A monopolist faces the demand of Q = 40p per customer and has a constant margina
ID: 1123914 • Letter: A
Question
A monopolist faces the demand of Q = 40p per customer and has a constant marginal cost of 10.
(a) What uniform price should the monopolist charge to maximize prots?
(b) If the rm can set a high price for the rst few units, and then a lower price afterwards, what
will these two prices be?
(c) What is the change in consumer surplus and deadweight loss from quantity discrimination?
(d) If the rm set instead a two-part tari, with a lump-sum entrance fee and then a price per unit,
what would these be?
(e) If there was also a second type of customer with the demand Q = 50 p, what should the entrance fee and the price per unit be?
Explanation / Answer
P = 500 – Q
TR = PQ = 500Q – Q^2
MR = Derivative of TR = 500 – 2Q
MC = 40
The equilibrium condition is MR = MC
500 – 2Q = 40
2Q = 460
Q = 230
Answer: Quantity = 230 units.
2.
Q = 230 should be placed to P = 500 – Q to get the price.
P = 500 – Q = 500 – 230 = $270 (Answer)
3.
Regarding the consumer surplus:
AR = TR/Q = 500 – Q
AR
500
270
Q
0
230
Consumer surplus = ½ × Base × Height
= ½ × 230 × (500 – 270)
= ½ × 230 × 230
= $26,450 (Answer)
4.
Regarding the producer surplus:
MC = 40
MC
40
40
Q
0
230
Consumer surplus = ½ × Base × Height
= ½ × 230 × (40 – 40)
= ½ × 230 × 0
= $0 (Answer)