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Answer to Practice Homework 5
6.11
For this production function
L
MP
a
=
and
K
MP
b
=
.
The
,
L K
MRTS
is therefore
,
L
L K
K
MP
a
MRTS
MP
b
=
=
which is constant all along the production function. As MRTS
LK
is the negative of the
slope of the production function, constant MRTS
LK
signifies that the production function
n in this particular situation is linear.
6.13
a)
At point
A
, the firm produces 18 units of output. Therefore, since
B
is on the same
isoquant, it must be that
L
= 17 at
B
.
b)
The capitaltolabor ratio at
A
is 3/5 and
MRTS
L,K
= ½. At
B
, the capitaltolabor
ratio is 1/17, and
MRTS
L,K
= 1/18.
Therefore the elasticity of substitution is
.
68
69
)
2
/
1
/(
)
2
/
1
18
/
1
(
)
5
/
3
/(
)
5
/
3
17
/
1
(
=


A CobbDouglas production function has an elasticity of substitution of 1.
Therefore this production function has a slightly higher elasticity of substitution,
indicating a slightly greater ease of substitutability of inputs.
6.20
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 Spring '08
 Bryant

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