Marginal Revenue and Elasticity
What is Marginal Revenue and Elasticity?
Marginal revenue is positive when demand is elastic, zero at unit elasticity, and negative when demand is inelastic, so a price-maker never sells in the inelastic range.
Cutting price raises quantity but lowers revenue on existing units; which effect wins depends on elasticity. Where demand is elastic, the quantity gain dominates, so MR is positive and total revenue rises as price falls. At unit elasticity, MR equals zero and total revenue peaks. Where demand is inelastic, MR is negative. Because a monopolist would never operate where extra output reduces revenue, it always produces on the elastic portion of its demand curve.
Marginal Revenue and Elasticity: a worked example
A monopolist charges $60 and measures price elasticity of demand at that point as 3. Apply MR = P(1 - 1/|E_d|): MR = 60 × (1 - 1/3) = 60 × 2/3 = $40. The next unit still adds $40 of revenue, so a small price cut raises total revenue. Slide down the same demand curve to $40, where elasticity has fallen to 1: MR = 40 × (1 - 1) = $0, and total revenue is at its peak. Keep going to $16, where elasticity is 0.25: MR = 16 × (1 - 1/0.25) = 16 × (1 - 4) = negative $48. Selling one more unit there wipes out $48 of revenue. Marginal cost cannot be negative, so MR = MC can never hold at $16, and the profit-maximizing price cannot sit below $40. It sits strictly above $40 whenever marginal cost is positive.
The mistake students make with marginal revenue and elasticity
The formula punishes sign errors. Feeding in E_d = negative 3 rather than 3 gives MR = P(1 + 1/3) = 1.33P, marginal revenue above price, which cannot happen when a firm must drop its price on every unit to sell one more. Take the absolute value before dividing. The second trap is arguing that a monopolist charges a high price because demand is inelastic. Inelastic demand is exactly the range where marginal revenue is negative, so trimming output there would raise revenue and cut cost at the same time. A price setter never settles in the inelastic range.
Marginal Revenue and Elasticity questions
Why is marginal revenue negative when demand is inelastic?
Marginal revenue turns negative because the revenue given up on units the firm was already selling outweighs the revenue collected from the new buyers. Inelastic demand means quantity barely responds to price, so a five percent price cut might lift quantity only two percent. That small quantity gain cannot pay for the discount handed to every existing customer, so total revenue falls. Marginal revenue is just the change in total revenue per extra unit, and a falling total revenue makes it negative.
How do you find elasticity when you know price and marginal revenue?
Rearrange MR = P(1 - 1/|E_d|) and solve for elasticity. Suppose price is $30 and marginal revenue is $10. Then 10 = 30(1 - 1/|E_d|), so 1 - 1/|E_d| = 1/3, which makes 1/|E_d| = 2/3 and |E_d| = 1.5. Demand is elastic at that point, which fits the positive marginal revenue. The check runs both directions on an exam: any point with positive marginal revenue must have elasticity above one, and a marginal revenue of zero pins elasticity at exactly one.
Is marginal revenue always below price?
Marginal revenue sits below price for any firm facing a downward-sloping demand curve, because selling an extra unit means charging less on every unit, not only on the new one. The perfectly competitive firm is the exception. Demand facing it is perfectly elastic, so it sells any quantity at the going price, and as elasticity becomes infinite the term 1/|E_d| goes to zero and MR = P(1 - 1/|E_d|) collapses to MR = P.
Formula / Example
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