1.
(a)
ATC
(
q
) =
F=q
+
c
.
So
ATC
is decreasing for all
q >
0
:
Thus, the average cost is not minimized
for any °nite value of
q
.
(b) First, °nd
q
that equates
MR
and
MC
:
MR
(
q
)
=
dTR
(
q
)
dq
=
°
2
q
+ 100
MC
(
q
)
=
dTC
(
q
)
dq
= 10
Thus
q
°
= 45
and
p
°
= 55
. The consumer surplus is
(100
°
55)
±
45
±
1
2
= 1012
:
5
:
The total surplus
in this case is
CS
+
PS
= 1012
:
5 + (
p
m
°
MC
(
q
m
))
±
q
m
= 3037
:
5
:
The total surplus in the case
of perfect competition is
(100
°
10)
±
90
±
1
2
= 4050
:
Thus, the di/erence is
1012
:
5
, which equals
to the dead-weight loss.
(c)
AC
(
q
) = 10 + 800
=q:
Now we are considering a monopolist, so
q
=
Q:
Using the demand function,
p
= 100
°
q
=
AC
(
q
)
:
Thus, we have
q
= 80
(mathematically
q
= 10
is also a solution to this
equation, but let±s focus on the larger
q
as we discussed in class). The total surplus is
CS
+
PS
=
80
±
80
±
1
2
+0 = 3200
:
The total surplus in the case of perfect competition is
90
±
90
±
1
2
°
800 = 3250
:
The dead-weight loss is
50
.
(d) The marginal revenue for each market is
MR
1
(
q
1
) = 50
°
q
1
and
MR
2
(
q
2
) = 100
°
4
q
2
;
respectively.

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- Spring '08
- Staff
- Supply And Demand, nd Q