Econ 100B: Tang
Spring Quarter 2008
Homework 3: Ch 8 and Ch 9
Due Thursday May 8, at the beginning of class.
Please write your name and PID on your homework.
1)
Suppose the competitive market price for lunchboxes is $11/unit.
Short run
total costs for lunchboxes have been found to be:
C
=
9
+
3
Q
+
Q
2
a) How many lunchboxes will this firm make?
b) Does the secondorder condition for this problem hold?
c) At what price does profit maximizing supply fall to 0 (what’s the shutdown
point)?
d) What’s the profit at the optimal point?
e) Graph profitmaximizing supply as a function of the market price
P
.
a) max profit, profit=TRTC
π
Q
( 29
=
11
Q

9
+
3
Q
+
Q
2
(
29
∂
π
Q
( 29
∂
Q
=
11

3

2
Q
=
0
2
Q
=
8
Q
*
=
4
could also jump directly to FOC
set Q* where P=MC, solve for Q in 11=3+2Q
b)
∂
2
π
Q
( 29
∂
Q
2
= 
2
<
0.
yep
c) shutdown when P<min AVC
min AVC where MC(Q)=AVC(Q)
3+2Q=3+Q, so at Q=0
MC(0)=3
>
shutdown when P<3
d)
π
Q
*
(
29
=
11 4
( 29

9
+
3 4
( 29
+
4
( 29
2
=
7
e) Supply equals MC while MC>AVC and equals 0 when MC is below AVC
(recall min AVC, where MC=AVC, is the shutdown point).
MC=3+2Q
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Econ 100B: Tang
Spring Quarter 2008
2)
A firm’s shortrun production function is given by:
Q
=
KL
where the level of capital is fixed at
K
Define the wage as the constant
w
, and the rental price of capital to be
r
.
The
competitive price of output is
P
.
a) What is the firm’s short run marginal cost?
b) At what levels of
P
(with respect to the other variables) will the firm want to
shut down?
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 Winter '07
 RAUCH
 Microeconomics, Supply And Demand, Spring Quarter, Econ 100B

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