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Lesson 23
1
Proof of Rybczynski theorem
In this lesson, we “prove” the Rybczynski
theorem
The “proof” is by way of example, and is
therefore not completely general
Generalization requires more advanced
mathematical techniques
Lesson 23
2
Proof is strikingly similar to proof of
StolperSamuelson
The difference is that we work with full
employment conditions, rather than zero
profit conditions
Lesson 23
3
Using standard notation, the full
employment conditions can be written:
Labor used
to produce
X
Labor used
to produce
Y
Supply of
Labor
+=
L
XX
aQ
⋅
L
YY
⋅
L
+
=
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Lesson 23
4
Using standard notation, the full
employment conditions can be written:
Capital used
to produce
X
Capital used
to produce
Y
Supply of
Capital
+=
K
XX
aQ
⋅
K
YY
⋅
K
+
=
Lesson 23
5
As with the proof of StolperSamuelson,
we now graph these two conditions
Lesson 23
6
The fullemployment condition for labor
X
Q
Y
Q
LX
La
LY
Slope =
LX
LY
a
a
−
3
Lesson 23
7
The fullemployment condition for capital
X
Q
Y
Q
KX
Ka
KY
Slope =
KX
KY
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This note was uploaded on 09/14/2009 for the course ECON 340 taught by Professor Leidholm during the Summer '08 term at Michigan State University.
 Summer '08
 leidholm
 Economics

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