Question

Suppose there are two types of consumers: Type A and Type B. The demands for a monopolist’s product for each type of consumers are given by:

Type A: Q = 90 – 2P

Type B: Q = 60 – 4P

Assume the marginal cost of production is constant and MC = 4, and there are no fixed costs.

a)Suppose the firm is unable to distinguish between the two types of consumers, and therefore cannot engage in price discrimination. Sketch the demand curve facing the firm. Make sure your graph is accurate and carefully labeled.

b) What price will the monopolist charge?

c) How much profit will the monopolist make?

d) If the monopolist is able to charge different prices to each type of consumer, what price will she charge to type A consumers?

e) What is the Price Elasticity of Demand for Type A consumers?

f) If the monopolist is able to charge different prices to each type of consumer, what price will she charge to type B consumers?

g) What is the Price Elasticity of Demand for Type B consumers?

Answer 1

(a)

For Type A consumers, demand function:

QA = 90 - 2P

For Type B consumers, demand function:

QB = 60 - 4P

When firm cannot price discriminate, Aggregated demand (Q) = QA + QB

Q = 90 - 2P + 60 - 4P

Q = 150 - 6P

When Q = 0, P = 150/6 = 25 (Vertical intercept) and when P = 0, Q = 150 (Horizontal intercept).

In following graph, price (P) and aggregated quantity (Q) are measured along vertical axis and horizontal axis respectively. D represents aggregated demand curve.

(b) Monopolist maximizes Profit by equating Marginal revenue (MR) with MC.

Q = 150 - 6P

6P = 150 - Q

P = (150 - Q) / 6

Total revenue (TR) = P x Q = (150Q - Q²) / 6

MR = dTR/dQ = (150 - 2Q) / 6

Equating MR and MC,

(150 - 2Q) / 6 = 4

150 - 2Q = 24

2Q = 126

Q = 63

P = (150 - 63) / 6 = 87 / 6 = 14.5

(c) Profit = Q x (P - MC) = 63 x (14.5 - 4) = 63 x 10.5 = 661.5

(d) When monopolist can price discriminate, profit is maximized when MRA = MC and MR2 = MC.

For Type A consumers,

QA = 90 - 2PA

2PA = 90 - QA

PA = 45 - 0.5QA

TRA = PA x QA = 45QA - 0.5QA²

MRA = dTRA/dQA = 45 - QA

Equating MRA with MC,

45 - QA = 4

QA = 41

PA = 45 - (0.5 x 41) = 45 - 20.5 = 24.5

(e) Price Elasticity of demand = (dQA/dPA) x (PA/QA) = - 2 x (24.5 / 41) = - 1.20

(f) For Type 2 consumers,

QB = 60 - 4PB

4PB = 60 - QB

PB = 15 - 0.25QB

TRB = PB x QB = 15QB - 0.25QB²

MRB = dTRB/dQB = 15 - 0.5QB

Equating with MC,

15 - 0.5QB = 4

0.5QB = 11

QB = 22

PB = 15 - (0.25 x 22) = 15 - 5.5 = 9.5

(g) Price Elasticity of demand = (dQB/dPB) x (PB/QB) = - 4 x (9.5 / 22) = - 1.73