
Effects of Increasing PXw/PYw in
Presence of Trade Costs
TX,TY
autarky
TX
ρA
ρw =PXw/PYw
TY
Y-export X-export
cone Nottingham
cone I
45
Effects of Increasing PXw/PYw in
Presence of Trade Costs
wK/PY
autarky
wK/PY
ρA
Y-export X-export
cone Nottingham
cone I
ρw =PXw/PYw
46
Effects of Increasing PXw/PYw in
Presence of Trade Costs
wL/PY
autarky
wL/PY
ρA
Y-export X-export
cone Nottingham
cone I
ρw =PXw/PYw
47
Effects of Increasing Trade Costs
• As trade cost, t, rises from zero, Y-export
cone and the X-export cone move further
apart, and the “autarky” range of factor
endowments and world prices gets larger
• For any given endowment and world
prices, a rise in t reduces the volume of
trade and moves other variables in the
direction of their autarky values.
Nottingham I
48
Effects of Increasing Trade Costs
• Example:
– Consider a country whose factor endowments
have it completely specialized in good X at
world prices
Nottingham I
49
Effects of Increasing Trade Costs:
Example
SX,SY
autarky
SX
SY
X-export
coneNottingham I
t
50
The World Market:
The Textbook 2×2×2 H-O Model
• To model the world economy, add a second
country (country “*”)
• Solve for world (relative) price that clears the
world market
TX ( EK , EL , PX / PY )  T ( E , E , PX / PY )
*
X
Nottingham I
*
K
*
L
51
The World Market:
The Textbook 2×2×2 H-O Model
• Results
S I  S I ( EK , EL , EK* , EL* ),
I  X ,Y
DI  DI ( EK , EL , EK* , EL* ),
I  X ,Y
TI  TI ( EK , EL , EK* , EL* ),
I  X ,Y
wJ  w j ( EK , EL , EK* , EL* , PY ), J  K , L
with analogous expressions for the other
country
Nottingham I
52
The World Market:
The Textbook 2×2×2 H-O Model
• Depictions of world equilibrium
– Offer curves (Meade)
– Integrated-world-economy diagram (Dixit-Norman)
– Sufficient (but not elegant) to use supply and
demand of just one of the goods
Nottingham I
53
World Equilibrium
TX, −TX*
TX
(PX/PY)w
PX/PY
−TX*
(cone) (cone)*
Nottingham I
54
Conclusions from the
2×2(×2) H-O Model
• Equilibria are well defined
• Equilibrium quantities are unique
• Equilibrium prices are unique up to a
numeraire
Nottingham I
55
Conclusions from the
2×2(×2) H-O Model
• Includes three types of equilibria
– Autarky (when there are trade costs)
– Diversified
– Specialized
• Determinants of equilibrium type are
mostly clear
• Several relationships between variables
depend importantly on type of equilibrium
Nottingham I
56
Conclusions from the
2×2(×2) H-O Model
• Classic “Theorems” are clear and precise
• Countries specialize, but only if endowment
differences are large
• Prices and quantities vary continuously with
exogenous changes in
– Endowments
– Trade costs
• In particular, trade responds sensibly to
– Prices and
– Trade costs
Nottingham I
57
What’s Next?
• My point in the next lecture will be that
some of these attractive properties are lost
in higher dimensions – i.e., especially
when there are more than 2 of goods and
countries
Nottingham I
58