Marginal Revenue Calculator
Enter two revenue-and-quantity snapshots, plug in direct change values, or supply a linear demand curve to find marginal revenue per unit. The calculator also shows how your MR compares to a marginal cost you specify, so you can read off whether to expand or cut output. Results update as you type.
Formula
Worked example
A firm lowers price from $50 to $48, causing quantity sold to rise from 1,000 to 1,200 units. TR before = $50 x 1,000 = $50,000. TR after = $48 x 1,200 = $57,600. Delta TR = $7,600, delta Q = 200. MR = $7,600 / 200 = $38 per unit. If marginal cost is $30, MR ($38) > MC ($30), so the firm should continue expanding output.
What is marginal revenue?
Marginal revenue (MR) is the additional income a firm earns from selling exactly one more unit of a good or service. It is the slope of the total revenue curve at any given output level. In practice it is usually measured as the average over a small interval: the change in total revenue divided by the change in quantity sold. For a perfectly competitive firm, where a single seller cannot affect price, marginal revenue equals the market price. For any downward-sloping demand curve, such as a monopoly or monopolistically competitive firm, marginal revenue is less than price because selling more requires lowering the price on all units, not just the additional one.
How to use this calculator
Select a mode. Before/After asks for the price and quantity at two points in time; the calculator computes both total revenues and divides the difference to give MR. Change Values is a shortcut if you already know delta TR and delta Q. Demand Curve is the most powerful option: enter the intercept (a) and slope (b) of a linear inverse demand function P = a - bQ, plus the quantity you want to evaluate; the calculator derives MR = a - 2bQ, shows price and total revenue at that quantity, plots the full demand and MR curves, and marks where MR = 0 (total revenue is maximized). In all modes, enter a marginal cost to get an instant MR vs MC profit decision.
MR vs MC and the profit-maximizing rule
The most important use of marginal revenue is comparing it to marginal cost (MC). Economists show that profit is maximized at the output where MR = MC. If MR > MC, producing one more unit adds more to revenue than to cost, so profit rises and you should expand. If MR < MC, the extra unit costs more to produce than it earns, so profit falls and you should cut back. This rule applies to every market structure, from perfect competition through to monopoly, because it is simply the condition that the next unit neither adds to nor subtracts from profit.
Marginal revenue on a linear demand curve
For a linear inverse demand curve P = a - bQ, total revenue is TR = PQ = aQ - bQ squared. Differentiating with respect to Q gives MR = a - 2bQ. Notice that MR has the same intercept as the demand curve but exactly twice the slope, so it always crosses the quantity axis at half the quantity where demand reaches zero. MR equals zero at Q = a / (2b), which is the revenue-maximizing output. Any further production makes total revenue fall, which is why no rational monopolist produces in the inelastic region of demand.
MR and market structure
| Market structure | Price control | Marginal revenue vs. price | MR curve shape |
|---|---|---|---|
| Perfect competition | None (price taker) | MR = P | Flat (horizontal) |
| Monopolistic competition | Some | MR < P | Downward sloping |
| Oligopoly | Significant (kinked demand) | MR < P | Kinked / discontinuous |
| Monopoly | Full (price setter) | MR < P (MR = a - 2bQ) | Steeply downward sloping |
How marginal revenue behaves depends on whether a firm is a price taker or a price setter.
Frequently asked questions
What is the marginal revenue formula?
The general formula is MR = change in total revenue / change in quantity = (TR2 - TR1) / (Q2 - Q1). For a firm facing a linear demand curve P = a - bQ, the exact (point) MR at any quantity is MR = a - 2bQ. In perfect competition the price is fixed, so MR = P.
Why is marginal revenue less than price for a monopoly?
A monopolist must lower its price to sell an extra unit, and that lower price applies to all units already being sold, not just the new one. The lost revenue on existing units offsets part of the gain from selling one more, so the marginal revenue of the additional unit is less than the price it fetches. In a perfectly competitive market, a firm can sell as many units as it likes at the going price without affecting that price, so MR = P.
Where does MR = MC and why does that maximize profit?
Profit equals total revenue minus total cost. Each additional unit changes profit by MR - MC. When MR > MC, the unit adds to profit, so producing it is worthwhile. When MR < MC, the unit subtracts from profit, so it should not be produced. Profit is therefore at its highest at the output where MR = MC and there is no further gain from either expanding or contracting.
Can marginal revenue be negative?
Yes. When demand is price-inelastic, a price cut raises quantity but the volume gain does not compensate for the lower price on every unit. Total revenue falls, meaning the change in total revenue is negative even though the change in quantity is positive, so MR is negative. A profit-maximizing firm will never voluntarily operate in the inelastic region of its demand curve.
How does marginal revenue relate to price elasticity of demand?
There is a direct link: MR = P x (1 + 1/E), where E is the own-price elasticity of demand (a negative number). When demand is perfectly elastic (E = negative infinity), MR = P. When demand is unit elastic (E = -1), MR = 0. When demand is inelastic (E between -1 and 0), MR is negative. This relationship shows that a firm raises revenue by cutting price only when demand is elastic, and raises revenue by raising price only when demand is inelastic.
What is the difference between marginal revenue and average revenue?
Average revenue (AR) is simply total revenue divided by quantity: AR = TR / Q = P (for a single-price seller). Marginal revenue is the change in TR from the last unit. In perfect competition AR = MR = P because every unit sells at the same price. In imperfect competition AR = P > MR because the price must fall to sell more, dragging the marginal gain below the average.