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Revenue and Producer's Equilibrium: MR-MC, TR-TC ISC 12

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EconomicsISC Class 12 · Cost and Revenue

Revenue Concepts and Producer's Equilibrium: TR, AR, MR and the Two Approaches to Profit Maximisation

Updated 17 October 2026 · Fact-checked

Total revenue (TR) is price multiplied by quantity, average revenue (AR) is TR/Q (the price) and marginal revenue (MR) is the change in TR from one more unit. Under perfect competition AR = MR = price; under imperfect competition AR slopes down and MR lies below it. A producer maximising profit is in equilibrium where MR = MC and MC cuts MR from below, which is the same output at which TR minus TC is greatest.

Profit is greatest at E, where MR = MC and MC cuts MR from below: expand output before Q*, cut it beyond Q*.

Illustration drawn for QuestionBuddy.

Understand Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches

1. Revenue concepts.

  • Total revenue (TR) = price x quantity sold = AR x Q.
  • Average revenue (AR) = TR / Q. Since TR = P x Q, AR = price, so the AR curve is the firm's demand curve.
  • Marginal revenue (MR) = TRn - TRn-1 (the addition to TR from selling one more unit).

2. Perfect competition. The firm is a price taker: it can sell any quantity at the market price. So AR = MR = P, a horizontal line, and TR is a straight line from the origin, rising at a constant rate.

3. Imperfect competition (monopoly, monopolistic competition, oligopoly). The firm must lower its price to sell more, so the AR (demand) curve slopes downward and MR < AR, because the lower price applies to all units sold. For a straight-line AR, the MR curve is also a straight line, below AR and falling twice as fast. TR rises while MR is positive, is maximum when MR = 0, and falls when MR is negative.

4. Producer's equilibrium (profit maximisation goal). The producer is in equilibrium at the output at which profit is maximum and he has no incentive to change output.

*(a) TR-TC approach.* Profit = TR - TC. Equilibrium is the output where the vertical gap between TR and TC is greatest (TR above TC). In the diagram, it is where the tangent to TC is parallel to the TR curve (equal slopes, so MR = MC). Output levels where TR = TC are break-even points.

*(b) MR-MC approach.* Conditions: (i) MR = MC and (ii) MC cuts MR from below (MC is rising and exceeds MR beyond the equilibrium output). If MR > MC, an extra unit adds more revenue than cost, so output should rise. If MR < MC, producing the last unit loses money, so output should fall. In discrete data, produce up to the last unit whose MC does not exceed MR.

5. Under which market form? The same two conditions apply to every market form. Under perfect competition MR = P so the condition is MC = P; under monopoly, price is read from the AR curve at the equilibrium quantity and exceeds MC.

6. Normal and abnormal profit (brief). If AR > AC at equilibrium the firm earns abnormal profit; if AR = AC, only normal profit; if AR < AC, a loss (the short-run decision to continue is covered under market forms).

Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches: key facts

Total revenue
TR = P x Q = AR x Q
Average revenue
AR = TR / Q = P
Marginal revenue
MRn = TRn - TRn-1
Profit
Profit = TR - TC = (AR - AC) x Q
Equilibrium
MR = MC and MC cuts MR from below

How to answer Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches questions

Revenue-cost problems use a table with columns for P, Q, TR, MR, TC, MC and profit.

  1. 1Write TR = P x Q for each output level.
  2. 2Find MR as the difference between consecutive TR values and MC as the difference between consecutive TC values.
  3. 3Compute profit = TR - TC at each output; find the highest profit.
  4. 4Check the MR-MC condition: MR is at least MC for the equilibrium unit and MC exceeds MR for the next unit.
  5. 5Under perfect competition MR equals price at every output.
  6. 6State both approaches give the same output.

Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

A stall owner choosing how many to make

Suppose a street vendor can sell any number of sandwiches at Rs 20 each (a price taker). Her total cost of making 1 to 6 sandwiches is Rs 30, 42, 52, 64, 80 and 102, and a fixed cost of Rs 15 is paid even if she makes none.

How many sandwiches should she make, and what is her profit?

Try it first, then show the solutionSolution
  1. Profit = 20Q - TC: Rs -10, -2, 8, 16, 20, 18 for 1 to 6 sandwiches.
  2. MC of the 5th = 80 - 64 = Rs 16 < Rs 20 (worth making); MC of the 6th = 102 - 80 = Rs 22 > Rs 20 (not worth making).

Answer: She makes 5 sandwiches and earns a maximum profit of Rs 20.

Memory hook: Make one more only if it adds more than it costs.

Tricks to remember Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches

Short memory aids. Say each one aloud once, then use it on a question the same day.

  • Price taker: P = AR = MR

    A horizontal demand line means each extra unit sells at the same price, so the extra revenue equals the price.

    Use it when: Perfect competition questions.

