Marginal Revenue Calculator

Background.

Selling more of something rarely brings in as much extra money as the price tag suggests. If a business has to cut its price to move the extra units, the cut applies to everything it would have sold anyway, and that loss is netted against the new sales. Marginal revenue is the measure that captures this: the change in total revenue divided by the change in the number of units sold.

For a wheat farmer selling into a large market, marginal revenue and price are the same thing — one more tonne fetches the going rate. For almost any business with a brand, a location or a product nobody else sells quite the same way, the two part company. Marginal revenue falls below price, and the gap widens as the price cuts deepen. That gap is why the textbook rule for maximum profit is to expand output only while marginal revenue exceeds marginal cost, the cost of making one more, rather than while price does.

What you get here is the finite, two-observation version. Enter how much total revenue changed between two situations and how many more units were sold, and the result is the average extra revenue per extra unit across that step. It describes what happened between two data points; it does not forecast what the next price cut would do, and it assumes both revenue figures cover the same products, customers and length of period.

Both entries must be positive. When revenue and quantity fall together, enter the sizes of the two falls and the ratio comes out the same. When they move in opposite directions — more units sold but less revenue taken — marginal revenue is negative, which happens when demand is price-inelastic, and the page will not accept that case.

What is marginal revenue calculator?

Marginal revenue is the additional total revenue earned by selling one more unit of output. In calculus it is the derivative of total revenue with respect to quantity; with real sales data you only ever see two points, so it is estimated as ΔR ÷ ΔQ, the average change per unit between them. For a price-taking firm it equals the market price. For a firm facing a downward-sloping demand curve it is lower than price, and it turns negative once demand becomes price-inelastic.

How to use this calculator.

1. 01Pick two comparable observations — the month before and the month after a price change, say — covering the same product range and the same length of time.
2. 02Enter the change in total revenue: revenue in the second situation minus revenue in the first, net of discounts and returns if those changed too. Keep to one currency.
3. 03Enter the change in quantity: units sold in the second situation minus the first. If both changes are negative, enter them as positive numbers; the ratio is unaffected.
4. 04Set the result beside the cost of producing one more unit. If marginal revenue is below that marginal cost, the extra sales cost more than they earned.

The formula.

MR ≈ ΔR ÷ ΔQ, where ΔR is the change in total revenue and ΔQ the change in units sold between the same two observations; the answer is in currency per unit. It is an arc estimate: it averages marginal revenue over the whole step, so a big step can hide the fact that the first extra units added more than the last. Behind the ratio, ΔR splits into two pieces — the price earned on the new units, minus the price reduction given away on units that would have sold anyway. That is why marginal revenue links to price elasticity of demand ε through MR = P × (1 − 1/|ε|): it is positive when demand is elastic, zero at unit elasticity, where total revenue peaks, and negative below it. With a straight-line demand curve, marginal revenue falls twice as fast as price as quantity rises.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Principles of Economics 3e, section 8.2, How a Profit-Maximizing Monopoly Chooses Output and Price.
2. [2]OECD Glossary of Statistical Terms, marginal concepts.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.