Business Economics · Production, costs, revenue and profit in price and output decisions

Revenue Concepts: Total, Average and Marginal Revenue

Q: What is the difference between average revenue and marginal revenue?

Average revenue is total revenue per unit, which equals the price. Marginal revenue is the extra revenue from selling one more unit. They are equal only for a price taker. With downward-sloping demand, MR is less than AR.

Q: Why is the marginal revenue curve below the demand curve for a monopolist?

To sell one more unit, the monopolist must cut the price on all units. The extra unit adds its price to revenue, but the price cut reduces revenue on the earlier units. So MR is less than price.

Q: How do you derive the marginal revenue curve from a linear demand curve?

Write P = a − bQ, so TR = aQ − bQ². Differentiate with respect to Q to get MR = a − 2bQ. It starts at the same price intercept as demand but falls twice as fast.

Q: What is the formula linking marginal revenue and price elasticity of demand?

MR = P(1 + 1/E), where E is the price elasticity of demand, which is negative for a normal demand curve. Equivalently, MR = P(1 − 1/|E|). MR is positive when |E| > 1 and negative when |E| < 1.

Updated 11 October 2026 · Fact-checked

Total revenue (TR) is price times quantity. Average revenue (AR) is TR ÷ Q, which equals price. Marginal revenue (MR) is the change in TR from selling one more unit. Under perfect competition AR = MR = price. With downward-sloping demand, MR is below AR, and MR = P(1 + 1/E), where E is price elasticity of demand.

Understand Revenue Concepts: Total, Average and Marginal Revenue

Revenue is the money a firm receives from selling its output. You need three measures, and the exam asks how they relate to each other.

Total revenue (TR) is price times quantity sold: TR = P × Q. Average revenue (AR) is revenue per unit: AR = TR ÷ Q. Since TR = P × Q, AR is always equal to the price. So the AR curve is the firm's demand curve. Marginal revenue (MR) is the extra revenue from selling one more unit: MR = ΔTR ÷ ΔQ, or dTR/dQ for a continuous function.

Under perfect competition, the firm is a price taker. It can sell any quantity at the market price P. So AR = MR = P at every output, the demand curve is horizontal, and TR is a straight line through the origin with slope P.

Under downward-sloping demand (monopoly, and other firms with market power), to sell more the firm must cut the price. The lower price applies to all units, not just the extra one. So the firm gains revenue from the new unit but loses revenue on the units it could have sold at the higher price. Hence MR < AR = P at every positive output. For a straight-line demand curve P = a − bQ, we get TR = aQ − bQ², so MR = a − 2bQ. MR has the same intercept as demand and twice the slope. It cuts the quantity axis at half the quantity where demand does.

MR links to price elasticity of demand. Where demand is elastic (|E| > 1), MR is positive and TR rises as output rises. Where demand is unit elastic (|E| = 1), MR = 0 and TR is at its maximum. Where demand is inelastic (|E| < 1), MR is negative and TR falls as output rises. So a revenue-maximising firm with a linear demand curve sells where MR = 0. A profit-maximising firm with positive marginal cost operates on the elastic part of demand.

Key rules to remember

Total revenue: TR = P × Q; Price times quantity sold.
Average revenue: AR = TR ÷ Q = P; AR is the price, so the AR curve is the demand curve.
Marginal revenue (discrete): MR = ΔTR ÷ ΔQ; Use for tables. For a one-unit step, MR = TR(n) − TR(n−1).
Marginal revenue (continuous): MR = dTR/dQ; Differentiate TR as a function of Q.
Perfect competition: AR = MR = P; Horizontal demand curve for the individual firm.
Linear demand: P = a − bQ gives TR = aQ − bQ² and MR = a − 2bQ; MR has twice the slope of demand and the same price intercept.
MR and elasticity: MR = P(1 + 1/E) = P(1 − 1/|E|), where E is the (negative) price elasticity of demand; MR > 0 if |E| > 1, MR = 0 if |E| = 1, MR < 0 if |E| < 1.

How to solve Revenue Concepts: Total, Average and Marginal Revenue questions

Use this method for any question on revenue curves, tables or elasticity.

