ECO364 - International Trade
Chapter 3 - Heckscher Ohlin
Christian Dippel
University of Toronto
Summer 2009
Christian Dippel (University of Toronto)
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The Heckscher-Ohlin Model
Model Set-Up
Difference To Ricardo
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In Ricardo:
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everyone wins from Trade.
there is only one factor of production
outcome is complete specialization
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This is very simplistic
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The Heckscher-Ohlin model aims to remedy some of these
shortcomings.
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It is more complex than Ricardo but gives far more subtle and
nuanced predictions.
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The Heckscher-Ohlin Model
Model Set-Up
Framework
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2x2x2 Model: 2 Countries, 2 Goods (Outputs), 2 Factors (Inputs).
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No productivity differences. All countries share the same technology.
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Identical Homothetic Preferences.
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Output can be produced with different input mixes (depending on
relative input prices).
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Factors are mobile across sectors.
Countries differ in the relative abundance of factors. This is the key
of Comparative Advantage in the HO Model.
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HO is often referred to as the factor proportions theory.
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The Heckscher-Ohlin Model
Model Set-Up
Preview of Insights to Come
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Factor Abundance determined at Country Level
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Factor Intensity determined at Industry (=Sector) Level
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Specialization according to both Factor Abundance and Intensity
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Countries gain from Trade but Industries may loose and Factors may
loose
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Trade has Subtle Effects on Industrial Restructuring
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Under certain conditions, Factor Prices (e.g. wages) are equalized
across countries
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The Heckscher-Ohlin Model
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Model Set-Up
Recall patterns of specialization from the first class:
Table: Trade by Commodities (1995)
Type of Goods
Canada
Machinery
0.383
Food and Live Animals
0.066
Chemicals
0.059
Misc. Manufactures
0.049
Source: Robert Feenstra, “World Trade
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China
Thailand
United States
0.230
0.045
0.041
0.455
Flows”
0.382
0.190
0.031
0.196
0.472
0.072
0.109
0.113
Canada and the United States specialize in skilled labor/capital
intensive goods while China and Thailand specialize in goods that use
unskilled labor relatively intensively.
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The Heckscher-Ohlin Model
Model Set-Up
Set-Up Again
1. Two countries.
2. Two goods.
3. Two productive factors
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Because of (1)-(3), this is referred to as the 2x2x2 model.
4. Constant returns to scale
5. Perfect competition (all agents are price takers).
6. Countries differ only in terms of their (relative) factor endowments.
7. Factors are immobile across countries but mobile across sectors.
8. Identical Homothetic Preferences
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The Heckscher-Ohlin Model
Model Set-Up
We first set up the equilibrium relations between goods prices, factor
prices and factor inputs
1. Derive relationship between relative factor prices and relative factor
demand.
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Based on firm profit maximization.
FF curves (to be derived).
2. Derive relationship between relative goods prices and relative factor
prices.
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Based on iso-value and iso-cost curves from Lerner diagram (to be
derived).
SS curve (to be derived).
3. Use (1) and (2), derive three-way relationship between relative factor
prices, relative factor demand and relative goods prices (see slide
33/98 for an application).
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The Heckscher-Ohlin Model
Model Set-Up
This is a General Equilibrium (GE) Framework. It is important to
remember what GE means (as opposed to Partial Equilibrium):
1. Firms maximize profits
2. Consumers maximize utility
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Utility/Preferences stay in the background throughout the analysis
Because of homothetic preferences: Relative Demand unaffected by
income
3. Labor markets clear
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This is the basic set-up for any GE Framework!
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The equilibrium is a set of (factor market clearing) factor prices,
(goods market clearing) goods prices and sector-specific factor
allocations.
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The Heckscher-Ohlin Model
Model Set-Up
We consider a small open economy where prices are exogenously given and
predict:
1. What happens to equilibrium relative factor prices and factor demand
if goods prices change (can be interpreted as movement from autarky
to free trade).
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Stolper-Samuelson Theorem and Jones Magnification.
