1
COMM/FRE 295
Monopoly/Price discrimination
Solutions to Practice Questions
Question #1
ACME Widgets is a monopoly producer of widgets in the world. ACME faces 100
consumers, each
with a demand curve of Q = 0.7- 0.02P and C(Q)=10+5Q.
A.
Find the optimal P and Q for ACME when it cannot price discriminate. Also find
monopolist’s profits.
Demand function:
Q = 70 – 2P or P = 35 – ½Q
MR = 35 – Q
MC = 5
For profit maximization:
MR = MC
→
Q = 30
P = $20
Profits = R – C
= PQ – (10 + 5Q) = 20*30 – (10+5*30)
= ?
B.
Find DWL (social cost). Please use a diagram in your answer.
Optimum solution is at P* = MC = 5;
Q* = 70 – 2(5) = 60
DWL =
(1/2)(20 – 5)(60 – 30) =
$225
C. If ACME could perfectly price discriminate, what would be ACME’s Q?
The optimal Q for a perfectly price discriminating monopolist = competitive Q = 60.
D. Based only on the cost structure of ACME, is it conceivable that ACME is a natural
monopoly?
Yes ACME is a natural monopoly:
Since AC= 5 + 10/Q, the AC is falling for all Q.
E. What are two-part tariff P and Q?
Usage fee P* = MC = 5.
Entrance fee, T* = CS per consumer = 0.5 (35 – 5)(0.6) = 9.

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