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Business Economics · Price Determination in Different Markets

Revenue Concepts: TR, AR and MR for CA Foundation

Updated 1 October 2026 · Fact-checked

Total revenue (TR) is price × quantity sold. 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. Under monopoly AR slopes down and MR lies below it. Solve by finding TR first, then differentiating or taking differences.

Understand Revenue Concepts: TR, AR and MR

Revenue is the money a firm earns from selling its output. Three measures are used: total, average and marginal revenue. Each answers a different question.

Total revenue (TR) is the full amount received from sales. TR = P × Q. If you sell 10 units at ₹50, TR is ₹500.

Average revenue (AR) is revenue per unit sold. AR = TR ÷ Q. Since TR = P × Q, AR = P. So the AR curve is the same as the demand curve of the firm. This is why exam questions treat AR and price as the same thing.

Marginal revenue (MR) is the extra revenue from selling one more unit. MR = change in TR ÷ change in Q. It tells the firm whether selling more adds to revenue or not.

The shape of the curves depends on the market. Under perfect competition, the firm is a price taker. It can sell any quantity at the market price. So price is constant, AR is a horizontal line, and MR equals AR. TR is an upward sloping straight line from the origin.

Under monopoly (and monopolistic competition), the firm must cut price to sell more. So AR slopes downward. MR falls faster than AR, so the MR curve lies below AR. With a straight-line demand curve, MR has twice the slope of AR and cuts the quantity axis at half the distance of AR. TR rises, reaches a maximum where MR = 0, then falls when MR turns negative. TR is maximum where elasticity of demand equals 1.

Key formulas to remember

Total revenue
TR = P × Q
Price times quantity sold.
Average revenue
AR = TR ÷ Q = P
AR curve is the demand curve facing the firm.
Marginal revenue (discrete)
MR = ΔTR ÷ ΔQ = TRn − TRn−1
Use when a table of quantities is given. Valid for one-unit changes in the second form.
Marginal revenue (calculus)
MR = dTR/dQ
Use when TR or price is given as a function of Q.
Perfect competition
AR = MR = P
Both are horizontal at the market price.
Linear demand
If P = a − bQ, then TR = aQ − bQ² and MR = a − 2bQ
MR has the same intercept but double the slope.
AR, MR and elasticity
MR = AR × (e − 1) ÷ e, where e = absolute value of price elasticity
MR > 0 when e > 1, MR = 0 when e = 1, MR < 0 when e < 1.

How to solve Revenue Concepts: TR, AR and MR questions

Use this order for any revenue question, whether it gives a table, a demand function or an elasticity.

  1. 1Identify the market form. Perfect competition means constant price and AR = MR. Monopoly means falling AR and MR below AR.
  2. 2Write what is given: a table of P and Q, a demand function, or TR.
  3. 3Find TR = P × Q. If price is a function of Q, substitute to get TR in terms of Q.
  4. 4Find AR = TR ÷ Q, which is just the price.
  5. 5Find MR: take TR(n) − TR(n−1) for a table, or differentiate TR for a function.
  6. 6Check the relationship: MR must be below AR for a downward sloping demand curve.
  7. 7If elasticity is involved, use MR = AR × (e − 1) ÷ e and the signs of MR to judge e.
  8. 8Read the question again and confirm you are giving TR, AR or MR as asked.

Quickest way: Shortcut for linear demand and elasticity questions

When to use it: Use when demand is a straight line, P = a − bQ, or when the question links MR to elasticity.

  1. For P = a − bQ, write MR = a − 2bQ at once. No need to build TR.
  2. MR = 0 at Q = a ÷ 2b. TR is maximum there, and e = 1 there.
  3. For a table, compute TR in a column, then subtract successive TR values to get MR.
  4. For elasticity, memorise: MR positive means e > 1, zero means e = 1, negative means e < 1.
  5. Eliminate options where MR is above AR under a falling demand curve, or where MR differs from AR in perfect competition.
  6. If a calculation takes more than a minute, mark the question and move on. A wrong answer costs 0.25 marks.

