Marginal Revenue Calculator: From Revenue, Prices or a Demand Curve
Calculate marginal revenue (ΔTR ÷ ΔQ) from two revenue or price points or a linear demand curve, with elasticity, the revenue-maximizing and MR = MC output.
How it works
Marginal revenue (MR) = ΔTR ÷ ΔQ = (TR₂ − TR₁) ÷ (Q₂ − Q₁) · TR = P × Q · Linear demand P = a − bQ: MR = a − 2bQ · MR = P × (1 + 1/E) · Revenue peaks where MR = 0 (Q = a ÷ 2b) · Profit peaks where MR = MC
Marginal revenue is the extra revenue from selling one more unit. Over a range it is the change in total revenue divided by the change in quantity. If you sell at a fixed market price, every extra unit adds that price, so MR equals price. Most businesses, though, must lower the price to sell more, and the lower price applies to all units, so marginal revenue is below the price and can even turn negative. Choose Total revenue if you know revenue at two sales levels, Prices if you know what price sold each quantity, or Demand curve for the textbook straight-line demand P = a − bQ, where MR = a − 2bQ falls twice as fast as price. The calculator also gives the price elasticity between your two points (demand is elastic where MR is positive and inelastic where it is negative), the quantity that maximizes revenue, and, with a marginal cost under More options, the profit-maximizing output where MR = MC. The price elasticity calculator gives only the elasticity; this page turns the same data into the money value of the next sale. It assumes one price for all buyers in each period.
Worked example
A seller moves from 1,000 units and $40,000 of revenue to 1,250 units and $47,500 (the price fell from $40 to $38). ΔTR = $7,500 and ΔQ = 250, so marginal revenue = $7,500 ÷ 250 = $30.00 per unit, well below the $38 price. The midpoint price elasticity is −4.333, so demand is elastic. If the extra units cost $20 each to make, they add (30 − 20) × 250 = $2,500 of profit. Treating demand as a straight line through the two points gives a point MR of $28.00 at 1,250 units.
Sources: Omni Calculator: Marginal revenue (Magic 8 Ball example) · OpenStax Principles of Economics 3e, 9.2: monopoly marginal revenue and MR = MC (HealthPill tables) · Corporate Finance Institute: Marginal revenue
Frequently asked questions
How do you calculate marginal revenue?
Divide the change in total revenue by the change in quantity sold. If revenue rises from $50,000 to $62,000 when sales rise by 200 units, MR = $12,000 ÷ 200 = $60 per unit.
Why is marginal revenue less than price?
When a firm must cut its price to sell one more unit, it gets the new price on that unit but loses the price cut on every unit it was already selling. So the extra revenue is smaller than the price. Only a price-taker in perfect competition has MR equal to price.
What is the marginal revenue formula for a linear demand curve?
If demand is P = a − bQ, total revenue is aQ − bQ², and marginal revenue is MR = a − 2bQ. The MR line starts at the same price intercept but is twice as steep, so it hits zero at half the quantity where demand hits zero.
What does negative marginal revenue mean?
Selling more units lowers total revenue, because demand is inelastic in that range: the price cut needed costs more than the extra volume brings in. A firm should never choose to produce where marginal revenue is negative.
Why do firms produce where marginal revenue equals marginal cost?
As long as an extra unit brings in more revenue (MR) than it costs to make (MC), producing it adds profit. Once MR falls below MC, the extra unit loses money. Profit is highest at the output where the two are equal.
Related calculators
For study and planning. Real demand is rarely a straight line, and price changes can also affect competitors and customer loyalty.