Fundamentals of Business Economics and Management · Cost of Production

Revenue Concepts and Cost-Revenue Relationship Explained

Q: What is the relationship between AR and MR?

When price is constant, as in perfect competition, AR = MR. When price falls as output rises, MR is less than AR. For a straight-line demand curve, MR falls twice as fast as AR.

Q: Why is the AR curve the demand curve?

AR is TR ÷ Q, which equals price. The demand curve shows the price buyers pay at each quantity, so the AR curve and the demand curve are the same.

Q: How do I find the profit-maximising output using MC = MR?

Find the output where MC equals MR and MC is rising. Before that point each extra unit adds more to revenue than cost. Beyond it, each unit adds more cost than revenue.

Q: What is the break-even point in economics?

It is the output where total revenue equals total cost, so profit is zero. Equivalently, average revenue equals average cost. Above that output the firm earns a profit if revenue stays above cost.

Q: What is the difference between cost curves and revenue curves?

Cost curves show the expense of producing each level of output and are usually U-shaped for AC and MC. Revenue curves show the earnings from sales and are horizontal under perfect competition or downward sloping in other markets.

Updated 10 October 2026 · Fact-checked

Revenue is the money a firm earns from sales. Total revenue is price × quantity, average revenue is TR ÷ Q, and marginal revenue is the change in TR from one more unit. Compare revenue with cost: profit is TR − TC, and a firm maximises profit where MC = MR with MC rising.

Understand Revenue Concepts and Cost-Revenue Relationship

Revenue is the money a firm receives from selling its output. Cost is what the firm spends to produce it. Profit is the gap between the two, so you need both sides to judge a business.

Total revenue (TR) is the full sales receipt: price × quantity sold. Average revenue (AR) is revenue per unit: TR ÷ Q. Since TR = P × Q, AR is always the same as price. This is why the AR curve is also the demand curve. Marginal revenue (MR) is the extra revenue from selling one more unit: the change in TR ÷ the change in Q.

The shape of AR and MR depends on the market. Under perfect competition, the firm is a price taker and sells every unit at the same price. So AR = MR = price, and the curve is a horizontal line. Under monopoly or other imperfect markets, the firm must cut price to sell more. AR slopes downward, and MR falls faster than AR and lies below it. With a straight-line demand curve, MR falls twice as fast as AR.

Now link revenue with cost. Profit = TR − TC. Break-even output is where TR = TC, so profit is zero. Below it the firm makes a loss; above it, a profit (if revenue keeps ahead of cost). The profit-maximising output is where MC = MR, provided MC is rising (cuts MR from below). Up to that point each extra unit adds more revenue than cost. Beyond it, each extra unit adds more cost than revenue.

A cost curve and a revenue curve are different things. Cost curves (AC, MC) are usually U-shaped because of returns to a variable factor. Revenue curves (AR, MR) are horizontal in perfect competition or downward sloping in other markets.

Key formulas to remember

Total revenue: TR = P × Q; Price multiplied by quantity sold.
Average revenue: AR = TR ÷ Q = P; AR is the same as price, so the AR curve is the demand curve.
Marginal revenue: MR = ΔTR ÷ ΔQ = TRn − TRn−1; Extra revenue from one more unit. Use the difference of TR when Q rises by 1.
Perfect competition: AR = MR = P; Horizontal AR and MR curve at the market price.
Imperfect competition: MR < AR; When AR falls as output rises, MR is below AR. For a straight-line demand, MR falls twice as fast as AR.
Profit: Profit = TR − TC; Positive means profit, negative means loss.
Break-even: TR = TC; Profit is zero. Equivalent: AR = AC.
Profit-maximising output: MC = MR, with MC rising; The slope of MC must be greater than the slope of MR at that point (second-order condition).

How to solve Revenue Concepts and Cost-Revenue Relationship questions

Use this method for any question on revenue, profit or break-even.

1Identify the market type. If price is fixed, it is perfect competition and AR = MR = P. If price falls as quantity rises, MR is below AR.
2Write down what is given: price, quantity, TR, TC, MC or a schedule.
3Compute TR = P × Q for each output level if not given.
4Find AR = TR ÷ Q and MR = change in TR between successive outputs.
5Find the output where MC = MR, and check that MC is rising there.
6For break-even, find the output where TR = TC (or AR = AC).
7Calculate profit = TR − TC at the chosen output, and match with the options.

Quickest way: Scan for the MC = MR row

When to use it: When a table of output, price, TR and TC or MC is given with four options.