  • MR twice as steep

    For a straight-line AR the MR line is half way to the quantity axis and twice as steep.

    Use it when: Diagrams under imperfect competition.

  • Two ticks

    MR = MC, and MC rising through MR (cuts from below).

    Use it when: Producer's equilibrium condition.

Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: AR and MR under perfect competition · 1 mark · MCQBoard level

Under perfect competition, the AR and MR curves of a firm are:
(a) both downward sloping
(b) AR sloping down and MR below it
(c) identical horizontal lines
(d) MR horizontal and AR vertical

Try it first, then show the solutionSolution
  1. A price taker sells every unit at the market price, so AR = MR = P.

Answer: (c) identical horizontal lines

Example 2: Revenue schedule under imperfect competition · 3 marks · Short answerBoard level

A firm sells 1, 2, 3 and 4 units at prices Rs 50, 45, 40 and 35. Calculate TR, AR and MR, and compare AR with MR. (3 marks)

Try it first, then show the solutionSolution
  1. TR = 50, 90, 120, 140.
  2. AR = TR/Q = 50, 45, 40, 35 (equal to price).
  3. MR = 50, 90 - 50 = 40, 120 - 90 = 30, 140 - 120 = 20.
  4. MR is below AR from the second unit onwards because price falls on all units.

Answer: TR = 50, 90, 120, 140; AR = 50, 45, 40, 35; MR = 50, 40, 30, 20. MR < AR.

Example 3: TR-TC approach (price taker) · 4 marks · Long answerHarder board level

A firm can sell at a fixed price of Rs 20. Total cost of 0 to 6 units is Rs 15, 30, 42, 52, 64, 80 and 102. Find the profit-maximising output and the maximum profit by the TR-TC approach. (4 marks)

Try it first, then show the solutionSolution
  1. TR = 20, 40, 60, 80, 100, 120 for 1 to 6 units.
  2. Profit = TR - TC: 20 - 30 = -10; 40 - 42 = -2; 60 - 52 = 8; 80 - 64 = 16; 100 - 80 = 20; 120 - 102 = 18.
  3. The gap is greatest (Rs 20) at 5 units; the firm breaks even between the 2nd and 3rd unit.
  4. At 6 units profit falls to Rs 18, so the firm stops at 5.

Answer: Equilibrium output is 5 units with maximum profit Rs 20.

Example 4: MR-MC approach (same firm) · 4 marks · Short answerHarder board level

For the same firm (price Rs 20, same cost data), find MC for 1 to 6 units and use the MR-MC approach to find equilibrium. Show that MC cuts MR from below at the equilibrium. (4 marks)

Try it first, then show the solutionSolution
  1. MR = P = 20 at every output.
  2. MC = TCn - TCn-1: 30 - 15 = 15; 42 - 30 = 12; 52 - 42 = 10; 64 - 52 = 12; 80 - 64 = 16; 102 - 80 = 22.
  3. Up to the 5th unit MC (15, 12, 10, 12, 16) is below MR = 20, so each unit adds to profit.
  4. The 6th unit has MC = 22 > MR = 20, so it reduces profit by Rs 2 (20 to 18). MC is rising and crosses MR between the 5th and 6th units.

Answer: Equilibrium output = 5 units: MC (16) is just below MR (20) and MC of the next unit (22) exceeds it, so MC cuts MR from below. Both approaches give 5 units.

Example 5: Imperfect competition equilibrium · 4 marks · Long answerHOTS / competency

A firm faces the demand: price Rs 50, 45, 40, 35, 30, 25 at 1 to 6 units, with the cost data of the earlier example. Find the equilibrium output and price by the MR-MC approach and verify using TR - TC. (4 marks)

Try it first, then show the solutionSolution
  1. TR = 50, 90, 120, 140, 150, 150; MR = 50, 40, 30, 20, 10, 0. MC = 15, 12, 10, 12, 16, 22.
  2. 4th unit: MR = 20 > MC = 12, so produce it. 5th unit: MR = 10 < MC = 16, so do not produce.
  3. Equilibrium output is 4 units at price Rs 35 (from the demand schedule).
  4. Check TR - TC: 20, 48, 68, 76, 70, 48. Maximum Rs 76 at 4 units.

Answer: Equilibrium: 4 units at Rs 35 with profit Rs 76; the price (Rs 35) is above MC (Rs 12) because MR lies below AR.

Where students lose marks in Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches

The slips examiners see most often, and what to write instead.

  • Mistake: Taking MR = TR/Q

    Confusing MR with AR.

    Wrong working

    MR of 3 units = 120/3 = 40.

    Right working

    MR of the 3rd unit = 120 - 90 = Rs 30.

    Do this: MR is a difference, AR is a division.

    Usually costs: 2 marks.

  • Mistake: Stopping at MR = MC without the second condition

    Forgetting MC cuts from below.

    Wrong working

    Equilibrium at the first output where MR = MC (while MC is falling).

