Question

In a Cournot market with two firms, the inverse market demand curve is P = 20 – 0.5Q, where Q = q1 + q2. (Firm 1's output = q1; Firm 2's output = q2.) If Firm 2 produces 20 units of output, Firm 1's residual marginal revenue curve is depicted in:

Answer 1

MR = 10 – 1q1.

Step-by-step explanation:

Demand function, P = 20 – 0.5Q

Q = q1 + q2

Now insert Q in the P = 20 – 0.5Q.

P = 20 – 0.5 (q1 + q2)

We have the value of q2 = 20.

P = 20 – 0.5 (q1 + q2)

P = 20 – 0.5 (q1 + 20)

P = 20 – 0.5q1 – 10

P = 10 – 0.5q1

Total revenue of firm 1, TR = Pq1

TR = 10q1 – (0.5q1)^2

Now MR is the differentiation of TR. So the MR after differentiation if TR of firm 1 is:

MR = 10 – 1q1