Why a Monopolist Avoids the Inelastic Range

A straight-line demand curve has two halves. On the upper half, demand is elastic, a price cut raises total revenue because the gain in quantity sold outweighs the lower price on each unit. On the lower half, demand is inelastic, a price cut lowers total revenue because the price drop hurts more than the extra units sold help. Marginal revenue tracks this directly: it's positive on the elastic half, zero at the midpoint, and negative on the inelastic half. A monopolist choosing output to maximize profit sets marginal revenue equal to marginal cost. Since marginal cost is essentially never negative, the firm will never push output to a point where marginal revenue is negative either, so it always stops somewhere on the elastic stretch of demand.

The mechanism is just the total revenue and marginal revenue relationship. Marginal revenue is the slope of total revenue. When marginal revenue is positive, total revenue is still climbing, so producing more helps. When marginal revenue turns negative, total revenue is falling, so producing more actively hurts, on top of adding more cost. No profit-maximizing firm would ever choose that. For demand P = 60 - 3Q, marginal revenue is MR = 60 - 6Q, which is positive for Q between 0 and 10, zero at Q = 10, and negative beyond. Total revenue peaks exactly at Q = 10.

This sets up everything else in imperfect competition: since the monopolist stops on the elastic range, price sits above marginal cost, output is lower than the competitive level, and that gap is the source of the deadweight loss covered next.