Compute MR by subtracting each TR from the next TR.
Write MC next to it, or compute it from TC the same way.
Pick the highest output where MR ≥ MC. The next unit should have MR < MC.
If asked for profit, compute TR − TC only at that one row.
For break-even, scan for the row where TR equals TC and ignore the rest.

Common mistakes in Revenue Concepts and Cost-Revenue Relationship

Thinking AR and price are different things.
Students treat AR as a separate quantity from the demand curve.
Fix: Remember AR = TR ÷ Q = (P × Q) ÷ Q = P. AR is the demand curve.
Calculating MR as TR ÷ Q.
It is confused with the AR formula.
Fix: MR is the change in TR for an extra unit. Always subtract successive TR values.
Saying MR equals AR in every market.
The perfect competition rule is applied everywhere.
Fix: AR = MR only when price is constant (perfect competition). Otherwise MR < AR.
Choosing the output where TR is highest as the profit-maximising output.
Students forget that costs also rise.
Fix: Profit is TR − TC. Use MC = MR, not maximum TR.
Treating the break-even point as the point of maximum profit.
Both are named as special points in the cost-revenue graph.
Fix: Break-even gives zero profit (TR = TC). Maximum profit is at MC = MR.
Applying MC = MR when MC is falling.
Students ignore the second condition.
Fix: Check that MC cuts MR from below. Where MC is falling, more output still adds profit.

Worked examples

Example 1

A monopolist sells 1 unit at ₹50, 2 units at ₹45, 3 units at ₹40 and 4 units at ₹35 (price falls with quantity). The marginal cost of the 1st to 4th unit is ₹20, ₹25, ₹28 and ₹45 respectively. What output maximises profit?

Show the solution

TR: 1 unit = ₹50; 2 units = 45 × 2 = ₹90; 3 units = 40 × 3 = ₹120; 4 units = 35 × 4 = ₹140.
MR: 1st unit = ₹50; 2nd = 90 − 50 = ₹40; 3rd = 120 − 90 = ₹30; 4th = 140 − 120 = ₹20.
Compare MR with MC (20, 25, 28, 45): MR is above MC for units 1, 2 and 3 (50 > 20, 40 > 25, 30 > 28), so each of these units adds to profit.
The 4th unit has MR ₹20 < MC ₹45, so it reduces profit. MC is rising and crosses MR from below between the 3rd and 4th unit.
Check with profit: TC = 20, 45, 73, 118 for 1 to 4 units, so profit = 30, 45, 47, 22. The highest profit, ₹47, is at 3 units.

Answer: 3 units (profit ₹47). MR is above MC for the 3rd unit and below MC for the 4th.

Example 2

A firm sells each unit at ₹20. Its fixed cost is ₹600 and its variable cost is ₹8 per unit. Find the break-even output and the profit at 80 units.

Show the solution

TR = 20 × Q. TC = 600 + 8Q.
Break-even: TR = TC, so 20Q = 600 + 8Q.
12Q = 600, so Q = 50 units.
At 80 units: TR = 20 × 80 = ₹1,600.
TC = 600 + 8 × 80 = 600 + 640 = ₹1,240.
Profit = 1,600 − 1,240 = ₹360.

Answer: Break-even output is 50 units; profit at 80 units is ₹360.

Exam tips

Questions often ask for the shape of AR and MR under perfect competition and monopoly. Remember horizontal and equal versus downward and MR below AR.
Compute MR from successive TR values. Do not divide TR by Q.
If the question says maximise profit, go straight to MC = MR.
If the question says no profit no loss, think TR = TC or AR = AC.
Check that the answer is a realistic output in the table before marking.

Practice questions from Cost of Production

Revenue Concepts and Cost-Revenue Relationship in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Revenue Concepts and Cost-Revenue Relationship: frequently asked questions

What is the relationship between AR and MR?

When price is constant, as in perfect competition, AR = MR. When price falls as output rises, MR is less than AR. For a straight-line demand curve, MR falls twice as fast as AR.

Why is the AR curve the demand curve?

AR is TR ÷ Q, which equals price. The demand curve shows the price buyers pay at each quantity, so the AR curve and the demand curve are the same.

How do I find the profit-maximising output using MC = MR?

Find the output where MC equals MR and MC is rising. Before that point each extra unit adds more to revenue than cost. Beyond it, each unit adds more cost than revenue.

What is the break-even point in economics?

It is the output where total revenue equals total cost, so profit is zero. Equivalently, average revenue equals average cost. Above that output the firm earns a profit if revenue stays above cost.

What is the difference between cost curves and revenue curves?

Cost curves show the expense of producing each level of output and are usually U-shaped for AC and MC. Revenue curves show the earnings from sales and are horizontal under perfect competition or downward sloping in other markets.