The Heckscher-Ohlin
Model
J. Peter Neary
Oxford University and CEPR
Preview: Simple General Equilibrium Models
The Heckscher-Ohlin Model:
• Factor-price equalisation
• The Stolper-Samuelson Theorem
• The Rybczynski Theorem
• The Heckscher-Ohlin Theorem
The Specific-Factors Model:
• Comparative statics
• Short-run to long-run interpretation
The Heckscher-Ohlin Model
[A special case of the general competitive model]
Assumptions:
•
•
•
•
•
Perfect competition, constant returns to scale
2 countries: Home and Foreign (*)
2 factors: Capital K and Labour L
2 sectors: y1 and y2 [Sometimes, to fix ideas: Manufacturing M and Food F]
Complete intersectoral factor mobility
Key Concepts:
1. Factor Abundance (of countries):
• Home more labour-abundant: k < k*.
2. Factor Intensity (of industries/sectors):
• Facing the same factor prices, sector 1 [M] is more capital-intensive:
K1/L1 > K2/L2 or k1 > k2
• Assume: No "factor-intensity reversals": One sector always more capitalintensive
3
Digression: The Unit Cost Function
Proofs require a new diagram: Unit cost or “isocost” diagram
• Profitability of an industry depends on price of its output
(p) and prices of its inputs (w and r)
• Equilibrium given by the unit cost function: p = c(w,r)
• Consider the space of factor prices, w and r:
w
• Given p, we seek the locus of points in
this space at which the industry just
breaks even (the zero-profit locus)
r
Digression: The Unit Cost Function (cont.)
• With fixed coefficients, this must w
be a downward-sloping straight
line: p = aLw + aKr
• Its slope is: dw/dr = aK/aL = K/L
• If coefficients are variable, firms
can substitute away from the
factor which becomes more
w
expensive
• So, as w/r rises, the curve
becomes steeper
• Hence curve is convex to origin
• At any point, the slope of the
tangent to it equals the optimal
capital-labour ratio at that wagerental ratio
Fixed
Coefficients
K/L
r
Variable
Coefficients
K/L
r
Digression: The Unit Cost Function (cont.)
Alternative Ways of
Representing a Sector’s
Technology
K
Q>1
Q<1
1. Unit Isoquant Diagram
Q = F(K,L) = 1
slope = MRS =  w/r
2. Unit Cost Curve Diagram
p = c(w,r)
slope =  K/L
[ Exercises: Draw both for cases of: (a) Fixed coefficients
(Leontief); (b) Perfect substitutes; (c) Cobb-Douglas.]
Q = F(K,L) = 1
w/r
L
w
p < AC
p = c(w,r)
p > AC
K/L
r
“Factor Price Equalisation” (FPE)
Consider any industry:
• The zero-profit condition implies that price equals unit costs:
p = c(w,r)
• Given p, this defines a locus in (w,r) space
(convex to origin, because c is concave in (w,r))
• Equilibrium must lie on this locus
(since points above imply factor prices too high: losses, leading to exit; and points
below imply factor prices too low: super-normal profits, leading to entry)
• So, equilibrium for both industries is where the loci meet
w
w
p<0
p>0
[slope=K/L]
c2
c1
r
r
7
Qualifications to FPE
(i) Non-Existence:
(More specifically: non-existence of a fully diversified equilibrium)
Taken literally, the theorem suggests that, under free trade, countries with
very different factor endowments (e.g., U.S. and India) would have the
same factor prices
BUT It requires that each country produces both goods.
Here is where endowments play a role: They determine whether the two
countries will produce both goods.
K
To see this, consider factor space:
M
We saw that factor usage in both sectors can
be determined given the endowment
point G
• BUT Key assumption was that G lay
between OM and OF
.
G'
.G
F
. G"
• If not (e.g., G' or G"), then country can
not produce both goods
O
L
Qualifications to FPE (cont.)
(ii) Non-Uniqueness:
Factor intensity reversals are possible
If: Elasticities of substitution differ enough between sectors
(iii) Same number of goods and factors required:
• More goods: each country may produce a different mix of goods, more
suited to its own factor endowments.
• More factors: Specific-factors model a simple example of a model with m >
n, which rules out FPE.
9
The Stolper-Samuelson Theorem
Theorem: An increase in the relative price of the capitalintensive good will increase the rental and reduce the wage,
relative to the prices of both goods
• Note: It refers to “real” wages and rentals
• This implies that wage-earners are unambiguously worse off
and capital-owners unambiguously better off
Proof of Stolper-Samuelson
w
E
Initial equilibrium at D.
Exogenous Shock:
D
• Price of M rises
• So, values of w and r which M sector
can pay and still break even are higher
• i.e., M unit cost curve moves out
H
cF
cM
O
• BUT: Equilibrium moves sideways to H
• M is K-intensive: Return to K (r) rises
• F is L-intensive: Return to L (w) falls
• Price of M rises by DE/OD%: % increase in r is greater.
• So: Unambiguous change in real rental and real wage:
pˆ M  pˆ F

rˆ  pˆ M  pˆ F  wˆ
– ^pF =0 in diagram but this is only a choice of numeraire
– Like Rybczynski, price change has a “magnification effect”
c M2
1
r
Algebra of Stolper-Samuelson
 LM

