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1.
Suppose output is produced according to the production function
QK =min(
K
, 2
L
), what is the expansion path of this production function?
K=2L
2.
Suppose a firm’s average cost curve is described by the equation
AC =
2
q
2
16
q +
90. At what output level does the marginal cost curve cross the average
cost curve?
Q*=4
3.
If input prices are
w=
4, and
r =
1, and
q
=4
K
0.5
L
0.5
, what is the least cost input combination
required to produce 40 units of output?
L*=5, K*=20
4.
Suppose a perfectly competitive firm has the shortrun cost function
C=
125 +
q
2
. Determine the firm’s output level and profit at prices of $30 and $20. At what
price does the firm reach the shutdown point?
when P=30, Q*=15, profit=100 , when P=20, Q*=15, profit=25
operate at all positive prices P=0 (shutdown when P<min(AVC), that happens when
MC=AVC, in this case, when 2Q=Q or Q=0, AVC(0)=0)
5.
Demand in Market 1 for
X
is
Q
d
=80 
p
. Demand in Market 2 is
Q
d
=120 2
p
. At a price of
$20, which has a larger consumer surplus?
Market 1 (180 > 160)
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 Winter '07
 RAUCH
 Microeconomics

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