Business Economics · Theory of Demand and Supply

Total Revenue, Marginal Revenue and Elasticity

Q: What is the relationship between elasticity and total revenue?

If demand is elastic, TR moves in the opposite direction to price. If demand is inelastic, TR moves in the same direction as price. If demand is unit elastic, TR stays the same when price changes.

Q: How do I find marginal revenue from a demand function?

Write price in terms of quantity, multiply by Q to get TR, then differentiate TR with respect to Q. For P = a − bQ, this gives MR = a − 2bQ.

Q: Why is MR zero when elasticity is one?

At e = 1 the gain from selling an extra unit exactly offsets the loss from the lower price on other units. TR does not change, so MR = 0. This is also where TR is at its maximum.

Q: Can MR be negative?

Yes. MR is negative when demand is inelastic (e < 1), because TR falls as output rises. A firm facing a downward-sloping demand curve will not choose to operate there.

Updated 1 October 2026 · Fact-checked

Total revenue (TR) is price × quantity. Marginal revenue (MR) is the change in TR from selling one more unit. Elasticity tells you how TR moves when price changes: if demand is elastic, TR moves opposite to price; if inelastic, TR moves with price. MR = P(1 − 1/e) links all three.

Understand Total Revenue, Marginal Revenue and Elasticity

Total revenue (TR) is what a firm earns from sales: TR = P × Q. Average revenue (AR) is TR ÷ Q, which equals price. So the AR curve is the demand curve.

Marginal revenue (MR) is the extra revenue from selling one more unit: MR = ΔTR ÷ ΔQ. When a firm must cut price to sell more, it gains on the extra unit but loses on all earlier units, which now sell cheaper. So MR is below price.

Elasticity decides which effect wins. If demand is elastic (e > 1), a price cut raises quantity by a larger percentage, so TR rises. If demand is inelastic (e < 1), quantity rises by a smaller percentage, so TR falls. If demand is unit elastic (e = 1), TR does not change.

This gives the sign of MR. When e > 1, MR is positive and TR is rising. When e = 1, MR = 0 and TR is at its maximum. When e < 1, MR is negative and TR is falling. A firm facing a downward-sloping demand curve will not operate where demand is inelastic, because it could raise TR by cutting output and raising price.

For a straight-line demand curve, elasticity falls as you move down the curve. It is above 1 on the upper half, equal to 1 at the midpoint, and below 1 on the lower half. The MR curve cuts the quantity axis at the midpoint's quantity.

Key formulas to remember

Total revenue: TR = P × Q; AR = TR ÷ Q = P.
Marginal revenue: MR = ΔTR ÷ ΔQ = TRn − TRn−1; With a demand function, MR = d(TR)/dQ.
AR, MR and elasticity: MR = AR × (1 − 1/e) = AR × (e − 1) ÷ e; Use e as a positive number (absolute value). Valid for a downward-sloping demand curve.
Elasticity from AR and MR: e = AR ÷ (AR − MR); Rearranged form of the formula above.
Total revenue test: Price falls and TR rises → e > 1. Price falls and TR unchanged → e = 1. Price falls and TR falls → e < 1.; For a price rise, the signs reverse: TR falls means e > 1; TR rises means e < 1.
MR for linear demand: If P = a − bQ, then TR = aQ − bQ² and MR = a − 2bQ; MR has the same intercept and twice the slope of the demand curve.

How to solve Total Revenue, Marginal Revenue and Elasticity questions

Most questions give you either a price-and-TR change, a demand function, or two of AR, MR and e. Use this order.

1Identify what is given: price and quantity data, TR values, a demand function, or AR/MR/e.
2If a demand function is given, write P in terms of Q, then form TR = P × Q.
3Find MR: take the difference in TR for a table, or differentiate TR with respect to Q for a function.
4For a TR-based question, compare the direction of price and TR to decide whether demand is elastic, inelastic or unit elastic.
5For AR-MR-e questions, substitute into MR = AR(1 − 1/e) or e = AR ÷ (AR − MR). Keep e positive.
6Check your answer: MR must be below AR for a downward-sloping demand curve, and MR = 0 must match e = 1.
7Match the result to the options and pick the single value that fits.

