—
It then, gives up some capital as well, and output of sector 1 falls
Endowments appear on the axes. Note the shift in the isoquants as the en-
dowment of L is increased.
The isoquant of the labor intensive advances, while
the isoquant of the capital intensive sector shifts backwards.
4. Generalizations
This part of the notes introduce the model with home goods and intermediate
factors, and more general results are then derived. Only brief "claims" are made
here:
1. Rybczynski: For the case of an equilibrium with M traded goods and N en-
dowments, and
M
=
N.
Suppose factor
i
increases and the country remains
within its cone of diversification.
If a subset of industries ONLY employ
factor
i,
then at least one of these industries’ output will expand by at least
16

in proportion to the proportional increase in the factor, and the output of
other industries will not change. If the subset of industries employ MORE
than one factor that increases, then it must be that one of these industries
(say industry
k
)
expands output in greater proportion to the proportional in-
crease in the factor and at least one industry (say industry
j
)
must contract.
In this case,
ˆ
y
k
>
ˆ
v
i
>
0
>
ˆ
y
j
.
(See Woodland, p. 82)
2. Stopler-Samuelson:
For the case of an equilibrium with M traded goods
and N endowments, and
M
=
N.
Suppose output price
j
increases and the
country remains within its cone of diversification.
At least one factor price
must rise in at least proportion to the rise in output price.
If one of the
factors whose price rises is used in an industry other than
j,
then the price
of some other factor, say
i,
must fall; this implies
ˆ
w
k
>
ˆ
p
j
>
0
>
ˆ
w
i
(See
Woodland, p 88)
4
4
Consider
M
=
N
= 3
.
Then
˜
w
i
=
ξ
i
p
1
˜
p
1
+
ξ
i
p
2
˜
p
2
+
ξ
i
p
3
˜
p
3
where the elasticities sum to unity.
If
ξ
i
p
j
<
0
,
then the sum of the remaining elasticities must
exceed unity.
17

5. A specific characterization: algebra
Operating on the principle that an algebraic specification strengthens the under-
standing of the theory, consider the following example.
Given:
U
=
q
λ
1
q
(1
−
λ
)
2
utility
L, K
resource endowments at the economy level
y
1
=
A
1
`
α
1
k
1
−
α
1
: technology sector 1
y
2
=
A
2
`
β
2
k
1
−
β
2
:
technology sector 2
and hence
tc
1
=
α
−
α
(1
−
α
)
α
−
1
w
α
r
1
−
α
y
1
A
1
(5.1)
tc
2
=
β
−
β
(1
−
β
)
β
−
1
w
β
r
1
−
β
y
2
A
2
(5.2)
α
−
α
(1
−
α
)
α
−
1
A
1
w
α
r
1
−
α
−
p
1
=
0
β
−
β
(1
−
β
)
β
−
1
A
2
w
β
r
1
−
β
−
p
2
=
0
.
α
1
−
α
(1
−
α
)
α
−
1
A
1
w
α
−
1
r
1
−
α
Y
1
+
β
1
−
β
(1
−
β
)
β
−
1
A
2
w
β
−
1
r
1
−
β
Y
2
=
L
α
−
α
(1
−
α
)
α
A
1
w
α
r
−
α
Y
1
+
β
−
β
(1
−
β
)
β
A
2
w
β
r
−
β
Y
2
=
K
18

5.1. The factor market "rental" equations
Solve the zero profit equations for
w
and
r
as functions of
p
1
and
p
2
to obtain
w
=
p
1
−
β
(
α
−
β
)
1
p
α
−
1
α
−
β
2
α
−
α
(1
−
α
)
(
α
−
1)
A
1
!

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- Spring '14
- Roe,TerryLee
- Economics, Austrian School, yj