2. What happens to equilibrium relative factor prices and the production
structure (sectorial composition) if the distribution of productive
factors changes (can interpret as immigration).
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Factor Price Insensitivity and Rybczynski Theorem.
3. Who specializes in what:
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Heckscher-Ohlin Theorem
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
To determine the optimal factor-intensity, we use the iso-value and
iso-cost lines in the following Lerner Diagram.
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
The iso-value curves map combinations of capital and labor that
yield $1 of output.
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Start with 1 = p x F x (K , L).
For a given value of p x , what values of K and L produce $1 of output?
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
Some iso-value schedules where px,3 < px,2 < px,1 ... (at a lower
price, firm needs more inputs to yield $1 of input)
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
The iso-cost curve gives combinations of capital and labor that (as a
bundle) cost $1. Values of w and r are taken as given. It is derived
from the following equation
wL + rK = 1
K=
Christian Dippel (University of Toronto)
1
r
−
w
r L
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
If w and r rise by the same proportion, the iso-cost curve shifts in
parallel. Using less K and L now costs $1
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
With zero profits, both revenue and costs are equal to 1. Therefore, K and
L must lie on both curves.
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
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Equilibrium has to be at point of tangency (demonstrated on next few
slides)
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The straight line from the origin to the point of tangency is called the
Output Expansion Path (OEP)
The slope of the OEP gives us the factor intensity in a sector.
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A flatter OEP in our graph means a sector is more labor intensive
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
Value of output is $1 and costs are less than $1. Positive profits (firm
entry). Not an equilibrium.
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
Could use a different mix of K and L to attain positive profits. Not
an equilibrium.
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
Could use a different mix of K and L to attain positive profits. Not
an equilibrium.
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
Value of output is $1 and costs are more than $1. Negative profits
and firm exit. Not an equilibrium.
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
With a second good of another factor intensity, we can add a second
iso-value curve.
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
The preceding slide determines equilibrium factor intensities ( KLTT , KLCC )
in both sectors
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for a given set of goods prices pC , pT
and a given set of input prices w , r
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These goods prices and input prices are an equilibrium because both
iso-value lines are tangent to the iso-cost curve
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Suppose that pT increases. In order to produce $1 worth of textiles,
fewer inputs are needed.
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Consequently, the iso-value curve T shifts in while the iso-value
curve C does not move
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
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Now, there are profit opportunities in the textile sector because costs
are unchanged but revenue has increased.
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Capital and labor flow into the textile sector.
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Because textiles are relatively labor intensive (flatter OEP), labor’s
wage is bid up more than capital’s rental rate.
(w /r ) rises in response to pT /pc increasing.
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Importantly, r actually falls in this case to allow for non-negative
profits in the Computer-sector
Intuition: for every unit of labor that shifts from the Computer to
Textile-sector, Computer-firms want to free up more capital than
textile-firms are demanding.
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
note that r has to fall if pC is fixed.
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
This relationship between goods and factor prices is represented in the SS
curve:
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
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This SS curve gives us the relationship between goods prices and
factor prices
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What about the relationship between factor prices and factor
intensities?
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We saw that a rise in PT /PC raises w /r
This makes labor more expensive and naturally leads to substitution
effects where each firm demands a higher K /L ratio
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Note that for markets to clear this has to imply that the labor-intensive
sector expands (intuition: PT rises)
There is therefore a positive relationship between w /r and K /L in
both sectors
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
restructuring if w /r increases
Figure: Lerner Diagram
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
There is therefore a positive relationship between w /r and K /L in
both sectors
Supposing computers are relatively capital intensive (F C F C is below
and to the right of F T F T ):
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
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We can soon combine the graphs on slides 27 and 30 to have a
graphical representation of the General Equilibrium in a Small Open
Economy (with prices exogenous)
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But first, let’s make this more formal through the firm’s profit
maximization problem.
