The Heckscher-Ohlin Model
Sanna-Randaccio Lecture n. 8
•Assumptions (Production, Demand)
•Goods differ in terms of: factor intensity
•Factor-intensity reversals are excluded
(elasticity of substitution between factors)
•Countries differ in terms of: relative factor endowments
•Transformation curves when factor endowments differ
Assumptios
PRODUCTION
•2 primary factors of production
•Production functions with positive but decreasing MPi and constant
returns to scale (first degree homogeneity)
•Perfect competition
•International immobility of factors (while perfect mobility of goods)
•Production functions are internationally identical
DEMAND
•Structure of demand identical in both countries and independent of the
level of income
•Homothetic preferences (
)
OTHER TWO ASSUMPTIONS
•Countries differ in terms of their relative factor endowments
•Factor-intensity reversals are excluded
Optimum factor ratio (K/L)
•Definition: the K/L ratio at which the condition for cost minimisation
holds for a given factor-price ratio.
•Condition for cost minimization
•How the optimum factor ratio K/L changes if w/r increases
(decreases): capital is substituted to labour (viceversa)
•First degree homogeneous production functions: the optimum K/L
ratio depends only on w independently from the scale of
production.
r
(Relative) factor intensities of the two goods
It depends on the optimum capital/labour ratio in production (factor
ratio at which the cost minimization condition holds) at a given
We define good X as labour-intensive (capital-intensive) relative
to Y if for a given w/r :
Kx Ky
<
Lx L y
K
( Kx > y )
Lx
Ly
Stong factor intensity assumption
Kx Ky
<
Lx L y
Elasticity of substitution between factors
d ( K i / Li )
( K i / Li )
σi =
d (w / r )
w/ r
i = X ,Y
Relative change in K/L for a given change of the factor prices ratio
The curvature of the isoquant is associated to the elasticity of
substituiton between factors (greater the curvatura of the isoquant, the
lower the substitutability of factors in production).
.
d ( K i / Li )
( K i / Li )
σi =
d (w / r )
w/ r
d ( K i / Li )
d (w / r )
σi =
( K i / Li )
w/ r
In the case of Cobb-Douglas functions
Q = f ( L, K ) = Lα K β
Condition for cost minimization
K βw
=
L α r
d ( K i / Li ) β
=
d (w / r ) α
from which:
K/L β
=
w/ r α
thus
The elasticity of substitution is constant and equal 1.
σi =1
(Relative) factor abundance
Definition in physical terms
given
K h = endowment of K in H
Lh = endowment of L in H
if
Kh K f
>
Lh L f
country H is abundant in capital relative to country F
Price definition
Considering the autarkic equilibrium factor prices if
wh w f
>
rh
rf
country H is abundant in capital relative to country F if capital is relative
cheaper than in F at pre-trade
Factor Endowments and the Transformation Curve
Markusen et al. p. 103
Transformation curves for countries with different relative factor
endowments (country H is the relatively capital-abundant
country, good Y is the capital-intensive good)
Markusen et al. P. 103
The slope of the transformation curve (for a given
Y
) depends on the relative
X
(and not on the absolute) value of factor endowments
Yh
Y 'h
X 'h
Xh
Relative factor endowments remain constant but the country size is
halved.