This preview shows pages 1–2. Sign up to view the full content.
Chapter 10
1.
Suppose a firm has a cost curve
=
+
C 50 Q2
. Demand is given by
=

Qd 50 P
. Find the equilibrium
*
P
and
*
Q
for the monopolist.
Graph the optimum along with the demand curve, MR and AC. Find
the area that represents the profit for the monopolist.
*
Dr. S mentioned that he wouldn’t test us on profit maximizing for a
monopoly; however, here is the answer.
The monopolist will maximize profit by setting MC=MR.
•
We are given the cost equation, which we may use to find MC.
o
=
+
→
=
C 50 Q2
MC 2Q
o
•
We are given the equation for demand, which we may use to find MR.
Recall that the MR curve has twice the slope of the demand curve.
o
:
=

The inverse form of the demand curve is
P 50 Qd
o
The MR curve has twice the slope:
=

MR 50 2Qd
o
•
We may now set MC equal to MR and find Q
o
=

→
*=
.
2Q 50 2Q
Q
12 5
o
•
We may now find P* by substituting Q* into the demand equation
o
. =

→
*=
.
12 5 50 P
P
37 5
o
•
The optimum therefore lies where
Q=12.5 and P=37.5
o
o
Figure 10.2 on page 10.3 represents a similar problem.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 BARTZMAVEZ

Click to edit the document details