Quickest way: Sign and substitute shortcut

When to use it: Use it for MCQs where you can reason from direction or plug into a single formula in under a minute.

For price-TR questions, only look at directions. Opposite directions mean elastic. Same direction means inelastic. No change means unit elastic.
For AR-MR-e problems, plug into e = AR ÷ (AR − MR) directly. Do not derive anything.
For linear demand P = a − bQ, write MR = a − 2bQ at once. Set it to 0 for TR maximum: Q = a ÷ 2b.
Eliminate options that make MR larger than AR, or that give a negative e.
If the question needs a long table of TR values and you are stuck, skip it and return later. Wrong answers cost 0.25 marks.

Common mistakes in Total Revenue, Marginal Revenue and Elasticity

Saying TR rises with a price cut for any demand.
Students assume more sales always means more revenue.
Fix: TR rises with a price cut only if e > 1. If e < 1, TR falls.
Using a negative value of e in MR = AR(1 − 1/e).
The slope of demand is negative, so e can appear as −2.
Fix: Use the absolute value. Write e = 2, not −2, before substituting.
Taking MR = P for a firm with a downward-sloping demand curve.
MR = AR is true only for perfect competition, where price is fixed.
Fix: For a firm that must cut price to sell more, MR < AR. Equality holds only when demand is perfectly elastic.
Doubling the intercept instead of the slope when finding MR for linear demand.
Students memorise 'MR is twice' without the detail.
Fix: For P = a − bQ, MR = a − 2bQ. The intercept stays the same and the slope doubles.
Computing MR as TR ÷ Q.
Confusion between average and marginal.
Fix: TR ÷ Q is AR. MR is the change in TR for one more unit.
Reversing the TR test for a price rise.
Students memorise the rule only for price cuts.
Fix: Look at direction. Opposite directions of P and TR mean elastic, whether price rises or falls.

Worked examples

Example 1

A firm raises the price of its product from ₹50 to ₹60 and its total revenue falls. Demand for the product is:
(a) Elastic
(b) Inelastic
(c) Unit elastic
(d) Perfectly inelastic

Show the solution

Price rises and TR falls, so they move in opposite directions.
Opposite movement means the quantity fall outweighed the price gain.
That happens only when the percentage fall in quantity is larger than the percentage rise in price, so e > 1.

Answer: (a) Elastic

Example 2

At a certain output, a monopolist's AR is ₹40 and the price elasticity of demand is 4. Marginal revenue is:
(a) ₹10
(b) ₹30
(c) ₹36
(d) ₹160

Show the solution

Use MR = AR × (1 − 1/e).
MR = 40 × (1 − 1/4) = 40 × 3/4.
MR = ₹30.
Check: MR is below AR, and e > 1 gives a positive MR.

Answer: (b) ₹30

Example 3

The demand function is P = 100 − 2Q. At what quantity is total revenue maximum, and what is TR there?
(a) Q = 25, TR = ₹1,250
(b) Q = 50, TR = ₹0
(c) Q = 25, TR = ₹2,500
(d) Q = 20, TR = ₹1,200

Show the solution

TR = P × Q = 100Q − 2Q².
MR = 100 − 4Q.
TR is maximum where MR = 0, so 100 − 4Q = 0 and Q = 25.
P = 100 − 2 × 25 = ₹50.
TR = 50 × 25 = ₹1,250.
Check: at this point e = 1, since MR = 0.

Answer: (a) Q = 25, TR = ₹1,250

Exam tips

Questions often give two lines of data (price change, TR change) and ask only about elasticity. Use direction, not calculation.
Memorise MR = AR(1 − 1/e) and the rearranged e = AR ÷ (AR − MR). Most numeric questions are one substitution.
Remember the three markers on a straight-line demand curve: e > 1 above the midpoint, e = 1 at the midpoint, e < 1 below it. TR peaks at the midpoint where MR = 0.
Watch for 'perfectly competitive firm' in the question. There, MR = AR = P and demand is perfectly elastic.
If a calculation looks long, skip it first and return later. Negative marking is 0.25 per wrong answer.

Practice questions from Theory of Demand and Supply