The Heckscher-Ohlin Model: Features, Flaws, and Fixes I: What's the H-O Model Like Alan V. Deardorff...

The Heckscher-Ohlin Model: Features, Flaws, and Fixes

I: What's the H-O ModelLike

Alan V. Deardorff

University of Michigan

Nottingham I 2

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 3

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 4

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 5

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 6

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 7


• Analysis: Expanded Lerner Diagram shows– Production– Factor allocations– Factor Prices– Trade

for given– Goods prices– Factor endowments

• Thus– Full solution for

small open economy

– Dependence on prices for large economy

Nottingham I 8

Lerner Diagram

L

K

Y=1/PY0

X=

1/P

X0

1/wK0

1/wL0

Nottingham I 9

Lerner Diagram

L

K

Y=1/PY0

X=

1/P

X0

E0

Y0

X0

1/wK0

1/wL0

Nottingham I 10

Lerner Diagram

L

K

Y=1/PY0

X=

1/P

X0

E0

XC

Y0

ECX0

YC

1/wK0

1/wL0

= EW

Export

Import

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• 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

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• 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 13


• Summary– With free and frictionless trade:

LKJPPEEww

YXIPPEETDST

YXIPPEEDD

YXIPPEESS

YXLKjJ

YXLKIIII

YXLKII

YXLKII

, ),,,,(

,),/,,()(

, ),/,,(

, ),/,,(

Nottingham I 14


• Summary– With iceberg trade costs, t:

LKJttPPEEww

YXIttPPEETDST

YXIttPPEEDD

YXIttPPEESS

YXYXLKjJ

YXYXLKIIII

YXYXLKII

YXYXLKII

, ),,,,,,(

,),,,/,,()(

, ),,,/,,(

, ),,,/,,(

Nottingham I 15

Effects of Increasing Capital Endowment, EK

L

K

Y=1/PY0

X=

1/P

X0

1/wL0

1/wK0

EK

cone

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SX

EK

SX

cone

Effects of Increasing EK

Rybczynski Thm: SX/EK, rises with EK

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SY

EKcone

SY

Rybczynski Thm: SY Falls with EK

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DX, DY

EK

DX

cone

DY

Nottingham I 19


EK

TX

cone

TY

TX, TY

Nottingham I 20


wK

EKcone

wL

EK

wK

wL

wK0

wL0

Nottingham I 21

Effects of Increasing Labor Endowment, EL

L

K

Y=1/PY0

X=

1/P

X0

1/wL0

1/wK0

EL

Effects are mirror image of increasing EK

Nottingham I 22

Effects of Increasing Price of X, PX

L

K

Y=1/PY0

X=

1/P

X0

1/wL0

1/wK0

Nottingham I 23


L

K

Y=1/PY0

X=

1/P

X0

1/wL0

1/wK0

Nottingham I 24


L

K

Y=1/PY0

X=

1/P

X0

1/wL0

1/wK0

Nottingham I 25

SX

PX

SX

(cone)


Nottingham I 26

SY

PX

SY

(cone)


Nottingham I 27

PX

DX

(cone)


DX, DY

DY

Nottingham I 28

PX

TY

(cone)


TX

TX, TY

Nottingham I 29

PX

wK

(cone)


wK

Stolper-Samuelson Thm: wK/PX, wK/PY rise with PX

Nottingham I 30

PX

wL

(cone)


wLStolper-Samuelson Thm: wL/PX, wL/PY fall with PX

Nottingham I 31

Effects of Increasing Price of Y, PY

• Effects are mirror image of increasing PX

Nottingham I 32

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 PX

w, PYw:

– If country exports X: PX=PXw/t; PY=tPY

w

– If country exports Y: PY=PYw/t; PX=tPX

w

– If country does not trade:

(PXw/PY

w)/t2 ≤ PX/PY ≤ t2(PXw/PY

w)

Nottingham I 33

Presence of Trade Costs

L

K

Y=1/PYw

X=

1/P

Xw

1/wLw

1/wKw

EC

Nottingham I 34


L

K

Y=1/PYw

X=

1/P

Xw

1/wLw

1/wKw

If country exports X

EC

ECX

…which it will if endowment is above this line

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L

K

Y=1/PYw

X=

1/P

Xw

1/wLw

1/wKw

If country exports Y

ECY

…which it will if endowment is below this line

EC

Nottingham I 36


L

K

Y=1/PYw

X=

1/P

Xw

1/wLw

1/wKw



EC

ECX

ECY

autarky

Nottingham I 37

Effects of Increasing EK in Presence of Trade Costs

L

K

Y=1/PYw

X=

1/P

Xw

1/wLw

1/wKw



EC

ECX

ECY

autarky

Nottingham I 38

autarky

EK

t2PXw/PY

w


X-export cone

Y-export cone

PXw/PY

wt2

PX/PY

Nottingham I 39

autarky

EK


X-export cone

Y-export cone

SX

Nottingham I 40

autarky

EK


X-export cone

Y-export cone

SY

Nottingham I 41

autarky

EK


X-export cone

Y-export cone

TX, TY

TY

TX

Nottingham I 42


wK

EK

wL

EK

wK

wL

autarky

X-export cone

Y-export cone

Nottingham I 43

autarky

ρw =PXw/PY

w

Effects of Increasing PXw/PY

w in


X-export cone

Y-export cone

SX,SY

ρA

(ρA =PXA/PY

A = autarky price)

SX

SY

Nottingham I 44

autarky

ρw =PXw/PY

w


w in


X-export cone

Y-export cone

DX,DY

ρA

DY

DX

Nottingham I 45

autarky

ρw =PXw/PY

w


w in


X-export cone

Y-export cone

TX,TY

ρA

TX

TY

Nottingham I 46

autarky

ρw =PXw/PY

w


w in


X-export cone

Y-export cone

wK/PY

ρA

wK/PY

Nottingham I 47

autarky

ρw =PXw/PY

w


w in


X-export cone

Y-export cone

wL/PY

ρA

wL/PY

Nottingham I 48

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 49

Effects of Increasing Trade Costs

• Example:– Consider a country whose factor endowments

have it completely specialized in good X at world prices

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autarky

t

Effects of Increasing Trade Costs: Example

X-export cone

SX,SY

SX

SY

Nottingham I 51

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

)/,,()/,,( ***YXLKXYXLKX PPEETPPEET

Nottingham I 52


• Results

with analogous expressions for the other country

LKJPEEEEww

YXIEEEETT

YXIEEEEDD

YXIEEEESS

YLKLKjJ

LKLKII

LKLKII

LKLKII

,),,,,,(

, ),,,,(

, ),,,,(

, ),,,,(

**

**

**

**

Nottingham I 53


• 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 54

PX/PY

−TX*

(cone)

World Equilibrium

TX

TX, −TX*

(cone)*

(PX/PY)w

Nottingham I 55

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 56


• 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 57


• 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 58

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

The Heckscher-Ohlin Model: Features, Flaws, and Fixes I: What's the H-O Model Like Alan V. Deardorff...

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