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In competition, the nominal wage paid to a factor in production of
good X equals its marginal revenue product such that where w is the
wage and r is the rental rate of capital
w = px mpl(K , L)
Christian Dippel (University of Toronto)
r = px mpk(K , L)
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
We can divide these two expressions such that
px mpl(K /L)
mpl(K /L)
w
=
=
r
px mpk(K /L)
mpk(K /L)
Because the marginal product of labor is increasing in and the marginal
product of capital is decreasing in K /L, we can rewrite the right hand side
into a single expression that is increasing in K /L.
w
= f (K /L)
r
Christian Dippel (University of Toronto)
,
∂ wr
= f 0 (K /L) > 0
∂(K /L)
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The Heckscher-Ohlin Model
General Equilibrium in a Small Open Economy
Example: Suppose that computers are capital intensive and textiles are
labor intensive with Cobb-Douglas production functions.
QT = K 1/3 L2/3
QC = K 2/3 L1/3
Firms producing X maximize PX QX − wLX − rKX
First Order Conditions (FOC) give {KC , KT , LC , LT } as functions of
{w , r , pC , pT } :
(1)
(2)
1/3 −1/3
w = pT 23 KT LT
−2/3 2/3
LT
r = pT 13 KT
2/3 −2/3
(3)
w = pC 13 KC LC
(4)
r = pC 23 KC
−1/3 1/3
LC
But {w , r } are also unknown so we need 2 more equations given by the
endowments. (5) KT + KC = K (6) LT + LC = L
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The Heckscher-Ohlin Model
Dividing (1)/(2) and (3)/(4) gives us:
General Equilibrium in a Small Open Economy
KT
w
w
1 KC
r = 2 LT
r = 2 LC
pT
KT −1/3 KC 2/3
( LC )
pC 2 = ( LT )
Setting (1)=(3) (or (2)=(4)) gives us:
Combining these expressions gives us a solution for w/r (as a function of
pT
1/3 which we can plug back in to solve for
prices):
pC = (w /r )
{KC , KT , LC , LT }
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The Heckscher-Ohlin Model
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General Equilibrium in a Small Open Economy
We can now combine these two graphs into one picture.
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The Heckscher-Ohlin Model
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For a given set of relative goods prices, we can now predict:
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General Equilibrium in a Small Open Economy
Relative factor prices
Factor intensities
For a given set of relative factor prices, we can now predict
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Relative goods prices.
Factor intensities
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In a small open economy (where prices are exogenous) we predict
relative factor prices and factor intensities given output prices.
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This can be represented in the following picture:
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
General Equilibrium in a Small Open Economy
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The Heckscher-Ohlin Model
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The SS curve is the graphical representation of the
Stolper-Samuelson theorem:
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Stolper Samuelson and Rybczynski Theorems
As the relative price of a good increases, the nominal wages of the
factor used relatively intensively in that good increase relative to the
nominal wages of the other factor.
Jones Magnification is an important corrollary that the real wages
of the factor used relatively intensively in that good increase and the
real wage to the other factor decreases.
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
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Example 1: If pT rises relative to pC , then the relative return to
labor over capital rises, the real wages of workers increase and the
real return to capital falls.
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Example 2: If pT falls relative to pC , then the relative return to
labor over capital falls, the real wages of workers falls and the real
return to capital rises.
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Using “Jones’ Hat-Notation”, denote a change in x by x̂
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Then it can be shown for Example 1, that: ŵ > p̂T > p̂C > r̂
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Figure: The Price of Textiles Rises Relative to the Price of Computers
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pT
pC
↑
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Figure: The Price of Textiles Falls Relative to the Price of Computers
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pT
pC
↓
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The Heckscher-Ohlin Model
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Stolper Samuelson and Rybczynski Theorems
If the price of textiles rises and the price of computers stays
unchanged, how do we know...
1. that the nominal wage of labor rises and falls for capital?
2. that the real wage of labor rises and falls for capital?
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Figure: nominal wage changes follow from the Lerner Diagram
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
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We now know that r falls and w rises.
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But how do we know that the real wage of labor rises and falls for
capital?
