INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 1
Rybczynski
We will use the Edgeworth-Bowley box and results from factor price
equalization (FPE) to derive Rybczynski’s theorem
It applies to the effect of an increase in the available level of an input,
say labor, at constant prices for final goods
From FPE we know that if the prices of final goods do not change,
then the rewards to factors of production do not change
That, in turn, implies that the capital-intensity with which the two
goods are produced (the capital-labor ratio) does not change
Suppose that good X uses capital relatively intensively
Kx/Lx > Ky/Ly
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 2
Rybczynski
Oy
K
Kx/Lx
The capital-labor
intensities for
goods X and Y
determine the
allocation of
capital and labor
(on the contract
curve)
Ky/Ly
Ox
L0
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 3
Rybczynski
More labor available increases the Edgeworth Box
Oy
K
Kx/Lx
Oy’
Ky/Ly
Ox
The Y-origin is shifted to the right
L0
L1
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 4
Rybczynski
The goods prices do not change, so K/L intensities do not change
Oy’
Oy
K
Kx/Lx
E0
Ky/Ly
E1
Ox
The equilibrium moves from E0 to E1
L0
L1
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 5
Rybczynski
Less capital and labor is allocated to produce good X
Oy
K
Kx/Lx
Oy’
E0
Ky/Ly
Ox
E1
L0
L1
The production of X falls; similarly, the production of Y rises
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 6
Rybczynski
Rybczynski’s result makes perfect sense. After all the economy-wide
K/L ratio must be a weighted average of Kx/Lx and Ky/Ly. If the
economy-wide K/L ratio falls as a result of an increase in labor, while
the sectoral rates Kx/Lx and Ky/Ly do not change because the prices of
final goods do not change, then the weight attached to the relatively
capital-intensive sector (good X) must decrease, pulling capital and
labor away and causing a fall in its output.
Rybczynski’s result can be nicely illustrated in goods space to show
the impact on the production possibility frontier (ppf).
In this respect it is important to note that the demonstration of the
Rybczynski result above using the Edgeworth Box is exclusively
based on straight lines. Any other change in the available labor
supply results in equiproportional changes in produced output
 Charles van Marrewijk, 2006; 7
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
Rybczynski
If the economy produces at point A and labor rises10
units, causing a rise in the output of Y of, say, 4 units
and a fall in the output of X by 3 units, then
Y
a further increase in labor of 10 units
also leads to 4 more Y and 3 less X
Labor
Rybczynski
line
This process continues until X is no
longer produced; it is summarized by
the blue Labor Rybczynski line
A
Capital
Rybczynski
line
0
A similar procedure can be
used to derive the dotted red
Capital Rybczynski line
indicating the effect of
increasing the supply of capital
X
 Charles van Marrewijk, 2006; 8
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
Rybczynski
We can draw the ppf through the initial production
point A; the income line must be tangent there
As the labor stock increases
Labor Rybczynski line production moves along the Labor
Rybczynski line to the eq. at point
B
The increase in labor also
B
shifts the ppf outward; it
must be tangent to a parallel
income line at point B
A
The outward shift of
the ppf is biased toward
good Y, that is the
labor-intensive good
Y
0
X
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 9
Rybczynski
Production possibility frontiers; L = 5
6
5
good Y
4
A
3
capital
B
Rybczynksi
line
2
C
1
K=2
K=5
K=8
0
0
1
2
3
4
good X
5
6
7
8