Common mistakes in Revenue Concepts: TR, AR and MR

  • Writing MR = P for a monopolist.

    Students carry over the perfect competition rule to every market.

    Fix: MR = P only when price is constant. For a falling demand curve, MR is less than P.

  • Doubling the intercept instead of the slope when finding MR.

    Students remember 'twice' but forget which part it applies to.

    Fix: For P = a − bQ, MR = a − 2bQ. The intercept stays a. The slope b doubles.

  • Dividing TR by the change in quantity to get AR.

    AR and MR formulas get mixed up.

    Fix: AR uses total Q. MR uses the change in Q and the change in TR.

  • Saying TR falls whenever MR falls.

    Students confuse a falling MR with a negative MR.

    Fix: TR keeps rising while MR is positive, even if MR is falling. TR falls only when MR is negative.

  • Taking elasticity as negative and getting the MR sign wrong.

    Price elasticity of a normal demand curve is a negative number.

    Fix: Use the absolute value of e in MR = AR × (e − 1) ÷ e.

  • Treating the perfect competition TR curve as horizontal.

    Students mix up TR with AR and MR, which are horizontal.

    Fix: TR is an upward sloping straight line through the origin, because each extra unit adds the same price.

Worked examples

Example 1

A monopolist faces the demand function P = 40 − 2Q. What is marginal revenue at Q = 5?

(a) ₹10
(b) ₹20
(c) ₹30
(d) ₹40

Show the solution
  1. TR = P × Q = (40 − 2Q)Q = 40Q − 2Q².
  2. MR = dTR/dQ = 40 − 4Q.
  3. At Q = 5, MR = 40 − 4 × 5 = 40 − 20 = 20.
  4. Check with the shortcut: a = 40, b = 2, so MR = 40 − 2 × 2 × 5 = 20.

Answer: (b) ₹20

Example 2

A firm sells 4 units at ₹30 each and 5 units at ₹27 each (the price must be cut to sell more). What is the marginal revenue of the fifth unit?

(a) ₹15
(b) ₹27
(c) ₹30
(d) ₹135

Show the solution
  1. TR at 4 units = 4 × 30 = ₹120.
  2. TR at 5 units = 5 × 27 = ₹135.
  3. MR of the fifth unit = 135 − 120 = ₹15.
  4. ₹27 is the price (AR), not MR. ₹135 is TR.

Answer: (a) ₹15

Example 3

At a certain output, a firm's marginal revenue is zero. What is the price elasticity of demand at that output?

(a) Zero
(b) Less than one
(c) Equal to one
(d) Infinite

Show the solution
  1. Use MR = AR × (e − 1) ÷ e.
  2. Set MR = 0. Since AR is positive, (e − 1) must be zero.
  3. So e = 1.
  4. At this point TR is at its maximum.

Answer: (c) Equal to one

Exam tips

  • Memorise the three shapes: horizontal AR = MR for perfect competition, downward AR with lower MR for monopoly, and TR as a hill for monopoly.
  • For linear demand, use MR = a − 2bQ straight away. It saves a full minute.
  • Questions often link MR sign to elasticity. Learn: MR > 0 is elastic, MR = 0 is unit elastic, MR < 0 is inelastic.
  • When a table is given, build the TR column first and work out MR from differences.
  • Do not guess when unsure between two options. Each wrong answer costs 0.25 marks.

Practice questions from Price Determination in Different Markets

Revenue Concepts: TR, AR and MR: frequently asked questions

Why is AR the same as price?

AR is TR ÷ Q, and TR is P × Q. Cancelling Q leaves P. So AR always equals price, which is why the AR curve is the demand curve.

Why is MR below AR for a monopolist?

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

How do I find MR from a demand function?

Multiply price by Q to get TR, then differentiate TR with respect to Q. For P = a − bQ, the result is MR = a − 2bQ.

When is total revenue maximum?

TR is maximum where MR = 0. At that output, price elasticity of demand equals one. Beyond it, MR is negative and TR falls.