Marginal Revenue Calculator

One more sale is not one more price

You sell something for 98. How much does selling one more add to your revenue?

Ninety eight, obviously.

Except quite often it is not, and the gap is bigger than you would guess. In the example this page works through, that 98 sale adds 78 to the business.

Marginal revenue is the actual change in total revenue from selling one more unit. Sometimes it equals the price. Sometimes it is well below it. And sometimes it is negative, which means selling more leaves you with less money.

Four boxes, three results, and one genuinely useful idea underneath.

Four boxes

1. Initial revenue. Total revenue before.
2. Final revenue. Total revenue after.
3. Initial quantity. Units sold before.
4. Final quantity. Units sold after.

Note that these are totals at two points, not changes. The tool works out the changes for you, which is a better design than asking for deltas because it is what your sales records actually contain.

It will stop you if the two quantities are the same, since a change of zero would mean dividing by nothing.

The two revenue figures should be total revenue at each point, meaning quantity multiplied by price. Not the revenue from the extra units alone.

Three results from four numbers

Change in total revenue = final revenue - initial revenue

Change in quantity = final quantity - initial quantity

Marginal revenue = change in revenue ÷ change in quantity

The tool shows all three, and showing the two intermediate figures is more helpful than it first appears. If your marginal revenue looks wrong, one of those two lines will usually tell you which input was mistyped.

Watch the signs. Both changes can be negative, and the arithmetic handles it. If you cut output and revenue fell, both are negative and the marginal revenue comes out positive, which is correct: those units were bringing money in.

Selling the eleventh unit

A seller who has to reduce the price to shift more. Each extra unit sold means dropping the price by 2 across the board.

The eleventh unit sold for 98. Marginal revenue was 78.

The twelfth sold for 96. Marginal revenue was 74.

Every row, the marginal revenue is well below the price, and the gap widens as you go down.

So where does the difference go?

Where the missing twenty went

Take the eleventh unit and split it apart.

You gained 98 from the customer who bought the eleventh unit.

You lost 20 from the ten customers who were already buying, because to sell the eleventh you dropped the price by 2 and they all paid 2 less.

98 minus 20 is 78.

That is the whole explanation, and once you have seen it you cannot unsee it. Whenever you cut a price to win volume, you cut it for everyone, including all the customers who would have paid the old price without complaint.

Which is why the gap widens as you sell more. At 11 units you are giving up 2 on ten existing customers. At 15 units you are giving up 2 on fourteen of them. The more you have already sold, the more expensive each further price cut becomes.

And it is why marginal revenue falls twice as fast as price in a straight-line case like this one. The price drops by 2 per unit and the marginal revenue drops by 4.

There is a practical version of this that has nothing to do with economics theory. Before you run a discount to boost volume, work out what the discount costs you on the customers who were buying anyway. That figure is frequently larger than the profit on the new sales, and the markdown calculator quantifies the same trade from the pricing side.

The one case where it does equal the price

Everything above assumed you have to cut the price to sell more. Sometimes you do not.

A farmer selling wheat into a commodity market can sell as much as they like at the going rate. One more tonne does not move the world price, because the farm is far too small relative to the market.

For a seller like that:

Marginal revenue equals the price, exactly, at every quantity.

Economists call this a price taker, meaning a seller who takes the market price as given rather than setting it. And for a price taker, and only for a price taker, the intuition everybody starts with is correct.

So the useful question is which of the two you are.

If you could double your output tomorrow and sell it all at today's price, you are close to a price taker and marginal revenue is roughly your price. If pushing volume means running a promotion, cutting a deal, or dropping your list price, you are not, and your marginal revenue is meaningfully below what the invoice says.

Most small businesses are somewhere in between, and most of them assume they are the first kind.

When selling more brings in less

Keep going down that first table and something strange happens.

At 25 units the business takes 1,250. At 26 units it takes 1,248.

It sold one more and got less money.

That is not a mistake in the table. Past a certain point, the price cut needed to shift another unit costs more across the existing customers than the new sale brings in. Revenue peaks and then falls.

