Question

Explain why it is true that at every level of output except the first unit, a monopolist firms marginal revenue (MR) is below the selling price?

Answer 1

The Marginal revenue is the additional revenue from the sale of one additional unit of output. Since the monopolist firm faces a downward-sloping demand curve, the price must decrease to sell one additional unit of output. Thus, P(Q) < P(Q-1)

Now, MR(Q) = [P(Q)×Q]−[P(Q−1)×(Q−1)] < [P(Q)×Q]− [P(Q)×(Q−1)] = P(Q)

Thus, we prove that MR is below the price curve except at the first unit where the marginal revenue is indeed just the price as MR(1) = P1*Q1 - P0*Q0 = P1*1 = P1