ECO 100B
Problem Set 1
Answers will be posted on April 11, 2008
MRTS, (ii) Diminishing Marginal Product in each input, and (iii) Constant Returns to Scale
(assume throughout that
L;K >
1
):
(a)
f
(
L;K
) =
L
+
K
Solution
:
MP
L
=
df
dL
= 1 =
df
dk
=
MP
K
, and
MRTS
=
MP
L
MP
K
=
1
.
Hence, the
product does not satisfy (i) or (ii). The technology does satisfy CRS.
(b)
f
(
L;K
) =
p
LK
Solution
:
MP
L
=
df
dL
=
1
2
K
L
±
1
2
,
MP
K
=
1
2
K
L
±
1
2
.
MRTS
=
K
L
. By observation,
j
MRTS
j
is strictly decreasing in
L
. The technology also
d
dL
MP
L
=
1
4
K
1
2
L
3
2
<
0
, and
d
dK
MP
K
=
1
4
K
3
2
L
1
2
<
0
. Finally,
f
(
&L;
) =
p
(
) (
) =
p
LK
, and hence, the technology does satisfy CRS.
(c)
f
(
L;K
) = (
LK
)
2
Solution
:
MP
L
= 2
LK
2
, and
MP
K
= 2
KL
2
. So,
MRTS
=
K
L
. So, the technology
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 Spring '07
 RAUCH
 Economics of production, 1 K, Monotonic function, 2 m, 1 4 L

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