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w
pC
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If consumers consume both goods, the price level that consumers face
will be a combination of the price of textiles and computers.
and
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w
pT
are not real wages!
e.g p = 21 (pC + pT )
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If pT rises and pC stays unchanged, the aggregate price level (p) that
consumers face must go up!
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Because r falls,
r
p
Christian Dippel (University of Toronto)
must fall!
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
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How do we know that the real wage of labor rises?
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Label the cost share of labor in textile production as α and the cost
share of capital in textile production as (1 − α) (see Question 2c on
2nd HO Problem Set)
Recalling “Jones’ Hat-Notation” from previous slide and with zero
profits, we have:
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p̂T = αŵ + (1 − α)r̂
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Because r falls, w has to rise by more than pT
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Therefore
w
pC
and
Christian Dippel (University of Toronto)
w
pT
must both rise and
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w
p
must rise!
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The Heckscher-Ohlin Model
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Stolper Samuelson and Rybczynski Theorems
The results on real wages and return to capital are an extension to
the Stolper-Samuelson Theorem called Jones Magnification.
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Jones Magnification holds very generally (i.e. without holding PC
constant) but that is harder to show.
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Jones Magnification matters because it is real wages (i.e. purchasing
power) that determine welfare!
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It can be shown more generally than here but the algebra gets a bit
involved.
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
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We will now derive a very important result called the Rybczynski
Theorem.
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To do this, we will use an Edgeworth Box...
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First, note that LT + LC = L and KT + KC = K .
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
Stolper Samuelson and Rybczynski Theorems
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Figure: The Textile Sector is Relatively Large
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Figure: The Computer Sector is Relatively Large
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The Heckscher-Ohlin Model
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Stolper Samuelson and Rybczynski Theorems
Remember from the “relative prices graph” that we know the ratio of
K to L in each sector.
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
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For given factor and goods prices, the Lerner Diagram gives us the
ratio of K to L (slope of OEP) in each sector.
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We can use this information in the Edgeworth Box.
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The Heckscher-Ohlin Model
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Stolper Samuelson and Rybczynski Theorems
Combinations of capital and labor in each sector must lie on the rays
below:
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
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These curves only intersect at one location.
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Therefore we know what inputs will be in each sector (and, therefore,
what output will be).
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The Heckscher-Ohlin Model
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Stolper Samuelson and Rybczynski Theorems
How do production patterns change if we increase one of the
endowments?
To do this, we simply expand the Edgeworth Box along the dimension
whose factor has increased in quantity
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Suppose we increase the amount of labor in the economy.
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
Stolper Samuelson and Rybczynski Theorems
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
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Labor and capital employed in computers both fall.
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Labor and capital employed in textiles both increase.
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Production of computers falls and production of textiles increases.
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Rybczynski Theorem: As endowments of one factor change, a
country will produce more of the goods that use that factor
intensively and less of those that don’t
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A corollary is that Migration leads to industrial restructuring because
it changes relative factor abundance
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Factor Price Insensitivity
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Notice that the OEP’s did not change slope as we expanded the
Edgeworth Box. This means that w/r did not change and this
irresponsiveness of w/r with respect to changes in factor endowments
is referred to as Factor Price Insensitivity (FPI) .
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When does it hold? Intuitively, w/r cannot change in the Lerner
diagram because goods prices are exogenously given to a SOE.
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The only way w/r can change is if the country specializes in only one
good.
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This implies that the condition for FPI is that both countries are
diversified (produce both goods).
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Diversification vs. Specialization
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The discussion of FPI is a good point to check your understanding of
production functions in the Ricardian and HO Model.
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Why is there a tendency to fully specialize in the Ricardian Model but
not in the HO Model although both models have CRS production
function?
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The reason is that the HO Model is a two-factor model and the
production function has declining marginal products in each factor
(despite being CRS - make sure you get the difference).
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This implies that as one sector expands at the expense of the other,
the marginal product of the scarce factor will eventually tend to
infinity in the shrinking sector.
