Question

Q1. A monopolist has the following demand function and marginal cost function P = 120 – Q and MC = 30 + Q.

i. Derive the monopolist’s marginal revenue function. ii. Calculate the output the monopolist should produce to maximize its profit.

ii. (continuation) iii. What price does the monopolist charge to maximize its profit?

Now assume that the monopolist above split into two large firms (Firm A and Firm B) with the same marginal cost as the monopolist.

Let q_A = Firm A output

       q_B = Firm B output

where Q = q_A + q_B

MC = 30 + Q

Each firm’s response to the other firm’s output is as follows:

Firm A: q_A =30 – 2/3 q_B

Firm B: q_B = 30 – 2/3q_A

iv. Calculate each firm’s output (i.e. qA and qB)

v. Calculate the market price

vi. How do the monopoly price and quantity compare with those of the oligopoly?

Answer 1

Q1)

a) Total revenue = Price x Quantity

= (120 - Q) x Q

= 120Q - Q²

Marginal revenue can be found out by differentiating the total revenue function with respect to Q.

So, marginal revenue = 120 - 2Q is the answer.

b) The firm will maximize the profit at the output level where marginal revenue is equal to marginal cost. So, setting them equal,

Marginal revenue = Marginal cost

120 - 2Q = 30 + Q

2Q + Q = 120 - 30

3Q = 90

Q = 30 is the answer.

c) Price = 120 - Q = 120 - 30 = 90 is the answer.