The firm’s marginal revenue, the change in total revenue associated with the sale of one more unit, is the slope of the total revenue function: MR = dR(Q)/dQ = R’(Q). Using the product rule for differentiation, R’(Q) = Qf ’(Q) + f(Q). Average revenue is simply total revenue divided by output: AR = Qf(Q)/Q = f(Q) = P.

Suppose markets are competitive. From the firm’s perspective, then, price is constant over all reasonable ranges of output so that f ’(Q) = 0. In that special case, MR = f(Q) = P. That is, the firm’s marginal revenue and average revenue are both equal to the product price.