1Identify the market structure. A price taker has AR = MR = P. A firm facing downward-sloping demand has MR < P.
2Write the demand function as P in terms of Q. If you are given Q in terms of P, invert it first.
3Compute TR = P × Q as a function of Q.
4Find MR by differentiating TR with respect to Q, or by taking TR differences in a table.
5Compute AR = TR ÷ Q and check that it equals P.
6If elasticity is asked, use MR = P(1 + 1/E), or check the sign of MR to decide whether demand is elastic or inelastic.
7For maximum revenue, set MR = 0 and check TR is a maximum. State units and sensible bounds on Q and P.

Quickest way: Linear demand shortcut

When to use it: When demand is a straight line P = a − bQ and you need MR, the maximum-revenue output or the elasticity point.

Write MR by doubling the slope: MR = a − 2bQ.
Revenue is maximised at Q = a ÷ 2b, where MR = 0. The price there is a ÷ 2.
At that point |E| = 1. Above it, demand is elastic. Below it, inelastic.
Check any MR table with MR(n) = TR(n) − TR(n−1).
For elasticity questions, rearrange MR = P(1 + 1/E) to find whichever of MR, P or E is missing.

Common mistakes in Revenue Concepts: Total, Average and Marginal Revenue

Saying MR = P for a monopolist.
Students carry over the perfect competition result.
Fix: Only a price taker has MR = P. With downward-sloping demand, MR < P because the price cut applies to all units.
Using the wrong slope for the MR curve, such as the same slope as demand.
Students forget that TR = aQ − bQ² has a squared term.
Fix: Differentiate TR. For P = a − bQ, MR = a − 2bQ, twice as steep.
Computing MR as TR ÷ Q.
Confusing marginal with average.
Fix: TR ÷ Q is AR. MR is the change in TR from one more unit.
Writing the elasticity formula with the wrong sign, giving MR above price.
E is negative for normal demand, and the sign is dropped or flipped.
Fix: Use MR = P(1 + 1/E) with E negative, or MR = P(1 − 1/|E|). MR is always below P when demand slopes down.
Thinking negative MR means TR is negative.
Mixing the level of TR with its rate of change.
Fix: Negative MR means TR is falling as Q rises. TR itself stays positive.
Treating the competitive firm's demand curve as the market demand curve.
Confusing firm and industry.
Fix: The market curve slopes down. The single firm faces a horizontal line at the market price.

Worked examples

Example 1

A firm faces demand P = 120 − 4Q, where P is in ₹ and Q is in units. Find TR, AR and MR, the output that maximises TR, and the maximum TR.

Show the solution

TR = P × Q = 120Q − 4Q².
AR = TR ÷ Q = 120 − 4Q, which equals P.
MR = dTR/dQ = 120 − 8Q.
Set MR = 0: 120 − 8Q = 0, so Q = 15.
Check the second derivative: d²TR/dQ² = −8 < 0, so this is a maximum.
Price at Q = 15 is 120 − 60 = ₹60.
TR = 60 × 15 = ₹900.

Answer: TR = 120Q − 4Q², AR = 120 − 4Q, MR = 120 − 8Q. TR is maximised at Q = 15 with P = ₹60 and TR = ₹900.

Example 2

A monopolist faces demand P = 100 − 2Q. At Q = 10, calculate price, MR and the price elasticity of demand, and verify that MR = P(1 + 1/E).

Show the solution

P = 100 − 2(10) = ₹80.
TR = 100Q − 2Q², so MR = 100 − 4Q. At Q = 10, MR = 100 − 40 = ₹60.
Slope dQ/dP = −1/2, since Q = 50 − P/2.
E = (dQ/dP) × (P ÷ Q) = (−0.5) × (80 ÷ 10) = −4.
Check: MR = 80 × (1 + 1/(−4)) = 80 × 0.75 = ₹60.
Since |E| = 4 > 1, demand is elastic and MR is positive, which agrees.

Answer: P = ₹80, MR = ₹60, E = −4. The formula MR = P(1 + 1/E) gives ₹60, matching the direct calculation.

Exam tips

MCQs often test the statement that AR = P and that MR < AR under downward-sloping demand. Learn these as fixed facts.
If a question gives a table, compute TR first and then take differences for MR. Do not read MR from the price column.
Link MR sign to elasticity in one line: MR > 0 elastic, MR = 0 unit elastic, MR < 0 inelastic.
In written answers, state the demand function, show the differentiation, and give units in ₹ and quantity.
Sketch a diagram with demand, MR and the Q where MR = 0. Mark the elastic and inelastic sections.

Practice questions from Production, costs, revenue and profit in price and output decisions