 LF
ˆ 
w
 KF

ˆM  0
p
rˆ  
 LF

ˆM 
ˆ
 KM   w
p
   

ˆF 
 KF   rˆ   p
ˆM  0
p
 
 LM
 KM
 LF
 KF
Multi-sectoral extension (Ethier 1974):
  LM   LF   KF   KM  0

ji
wˆ j  pˆ i
 i (*)
j
Suppose:
pˆ 1  0 ,
pˆ i  0
i  1
Hence:
• Equation (*) for i=1 implies that at least one wj must increase
relative to all goods prices.
• Equation (*) for i1 implies that at least one wj must decrease
relative to all goods prices.
12
Policy Application: Trade and Wages
The debate:
• Increase in relative demand for skilled labour in OECD
• Higher wage dispersion in U.S. and U.K., higher and more
dispersed unemployment rates in Continental Europe
Is Trade the Explanation?
• Increased competition from low-wage countries
=> Lower price of unskilled-intensive good (“S” instead of “K”)
=> Lower relative wage, by the Stolper-Samuelson Theorem:
w
[slope=S/L]
r
13
Policy Application: Trade and Wages (cont.)
Problems with the Trade Explanation:
• Predicts a fall in S/L in both sectors
• Predicts a rise in w/r in exporting countries (LDC’s)
• Observed changes in price and import volume are not
sufficient to explain the changes
• More plausible explanations:
• Labour-saving technical progress
• Outsourcing
BUT: Existing explanations assume perfect competition:
• Cannot explain changes in profits or mark-ups
• Lower import prices the only form of “increased competition”
• Empirical evidence that market structure affects trade impact
on unskilled wages
[Oliveira-Martins (1994), Borjas and Ramey (1995), Neary (RIE 2002)]
14
The Rybczynski Theorem
At constant prices, an increase in one factor endowment will
increase the output of the good intensive in that factor by a
greater proportion and reduce the output of the other good
• Isoquant diagram Fig. 4-1
illustrates technology in one
sector
• If factor prices are fixed, then
least-cost point on any
particular isoquant is
determined:
slope = MRS = w/r
•
•
•
•
K
Expansion Path
Q2 = F(K,L)
w/r
Q1 = F(K,L)
L
Assume that factor prices remain fixed; from FPE, we know
that this must be true if goods prices are fixed
With CRS, locus of least-cost points on different isoquants is
a straight line from origin [“Expansion Path”]
Now, combine the expansion paths for the two sectors in one
country to give the “Edgeworth-Bowley Box”: Fig. 4-8.
Assumptions of fixed endowments (dimensions of box) and
full employment pick out production points in both sectors
The Edgeworth-Bowley Box I
Start with expansion path for sector F
(Leave out the isoquants)
Add expansion path for sector M
Recall: M is more K-intensive
M
KF
F
O
LF
KM
G
LM
Now: Rotate the second through 180° (not just 90°);
and set axes equal to home endowments of both factors
The Edgeworth-Bowley Box II
LM
G
KM
K = KF + KM
KF
E
F
M
O
LF
L = LF + LM
Point E illustrates
equilibrium factor inputs
and outputs in both sectors
The Rybczynski Theorem
G’
G
K
F
E
O
E’
L
• Now: consider a change in factor endowments; e.g., an increase in L
• Goods prices do not change, hence neither to factor prices and factor
proportions
• Output and usage of both factors in K-intensive sector (M) must fall; while
they must rise in L-intensive sector (F)
Summary of Rybczynski Theorem
N.B. Use a “hat” to denote a rate of change (a.k.a. growth rate):
Kˆ  Lˆ

Xˆ M  Kˆ  Lˆ  Xˆ F ,
dX
Xˆ 
X
wˆ  rˆ  0
(^K=0 in diagram, but because of CRS this is not crucial: only relative factor endowments matters for relative outputs)
Economic mechanism?
• Increase in L puts downward pressure on wage w
[though in equilibrium the wage does not actually fall]
• This encourages expansion of L-intensive sector, F
• L-intensive sector draws capital and labour from other sector
[Note from diagram: F-sector ends up absorbing more labour than the economy’s extra
endowment]
• Since factor prices settle at their original level, both sectors
end up with the same factor proportions as initially
• Expanding sector grows by more than the economy average
Rybczynski Theorem (cont.)
Note: Theorem is very surprising - Economic growth occurs,
yet output of one industry falls
Basic idea: Source of growth is asymmetric; effect on pattern
of outputs is even more asymmetric: asymmetry is magnified.
Real-world examples?
• Black Death in 13th century Europe
• Great Famine in Ireland, 1846-49
• Russian emigration to Israel in 1990’s
Heckscher-Ohlin Theorem
Theorem: A country has a comparative advantage in the good
that uses relatively intensively the country’s relatively
abundant factor
Basically, extends the Rybczynski theorem from a time-series to a
cross-section context, and neutralises the effects of demand
differences between countries
Steps in Proof:
• Illustrate Rybczynski theorem in PPF diagram and reinterpret
it in terms of a cross-section comparison between countries,
which differ only in endowments of K (not L)
• This shows that at the same prices, the more K-abundant
country produces relatively more of the more K-intensive good.
• Hence its relative supply curve (XM/XF) lies to right of the other
country’s
The Rybczynski Theorem in Output Space
y2
A
B
p
p
y1
Rise in labour endowment => PPF shifts out, but in a biased way
“Rybczynski line” links points on old and new PPF with same
slope: The theorem implies that it must be downward-sloping
23
Heckscher-Ohlin Theorem (cont.)
Now: Interpret Rybsczynski Theorem in a Cross-Section
y2
Home PPF
Q*
Q
Foreign PPF
Home is more capital-abundant; so at the same prices, it has:
• Higher output of the capital intensive good y1; and
• Lower output of the labour-intensive good y2
y1
Heckscher-Ohlin Theorem (cont.)
Final step: Homothetic tastes
• Imply that relative demands are the same at home and abroad
• So: Production bias translates into a trade bias
O*
A
D
E
K
C
G
O
L
The FPE Set and Inter-Industry Trade
B