Answers to Selected Questions in Practice Problem Set 3
ECON 11
Summer Session C 2010
Microeconomic Theory
Yong Yang
1. [Production and cost]
(a)
L
= 1
(b)
q
=
√
L
yields
L
=
q
2
.
(c) The cost is 100
L
, so the cost function is 100
q
2
.
(d)
MC
= 200
q
and
AC
= 100
q
. A figure is omitted.
(e) The cost is
wL
= 300
L

L
2
. Since
L
=
q
2
, the cost function is
C
(
q
) = 300
q
2

q
4
.
(f)
MC
= 600
q

4
q
3
and
AC
= 300
q

q
3
.
(g)
MC
=
AC
gives 300
q
= 3
q
3
, so
q
= 10.
(h) A figure is omitted.
Both
MC
and
AC
are cubic functions, and
MC
lies above
AC
for
q <
10, but below for
q >
10. Make sure that
AC
reaches its maximum at
q
= 10.
2. [Optimal choice of inputs]
(a)
MP
L
=
√
K
2
√
L
, and
MP
K
=
√
L
2
√
K
.
(b)
MRTS
=
MP
L
/MP
K
=
K/L
.
(c) Let
K/L
= 4
/
9 and solve with 30 =
√
LK
, then
L
= 45 and
K
= 20.
(d) The cost is
P
L
L
+
P
K
K
= 360.
P
L
L
is 180, so half of the total cost was distributed to the
labor, and the same for capital.
(e) Let
K/L
= 9
/
9 and solve with 30 =
√
LK
, then
L
= 30 and
K
= 30.
(f) The cost is 540, and both the labor share and the capital share are half of the total cost.
(g) The statement is true. For CobbDouglas production function, the labor share is always fixed
no matter what the input price ratio is and what amount is produced.
(h) For
P
L
=
P
K
= 4, we have
L
=
K
= 30, and the labor share is half of the total cost.
P
L
= 9
and
P
K
= 4 yields
L
= 20 and
K
= 45, and the labor share is half of the total cost.
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 Summer '08
 cunningham
 Economics, AP

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