Which gives you a hard rule with no economics required. If marginal revenue is negative, selling more is making you poorer, and that is before you have paid a single cost of producing the extra units.

Anyone chasing a volume target without watching this can hit the target and reduce the revenue at the same time. It happens, and it usually gets discovered a quarter later.

The rule this number exists for

Marginal revenue on its own tells you what one more sale earns. Useful, and only half of a decision.

The other half is what one more sale costs, which is marginal cost.

Put them side by side and you get the answer to a question every business has: how much should we make?

Somewhere between 40 and 50 units, the two lines cross. Before it, every extra unit adds more than it costs. After it, every extra unit subtracts.

That crossing point is where profit is highest, and the rule that finds it is one line:

Produce while marginal revenue exceeds marginal cost. Stop where they meet.

Notice what it is not. It is not where revenue is highest, because revenue keeps rising for a while after profit has started falling. It is not where average cost is lowest either. It is where the two marginal figures meet, and that is a different place from both.

So this tool answers half the question and the marginal cost calculator answers the other half. Run both at a few output levels, put the two columns next to each other, and the crossing point is your answer.

This is a measurement of figures you supply rather than an assessment of a business, and nothing here is financial advice.

Questions people ask

How is marginal revenue calculated?

The change in total revenue divided by the change in quantity. Revenue rising from 1,000 to 1,078 while quantity rises from 10 to 11 gives a marginal revenue of 78.

Why is it lower than my selling price?

Because to sell the extra unit you cut the price for everyone. On the worked example, the eleventh unit sold for 98 but the 2 price cut cost 20 across the ten existing customers, leaving 78.

When does it equal the price?

When you can sell more without cutting the price, which describes a price taker in a competitive market. Then marginal revenue equals price at every quantity.

Can marginal revenue be negative?

Yes. Past a point, the price cut needed to sell one more costs more across existing customers than the new sale brings in, so total revenue falls even as volume rises.

Do I enter totals or changes?

Totals at two points. Enter revenue and quantity before and after, and the tool works out both changes for you.

Why does it fall twice as fast as the price?

In a straight-line demand case, each extra unit costs you the price cut on itself plus the same cut across everything already sold. That doubles the rate at which marginal revenue declines.

How do I use it to decide how much to sell?

Compare it against marginal cost. Keep producing while marginal revenue is higher, and stop where the two meet. That point maximises profit, and it is not the same as maximising revenue.

Should I discount to increase volume?

Work out what the discount costs across customers who would have paid full price. That figure is often larger than the profit on the additional sales, which is why volume-chasing promotions frequently reduce total profit.

References

Marginal revenue as the change in total revenue divided by the change in quantity, the result that marginal revenue lies below price for a seller facing a downward-sloping demand curve and equals price for a price taker, and the profit-maximising condition that output should expand while marginal revenue exceeds marginal cost, are standard results in microeconomic theory. The treatment of gross receipts, returns and allowances in arriving at revenue, and of gross profit as receipts less cost of goods sold, follows Internal Revenue Service small business guidance. The requirement that net sales be stated as gross sales less discounts, returns and allowances, which is the revenue basis used here, comes from Regulation S-X.

1. Internal Revenue Service, Publication 334: Tax Guide for Small Business. https://www.irs.gov/publications/p334
2. United States Securities and Exchange Commission, Regulation S-X, Rule 5-03: Statements of Comprehensive Income (17 CFR 210.5-03), under which net sales is stated as gross sales less discounts, returns and allowances. Text quoted in SEC staff correspondence at https://www.sec.gov/Archives/edgar/data/0001019361/000101936112000010/filename1.txt
3. US Chamber of Commerce, Pricing Markups Explained: Definition and Similar Terms. https://www.uschamber.com/co/start/strategy/what-are-pricing-markups
4. Corporate Finance Institute, Markup: How to Calculate Markup and Markup Percentage. https://corporatefinanceinstitute.com/resources/accounting/markup/