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The Heckscher-Ohlin Model
Stolper Samuelson and Rybczynski Theorems
Recap
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We have learnt how wages and factor intensities respond to price
changes
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... and how factor intensities and industry structure (how much labor
employed in each sector) respond to factor endowments
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This is Stolper Samuelson
This is Rybczynski
Now we learn about the patterns of specialization.
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The Heckscher-Ohlin Model
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Heckscher Ohlin
Unlike the Ricardian model, the PPF in the HO model is bowed out
to reflect imperfect substitutability across sectors...
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The Heckscher-Ohlin Model
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Heckscher Ohlin
Optimal output will be attained when the value of output is
maximized.
V = pC QC + pT QT
We can rewrite this as
QT =
V
pT
−
pc
pT
QT
We can also think of this as an isovalue line that keeps the value of
production constant while varying the composition of production. Utility
will be maximized when the value of production is maximized and this
curve is as far up and to the right as possible.
Do not confuse this isovalue line with the isovalue curve in the Lerner
diagram.
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The Heckscher-Ohlin Model
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Heckscher Ohlin
Value, and consequently utility, is higher as these curves shift up and
to the right
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The Heckscher-Ohlin Model
Heckscher Ohlin
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A key insight is that, when there is no trade (autarky), the
consumption bundle must lie on both the iso-value line and the PPF.
I
This is similar to the Ricardian model in which a consumption bundle
must lie on both the PPF and the budget constraint.
I
Of course, in autarky, the production point is actually determined by
tangency of PPF and indifference curve and the price ratio adjusts to
be equal to the slope of both.
I
In autarky, an economy can only consume what it produces.
I
But under trade, the iso-value line can be thought of as a budget
constraint in that it gives all the consumption bundle that a country
can afford.
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The Heckscher-Ohlin Model
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Heckscher Ohlin
As ppTC increases, the economy produces more computers relative to
textiles.
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
This also gives us a relative supply curve for the two goods
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The Heckscher-Ohlin Model
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Heckscher Ohlin
Combine with Relative Demand
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The Heckscher-Ohlin Model
Heckscher Ohlin
I
The relative supply (RS) curve comes from the PPF and the iso-value
lines.
I
The relative demand (RD) curve comes from utility maximization as
in the Ricardian model.
I
Two countries in autarky:
I
Because preferences are identical and homothetic, the relative
demand curve is the same in both countries in autarky.
I
Using the Rybczynski theorem, we know that the relative supply curve
for the North is to the left of the relative supply curve for the South
in autarky. To see this:..
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
With free trade in goods, both pT and pC must equate across
countries. Therefore ppTC must equate across countries.
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
Heckscher Ohlin
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Summer 2009
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
With free trade and perfect competition, relative prices equate across
countries. The relative price of a given good will rise in one country
and fall in the other.
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
For a given good, there will be excess relative supply in one country
and excess relative demand in the other country. This good will be
exported by the first country and imported by the other.
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The Heckscher-Ohlin Model
Heckscher Ohlin
I
We can use the PPF graph to present the same information and to
illustrate the gains from trade.
I
The following equation presents a country’s balanced trade condition:
PC CC + PT CT = PC QC + PT QT
This can be rewritten as
CT − QT =
pc
pT
(QC − CC )
This is a budget constraint in that the value of goods consumed must be
no greater than the value of goods produced.
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The Heckscher-Ohlin Model
Heckscher Ohlin
I
Looking at the South, recall that in Autarky, consumption equals
production.
I
In equilibrium in autarky, we see production and consumption occur
at the point where the indifference curve is tangent to the PPF.
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
Heckscher Ohlin
ECO364 - International Trade
Summer 2009
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
However, with trade, countries are no longer constrained to QC = CC
and QT = CT . Now, they can trade at any point along their budget
constraint.
I pT
pC
rises ( ppTC falls) in the South.
Christian Dippel (University of Toronto)
pT
pC
falls ( ppTC rises) in the North.
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
For the South:
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
For the North:
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The Heckscher-Ohlin Model
Heckscher Ohlin
I
In the above example, the price of computers relative to textiles rises
in the North and falls in the South.
