Answer to Question #106168 in Economics for Elaine

Question

Exercise 1 A monopolist produces output with a constant marginal cost MC = 2. Suppose there is one group of consumers with the demand function
P1 = 16 − Q1, and another group with the demand function
P2 = 10 − 12Q2.
(a) Calculate the equilibrium prices and quantities under third degree price
discrimination. (b) Calculate the equilibrium price and quantity when price discrimination is
not allowed (uniform pricing policy). (c) Explain whether in this case the government should tolerate price
discrimination.
Suppose now the monopolist cannot discriminate between the two types of consumers and decides to apply a fixed tariff T and to charge a price p per unit sold. Both types of consumers will pay the same membership fee and the same price per unit.
(d) What would be the highest tariff the monopolist can charge if the
government capped the price so that the efficient quantity is sold?

Answer 1

(a) P1 = 16 − Q1, so MR1 = TR1' = 16 - 2Q1,

P2 = 10 − 12Q2, so MR2 = 10 - 24Q2.

The equilibrium prices quantities under third degree price discrimination are:

MR1 = MC and MR2 = MC, so:

$16 - 2Q1 = 2,$

Q1 = 7 units,

$P1 = 16 - 7 = 9,$

$10 - 24Q2 = 2,$

Q2 = 1/3 unit, 

$P2 = 10 - 12×1/3 = 6.$

(b) If price discrimination is

not allowed (uniform pricing policy), the monopolist will set average price and quantity according to total demand and marginal revenue, so the second group will be worse off.

(c) In this case the government should tolerate price

discrimination.

(d) If the monopolist cannot discriminate between the two types of consumers and decides to apply a fixed tariff T and to charge a price p per unit sold, then the highest tariff the monopolist can charge is T = MC = 2.