Why Marginal Revenue Lies Below Demand

You’ll be able to

Explain why a price-searching firm faces marginal revenue below price
Compute marginal revenue from a demand schedule
Relate the marginal revenue curve to elasticity along demand

Selling one more unit costs you on all the others

A competitive firm can sell any quantity at the market price, so its marginal revenue equals price. A firm with market power faces a downward-sloping demand curve, so to sell one more unit it must lower the price on every unit. Marginal revenue is therefore the price of the new unit minus the revenue lost on all the previous ones — which makes MR less than price at every quantity above the first.

Marginal revenue for a linear demand curve

if P = a − bQ then MR = a − 2bQ

Same intercept, twice the slope. So MR hits zero at exactly half the quantity where demand hits zero — a useful graphing shortcut.

MR and elasticity

Where demand is elastic, lowering the price raises total revenue, so MR is positive. Where demand is inelastic, lowering price lowers revenue, so MR is negative. MR is exactly zero where demand is unit elastic, which is the revenue-maximizing quantity. A profit-maximizing firm therefore always operates on the elastic portion of its demand curve, because it stops where MR = MC and MC is positive.

Computing MR from a schedule

Multiply price by quantity to get total revenue at each row, then take the row-to-row difference. The result falls faster than price does, and it can go negative — a fact students distrust until they compute it. Negative MR means the firm sold an extra unit and ended up with less total revenue, because the price cut applied to everything.

Worked example

A monopolist faces this demand: at $10 it sells 1 unit, at $9 it sells 2, at $8 it sells 3, at $7 it sells 4. Compute total and marginal revenue and identify where MR turns negative.

1.Total revenue: 1 × 10 = 10; 2 × 9 = 18; 3 × 8 = 24; 4 × 7 = 28.
2.Marginal revenue: 10, then 18 − 10 = 8, then 24 − 18 = 6, then 28 − 24 = 4.
3.MR falls by $2 per unit while price falls by $1 — twice as fast, as the formula predicts.
4.Extending the pattern, MR reaches zero at 5.5 units and turns negative beyond that.

Answer: MR is 10, 8, 6, 4 — always below the corresponding price and falling twice as fast. It would turn negative past about 5.5 units, where the revenue lost on existing units exceeds the price of the new one.

Watch out

The monopolist charges the price read off the demand curve at its chosen quantity, not off the MR curve. Find quantity where MR = MC, then go up to demand for the price. Pricing at MR is the single most common monopoly-graph error.

Checkpoint

For a firm with market power, marginal revenue is below price because:

Checkpoint

Marginal revenue equals zero at the quantity where demand is:

Checkpoint

A monopolist finds MR = MC at 40 units. To set its price it should read:

On the exam

Draw MR with the same vertical intercept as demand and twice the slope, so it bisects the horizontal distance to the quantity axis. A visibly wrong MR curve makes every subsequent area on the graph wrong too.

Answer the 3 checkpoints as you read.