    Right working

    Equilibrium needs MC rising through MR; the first crossing on a falling MC is not a maximum.

    Do this: State both conditions.

    Usually costs: 1-2 marks.

  • Mistake: Showing MR above AR under monopoly

    Carrying the perfect-competition picture.

    Wrong working

    MR curve drawn above the AR curve.

    Right working

    MR is below AR when AR falls.

    Do this: Draw MR starting from the same point on the price axis but falling faster.

    Usually costs: 1 mark.

  • Mistake: Equating profit with revenue

    Ignoring cost.

    Wrong working

    Equilibrium where TR is maximum.

    Right working

    Profit is maximum where TR - TC is maximum, i.e. MR = MC; TR is maximum where MR = 0.

    Do this: Subtract TC before choosing output.

    Usually costs: 2 marks.

Exam tips

  • Draw two diagrams for producer's equilibrium: (a) TR and TC curves with the largest gap, (b) MR, MC, AR and AC with the point E where MC cuts MR from below.
  • Mark the break-even points on the TR-TC diagram.
  • State both conditions for the MR-MC approach in every answer.
  • Show the revenue schedule as a table before drawing curves.
  • The same equilibrium output must come from both approaches in numericals.

Practice questions on Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

  1. Q1 · 1 mark · MCQBoard level

    Under imperfect competition, the marginal revenue curve lies:
    (a) above the AR curve
    (b) on the AR curve
    (c) below the AR curve
    (d) horizontal at the price

    Hint

    To sell more, price must fall on all units.

    Answer

    (c) below the AR curve

  2. Q2 · 3 marks · Short answerBoard level

    A firm sells 1, 2, 3 and 4 units at prices Rs 30, 27, 24 and 21. Calculate TR and MR for each. (3 marks)

    Hint

    MR is the difference in TR.

    Answer

    TR = 30, 54, 72, 84; MR = 30, 24, 18, 12.

  3. Q3 · 4 marks · Short answerHarder board level

    A price-taking firm sells at Rs 13. Its total cost of 0 to 5 units is Rs 10, 20, 26, 34, 46 and 62. Find MC, profit and the equilibrium output using both approaches. (4 marks)

    Hint

    MR = 13 at every output.

    Answer

    MC = 10, 6, 8, 12, 16. TR = 13, 26, 39, 52, 65; profit = TR - TC = -7, 0, 5, 6, 3. Maximum profit Rs 6 at 4 units. MR-MC: the 4th unit has MC = 12 < MR = 13 (produce), the 5th has MC = 16 > 13 (do not produce). Equilibrium: 4 units, found by both methods.

  4. Q4 · 4 marks · Short answerHarder board level

    The AR curve of a firm is given by price = 50 - 10 x quantity. Find TR and MR for 1 to 5 units and show the relation between MR and the maximum of TR. (4 marks)

    Hint

    Price at Q = 1 to 5 is 40, 30, 20, 10, 0.

    Answer

    Price = 40, 30, 20, 10, 0; TR = 40, 60, 60, 40, 0; MR = 40, 20, 0, -20, -40. TR is at its maximum (60) when MR = 0 at the 3rd unit (TR rises while MR > 0 and falls once MR < 0).

  5. Q5 · 3 marks · Short answerHOTS / competency

    A seller of a branded product sells 3 units at Rs 40 each and 4 units at Rs 35 each. Calculate the MR of the 4th unit and explain why it is far below the price, whereas a perfectly competitive seller's MR equals price. (3 marks)

    Hint

    Think about what happens to the first three units.

    Answer

    TR for 3 units = 120 and for 4 units = 140, so MR = Rs 20. The 4th unit sells at Rs 35, but to sell it the price on the first three units falls by Rs 5 each, a loss of Rs 15; so MR = 35 - 15 = Rs 20, far below the price. A perfectly competitive seller sells at the same market price whatever the quantity, so no revenue is lost on earlier units and MR = price.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

  1. 1.AR equals what?Show answer

    Price (TR divided by quantity).

  2. 2.MR under perfect competition?Show answer

    Equal to price and AR.

  3. 3.TR is maximum when?Show answer

    MR = 0.

  4. 4.Two conditions for equilibrium?Show answer

    MR = MC and MC cuts MR from below.

  5. 5.What is the TR-TC condition?Show answer

    The greatest positive gap between TR and TC.

Revenue Concepts and Producer's Equilibrium: TR-TC and MR-MC Approaches: frequently asked questions

Why is AR the demand curve?

AR equals price at each quantity, and the demand curve shows the price at each quantity.

Why is MR less than AR under monopoly?

To sell an extra unit, the price on all units must fall.

What is the producer's equilibrium?

The output at which profit is maximum, where MR = MC and MC cuts MR from below.

Do both approaches give the same output?

Yes. The largest TR - TC gap occurs at the output where MR = MC.