I
More generally, the relative price of the good that intensively uses the
relatively abundant factor rises. The relative price of the good that
intensively uses the relatively scarce factor falls.
I
By the Stolper-Samuelson Theorem, the abundant factor wins and
the scarce factor loses.
“Society” gains in each country because consumers can attain higher
indifference curves
I
I
This can be easily seen on the last two slides
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The Heckscher-Ohlin Model
I
Heckscher Ohlin
The Heckscher-Ohlin Theorem: Under all of the previously stated
assumptions, a country will export the good that relatively intensively
uses its relatively abundant good. The same country will import the
good that relatively intensively uses its relatively scarce factor.
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The Heckscher-Ohlin Model
Factor Price Equalization
I
Stolper-Samuelson tells us what happens to relative factor prices in
each country.
I
Owners of each country’s relatively abundant factor win as its factor
wage rises.
I
Owners of each country’s relatively scarce factor lose as its relative
factor wage falls.
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
Factor Price Equalization
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
Factor Price Equalization
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The Heckscher-Ohlin Model
Factor Price Equalization
I
How far does this factor price convergence go?
I
With Factor Price Equalization (FPE), goods price equalizing
across countries leads to factor prices equalizing across countries.
I
Relative factor prices converge across countries even though factors
are immobile across countries!
I
This is a striking result but when is it true?
I
The next slides show that FPE will happen as long as endowments are
not “too” different.
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The Heckscher-Ohlin Model
I
Factor Price Equalization
Recall the Lerner Diagram
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The Heckscher-Ohlin Model
I
Factor Price Equalization
... and the Edgeworth Box.
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The Heckscher-Ohlin Model
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Factor Price Equalization
Equilibrium Allocations can be found in two equivalent ways. Points
A and B are equivalent.
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The Heckscher-Ohlin Model
Factor Price Equalization
The “Integrated Equilibrium Approach”
I
I
So far, we have considered how factors are divided across sectors in
one country.
Now, let’s engage in a thought experiment:
I
I
I
I
Suppose we combine 2 countries and drop all barriers between them
(we have already assumed free trade and ignore financial flows so the
only addition is free migration)
The two countries are now “like one” and there will be a unique
General Equilibrium set of goods and factor prices.
This can again be represented in an Edgeworth Box that looks exactly
like before.
The boundaries given by the OEP’s mark the “Cone of
Diversification”.
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The Heckscher-Ohlin Model
Factor Price Equalization
Figure: the Cone of Diversification
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The Heckscher-Ohlin Model
Factor Price Equalization
I
We can pick a factor allocation anywhere in the Edgeworth box to
slice the country into two (drawing national boundaries).
I
Claim: Any factor allocation inside the Cone of Diversification will
lead to FPE.
FPE is equivalent to saying the OEP’s in the two countries are the
same.
I
I
I
I
I
The goods prices have to be the same under free trade
Also, countries have the same technology.
Together, this implies the iso-value curves in each country’s Lerner
Diagram are the same.
The OEP’s can then only be the same under FPE (only then are the
iso-cost curves the same)
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The Heckscher-Ohlin Model
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Factor Price Equalization
Allocation α lies inside the Cone of Diversification and FPE is attained
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The Heckscher-Ohlin Model
Factor Price Equalization
I
More intuitively, factor prices will be equalized if endowments are not
too different.
I
Endowments that are similar lie inside the Cone of Diversification
because it is “centered around the diagonal” in the Edgeworth Box.
I
Free Trade between Canada and the USA is likely to erase
wage-differences.
But Free Trade between Canada and China? The endowments are
likely too different.
I
I
I
Let’s say the last point α sliced the world into Canada and the US.
Instead, let’s slice the world into Switzerland and Bangladesh:
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The Heckscher-Ohlin Model
I
Factor Price Equalization
The North runs out of labor and the South runs out of capital
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The Heckscher-Ohlin Model
Volume of Trade
Volume of Trade
I
I
With identical preferences, all countries consume on the diagonal of
the global Edgeworth-Box (understand this!)
