Marginal Revenue Calculator
Marginal revenue between two price points, the elasticity behind it, and whether the extra volume from a price cut is worth having once cost is counted.
Before
price $49.00
quantity 1,200
revenue $58,800.00
After
price $39.00
quantity 1,560
revenue $60,840.00
Change in revenue $2,040.00
Change in quantity 360
Marginal revenue a unit $5.67
average revenue a unit $39.00 after, $49.00 before
Price elasticity 1.148
which means demand is elastic: volume responds more than proportionally to price
so a price cut raises revenue
With a unit cost of $18.00
marginal cost a unit $18.00
marginal profit a unit -$12.33
gross profit before $37,200.00
gross profit after $32,760.00
change -$4,440.00 ← worse off
verdict each extra unit adds less revenue than it costs, so the extra volume destroys profit
What happened to the business
units 30% more
revenue 3.5%
summary more units and more revenue
Marginal revenue is $5.67 a unit: the $2,040.00 change in revenue
divided by the 360 extra units. It is positive, so the extra units did
add revenue.
The elasticity is 1.148, calculated by the midpoint method so a rise and
the matching cut give the same answer. Above one, so volume responds
more than proportionally and a price cut raises revenue.
Marginal revenue below the average selling price is normal whenever a
price cut applies to everybody. The discount is given to the customers
who would have paid full price as well as to the new ones, and that is
what pulls the marginal figure down.
Revenue is not the objective. The textbook rule is to keep producing
while marginal revenue exceeds marginal cost, and that point is usually
well below the volume that maximises revenue. Maximising revenue at zero
marginal profit is a busy way to earn nothing.
Two data points do not give you a demand curve. Elasticity measured
between one price and another describes that segment only, and it is not
constant: it changes at different price levels, over time, and with what
competitors did in the same week.
Something else probably changed too. A price cut that coincided with a
season, a campaign or a competitor going out of stock is not a
controlled experiment, and the elasticity you calculate absorbs all of
it. Price tests need randomised groups for the same reason A/B tests do.
Cutting price is hard to reverse. Customers anchor on the lower figure,
discount-seekers arrive, and putting the price back costs goodwill and
volume. The arithmetic above is symmetrical and the market is not.
A discount is cheaper than a price cut when you can target it. A voucher
for the price-sensitive segment preserves the full price for everyone
else, which is the whole point of segmentation and is invisible in a
single elasticity figure.
Output is valid and updates as you type.
Fix the highlighted fields to update the output.
A price cut from $49 to $39 moved 30 percent more units and raised revenue 3.5 percent. It also destroyed $4,440 of gross profit.
That is what marginal revenue is for. It is the change in total revenue divided by the change in quantity, and here it is $5.67 a unit against a $39 selling price and an $18 unit cost. Every extra unit sold added $5.67 of revenue and cost $18 to make, so the extra volume was worse than not selling it.
The reason marginal revenue sits so far below the price is that the discount went to everybody. The customers who would have paid $49 got $10 off, and that loss is set against the margin on the new units.
How to use
- Put in the price and units before, and after.
- Add the unit cost, which is what turns a revenue answer into a profit answer.
- Read the elasticity, and treat it as a description of that price range rather than a law.
Example
Change in revenue $2,040.00
Change in quantity 360
Marginal revenue a unit $5.67
average revenue a unit $39.00 after, $49.00 before
Price elasticity 1.148
which means demand is elastic: volume responds more than proportionally to price
so a price cut raises revenue
With a unit cost of $18.00
marginal profit a unit -$12.33
gross profit before $37,200.00
gross profit after $32,760.00
change -$4,440.00 ← worse off
verdict each extra unit adds less revenue than it costs
What happened to the business
units 30% more
revenue 3.5%
summary more units and more revenueRevenue up, profit down, 30 percent more orders to pack. That combination is common and it is invisible if you only look at the top line.
Pitfalls
Elastic demand raises revenue and can still cut profit. Elasticity above one means a price cut increases revenue. Whether it increases profit depends on the unit cost, and the crossing point is often between the two.
Marginal revenue below the selling price is normal. Whenever the discount applies to all customers, the money given up on the ones who would have paid more comes out of the marginal figure. That is the arithmetic of an untargeted price cut.
Two data points are not a demand curve. Elasticity measured between two prices describes that segment only. It changes at different price levels, over time, and with whatever competitors did in the same week.
Something else probably changed. A price cut that coincided with a season, a campaign or a competitor going out of stock is not a controlled experiment, and the elasticity absorbs all of it. Price tests need randomised groups for the same reason A/B tests do.
Revenue is not the objective. The textbook rule is to keep producing while marginal revenue exceeds marginal cost, and that point is well below the volume that maximises revenue. Maximising revenue at zero marginal profit is a busy way to earn nothing.
A price cut is hard to reverse. Customers anchor on the lower figure, discount-seekers arrive, and putting the price back costs goodwill and volume. The arithmetic is symmetrical; the market is not.
A targeted discount beats a price cut when you can target it. A voucher for the price-sensitive segment keeps the full price for everyone else. That is what segmentation is for, and a single elasticity figure cannot see it.
Compatibility
Arithmetic in the browser: nothing is uploaded and nothing is stored.
Elasticity uses the midpoint, or arc, formula, so a price rise and the matching cut give the same figure. The simple percentage-change version gives different answers depending on which point you start from, which makes it useless for comparing a rise against a cut, and the test suite checks that this one is symmetric.
Marginal revenue is the change in total revenue over the change in quantity between the two points given, which is the discrete version of the derivative. It is the right calculation for a step change in price and not for a continuous demand curve.
The profit comparison uses a constant unit cost, so it holds where marginal cost is roughly flat. If volume changes your unit cost, through freight, overtime or a volume discount from a supplier, do the profit arithmetic at both quantities rather than trusting a single cost.
Frequently asked questions
What is the marginal revenue formula?
MR = a − 2bQ where price is a − bQ, which is why marginal revenue falls twice as fast as price.