Question

The demand and marginal cost equations below represent those faced by a monopolist in the market for lunar exploratory vehicles. ​D: Qd​ = ​(minus​1/2) P​ + 10,000 ​MC: MC​ = 2Q​ + 50 What equation best represents the​ firm's marginal​ revenue?

Answer 1

MR = –P + 10,000

Step-by-step explanation:

Qd = (–1/2)P + 10,000 ................................................................ (1)

Total Revenue = TR = P.Qd = P[(–1/2)P + 10,000]

TR = P[(-1/2)P + 10,000)] = (–1/2)P^2 + 10,000P .................. (2)

To obtain MR, equation 2 is differentiated with respect P as follows:

MR = TR' = –P + 10,000

Therefore, the best equation to represent the​ firm's marginal​ revenue (MR) is MR = –P + 10,000.