The factor content of trade is determined by the endowment point
and the factor prices.
I
I
I
I
To see this, note that Home is capital-abundant if its endowment lies
above the diagonal.
It exports capital-intensive goods and imports labor-intensive goods.
factor content of trade is the labor and capital embedded in these
good-flows.
Home exports good B and imports good A. Can read the imported
and exported labor and capital of the Edgeworth-Box.
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The Heckscher-Ohlin Model
Christian Dippel (University of Toronto)
Volume of Trade
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The Heckscher-Ohlin Model
Volume of Trade
The aggregate volume of trade is larger, the more different endowments
are.
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The Heckscher-Ohlin Model
Size and Gains from Trade
Size and Gains from Trade
I
the integrated equilibrium graph suggests that the volume of trade is
larger if countries are more similar in size (as you get to the corners of
the box, the boundaries of the cone get closer to the diagonal)
I
Hoe does country-size relate to gains from trade?
I
Assertion: small countries gain more from the movement from
autarky to free trade than do large countries.
I
Recall that the gains from trade come from free trade prices being
different than autarky prices.
I
The more different free trade relative prices, the larger the gains from
trade.
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The Heckscher-Ohlin Model
Size and Gains from Trade
I
In autarky, relative factor prices are determined by aggregate relative
factor endowments in each country.
I
In a free trade equilibrium, relative factor prices are determined by
world relative factor endowments.
I
The larger a country, the closer its relative endowments are to world
relative endowments.
I
Suppose we look at the two countries as Canada and China...
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The Heckscher-Ohlin Model
I
Size and Gains from Trade
Let’s look at a couple of examples...
Table: Size and Equilibrium Factor Prices
Canada
China
World
I
Large Canada
K
L
K /L
200 100
2
5
20 0.25
205 120 1.71
Large China
K
L
K /L
20 10
2
50 200 0.25
70 210 0.33
(integrated) World equilibrium factor prices will more closely resemble
autarky factor prices in the large country than in the small country.
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The Heckscher-Ohlin Model
Size and Gains from Trade
Figure: Size and Factor Prices: Large Canada
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The Heckscher-Ohlin Model
Size and Gains from Trade
Figure: Size and Factor Prices: Large China
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The Heckscher-Ohlin Model
Wrapping Up
Wrapping Up
I
Unlike the Ricardian model, there are winners and losers from trade
liberalization.
I
Owners of the scare factor lose because they become relatively less
scarce.
I
Owners of the abundant factor win because they become relatively
more scarce.
Winners win by more than the losers lose due to the gains from
specialization.
I
I
I
In order for “everyone” to gain from trade, we must see transfer
payments from the owners of the relatively abundant factor to the
owners of the relatively scarce factor.
Aggregate gains from trade come from the fact that consumers can
attain a higher indifference curve.
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The Heckscher-Ohlin Model
Wrapping Up
I
Combining the Rybczynski and Heckscher-Ohlin theorems, a
country will export the good that relatively intensively uses its
relatively abundant factor and will import the other.
I
As a country moves from autarky to free trade, the relative price of
the good that relatively intensively uses its relatively abundant factor
increases.
I
As a country moves from autarky to free trade, the relative price of
the good that relatively intensively uses its relatively scarce factor
falls.
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The Heckscher-Ohlin Model
Wrapping Up
I
As a country moves from autarky to free trade, we can use the
Stolper-Samuelson theorem to show that the nominal wages of a
country’s relatively abundant factor rise and the nominal wages of the
country’s relatively scarce factor falls.
I
Jones Magnification shows that the same is true for real wages.
I
This will lead to owners of the relatively scarce factor ”losing” and
owners of the relatively abundant factor ”winning.”
I
However, winners win by more than losers lose so trade can lead to
gains for everyone.
I
For everyone to gain from trade, there must therefore be transfer
payments from the winners to the losers.
I
Factors of production are immobile across countries but goods are
mobile. Trade in goods is enough to lead to factor price
convergence.
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